From 3e2735c00585c6d31f012a2038aaccefa9679d3d Mon Sep 17 00:00:00 2001
From: Chris Watson <chris@watzon.me>
Date: Mon, 17 Jun 2019 15:01:05 -0700
Subject: [PATCH] Updated docs

---
 docs/Apatite.html                       | 281 +++++++++++++++++++++--
 docs/Apatite/LinearAlgebra.html         |  12 +-
 docs/Apatite/LinearAlgebra/Matrix.html  | 100 ++++-----
 docs/Apatite/LinearAlgebra/NDArray.html |  34 +--
 docs/Apatite/LinearAlgebra/Vector.html  | 286 ++++++++++++++++--------
 docs/Array.html                         |  10 +-
 docs/index.html                         |   4 +-
 docs/index.json                         |   2 +-
 docs/search-index.js                    |   2 +-
 9 files changed, 538 insertions(+), 193 deletions(-)

diff --git a/docs/Apatite.html b/docs/Apatite.html
index 64c797d..514f60a 100644
--- a/docs/Apatite.html
+++ b/docs/Apatite.html
@@ -131,28 +131,28 @@ of Crystal.</p>
   <h2>Defined in:</h2>
   
     
-      <a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/ndarray.cr#L1" target="_blank">
+      <a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/ndarray.cr#L1" target="_blank">
         apatite/linear_algebra/ndarray.cr
       </a>
     
     <br/>
   
     
-      <a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra.cr#L5" target="_blank">
+      <a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra.cr#L5" target="_blank">
         apatite/linear_algebra.cr
       </a>
     
     <br/>
   
     
-      <a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite.cr#L10" target="_blank">
+      <a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite.cr#L10" target="_blank">
         apatite.cr
       </a>
     
     <br/>
   
     
-      <a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/version.cr#L1" target="_blank">
+      <a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/version.cr#L1" target="_blank">
         apatite/version.cr
       </a>
     
@@ -210,11 +210,50 @@ of Crystal.</p>
 
 
 
+  <h2>Class Method Summary</h2>
+  <ul class="list-summary">
+    
+      <li class="entry-summary">
+        <a href="#approx_precision-class-method" class="signature"><strong>.approx_precision</strong></a>
+        
+      </li>
+    
+      <li class="entry-summary">
+        <a href="#approx_precision%3D%28approx_precision%29-class-method" class="signature"><strong>.approx_precision=</strong>(approx_precision)</a>
+        
+      </li>
+    
+      <li class="entry-summary">
+        <a href="#precision-class-method" class="signature"><strong>.precision</strong></a>
+        
+      </li>
+    
+      <li class="entry-summary">
+        <a href="#precision%3D%28precision%29-class-method" class="signature"><strong>.precision=</strong>(precision)</a>
+        
+      </li>
+    
+  </ul>
+
 
 
   <h2>Instance Method Summary</h2>
   <ul class="list-summary">
     
+      <li class="entry-summary">
+        <a href="#angle_from%28a%2Cb%29-instance-method" class="signature"><strong>#angle_from</strong>(a, b)</a>
+        
+          <div class="summary"><p>Returns the angle between this vector and another in radians.</p></div>
+        
+      </li>
+    
+      <li class="entry-summary">
+        <a href="#antiparallel_to%3F%28a%2Cb%29-instance-method" class="signature"><strong>#antiparallel_to?</strong>(a, b)</a>
+        
+          <div class="summary"><p>Returns whether the vectors are antiparallel to each other.</p></div>
+        
+      </li>
+    
       <li class="entry-summary">
         <a href="#as_vector%28input%3AIndexable%29-instance-method" class="signature"><strong>#as_vector</strong>(input : Indexable)</a>
         
@@ -236,6 +275,13 @@ of Crystal.</p>
         
       </li>
     
+      <li class="entry-summary">
+        <a href="#dot%28x%2Cy%29-instance-method" class="signature"><strong>#dot</strong>(x, y)</a>
+        
+          <div class="summary"><p>Get the scalar (dot) product of two vectors.</p></div>
+        
+      </li>
+    
       <li class="entry-summary">
         <a href="#empty-instance-method" class="signature"><strong>#empty</strong></a>
         
@@ -278,6 +324,20 @@ of Crystal.</p>
         
       </li>
     
+      <li class="entry-summary">
+        <a href="#parallel_to%3F%28a%2Cb%29-instance-method" class="signature"><strong>#parallel_to?</strong>(a, b)</a>
+        
+          <div class="summary"><p>Returns whether the vectors are parallel to each other.</p></div>
+        
+      </li>
+    
+      <li class="entry-summary">
+        <a href="#perpendicular_to%3F%28a%2Cb%29-instance-method" class="signature"><strong>#perpendicular_to?</strong>(a, b)</a>
+        
+          <div class="summary"><p>Returns whether the vectors are perpendicular to each other.</p></div>
+        
+      </li>
+    
       <li class="entry-summary">
         <a href="#random%28n%2Crange%3Dnil%29-instance-method" class="signature"><strong>#random</strong>(n, range = <span class="n">nil</span>)</a>
         
@@ -299,6 +359,13 @@ of Crystal.</p>
         
       </li>
     
+      <li class="entry-summary">
+        <a href="#similarity%28x%2Cy%29-instance-method" class="signature"><strong>#similarity</strong>(x, y)</a>
+        
+          <div class="summary"><p>Compute the cosine similarity between two vectors.</p></div>
+        
+      </li>
+    
       <li class="entry-summary">
         <a href="#vector%28n%2C%26block%29-instance-method" class="signature"><strong>#vector</strong>(n, &block)</a>
         
@@ -350,10 +417,114 @@ of Crystal.</p>
 
 
 
+  <h2>Class Method Detail</h2>
+  
+    <div class="entry-detail" id="approx_precision-class-method">
+      <div class="signature">
+        
+        def self.<strong>approx_precision</strong>
+
+        <a class="method-permalink" href="#approx_precision-class-method">#</a>
+      </div>
+      
+      <br/>
+      <div>
+        
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite.cr#L18" target="_blank">View source</a>]
+        
+      </div>
+    </div>
+  
+    <div class="entry-detail" id="approx_precision=(approx_precision)-class-method">
+      <div class="signature">
+        
+        def self.<strong>approx_precision=</strong>(approx_precision)
+
+        <a class="method-permalink" href="#approx_precision%3D%28approx_precision%29-class-method">#</a>
+      </div>
+      
+      <br/>
+      <div>
+        
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite.cr#L22" target="_blank">View source</a>]
+        
+      </div>
+    </div>
+  
+    <div class="entry-detail" id="precision-class-method">
+      <div class="signature">
+        
+        def self.<strong>precision</strong>
+
+        <a class="method-permalink" href="#precision-class-method">#</a>
+      </div>
+      
+      <br/>
+      <div>
+        
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite.cr#L17" target="_blank">View source</a>]
+        
+      </div>
+    </div>
+  
+    <div class="entry-detail" id="precision=(precision)-class-method">
+      <div class="signature">
+        
+        def self.<strong>precision=</strong>(precision)
+
+        <a class="method-permalink" href="#precision%3D%28precision%29-class-method">#</a>
+      </div>
+      
+      <br/>
+      <div>
+        
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite.cr#L21" target="_blank">View source</a>]
+        
+      </div>
+    </div>
+  
+
 
 
   <h2>Instance Method Detail</h2>
   
+    <div class="entry-detail" id="angle_from(a,b)-instance-method">
+      <div class="signature">
+        
+        def <strong>angle_from</strong>(a, b)
+
+        <a class="method-permalink" href="#angle_from%28a%2Cb%29-instance-method">#</a>
+      </div>
+      
+        <div class="doc"><p>Returns the angle between this vector and another in radians.
+If the vectors are mirrored across their axes this will return <code>nil</code>.</p></div>
+      
+      <br/>
+      <div>
+        
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite.cr#L145" target="_blank">View source</a>]
+        
+      </div>
+    </div>
+  
+    <div class="entry-detail" id="antiparallel_to?(a,b)-instance-method">
+      <div class="signature">
+        
+        def <strong>antiparallel_to?</strong>(a, b)
+
+        <a class="method-permalink" href="#antiparallel_to%3F%28a%2Cb%29-instance-method">#</a>
+      </div>
+      
+        <div class="doc"><p>Returns whether the vectors are antiparallel to each other.</p></div>
+      
+      <br/>
+      <div>
+        
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite.cr#L178" target="_blank">View source</a>]
+        
+      </div>
+    </div>
+  
     <div class="entry-detail" id="as_vector(input:Indexable)-instance-method">
       <div class="signature">
         
@@ -368,7 +539,7 @@ of Crystal.</p>
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite.cr#L61" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite.cr#L65" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -386,7 +557,7 @@ of Crystal.</p>
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite.cr#L66" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite.cr#L70" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -404,7 +575,27 @@ of Crystal.</p>
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite.cr#L89" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite.cr#L93" target="_blank">View source</a>]
+        
+      </div>
+    </div>
+  
+    <div class="entry-detail" id="dot(x,y)-instance-method">
+      <div class="signature">
+        
+        def <strong>dot</strong>(x, y)
+
+        <a class="method-permalink" href="#dot%28x%2Cy%29-instance-method">#</a>
+      </div>
+      
+        <div class="doc"><p>Get the scalar (dot) product of two vectors.</p>
+
+<p>[https://en.wikipedia.org/wiki/Scalar_product](https://en.wikipedia.org/wiki/Scalar_product</p></div>
+      
+      <br/>
+      <div>
+        
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite.cr#L125" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -422,7 +613,7 @@ of Crystal.</p>
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite.cr#L34" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite.cr#L38" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -442,7 +633,7 @@ of Crystal.</p>
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite.cr#L84" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite.cr#L88" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -461,7 +652,7 @@ and zeros elsewhere.</p></div>
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite.cr#L95" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite.cr#L99" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -479,7 +670,7 @@ and zeros elsewhere.</p></div>
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite.cr#L49" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite.cr#L53" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -497,7 +688,7 @@ and zeros elsewhere.</p></div>
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite.cr#L100" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite.cr#L104" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -515,7 +706,43 @@ and zeros elsewhere.</p></div>
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite.cr#L39" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite.cr#L43" target="_blank">View source</a>]
+        
+      </div>
+    </div>
+  
+    <div class="entry-detail" id="parallel_to?(a,b)-instance-method">
+      <div class="signature">
+        
+        def <strong>parallel_to?</strong>(a, b)
+
+        <a class="method-permalink" href="#parallel_to%3F%28a%2Cb%29-instance-method">#</a>
+      </div>
+      
+        <div class="doc"><p>Returns whether the vectors are parallel to each other.</p></div>
+      
+      <br/>
+      <div>
+        
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite.cr#L172" target="_blank">View source</a>]
+        
+      </div>
+    </div>
+  
+    <div class="entry-detail" id="perpendicular_to?(a,b)-instance-method">
+      <div class="signature">
+        
+        def <strong>perpendicular_to?</strong>(a, b)
+
+        <a class="method-permalink" href="#perpendicular_to%3F%28a%2Cb%29-instance-method">#</a>
+      </div>
+      
+        <div class="doc"><p>Returns whether the vectors are perpendicular to each other.</p></div>
+      
+      <br/>
+      <div>
+        
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite.cr#L184" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -535,7 +762,7 @@ to a given range.</p></div>
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite.cr#L73" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite.cr#L77" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -553,7 +780,7 @@ to a given range.</p></div>
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite.cr#L105" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite.cr#L109" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -571,7 +798,25 @@ to a given range.</p></div>
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite.cr#L110" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite.cr#L114" target="_blank">View source</a>]
+        
+      </div>
+    </div>
+  
+    <div class="entry-detail" id="similarity(x,y)-instance-method">
+      <div class="signature">
+        
+        def <strong>similarity</strong>(x, y)
+
+        <a class="method-permalink" href="#similarity%28x%2Cy%29-instance-method">#</a>
+      </div>
+      
+        <div class="doc"><p>Compute the cosine similarity between two vectors.</p></div>
+      
+      <br/>
+      <div>
+        
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite.cr#L136" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -590,7 +835,7 @@ for each index of <code>self</code>, assigning the block's value in that index.<
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite.cr#L55" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite.cr#L59" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -608,7 +853,7 @@ for each index of <code>self</code>, assigning the block's value in that index.<
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite.cr#L44" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite.cr#L48" target="_blank">View source</a>]
         
       </div>
     </div>
diff --git a/docs/Apatite/LinearAlgebra.html b/docs/Apatite/LinearAlgebra.html
index 4305b0c..887d6c1 100644
--- a/docs/Apatite/LinearAlgebra.html
+++ b/docs/Apatite/LinearAlgebra.html
@@ -123,28 +123,28 @@
   <h2>Defined in:</h2>
   
     
-      <a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/ndarray.cr#L1" target="_blank">
+      <a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/ndarray.cr#L1" target="_blank">
         apatite/linear_algebra/ndarray.cr
       </a>
     
     <br/>
   
     
-      <a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L1" target="_blank">
+      <a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L1" target="_blank">
         apatite/linear_algebra/vector.cr
       </a>
     
     <br/>
   
     
-      <a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/matrix.cr#L3" target="_blank">
+      <a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/matrix.cr#L3" target="_blank">
         apatite/linear_algebra/matrix.cr
       </a>
     
     <br/>
   
     
-      <a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra.cr#L6" target="_blank">
+      <a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra.cr#L6" target="_blank">
         apatite/linear_algebra.cr
       </a>
     
@@ -210,7 +210,7 @@
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra.cr#L14" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra.cr#L14" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -230,7 +230,7 @@
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra.cr#L22" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra.cr#L22" target="_blank">View source</a>]
         
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diff --git a/docs/Apatite/LinearAlgebra/Matrix.html b/docs/Apatite/LinearAlgebra/Matrix.html
index 63f1d74..71d1a16 100644
--- a/docs/Apatite/LinearAlgebra/Matrix.html
+++ b/docs/Apatite/LinearAlgebra/Matrix.html
@@ -122,7 +122,7 @@
   <h2>Defined in:</h2>
   
     
-      <a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/matrix.cr#L4" target="_blank">
+      <a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/matrix.cr#L4" target="_blank">
         apatite/linear_algebra/matrix.cr
       </a>
     
@@ -539,7 +539,7 @@
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/matrix.cr#L15" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/matrix.cr#L15" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -562,7 +562,7 @@
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/matrix.cr#L22" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/matrix.cr#L22" target="_blank">View source</a>]
         
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     </div>
@@ -581,7 +581,7 @@ the given block, passing the current row and column.</p></div>
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/matrix.cr#L28" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/matrix.cr#L28" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -599,7 +599,7 @@ the given block, passing the current row and column.</p></div>
       <br/>
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-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/matrix.cr#L39" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/matrix.cr#L39" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -617,7 +617,7 @@ the given block, passing the current row and column.</p></div>
       <br/>
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-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/matrix.cr#L44" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/matrix.cr#L44" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -635,7 +635,7 @@ the given block, passing the current row and column.</p></div>
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/matrix.cr#L70" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/matrix.cr#L70" target="_blank">View source</a>]
         
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@@ -653,7 +653,7 @@ the given block, passing the current row and column.</p></div>
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/matrix.cr#L84" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/matrix.cr#L84" target="_blank">View source</a>]
         
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@@ -672,7 +672,7 @@ the given block, passing the current row and column.</p></div>
       <br/>
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-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/matrix.cr#L90" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/matrix.cr#L90" target="_blank">View source</a>]
         
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@@ -691,7 +691,7 @@ and zeros elsewhere.</p></div>
       <br/>
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-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/matrix.cr#L98" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/matrix.cr#L98" target="_blank">View source</a>]
         
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@@ -709,7 +709,7 @@ and zeros elsewhere.</p></div>
       <br/>
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-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/matrix.cr#L103" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/matrix.cr#L103" target="_blank">View source</a>]
         
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@@ -727,7 +727,7 @@ and zeros elsewhere.</p></div>
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-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/matrix.cr#L107" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/matrix.cr#L107" target="_blank">View source</a>]
         
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@@ -745,7 +745,7 @@ and zeros elsewhere.</p></div>
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-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/matrix.cr#L112" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/matrix.cr#L112" target="_blank">View source</a>]
         
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@@ -763,7 +763,7 @@ and zeros elsewhere.</p></div>
       <br/>
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-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/matrix.cr#L117" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/matrix.cr#L117" target="_blank">View source</a>]
         
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@@ -781,7 +781,7 @@ and zeros elsewhere.</p></div>
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/matrix.cr#L126" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/matrix.cr#L126" target="_blank">View source</a>]
         
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@@ -799,7 +799,7 @@ and zeros elsewhere.</p></div>
       <br/>
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-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/matrix.cr#L131" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/matrix.cr#L131" target="_blank">View source</a>]
         
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@@ -817,7 +817,7 @@ and zeros elsewhere.</p></div>
       <br/>
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-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/matrix.cr#L135" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/matrix.cr#L135" target="_blank">View source</a>]
         
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@@ -838,7 +838,7 @@ and zeros elsewhere.</p></div>
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-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/matrix.cr#L140" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/matrix.cr#L140" target="_blank">View source</a>]
         
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@@ -854,7 +854,7 @@ and zeros elsewhere.</p></div>
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-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/matrix.cr#L154" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/matrix.cr#L154" target="_blank">View source</a>]
         
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@@ -870,7 +870,7 @@ and zeros elsewhere.</p></div>
       <br/>
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-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/matrix.cr#L161" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/matrix.cr#L161" target="_blank">View source</a>]
         
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@@ -886,7 +886,7 @@ and zeros elsewhere.</p></div>
       <br/>
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-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/matrix.cr#L167" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/matrix.cr#L167" target="_blank">View source</a>]
         
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@@ -902,7 +902,7 @@ and zeros elsewhere.</p></div>
       <br/>
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-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/matrix.cr#L176" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/matrix.cr#L176" target="_blank">View source</a>]
         
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@@ -918,7 +918,7 @@ and zeros elsewhere.</p></div>
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/matrix.cr#L188" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/matrix.cr#L188" target="_blank">View source</a>]
         
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@@ -934,7 +934,7 @@ and zeros elsewhere.</p></div>
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/matrix.cr#L205" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/matrix.cr#L205" target="_blank">View source</a>]
         
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@@ -950,7 +950,7 @@ and zeros elsewhere.</p></div>
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-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/matrix.cr#L193" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/matrix.cr#L193" target="_blank">View source</a>]
         
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@@ -966,7 +966,7 @@ and zeros elsewhere.</p></div>
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-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/matrix.cr#L210" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/matrix.cr#L210" target="_blank">View source</a>]
         
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@@ -982,7 +982,7 @@ and zeros elsewhere.</p></div>
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-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/matrix.cr#L214" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/matrix.cr#L214" target="_blank">View source</a>]
         
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@@ -998,7 +998,7 @@ and zeros elsewhere.</p></div>
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-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/matrix.cr#L221" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/matrix.cr#L221" target="_blank">View source</a>]
         
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@@ -1016,7 +1016,7 @@ and zeros elsewhere.</p></div>
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-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/matrix.cr#L228" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/matrix.cr#L228" target="_blank">View source</a>]
         
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@@ -1034,7 +1034,7 @@ and zeros elsewhere.</p></div>
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-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/matrix.cr#L233" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/matrix.cr#L233" target="_blank">View source</a>]
         
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@@ -1052,7 +1052,7 @@ and zeros elsewhere.</p></div>
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-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/matrix.cr#L239" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/matrix.cr#L239" target="_blank">View source</a>]
         
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@@ -1070,7 +1070,7 @@ and zeros elsewhere.</p></div>
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-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/matrix.cr#L247" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/matrix.cr#L247" target="_blank">View source</a>]
         
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@@ -1088,7 +1088,7 @@ and zeros elsewhere.</p></div>
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-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/matrix.cr#L274" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/matrix.cr#L274" target="_blank">View source</a>]
         
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@@ -1106,7 +1106,7 @@ and zeros elsewhere.</p></div>
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-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/matrix.cr#L265" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/matrix.cr#L265" target="_blank">View source</a>]
         
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@@ -1124,7 +1124,7 @@ and zeros elsewhere.</p></div>
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-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/matrix.cr#L256" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/matrix.cr#L256" target="_blank">View source</a>]
         
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@@ -1140,7 +1140,7 @@ and zeros elsewhere.</p></div>
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-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/matrix.cr#L11" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/matrix.cr#L11" target="_blank">View source</a>]
         
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@@ -1158,7 +1158,7 @@ and zeros elsewhere.</p></div>
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-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/matrix.cr#L283" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/matrix.cr#L283" target="_blank">View source</a>]
         
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@@ -1174,7 +1174,7 @@ and zeros elsewhere.</p></div>
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-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/matrix.cr#L354" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/matrix.cr#L354" target="_blank">View source</a>]
         
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@@ -1190,7 +1190,7 @@ and zeros elsewhere.</p></div>
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-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/matrix.cr#L429" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/matrix.cr#L429" target="_blank">View source</a>]
         
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@@ -1208,7 +1208,7 @@ and zeros elsewhere.</p></div>
       <br/>
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-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/matrix.cr#L304" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/matrix.cr#L304" target="_blank">View source</a>]
         
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@@ -1226,7 +1226,7 @@ and zeros elsewhere.</p></div>
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-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/matrix.cr#L450" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/matrix.cr#L450" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -1242,7 +1242,7 @@ and zeros elsewhere.</p></div>
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/matrix.cr#L516" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/matrix.cr#L516" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -1258,7 +1258,7 @@ and zeros elsewhere.</p></div>
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/matrix.cr#L475" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/matrix.cr#L475" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -1274,7 +1274,7 @@ and zeros elsewhere.</p></div>
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/matrix.cr#L480" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/matrix.cr#L480" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -1290,7 +1290,7 @@ and zeros elsewhere.</p></div>
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/matrix.cr#L13" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/matrix.cr#L13" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -1306,7 +1306,7 @@ and zeros elsewhere.</p></div>
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/matrix.cr#L484" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/matrix.cr#L484" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -1322,7 +1322,7 @@ and zeros elsewhere.</p></div>
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/matrix.cr#L492" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/matrix.cr#L492" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -1338,7 +1338,7 @@ and zeros elsewhere.</p></div>
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/matrix.cr#L502" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/matrix.cr#L502" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -1354,7 +1354,7 @@ and zeros elsewhere.</p></div>
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/matrix.cr#L496" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/matrix.cr#L496" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -1370,7 +1370,7 @@ and zeros elsewhere.</p></div>
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/matrix.cr#L525" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/matrix.cr#L525" target="_blank">View source</a>]
         
       </div>
     </div>
diff --git a/docs/Apatite/LinearAlgebra/NDArray.html b/docs/Apatite/LinearAlgebra/NDArray.html
index d2f1e83..dae0b0c 100644
--- a/docs/Apatite/LinearAlgebra/NDArray.html
+++ b/docs/Apatite/LinearAlgebra/NDArray.html
@@ -122,7 +122,7 @@
   <h2>Defined in:</h2>
   
     
-      <a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/ndarray.cr#L2" target="_blank">
+      <a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/ndarray.cr#L2" target="_blank">
         apatite/linear_algebra/ndarray.cr
       </a>
     
@@ -323,7 +323,7 @@
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/ndarray.cr#L18" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/ndarray.cr#L18" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -346,7 +346,7 @@
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/ndarray.cr#L11" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/ndarray.cr#L11" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -362,7 +362,7 @@
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/ndarray.cr#L11" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/ndarray.cr#L11" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -378,7 +378,7 @@
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/ndarray.cr#L13" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/ndarray.cr#L13" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -394,7 +394,7 @@
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/ndarray.cr#L12" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/ndarray.cr#L12" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -410,7 +410,7 @@
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/ndarray.cr#L12" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/ndarray.cr#L12" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -428,7 +428,7 @@
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/ndarray.cr#L24" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/ndarray.cr#L24" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -446,7 +446,7 @@
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/ndarray.cr#L29" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/ndarray.cr#L29" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -462,7 +462,7 @@
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/ndarray.cr#L9" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/ndarray.cr#L9" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -478,7 +478,7 @@
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/ndarray.cr#L11" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/ndarray.cr#L11" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -494,7 +494,7 @@
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/ndarray.cr#L16" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/ndarray.cr#L16" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -510,7 +510,7 @@
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/ndarray.cr#L16" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/ndarray.cr#L16" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -526,7 +526,7 @@
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/ndarray.cr#L15" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/ndarray.cr#L15" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -542,7 +542,7 @@
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/ndarray.cr#L15" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/ndarray.cr#L15" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -558,7 +558,7 @@
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/ndarray.cr#L14" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/ndarray.cr#L14" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -574,7 +574,7 @@
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/ndarray.cr#L14" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/ndarray.cr#L14" target="_blank">View source</a>]
         
       </div>
     </div>
diff --git a/docs/Apatite/LinearAlgebra/Vector.html b/docs/Apatite/LinearAlgebra/Vector.html
index 00171cd..915a57d 100644
--- a/docs/Apatite/LinearAlgebra/Vector.html
+++ b/docs/Apatite/LinearAlgebra/Vector.html
@@ -127,7 +127,7 @@ of a <code><a href="../../Apatite/LinearAlgebra/Matrix.html">Matrix</a></code></
   <h2>Defined in:</h2>
   
     
-      <a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L4" target="_blank">
+      <a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L4" target="_blank">
         apatite/linear_algebra/vector.cr
       </a>
     
@@ -279,10 +279,15 @@ of a <code><a href="../../Apatite/LinearAlgebra/Matrix.html">Matrix</a></code></
         
       </li>
     
+      <li class="entry-summary">
+        <a href="#%2F%28other%29-instance-method" class="signature"><strong>#/</strong>(other)</a>
+        
+      </li>
+    
       <li class="entry-summary">
         <a href="#%3C%3C%28value%3AFloat64%29-instance-method" class="signature"><strong>#<<</strong>(value : Float64)</a>
         
-          <div class="summary"><p>Alias for <code><a href="../../Apatite/LinearAlgebra/Vector.html#push%28%2Avalues%3AFloat64%29-instance-method">#push</a></code></p></div>
+          <div class="summary"><p>Alias for <code><a href="../../Apatite/LinearAlgebra/Vector.html#push%28value%3AFloat64%29-instance-method">#push</a></code></p></div>
         
       </li>
     
@@ -413,6 +418,13 @@ of a <code><a href="../../Apatite/LinearAlgebra/Matrix.html">Matrix</a></code></
         
       </li>
     
+      <li class="entry-summary">
+        <a href="#divide%28value%29-instance-method" class="signature"><strong>#divide</strong>(value)</a>
+        
+          <div class="summary"><p>When the input is a number, this returns the result of dividing it to all vector elements.</p></div>
+        
+      </li>
+    
       <li class="entry-summary">
         <a href="#dot%28other%29-instance-method" class="signature"><strong>#dot</strong>(other)</a>
         
@@ -511,6 +523,13 @@ of a <code><a href="../../Apatite/LinearAlgebra/Matrix.html">Matrix</a></code></
         
       </li>
     
+      <li class="entry-summary">
+        <a href="#normalize-instance-method" class="signature"><strong>#normalize</strong></a>
+        
+          <div class="summary"><p>Returns a new vector created by normalizing this one to have a magnitude of <code>1</code>.</p></div>
+        
+      </li>
+    
       <li class="entry-summary">
         <a href="#parallel_to%3F%28vector%29-instance-method" class="signature"><strong>#parallel_to?</strong>(vector)</a>
         
@@ -538,12 +557,12 @@ of a <code><a href="../../Apatite/LinearAlgebra/Matrix.html">Matrix</a></code></
       </li>
     
       <li class="entry-summary">
-        <a href="#push%28%2Avalues%3AFloat64%29-instance-method" class="signature"><strong>#push</strong>(*values : Float64)</a>
+        <a href="#push%28value%3AFloat64%29-instance-method" class="signature"><strong>#push</strong>(value : Float64)</a>
         
       </li>
     
       <li class="entry-summary">
-        <a href="#push%28value%3AFloat64%29-instance-method" class="signature"><strong>#push</strong>(value : Float64)</a>
+        <a href="#push%28%2Avalues%3AFloat64%29-instance-method" class="signature"><strong>#push</strong>(*values : Float64)</a>
         
       </li>
     
@@ -580,6 +599,13 @@ of a <code><a href="../../Apatite/LinearAlgebra/Matrix.html">Matrix</a></code></
         
       </li>
     
+      <li class="entry-summary">
+        <a href="#similarity%28other%29-instance-method" class="signature"><strong>#similarity</strong>(other)</a>
+        
+          <div class="summary"><p>Compute the cosine similarity between this vector and another.</p></div>
+        
+      </li>
+    
       <li class="entry-summary">
         <a href="#size%3AInt32-instance-method" class="signature"><strong>#size</strong> : Int32</a>
         
@@ -773,7 +799,7 @@ and yielding that buffer. The given block must return the desired size of the ve
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L106" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L106" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -793,7 +819,7 @@ and yielding that buffer. The given block must return the desired size of the ve
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L63" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L63" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -820,7 +846,7 @@ vec.size <span class="c"># =&gt; 0</span></code></pre></div>
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L43" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L43" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -838,7 +864,7 @@ vec.size <span class="c"># =&gt; 0</span></code></pre></div>
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L25" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L25" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -862,7 +888,7 @@ vec <span class="c"># =&gt; Vector{5.0, 5.0, 5.0}</span></code></pre></div>
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L87" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L87" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -883,7 +909,7 @@ vec <span class="c"># =&gt; Vector{5.0, 5.0, 5.0}</span></code></pre></div>
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L156" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L156" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -901,7 +927,7 @@ vec <span class="c"># =&gt; Vector{5.0, 5.0, 5.0}</span></code></pre></div>
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L138" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L138" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -922,7 +948,7 @@ collection.</p>
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L118" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L118" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -940,7 +966,7 @@ collection.</p>
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L152" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L152" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -960,7 +986,7 @@ to a given range.</p></div>
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L129" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L129" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -978,7 +1004,7 @@ to a given range.</p></div>
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L147" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L147" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -999,7 +1025,7 @@ to a given range.</p></div>
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L370" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L370" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -1015,7 +1041,7 @@ to a given range.</p></div>
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L362" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L362" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -1031,7 +1057,23 @@ to a given range.</p></div>
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L366" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L366" target="_blank">View source</a>]
+        
+      </div>
+    </div>
+  
+    <div class="entry-detail" id="/(other)-instance-method">
+      <div class="signature">
+        
+        def <strong>/</strong>(other)
+
+        <a class="method-permalink" href="#%2F%28other%29-instance-method">#</a>
+      </div>
+      
+      <br/>
+      <div>
+        
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L374" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -1044,12 +1086,12 @@ to a given range.</p></div>
         <a class="method-permalink" href="#%3C%3C%28value%3AFloat64%29-instance-method">#</a>
       </div>
       
-        <div class="doc"><p>Alias for <code><a href="../../Apatite/LinearAlgebra/Vector.html#push%28%2Avalues%3AFloat64%29-instance-method">#push</a></code></p></div>
+        <div class="doc"><p>Alias for <code><a href="../../Apatite/LinearAlgebra/Vector.html#push%28value%3AFloat64%29-instance-method">#push</a></code></p></div>
       
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L349" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L349" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -1078,7 +1120,7 @@ value, that result is the return value of the comparison.</p>
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L339" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L339" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -1094,7 +1136,7 @@ value, that result is the return value of the comparison.</p>
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L353" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L353" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -1123,7 +1165,7 @@ v[<span class="n">6</span>, <span class="n">10</span>] <span class="c"># raise I
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L191" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L191" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -1151,7 +1193,7 @@ v[<span class="n">6</span>..<span class="n">10</span>] <span class="c"># raise I
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L173" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L173" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -1177,7 +1219,7 @@ vec <span class="c"># = Vector{1.0, 6.0, 7.0, 5.0}</span></code></pre></div>
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L297" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L297" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -1209,7 +1251,7 @@ vec <span class="c"># =&gt; Vector{1.0, 6.0, 2.0, 3.0, 4.0, 5.0}</span></code></
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L248" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L248" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -1236,7 +1278,7 @@ vec[<span class="n">3</span>] <span class="o">=</span> <span class="n">5.0</span
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L226" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L226" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -1262,7 +1304,7 @@ vec <span class="c"># = Vector{1.0, 6.0, 2.0, 3.0, 4.0, 5.0}</span></code></pre>
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L282" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L282" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -1282,7 +1324,7 @@ will be added together.</p></div>
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L488" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L476" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -1301,7 +1343,7 @@ If the vectors are mirrored across their axes this will return <code>nil</code>.
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L440" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L449" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -1319,7 +1361,7 @@ If the vectors are mirrored across their axes this will return <code>nil</code>.
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L475" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L464" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -1338,7 +1380,7 @@ on the end.</p></div>
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L556" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L551" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -1357,7 +1399,7 @@ the beginning.</p></div>
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L541" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L536" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -1378,7 +1420,7 @@ vec.clear <span class="c"># =&gt; Vector{}</span></code></pre></div>
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L782" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L768" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -1394,7 +1436,7 @@ vec.clear <span class="c"># =&gt; Vector{}</span></code></pre></div>
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L374" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L378" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -1410,7 +1452,7 @@ vec.clear <span class="c"># =&gt; Vector{}</span></code></pre></div>
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L731" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L717" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -1428,7 +1470,7 @@ vec.clear <span class="c"># =&gt; Vector{}</span></code></pre></div>
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L601" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L587" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -1450,7 +1492,7 @@ v1.cross(v2) => <span class="t">Vector</span>{<span class="n">0.0</span>, <span
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L518" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L513" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -1469,7 +1511,27 @@ a point in space.</p></div>
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L629" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L615" target="_blank">View source</a>]
+        
+      </div>
+    </div>
+  
+    <div class="entry-detail" id="divide(value)-instance-method">
+      <div class="signature">
+        
+        def <strong>divide</strong>(value)
+
+        <a class="method-permalink" href="#divide%28value%29-instance-method">#</a>
+      </div>
+      
+        <div class="doc"><p>When the input is a number, this returns the result of dividing
+it to all vector elements. When it's a vector, the vectors
+will be element-wise divided.</p></div>
+      
+      <br/>
+      <div>
+        
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L497" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -1489,7 +1551,7 @@ a point in space.</p></div>
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L574" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L569" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -1508,7 +1570,7 @@ is out of bounds. Indexing starts from 1.</p></div>
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L426" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L430" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -1526,7 +1588,7 @@ is out of bounds. Indexing starts from 1.</p></div>
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L384" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L388" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -1544,7 +1606,7 @@ is out of bounds. Indexing starts from 1.</p></div>
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L654" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L640" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -1562,7 +1624,7 @@ is out of bounds. Indexing starts from 1.</p></div>
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L649" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L635" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -1580,7 +1642,7 @@ is out of bounds. Indexing starts from 1.</p></div>
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L562" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L557" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -1600,7 +1662,7 @@ is out of bounds. Indexing starts from 1.</p></div>
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L419" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L423" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -1618,7 +1680,7 @@ is out of bounds. Indexing starts from 1.</p></div>
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L379" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L383" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -1641,7 +1703,7 @@ a <span class="c"># =&gt; Vector{1.0, 4.0, 9.0}</span></code></pre></div>
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L400" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L404" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -1659,7 +1721,7 @@ a <span class="c"># =&gt; Vector{1.0, 4.0, 9.0}</span></code></pre></div>
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L406" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L410" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -1677,7 +1739,7 @@ a <span class="c"># =&gt; Vector{1.0, 4.0, 9.0}</span></code></pre></div>
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L411" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L415" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -1695,7 +1757,7 @@ a <span class="c"># =&gt; Vector{1.0, 4.0, 9.0}</span></code></pre></div>
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L589" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L575" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -1713,7 +1775,7 @@ a <span class="c"># =&gt; Vector{1.0, 4.0, 9.0}</span></code></pre></div>
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L594" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L580" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -1733,7 +1795,27 @@ will be element-wise multiplied.</p></div>
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L502" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L490" target="_blank">View source</a>]
+        
+      </div>
+    </div>
+  
+    <div class="entry-detail" id="normalize-instance-method">
+      <div class="signature">
+        
+        def <strong>normalize</strong>
+
+        <a class="method-permalink" href="#normalize-instance-method">#</a>
+      </div>
+      
+        <div class="doc"><p>Returns a new vector created by normalizing this one
+to have a magnitude of <code>1</code>. If the vector is a zero
+vector, it will not be modified.</p></div>
+      
+      <br/>
+      <div>
+        
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L443" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -1751,7 +1833,7 @@ will be element-wise multiplied.</p></div>
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L469" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L459" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -1769,7 +1851,7 @@ will be element-wise multiplied.</p></div>
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L481" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L469" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -1785,7 +1867,7 @@ will be element-wise multiplied.</p></div>
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L754" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L740" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -1803,23 +1885,7 @@ will be element-wise multiplied.</p></div>
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L567" target="_blank">View source</a>]
-        
-      </div>
-    </div>
-  
-    <div class="entry-detail" id="push(*values:Float64)-instance-method">
-      <div class="signature">
-        
-        def <strong>push</strong>(*values : Float64)
-
-        <a class="method-permalink" href="#push%28%2Avalues%3AFloat64%29-instance-method">#</a>
-      </div>
-      
-      <br/>
-      <div>
-        
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L665" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L562" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -1835,7 +1901,23 @@ will be element-wise multiplied.</p></div>
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L658" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L644" target="_blank">View source</a>]
+        
+      </div>
+    </div>
+  
+    <div class="entry-detail" id="push(*values:Float64)-instance-method">
+      <div class="signature">
+        
+        def <strong>push</strong>(*values : Float64)
+
+        <a class="method-permalink" href="#push%28%2Avalues%3AFloat64%29-instance-method">#</a>
+      </div>
+      
+      <br/>
+      <div>
+        
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L651" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -1854,7 +1936,7 @@ will be element-wise multiplied.</p></div>
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L684" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L670" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -1874,7 +1956,7 @@ careful with line directions!</p></div>
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L678" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L664" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -1892,7 +1974,7 @@ careful with line directions!</p></div>
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L612" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L598" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -1908,7 +1990,7 @@ careful with line directions!</p></div>
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L726" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L712" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -1927,7 +2009,25 @@ across the whole vector.</p></div>
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L707" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L693" target="_blank">View source</a>]
+        
+      </div>
+    </div>
+  
+    <div class="entry-detail" id="similarity(other)-instance-method">
+      <div class="signature">
+        
+        def <strong>similarity</strong>(other)
+
+        <a class="method-permalink" href="#similarity%28other%29-instance-method">#</a>
+      </div>
+      
+        <div class="doc"><p>Compute the cosine similarity between this vector and another.</p></div>
+      
+      <br/>
+      <div>
+        
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L454" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -1945,7 +2045,7 @@ across the whole vector.</p></div>
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L24" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L24" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -1964,7 +2064,7 @@ they differ from it by less than <code>Apetite.precision</code></p></div>
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L623" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L609" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -1984,7 +2084,7 @@ will be subtracted.</p></div>
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L495" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L483" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -2002,7 +2102,7 @@ will be subtracted.</p></div>
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L507" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L502" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -2021,7 +2121,7 @@ z-component is added.</p></div>
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L713" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L699" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -2037,7 +2137,7 @@ z-component is added.</p></div>
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L744" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L730" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -2056,7 +2156,7 @@ diagonal elements.</p></div>
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L607" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L593" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -2072,7 +2172,7 @@ diagonal elements.</p></div>
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L748" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L734" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -2092,7 +2192,7 @@ vector, it will not be modified.</p></div>
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L433" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L437" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -2116,7 +2216,7 @@ vec.to_unsafe[<span class="n">0</span>] <span class="c"># =&gt; 1.0</span></code
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L772" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L758" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -2134,7 +2234,7 @@ vec.to_unsafe[<span class="n">0</span>] <span class="c"># =&gt; 1.0</span></code
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L548" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L543" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -2152,7 +2252,7 @@ vec.to_unsafe[<span class="n">0</span>] <span class="c"># =&gt; 1.0</span></code
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L617" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L603" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -2168,7 +2268,7 @@ vec.to_unsafe[<span class="n">0</span>] <span class="c"># =&gt; 1.0</span></code
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L759" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L745" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -2184,7 +2284,7 @@ vec.to_unsafe[<span class="n">0</span>] <span class="c"># =&gt; 1.0</span></code
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L788" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L774" target="_blank">View source</a>]
         
       </div>
     </div>
diff --git a/docs/Array.html b/docs/Array.html
index 6368dcb..da0c068 100644
--- a/docs/Array.html
+++ b/docs/Array.html
@@ -160,7 +160,7 @@ set <span class="o">&lt;&lt;</span> <span class="n">3</span></code></pre>
   <h2>Defined in:</h2>
   
     
-      <a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/core_ext/array.cr#L1" target="_blank">
+      <a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/core_ext/array.cr#L1" target="_blank">
         apatite/core_ext/array.cr
       </a>
     
@@ -294,7 +294,7 @@ set <span class="o">&lt;&lt;</span> <span class="n">3</span></code></pre>
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/core_ext/array.cr#L3" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/core_ext/array.cr#L3" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -312,7 +312,7 @@ set <span class="o">&lt;&lt;</span> <span class="n">3</span></code></pre>
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/core_ext/array.cr#L11" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/core_ext/array.cr#L11" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -330,7 +330,7 @@ set <span class="o">&lt;&lt;</span> <span class="n">3</span></code></pre>
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/core_ext/array.cr#L19" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/core_ext/array.cr#L19" target="_blank">View source</a>]
         
       </div>
     </div>
@@ -346,7 +346,7 @@ set <span class="o">&lt;&lt;</span> <span class="n">3</span></code></pre>
       <br/>
       <div>
         
-          [<a href="https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/core_ext/array.cr#L24" target="_blank">View source</a>]
+          [<a href="https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/core_ext/array.cr#L24" target="_blank">View source</a>]
         
       </div>
     </div>
diff --git a/docs/index.html b/docs/index.html
index 361f104..cdb5485 100644
--- a/docs/index.html
+++ b/docs/index.html
@@ -105,11 +105,11 @@
 
 <pre><code class="language-crystal"><span class="k">require</span> <span class="s">&quot;apatite&quot;</span></code></pre>
 
-<p><span class="flag orange">TODO</span>  Write usage instructions here, but first write the library...</p>
+<p>Check out the <a href="https://watzon.github.io/apatite/" target="_blank">documentation</a> for usage examples.</p>
 
 <h2>Roadmap</h2>
 
-<ul><li>[ ] Apetite</li><li>[ ] Vector Math</li><li>[ ] Matrix</li><li>[ ] NDArray</li><li>[x] Vector</li><li>[ ] Line</li><li>[ ] Plane</li><li>[ ] Polygon</li><li>[ ] LinkedList
+<ul><li>[ ] Linear Algebra</li><li>[x] Vector</li><li>[ ] Matrix (_in progress_)</li><li>[ ] NDArray</li><li>[ ] Line</li><li>[ ] Plane</li><li>[ ] Polygon</li><li>[ ] LinkedList
 	</li></ul>
 
 <h2>Contributing</h2>
diff --git a/docs/index.json b/docs/index.json
index a65997e..7e8f06d 100644
--- a/docs/index.json
+++ b/docs/index.json
@@ -1 +1 @@
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Indexable)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/matrix.cr#L214","def":{"name":"/","args":[{"name":"vec","doc":null,"default_value":"","external_name":"vec","restriction":"Indexable"}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"rows = self.rows.map do |row|\n  row.map do |e|\n    e / other\n  end\nend\nreturn new_matrix(rows, column_count)\n"}},{"id":"==(other:Matrix)-instance-method","html_id":"==(other:Matrix)-instance-method","name":"==","doc":null,"summary":null,"abstract":false,"args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":"Matrix"}],"args_string":"(other : Matrix)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/matrix.cr#L221","def":{"name":"==","args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":"Matrix"}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"if (Matrix === other) && (column_count == other.column_count)\nelse\n  return false\nend\nrows == other.rows\n"}},{"id":"[](row:Int,col:Int)-instance-method","html_id":"[](row:Int,col:Int)-instance-method","name":"[]","doc":"Returns element `(row, col)` of the matrix. Throws error on index error.","summary":"<p>Returns element <code>(row, col)</code> of the matrix.</p>","abstract":false,"args":[{"name":"row","doc":null,"default_value":"","external_name":"row","restriction":"Int"},{"name":"col","doc":null,"default_value":"","external_name":"col","restriction":"Int"}],"args_string":"(row : Int, col : Int)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/matrix.cr#L228","def":{"name":"[]","args":[{"name":"row","doc":null,"default_value":"","external_name":"row","restriction":"Int"},{"name":"col","doc":null,"default_value":"","external_name":"col","restriction":"Int"}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"self[row][col]"}},{"id":"[]?(row:Int,col:Int)-instance-method","html_id":"[]?(row:Int,col:Int)-instance-method","name":"[]?","doc":"Returns element `(row, col)` of the matrix, or nil if the index is not found.","summary":"<p>Returns element <code>(row, col)</code> of the matrix, or nil if the index is not found.</p>","abstract":false,"args":[{"name":"row","doc":null,"default_value":"","external_name":"row","restriction":"Int"},{"name":"col","doc":null,"default_value":"","external_name":"col","restriction":"Int"}],"args_string":"(row : Int, col : Int)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/matrix.cr#L233","def":{"name":"[]?","args":[{"name":"row","doc":null,"default_value":"","external_name":"row","restriction":"Int"},{"name":"col","doc":null,"default_value":"","external_name":"col","restriction":"Int"}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"v = fetch(row) do\n  nil\nend\nif v.nil?\nelse\n  v[col]?\nend\n"}},{"id":"adjugate-instance-method","html_id":"adjugate-instance-method","name":"adjugate","doc":"Returns the adjugate of the matrix.","summary":"<p>Returns the adjugate of the matrix.</p>","abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/matrix.cr#L239","def":{"name":"adjugate","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"if square?\nelse\n  raise(\"Dimention mismatch: `Matrix#adjugate` requires a square matrix.\")\nend\nMatrix.build(row_count, column_count) do |row, column|\n  cofactor(column, row)\nend\n"}},{"id":"cofactor(row,column)-instance-method","html_id":"cofactor(row,column)-instance-method","name":"cofactor","doc":"Returns the (row, column) cofactor which is obtained by multiplying the first minor by (-1)**(row + column)","summary":"<p>Returns the (row, column) cofactor which is obtained by multiplying the first minor by (-1)**(row + column)</p>","abstract":false,"args":[{"name":"row","doc":null,"default_value":"","external_name":"row","restriction":""},{"name":"column","doc":null,"default_value":"","external_name":"column","restriction":""}],"args_string":"(row, column)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/matrix.cr#L247","def":{"name":"cofactor","args":[{"name":"row","doc":null,"default_value":"","external_name":"row","restriction":""},{"name":"column","doc":null,"default_value":"","external_name":"column","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"if empty?\n  raise(\"cofactor of empty matrix is not defined\")\nend\nif square?\nelse\n  raise(\"Dimention mismatch: `Matrix#cofactor` requires a square matrix.\")\nend\ndet_of_minor = (first_minor(row, column)).determinant\ndet_of_minor * ((-1.0) ** (row + column))\n"}},{"id":"column(j,&block)-instance-method","html_id":"column(j,&amp;block)-instance-method","name":"column","doc":"Iterates over the specified column in the matrix, returning the Vector's items.","summary":"<p>Iterates over the specified column in the matrix, returning the Vector's items.</p>","abstract":false,"args":[{"name":"j","doc":null,"default_value":"","external_name":"j","restriction":""}],"args_string":"(j, &block)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/matrix.cr#L274","def":{"name":"column","args":[{"name":"j","doc":null,"default_value":"","external_name":"j","restriction":""}],"double_splat":null,"splat_index":null,"yields":1,"block_arg":null,"return_type":"","visibility":"Public","body":"if j >= column_count || j < (-column_count)\n  return self\nend\nrow_count.times do |i|\n  yield rows[i][j]\nend\nself\n"}},{"id":"column(j)-instance-method","html_id":"column(j)-instance-method","name":"column","doc":"Returns column vector number `j` of the matrix as a `Vector` (starting at 0 like an array).","summary":"<p>Returns column vector number <code>j</code> of the matrix as a <code><a href=\"../../Apatite/LinearAlgebra/Vector.html\">Vector</a></code> (starting at 0 like an array).</p>","abstract":false,"args":[{"name":"j","doc":null,"default_value":"","external_name":"j","restriction":""}],"args_string":"(j)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/matrix.cr#L265","def":{"name":"column","args":[{"name":"j","doc":null,"default_value":"","external_name":"j","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"if j >= column_count || j < (-column_count)\n  raise(\"Index out of range\")\nend\ncol = Array(Float64).new(row_count) do |i|\n  rows[i][j]\nend\nVector.create(col)\n"}},{"id":"column?(j)-instance-method","html_id":"column?(j)-instance-method","name":"column?","doc":"Returns column vector number `j` of the matrix as a `Vector` (starting at 0 like an array).","summary":"<p>Returns column vector number <code>j</code> of the matrix as a <code><a href=\"../../Apatite/LinearAlgebra/Vector.html\">Vector</a></code> (starting at 0 like an array).</p>","abstract":false,"args":[{"name":"j","doc":null,"default_value":"","external_name":"j","restriction":""}],"args_string":"(j)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/matrix.cr#L256","def":{"name":"column?","args":[{"name":"j","doc":null,"default_value":"","external_name":"j","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"if j >= column_count || j < (-column_count)\n  return nil\nend\ncol = Array(Float64).new(row_count) do |i|\n  rows[i][j]\nend\nVector.create(col)\n"}},{"id":"column_count:Int32-instance-method","html_id":"column_count:Int32-instance-method","name":"column_count","doc":null,"summary":null,"abstract":false,"args":[],"args_string":" : Int32","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/matrix.cr#L11","def":{"name":"column_count","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"Int32","visibility":"Public","body":"@column_count"}},{"id":"column_vectors-instance-method","html_id":"column_vectors-instance-method","name":"column_vectors","doc":"Returns an array of the column vectors of the matrix. See `Vector`.","summary":"<p>Returns an array of the column vectors of the matrix.</p>","abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/matrix.cr#L283","def":{"name":"column_vectors","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"Array(Vector).new(column_count) do |i|\n  column(i)\nend"}},{"id":"determinant-instance-method","html_id":"determinant-instance-method","name":"determinant","doc":null,"summary":null,"abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/matrix.cr#L354","def":{"name":"determinant","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"if square?\nelse\n  raise(\"Dimention mismatch: `Matrix#determinant` requires a square matrix.\")\nend\nm = rows\ncase row_count\nwhen 0\n  +1\nwhen 1\n  +m[0][0]\nwhen 2\n  ((+m[0][0]) * m[1][1]) - (m[0][1] * m[1][0])\nwhen 3\n  m0, m1, m2 = m\n  (((((((+m0[0]) * m1[1]) * m2[2]) - ((m0[0] * m1[2]) * m2[1])) - ((m0[1] * m1[0]) * m2[2])) + ((m0[1] * m1[2]) * m2[0])) + ((m0[2] * m1[0]) * m2[1])) - ((m0[2] * m1[1]) * m2[0])\nwhen 4\n  m0, m1, m2, m3 = m\n  ((((((((((((((((((((((((((+m0[0]) * m1[1]) * m2[2]) * m3[3]) - (((m0[0] * m1[1]) * m2[3]) * m3[2])) - (((m0[0] * m1[2]) * m2[1]) * m3[3])) + (((m0[0] * m1[2]) * m2[3]) * m3[1])) + (((m0[0] * m1[3]) * m2[1]) * m3[2])) - (((m0[0] * m1[3]) * m2[2]) * m3[1])) - (((m0[1] * m1[0]) * m2[2]) * m3[3])) + (((m0[1] * m1[0]) * m2[3]) * m3[2])) + (((m0[1] * m1[2]) * m2[0]) * m3[3])) - (((m0[1] * m1[2]) * m2[3]) * m3[0])) - (((m0[1] * m1[3]) * m2[0]) * m3[2])) + (((m0[1] * m1[3]) * m2[2]) * m3[0])) + (((m0[2] * m1[0]) * m2[1]) * m3[3])) - (((m0[2] * m1[0]) * m2[3]) * m3[1])) - (((m0[2] * m1[1]) * m2[0]) * m3[3])) + (((m0[2] * m1[1]) * m2[3]) * m3[0])) + (((m0[2] * m1[3]) * m2[0]) * m3[1])) - (((m0[2] * m1[3]) * m2[1]) * m3[0])) - (((m0[3] * m1[0]) * m2[1]) * m3[2])) + (((m0[3] * m1[0]) * m2[2]) * m3[1])) + (((m0[3] * m1[1]) * m2[0]) * m3[2])) - (((m0[3] * m1[1]) * m2[2]) * m3[0])) - (((m0[3] * m1[2]) * m2[0]) * m3[1])) + (((m0[3] * m1[2]) * m2[1]) * m3[0])\nelse\n  determinant_bareiss\nend\n"}},{"id":"first_minor(row,column)-instance-method","html_id":"first_minor(row,column)-instance-method","name":"first_minor","doc":null,"summary":null,"abstract":false,"args":[{"name":"row","doc":null,"default_value":"","external_name":"row","restriction":""},{"name":"column","doc":null,"default_value":"","external_name":"column","restriction":""}],"args_string":"(row, column)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/matrix.cr#L429","def":{"name":"first_minor","args":[{"name":"row","doc":null,"default_value":"","external_name":"row","restriction":""},{"name":"column","doc":null,"default_value":"","external_name":"column","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"if empty?\n  raise(\"first_minor of empty matrix is not defined\")\nend\nif 0 <= row && row < row_count\nelse\n  raise(ArgumentError.new(\"invalid row (#{row.inspect} for 0..#{row_count - 1})\"))\nend\nif 0 <= column && column < column_count\nelse\n  raise(ArgumentError.new(\"invalid column (#{column.inspect} for 0..#{column_count - 1})\"))\nend\narrays = to_a.map(&.to_a)\narrays.delete_at(row)\narrays.each do |array|\n  array.delete_at(column)\nend\nMatrix.new(arrays, column_count - 1)\n"}},{"id":"inverse-instance-method","html_id":"inverse-instance-method","name":"inverse","doc":"Returns the inverse of the matrix.","summary":"<p>Returns the inverse of the matrix.</p>","abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/matrix.cr#L304","def":{"name":"inverse","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"if square?\nelse\n  if square?\n  else\n    raise(\"Dimention mismatch: `Matrix#inverse` requires a square matrix.\")\n  end\nend\n(Matrix.identity(row_count)).inverse_from(self)\n"}},{"id":"laplace_expansion(*,row=nil,column=nil)-instance-method","html_id":"laplace_expansion(*,row=nil,column=nil)-instance-method","name":"laplace_expansion","doc":"Returns the Laplace expansion along given row or column.","summary":"<p>Returns the Laplace expansion along given row or column.</p>","abstract":false,"args":[{"name":"","doc":null,"default_value":"","external_name":"","restriction":""},{"name":"row","doc":null,"default_value":"nil","external_name":"row","restriction":""},{"name":"column","doc":null,"default_value":"nil","external_name":"column","restriction":""}],"args_string":"(*, row = <span class=\"n\">nil</span>, column = <span class=\"n\">nil</span>)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/matrix.cr#L450","def":{"name":"laplace_expansion","args":[{"name":"","doc":null,"default_value":"","external_name":"","restriction":""},{"name":"row","doc":null,"default_value":"nil","external_name":"row","restriction":""},{"name":"column","doc":null,"default_value":"nil","external_name":"column","restriction":""}],"double_splat":null,"splat_index":0,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"num = row || column\nif (!num) || (row && column)\n  raise(ArgumentError.new(\"exactly one the row or column arguments must be specified\"))\nend\nif square?\nelse\n  raise(\"Dimention mismatch: `Matrix#determinant` requires a square matrix.\")\nend\nif empty?\n  raise(\"laplace_expansion of empty matrix is not defined\")\nend\nif 0 <= num && num < row_count\nelse\n  raise(ArgumentError.new(\"invalid num (#{num.inspect} for 0..#{row_count - 1})\"))\nend\nif row\n  (row(num)).map_with_index do |e, k|\n    e * (cofactor(num, k))\n  end.reduce(&.+)\nelse\n  (column(num)).map_with_index do |e, k|\n    e * (cofactor(k, num))\n  end.reduce(&.+)\nend\n"}},{"id":"pretty_print(pp):Nil-instance-method","html_id":"pretty_print(pp):Nil-instance-method","name":"pretty_print","doc":null,"summary":null,"abstract":false,"args":[{"name":"pp","doc":null,"default_value":"","external_name":"pp","restriction":""}],"args_string":"(pp) : Nil","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/matrix.cr#L516","def":{"name":"pretty_print","args":[{"name":"pp","doc":null,"default_value":"","external_name":"pp","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"Nil","visibility":"Public","body":"pp.list(\"[\", self, \"]\") do |vec|\n  pp.group do\n    vec.to_a.pretty_print(pp)\n  end\nend"}},{"id":"row(i,&block)-instance-method","html_id":"row(i,&amp;block)-instance-method","name":"row","doc":null,"summary":null,"abstract":false,"args":[{"name":"i","doc":null,"default_value":"","external_name":"i","restriction":""}],"args_string":"(i, &block)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/matrix.cr#L475","def":{"name":"row","args":[{"name":"i","doc":null,"default_value":"","external_name":"i","restriction":""}],"double_splat":null,"splat_index":null,"yields":0,"block_arg":{"name":"block","doc":null,"default_value":"","external_name":"block","restriction":""},"return_type":"","visibility":"Public","body":"(@rows.fetch(i) do\n  return self\nend).each(&block)\nself\n"}},{"id":"row(i)-instance-method","html_id":"row(i)-instance-method","name":"row","doc":null,"summary":null,"abstract":false,"args":[{"name":"i","doc":null,"default_value":"","external_name":"i","restriction":""}],"args_string":"(i)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/matrix.cr#L480","def":{"name":"row","args":[{"name":"i","doc":null,"default_value":"","external_name":"i","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"Vector.create(rows.fetch(i) do\n  [] of Float64\nend)"}},{"id":"row_count:Int32-instance-method","html_id":"row_count:Int32-instance-method","name":"row_count","doc":null,"summary":null,"abstract":false,"args":[],"args_string":" : Int32","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/matrix.cr#L13","def":{"name":"row_count","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"Int32","visibility":"Public","body":"@row_count"}},{"id":"rows-instance-method","html_id":"rows-instance-method","name":"rows","doc":null,"summary":null,"abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/matrix.cr#L484","def":{"name":"rows","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"rows = [] of Vector\nrow_count.times do |i|\n  rows << self[i - 1]\nend\nrows\n"}},{"id":"square?-instance-method","html_id":"square?-instance-method","name":"square?","doc":null,"summary":null,"abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/matrix.cr#L492","def":{"name":"square?","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"row_count == 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A `range`\ncan optionally be passed in if you want to limit the random numbers\nto a given range.","summary":"<p>Creates a new <code><a href=\"../../Apatite/LinearAlgebra/Vector.html\">Vector</a></code> of size <code>n</code> filled with random numbers.</p>","abstract":false,"args":[{"name":"n","doc":null,"default_value":"","external_name":"n","restriction":""},{"name":"range","doc":null,"default_value":"nil","external_name":"range","restriction":""}],"args_string":"(n, range = <span class=\"n\">nil</span>)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L129","def":{"name":"random","args":[{"name":"n","doc":null,"default_value":"","external_name":"n","restriction":""},{"name":"range","doc":null,"default_value":"nil","external_name":"range","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"vec = Vector.new(n)\nn.times do\n  vec.push(rand((range || -1e+1)..1e+1))\nend\nvec\n"}},{"id":"zeros(n)-class-method","html_id":"zeros(n)-class-method","name":"zeros","doc":"Create a new vector of size `n` filled with zeros.","summary":"<p>Create a new vector of size <code>n</code> filled with zeros.</p>","abstract":false,"args":[{"name":"n","doc":null,"default_value":"","external_name":"n","restriction":""}],"args_string":"(n)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L147","def":{"name":"zeros","args":[{"name":"n","doc":null,"default_value":"","external_name":"n","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"Vector.new(n, 0.0)"}}],"constructors":[{"id":"build(capacity:Int,&block):self-class-method","html_id":"build(capacity:Int,&amp;block):self-class-method","name":"build","doc":"Creates a new `Vector`, allocating an internal buffer with the given *capacity*,\nand yielding that buffer. The given block must return the desired size of the vector.\n\nThis method is **unsafe**.\n\n```\nVector.build(3) do |buffer|\n  LibSome.fill_buffer_and_return_number_of_elements_filled(buffer)\nend\n```","summary":"<p>Creates a new <code><a href=\"../../Apatite/LinearAlgebra/Vector.html\">Vector</a></code>, allocating an internal buffer with the given <em>capacity</em>, and yielding that buffer.</p>","abstract":false,"args":[{"name":"capacity","doc":null,"default_value":"","external_name":"capacity","restriction":"Int"}],"args_string":"(capacity : Int, &block) : <span class=\"k\">self</span>","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L106","def":{"name":"build","args":[{"name":"capacity","doc":null,"default_value":"","external_name":"capacity","restriction":"Int"}],"double_splat":null,"splat_index":null,"yields":1,"block_arg":null,"return_type":"self","visibility":"Public","body":"vec = Vector.new(capacity)\nvec.size = (yield vec.to_unsafe).to_i\nvec\n"}},{"id":"new(size:Int,value:Float64)-class-method","html_id":"new(size:Int,value:Float64)-class-method","name":"new","doc":"Creates a new `Vector` of the given *size* filled with the same *value* in each position.\n\n```\nVector.new(3, 1.0) # => Vector{1.0, 1.0, 1.0}\n```","summary":"<p>Creates a new <code><a href=\"../../Apatite/LinearAlgebra/Vector.html\">Vector</a></code> of the given <em>size</em> filled with the same <em>value</em> in each position.</p>","abstract":false,"args":[{"name":"size","doc":null,"default_value":"","external_name":"size","restriction":"Int"},{"name":"value","doc":null,"default_value":"","external_name":"value","restriction":"Float64"}],"args_string":"(size : Int, value : Float64)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L63","def":{"name":"new","args":[{"name":"size","doc":null,"default_value":"","external_name":"size","restriction":"Int"},{"name":"value","doc":null,"default_value":"","external_name":"value","restriction":"Float64"}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"_ = allocate\n_.initialize(size, value)\nif _.responds_to?(:finalize)\n  ::GC.add_finalizer(_)\nend\n_\n"}},{"id":"new(initial_capacity:Int)-class-method","html_id":"new(initial_capacity:Int)-class-method","name":"new","doc":"Creates a new empty `Vector` backed by a buffer that is initially\n`initial_capacity` big.\n\nThe *initial_capacity* is useful to avoid unnecessary reallocations\nof the internal buffer in case of growth. If you have an estimate\nof the maximum number of elements an vector will hold, the vector should\nbe initialized with that capacity for improved performance.\n\n```\nvec = Vector.new(5)\nvec.size # => 0\n```","summary":"<p>Creates a new empty <code><a href=\"../../Apatite/LinearAlgebra/Vector.html\">Vector</a></code> backed by a buffer that is initially <code>initial_capacity</code> big.</p>","abstract":false,"args":[{"name":"initial_capacity","doc":null,"default_value":"","external_name":"initial_capacity","restriction":"Int"}],"args_string":"(initial_capacity : Int)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L43","def":{"name":"new","args":[{"name":"initial_capacity","doc":null,"default_value":"","external_name":"initial_capacity","restriction":"Int"}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"_ = allocate\n_.initialize(initial_capacity)\nif _.responds_to?(:finalize)\n  ::GC.add_finalizer(_)\nend\n_\n"}},{"id":"new-class-method","html_id":"new-class-method","name":"new","doc":"Create a new empty `Vector`.","summary":"<p>Create a new empty <code><a href=\"../../Apatite/LinearAlgebra/Vector.html\">Vector</a></code>.</p>","abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L25","def":{"name":"new","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"_ = allocate\n_.initialize\nif _.responds_to?(:finalize)\n  ::GC.add_finalizer(_)\nend\n_\n"}},{"id":"new(size:Int,&block:Int32->Float64)-class-method","html_id":"new(size:Int,&amp;block:Int32-&gt;Float64)-class-method","name":"new","doc":"Creates a new `Vector` of the given *size* and invokes the given block once\nfor each index of `self`, assigning the block's value in that index.\n\n```\nVector.new(3) { |i| (i + 1.0) ** 2.0 } # => Vector{1.0, 4.0, 9.0}\n\nvec = Vector.new(3) { 5.0 }\nvec # => Vector{5.0, 5.0, 5.0}\n```","summary":"<p>Creates a new <code><a href=\"../../Apatite/LinearAlgebra/Vector.html\">Vector</a></code> of the given <em>size</em> and invokes the given block once for each index of <code>self</code>, assigning the block's value in that index.</p>","abstract":false,"args":[{"name":"size","doc":null,"default_value":"","external_name":"size","restriction":"Int"}],"args_string":"(size : Int, &block : Int32 -> Float64)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L87","def":{"name":"new","args":[{"name":"size","doc":null,"default_value":"","external_name":"size","restriction":"Int"}],"double_splat":null,"splat_index":null,"yields":1,"block_arg":{"name":"block","doc":null,"default_value":"","external_name":"block","restriction":"(Int32 -> Float64)"},"return_type":"","visibility":"Public","body":"Vector.build(size) do |buffer|\n  size.to_i.times do |i|\n    buffer[i] = yield i\n  end\n  size\nend"}}],"instance_methods":[{"id":"*(other)-instance-method","html_id":"*(other)-instance-method","name":"*","doc":null,"summary":null,"abstract":false,"args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":""}],"args_string":"(other)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L370","def":{"name":"*","args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"multiply(other)"}},{"id":"+(other)-instance-method","html_id":"+(other)-instance-method","name":"+","doc":null,"summary":null,"abstract":false,"args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":""}],"args_string":"(other)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L362","def":{"name":"+","args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"add(other)"}},{"id":"-(other)-instance-method","html_id":"-(other)-instance-method","name":"-","doc":null,"summary":null,"abstract":false,"args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":""}],"args_string":"(other)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L366","def":{"name":"-","args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"subtract(other)"}},{"id":"<<(value:Float64)-instance-method","html_id":"&lt;&lt;(value:Float64)-instance-method","name":"<<","doc":"Alias for `#push`","summary":"<p>Alias for <code><a href=\"../../Apatite/LinearAlgebra/Vector.html#push%28%2Avalues%3AFloat64%29-instance-method\">#push</a></code></p>","abstract":false,"args":[{"name":"value","doc":null,"default_value":"","external_name":"value","restriction":"Float64"}],"args_string":"(value : Float64)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L349","def":{"name":"<<","args":[{"name":"value","doc":null,"default_value":"","external_name":"value","restriction":"Float64"}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"push(value)"}},{"id":"(other)-instance-method","html_id":"(other)-instance-method","name":"<=>","doc":"Combined comparison operator. Returns *0* if `self` equals *other*, *1* if\n`self` is greater than *other* and *-1* if `self` is smaller than *other*.\n\nIt compares the elements of both vectors in the same position using the\n`<=>` operator.  As soon as one of such comparisons returns a non-zero\nvalue, that result is the return value of the comparison.\n\nIf all elements are equal, the comparison is based on the size of the vectors.\n\n```\nVector{8.0} <=> Vector(1.0, 2.0, 3.0} # => 1\nVector{2.0} <=> Vector{4.0, 2.0, 3.0} # => -1\nVector{1.0, 2.0} <=> Vector{1.0, 2.0} # => 0\n```","summary":"<p>Combined comparison operator.</p>","abstract":false,"args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":""}],"args_string":"(other)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L339","def":{"name":"<=>","args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"min_size = Math.min(size, other.size)\n0.upto(min_size - 1) do |i|\n  n = @buffer[i] <=> other.to_unsafe[i]\n  if n != 0\n    return n\n  end\nend\nsize <=> other.size\n"}},{"id":"==(other:Vector)-instance-method","html_id":"==(other:Vector)-instance-method","name":"==","doc":null,"summary":null,"abstract":false,"args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":"Vector"}],"args_string":"(other : Vector)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L353","def":{"name":"==","args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":"Vector"}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"equals?(other) do |x, y|\n  x == y\nend"}},{"id":"[](start:Int,count:Int)-instance-method","html_id":"[](start:Int,count:Int)-instance-method","name":"[]","doc":"Returns count or less (if there aren't enough) elements starting at the\ngiven start index.\n\nNegative indices count backward from the end of the vector (-1 is the last\nelement). Additionally, an empty vector is returned when the starting index\nfor an element range is at the end of the vector.\n\nRaises `IndexError` if the starting index is out of range.\n\n```\nv = Vector{1.0, 2.0, 3.0, 4.0, 5.0}\nv[1, 3]  # => Vector{2.0, 3.0, 4.0}\nv[6, 10] # raise IndexError\n```","summary":"<p>Returns count or less (if there aren't enough) elements starting at the given start index.</p>","abstract":false,"args":[{"name":"start","doc":null,"default_value":"","external_name":"start","restriction":"Int"},{"name":"count","doc":null,"default_value":"","external_name":"count","restriction":"Int"}],"args_string":"(start : Int, count : Int)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L191","def":{"name":"[]","args":[{"name":"start","doc":null,"default_value":"","external_name":"start","restriction":"Int"},{"name":"count","doc":null,"default_value":"","external_name":"count","restriction":"Int"}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"if count < 0\n  raise(ArgumentError.new(\"Negative count: #{count}\"))\nend\nif start == size\n  return Vector.new\nend\nif start < 0\n  start = start + size\nend\nif 0 <= start && start <= size\nelse\n  raise(IndexError.new)\nend\nif count == 0\n  return Vector.new\nend\ncount = Math.min(count, size - start)\nVector.build(count) do |buffer|\n  buffer.copy_from(@buffer + start, count)\n  count\nend\n"}},{"id":"[](range:Range(Int,Int))-instance-method","html_id":"[](range:Range(Int,Int))-instance-method","name":"[]","doc":"Returns all elements that are within the given range.\n\nNegative indices count backward from the end of the vector (-1 is the last\nelement). Additionally, an empty vector is returned when the starting index\nfor an element range is at the end of the vector.\n\nRaises `IndexError` if the starting index is out of range.\n\n```\nv = Vector{1.0, 2.0, 3.0, 4.0, 5.0}\nv[1..3]  # => Vector{2.0, 3.0, 4.0}\nv[6..10] # raise IndexError\n```","summary":"<p>Returns all elements that are within the given range.</p>","abstract":false,"args":[{"name":"range","doc":null,"default_value":"","external_name":"range","restriction":"Range(Int, Int)"}],"args_string":"(range : Range(Int, Int))","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L173","def":{"name":"[]","args":[{"name":"range","doc":null,"default_value":"","external_name":"range","restriction":"Range(Int, Int)"}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"self[*Indexable.range_to_index_and_count(range, size)]"}},{"id":"[]=(index:Int,count:Int,values:Vector)-instance-method","html_id":"[]=(index:Int,count:Int,values:Vector)-instance-method","name":"[]=","doc":"Replaces a subrange with the elements of the given vector.\n\n```\nvec = Vector{1.0, 2.0, 3.0, 4.0, 5.0}\nvec[1, 3] = Vector{6.0, 7.0, 8.0}\nvec # = Vector{1.0, 6.0, 7.0, 8.0, 5.0}\n\nvec = Vector{1.0, 2.0, 3.0, 4.0, 5.0}\nvec[1, 3] = Vector{6.0, 7.0}\nvec # = Vector{1.0, 6.0, 7.0, 5.0}\n```","summary":"<p>Replaces a subrange with the elements of the given vector.</p>","abstract":false,"args":[{"name":"index","doc":null,"default_value":"","external_name":"index","restriction":"Int"},{"name":"count","doc":null,"default_value":"","external_name":"count","restriction":"Int"},{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":"Vector"}],"args_string":"(index : Int, count : Int, values : Vector)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L297","def":{"name":"[]=","args":[{"name":"index","doc":null,"default_value":"","external_name":"index","restriction":"Int"},{"name":"count","doc":null,"default_value":"","external_name":"count","restriction":"Int"},{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":"Vector"}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"if count < 0\n  raise(ArgumentError.new(\"Negative count: #{count}\"))\nend\nindex = check_index_out_of_bounds(index)\ncount = ((index + count) <= size) ? count : size - index\ndiff = values.size - count\nif diff == 0\n  (@buffer + index).copy_from(values.to_unsafe, values.size)\nelse\n  if diff < 0\n    diff = -diff\n    (@buffer + index).copy_from(values.to_unsafe, values.size)\n    ((@buffer + index) + values.size).move_from((@buffer + index) + count, (size - index) - count)\n    ((@buffer + @size) - diff).clear(diff)\n    @size = @size - diff\n  else\n    resize_to_capacity(Math.pw2ceil(@size + diff))\n    ((@buffer + index) + values.size).move_from((@buffer + index) + count, (size - index) - count)\n    (@buffer + index).copy_from(values.to_unsafe, values.size)\n    @size = @size + diff\n  end\nend\nvalues\n"}},{"id":"[]=(index:Int,count:Int,value)-instance-method","html_id":"[]=(index:Int,count:Int,value)-instance-method","name":"[]=","doc":"Replaces a subrange with a single value. All elements in the range\n`index...index+count` are removed and replaced by a single element\n*value*.\n\nIf *count* is zero, *value* is inserted at *index*.\n\nNegative values of *index* count from the end of the vector.\n\n```\nvec = Vector{1.0, 2.0, 3.0, 4.0, 5.0}\nvec[1, 3] = 6.0\nvec # => Vector{1.0, 6.0, 5.0}\n\nvec = Vector{1.0, 2.0, 3.0, 4.0, 5.0}\nvec[1, 0] = 6.0\nvec # => Vector{1.0, 6.0, 2.0, 3.0, 4.0, 5.0}\n```","summary":"<p>Replaces a subrange with a single value.</p>","abstract":false,"args":[{"name":"index","doc":null,"default_value":"","external_name":"index","restriction":"Int"},{"name":"count","doc":null,"default_value":"","external_name":"count","restriction":"Int"},{"name":"value","doc":null,"default_value":"","external_name":"value","restriction":""}],"args_string":"(index : Int, count : Int, value)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L248","def":{"name":"[]=","args":[{"name":"index","doc":null,"default_value":"","external_name":"index","restriction":"Int"},{"name":"count","doc":null,"default_value":"","external_name":"count","restriction":"Int"},{"name":"value","doc":null,"default_value":"","external_name":"value","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"if count < 0\n  raise(ArgumentError.new(\"Negative count: #{count}\"))\nend\nvalue = value.to_f64\nindex = check_index_out_of_bounds(index)\ncount = ((index + count) <= size) ? count : size - index\ncase count\nwhen 0\n  insert(index, value)\nwhen 1\n  @buffer[index] = value\nelse\n  diff = count - 1\n  ((@buffer + index) + 1).move_from((@buffer + index) + count, (size - index) - count)\n  ((@buffer + @size) - diff).clear(diff)\n  @buffer[index] = value\n  @size = @size - diff\nend\nvalue\n"}},{"id":"[]=(index:Int,value)-instance-method","html_id":"[]=(index:Int,value)-instance-method","name":"[]=","doc":"Sets the given value at the given index.\n\nNegative indices can be used to start counting from the end of the array.\nRaises `IndexError` if trying to set an element outside the array's range.\n\n```\nvec = Vector{1.0, 2.0, 3.0}\nvec[0] = 5.0\np vec # => Vec{5.0, 2.0, 3.0}\n\nvec[3] = 5.0 # raises IndexError\n```","summary":"<p>Sets the given value at the given index.</p>","abstract":false,"args":[{"name":"index","doc":null,"default_value":"","external_name":"index","restriction":"Int"},{"name":"value","doc":null,"default_value":"","external_name":"value","restriction":""}],"args_string":"(index : Int, value)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L226","def":{"name":"[]=","args":[{"name":"index","doc":null,"default_value":"","external_name":"index","restriction":"Int"},{"name":"value","doc":null,"default_value":"","external_name":"value","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"index = check_index_out_of_bounds(index)\n@buffer[index] = value.to_f64\n"}},{"id":"[]=(range:Range(Int,Int),value)-instance-method","html_id":"[]=(range:Range(Int,Int),value)-instance-method","name":"[]=","doc":"Replaces a subrange with a single value.\n\n```\nvec = Vector{1.0, 2.0, 3.0, 4.0, 5.0}\nvec[1..3] = 6.0\nvec # = Vector{1.0, 6.0, 5.0}\n\nvec = Vector{1.0, 2.0, 3.0, 4.0, 5.0}\nvec[1...1] = 6\nvec # = Vector{1.0, 6.0, 2.0, 3.0, 4.0, 5.0}\n```","summary":"<p>Replaces a subrange with a single value.</p>","abstract":false,"args":[{"name":"range","doc":null,"default_value":"","external_name":"range","restriction":"Range(Int, Int)"},{"name":"value","doc":null,"default_value":"","external_name":"value","restriction":""}],"args_string":"(range : Range(Int, Int), value)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L282","def":{"name":"[]=","args":[{"name":"range","doc":null,"default_value":"","external_name":"range","restriction":"Range(Int, Int)"},{"name":"value","doc":null,"default_value":"","external_name":"value","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"self[*Indexable.range_to_index_and_count(range, size)] = value.to_f64"}},{"id":"add(value)-instance-method","html_id":"add(value)-instance-method","name":"add","doc":"When the input is a number, this returns the result of adding\nit to all vector elements. When it's a vector, the vectors\nwill be added together.","summary":"<p>When the input is a number, this returns the result of adding it to all vector elements.</p>","abstract":false,"args":[{"name":"value","doc":null,"default_value":"","external_name":"value","restriction":""}],"args_string":"(value)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L488","def":{"name":"add","args":[{"name":"value","doc":null,"default_value":"","external_name":"value","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"run_binary_op(value) do |a, b|\n  a + b\nend"}},{"id":"angle_from(vector)-instance-method","html_id":"angle_from(vector)-instance-method","name":"angle_from","doc":"Returns the angle between this vector and another in radians.\nIf the vectors are mirrored across their axes this will return `nil`.","summary":"<p>Returns the angle between this vector and another in radians.</p>","abstract":false,"args":[{"name":"vector","doc":null,"default_value":"","external_name":"vector","restriction":""}],"args_string":"(vector)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L440","def":{"name":"angle_from","args":[{"name":"vector","doc":null,"default_value":"","external_name":"vector","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"v = vector.is_a?(Vector) ? vector : Vector.create(vector)\nif size == v.size\nelse\n  raise(\"Cannot compute the angle between vectors with different dimensionality\")\nend\ndot = 0_f64\nmod1 = 0_f64\nmod2 = 0_f64\n(zip(vector)).each do |x, v|\n  dot = dot + (x * v)\n  mod1 = mod1 + (x * x)\n  mod2 = mod2 + (v * v)\nend\nmod1 = Math.sqrt(mod1)\nmod2 = Math.sqrt(mod2)\nif (mod2 * mod2) == 0\n  return 0.0\nend\ntheta = (dot / (mod1 * mod2)).clamp(-1, 1)\nMath.acos(theta)\n"}},{"id":"antiparallel_to?(vector)-instance-method","html_id":"antiparallel_to?(vector)-instance-method","name":"antiparallel_to?","doc":"Returns whether the vectors are antiparallel to each other.","summary":"<p>Returns whether the vectors are antiparallel to each other.</p>","abstract":false,"args":[{"name":"vector","doc":null,"default_value":"","external_name":"vector","restriction":""}],"args_string":"(vector)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L475","def":{"name":"antiparallel_to?","args":[{"name":"vector","doc":null,"default_value":"","external_name":"vector","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"angle = angle_from(vector)\n(angle - Math::PI).abs <= Apatite.precision\n"}},{"id":"augment(elements)-instance-method","html_id":"augment(elements)-instance-method","name":"augment","doc":"Returns a new vector with the provided `elements` concatenated\non the end.","summary":"<p>Returns a new vector with the provided <code>elements</code> concatenated on the end.</p>","abstract":false,"args":[{"name":"elements","doc":null,"default_value":"","external_name":"elements","restriction":""}],"args_string":"(elements)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L556","def":{"name":"augment","args":[{"name":"elements","doc":null,"default_value":"","external_name":"elements","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"elements = elements.is_a?(Vector) ? elements : Vector.create(elements)\nconcat(elements)\n"}},{"id":"chomp(n)-instance-method","html_id":"chomp(n)-instance-method","name":"chomp","doc":"Returns a new vector with the first `n` elements removed from\nthe beginning.","summary":"<p>Returns a new vector with the first <code>n</code> elements removed from the beginning.</p>","abstract":false,"args":[{"name":"n","doc":null,"default_value":"","external_name":"n","restriction":""}],"args_string":"(n)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L541","def":{"name":"chomp","args":[{"name":"n","doc":null,"default_value":"","external_name":"n","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"elements = [] of Float64\neach_with_index do |e, i|\n  if i >= n\n    elements << e\n  end\nend\nVector.create(elements)\n"}},{"id":"clear-instance-method","html_id":"clear-instance-method","name":"clear","doc":"Removes all elements from self.\n\n```\nvec = Vector{1.0, 2.0, 3.0}\nvec.clear # => Vector{}\n```","summary":"<p>Removes all elements from self.</p>","abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L782","def":{"name":"clear","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"@buffer.clear(@size)\n@size = 0\nself\n"}},{"id":"clone-instance-method","html_id":"clone-instance-method","name":"clone","doc":null,"summary":null,"abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L374","def":{"name":"clone","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"Vector.create(@elements.clone)"}},{"id":"concat(other:Vector)-instance-method","html_id":"concat(other:Vector)-instance-method","name":"concat","doc":null,"summary":null,"abstract":false,"args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":"Vector"}],"args_string":"(other : Vector)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L731","def":{"name":"concat","args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":"Vector"}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"other_size = other.size\nnew_size = size + other_size\nif new_size > @capacity\n  resize_to_capacity(Math.pw2ceil(new_size))\nend\n(@buffer + @size).copy_from(other.to_unsafe, other_size)\n@size = new_size\nself\n"}},{"id":"covector-instance-method","html_id":"covector-instance-method","name":"covector","doc":"Creates a single-row matrix from this vector.","summary":"<p>Creates a single-row matrix from this vector.</p>","abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L601","def":{"name":"covector","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"Matrix.row_vector(self)"}},{"id":"cross(*vs)-instance-method","html_id":"cross(*vs)-instance-method","name":"cross","doc":"Returns the cross product of this vector with the others.\n\n```\nv1 = Vector{1.0, 0.0, 0.0}\nv2 = Vector{0.0, 1.0, 0.0}\nv1.cross(v2) => Vector{0.0, 0.0, 1.0}\n```","summary":"<p>Returns the cross product of this vector with the others.</p>","abstract":false,"args":[{"name":"vs","doc":null,"default_value":"","external_name":"vs","restriction":""}],"args_string":"(*vs)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L518","def":{"name":"cross","args":[{"name":"vs","doc":null,"default_value":"","external_name":"vs","restriction":""}],"double_splat":null,"splat_index":0,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"if size >= 2\nelse\n  raise(\"cross product is not defined on vectors of dimension #{size}\")\nend\nif vs.size == (size - 2)\nelse\n  raise(ArgumentError.new(\"wrong number of arguments (#{vs.size} for #{size - 2})\"))\nend\nvs.each do |v|\n  if v.size == size\n  else\n    raise(\"Dimension mismatch. Vectors not all the same size.\")\n  end\nend\ncase size\nwhen 2\n  Vector[-@buffer[1], @buffer[0]]\nwhen 3\n  v = vs[0]\n  Vector[(v[2] * @buffer[1]) - (v[1] * @buffer[2]), (v[0] * @buffer[2]) - (v[2] * @buffer[0]), (v[1] * @buffer[0]) - (v[0] * @buffer[1])]\nelse\nend\n"}},{"id":"distance_from(obj)-instance-method","html_id":"distance_from(obj)-instance-method","name":"distance_from","doc":"Gets this vector's distance from the argument, when considered\na point in space.","summary":"<p>Gets this vector's distance from the argument, when considered a point in space.</p>","abstract":false,"args":[{"name":"obj","doc":null,"default_value":"","external_name":"obj","restriction":""}],"args_string":"(obj)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L629","def":{"name":"distance_from","args":[{"name":"obj","doc":null,"default_value":"","external_name":"obj","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"if object.is_a?(Plane) || object.is_a?(Line)\n  return object.distance_from(self)\nend\nv = elements.is_a?(Vector) ? elements.elements : elements\nif v.size == @elements.size\nelse\n  return nil\nend\nsum = 0\npart = 0\neach_with_index do |x, i|\n  part = x - v[i - 1]\n  sum = sum + (part * part)\nend\nMath.sqrt(sum)\n"}},{"id":"dot(other)-instance-method","html_id":"dot(other)-instance-method","name":"dot","doc":"Get the scalar (dot) product of this vector with `vector`.\n\n[https://en.wikipedia.org/wiki/Scalar_product](https://en.wikipedia.org/wiki/Scalar_product)","summary":"<p>Get the scalar (dot) product of this vector with <code>vector</code>.</p>","abstract":false,"args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":""}],"args_string":"(other)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L574","def":{"name":"dot","args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"other = other.is_a?(Vector) ? other : Vector.create(other)\nif size == other.size\nelse\n  raise(\"Cannot compute the dot product of vectors with different dimensionality\")\nend\nproduct = 0\n(0...size).each do |i|\n  product = product + (self[i] * other[i])\nend\nproduct\n"}},{"id":"e(i)-instance-method","html_id":"e(i)-instance-method","name":"e","doc":"Returns the `ith` element of the vector. Returns `nil` if `i`\nis out of bounds. Indexing starts from 1.","summary":"<p>Returns the <code>ith</code> element of the vector.</p>","abstract":false,"args":[{"name":"i","doc":null,"default_value":"","external_name":"i","restriction":""}],"args_string":"(i)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L426","def":{"name":"e","args":[{"name":"i","doc":null,"default_value":"","external_name":"i","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"(i < 1 || i > @size) ? nil : self[i - 1]"}},{"id":"independent?(*vs)-instance-method","html_id":"independent?(*vs)-instance-method","name":"independent?","doc":"Returns true if all vectors are linearly independent.","summary":"<p>Returns true if all vectors are linearly independent.</p>","abstract":false,"args":[{"name":"vs","doc":null,"default_value":"","external_name":"vs","restriction":""}],"args_string":"(*vs)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L384","def":{"name":"independent?","args":[{"name":"vs","doc":null,"default_value":"","external_name":"vs","restriction":""}],"double_splat":null,"splat_index":0,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"vs.each do |v|\n  if v.size == vs.first.size\n  else\n    raise(\"Dimension mismatch. Vectors not all the same size.\")\n  end\nend\nif vs.size > sv.first.size\n  return false\nend\nMatrix[*vs].rank.equal?(vs.count)\n"}},{"id":"lies_in(plane)-instance-method","html_id":"lies_in(plane)-instance-method","name":"lies_in","doc":"Returns true if the vector is a point on the given plane.","summary":"<p>Returns true if the vector is a point on the given plane.</p>","abstract":false,"args":[{"name":"plane","doc":null,"default_value":"","external_name":"plane","restriction":""}],"args_string":"(plane)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L654","def":{"name":"lies_in","args":[{"name":"plane","doc":null,"default_value":"","external_name":"plane","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"plane.contains(self)"}},{"id":"lies_on(line)-instance-method","html_id":"lies_on(line)-instance-method","name":"lies_on","doc":"Returns true if the vector is a point on the given line","summary":"<p>Returns true if the vector is a point on the given line</p>","abstract":false,"args":[{"name":"line","doc":null,"default_value":"","external_name":"line","restriction":""}],"args_string":"(line)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L649","def":{"name":"lies_on","args":[{"name":"line","doc":null,"default_value":"","external_name":"line","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"line.contains(self)"}},{"id":"log-instance-method","html_id":"log-instance-method","name":"log","doc":"Return a new `Vector` with the log of every item in `self`.","summary":"<p>Return a new <code><a href=\"../../Apatite/LinearAlgebra/Vector.html\">Vector</a></code> with the log of every item in <code>self</code>.</p>","abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L562","def":{"name":"log","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"map do |x|\n  Math.log(x)\nend"}},{"id":"magnitude-instance-method","html_id":"magnitude-instance-method","name":"magnitude","doc":"Returns the magnitude/euclidian norm of this vector.\n\n[https://en.wikipedia.org/wiki/Euclidean_distance](https://en.wikipedia.org/wiki/Euclidean_distance)","summary":"<p>Returns the magnitude/euclidian norm of this vector.</p>","abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L419","def":{"name":"magnitude","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"sum = reduce(0.0) do |acc, e|\n  acc = acc + (e * e)\nend\nMath.sqrt(sum)\n"}},{"id":"map(&block)-instance-method","html_id":"map(&amp;block)-instance-method","name":"map","doc":"Invokes the given block for each element of `self`.","summary":"<p>Invokes the given block for each element of <code>self</code>.</p>","abstract":false,"args":[],"args_string":"(&block)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L379","def":{"name":"map","args":[],"double_splat":null,"splat_index":null,"yields":1,"block_arg":null,"return_type":"","visibility":"Public","body":"Vector.new(size) do |i|\n  yield @buffer[i]\nend"}},{"id":"map!(&block)-instance-method","html_id":"map!(&amp;block)-instance-method","name":"map!","doc":"Invokes the given block for each element of `self`, replacing the element\nwith the value returned by the block. Returns `self`.\n\n```\nvec = Vector{1.0, 2.0, 3.0}\nvec.map! { |x| x * x }\na # => Vector{1.0, 4.0, 9.0}\n```","summary":"<p>Invokes the given block for each element of <code>self</code>, replacing the element with the value returned by the block.</p>","abstract":false,"args":[],"args_string":"(&block)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L400","def":{"name":"map!","args":[],"double_splat":null,"splat_index":null,"yields":1,"block_arg":null,"return_type":"","visibility":"Public","body":"@buffer.map!(size) do |e|\n  yield e\nend\nself\n"}},{"id":"map_with_index(&block)-instance-method","html_id":"map_with_index(&amp;block)-instance-method","name":"map_with_index","doc":"Optimized version of `Enumerable#map_with_index`.","summary":"<p>Optimized version of <code>Enumerable#map_with_index</code>.</p>","abstract":false,"args":[],"args_string":"(&block)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L406","def":{"name":"map_with_index","args":[],"double_splat":null,"splat_index":null,"yields":2,"block_arg":null,"return_type":"","visibility":"Public","body":"Vector.new(size) do |i|\n  yield @buffer[i], i\nend"}},{"id":"map_with_index!(&block)-instance-method","html_id":"map_with_index!(&amp;block)-instance-method","name":"map_with_index!","doc":"Like `map_with_index`, but mutates `self` instead of allocating a new object.","summary":"<p>Like <code><a href=\"../../Apatite/LinearAlgebra/Vector.html#map_with_index%28%26block%29-instance-method\">#map_with_index</a></code>, but mutates <code>self</code> instead of allocating a new object.</p>","abstract":false,"args":[],"args_string":"(&block)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L411","def":{"name":"map_with_index!","args":[],"double_splat":null,"splat_index":null,"yields":2,"block_arg":null,"return_type":"","visibility":"Public","body":"to_unsafe.map_with_index!(size) do |e, i|\n  yield e, i\nend\nself\n"}},{"id":"max-instance-method","html_id":"max-instance-method","name":"max","doc":"Returns the (absolute) largest element in this vector.","summary":"<p>Returns the (absolute) largest element in this vector.</p>","abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L589","def":{"name":"max","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"reduce do |acc, i|\n  i.abs > acc.abs ? i : acc\nend"}},{"id":"max_index-instance-method","html_id":"max_index-instance-method","name":"max_index","doc":"Gets the index of the largest element in this vector.","summary":"<p>Gets the index of the largest element in this vector.</p>","abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L594","def":{"name":"max_index","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"idx = 0\neach_with_index do |e, i|\n  idx = e.abs > self[idx].abs ? i : idx\nend\nidx\n"}},{"id":"multiply(value)-instance-method","html_id":"multiply(value)-instance-method","name":"multiply","doc":"When the input is a number, this returns the result of multiplying\nit to all vector elements. When it's a vector, the vectors\nwill be element-wise multiplied.","summary":"<p>When the input is a number, this returns the result of multiplying it to all vector elements.</p>","abstract":false,"args":[{"name":"value","doc":null,"default_value":"","external_name":"value","restriction":""}],"args_string":"(value)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L502","def":{"name":"multiply","args":[{"name":"value","doc":null,"default_value":"","external_name":"value","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"run_binary_op(value) do |a, b|\n  a * b\nend"}},{"id":"parallel_to?(vector)-instance-method","html_id":"parallel_to?(vector)-instance-method","name":"parallel_to?","doc":"Returns whether the vectors are parallel to each other.","summary":"<p>Returns whether the vectors are parallel to each other.</p>","abstract":false,"args":[{"name":"vector","doc":null,"default_value":"","external_name":"vector","restriction":""}],"args_string":"(vector)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L469","def":{"name":"parallel_to?","args":[{"name":"vector","doc":null,"default_value":"","external_name":"vector","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"angle = angle_from(vector)\nangle <= Apatite.precision\n"}},{"id":"perpendicular_to?(vector)-instance-method","html_id":"perpendicular_to?(vector)-instance-method","name":"perpendicular_to?","doc":"Returns whether the vectors are perpendicular to each other.","summary":"<p>Returns whether the vectors are perpendicular to each other.</p>","abstract":false,"args":[{"name":"vector","doc":null,"default_value":"","external_name":"vector","restriction":""}],"args_string":"(vector)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L481","def":{"name":"perpendicular_to?","args":[{"name":"vector","doc":null,"default_value":"","external_name":"vector","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"(dot(vector)).abs <= Apatite.precision"}},{"id":"pretty_print(pp):Nil-instance-method","html_id":"pretty_print(pp):Nil-instance-method","name":"pretty_print","doc":null,"summary":null,"abstract":false,"args":[{"name":"pp","doc":null,"default_value":"","external_name":"pp","restriction":""}],"args_string":"(pp) : Nil","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L754","def":{"name":"pretty_print","args":[{"name":"pp","doc":null,"default_value":"","external_name":"pp","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"Nil","visibility":"Public","body":"pp.list(\"Vector{\", self, \"}\")"}},{"id":"product-instance-method","html_id":"product-instance-method","name":"product","doc":"Get the product of all elements in this vector.","summary":"<p>Get the product of all elements in this vector.</p>","abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L567","def":{"name":"product","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"reduce do |acc, v|\n  acc = acc * v\nend"}},{"id":"push(*values:Float64)-instance-method","html_id":"push(*values:Float64)-instance-method","name":"push","doc":null,"summary":null,"abstract":false,"args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":"Float64"}],"args_string":"(*values : Float64)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L665","def":{"name":"push","args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":"Float64"}],"double_splat":null,"splat_index":0,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"new_size = @size + values.size\nif new_size > @capacity\n  resize_to_capacity(Math.pw2ceil(new_size))\nend\nvalues.each_with_index do |value, i|\n  @buffer[@size + i] = value\nend\n@size = new_size\nself\n"}},{"id":"push(value:Float64)-instance-method","html_id":"push(value:Float64)-instance-method","name":"push","doc":null,"summary":null,"abstract":false,"args":[{"name":"value","doc":null,"default_value":"","external_name":"value","restriction":"Float64"}],"args_string":"(value : Float64)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L658","def":{"name":"push","args":[{"name":"value","doc":null,"default_value":"","external_name":"value","restriction":"Float64"}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"check_needs_resize\n@buffer[@size] = value\n@size = @size + 1\nself\n"}},{"id":"reflection_in(object)-instance-method","html_id":"reflection_in(object)-instance-method","name":"reflection_in","doc":"Returns the result of reflecting the point in the given `object`\n(point, line, or plane).","summary":"<p>Returns the result of reflecting the point in the given <code>object</code> (point, line, or plane).</p>","abstract":false,"args":[{"name":"object","doc":null,"default_value":"","external_name":"object","restriction":""}],"args_string":"(object)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L684","def":{"name":"reflection_in","args":[{"name":"object","doc":null,"default_value":"","external_name":"object","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"if object.is_a?(Plane) || object.is_a?(Line)\n  p = @elements.dup\n  c = (object.point_closest_to(p)).elements\n  return Vector.create([C[0] + (C[0] - P[0]), C[1] + (C[1] - P[1]), C[2] + (C[2] - (P[2] || 0))])\nend\nq = object.is_a?(Vector) ? object.elements : object\nif @elements.size == q.size\nelse\n  return nil\nend\nmap_with_index do |x, i|\n  q[i - 1] + (q[i - 1] - x)\nend\n"}},{"id":"rotate(t,object)-instance-method","html_id":"rotate(t,object)-instance-method","name":"rotate","doc":"Rotates the vector about the given `object`. The object should\nbe a point if the vector is 2D, and a line if it is 3D. Be\ncareful with line directions!","summary":"<p>Rotates the vector about the given <code>object</code>.</p>","abstract":false,"args":[{"name":"t","doc":null,"default_value":"","external_name":"t","restriction":""},{"name":"object","doc":null,"default_value":"","external_name":"object","restriction":""}],"args_string":"(t, object)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L678","def":{"name":"rotate","args":[{"name":"t","doc":null,"default_value":"","external_name":"t","restriction":""},{"name":"object","doc":null,"default_value":"","external_name":"object","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":""}},{"id":"round-instance-method","html_id":"round-instance-method","name":"round","doc":"Gets the result of rounding the elements of the vector.","summary":"<p>Gets the result of rounding the elements of the vector.</p>","abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L612","def":{"name":"round","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"map do |x|\n  x.round\nend"}},{"id":"set_elements(elements)-instance-method","html_id":"set_elements(elements)-instance-method","name":"set_elements","doc":null,"summary":null,"abstract":false,"args":[{"name":"elements","doc":null,"default_value":"","external_name":"elements","restriction":""}],"args_string":"(elements)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L726","def":{"name":"set_elements","args":[{"name":"elements","doc":null,"default_value":"","external_name":"elements","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"@elements = elements.is_a?(Vector) ? elements.elements : elements\nself\n"}},{"id":"sigmoid-instance-method","html_id":"sigmoid-instance-method","name":"sigmoid","doc":"Sums the numbers in the vector and returns a sigmoid value\nacross the whole vector.","summary":"<p>Sums the numbers in the vector and returns a sigmoid value across the whole vector.</p>","abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L707","def":{"name":"sigmoid","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"LinearAlgebra.sigmoid(sum)"}},{"id":"size:Int32-instance-method","html_id":"size:Int32-instance-method","name":"size","doc":"Returns the number of elements in the vector","summary":"<p>Returns the number of elements in the vector</p>","abstract":false,"args":[],"args_string":" : Int32","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L24","def":{"name":"size","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"Int32","visibility":"Public","body":"@size"}},{"id":"snap_to(value)-instance-method","html_id":"snap_to(value)-instance-method","name":"snap_to","doc":"Returns a copy of the vector with elements set to `value` if\nthey differ from it by less than `Apetite.precision`","summary":"<p>Returns a copy of the vector with elements set to <code>value</code> if they differ from it by less than <code>Apetite.precision</code></p>","abstract":false,"args":[{"name":"value","doc":null,"default_value":"","external_name":"value","restriction":""}],"args_string":"(value)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L623","def":{"name":"snap_to","args":[{"name":"value","doc":null,"default_value":"","external_name":"value","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"map do |y|\n  (y - x).abs <= Apetite.precision ? value : y\nend"}},{"id":"subtract(value)-instance-method","html_id":"subtract(value)-instance-method","name":"subtract","doc":"When the input is a number, this returns the result of subtracting\nit to all vector elements. 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If they are 2D, a zero\nz-component is added.","summary":"<p>Utility to make sure vectors are 3D.</p>","abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L713","def":{"name":"to_3d","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"v = dup\ncase v.elements.size\nwhen 3\n  break\nwhen 2\n  v.elements.push(0)\nelse\n  return nil\nend\nreturn v\n"}},{"id":"to_a-instance-method","html_id":"to_a-instance-method","name":"to_a","doc":null,"summary":null,"abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L744","def":{"name":"to_a","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"Array(Float64).new(size) do |i|\n  self[i]\nend"}},{"id":"to_diagonal_matrix-instance-method","html_id":"to_diagonal_matrix-instance-method","name":"to_diagonal_matrix","doc":"Returns a diagonal `Matrix` with the vectors elements as its\ndiagonal elements.","summary":"<p>Returns a diagonal <code><a href=\"../../Apatite/LinearAlgebra/Matrix.html\">Matrix</a></code> with the vectors elements as its diagonal elements.</p>","abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L607","def":{"name":"to_diagonal_matrix","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"Matrix::Diagonal.new(elements)"}},{"id":"to_s(io)-instance-method","html_id":"to_s(io)-instance-method","name":"to_s","doc":null,"summary":null,"abstract":false,"args":[{"name":"io","doc":null,"default_value":"","external_name":"io","restriction":""}],"args_string":"(io)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L748","def":{"name":"to_s","args":[{"name":"io","doc":null,"default_value":"","external_name":"io","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"io << \"{\"\njoin(\", \", io, &.inspect(io))\nio << \"}\"\n"}},{"id":"to_unit_vector-instance-method","html_id":"to_unit_vector-instance-method","name":"to_unit_vector","doc":"Returns a new vector created by normalizing this one\nto have a magnitude of `1`. 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\ No newline at end of file
+{"repository_name":"github.com/watzon/apatite","body":"# Apatite\n\nApatite is meant to be a collecion of mathmatical and scientific computing algorithms for the Crystal programming language. I don't expect it to ever reach the level of completeness as numpy, but hopefully it can save some people the trouble of implementing these methods on their own.\n\n## Installation\n\n1. Add the dependency to your `shard.yml`:\n\n   ```yaml\n   dependencies:\n     apatite:\n       github: watzon/apatite\n   ```\n\n2. Run `shards install`\n\n## Usage\n\n```crystal\nrequire \"apatite\"\n```\n\nCheck out the [documentation](https://watzon.github.io/apatite/) for usage examples.\n\n## Roadmap\n\n- [ ] Linear Algebra\n\t- [x] Vector\n\t- [ ] Matrix (_in progress_)\n\t- [ ] NDArray\n\t- [ ] Line\n\t- [ ] Plane\n\t- [ ] Polygon\n\t- [ ] LinkedList\n\t\n\n\n## Contributing\n\n1. Fork it (<https://github.com/watzon/apatite/fork>)\n2. Create your feature branch (`git checkout -b my-new-feature`)\n3. Commit your changes (`git commit -am 'Add some feature'`)\n4. Push to the branch (`git push origin my-new-feature`)\n5. 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If that\nsounds like a modified version of the first line from the NumPy homepage,\nthat's because it is. 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other.column_count)\n"}},{"id":"+(vec:Indexable)-instance-method","html_id":"+(vec:Indexable)-instance-method","name":"+","doc":null,"summary":null,"abstract":false,"args":[{"name":"vec","doc":null,"default_value":"","external_name":"vec","restriction":"Indexable"}],"args_string":"(vec : Indexable)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/matrix.cr#L188","def":{"name":"+","args":[{"name":"vec","doc":null,"default_value":"","external_name":"vec","restriction":"Indexable"}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"vec = vec.is_a?(Vector) ? vec : Vector.create(vec)\nself + (column_vector(vec))\n"}},{"id":"-(vec:Indexable)-instance-method","html_id":"-(vec:Indexable)-instance-method","name":"-","doc":null,"summary":null,"abstract":false,"args":[{"name":"vec","doc":null,"default_value":"","external_name":"vec","restriction":"Indexable"}],"args_string":"(vec : Indexable)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/matrix.cr#L205","def":{"name":"-","args":[{"name":"vec","doc":null,"default_value":"","external_name":"vec","restriction":"Indexable"}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"vec = vec.is_a?(Vector) ? vec : Vector.create(vec)\nself + (column_vector(vec))\n"}},{"id":"-(other:Matrix)-instance-method","html_id":"-(other:Matrix)-instance-method","name":"-","doc":null,"summary":null,"abstract":false,"args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":"Matrix"}],"args_string":"(other : Matrix)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/matrix.cr#L193","def":{"name":"-","args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":"Matrix"}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"if column_count != other.column_count\n  raise(\"Dimension mismatch\")\nend\nrows = Array.new(row_count) do |i|\n  Vector.new(other.column_count) do |j|\n    self[i, j] - other[i, j]\n  end\nend\nreturn Matrix.new(rows, other.column_count)\n"}},{"id":"/(other:Matrix)-instance-method","html_id":"/(other:Matrix)-instance-method","name":"/","doc":null,"summary":null,"abstract":false,"args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":"Matrix"}],"args_string":"(other : Matrix)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/matrix.cr#L210","def":{"name":"/","args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":"Matrix"}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"self * other.inverse"}},{"id":"/(vec:Indexable)-instance-method","html_id":"/(vec:Indexable)-instance-method","name":"/","doc":null,"summary":null,"abstract":false,"args":[{"name":"vec","doc":null,"default_value":"","external_name":"vec","restriction":"Indexable"}],"args_string":"(vec : Indexable)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/matrix.cr#L214","def":{"name":"/","args":[{"name":"vec","doc":null,"default_value":"","external_name":"vec","restriction":"Indexable"}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"rows = self.rows.map do |row|\n  row.map do |e|\n    e / other\n  end\nend\nreturn new_matrix(rows, column_count)\n"}},{"id":"==(other:Matrix)-instance-method","html_id":"==(other:Matrix)-instance-method","name":"==","doc":null,"summary":null,"abstract":false,"args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":"Matrix"}],"args_string":"(other : Matrix)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/matrix.cr#L221","def":{"name":"==","args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":"Matrix"}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"if (Matrix === other) && (column_count == other.column_count)\nelse\n  return false\nend\nrows == other.rows\n"}},{"id":"[](row:Int,col:Int)-instance-method","html_id":"[](row:Int,col:Int)-instance-method","name":"[]","doc":"Returns element `(row, col)` of the matrix. Throws error on index error.","summary":"<p>Returns element <code>(row, col)</code> of the matrix.</p>","abstract":false,"args":[{"name":"row","doc":null,"default_value":"","external_name":"row","restriction":"Int"},{"name":"col","doc":null,"default_value":"","external_name":"col","restriction":"Int"}],"args_string":"(row : Int, col : Int)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/matrix.cr#L228","def":{"name":"[]","args":[{"name":"row","doc":null,"default_value":"","external_name":"row","restriction":"Int"},{"name":"col","doc":null,"default_value":"","external_name":"col","restriction":"Int"}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"self[row][col]"}},{"id":"[]?(row:Int,col:Int)-instance-method","html_id":"[]?(row:Int,col:Int)-instance-method","name":"[]?","doc":"Returns element `(row, col)` of the matrix, or nil if the index is not found.","summary":"<p>Returns element <code>(row, col)</code> of the matrix, or nil if the index is not found.</p>","abstract":false,"args":[{"name":"row","doc":null,"default_value":"","external_name":"row","restriction":"Int"},{"name":"col","doc":null,"default_value":"","external_name":"col","restriction":"Int"}],"args_string":"(row : Int, col : Int)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/matrix.cr#L233","def":{"name":"[]?","args":[{"name":"row","doc":null,"default_value":"","external_name":"row","restriction":"Int"},{"name":"col","doc":null,"default_value":"","external_name":"col","restriction":"Int"}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"v = fetch(row) do\n  nil\nend\nif v.nil?\nelse\n  v[col]?\nend\n"}},{"id":"adjugate-instance-method","html_id":"adjugate-instance-method","name":"adjugate","doc":"Returns the adjugate of the matrix.","summary":"<p>Returns the adjugate of the matrix.</p>","abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/matrix.cr#L239","def":{"name":"adjugate","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"if square?\nelse\n  raise(\"Dimention mismatch: `Matrix#adjugate` requires a square matrix.\")\nend\nMatrix.build(row_count, column_count) do |row, column|\n  cofactor(column, row)\nend\n"}},{"id":"cofactor(row,column)-instance-method","html_id":"cofactor(row,column)-instance-method","name":"cofactor","doc":"Returns the (row, column) cofactor which is obtained by multiplying the first minor by (-1)**(row + column)","summary":"<p>Returns the (row, column) cofactor which is obtained by multiplying the first minor by (-1)**(row + column)</p>","abstract":false,"args":[{"name":"row","doc":null,"default_value":"","external_name":"row","restriction":""},{"name":"column","doc":null,"default_value":"","external_name":"column","restriction":""}],"args_string":"(row, column)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/matrix.cr#L247","def":{"name":"cofactor","args":[{"name":"row","doc":null,"default_value":"","external_name":"row","restriction":""},{"name":"column","doc":null,"default_value":"","external_name":"column","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"if empty?\n  raise(\"cofactor of empty matrix is not defined\")\nend\nif square?\nelse\n  raise(\"Dimention mismatch: `Matrix#cofactor` requires a square matrix.\")\nend\ndet_of_minor = (first_minor(row, column)).determinant\ndet_of_minor * ((-1.0) ** (row + column))\n"}},{"id":"column(j,&block)-instance-method","html_id":"column(j,&amp;block)-instance-method","name":"column","doc":"Iterates over the specified column in the matrix, returning the Vector's items.","summary":"<p>Iterates over the specified column in the matrix, returning the Vector's items.</p>","abstract":false,"args":[{"name":"j","doc":null,"default_value":"","external_name":"j","restriction":""}],"args_string":"(j, &block)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/matrix.cr#L274","def":{"name":"column","args":[{"name":"j","doc":null,"default_value":"","external_name":"j","restriction":""}],"double_splat":null,"splat_index":null,"yields":1,"block_arg":null,"return_type":"","visibility":"Public","body":"if j >= column_count || j < (-column_count)\n  return self\nend\nrow_count.times do |i|\n  yield rows[i][j]\nend\nself\n"}},{"id":"column(j)-instance-method","html_id":"column(j)-instance-method","name":"column","doc":"Returns column vector number `j` of the matrix as a `Vector` (starting at 0 like an array).","summary":"<p>Returns column vector number <code>j</code> of the matrix as a <code><a href=\"../../Apatite/LinearAlgebra/Vector.html\">Vector</a></code> (starting at 0 like an array).</p>","abstract":false,"args":[{"name":"j","doc":null,"default_value":"","external_name":"j","restriction":""}],"args_string":"(j)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/matrix.cr#L265","def":{"name":"column","args":[{"name":"j","doc":null,"default_value":"","external_name":"j","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"if j >= column_count || j < (-column_count)\n  raise(\"Index out of range\")\nend\ncol = Array(Float64).new(row_count) do |i|\n  rows[i][j]\nend\nVector.create(col)\n"}},{"id":"column?(j)-instance-method","html_id":"column?(j)-instance-method","name":"column?","doc":"Returns column vector number `j` of the matrix as a `Vector` (starting at 0 like an array).","summary":"<p>Returns column vector number <code>j</code> of the matrix as a <code><a href=\"../../Apatite/LinearAlgebra/Vector.html\">Vector</a></code> (starting at 0 like an array).</p>","abstract":false,"args":[{"name":"j","doc":null,"default_value":"","external_name":"j","restriction":""}],"args_string":"(j)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/matrix.cr#L256","def":{"name":"column?","args":[{"name":"j","doc":null,"default_value":"","external_name":"j","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"if j >= column_count || j < (-column_count)\n  return nil\nend\ncol = Array(Float64).new(row_count) do |i|\n  rows[i][j]\nend\nVector.create(col)\n"}},{"id":"column_count:Int32-instance-method","html_id":"column_count:Int32-instance-method","name":"column_count","doc":null,"summary":null,"abstract":false,"args":[],"args_string":" : Int32","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/matrix.cr#L11","def":{"name":"column_count","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"Int32","visibility":"Public","body":"@column_count"}},{"id":"column_vectors-instance-method","html_id":"column_vectors-instance-method","name":"column_vectors","doc":"Returns an array of the column vectors of the matrix. See `Vector`.","summary":"<p>Returns an array of the column vectors of the matrix.</p>","abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/matrix.cr#L283","def":{"name":"column_vectors","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"Array(Vector).new(column_count) do |i|\n  column(i)\nend"}},{"id":"determinant-instance-method","html_id":"determinant-instance-method","name":"determinant","doc":null,"summary":null,"abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/matrix.cr#L354","def":{"name":"determinant","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"if square?\nelse\n  raise(\"Dimention mismatch: `Matrix#determinant` requires a square matrix.\")\nend\nm = rows\ncase row_count\nwhen 0\n  +1\nwhen 1\n  +m[0][0]\nwhen 2\n  ((+m[0][0]) * m[1][1]) - (m[0][1] * m[1][0])\nwhen 3\n  m0, m1, m2 = m\n  (((((((+m0[0]) * m1[1]) * m2[2]) - ((m0[0] * m1[2]) * m2[1])) - ((m0[1] * m1[0]) * m2[2])) + ((m0[1] * m1[2]) * m2[0])) + ((m0[2] * m1[0]) * m2[1])) - ((m0[2] * m1[1]) * m2[0])\nwhen 4\n  m0, m1, m2, m3 = m\n  ((((((((((((((((((((((((((+m0[0]) * m1[1]) * m2[2]) * m3[3]) - (((m0[0] * m1[1]) * m2[3]) * m3[2])) - (((m0[0] * m1[2]) * m2[1]) * m3[3])) + (((m0[0] * m1[2]) * m2[3]) * m3[1])) + (((m0[0] * m1[3]) * m2[1]) * m3[2])) - (((m0[0] * m1[3]) * m2[2]) * m3[1])) - (((m0[1] * m1[0]) * m2[2]) * m3[3])) + (((m0[1] * m1[0]) * m2[3]) * m3[2])) + (((m0[1] * m1[2]) * m2[0]) * m3[3])) - (((m0[1] * m1[2]) * m2[3]) * m3[0])) - (((m0[1] * m1[3]) * m2[0]) * m3[2])) + (((m0[1] * m1[3]) * m2[2]) * m3[0])) + (((m0[2] * m1[0]) * m2[1]) * m3[3])) - (((m0[2] * m1[0]) * m2[3]) * m3[1])) - (((m0[2] * m1[1]) * m2[0]) * m3[3])) + (((m0[2] * m1[1]) * m2[3]) * m3[0])) + (((m0[2] * m1[3]) * m2[0]) * m3[1])) - (((m0[2] * m1[3]) * m2[1]) * m3[0])) - (((m0[3] * m1[0]) * m2[1]) * m3[2])) + (((m0[3] * m1[0]) * m2[2]) * m3[1])) + (((m0[3] * m1[1]) * m2[0]) * m3[2])) - (((m0[3] * m1[1]) * m2[2]) * m3[0])) - (((m0[3] * m1[2]) * m2[0]) * m3[1])) + (((m0[3] * m1[2]) * m2[1]) * m3[0])\nelse\n  determinant_bareiss\nend\n"}},{"id":"first_minor(row,column)-instance-method","html_id":"first_minor(row,column)-instance-method","name":"first_minor","doc":null,"summary":null,"abstract":false,"args":[{"name":"row","doc":null,"default_value":"","external_name":"row","restriction":""},{"name":"column","doc":null,"default_value":"","external_name":"column","restriction":""}],"args_string":"(row, column)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/matrix.cr#L429","def":{"name":"first_minor","args":[{"name":"row","doc":null,"default_value":"","external_name":"row","restriction":""},{"name":"column","doc":null,"default_value":"","external_name":"column","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"if empty?\n  raise(\"first_minor of empty matrix is not defined\")\nend\nif 0 <= row && row < row_count\nelse\n  raise(ArgumentError.new(\"invalid row (#{row.inspect} for 0..#{row_count - 1})\"))\nend\nif 0 <= column && column < column_count\nelse\n  raise(ArgumentError.new(\"invalid column (#{column.inspect} for 0..#{column_count - 1})\"))\nend\narrays = to_a.map(&.to_a)\narrays.delete_at(row)\narrays.each do |array|\n  array.delete_at(column)\nend\nMatrix.new(arrays, column_count - 1)\n"}},{"id":"inverse-instance-method","html_id":"inverse-instance-method","name":"inverse","doc":"Returns the inverse of the matrix.","summary":"<p>Returns the inverse of the matrix.</p>","abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/matrix.cr#L304","def":{"name":"inverse","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"if square?\nelse\n  if square?\n  else\n    raise(\"Dimention mismatch: `Matrix#inverse` requires a square matrix.\")\n  end\nend\n(Matrix.identity(row_count)).inverse_from(self)\n"}},{"id":"laplace_expansion(*,row=nil,column=nil)-instance-method","html_id":"laplace_expansion(*,row=nil,column=nil)-instance-method","name":"laplace_expansion","doc":"Returns the Laplace expansion along given row or column.","summary":"<p>Returns the Laplace expansion along given row or column.</p>","abstract":false,"args":[{"name":"","doc":null,"default_value":"","external_name":"","restriction":""},{"name":"row","doc":null,"default_value":"nil","external_name":"row","restriction":""},{"name":"column","doc":null,"default_value":"nil","external_name":"column","restriction":""}],"args_string":"(*, row = <span class=\"n\">nil</span>, column = <span class=\"n\">nil</span>)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/matrix.cr#L450","def":{"name":"laplace_expansion","args":[{"name":"","doc":null,"default_value":"","external_name":"","restriction":""},{"name":"row","doc":null,"default_value":"nil","external_name":"row","restriction":""},{"name":"column","doc":null,"default_value":"nil","external_name":"column","restriction":""}],"double_splat":null,"splat_index":0,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"num = row || column\nif (!num) || (row && column)\n  raise(ArgumentError.new(\"exactly one the row or column arguments must be specified\"))\nend\nif square?\nelse\n  raise(\"Dimention mismatch: `Matrix#determinant` requires a square matrix.\")\nend\nif empty?\n  raise(\"laplace_expansion of empty matrix is not defined\")\nend\nif 0 <= num && num < row_count\nelse\n  raise(ArgumentError.new(\"invalid num (#{num.inspect} for 0..#{row_count - 1})\"))\nend\nif row\n  (row(num)).map_with_index do |e, k|\n    e * (cofactor(num, k))\n  end.reduce(&.+)\nelse\n  (column(num)).map_with_index do |e, k|\n    e * (cofactor(k, num))\n  end.reduce(&.+)\nend\n"}},{"id":"pretty_print(pp):Nil-instance-method","html_id":"pretty_print(pp):Nil-instance-method","name":"pretty_print","doc":null,"summary":null,"abstract":false,"args":[{"name":"pp","doc":null,"default_value":"","external_name":"pp","restriction":""}],"args_string":"(pp) : Nil","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/matrix.cr#L516","def":{"name":"pretty_print","args":[{"name":"pp","doc":null,"default_value":"","external_name":"pp","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"Nil","visibility":"Public","body":"pp.list(\"[\", self, \"]\") do |vec|\n  pp.group do\n    vec.to_a.pretty_print(pp)\n  end\nend"}},{"id":"row(i,&block)-instance-method","html_id":"row(i,&amp;block)-instance-method","name":"row","doc":null,"summary":null,"abstract":false,"args":[{"name":"i","doc":null,"default_value":"","external_name":"i","restriction":""}],"args_string":"(i, &block)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/matrix.cr#L475","def":{"name":"row","args":[{"name":"i","doc":null,"default_value":"","external_name":"i","restriction":""}],"double_splat":null,"splat_index":null,"yields":0,"block_arg":{"name":"block","doc":null,"default_value":"","external_name":"block","restriction":""},"return_type":"","visibility":"Public","body":"(@rows.fetch(i) do\n  return self\nend).each(&block)\nself\n"}},{"id":"row(i)-instance-method","html_id":"row(i)-instance-method","name":"row","doc":null,"summary":null,"abstract":false,"args":[{"name":"i","doc":null,"default_value":"","external_name":"i","restriction":""}],"args_string":"(i)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/matrix.cr#L480","def":{"name":"row","args":[{"name":"i","doc":null,"default_value":"","external_name":"i","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"Vector.create(rows.fetch(i) do\n  [] of Float64\nend)"}},{"id":"row_count:Int32-instance-method","html_id":"row_count:Int32-instance-method","name":"row_count","doc":null,"summary":null,"abstract":false,"args":[],"args_string":" : 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A `range`\ncan optionally be passed in if you want to limit the random numbers\nto a given range.","summary":"<p>Creates a new <code><a href=\"../../Apatite/LinearAlgebra/Vector.html\">Vector</a></code> of size <code>n</code> filled with random numbers.</p>","abstract":false,"args":[{"name":"n","doc":null,"default_value":"","external_name":"n","restriction":""},{"name":"range","doc":null,"default_value":"nil","external_name":"range","restriction":""}],"args_string":"(n, range = <span class=\"n\">nil</span>)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L129","def":{"name":"random","args":[{"name":"n","doc":null,"default_value":"","external_name":"n","restriction":""},{"name":"range","doc":null,"default_value":"nil","external_name":"range","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"vec = Vector.new(n)\nn.times do\n  vec.push(rand((range || -1e+1)..1e+1))\nend\nvec\n"}},{"id":"zeros(n)-class-method","html_id":"zeros(n)-class-method","name":"zeros","doc":"Create a new vector of size `n` filled with zeros.","summary":"<p>Create a new vector of size <code>n</code> filled with zeros.</p>","abstract":false,"args":[{"name":"n","doc":null,"default_value":"","external_name":"n","restriction":""}],"args_string":"(n)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L147","def":{"name":"zeros","args":[{"name":"n","doc":null,"default_value":"","external_name":"n","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"Vector.new(n, 0.0)"}}],"constructors":[{"id":"build(capacity:Int,&block):self-class-method","html_id":"build(capacity:Int,&amp;block):self-class-method","name":"build","doc":"Creates a new `Vector`, allocating an internal buffer with the given *capacity*,\nand yielding that buffer. 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If you have an estimate\nof the maximum number of elements an vector will hold, the vector should\nbe initialized with that capacity for improved performance.\n\n```\nvec = Vector.new(5)\nvec.size # => 0\n```","summary":"<p>Creates a new empty <code><a href=\"../../Apatite/LinearAlgebra/Vector.html\">Vector</a></code> backed by a buffer that is initially <code>initial_capacity</code> big.</p>","abstract":false,"args":[{"name":"initial_capacity","doc":null,"default_value":"","external_name":"initial_capacity","restriction":"Int"}],"args_string":"(initial_capacity : Int)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L43","def":{"name":"new","args":[{"name":"initial_capacity","doc":null,"default_value":"","external_name":"initial_capacity","restriction":"Int"}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"_ = allocate\n_.initialize(initial_capacity)\nif _.responds_to?(:finalize)\n  ::GC.add_finalizer(_)\nend\n_\n"}},{"id":"new-class-method","html_id":"new-class-method","name":"new","doc":"Create a new empty `Vector`.","summary":"<p>Create a new empty <code><a href=\"../../Apatite/LinearAlgebra/Vector.html\">Vector</a></code>.</p>","abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L25","def":{"name":"new","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"_ = allocate\n_.initialize\nif _.responds_to?(:finalize)\n  ::GC.add_finalizer(_)\nend\n_\n"}},{"id":"new(size:Int,&block:Int32->Float64)-class-method","html_id":"new(size:Int,&amp;block:Int32-&gt;Float64)-class-method","name":"new","doc":"Creates a new `Vector` of the given *size* and invokes the given block once\nfor each index of `self`, assigning the block's value in that index.\n\n```\nVector.new(3) { |i| (i + 1.0) ** 2.0 } # => Vector{1.0, 4.0, 9.0}\n\nvec = Vector.new(3) { 5.0 }\nvec # => Vector{5.0, 5.0, 5.0}\n```","summary":"<p>Creates a new <code><a href=\"../../Apatite/LinearAlgebra/Vector.html\">Vector</a></code> of the given <em>size</em> and invokes the given block once for each index of <code>self</code>, assigning the block's value in that index.</p>","abstract":false,"args":[{"name":"size","doc":null,"default_value":"","external_name":"size","restriction":"Int"}],"args_string":"(size : Int, &block : Int32 -> Float64)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L87","def":{"name":"new","args":[{"name":"size","doc":null,"default_value":"","external_name":"size","restriction":"Int"}],"double_splat":null,"splat_index":null,"yields":1,"block_arg":{"name":"block","doc":null,"default_value":"","external_name":"block","restriction":"(Int32 -> Float64)"},"return_type":"","visibility":"Public","body":"Vector.build(size) do |buffer|\n  size.to_i.times do |i|\n    buffer[i] = yield i\n  end\n  size\nend"}}],"instance_methods":[{"id":"*(other)-instance-method","html_id":"*(other)-instance-method","name":"*","doc":null,"summary":null,"abstract":false,"args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":""}],"args_string":"(other)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L370","def":{"name":"*","args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"multiply(other)"}},{"id":"+(other)-instance-method","html_id":"+(other)-instance-method","name":"+","doc":null,"summary":null,"abstract":false,"args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":""}],"args_string":"(other)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L362","def":{"name":"+","args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"add(other)"}},{"id":"-(other)-instance-method","html_id":"-(other)-instance-method","name":"-","doc":null,"summary":null,"abstract":false,"args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":""}],"args_string":"(other)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L366","def":{"name":"-","args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"subtract(other)"}},{"id":"/(other)-instance-method","html_id":"/(other)-instance-method","name":"/","doc":null,"summary":null,"abstract":false,"args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":""}],"args_string":"(other)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L374","def":{"name":"/","args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"divide(other)"}},{"id":"<<(value:Float64)-instance-method","html_id":"&lt;&lt;(value:Float64)-instance-method","name":"<<","doc":"Alias for `#push`","summary":"<p>Alias for <code><a href=\"../../Apatite/LinearAlgebra/Vector.html#push%28value%3AFloat64%29-instance-method\">#push</a></code></p>","abstract":false,"args":[{"name":"value","doc":null,"default_value":"","external_name":"value","restriction":"Float64"}],"args_string":"(value : Float64)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L349","def":{"name":"<<","args":[{"name":"value","doc":null,"default_value":"","external_name":"value","restriction":"Float64"}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"push(value)"}},{"id":"(other)-instance-method","html_id":"(other)-instance-method","name":"<=>","doc":"Combined comparison operator. Returns *0* if `self` equals *other*, *1* if\n`self` is greater than *other* and *-1* if `self` is smaller than *other*.\n\nIt compares the elements of both vectors in the same position using the\n`<=>` operator.  As soon as one of such comparisons returns a non-zero\nvalue, that result is the return value of the comparison.\n\nIf all elements are equal, the comparison is based on the size of the vectors.\n\n```\nVector{8.0} <=> Vector(1.0, 2.0, 3.0} # => 1\nVector{2.0} <=> Vector{4.0, 2.0, 3.0} # => -1\nVector{1.0, 2.0} <=> Vector{1.0, 2.0} # => 0\n```","summary":"<p>Combined comparison operator.</p>","abstract":false,"args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":""}],"args_string":"(other)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L339","def":{"name":"<=>","args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"min_size = Math.min(size, other.size)\n0.upto(min_size - 1) do |i|\n  n = @buffer[i] <=> other.to_unsafe[i]\n  if n != 0\n    return n\n  end\nend\nsize <=> other.size\n"}},{"id":"==(other:Vector)-instance-method","html_id":"==(other:Vector)-instance-method","name":"==","doc":null,"summary":null,"abstract":false,"args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":"Vector"}],"args_string":"(other : Vector)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L353","def":{"name":"==","args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":"Vector"}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"equals?(other) do |x, y|\n  x == y\nend"}},{"id":"[](start:Int,count:Int)-instance-method","html_id":"[](start:Int,count:Int)-instance-method","name":"[]","doc":"Returns count or less (if there aren't enough) elements starting at the\ngiven start index.\n\nNegative indices count backward from the end of the vector (-1 is the last\nelement). Additionally, an empty vector is returned when the starting index\nfor an element range is at the end of the vector.\n\nRaises `IndexError` if the starting index is out of range.\n\n```\nv = Vector{1.0, 2.0, 3.0, 4.0, 5.0}\nv[1, 3]  # => Vector{2.0, 3.0, 4.0}\nv[6, 10] # raise IndexError\n```","summary":"<p>Returns count or less (if there aren't enough) elements starting at the given start index.</p>","abstract":false,"args":[{"name":"start","doc":null,"default_value":"","external_name":"start","restriction":"Int"},{"name":"count","doc":null,"default_value":"","external_name":"count","restriction":"Int"}],"args_string":"(start : Int, count : Int)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L191","def":{"name":"[]","args":[{"name":"start","doc":null,"default_value":"","external_name":"start","restriction":"Int"},{"name":"count","doc":null,"default_value":"","external_name":"count","restriction":"Int"}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"if count < 0\n  raise(ArgumentError.new(\"Negative count: #{count}\"))\nend\nif start == size\n  return Vector.new\nend\nif start < 0\n  start = start + size\nend\nif 0 <= start && start <= size\nelse\n  raise(IndexError.new)\nend\nif count == 0\n  return Vector.new\nend\ncount = Math.min(count, size - start)\nVector.build(count) do |buffer|\n  buffer.copy_from(@buffer + start, count)\n  count\nend\n"}},{"id":"[](range:Range(Int,Int))-instance-method","html_id":"[](range:Range(Int,Int))-instance-method","name":"[]","doc":"Returns all elements that are within the given range.\n\nNegative indices count backward from the end of the vector (-1 is the last\nelement). Additionally, an empty vector is returned when the starting index\nfor an element range is at the end of the vector.\n\nRaises `IndexError` if the starting index is out of range.\n\n```\nv = Vector{1.0, 2.0, 3.0, 4.0, 5.0}\nv[1..3]  # => Vector{2.0, 3.0, 4.0}\nv[6..10] # raise IndexError\n```","summary":"<p>Returns all elements that are within the given range.</p>","abstract":false,"args":[{"name":"range","doc":null,"default_value":"","external_name":"range","restriction":"Range(Int, Int)"}],"args_string":"(range : Range(Int, Int))","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L173","def":{"name":"[]","args":[{"name":"range","doc":null,"default_value":"","external_name":"range","restriction":"Range(Int, Int)"}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"self[*Indexable.range_to_index_and_count(range, size)]"}},{"id":"[]=(index:Int,count:Int,values:Vector)-instance-method","html_id":"[]=(index:Int,count:Int,values:Vector)-instance-method","name":"[]=","doc":"Replaces a subrange with the elements of the given vector.\n\n```\nvec = Vector{1.0, 2.0, 3.0, 4.0, 5.0}\nvec[1, 3] = Vector{6.0, 7.0, 8.0}\nvec # = Vector{1.0, 6.0, 7.0, 8.0, 5.0}\n\nvec = Vector{1.0, 2.0, 3.0, 4.0, 5.0}\nvec[1, 3] = Vector{6.0, 7.0}\nvec # = Vector{1.0, 6.0, 7.0, 5.0}\n```","summary":"<p>Replaces a subrange with the elements of the given vector.</p>","abstract":false,"args":[{"name":"index","doc":null,"default_value":"","external_name":"index","restriction":"Int"},{"name":"count","doc":null,"default_value":"","external_name":"count","restriction":"Int"},{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":"Vector"}],"args_string":"(index : Int, count : Int, values : Vector)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L297","def":{"name":"[]=","args":[{"name":"index","doc":null,"default_value":"","external_name":"index","restriction":"Int"},{"name":"count","doc":null,"default_value":"","external_name":"count","restriction":"Int"},{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":"Vector"}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"if count < 0\n  raise(ArgumentError.new(\"Negative count: #{count}\"))\nend\nindex = check_index_out_of_bounds(index)\ncount = ((index + count) <= size) ? count : size - index\ndiff = values.size - count\nif diff == 0\n  (@buffer + index).copy_from(values.to_unsafe, values.size)\nelse\n  if diff < 0\n    diff = -diff\n    (@buffer + index).copy_from(values.to_unsafe, values.size)\n    ((@buffer + index) + values.size).move_from((@buffer + index) + count, (size - index) - count)\n    ((@buffer + @size) - diff).clear(diff)\n    @size = @size - diff\n  else\n    resize_to_capacity(Math.pw2ceil(@size + diff))\n    ((@buffer + index) + values.size).move_from((@buffer + index) + count, (size - index) - count)\n    (@buffer + index).copy_from(values.to_unsafe, values.size)\n    @size = @size + diff\n  end\nend\nvalues\n"}},{"id":"[]=(index:Int,count:Int,value)-instance-method","html_id":"[]=(index:Int,count:Int,value)-instance-method","name":"[]=","doc":"Replaces a subrange with a single value. All elements in the range\n`index...index+count` are removed and replaced by a single element\n*value*.\n\nIf *count* is zero, *value* is inserted at *index*.\n\nNegative values of *index* count from the end of the vector.\n\n```\nvec = Vector{1.0, 2.0, 3.0, 4.0, 5.0}\nvec[1, 3] = 6.0\nvec # => Vector{1.0, 6.0, 5.0}\n\nvec = Vector{1.0, 2.0, 3.0, 4.0, 5.0}\nvec[1, 0] = 6.0\nvec # => Vector{1.0, 6.0, 2.0, 3.0, 4.0, 5.0}\n```","summary":"<p>Replaces a subrange with a single value.</p>","abstract":false,"args":[{"name":"index","doc":null,"default_value":"","external_name":"index","restriction":"Int"},{"name":"count","doc":null,"default_value":"","external_name":"count","restriction":"Int"},{"name":"value","doc":null,"default_value":"","external_name":"value","restriction":""}],"args_string":"(index : Int, count : Int, value)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L248","def":{"name":"[]=","args":[{"name":"index","doc":null,"default_value":"","external_name":"index","restriction":"Int"},{"name":"count","doc":null,"default_value":"","external_name":"count","restriction":"Int"},{"name":"value","doc":null,"default_value":"","external_name":"value","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"if count < 0\n  raise(ArgumentError.new(\"Negative count: #{count}\"))\nend\nvalue = value.to_f64\nindex = check_index_out_of_bounds(index)\ncount = ((index + count) <= size) ? count : size - index\ncase count\nwhen 0\n  insert(index, value)\nwhen 1\n  @buffer[index] = value\nelse\n  diff = count - 1\n  ((@buffer + index) + 1).move_from((@buffer + index) + count, (size - index) - count)\n  ((@buffer + @size) - diff).clear(diff)\n  @buffer[index] = value\n  @size = @size - diff\nend\nvalue\n"}},{"id":"[]=(index:Int,value)-instance-method","html_id":"[]=(index:Int,value)-instance-method","name":"[]=","doc":"Sets the given value at the given index.\n\nNegative indices can be used to start counting from the end of the array.\nRaises `IndexError` if trying to set an element outside the array's range.\n\n```\nvec = Vector{1.0, 2.0, 3.0}\nvec[0] = 5.0\np vec # => Vec{5.0, 2.0, 3.0}\n\nvec[3] = 5.0 # raises IndexError\n```","summary":"<p>Sets the given value at the given index.</p>","abstract":false,"args":[{"name":"index","doc":null,"default_value":"","external_name":"index","restriction":"Int"},{"name":"value","doc":null,"default_value":"","external_name":"value","restriction":""}],"args_string":"(index : Int, value)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L226","def":{"name":"[]=","args":[{"name":"index","doc":null,"default_value":"","external_name":"index","restriction":"Int"},{"name":"value","doc":null,"default_value":"","external_name":"value","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"index = check_index_out_of_bounds(index)\n@buffer[index] = value.to_f64\n"}},{"id":"[]=(range:Range(Int,Int),value)-instance-method","html_id":"[]=(range:Range(Int,Int),value)-instance-method","name":"[]=","doc":"Replaces a subrange with a single value.\n\n```\nvec = Vector{1.0, 2.0, 3.0, 4.0, 5.0}\nvec[1..3] = 6.0\nvec # = Vector{1.0, 6.0, 5.0}\n\nvec = Vector{1.0, 2.0, 3.0, 4.0, 5.0}\nvec[1...1] = 6\nvec # = Vector{1.0, 6.0, 2.0, 3.0, 4.0, 5.0}\n```","summary":"<p>Replaces a subrange with a single value.</p>","abstract":false,"args":[{"name":"range","doc":null,"default_value":"","external_name":"range","restriction":"Range(Int, Int)"},{"name":"value","doc":null,"default_value":"","external_name":"value","restriction":""}],"args_string":"(range : Range(Int, Int), value)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L282","def":{"name":"[]=","args":[{"name":"range","doc":null,"default_value":"","external_name":"range","restriction":"Range(Int, Int)"},{"name":"value","doc":null,"default_value":"","external_name":"value","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"self[*Indexable.range_to_index_and_count(range, size)] = value.to_f64"}},{"id":"add(value)-instance-method","html_id":"add(value)-instance-method","name":"add","doc":"When the input is a number, this returns the result of adding\nit to all vector elements. When it's a vector, the vectors\nwill be added together.","summary":"<p>When the input is a number, this returns the result of adding it to all vector elements.</p>","abstract":false,"args":[{"name":"value","doc":null,"default_value":"","external_name":"value","restriction":""}],"args_string":"(value)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L476","def":{"name":"add","args":[{"name":"value","doc":null,"default_value":"","external_name":"value","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"run_binary_op(value) do |a, b|\n  a + b\nend"}},{"id":"angle_from(vector)-instance-method","html_id":"angle_from(vector)-instance-method","name":"angle_from","doc":"Returns the angle between this vector and another in radians.\nIf the vectors are mirrored across their axes this will return `nil`.","summary":"<p>Returns the angle between this vector and another in radians.</p>","abstract":false,"args":[{"name":"vector","doc":null,"default_value":"","external_name":"vector","restriction":""}],"args_string":"(vector)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L449","def":{"name":"angle_from","args":[{"name":"vector","doc":null,"default_value":"","external_name":"vector","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"Apatite.angle_from(self, vector)"}},{"id":"antiparallel_to?(vector)-instance-method","html_id":"antiparallel_to?(vector)-instance-method","name":"antiparallel_to?","doc":"Returns whether the vectors are antiparallel to each other.","summary":"<p>Returns whether the vectors are antiparallel to each other.</p>","abstract":false,"args":[{"name":"vector","doc":null,"default_value":"","external_name":"vector","restriction":""}],"args_string":"(vector)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L464","def":{"name":"antiparallel_to?","args":[{"name":"vector","doc":null,"default_value":"","external_name":"vector","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"Apatite.antiparallel_to?(self, vector)"}},{"id":"augment(elements)-instance-method","html_id":"augment(elements)-instance-method","name":"augment","doc":"Returns a new vector with the provided `elements` concatenated\non the end.","summary":"<p>Returns a new vector with the provided <code>elements</code> concatenated on the end.</p>","abstract":false,"args":[{"name":"elements","doc":null,"default_value":"","external_name":"elements","restriction":""}],"args_string":"(elements)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L551","def":{"name":"augment","args":[{"name":"elements","doc":null,"default_value":"","external_name":"elements","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"elements = elements.is_a?(Vector) ? elements : Vector.create(elements)\nconcat(elements)\n"}},{"id":"chomp(n)-instance-method","html_id":"chomp(n)-instance-method","name":"chomp","doc":"Returns a new vector with the first `n` elements removed from\nthe beginning.","summary":"<p>Returns a new vector with the first <code>n</code> elements removed from the beginning.</p>","abstract":false,"args":[{"name":"n","doc":null,"default_value":"","external_name":"n","restriction":""}],"args_string":"(n)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L536","def":{"name":"chomp","args":[{"name":"n","doc":null,"default_value":"","external_name":"n","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"elements = [] of Float64\neach_with_index do |e, i|\n  if i >= n\n    elements << e\n  end\nend\nVector.create(elements)\n"}},{"id":"clear-instance-method","html_id":"clear-instance-method","name":"clear","doc":"Removes all elements from self.\n\n```\nvec = Vector{1.0, 2.0, 3.0}\nvec.clear # => Vector{}\n```","summary":"<p>Removes all elements from self.</p>","abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L768","def":{"name":"clear","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"@buffer.clear(@size)\n@size = 0\nself\n"}},{"id":"clone-instance-method","html_id":"clone-instance-method","name":"clone","doc":null,"summary":null,"abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L378","def":{"name":"clone","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"Vector.create(@elements.clone)"}},{"id":"concat(other:Vector)-instance-method","html_id":"concat(other:Vector)-instance-method","name":"concat","doc":null,"summary":null,"abstract":false,"args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":"Vector"}],"args_string":"(other : Vector)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L717","def":{"name":"concat","args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":"Vector"}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"other_size = other.size\nnew_size = size + other_size\nif new_size > @capacity\n  resize_to_capacity(Math.pw2ceil(new_size))\nend\n(@buffer + @size).copy_from(other.to_unsafe, other_size)\n@size = new_size\nself\n"}},{"id":"covector-instance-method","html_id":"covector-instance-method","name":"covector","doc":"Creates a single-row matrix from this vector.","summary":"<p>Creates a single-row matrix from this vector.</p>","abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L587","def":{"name":"covector","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"Matrix.row_vector(self)"}},{"id":"cross(*vs)-instance-method","html_id":"cross(*vs)-instance-method","name":"cross","doc":"Returns the cross product of this vector with the others.\n\n```\nv1 = Vector{1.0, 0.0, 0.0}\nv2 = Vector{0.0, 1.0, 0.0}\nv1.cross(v2) => Vector{0.0, 0.0, 1.0}\n```","summary":"<p>Returns the cross product of this vector with the others.</p>","abstract":false,"args":[{"name":"vs","doc":null,"default_value":"","external_name":"vs","restriction":""}],"args_string":"(*vs)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L513","def":{"name":"cross","args":[{"name":"vs","doc":null,"default_value":"","external_name":"vs","restriction":""}],"double_splat":null,"splat_index":0,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"if size >= 2\nelse\n  raise(\"cross product is not defined on vectors of dimension #{size}\")\nend\nif vs.size == (size - 2)\nelse\n  raise(ArgumentError.new(\"wrong number of arguments (#{vs.size} for #{size - 2})\"))\nend\nvs.each do |v|\n  if v.size == size\n  else\n    raise(\"Dimension mismatch. Vectors not all the same size.\")\n  end\nend\ncase size\nwhen 2\n  Vector[-@buffer[1], @buffer[0]]\nwhen 3\n  v = vs[0]\n  Vector[(v[2] * @buffer[1]) - (v[1] * @buffer[2]), (v[0] * @buffer[2]) - (v[2] * @buffer[0]), (v[1] * @buffer[0]) - (v[0] * @buffer[1])]\nelse\nend\n"}},{"id":"distance_from(obj)-instance-method","html_id":"distance_from(obj)-instance-method","name":"distance_from","doc":"Gets this vector's distance from the argument, when considered\na point in space.","summary":"<p>Gets this vector's distance from the argument, when considered a point in space.</p>","abstract":false,"args":[{"name":"obj","doc":null,"default_value":"","external_name":"obj","restriction":""}],"args_string":"(obj)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L615","def":{"name":"distance_from","args":[{"name":"obj","doc":null,"default_value":"","external_name":"obj","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"if object.is_a?(Plane) || object.is_a?(Line)\n  return object.distance_from(self)\nend\nv = elements.is_a?(Vector) ? elements.elements : elements\nif v.size == @elements.size\nelse\n  return nil\nend\nsum = 0\npart = 0\neach_with_index do |x, i|\n  part = x - v[i - 1]\n  sum = sum + (part * part)\nend\nMath.sqrt(sum)\n"}},{"id":"divide(value)-instance-method","html_id":"divide(value)-instance-method","name":"divide","doc":"When the input is a number, this returns the result of dividing\nit to all vector elements. When it's a vector, the vectors\nwill be element-wise divided.","summary":"<p>When the input is a number, this returns the result of dividing it to all vector elements.</p>","abstract":false,"args":[{"name":"value","doc":null,"default_value":"","external_name":"value","restriction":""}],"args_string":"(value)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L497","def":{"name":"divide","args":[{"name":"value","doc":null,"default_value":"","external_name":"value","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"run_binary_op(value) do |a, b|\n  a / b\nend"}},{"id":"dot(other)-instance-method","html_id":"dot(other)-instance-method","name":"dot","doc":"Get the scalar (dot) product of this vector with `vector`.\n\n[https://en.wikipedia.org/wiki/Scalar_product](https://en.wikipedia.org/wiki/Scalar_product)","summary":"<p>Get the scalar (dot) product of this vector with <code>vector</code>.</p>","abstract":false,"args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":""}],"args_string":"(other)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L569","def":{"name":"dot","args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"other = other.is_a?(Vector) ? other : Vector.create(other)\nApatite.dot(self, other)\n"}},{"id":"e(i)-instance-method","html_id":"e(i)-instance-method","name":"e","doc":"Returns the `ith` element of the vector. Returns `nil` if `i`\nis out of bounds. Indexing starts from 1.","summary":"<p>Returns the <code>ith</code> element of the vector.</p>","abstract":false,"args":[{"name":"i","doc":null,"default_value":"","external_name":"i","restriction":""}],"args_string":"(i)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L430","def":{"name":"e","args":[{"name":"i","doc":null,"default_value":"","external_name":"i","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"(i < 1 || i > @size) ? nil : self[i - 1]"}},{"id":"independent?(*vs)-instance-method","html_id":"independent?(*vs)-instance-method","name":"independent?","doc":"Returns true if all vectors are linearly independent.","summary":"<p>Returns true if all vectors are linearly independent.</p>","abstract":false,"args":[{"name":"vs","doc":null,"default_value":"","external_name":"vs","restriction":""}],"args_string":"(*vs)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L388","def":{"name":"independent?","args":[{"name":"vs","doc":null,"default_value":"","external_name":"vs","restriction":""}],"double_splat":null,"splat_index":0,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"vs.each do |v|\n  if v.size == vs.first.size\n  else\n    raise(\"Dimension mismatch. Vectors not all the same size.\")\n  end\nend\nif vs.size > sv.first.size\n  return false\nend\nMatrix[*vs].rank.equal?(vs.count)\n"}},{"id":"lies_in(plane)-instance-method","html_id":"lies_in(plane)-instance-method","name":"lies_in","doc":"Returns true if the vector is a point on the given plane.","summary":"<p>Returns true if the vector is a point on the given plane.</p>","abstract":false,"args":[{"name":"plane","doc":null,"default_value":"","external_name":"plane","restriction":""}],"args_string":"(plane)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L640","def":{"name":"lies_in","args":[{"name":"plane","doc":null,"default_value":"","external_name":"plane","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"plane.contains(self)"}},{"id":"lies_on(line)-instance-method","html_id":"lies_on(line)-instance-method","name":"lies_on","doc":"Returns true if the vector is a point on the given line","summary":"<p>Returns true if the vector is a point on the given line</p>","abstract":false,"args":[{"name":"line","doc":null,"default_value":"","external_name":"line","restriction":""}],"args_string":"(line)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L635","def":{"name":"lies_on","args":[{"name":"line","doc":null,"default_value":"","external_name":"line","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"line.contains(self)"}},{"id":"log-instance-method","html_id":"log-instance-method","name":"log","doc":"Return a new `Vector` with the log of every item in `self`.","summary":"<p>Return a new <code><a href=\"../../Apatite/LinearAlgebra/Vector.html\">Vector</a></code> with the log of every item in <code>self</code>.</p>","abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L557","def":{"name":"log","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"map do |x|\n  Math.log(x)\nend"}},{"id":"magnitude-instance-method","html_id":"magnitude-instance-method","name":"magnitude","doc":"Returns the magnitude/euclidian norm of this vector.\n\n[https://en.wikipedia.org/wiki/Euclidean_distance](https://en.wikipedia.org/wiki/Euclidean_distance)","summary":"<p>Returns the magnitude/euclidian norm of this vector.</p>","abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L423","def":{"name":"magnitude","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"sum = reduce(0.0) do |acc, e|\n  acc = acc + (e * e)\nend\nMath.sqrt(sum)\n"}},{"id":"map(&block)-instance-method","html_id":"map(&amp;block)-instance-method","name":"map","doc":"Invokes the given block for each element of `self`.","summary":"<p>Invokes the given block for each element of <code>self</code>.</p>","abstract":false,"args":[],"args_string":"(&block)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L383","def":{"name":"map","args":[],"double_splat":null,"splat_index":null,"yields":1,"block_arg":null,"return_type":"","visibility":"Public","body":"Vector.new(size) do |i|\n  yield @buffer[i]\nend"}},{"id":"map!(&block)-instance-method","html_id":"map!(&amp;block)-instance-method","name":"map!","doc":"Invokes the given block for each element of `self`, replacing the element\nwith the value returned by the block. Returns `self`.\n\n```\nvec = Vector{1.0, 2.0, 3.0}\nvec.map! { |x| x * x }\na # => Vector{1.0, 4.0, 9.0}\n```","summary":"<p>Invokes the given block for each element of <code>self</code>, replacing the element with the value returned by the block.</p>","abstract":false,"args":[],"args_string":"(&block)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L404","def":{"name":"map!","args":[],"double_splat":null,"splat_index":null,"yields":1,"block_arg":null,"return_type":"","visibility":"Public","body":"@buffer.map!(size) do |e|\n  yield e\nend\nself\n"}},{"id":"map_with_index(&block)-instance-method","html_id":"map_with_index(&amp;block)-instance-method","name":"map_with_index","doc":"Optimized version of `Enumerable#map_with_index`.","summary":"<p>Optimized version of <code>Enumerable#map_with_index</code>.</p>","abstract":false,"args":[],"args_string":"(&block)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L410","def":{"name":"map_with_index","args":[],"double_splat":null,"splat_index":null,"yields":2,"block_arg":null,"return_type":"","visibility":"Public","body":"Vector.new(size) do |i|\n  yield @buffer[i], i\nend"}},{"id":"map_with_index!(&block)-instance-method","html_id":"map_with_index!(&amp;block)-instance-method","name":"map_with_index!","doc":"Like `map_with_index`, but mutates `self` instead of allocating a new object.","summary":"<p>Like <code><a href=\"../../Apatite/LinearAlgebra/Vector.html#map_with_index%28%26block%29-instance-method\">#map_with_index</a></code>, but mutates <code>self</code> instead of allocating a new object.</p>","abstract":false,"args":[],"args_string":"(&block)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L415","def":{"name":"map_with_index!","args":[],"double_splat":null,"splat_index":null,"yields":2,"block_arg":null,"return_type":"","visibility":"Public","body":"to_unsafe.map_with_index!(size) do |e, i|\n  yield e, i\nend\nself\n"}},{"id":"max-instance-method","html_id":"max-instance-method","name":"max","doc":"Returns the (absolute) largest element in this vector.","summary":"<p>Returns the (absolute) largest element in this vector.</p>","abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L575","def":{"name":"max","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"reduce do |acc, i|\n  i.abs > acc.abs ? i : acc\nend"}},{"id":"max_index-instance-method","html_id":"max_index-instance-method","name":"max_index","doc":"Gets the index of the largest element in this vector.","summary":"<p>Gets the index of the largest element in this vector.</p>","abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L580","def":{"name":"max_index","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"idx = 0\neach_with_index do |e, i|\n  idx = e.abs > self[idx].abs ? i : idx\nend\nidx\n"}},{"id":"multiply(value)-instance-method","html_id":"multiply(value)-instance-method","name":"multiply","doc":"When the input is a number, this returns the result of multiplying\nit to all vector elements. When it's a vector, the vectors\nwill be element-wise multiplied.","summary":"<p>When the input is a number, this returns the result of multiplying it to all vector elements.</p>","abstract":false,"args":[{"name":"value","doc":null,"default_value":"","external_name":"value","restriction":""}],"args_string":"(value)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L490","def":{"name":"multiply","args":[{"name":"value","doc":null,"default_value":"","external_name":"value","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"run_binary_op(value) do |a, b|\n  a * b\nend"}},{"id":"normalize-instance-method","html_id":"normalize-instance-method","name":"normalize","doc":"Returns a new vector created by normalizing this one\nto have a magnitude of `1`. If the vector is a zero\nvector, it will not be modified.","summary":"<p>Returns a new vector created by normalizing this one to have a magnitude of <code>1</code>.</p>","abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L443","def":{"name":"normalize","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"to_unit_vector"}},{"id":"parallel_to?(vector)-instance-method","html_id":"parallel_to?(vector)-instance-method","name":"parallel_to?","doc":"Returns whether the vectors are parallel to each other.","summary":"<p>Returns whether the vectors are parallel to each other.</p>","abstract":false,"args":[{"name":"vector","doc":null,"default_value":"","external_name":"vector","restriction":""}],"args_string":"(vector)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L459","def":{"name":"parallel_to?","args":[{"name":"vector","doc":null,"default_value":"","external_name":"vector","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"Apatite.parallel_to?(self, vector)"}},{"id":"perpendicular_to?(vector)-instance-method","html_id":"perpendicular_to?(vector)-instance-method","name":"perpendicular_to?","doc":"Returns whether the vectors are perpendicular to each other.","summary":"<p>Returns whether the vectors are perpendicular to each other.</p>","abstract":false,"args":[{"name":"vector","doc":null,"default_value":"","external_name":"vector","restriction":""}],"args_string":"(vector)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L469","def":{"name":"perpendicular_to?","args":[{"name":"vector","doc":null,"default_value":"","external_name":"vector","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"Apatite.perpendicular_to?(self, vector)"}},{"id":"pretty_print(pp):Nil-instance-method","html_id":"pretty_print(pp):Nil-instance-method","name":"pretty_print","doc":null,"summary":null,"abstract":false,"args":[{"name":"pp","doc":null,"default_value":"","external_name":"pp","restriction":""}],"args_string":"(pp) : Nil","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L740","def":{"name":"pretty_print","args":[{"name":"pp","doc":null,"default_value":"","external_name":"pp","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"Nil","visibility":"Public","body":"pp.list(\"Vector{\", self, \"}\")"}},{"id":"product-instance-method","html_id":"product-instance-method","name":"product","doc":"Get the product of all elements in this vector.","summary":"<p>Get the product of all elements in this vector.</p>","abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L562","def":{"name":"product","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"reduce do |acc, v|\n  acc = acc * v\nend"}},{"id":"push(value:Float64)-instance-method","html_id":"push(value:Float64)-instance-method","name":"push","doc":null,"summary":null,"abstract":false,"args":[{"name":"value","doc":null,"default_value":"","external_name":"value","restriction":"Float64"}],"args_string":"(value : Float64)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L644","def":{"name":"push","args":[{"name":"value","doc":null,"default_value":"","external_name":"value","restriction":"Float64"}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"check_needs_resize\n@buffer[@size] = value\n@size = @size + 1\nself\n"}},{"id":"push(*values:Float64)-instance-method","html_id":"push(*values:Float64)-instance-method","name":"push","doc":null,"summary":null,"abstract":false,"args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":"Float64"}],"args_string":"(*values : Float64)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L651","def":{"name":"push","args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":"Float64"}],"double_splat":null,"splat_index":0,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"new_size = @size + values.size\nif new_size > @capacity\n  resize_to_capacity(Math.pw2ceil(new_size))\nend\nvalues.each_with_index do |value, i|\n  @buffer[@size + i] = value\nend\n@size = new_size\nself\n"}},{"id":"reflection_in(object)-instance-method","html_id":"reflection_in(object)-instance-method","name":"reflection_in","doc":"Returns the result of reflecting the point in the given `object`\n(point, line, or plane).","summary":"<p>Returns the result of reflecting the point in the given <code>object</code> (point, line, or plane).</p>","abstract":false,"args":[{"name":"object","doc":null,"default_value":"","external_name":"object","restriction":""}],"args_string":"(object)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L670","def":{"name":"reflection_in","args":[{"name":"object","doc":null,"default_value":"","external_name":"object","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"if object.is_a?(Plane) || object.is_a?(Line)\n  p = @elements.dup\n  c = (object.point_closest_to(p)).elements\n  return Vector.create([C[0] + (C[0] - P[0]), C[1] + (C[1] - P[1]), C[2] + (C[2] - (P[2] || 0))])\nend\nq = object.is_a?(Vector) ? object.elements : object\nif @elements.size == q.size\nelse\n  return nil\nend\nmap_with_index do |x, i|\n  q[i - 1] + (q[i - 1] - x)\nend\n"}},{"id":"rotate(t,object)-instance-method","html_id":"rotate(t,object)-instance-method","name":"rotate","doc":"Rotates the vector about the given `object`. The object should\nbe a point if the vector is 2D, and a line if it is 3D. Be\ncareful with line directions!","summary":"<p>Rotates the vector about the given <code>object</code>.</p>","abstract":false,"args":[{"name":"t","doc":null,"default_value":"","external_name":"t","restriction":""},{"name":"object","doc":null,"default_value":"","external_name":"object","restriction":""}],"args_string":"(t, object)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L664","def":{"name":"rotate","args":[{"name":"t","doc":null,"default_value":"","external_name":"t","restriction":""},{"name":"object","doc":null,"default_value":"","external_name":"object","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":""}},{"id":"round-instance-method","html_id":"round-instance-method","name":"round","doc":"Gets the result of rounding the elements of the vector.","summary":"<p>Gets the result of rounding the elements of the vector.</p>","abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L598","def":{"name":"round","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"map do |x|\n  x.round\nend"}},{"id":"set_elements(elements)-instance-method","html_id":"set_elements(elements)-instance-method","name":"set_elements","doc":null,"summary":null,"abstract":false,"args":[{"name":"elements","doc":null,"default_value":"","external_name":"elements","restriction":""}],"args_string":"(elements)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L712","def":{"name":"set_elements","args":[{"name":"elements","doc":null,"default_value":"","external_name":"elements","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"@elements = elements.is_a?(Vector) ? elements.elements : elements\nself\n"}},{"id":"sigmoid-instance-method","html_id":"sigmoid-instance-method","name":"sigmoid","doc":"Sums the numbers in the vector and returns a sigmoid value\nacross the whole vector.","summary":"<p>Sums the numbers in the vector and returns a sigmoid value across the whole vector.</p>","abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L693","def":{"name":"sigmoid","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"LinearAlgebra.sigmoid(sum)"}},{"id":"similarity(other)-instance-method","html_id":"similarity(other)-instance-method","name":"similarity","doc":"Compute the cosine similarity between this vector and another.","summary":"<p>Compute the cosine similarity between this vector and another.</p>","abstract":false,"args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":""}],"args_string":"(other)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L454","def":{"name":"similarity","args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"Apatite.similarity(self, other)"}},{"id":"size:Int32-instance-method","html_id":"size:Int32-instance-method","name":"size","doc":"Returns the number of elements in the vector","summary":"<p>Returns the number of elements in the vector</p>","abstract":false,"args":[],"args_string":" : Int32","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L24","def":{"name":"size","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"Int32","visibility":"Public","body":"@size"}},{"id":"snap_to(value)-instance-method","html_id":"snap_to(value)-instance-method","name":"snap_to","doc":"Returns a copy of the vector with elements set to `value` if\nthey differ from it by less than `Apetite.precision`","summary":"<p>Returns a copy of the vector with elements set to <code>value</code> if they differ from it by less than <code>Apetite.precision</code></p>","abstract":false,"args":[{"name":"value","doc":null,"default_value":"","external_name":"value","restriction":""}],"args_string":"(value)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L609","def":{"name":"snap_to","args":[{"name":"value","doc":null,"default_value":"","external_name":"value","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"map do |y|\n  (y - x).abs <= Apetite.precision ? 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If the vector is a zero\nvector, it will not be modified.","summary":"<p>Returns a new vector created by normalizing this one to have a magnitude of <code>1</code>.</p>","abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L437","def":{"name":"to_unit_vector","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"r = magnitude\nr == 0 ? dup : map do |x|\n  x.to_f64 / r\nend\n"}},{"id":"to_unsafe:Pointer(Float64)-instance-method","html_id":"to_unsafe:Pointer(Float64)-instance-method","name":"to_unsafe","doc":"Returns a pointer to the internal buffer where `self`'s elements are stored.\n\nThis method is **unsafe** because it returns a pointer, and the pointed might eventually\nnot be that of `self` if the array grows and its internal buffer is reallocated.\n\n```\nvec = Vector{1.0, 2.0, 3.0}\nvec.to_unsafe[0] # 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This is normally known as a [dynamic array](http://en.wikipedia.org/wiki/Dynamic_array).\n\nYou can use a special array literal syntax with other types too, as long as they define an argless\n`new` method and a `<<` method. `Set` is one such type:\n\n```\nset = Set{1, 2, 3} # => Set{1, 2, 3}\nset.class          # => Set(Int32)\n```\n\nThe above is the same as this:\n\n```\nset = Set(typeof(1, 2, 3)).new\nset << 1\nset << 2\nset << 3\n```","summary":"<p>An <code><a href=\"Array.html\">Array</a></code> is an ordered, integer-indexed collection of objects of type T.</p>","class_methods":[],"constructors":[],"instance_methods":[{"id":"all?-instance-method","html_id":"all?-instance-method","name":"all?","doc":"Tests whether all elements evaluate to true","summary":"<p>Tests whether all elements evaluate to true</p>","abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/core_ext/array.cr#L3","def":{"name":"all?","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"each do |i|\n  if (!(!i)) == false\n    return false\n  end\nend\ntrue\n"}},{"id":"any?-instance-method","html_id":"any?-instance-method","name":"any?","doc":"Tests whether any of the elements evaluate to true","summary":"<p>Tests whether any of the elements evaluate to true</p>","abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/core_ext/array.cr#L11","def":{"name":"any?","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"each do |i|\n  if (!(!i)) == true\n    return true\n  end\nend\nfalse\n"}},{"id":"shape-instance-method","html_id":"shape-instance-method","name":"shape","doc":"Get the array's dimensions","summary":"<p>Get the array's dimensions</p>","abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/core_ext/array.cr#L19","def":{"name":"shape","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"max = max_by do |i|\n  i.is_a?(Array) ? i.size : i\nend\nmax.is_a?(Array) ? 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\ No newline at end of file
diff --git a/docs/search-index.js b/docs/search-index.js
index 67791fc..0d3baee 100644
--- a/docs/search-index.js
+++ b/docs/search-index.js
@@ -1 +1 @@
-crystal_doc_search_index_callback({"repository_name":"github.com/watzon/apatite","body":"# Apatite\n\nApatite is meant to be a collecion of mathmatical and scientific computing algorithms for the Crystal programming language. I don't expect it to ever reach the level of completeness as numpy, but hopefully it can save some people the trouble of implementing these methods on their own.\n\n## Installation\n\n1. Add the dependency to your `shard.yml`:\n\n   ```yaml\n   dependencies:\n     apatite:\n       github: watzon/apatite\n   ```\n\n2. Run `shards install`\n\n## Usage\n\n```crystal\nrequire \"apatite\"\n```\n\nTODO: Write usage instructions here, but first write the library...\n\n## Roadmap\n\n- [ ] Apetite\n\t- [ ] Vector Math\n\t\t- [ ] Matrix\n\t\t- [ ] NDArray\n\t\t- [x] Vector\n\t\t- [ ] Line\n\t\t- [ ] Plane\n\t\t- [ ] Polygon\n\t\t- [ ] LinkedList\n\t\n\n\n## Contributing\n\n1. Fork it (<https://github.com/watzon/apatite/fork>)\n2. Create your feature branch (`git checkout -b my-new-feature`)\n3. Commit your changes (`git commit -am 'Add some feature'`)\n4. Push to the branch (`git push origin my-new-feature`)\n5. 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raise(ArgumentError.new(\"One size must be 0\"))\nend\nif column_count < 0 || row_count < 0\n  raise(ArgumentError.new(\"Negative size\"))\nend\nMatrix.new(([] of Vector) * row_count, column_count)\n"}},{"id":"eye(n)-class-method","html_id":"eye(n)-class-method","name":"eye","doc":"Creates a new diagonal matrix of size `n` with ones in the diagonal\nand zeros elsewhere.","summary":"<p>Creates a new diagonal matrix of size <code>n</code> with ones in the diagonal and zeros elsewhere.</p>","abstract":false,"args":[{"name":"n","doc":null,"default_value":"","external_name":"n","restriction":""}],"args_string":"(n)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/matrix.cr#L98","def":{"name":"eye","args":[{"name":"n","doc":null,"default_value":"","external_name":"n","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"Matrix.diagonal([1] * n)"}},{"id":"hstack(x,*matrices)-class-method","html_id":"hstack(x,*matrices)-class-method","name":"hstack","doc":"TODO","summary":"<p><span class=\"flag orange\">TODO</span> </p>","abstract":false,"args":[{"name":"x","doc":null,"default_value":"","external_name":"x","restriction":""},{"name":"matrices","doc":null,"default_value":"","external_name":"matrices","restriction":""}],"args_string":"(x, *matrices)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/matrix.cr#L103","def":{"name":"hstack","args":[{"name":"x","doc":null,"default_value":"","external_name":"x","restriction":""},{"name":"matrices","doc":null,"default_value":"","external_name":"matrices","restriction":""}],"double_splat":null,"splat_index":1,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":""}},{"id":"identity(n)-class-method","html_id":"identity(n)-class-method","name":"identity","doc":"Creates a `n x n` identity matrix.","summary":"<p>Creates a <code>n x n</code> identity matrix.</p>","abstract":false,"args":[{"name":"n","doc":null,"default_value":"","external_name":"n","restriction":""}],"args_string":"(n)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/matrix.cr#L107","def":{"name":"identity","args":[{"name":"n","doc":null,"default_value":"","external_name":"n","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"scalar(n, 1)"}},{"id":"row_vector(row)-class-method","html_id":"row_vector(row)-class-method","name":"row_vector","doc":"Creates a single-row matrix where the values of that row are as given in `row`.","summary":"<p>Creates a single-row matrix where the values of that row are as given in <code><a href=\"../../Apatite/LinearAlgebra/Matrix.html#row%28i%2C%26block%29-instance-method\">#row</a></code>.</p>","abstract":false,"args":[{"name":"row","doc":null,"default_value":"","external_name":"row","restriction":""}],"args_string":"(row)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/matrix.cr#L112","def":{"name":"row_vector","args":[{"name":"row","doc":null,"default_value":"","external_name":"row","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"Matrix.new([row], 0)"}},{"id":"rows(rows)-class-method","html_id":"rows(rows)-class-method","name":"rows","doc":"Creates a matrix where rows is an array of arrays, each of which is a row of the matrix.","summary":"<p>Creates a matrix where rows is an array of arrays, each of which is a row of the matrix.</p>","abstract":false,"args":[{"name":"rows","doc":null,"default_value":"","external_name":"rows","restriction":""}],"args_string":"(rows)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/matrix.cr#L117","def":{"name":"rows","args":[{"name":"rows","doc":null,"default_value":"","external_name":"rows","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"size = rows[0]? ? rows[0].size : 0\nrows.each do |row|\n  if row.size == size\n  else\n    raise(\"Dimension mismatch: row size differs (#{row.size} should be #{size})\")\n  end\nend\nMatrix.new(rows, size)\n"}},{"id":"scalar(n,value)-class-method","html_id":"scalar(n,value)-class-method","name":"scalar","doc":"Creates an `n` by `n` diagonal matrix where each diagonal element is value.","summary":"<p>Creates an <code>n</code> by <code>n</code> diagonal matrix where each diagonal element is value.</p>","abstract":false,"args":[{"name":"n","doc":null,"default_value":"","external_name":"n","restriction":""},{"name":"value","doc":null,"default_value":"","external_name":"value","restriction":""}],"args_string":"(n, value)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/matrix.cr#L126","def":{"name":"scalar","args":[{"name":"n","doc":null,"default_value":"","external_name":"n","restriction":""},{"name":"value","doc":null,"default_value":"","external_name":"value","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"Matrix.diagonal(Array.new(n, value))"}},{"id":"vstack(x,y)-class-method","html_id":"vstack(x,y)-class-method","name":"vstack","doc":"TODO","summary":"<p><span class=\"flag orange\">TODO</span> </p>","abstract":false,"args":[{"name":"x","doc":null,"default_value":"","external_name":"x","restriction":""},{"name":"y","doc":null,"default_value":"","external_name":"y","restriction":""}],"args_string":"(x, y)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/matrix.cr#L131","def":{"name":"vstack","args":[{"name":"x","doc":null,"default_value":"","external_name":"x","restriction":""},{"name":"y","doc":null,"default_value":"","external_name":"y","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":""}},{"id":"zero(row_count,column_count=row_count)-class-method","html_id":"zero(row_count,column_count=row_count)-class-method","name":"zero","doc":"Creates a zero matrix.","summary":"<p>Creates a zero matrix.</p>","abstract":false,"args":[{"name":"row_count","doc":null,"default_value":"","external_name":"row_count","restriction":""},{"name":"column_count","doc":null,"default_value":"row_count","external_name":"column_count","restriction":""}],"args_string":"(row_count, column_count = row_count)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/matrix.cr#L135","def":{"name":"zero","args":[{"name":"row_count","doc":null,"default_value":"","external_name":"row_count","restriction":""},{"name":"column_count","doc":null,"default_value":"row_count","external_name":"column_count","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"rows = Array.new(row_count) do\n  Vector.new(column_count)\nend\nMatrix.new(rows, column_count)\n"}}],"constructors":[{"id":"new(rows,column_count:Int32?=nil)-class-method","html_id":"new(rows,column_count:Int32?=nil)-class-method","name":"new","doc":null,"summary":null,"abstract":false,"args":[{"name":"rows","doc":null,"default_value":"","external_name":"rows","restriction":""},{"name":"column_count","doc":null,"default_value":"nil","external_name":"column_count","restriction":"Int32 | ::Nil"}],"args_string":"(rows, column_count : Int32? = <span class=\"n\">nil</span>)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/matrix.cr#L15","def":{"name":"new","args":[{"name":"rows","doc":null,"default_value":"","external_name":"rows","restriction":""},{"name":"column_count","doc":null,"default_value":"nil","external_name":"column_count","restriction":"Int32 | ::Nil"}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"_ = allocate\n_.initialize(rows, column_count)\nif _.responds_to?(:finalize)\n  ::GC.add_finalizer(_)\nend\n_\n"}}],"instance_methods":[{"id":"*(other:Matrix)-instance-method","html_id":"*(other:Matrix)-instance-method","name":"*","doc":null,"summary":null,"abstract":false,"args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":"Matrix"}],"args_string":"(other : Matrix)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/matrix.cr#L140","def":{"name":"*","args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":"Matrix"}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"if column_count != other.column_count\n  raise(\"Dimension mismatch\")\nend\nrows = Array.new(row_count) do |i|\n  Vector.new(other.column_count) do |j|\n    (0...column_count).reduce(0.0) do |vij, k|\n      vij + (self[i, k] * other[k, j])\n    end\n  end\nend\nreturn Matrix.new(rows, other.column_count)\n"}},{"id":"*(int:Int)-instance-method","html_id":"*(int:Int)-instance-method","name":"*","doc":null,"summary":null,"abstract":false,"args":[{"name":"int","doc":null,"default_value":"","external_name":"int","restriction":"Int"}],"args_string":"(int : Int)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/matrix.cr#L154","def":{"name":"*","args":[{"name":"int","doc":null,"default_value":"","external_name":"int","restriction":"Int"}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"rows = self.rows.map do |row|\n  row.map do |e|\n    e * int\n  end\nend\nMatrix.new(rows, column_count)\n"}},{"id":"*(ind:Indexable)-instance-method","html_id":"*(ind:Indexable)-instance-method","name":"*","doc":null,"summary":null,"abstract":false,"args":[{"name":"ind","doc":null,"default_value":"","external_name":"ind","restriction":"Indexable"}],"args_string":"(ind : Indexable)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/matrix.cr#L161","def":{"name":"*","args":[{"name":"ind","doc":null,"default_value":"","external_name":"ind","restriction":"Indexable"}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"m = column_vector\nr = self * m\nr.column(0)\n"}},{"id":"**(int)-instance-method","html_id":"**(int)-instance-method","name":"**","doc":null,"summary":null,"abstract":false,"args":[{"name":"int","doc":null,"default_value":"","external_name":"int","restriction":""}],"args_string":"(int)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/matrix.cr#L167","def":{"name":"**","args":[{"name":"int","doc":null,"default_value":"","external_name":"int","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"if int >= 1\nelse\n  raise(\"Number can not the less than 1\")\nend\nmat = self\n(int - 1).times do\n  mat = mat * self\nend\nmat\n"}},{"id":"+(other:Matrix)-instance-method","html_id":"+(other:Matrix)-instance-method","name":"+","doc":null,"summary":null,"abstract":false,"args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":"Matrix"}],"args_string":"(other : Matrix)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/matrix.cr#L176","def":{"name":"+","args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":"Matrix"}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"if column_count != other.column_count\n  raise(\"Dimension mismatch\")\nend\nrows = Array.new(row_count) do |i|\n  Vector.new(other.column_count) do |j|\n    self[i, j] + other[i, j]\n  end\nend\nreturn Matrix.new(rows, other.column_count)\n"}},{"id":"+(vec:Indexable)-instance-method","html_id":"+(vec:Indexable)-instance-method","name":"+","doc":null,"summary":null,"abstract":false,"args":[{"name":"vec","doc":null,"default_value":"","external_name":"vec","restriction":"Indexable"}],"args_string":"(vec : Indexable)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/matrix.cr#L188","def":{"name":"+","args":[{"name":"vec","doc":null,"default_value":"","external_name":"vec","restriction":"Indexable"}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"vec = vec.is_a?(Vector) ? vec : Vector.create(vec)\nself + (column_vector(vec))\n"}},{"id":"-(vec:Indexable)-instance-method","html_id":"-(vec:Indexable)-instance-method","name":"-","doc":null,"summary":null,"abstract":false,"args":[{"name":"vec","doc":null,"default_value":"","external_name":"vec","restriction":"Indexable"}],"args_string":"(vec : Indexable)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/matrix.cr#L205","def":{"name":"-","args":[{"name":"vec","doc":null,"default_value":"","external_name":"vec","restriction":"Indexable"}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"vec = vec.is_a?(Vector) ? vec : Vector.create(vec)\nself + (column_vector(vec))\n"}},{"id":"-(other:Matrix)-instance-method","html_id":"-(other:Matrix)-instance-method","name":"-","doc":null,"summary":null,"abstract":false,"args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":"Matrix"}],"args_string":"(other : Matrix)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/matrix.cr#L193","def":{"name":"-","args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":"Matrix"}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"if column_count != other.column_count\n  raise(\"Dimension mismatch\")\nend\nrows = Array.new(row_count) do |i|\n  Vector.new(other.column_count) do |j|\n    self[i, j] - other[i, j]\n  end\nend\nreturn Matrix.new(rows, other.column_count)\n"}},{"id":"/(other:Matrix)-instance-method","html_id":"/(other:Matrix)-instance-method","name":"/","doc":null,"summary":null,"abstract":false,"args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":"Matrix"}],"args_string":"(other : Matrix)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/matrix.cr#L210","def":{"name":"/","args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":"Matrix"}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"self * other.inverse"}},{"id":"/(vec:Indexable)-instance-method","html_id":"/(vec:Indexable)-instance-method","name":"/","doc":null,"summary":null,"abstract":false,"args":[{"name":"vec","doc":null,"default_value":"","external_name":"vec","restriction":"Indexable"}],"args_string":"(vec : Indexable)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/matrix.cr#L214","def":{"name":"/","args":[{"name":"vec","doc":null,"default_value":"","external_name":"vec","restriction":"Indexable"}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"rows = self.rows.map do |row|\n  row.map do |e|\n    e / other\n  end\nend\nreturn new_matrix(rows, column_count)\n"}},{"id":"==(other:Matrix)-instance-method","html_id":"==(other:Matrix)-instance-method","name":"==","doc":null,"summary":null,"abstract":false,"args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":"Matrix"}],"args_string":"(other : Matrix)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/matrix.cr#L221","def":{"name":"==","args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":"Matrix"}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"if (Matrix === other) && (column_count == other.column_count)\nelse\n  return false\nend\nrows == other.rows\n"}},{"id":"[](row:Int,col:Int)-instance-method","html_id":"[](row:Int,col:Int)-instance-method","name":"[]","doc":"Returns element `(row, col)` of the matrix. Throws error on index error.","summary":"<p>Returns element <code>(row, col)</code> of the matrix.</p>","abstract":false,"args":[{"name":"row","doc":null,"default_value":"","external_name":"row","restriction":"Int"},{"name":"col","doc":null,"default_value":"","external_name":"col","restriction":"Int"}],"args_string":"(row : Int, col : Int)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/matrix.cr#L228","def":{"name":"[]","args":[{"name":"row","doc":null,"default_value":"","external_name":"row","restriction":"Int"},{"name":"col","doc":null,"default_value":"","external_name":"col","restriction":"Int"}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"self[row][col]"}},{"id":"[]?(row:Int,col:Int)-instance-method","html_id":"[]?(row:Int,col:Int)-instance-method","name":"[]?","doc":"Returns element `(row, col)` of the matrix, or nil if the index is not found.","summary":"<p>Returns element <code>(row, col)</code> of the matrix, or nil if the index is not found.</p>","abstract":false,"args":[{"name":"row","doc":null,"default_value":"","external_name":"row","restriction":"Int"},{"name":"col","doc":null,"default_value":"","external_name":"col","restriction":"Int"}],"args_string":"(row : Int, col : Int)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/matrix.cr#L233","def":{"name":"[]?","args":[{"name":"row","doc":null,"default_value":"","external_name":"row","restriction":"Int"},{"name":"col","doc":null,"default_value":"","external_name":"col","restriction":"Int"}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"v = fetch(row) do\n  nil\nend\nif v.nil?\nelse\n  v[col]?\nend\n"}},{"id":"adjugate-instance-method","html_id":"adjugate-instance-method","name":"adjugate","doc":"Returns the adjugate of the matrix.","summary":"<p>Returns the adjugate of the matrix.</p>","abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/matrix.cr#L239","def":{"name":"adjugate","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"if square?\nelse\n  raise(\"Dimention mismatch: `Matrix#adjugate` requires a square matrix.\")\nend\nMatrix.build(row_count, column_count) do |row, column|\n  cofactor(column, row)\nend\n"}},{"id":"cofactor(row,column)-instance-method","html_id":"cofactor(row,column)-instance-method","name":"cofactor","doc":"Returns the (row, column) cofactor which is obtained by multiplying the first minor by (-1)**(row + column)","summary":"<p>Returns the (row, column) cofactor which is obtained by multiplying the first minor by (-1)**(row + column)</p>","abstract":false,"args":[{"name":"row","doc":null,"default_value":"","external_name":"row","restriction":""},{"name":"column","doc":null,"default_value":"","external_name":"column","restriction":""}],"args_string":"(row, column)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/matrix.cr#L247","def":{"name":"cofactor","args":[{"name":"row","doc":null,"default_value":"","external_name":"row","restriction":""},{"name":"column","doc":null,"default_value":"","external_name":"column","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"if empty?\n  raise(\"cofactor of empty matrix is not defined\")\nend\nif square?\nelse\n  raise(\"Dimention mismatch: `Matrix#cofactor` requires a square matrix.\")\nend\ndet_of_minor = (first_minor(row, column)).determinant\ndet_of_minor * ((-1.0) ** (row + 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The given block must return the desired size of the vector.\n\nThis method is **unsafe**.\n\n```\nVector.build(3) do |buffer|\n  LibSome.fill_buffer_and_return_number_of_elements_filled(buffer)\nend\n```","summary":"<p>Creates a new <code><a href=\"../../Apatite/LinearAlgebra/Vector.html\">Vector</a></code>, allocating an internal buffer with the given <em>capacity</em>, and yielding that buffer.</p>","abstract":false,"args":[{"name":"capacity","doc":null,"default_value":"","external_name":"capacity","restriction":"Int"}],"args_string":"(capacity : Int, &block) : <span class=\"k\">self</span>","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L106","def":{"name":"build","args":[{"name":"capacity","doc":null,"default_value":"","external_name":"capacity","restriction":"Int"}],"double_splat":null,"splat_index":null,"yields":1,"block_arg":null,"return_type":"self","visibility":"Public","body":"vec = Vector.new(capacity)\nvec.size = (yield vec.to_unsafe).to_i\nvec\n"}},{"id":"new(size:Int,value:Float64)-class-method","html_id":"new(size:Int,value:Float64)-class-method","name":"new","doc":"Creates a new `Vector` of the given *size* filled with the same *value* in each position.\n\n```\nVector.new(3, 1.0) # => Vector{1.0, 1.0, 1.0}\n```","summary":"<p>Creates a new <code><a href=\"../../Apatite/LinearAlgebra/Vector.html\">Vector</a></code> of the given <em>size</em> filled with the same <em>value</em> in each position.</p>","abstract":false,"args":[{"name":"size","doc":null,"default_value":"","external_name":"size","restriction":"Int"},{"name":"value","doc":null,"default_value":"","external_name":"value","restriction":"Float64"}],"args_string":"(size : Int, value : Float64)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L63","def":{"name":"new","args":[{"name":"size","doc":null,"default_value":"","external_name":"size","restriction":"Int"},{"name":"value","doc":null,"default_value":"","external_name":"value","restriction":"Float64"}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"_ = allocate\n_.initialize(size, value)\nif _.responds_to?(:finalize)\n  ::GC.add_finalizer(_)\nend\n_\n"}},{"id":"new(initial_capacity:Int)-class-method","html_id":"new(initial_capacity:Int)-class-method","name":"new","doc":"Creates a new empty `Vector` backed by a buffer that is initially\n`initial_capacity` big.\n\nThe *initial_capacity* is useful to avoid unnecessary reallocations\nof the internal buffer in case of growth. If you have an estimate\nof the maximum number of elements an vector will hold, the vector should\nbe initialized with that capacity for improved performance.\n\n```\nvec = Vector.new(5)\nvec.size # => 0\n```","summary":"<p>Creates a new empty <code><a href=\"../../Apatite/LinearAlgebra/Vector.html\">Vector</a></code> backed by a buffer that is initially <code>initial_capacity</code> big.</p>","abstract":false,"args":[{"name":"initial_capacity","doc":null,"default_value":"","external_name":"initial_capacity","restriction":"Int"}],"args_string":"(initial_capacity : Int)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L43","def":{"name":"new","args":[{"name":"initial_capacity","doc":null,"default_value":"","external_name":"initial_capacity","restriction":"Int"}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"_ = allocate\n_.initialize(initial_capacity)\nif _.responds_to?(:finalize)\n  ::GC.add_finalizer(_)\nend\n_\n"}},{"id":"new-class-method","html_id":"new-class-method","name":"new","doc":"Create a new empty `Vector`.","summary":"<p>Create a new empty <code><a href=\"../../Apatite/LinearAlgebra/Vector.html\">Vector</a></code>.</p>","abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L25","def":{"name":"new","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"_ = allocate\n_.initialize\nif _.responds_to?(:finalize)\n  ::GC.add_finalizer(_)\nend\n_\n"}},{"id":"new(size:Int,&block:Int32->Float64)-class-method","html_id":"new(size:Int,&amp;block:Int32-&gt;Float64)-class-method","name":"new","doc":"Creates a new `Vector` of the given *size* and invokes the given block once\nfor each index of `self`, assigning the block's value in that index.\n\n```\nVector.new(3) { |i| (i + 1.0) ** 2.0 } # => Vector{1.0, 4.0, 9.0}\n\nvec = Vector.new(3) { 5.0 }\nvec # => Vector{5.0, 5.0, 5.0}\n```","summary":"<p>Creates a new <code><a href=\"../../Apatite/LinearAlgebra/Vector.html\">Vector</a></code> of the given <em>size</em> and invokes the given block once for each index of <code>self</code>, assigning the block's value in that index.</p>","abstract":false,"args":[{"name":"size","doc":null,"default_value":"","external_name":"size","restriction":"Int"}],"args_string":"(size : Int, &block : Int32 -> Float64)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L87","def":{"name":"new","args":[{"name":"size","doc":null,"default_value":"","external_name":"size","restriction":"Int"}],"double_splat":null,"splat_index":null,"yields":1,"block_arg":{"name":"block","doc":null,"default_value":"","external_name":"block","restriction":"(Int32 -> Float64)"},"return_type":"","visibility":"Public","body":"Vector.build(size) do |buffer|\n  size.to_i.times do |i|\n    buffer[i] = yield i\n  end\n  size\nend"}}],"instance_methods":[{"id":"*(other)-instance-method","html_id":"*(other)-instance-method","name":"*","doc":null,"summary":null,"abstract":false,"args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":""}],"args_string":"(other)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L370","def":{"name":"*","args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"multiply(other)"}},{"id":"+(other)-instance-method","html_id":"+(other)-instance-method","name":"+","doc":null,"summary":null,"abstract":false,"args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":""}],"args_string":"(other)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L362","def":{"name":"+","args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"add(other)"}},{"id":"-(other)-instance-method","html_id":"-(other)-instance-method","name":"-","doc":null,"summary":null,"abstract":false,"args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":""}],"args_string":"(other)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L366","def":{"name":"-","args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"subtract(other)"}},{"id":"<<(value:Float64)-instance-method","html_id":"&lt;&lt;(value:Float64)-instance-method","name":"<<","doc":"Alias for `#push`","summary":"<p>Alias for <code><a href=\"../../Apatite/LinearAlgebra/Vector.html#push%28%2Avalues%3AFloat64%29-instance-method\">#push</a></code></p>","abstract":false,"args":[{"name":"value","doc":null,"default_value":"","external_name":"value","restriction":"Float64"}],"args_string":"(value : Float64)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L349","def":{"name":"<<","args":[{"name":"value","doc":null,"default_value":"","external_name":"value","restriction":"Float64"}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"push(value)"}},{"id":"(other)-instance-method","html_id":"(other)-instance-method","name":"<=>","doc":"Combined comparison operator. Returns *0* if `self` equals *other*, *1* if\n`self` is greater than *other* and *-1* if `self` is smaller than *other*.\n\nIt compares the elements of both vectors in the same position using the\n`<=>` operator.  As soon as one of such comparisons returns a non-zero\nvalue, that result is the return value of the comparison.\n\nIf all elements are equal, the comparison is based on the size of the vectors.\n\n```\nVector{8.0} <=> Vector(1.0, 2.0, 3.0} # => 1\nVector{2.0} <=> Vector{4.0, 2.0, 3.0} # => -1\nVector{1.0, 2.0} <=> Vector{1.0, 2.0} # => 0\n```","summary":"<p>Combined comparison operator.</p>","abstract":false,"args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":""}],"args_string":"(other)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L339","def":{"name":"<=>","args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"min_size = Math.min(size, other.size)\n0.upto(min_size - 1) do |i|\n  n = @buffer[i] <=> other.to_unsafe[i]\n  if n != 0\n    return n\n  end\nend\nsize <=> other.size\n"}},{"id":"==(other:Vector)-instance-method","html_id":"==(other:Vector)-instance-method","name":"==","doc":null,"summary":null,"abstract":false,"args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":"Vector"}],"args_string":"(other : Vector)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L353","def":{"name":"==","args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":"Vector"}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"equals?(other) do |x, y|\n  x == y\nend"}},{"id":"[](start:Int,count:Int)-instance-method","html_id":"[](start:Int,count:Int)-instance-method","name":"[]","doc":"Returns count or less (if there aren't enough) elements starting at the\ngiven start index.\n\nNegative indices count backward from the end of the vector (-1 is the last\nelement). Additionally, an empty vector is returned when the starting index\nfor an element range is at the end of the vector.\n\nRaises `IndexError` if the starting index is out of range.\n\n```\nv = Vector{1.0, 2.0, 3.0, 4.0, 5.0}\nv[1, 3]  # => Vector{2.0, 3.0, 4.0}\nv[6, 10] # raise IndexError\n```","summary":"<p>Returns count or less (if there aren't enough) elements starting at the given start index.</p>","abstract":false,"args":[{"name":"start","doc":null,"default_value":"","external_name":"start","restriction":"Int"},{"name":"count","doc":null,"default_value":"","external_name":"count","restriction":"Int"}],"args_string":"(start : Int, count : Int)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L191","def":{"name":"[]","args":[{"name":"start","doc":null,"default_value":"","external_name":"start","restriction":"Int"},{"name":"count","doc":null,"default_value":"","external_name":"count","restriction":"Int"}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"if count < 0\n  raise(ArgumentError.new(\"Negative count: #{count}\"))\nend\nif start == size\n  return Vector.new\nend\nif start < 0\n  start = start + size\nend\nif 0 <= start && start <= size\nelse\n  raise(IndexError.new)\nend\nif count == 0\n  return Vector.new\nend\ncount = Math.min(count, size - start)\nVector.build(count) do |buffer|\n  buffer.copy_from(@buffer + start, count)\n  count\nend\n"}},{"id":"[](range:Range(Int,Int))-instance-method","html_id":"[](range:Range(Int,Int))-instance-method","name":"[]","doc":"Returns all elements that are within the given range.\n\nNegative indices count backward from the end of the vector (-1 is the last\nelement). Additionally, an empty vector is returned when the starting index\nfor an element range is at the end of the vector.\n\nRaises `IndexError` if the starting index is out of range.\n\n```\nv = Vector{1.0, 2.0, 3.0, 4.0, 5.0}\nv[1..3]  # => Vector{2.0, 3.0, 4.0}\nv[6..10] # raise IndexError\n```","summary":"<p>Returns all elements that are within the given range.</p>","abstract":false,"args":[{"name":"range","doc":null,"default_value":"","external_name":"range","restriction":"Range(Int, Int)"}],"args_string":"(range : Range(Int, Int))","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L173","def":{"name":"[]","args":[{"name":"range","doc":null,"default_value":"","external_name":"range","restriction":"Range(Int, Int)"}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"self[*Indexable.range_to_index_and_count(range, size)]"}},{"id":"[]=(index:Int,count:Int,values:Vector)-instance-method","html_id":"[]=(index:Int,count:Int,values:Vector)-instance-method","name":"[]=","doc":"Replaces a subrange with the elements of the given vector.\n\n```\nvec = Vector{1.0, 2.0, 3.0, 4.0, 5.0}\nvec[1, 3] = Vector{6.0, 7.0, 8.0}\nvec # = Vector{1.0, 6.0, 7.0, 8.0, 5.0}\n\nvec = Vector{1.0, 2.0, 3.0, 4.0, 5.0}\nvec[1, 3] = Vector{6.0, 7.0}\nvec # = Vector{1.0, 6.0, 7.0, 5.0}\n```","summary":"<p>Replaces a subrange with the elements of the given vector.</p>","abstract":false,"args":[{"name":"index","doc":null,"default_value":"","external_name":"index","restriction":"Int"},{"name":"count","doc":null,"default_value":"","external_name":"count","restriction":"Int"},{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":"Vector"}],"args_string":"(index : Int, count : Int, values : Vector)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L297","def":{"name":"[]=","args":[{"name":"index","doc":null,"default_value":"","external_name":"index","restriction":"Int"},{"name":"count","doc":null,"default_value":"","external_name":"count","restriction":"Int"},{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":"Vector"}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"if count < 0\n  raise(ArgumentError.new(\"Negative count: #{count}\"))\nend\nindex = check_index_out_of_bounds(index)\ncount = ((index + count) <= size) ? count : size - index\ndiff = values.size - count\nif diff == 0\n  (@buffer + index).copy_from(values.to_unsafe, values.size)\nelse\n  if diff < 0\n    diff = -diff\n    (@buffer + index).copy_from(values.to_unsafe, values.size)\n    ((@buffer + index) + values.size).move_from((@buffer + index) + count, (size - index) - count)\n    ((@buffer + @size) - diff).clear(diff)\n    @size = @size - diff\n  else\n    resize_to_capacity(Math.pw2ceil(@size + diff))\n    ((@buffer + index) + values.size).move_from((@buffer + index) + count, (size - index) - count)\n    (@buffer + index).copy_from(values.to_unsafe, values.size)\n    @size = @size + diff\n  end\nend\nvalues\n"}},{"id":"[]=(index:Int,count:Int,value)-instance-method","html_id":"[]=(index:Int,count:Int,value)-instance-method","name":"[]=","doc":"Replaces a subrange with a single value. All elements in the range\n`index...index+count` are removed and replaced by a single element\n*value*.\n\nIf *count* is zero, *value* is inserted at *index*.\n\nNegative values of *index* count from the end of the vector.\n\n```\nvec = Vector{1.0, 2.0, 3.0, 4.0, 5.0}\nvec[1, 3] = 6.0\nvec # => Vector{1.0, 6.0, 5.0}\n\nvec = Vector{1.0, 2.0, 3.0, 4.0, 5.0}\nvec[1, 0] = 6.0\nvec # => Vector{1.0, 6.0, 2.0, 3.0, 4.0, 5.0}\n```","summary":"<p>Replaces a subrange with a single value.</p>","abstract":false,"args":[{"name":"index","doc":null,"default_value":"","external_name":"index","restriction":"Int"},{"name":"count","doc":null,"default_value":"","external_name":"count","restriction":"Int"},{"name":"value","doc":null,"default_value":"","external_name":"value","restriction":""}],"args_string":"(index : Int, count : Int, value)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L248","def":{"name":"[]=","args":[{"name":"index","doc":null,"default_value":"","external_name":"index","restriction":"Int"},{"name":"count","doc":null,"default_value":"","external_name":"count","restriction":"Int"},{"name":"value","doc":null,"default_value":"","external_name":"value","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"if count < 0\n  raise(ArgumentError.new(\"Negative count: #{count}\"))\nend\nvalue = value.to_f64\nindex = check_index_out_of_bounds(index)\ncount = ((index + count) <= size) ? count : size - index\ncase count\nwhen 0\n  insert(index, value)\nwhen 1\n  @buffer[index] = value\nelse\n  diff = count - 1\n  ((@buffer + index) + 1).move_from((@buffer + index) + count, (size - index) - count)\n  ((@buffer + @size) - diff).clear(diff)\n  @buffer[index] = value\n  @size = @size - diff\nend\nvalue\n"}},{"id":"[]=(index:Int,value)-instance-method","html_id":"[]=(index:Int,value)-instance-method","name":"[]=","doc":"Sets the given value at the given index.\n\nNegative indices can be used to start counting from the end of the array.\nRaises `IndexError` if trying to set an element outside the array's range.\n\n```\nvec = Vector{1.0, 2.0, 3.0}\nvec[0] = 5.0\np vec # => Vec{5.0, 2.0, 3.0}\n\nvec[3] = 5.0 # raises IndexError\n```","summary":"<p>Sets the given value at the given index.</p>","abstract":false,"args":[{"name":"index","doc":null,"default_value":"","external_name":"index","restriction":"Int"},{"name":"value","doc":null,"default_value":"","external_name":"value","restriction":""}],"args_string":"(index : Int, value)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L226","def":{"name":"[]=","args":[{"name":"index","doc":null,"default_value":"","external_name":"index","restriction":"Int"},{"name":"value","doc":null,"default_value":"","external_name":"value","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"index = check_index_out_of_bounds(index)\n@buffer[index] = value.to_f64\n"}},{"id":"[]=(range:Range(Int,Int),value)-instance-method","html_id":"[]=(range:Range(Int,Int),value)-instance-method","name":"[]=","doc":"Replaces a subrange with a single value.\n\n```\nvec = Vector{1.0, 2.0, 3.0, 4.0, 5.0}\nvec[1..3] = 6.0\nvec # = Vector{1.0, 6.0, 5.0}\n\nvec = Vector{1.0, 2.0, 3.0, 4.0, 5.0}\nvec[1...1] = 6\nvec # = Vector{1.0, 6.0, 2.0, 3.0, 4.0, 5.0}\n```","summary":"<p>Replaces a subrange with a single value.</p>","abstract":false,"args":[{"name":"range","doc":null,"default_value":"","external_name":"range","restriction":"Range(Int, Int)"},{"name":"value","doc":null,"default_value":"","external_name":"value","restriction":""}],"args_string":"(range : Range(Int, Int), value)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L282","def":{"name":"[]=","args":[{"name":"range","doc":null,"default_value":"","external_name":"range","restriction":"Range(Int, Int)"},{"name":"value","doc":null,"default_value":"","external_name":"value","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"self[*Indexable.range_to_index_and_count(range, size)] = value.to_f64"}},{"id":"add(value)-instance-method","html_id":"add(value)-instance-method","name":"add","doc":"When the input is a number, this returns the result of adding\nit to all vector elements. When it's a vector, the vectors\nwill be added together.","summary":"<p>When the input is a number, this returns the result of adding it to all vector elements.</p>","abstract":false,"args":[{"name":"value","doc":null,"default_value":"","external_name":"value","restriction":""}],"args_string":"(value)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L488","def":{"name":"add","args":[{"name":"value","doc":null,"default_value":"","external_name":"value","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"run_binary_op(value) do |a, b|\n  a + b\nend"}},{"id":"angle_from(vector)-instance-method","html_id":"angle_from(vector)-instance-method","name":"angle_from","doc":"Returns the angle between this vector and another in radians.\nIf the vectors are mirrored across their axes this will return `nil`.","summary":"<p>Returns the angle between this vector and another in radians.</p>","abstract":false,"args":[{"name":"vector","doc":null,"default_value":"","external_name":"vector","restriction":""}],"args_string":"(vector)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L440","def":{"name":"angle_from","args":[{"name":"vector","doc":null,"default_value":"","external_name":"vector","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"v = vector.is_a?(Vector) ? vector : Vector.create(vector)\nif size == v.size\nelse\n  raise(\"Cannot compute the angle between vectors with different dimensionality\")\nend\ndot = 0_f64\nmod1 = 0_f64\nmod2 = 0_f64\n(zip(vector)).each do |x, v|\n  dot = dot + (x * v)\n  mod1 = mod1 + (x * x)\n  mod2 = mod2 + (v * v)\nend\nmod1 = Math.sqrt(mod1)\nmod2 = Math.sqrt(mod2)\nif (mod2 * mod2) == 0\n  return 0.0\nend\ntheta = (dot / (mod1 * mod2)).clamp(-1, 1)\nMath.acos(theta)\n"}},{"id":"antiparallel_to?(vector)-instance-method","html_id":"antiparallel_to?(vector)-instance-method","name":"antiparallel_to?","doc":"Returns whether the vectors are antiparallel to each other.","summary":"<p>Returns whether the vectors are antiparallel to each other.</p>","abstract":false,"args":[{"name":"vector","doc":null,"default_value":"","external_name":"vector","restriction":""}],"args_string":"(vector)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L475","def":{"name":"antiparallel_to?","args":[{"name":"vector","doc":null,"default_value":"","external_name":"vector","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"angle = angle_from(vector)\n(angle - Math::PI).abs <= Apatite.precision\n"}},{"id":"augment(elements)-instance-method","html_id":"augment(elements)-instance-method","name":"augment","doc":"Returns a new vector with the provided `elements` concatenated\non the end.","summary":"<p>Returns a new vector with the provided <code>elements</code> concatenated on the end.</p>","abstract":false,"args":[{"name":"elements","doc":null,"default_value":"","external_name":"elements","restriction":""}],"args_string":"(elements)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L556","def":{"name":"augment","args":[{"name":"elements","doc":null,"default_value":"","external_name":"elements","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"elements = elements.is_a?(Vector) ? elements : Vector.create(elements)\nconcat(elements)\n"}},{"id":"chomp(n)-instance-method","html_id":"chomp(n)-instance-method","name":"chomp","doc":"Returns a new vector with the first `n` elements removed from\nthe beginning.","summary":"<p>Returns a new vector with the first <code>n</code> elements removed from the beginning.</p>","abstract":false,"args":[{"name":"n","doc":null,"default_value":"","external_name":"n","restriction":""}],"args_string":"(n)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L541","def":{"name":"chomp","args":[{"name":"n","doc":null,"default_value":"","external_name":"n","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"elements = [] of Float64\neach_with_index do |e, i|\n  if i >= n\n    elements << e\n  end\nend\nVector.create(elements)\n"}},{"id":"clear-instance-method","html_id":"clear-instance-method","name":"clear","doc":"Removes all elements from self.\n\n```\nvec = Vector{1.0, 2.0, 3.0}\nvec.clear # => Vector{}\n```","summary":"<p>Removes all elements from self.</p>","abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L782","def":{"name":"clear","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"@buffer.clear(@size)\n@size = 0\nself\n"}},{"id":"clone-instance-method","html_id":"clone-instance-method","name":"clone","doc":null,"summary":null,"abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L374","def":{"name":"clone","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"Vector.create(@elements.clone)"}},{"id":"concat(other:Vector)-instance-method","html_id":"concat(other:Vector)-instance-method","name":"concat","doc":null,"summary":null,"abstract":false,"args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":"Vector"}],"args_string":"(other : Vector)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L731","def":{"name":"concat","args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":"Vector"}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"other_size = other.size\nnew_size = size + other_size\nif new_size > @capacity\n  resize_to_capacity(Math.pw2ceil(new_size))\nend\n(@buffer + @size).copy_from(other.to_unsafe, other_size)\n@size = new_size\nself\n"}},{"id":"covector-instance-method","html_id":"covector-instance-method","name":"covector","doc":"Creates a single-row matrix from this vector.","summary":"<p>Creates a single-row matrix from this vector.</p>","abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L601","def":{"name":"covector","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"Matrix.row_vector(self)"}},{"id":"cross(*vs)-instance-method","html_id":"cross(*vs)-instance-method","name":"cross","doc":"Returns the cross product of this vector with the others.\n\n```\nv1 = Vector{1.0, 0.0, 0.0}\nv2 = Vector{0.0, 1.0, 0.0}\nv1.cross(v2) => Vector{0.0, 0.0, 1.0}\n```","summary":"<p>Returns the cross product of this vector with the others.</p>","abstract":false,"args":[{"name":"vs","doc":null,"default_value":"","external_name":"vs","restriction":""}],"args_string":"(*vs)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L518","def":{"name":"cross","args":[{"name":"vs","doc":null,"default_value":"","external_name":"vs","restriction":""}],"double_splat":null,"splat_index":0,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"if size >= 2\nelse\n  raise(\"cross product is not defined on vectors of dimension #{size}\")\nend\nif vs.size == (size - 2)\nelse\n  raise(ArgumentError.new(\"wrong number of arguments (#{vs.size} for #{size - 2})\"))\nend\nvs.each do |v|\n  if v.size == size\n  else\n    raise(\"Dimension mismatch. Vectors not all the same size.\")\n  end\nend\ncase size\nwhen 2\n  Vector[-@buffer[1], @buffer[0]]\nwhen 3\n  v = vs[0]\n  Vector[(v[2] * @buffer[1]) - (v[1] * @buffer[2]), (v[0] * @buffer[2]) - (v[2] * @buffer[0]), (v[1] * @buffer[0]) - (v[0] * @buffer[1])]\nelse\nend\n"}},{"id":"distance_from(obj)-instance-method","html_id":"distance_from(obj)-instance-method","name":"distance_from","doc":"Gets this vector's distance from the argument, when considered\na point in space.","summary":"<p>Gets this vector's distance from the argument, when considered a point in space.</p>","abstract":false,"args":[{"name":"obj","doc":null,"default_value":"","external_name":"obj","restriction":""}],"args_string":"(obj)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L629","def":{"name":"distance_from","args":[{"name":"obj","doc":null,"default_value":"","external_name":"obj","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"if object.is_a?(Plane) || object.is_a?(Line)\n  return object.distance_from(self)\nend\nv = elements.is_a?(Vector) ? elements.elements : elements\nif v.size == @elements.size\nelse\n  return nil\nend\nsum = 0\npart = 0\neach_with_index do |x, i|\n  part = x - v[i - 1]\n  sum = sum + (part * part)\nend\nMath.sqrt(sum)\n"}},{"id":"dot(other)-instance-method","html_id":"dot(other)-instance-method","name":"dot","doc":"Get the scalar (dot) product of this vector with `vector`.\n\n[https://en.wikipedia.org/wiki/Scalar_product](https://en.wikipedia.org/wiki/Scalar_product)","summary":"<p>Get the scalar (dot) product of this vector with <code>vector</code>.</p>","abstract":false,"args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":""}],"args_string":"(other)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L574","def":{"name":"dot","args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"other = other.is_a?(Vector) ? other : Vector.create(other)\nif size == other.size\nelse\n  raise(\"Cannot compute the dot product of vectors with different dimensionality\")\nend\nproduct = 0\n(0...size).each do |i|\n  product = product + (self[i] * other[i])\nend\nproduct\n"}},{"id":"e(i)-instance-method","html_id":"e(i)-instance-method","name":"e","doc":"Returns the `ith` element of the vector. Returns `nil` if `i`\nis out of bounds. Indexing starts from 1.","summary":"<p>Returns the <code>ith</code> element of the vector.</p>","abstract":false,"args":[{"name":"i","doc":null,"default_value":"","external_name":"i","restriction":""}],"args_string":"(i)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L426","def":{"name":"e","args":[{"name":"i","doc":null,"default_value":"","external_name":"i","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"(i < 1 || i > @size) ? nil : self[i - 1]"}},{"id":"independent?(*vs)-instance-method","html_id":"independent?(*vs)-instance-method","name":"independent?","doc":"Returns true if all vectors are linearly independent.","summary":"<p>Returns true if all vectors are linearly independent.</p>","abstract":false,"args":[{"name":"vs","doc":null,"default_value":"","external_name":"vs","restriction":""}],"args_string":"(*vs)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L384","def":{"name":"independent?","args":[{"name":"vs","doc":null,"default_value":"","external_name":"vs","restriction":""}],"double_splat":null,"splat_index":0,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"vs.each do |v|\n  if v.size == vs.first.size\n  else\n    raise(\"Dimension mismatch. Vectors not all the same size.\")\n  end\nend\nif vs.size > sv.first.size\n  return false\nend\nMatrix[*vs].rank.equal?(vs.count)\n"}},{"id":"lies_in(plane)-instance-method","html_id":"lies_in(plane)-instance-method","name":"lies_in","doc":"Returns true if the vector is a point on the given plane.","summary":"<p>Returns true if the vector is a point on the given plane.</p>","abstract":false,"args":[{"name":"plane","doc":null,"default_value":"","external_name":"plane","restriction":""}],"args_string":"(plane)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L654","def":{"name":"lies_in","args":[{"name":"plane","doc":null,"default_value":"","external_name":"plane","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"plane.contains(self)"}},{"id":"lies_on(line)-instance-method","html_id":"lies_on(line)-instance-method","name":"lies_on","doc":"Returns true if the vector is a point on the given line","summary":"<p>Returns true if the vector is a point on the given line</p>","abstract":false,"args":[{"name":"line","doc":null,"default_value":"","external_name":"line","restriction":""}],"args_string":"(line)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L649","def":{"name":"lies_on","args":[{"name":"line","doc":null,"default_value":"","external_name":"line","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"line.contains(self)"}},{"id":"log-instance-method","html_id":"log-instance-method","name":"log","doc":"Return a new `Vector` with the log of every item in `self`.","summary":"<p>Return a new <code><a href=\"../../Apatite/LinearAlgebra/Vector.html\">Vector</a></code> with the log of every item in <code>self</code>.</p>","abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L562","def":{"name":"log","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"map do |x|\n  Math.log(x)\nend"}},{"id":"magnitude-instance-method","html_id":"magnitude-instance-method","name":"magnitude","doc":"Returns the magnitude/euclidian norm of this vector.\n\n[https://en.wikipedia.org/wiki/Euclidean_distance](https://en.wikipedia.org/wiki/Euclidean_distance)","summary":"<p>Returns the magnitude/euclidian norm of this vector.</p>","abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L419","def":{"name":"magnitude","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"sum = reduce(0.0) do |acc, e|\n  acc = acc + (e * e)\nend\nMath.sqrt(sum)\n"}},{"id":"map(&block)-instance-method","html_id":"map(&amp;block)-instance-method","name":"map","doc":"Invokes the given block for each element of `self`.","summary":"<p>Invokes the given block for each element of <code>self</code>.</p>","abstract":false,"args":[],"args_string":"(&block)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L379","def":{"name":"map","args":[],"double_splat":null,"splat_index":null,"yields":1,"block_arg":null,"return_type":"","visibility":"Public","body":"Vector.new(size) do |i|\n  yield @buffer[i]\nend"}},{"id":"map!(&block)-instance-method","html_id":"map!(&amp;block)-instance-method","name":"map!","doc":"Invokes the given block for each element of `self`, replacing the element\nwith the value returned by the block. Returns `self`.\n\n```\nvec = Vector{1.0, 2.0, 3.0}\nvec.map! { |x| x * x }\na # => Vector{1.0, 4.0, 9.0}\n```","summary":"<p>Invokes the given block for each element of <code>self</code>, replacing the element with the value returned by the block.</p>","abstract":false,"args":[],"args_string":"(&block)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L400","def":{"name":"map!","args":[],"double_splat":null,"splat_index":null,"yields":1,"block_arg":null,"return_type":"","visibility":"Public","body":"@buffer.map!(size) do |e|\n  yield e\nend\nself\n"}},{"id":"map_with_index(&block)-instance-method","html_id":"map_with_index(&amp;block)-instance-method","name":"map_with_index","doc":"Optimized version of `Enumerable#map_with_index`.","summary":"<p>Optimized version of <code>Enumerable#map_with_index</code>.</p>","abstract":false,"args":[],"args_string":"(&block)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L406","def":{"name":"map_with_index","args":[],"double_splat":null,"splat_index":null,"yields":2,"block_arg":null,"return_type":"","visibility":"Public","body":"Vector.new(size) do |i|\n  yield @buffer[i], i\nend"}},{"id":"map_with_index!(&block)-instance-method","html_id":"map_with_index!(&amp;block)-instance-method","name":"map_with_index!","doc":"Like `map_with_index`, but mutates `self` instead of allocating a new object.","summary":"<p>Like <code><a href=\"../../Apatite/LinearAlgebra/Vector.html#map_with_index%28%26block%29-instance-method\">#map_with_index</a></code>, but mutates <code>self</code> instead of allocating a new object.</p>","abstract":false,"args":[],"args_string":"(&block)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L411","def":{"name":"map_with_index!","args":[],"double_splat":null,"splat_index":null,"yields":2,"block_arg":null,"return_type":"","visibility":"Public","body":"to_unsafe.map_with_index!(size) do |e, i|\n  yield e, i\nend\nself\n"}},{"id":"max-instance-method","html_id":"max-instance-method","name":"max","doc":"Returns the (absolute) largest element in this vector.","summary":"<p>Returns the (absolute) largest element in this vector.</p>","abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L589","def":{"name":"max","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"reduce do |acc, i|\n  i.abs > acc.abs ? i : acc\nend"}},{"id":"max_index-instance-method","html_id":"max_index-instance-method","name":"max_index","doc":"Gets the index of the largest element in this vector.","summary":"<p>Gets the index of the largest element in this vector.</p>","abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L594","def":{"name":"max_index","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"idx = 0\neach_with_index do |e, i|\n  idx = e.abs > self[idx].abs ? i : idx\nend\nidx\n"}},{"id":"multiply(value)-instance-method","html_id":"multiply(value)-instance-method","name":"multiply","doc":"When the input is a number, this returns the result of multiplying\nit to all vector elements. When it's a vector, the vectors\nwill be element-wise multiplied.","summary":"<p>When the input is a number, this returns the result of multiplying it to all vector elements.</p>","abstract":false,"args":[{"name":"value","doc":null,"default_value":"","external_name":"value","restriction":""}],"args_string":"(value)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L502","def":{"name":"multiply","args":[{"name":"value","doc":null,"default_value":"","external_name":"value","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"run_binary_op(value) do |a, b|\n  a * b\nend"}},{"id":"parallel_to?(vector)-instance-method","html_id":"parallel_to?(vector)-instance-method","name":"parallel_to?","doc":"Returns whether the vectors are parallel to each other.","summary":"<p>Returns whether the vectors are parallel to each other.</p>","abstract":false,"args":[{"name":"vector","doc":null,"default_value":"","external_name":"vector","restriction":""}],"args_string":"(vector)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L469","def":{"name":"parallel_to?","args":[{"name":"vector","doc":null,"default_value":"","external_name":"vector","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"angle = angle_from(vector)\nangle <= Apatite.precision\n"}},{"id":"perpendicular_to?(vector)-instance-method","html_id":"perpendicular_to?(vector)-instance-method","name":"perpendicular_to?","doc":"Returns whether the vectors are perpendicular to each other.","summary":"<p>Returns whether the vectors are perpendicular to each other.</p>","abstract":false,"args":[{"name":"vector","doc":null,"default_value":"","external_name":"vector","restriction":""}],"args_string":"(vector)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L481","def":{"name":"perpendicular_to?","args":[{"name":"vector","doc":null,"default_value":"","external_name":"vector","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"(dot(vector)).abs <= Apatite.precision"}},{"id":"pretty_print(pp):Nil-instance-method","html_id":"pretty_print(pp):Nil-instance-method","name":"pretty_print","doc":null,"summary":null,"abstract":false,"args":[{"name":"pp","doc":null,"default_value":"","external_name":"pp","restriction":""}],"args_string":"(pp) : Nil","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L754","def":{"name":"pretty_print","args":[{"name":"pp","doc":null,"default_value":"","external_name":"pp","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"Nil","visibility":"Public","body":"pp.list(\"Vector{\", self, \"}\")"}},{"id":"product-instance-method","html_id":"product-instance-method","name":"product","doc":"Get the product of all elements in this vector.","summary":"<p>Get the product of all elements in this vector.</p>","abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L567","def":{"name":"product","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"reduce do |acc, v|\n  acc = acc * v\nend"}},{"id":"push(*values:Float64)-instance-method","html_id":"push(*values:Float64)-instance-method","name":"push","doc":null,"summary":null,"abstract":false,"args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":"Float64"}],"args_string":"(*values : Float64)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L665","def":{"name":"push","args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":"Float64"}],"double_splat":null,"splat_index":0,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"new_size = @size + values.size\nif new_size > @capacity\n  resize_to_capacity(Math.pw2ceil(new_size))\nend\nvalues.each_with_index do |value, i|\n  @buffer[@size + i] = value\nend\n@size = new_size\nself\n"}},{"id":"push(value:Float64)-instance-method","html_id":"push(value:Float64)-instance-method","name":"push","doc":null,"summary":null,"abstract":false,"args":[{"name":"value","doc":null,"default_value":"","external_name":"value","restriction":"Float64"}],"args_string":"(value : Float64)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L658","def":{"name":"push","args":[{"name":"value","doc":null,"default_value":"","external_name":"value","restriction":"Float64"}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"check_needs_resize\n@buffer[@size] = value\n@size = @size + 1\nself\n"}},{"id":"reflection_in(object)-instance-method","html_id":"reflection_in(object)-instance-method","name":"reflection_in","doc":"Returns the result of reflecting the point in the given `object`\n(point, line, or plane).","summary":"<p>Returns the result of reflecting the point in the given <code>object</code> (point, line, or plane).</p>","abstract":false,"args":[{"name":"object","doc":null,"default_value":"","external_name":"object","restriction":""}],"args_string":"(object)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L684","def":{"name":"reflection_in","args":[{"name":"object","doc":null,"default_value":"","external_name":"object","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"if object.is_a?(Plane) || object.is_a?(Line)\n  p = @elements.dup\n  c = (object.point_closest_to(p)).elements\n  return Vector.create([C[0] + (C[0] - P[0]), C[1] + (C[1] - P[1]), C[2] + (C[2] - (P[2] || 0))])\nend\nq = object.is_a?(Vector) ? object.elements : object\nif @elements.size == q.size\nelse\n  return nil\nend\nmap_with_index do |x, i|\n  q[i - 1] + (q[i - 1] - x)\nend\n"}},{"id":"rotate(t,object)-instance-method","html_id":"rotate(t,object)-instance-method","name":"rotate","doc":"Rotates the vector about the given `object`. The object should\nbe a point if the vector is 2D, and a line if it is 3D. Be\ncareful with line directions!","summary":"<p>Rotates the vector about the given <code>object</code>.</p>","abstract":false,"args":[{"name":"t","doc":null,"default_value":"","external_name":"t","restriction":""},{"name":"object","doc":null,"default_value":"","external_name":"object","restriction":""}],"args_string":"(t, object)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L678","def":{"name":"rotate","args":[{"name":"t","doc":null,"default_value":"","external_name":"t","restriction":""},{"name":"object","doc":null,"default_value":"","external_name":"object","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":""}},{"id":"round-instance-method","html_id":"round-instance-method","name":"round","doc":"Gets the result of rounding the elements of the vector.","summary":"<p>Gets the result of rounding the elements of the vector.</p>","abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L612","def":{"name":"round","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"map do |x|\n  x.round\nend"}},{"id":"set_elements(elements)-instance-method","html_id":"set_elements(elements)-instance-method","name":"set_elements","doc":null,"summary":null,"abstract":false,"args":[{"name":"elements","doc":null,"default_value":"","external_name":"elements","restriction":""}],"args_string":"(elements)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L726","def":{"name":"set_elements","args":[{"name":"elements","doc":null,"default_value":"","external_name":"elements","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"@elements = elements.is_a?(Vector) ? elements.elements : elements\nself\n"}},{"id":"sigmoid-instance-method","html_id":"sigmoid-instance-method","name":"sigmoid","doc":"Sums the numbers in the vector and returns a sigmoid value\nacross the whole vector.","summary":"<p>Sums the numbers in the vector and returns a sigmoid value across the whole vector.</p>","abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L707","def":{"name":"sigmoid","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"LinearAlgebra.sigmoid(sum)"}},{"id":"size:Int32-instance-method","html_id":"size:Int32-instance-method","name":"size","doc":"Returns the number of elements in the vector","summary":"<p>Returns the number of elements in the vector</p>","abstract":false,"args":[],"args_string":" : Int32","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L24","def":{"name":"size","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"Int32","visibility":"Public","body":"@size"}},{"id":"snap_to(value)-instance-method","html_id":"snap_to(value)-instance-method","name":"snap_to","doc":"Returns a copy of the vector with elements set to `value` if\nthey differ from it by less than `Apetite.precision`","summary":"<p>Returns a copy of the vector with elements set to <code>value</code> if they differ from it by less than <code>Apetite.precision</code></p>","abstract":false,"args":[{"name":"value","doc":null,"default_value":"","external_name":"value","restriction":""}],"args_string":"(value)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L623","def":{"name":"snap_to","args":[{"name":"value","doc":null,"default_value":"","external_name":"value","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"map do |y|\n  (y - x).abs <= Apetite.precision ? value : y\nend"}},{"id":"subtract(value)-instance-method","html_id":"subtract(value)-instance-method","name":"subtract","doc":"When the input is a number, this returns the result of subtracting\nit to all vector elements. 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If they are 2D, a zero\nz-component is added.","summary":"<p>Utility to make sure vectors are 3D.</p>","abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L713","def":{"name":"to_3d","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"v = dup\ncase v.elements.size\nwhen 3\n  break\nwhen 2\n  v.elements.push(0)\nelse\n  return nil\nend\nreturn v\n"}},{"id":"to_a-instance-method","html_id":"to_a-instance-method","name":"to_a","doc":null,"summary":null,"abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L744","def":{"name":"to_a","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"Array(Float64).new(size) do |i|\n  self[i]\nend"}},{"id":"to_diagonal_matrix-instance-method","html_id":"to_diagonal_matrix-instance-method","name":"to_diagonal_matrix","doc":"Returns a diagonal `Matrix` with the vectors elements as its\ndiagonal elements.","summary":"<p>Returns a diagonal <code><a href=\"../../Apatite/LinearAlgebra/Matrix.html\">Matrix</a></code> with the vectors elements as its diagonal elements.</p>","abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L607","def":{"name":"to_diagonal_matrix","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"Matrix::Diagonal.new(elements)"}},{"id":"to_s(io)-instance-method","html_id":"to_s(io)-instance-method","name":"to_s","doc":null,"summary":null,"abstract":false,"args":[{"name":"io","doc":null,"default_value":"","external_name":"io","restriction":""}],"args_string":"(io)","source_link":"https://github.com/watzon/apatite/blob/49a30afcc07bc5354f335c6a6fb5244ed514b63b/src/apatite/linear_algebra/vector.cr#L748","def":{"name":"to_s","args":[{"name":"io","doc":null,"default_value":"","external_name":"io","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"io << \"{\"\njoin(\", \", io, &.inspect(io))\nio << \"}\"\n"}},{"id":"to_unit_vector-instance-method","html_id":"to_unit_vector-instance-method","name":"to_unit_vector","doc":"Returns a new vector created by normalizing this one\nto have a magnitude of `1`. 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\ No newline at end of file
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other.column_count)\n"}},{"id":"+(vec:Indexable)-instance-method","html_id":"+(vec:Indexable)-instance-method","name":"+","doc":null,"summary":null,"abstract":false,"args":[{"name":"vec","doc":null,"default_value":"","external_name":"vec","restriction":"Indexable"}],"args_string":"(vec : Indexable)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/matrix.cr#L188","def":{"name":"+","args":[{"name":"vec","doc":null,"default_value":"","external_name":"vec","restriction":"Indexable"}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"vec = vec.is_a?(Vector) ? vec : Vector.create(vec)\nself + (column_vector(vec))\n"}},{"id":"-(vec:Indexable)-instance-method","html_id":"-(vec:Indexable)-instance-method","name":"-","doc":null,"summary":null,"abstract":false,"args":[{"name":"vec","doc":null,"default_value":"","external_name":"vec","restriction":"Indexable"}],"args_string":"(vec : Indexable)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/matrix.cr#L205","def":{"name":"-","args":[{"name":"vec","doc":null,"default_value":"","external_name":"vec","restriction":"Indexable"}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"vec = vec.is_a?(Vector) ? vec : Vector.create(vec)\nself + (column_vector(vec))\n"}},{"id":"-(other:Matrix)-instance-method","html_id":"-(other:Matrix)-instance-method","name":"-","doc":null,"summary":null,"abstract":false,"args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":"Matrix"}],"args_string":"(other : Matrix)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/matrix.cr#L193","def":{"name":"-","args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":"Matrix"}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"if column_count != other.column_count\n  raise(\"Dimension mismatch\")\nend\nrows = Array.new(row_count) do |i|\n  Vector.new(other.column_count) do |j|\n    self[i, j] - other[i, j]\n  end\nend\nreturn Matrix.new(rows, other.column_count)\n"}},{"id":"/(other:Matrix)-instance-method","html_id":"/(other:Matrix)-instance-method","name":"/","doc":null,"summary":null,"abstract":false,"args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":"Matrix"}],"args_string":"(other : Matrix)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/matrix.cr#L210","def":{"name":"/","args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":"Matrix"}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"self * other.inverse"}},{"id":"/(vec:Indexable)-instance-method","html_id":"/(vec:Indexable)-instance-method","name":"/","doc":null,"summary":null,"abstract":false,"args":[{"name":"vec","doc":null,"default_value":"","external_name":"vec","restriction":"Indexable"}],"args_string":"(vec : Indexable)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/matrix.cr#L214","def":{"name":"/","args":[{"name":"vec","doc":null,"default_value":"","external_name":"vec","restriction":"Indexable"}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"rows = self.rows.map do |row|\n  row.map do |e|\n    e / other\n  end\nend\nreturn new_matrix(rows, column_count)\n"}},{"id":"==(other:Matrix)-instance-method","html_id":"==(other:Matrix)-instance-method","name":"==","doc":null,"summary":null,"abstract":false,"args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":"Matrix"}],"args_string":"(other : Matrix)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/matrix.cr#L221","def":{"name":"==","args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":"Matrix"}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"if (Matrix === other) && (column_count == other.column_count)\nelse\n  return false\nend\nrows == other.rows\n"}},{"id":"[](row:Int,col:Int)-instance-method","html_id":"[](row:Int,col:Int)-instance-method","name":"[]","doc":"Returns element `(row, col)` of the matrix. Throws error on index error.","summary":"<p>Returns element <code>(row, col)</code> of the matrix.</p>","abstract":false,"args":[{"name":"row","doc":null,"default_value":"","external_name":"row","restriction":"Int"},{"name":"col","doc":null,"default_value":"","external_name":"col","restriction":"Int"}],"args_string":"(row : Int, col : Int)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/matrix.cr#L228","def":{"name":"[]","args":[{"name":"row","doc":null,"default_value":"","external_name":"row","restriction":"Int"},{"name":"col","doc":null,"default_value":"","external_name":"col","restriction":"Int"}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"self[row][col]"}},{"id":"[]?(row:Int,col:Int)-instance-method","html_id":"[]?(row:Int,col:Int)-instance-method","name":"[]?","doc":"Returns element `(row, col)` of the matrix, or nil if the index is not found.","summary":"<p>Returns element <code>(row, col)</code> of the matrix, or nil if the index is not found.</p>","abstract":false,"args":[{"name":"row","doc":null,"default_value":"","external_name":"row","restriction":"Int"},{"name":"col","doc":null,"default_value":"","external_name":"col","restriction":"Int"}],"args_string":"(row : Int, col : Int)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/matrix.cr#L233","def":{"name":"[]?","args":[{"name":"row","doc":null,"default_value":"","external_name":"row","restriction":"Int"},{"name":"col","doc":null,"default_value":"","external_name":"col","restriction":"Int"}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"v = fetch(row) do\n  nil\nend\nif v.nil?\nelse\n  v[col]?\nend\n"}},{"id":"adjugate-instance-method","html_id":"adjugate-instance-method","name":"adjugate","doc":"Returns the adjugate of the matrix.","summary":"<p>Returns the adjugate of the matrix.</p>","abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/matrix.cr#L239","def":{"name":"adjugate","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"if square?\nelse\n  raise(\"Dimention mismatch: `Matrix#adjugate` requires a square matrix.\")\nend\nMatrix.build(row_count, column_count) do |row, column|\n  cofactor(column, row)\nend\n"}},{"id":"cofactor(row,column)-instance-method","html_id":"cofactor(row,column)-instance-method","name":"cofactor","doc":"Returns the (row, column) cofactor which is obtained by multiplying the first minor by (-1)**(row + column)","summary":"<p>Returns the (row, column) cofactor which is obtained by multiplying the first minor by (-1)**(row + column)</p>","abstract":false,"args":[{"name":"row","doc":null,"default_value":"","external_name":"row","restriction":""},{"name":"column","doc":null,"default_value":"","external_name":"column","restriction":""}],"args_string":"(row, column)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/matrix.cr#L247","def":{"name":"cofactor","args":[{"name":"row","doc":null,"default_value":"","external_name":"row","restriction":""},{"name":"column","doc":null,"default_value":"","external_name":"column","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"if empty?\n  raise(\"cofactor of empty matrix is not defined\")\nend\nif square?\nelse\n  raise(\"Dimention mismatch: `Matrix#cofactor` requires a square matrix.\")\nend\ndet_of_minor = (first_minor(row, column)).determinant\ndet_of_minor * ((-1.0) ** (row + column))\n"}},{"id":"column(j,&block)-instance-method","html_id":"column(j,&amp;block)-instance-method","name":"column","doc":"Iterates over the specified column in the matrix, returning the Vector's items.","summary":"<p>Iterates over the specified column in the matrix, returning the Vector's items.</p>","abstract":false,"args":[{"name":"j","doc":null,"default_value":"","external_name":"j","restriction":""}],"args_string":"(j, &block)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/matrix.cr#L274","def":{"name":"column","args":[{"name":"j","doc":null,"default_value":"","external_name":"j","restriction":""}],"double_splat":null,"splat_index":null,"yields":1,"block_arg":null,"return_type":"","visibility":"Public","body":"if j >= column_count || j < (-column_count)\n  return self\nend\nrow_count.times do |i|\n  yield rows[i][j]\nend\nself\n"}},{"id":"column(j)-instance-method","html_id":"column(j)-instance-method","name":"column","doc":"Returns column vector number `j` of the matrix as a `Vector` (starting at 0 like an array).","summary":"<p>Returns column vector number <code>j</code> of the matrix as a <code><a href=\"../../Apatite/LinearAlgebra/Vector.html\">Vector</a></code> (starting at 0 like an array).</p>","abstract":false,"args":[{"name":"j","doc":null,"default_value":"","external_name":"j","restriction":""}],"args_string":"(j)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/matrix.cr#L265","def":{"name":"column","args":[{"name":"j","doc":null,"default_value":"","external_name":"j","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"if j >= column_count || j < (-column_count)\n  raise(\"Index out of range\")\nend\ncol = Array(Float64).new(row_count) do |i|\n  rows[i][j]\nend\nVector.create(col)\n"}},{"id":"column?(j)-instance-method","html_id":"column?(j)-instance-method","name":"column?","doc":"Returns column vector number `j` of the matrix as a `Vector` (starting at 0 like an array).","summary":"<p>Returns column vector number <code>j</code> of the matrix as a <code><a href=\"../../Apatite/LinearAlgebra/Vector.html\">Vector</a></code> (starting at 0 like an array).</p>","abstract":false,"args":[{"name":"j","doc":null,"default_value":"","external_name":"j","restriction":""}],"args_string":"(j)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/matrix.cr#L256","def":{"name":"column?","args":[{"name":"j","doc":null,"default_value":"","external_name":"j","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"if j >= column_count || j < (-column_count)\n  return nil\nend\ncol = Array(Float64).new(row_count) do |i|\n  rows[i][j]\nend\nVector.create(col)\n"}},{"id":"column_count:Int32-instance-method","html_id":"column_count:Int32-instance-method","name":"column_count","doc":null,"summary":null,"abstract":false,"args":[],"args_string":" : Int32","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/matrix.cr#L11","def":{"name":"column_count","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"Int32","visibility":"Public","body":"@column_count"}},{"id":"column_vectors-instance-method","html_id":"column_vectors-instance-method","name":"column_vectors","doc":"Returns an array of the column vectors of the matrix. See `Vector`.","summary":"<p>Returns an array of the column vectors of the matrix.</p>","abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/matrix.cr#L283","def":{"name":"column_vectors","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"Array(Vector).new(column_count) do |i|\n  column(i)\nend"}},{"id":"determinant-instance-method","html_id":"determinant-instance-method","name":"determinant","doc":null,"summary":null,"abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/matrix.cr#L354","def":{"name":"determinant","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"if square?\nelse\n  raise(\"Dimention mismatch: `Matrix#determinant` requires a square matrix.\")\nend\nm = rows\ncase row_count\nwhen 0\n  +1\nwhen 1\n  +m[0][0]\nwhen 2\n  ((+m[0][0]) * m[1][1]) - (m[0][1] * m[1][0])\nwhen 3\n  m0, m1, m2 = m\n  (((((((+m0[0]) * m1[1]) * m2[2]) - ((m0[0] * m1[2]) * m2[1])) - ((m0[1] * m1[0]) * m2[2])) + ((m0[1] * m1[2]) * m2[0])) + ((m0[2] * m1[0]) * m2[1])) - ((m0[2] * m1[1]) * m2[0])\nwhen 4\n  m0, m1, m2, m3 = m\n  ((((((((((((((((((((((((((+m0[0]) * m1[1]) * m2[2]) * m3[3]) - (((m0[0] * m1[1]) * m2[3]) * m3[2])) - (((m0[0] * m1[2]) * m2[1]) * m3[3])) + (((m0[0] * m1[2]) * m2[3]) * m3[1])) + (((m0[0] * m1[3]) * m2[1]) * m3[2])) - (((m0[0] * m1[3]) * m2[2]) * m3[1])) - (((m0[1] * m1[0]) * m2[2]) * m3[3])) + (((m0[1] * m1[0]) * m2[3]) * m3[2])) + (((m0[1] * m1[2]) * m2[0]) * m3[3])) - (((m0[1] * m1[2]) * m2[3]) * m3[0])) - (((m0[1] * m1[3]) * m2[0]) * m3[2])) + (((m0[1] * m1[3]) * m2[2]) * m3[0])) + (((m0[2] * m1[0]) * m2[1]) * m3[3])) - (((m0[2] * m1[0]) * m2[3]) * m3[1])) - (((m0[2] * m1[1]) * m2[0]) * m3[3])) + (((m0[2] * m1[1]) * m2[3]) * m3[0])) + (((m0[2] * m1[3]) * m2[0]) * m3[1])) - (((m0[2] * m1[3]) * m2[1]) * m3[0])) - (((m0[3] * m1[0]) * m2[1]) * m3[2])) + (((m0[3] * m1[0]) * m2[2]) * m3[1])) + (((m0[3] * m1[1]) * m2[0]) * m3[2])) - (((m0[3] * m1[1]) * m2[2]) * m3[0])) - (((m0[3] * m1[2]) * m2[0]) * m3[1])) + (((m0[3] * m1[2]) * m2[1]) * m3[0])\nelse\n  determinant_bareiss\nend\n"}},{"id":"first_minor(row,column)-instance-method","html_id":"first_minor(row,column)-instance-method","name":"first_minor","doc":null,"summary":null,"abstract":false,"args":[{"name":"row","doc":null,"default_value":"","external_name":"row","restriction":""},{"name":"column","doc":null,"default_value":"","external_name":"column","restriction":""}],"args_string":"(row, column)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/matrix.cr#L429","def":{"name":"first_minor","args":[{"name":"row","doc":null,"default_value":"","external_name":"row","restriction":""},{"name":"column","doc":null,"default_value":"","external_name":"column","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"if empty?\n  raise(\"first_minor of empty matrix is not defined\")\nend\nif 0 <= row && row < row_count\nelse\n  raise(ArgumentError.new(\"invalid row (#{row.inspect} for 0..#{row_count - 1})\"))\nend\nif 0 <= column && column < column_count\nelse\n  raise(ArgumentError.new(\"invalid column (#{column.inspect} for 0..#{column_count - 1})\"))\nend\narrays = to_a.map(&.to_a)\narrays.delete_at(row)\narrays.each do |array|\n  array.delete_at(column)\nend\nMatrix.new(arrays, column_count - 1)\n"}},{"id":"inverse-instance-method","html_id":"inverse-instance-method","name":"inverse","doc":"Returns the inverse of the matrix.","summary":"<p>Returns the inverse of the matrix.</p>","abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/matrix.cr#L304","def":{"name":"inverse","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"if square?\nelse\n  if square?\n  else\n    raise(\"Dimention mismatch: `Matrix#inverse` requires a square matrix.\")\n  end\nend\n(Matrix.identity(row_count)).inverse_from(self)\n"}},{"id":"laplace_expansion(*,row=nil,column=nil)-instance-method","html_id":"laplace_expansion(*,row=nil,column=nil)-instance-method","name":"laplace_expansion","doc":"Returns the Laplace expansion along given row or column.","summary":"<p>Returns the Laplace expansion along given row or column.</p>","abstract":false,"args":[{"name":"","doc":null,"default_value":"","external_name":"","restriction":""},{"name":"row","doc":null,"default_value":"nil","external_name":"row","restriction":""},{"name":"column","doc":null,"default_value":"nil","external_name":"column","restriction":""}],"args_string":"(*, row = <span class=\"n\">nil</span>, column = <span class=\"n\">nil</span>)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/matrix.cr#L450","def":{"name":"laplace_expansion","args":[{"name":"","doc":null,"default_value":"","external_name":"","restriction":""},{"name":"row","doc":null,"default_value":"nil","external_name":"row","restriction":""},{"name":"column","doc":null,"default_value":"nil","external_name":"column","restriction":""}],"double_splat":null,"splat_index":0,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"num = row || column\nif (!num) || (row && column)\n  raise(ArgumentError.new(\"exactly one the row or column arguments must be specified\"))\nend\nif square?\nelse\n  raise(\"Dimention mismatch: `Matrix#determinant` requires a square matrix.\")\nend\nif empty?\n  raise(\"laplace_expansion of empty matrix is not defined\")\nend\nif 0 <= num && num < row_count\nelse\n  raise(ArgumentError.new(\"invalid num (#{num.inspect} for 0..#{row_count - 1})\"))\nend\nif row\n  (row(num)).map_with_index do |e, k|\n    e * (cofactor(num, k))\n  end.reduce(&.+)\nelse\n  (column(num)).map_with_index do |e, k|\n    e * (cofactor(k, num))\n  end.reduce(&.+)\nend\n"}},{"id":"pretty_print(pp):Nil-instance-method","html_id":"pretty_print(pp):Nil-instance-method","name":"pretty_print","doc":null,"summary":null,"abstract":false,"args":[{"name":"pp","doc":null,"default_value":"","external_name":"pp","restriction":""}],"args_string":"(pp) : Nil","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/matrix.cr#L516","def":{"name":"pretty_print","args":[{"name":"pp","doc":null,"default_value":"","external_name":"pp","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"Nil","visibility":"Public","body":"pp.list(\"[\", self, \"]\") do |vec|\n  pp.group do\n    vec.to_a.pretty_print(pp)\n  end\nend"}},{"id":"row(i,&block)-instance-method","html_id":"row(i,&amp;block)-instance-method","name":"row","doc":null,"summary":null,"abstract":false,"args":[{"name":"i","doc":null,"default_value":"","external_name":"i","restriction":""}],"args_string":"(i, &block)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/matrix.cr#L475","def":{"name":"row","args":[{"name":"i","doc":null,"default_value":"","external_name":"i","restriction":""}],"double_splat":null,"splat_index":null,"yields":0,"block_arg":{"name":"block","doc":null,"default_value":"","external_name":"block","restriction":""},"return_type":"","visibility":"Public","body":"(@rows.fetch(i) do\n  return self\nend).each(&block)\nself\n"}},{"id":"row(i)-instance-method","html_id":"row(i)-instance-method","name":"row","doc":null,"summary":null,"abstract":false,"args":[{"name":"i","doc":null,"default_value":"","external_name":"i","restriction":""}],"args_string":"(i)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/matrix.cr#L480","def":{"name":"row","args":[{"name":"i","doc":null,"default_value":"","external_name":"i","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"Vector.create(rows.fetch(i) do\n  [] of Float64\nend)"}},{"id":"row_count:Int32-instance-method","html_id":"row_count:Int32-instance-method","name":"row_count","doc":null,"summary":null,"abstract":false,"args":[],"args_string":" : 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A `range`\ncan optionally be passed in if you want to limit the random numbers\nto a given range.","summary":"<p>Creates a new <code><a href=\"../../Apatite/LinearAlgebra/Vector.html\">Vector</a></code> of size <code>n</code> filled with random numbers.</p>","abstract":false,"args":[{"name":"n","doc":null,"default_value":"","external_name":"n","restriction":""},{"name":"range","doc":null,"default_value":"nil","external_name":"range","restriction":""}],"args_string":"(n, range = <span class=\"n\">nil</span>)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L129","def":{"name":"random","args":[{"name":"n","doc":null,"default_value":"","external_name":"n","restriction":""},{"name":"range","doc":null,"default_value":"nil","external_name":"range","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"vec = Vector.new(n)\nn.times do\n  vec.push(rand((range || -1e+1)..1e+1))\nend\nvec\n"}},{"id":"zeros(n)-class-method","html_id":"zeros(n)-class-method","name":"zeros","doc":"Create a new vector of size `n` filled with zeros.","summary":"<p>Create a new vector of size <code>n</code> filled with zeros.</p>","abstract":false,"args":[{"name":"n","doc":null,"default_value":"","external_name":"n","restriction":""}],"args_string":"(n)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L147","def":{"name":"zeros","args":[{"name":"n","doc":null,"default_value":"","external_name":"n","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"Vector.new(n, 0.0)"}}],"constructors":[{"id":"build(capacity:Int,&block):self-class-method","html_id":"build(capacity:Int,&amp;block):self-class-method","name":"build","doc":"Creates a new `Vector`, allocating an internal buffer with the given *capacity*,\nand yielding that buffer. 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If you have an estimate\nof the maximum number of elements an vector will hold, the vector should\nbe initialized with that capacity for improved performance.\n\n```\nvec = Vector.new(5)\nvec.size # => 0\n```","summary":"<p>Creates a new empty <code><a href=\"../../Apatite/LinearAlgebra/Vector.html\">Vector</a></code> backed by a buffer that is initially <code>initial_capacity</code> big.</p>","abstract":false,"args":[{"name":"initial_capacity","doc":null,"default_value":"","external_name":"initial_capacity","restriction":"Int"}],"args_string":"(initial_capacity : Int)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L43","def":{"name":"new","args":[{"name":"initial_capacity","doc":null,"default_value":"","external_name":"initial_capacity","restriction":"Int"}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"_ = allocate\n_.initialize(initial_capacity)\nif _.responds_to?(:finalize)\n  ::GC.add_finalizer(_)\nend\n_\n"}},{"id":"new-class-method","html_id":"new-class-method","name":"new","doc":"Create a new empty `Vector`.","summary":"<p>Create a new empty <code><a href=\"../../Apatite/LinearAlgebra/Vector.html\">Vector</a></code>.</p>","abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L25","def":{"name":"new","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"_ = allocate\n_.initialize\nif _.responds_to?(:finalize)\n  ::GC.add_finalizer(_)\nend\n_\n"}},{"id":"new(size:Int,&block:Int32->Float64)-class-method","html_id":"new(size:Int,&amp;block:Int32-&gt;Float64)-class-method","name":"new","doc":"Creates a new `Vector` of the given *size* and invokes the given block once\nfor each index of `self`, assigning the block's value in that index.\n\n```\nVector.new(3) { |i| (i + 1.0) ** 2.0 } # => Vector{1.0, 4.0, 9.0}\n\nvec = Vector.new(3) { 5.0 }\nvec # => Vector{5.0, 5.0, 5.0}\n```","summary":"<p>Creates a new <code><a href=\"../../Apatite/LinearAlgebra/Vector.html\">Vector</a></code> of the given <em>size</em> and invokes the given block once for each index of <code>self</code>, assigning the block's value in that index.</p>","abstract":false,"args":[{"name":"size","doc":null,"default_value":"","external_name":"size","restriction":"Int"}],"args_string":"(size : Int, &block : Int32 -> Float64)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L87","def":{"name":"new","args":[{"name":"size","doc":null,"default_value":"","external_name":"size","restriction":"Int"}],"double_splat":null,"splat_index":null,"yields":1,"block_arg":{"name":"block","doc":null,"default_value":"","external_name":"block","restriction":"(Int32 -> Float64)"},"return_type":"","visibility":"Public","body":"Vector.build(size) do |buffer|\n  size.to_i.times do |i|\n    buffer[i] = yield i\n  end\n  size\nend"}}],"instance_methods":[{"id":"*(other)-instance-method","html_id":"*(other)-instance-method","name":"*","doc":null,"summary":null,"abstract":false,"args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":""}],"args_string":"(other)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L370","def":{"name":"*","args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"multiply(other)"}},{"id":"+(other)-instance-method","html_id":"+(other)-instance-method","name":"+","doc":null,"summary":null,"abstract":false,"args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":""}],"args_string":"(other)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L362","def":{"name":"+","args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"add(other)"}},{"id":"-(other)-instance-method","html_id":"-(other)-instance-method","name":"-","doc":null,"summary":null,"abstract":false,"args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":""}],"args_string":"(other)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L366","def":{"name":"-","args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"subtract(other)"}},{"id":"/(other)-instance-method","html_id":"/(other)-instance-method","name":"/","doc":null,"summary":null,"abstract":false,"args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":""}],"args_string":"(other)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L374","def":{"name":"/","args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"divide(other)"}},{"id":"<<(value:Float64)-instance-method","html_id":"&lt;&lt;(value:Float64)-instance-method","name":"<<","doc":"Alias for `#push`","summary":"<p>Alias for <code><a href=\"../../Apatite/LinearAlgebra/Vector.html#push%28value%3AFloat64%29-instance-method\">#push</a></code></p>","abstract":false,"args":[{"name":"value","doc":null,"default_value":"","external_name":"value","restriction":"Float64"}],"args_string":"(value : Float64)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L349","def":{"name":"<<","args":[{"name":"value","doc":null,"default_value":"","external_name":"value","restriction":"Float64"}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"push(value)"}},{"id":"(other)-instance-method","html_id":"(other)-instance-method","name":"<=>","doc":"Combined comparison operator. Returns *0* if `self` equals *other*, *1* if\n`self` is greater than *other* and *-1* if `self` is smaller than *other*.\n\nIt compares the elements of both vectors in the same position using the\n`<=>` operator.  As soon as one of such comparisons returns a non-zero\nvalue, that result is the return value of the comparison.\n\nIf all elements are equal, the comparison is based on the size of the vectors.\n\n```\nVector{8.0} <=> Vector(1.0, 2.0, 3.0} # => 1\nVector{2.0} <=> Vector{4.0, 2.0, 3.0} # => -1\nVector{1.0, 2.0} <=> Vector{1.0, 2.0} # => 0\n```","summary":"<p>Combined comparison operator.</p>","abstract":false,"args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":""}],"args_string":"(other)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L339","def":{"name":"<=>","args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"min_size = Math.min(size, other.size)\n0.upto(min_size - 1) do |i|\n  n = @buffer[i] <=> other.to_unsafe[i]\n  if n != 0\n    return n\n  end\nend\nsize <=> other.size\n"}},{"id":"==(other:Vector)-instance-method","html_id":"==(other:Vector)-instance-method","name":"==","doc":null,"summary":null,"abstract":false,"args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":"Vector"}],"args_string":"(other : Vector)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L353","def":{"name":"==","args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":"Vector"}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"equals?(other) do |x, y|\n  x == y\nend"}},{"id":"[](start:Int,count:Int)-instance-method","html_id":"[](start:Int,count:Int)-instance-method","name":"[]","doc":"Returns count or less (if there aren't enough) elements starting at the\ngiven start index.\n\nNegative indices count backward from the end of the vector (-1 is the last\nelement). Additionally, an empty vector is returned when the starting index\nfor an element range is at the end of the vector.\n\nRaises `IndexError` if the starting index is out of range.\n\n```\nv = Vector{1.0, 2.0, 3.0, 4.0, 5.0}\nv[1, 3]  # => Vector{2.0, 3.0, 4.0}\nv[6, 10] # raise IndexError\n```","summary":"<p>Returns count or less (if there aren't enough) elements starting at the given start index.</p>","abstract":false,"args":[{"name":"start","doc":null,"default_value":"","external_name":"start","restriction":"Int"},{"name":"count","doc":null,"default_value":"","external_name":"count","restriction":"Int"}],"args_string":"(start : Int, count : Int)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L191","def":{"name":"[]","args":[{"name":"start","doc":null,"default_value":"","external_name":"start","restriction":"Int"},{"name":"count","doc":null,"default_value":"","external_name":"count","restriction":"Int"}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"if count < 0\n  raise(ArgumentError.new(\"Negative count: #{count}\"))\nend\nif start == size\n  return Vector.new\nend\nif start < 0\n  start = start + size\nend\nif 0 <= start && start <= size\nelse\n  raise(IndexError.new)\nend\nif count == 0\n  return Vector.new\nend\ncount = Math.min(count, size - start)\nVector.build(count) do |buffer|\n  buffer.copy_from(@buffer + start, count)\n  count\nend\n"}},{"id":"[](range:Range(Int,Int))-instance-method","html_id":"[](range:Range(Int,Int))-instance-method","name":"[]","doc":"Returns all elements that are within the given range.\n\nNegative indices count backward from the end of the vector (-1 is the last\nelement). Additionally, an empty vector is returned when the starting index\nfor an element range is at the end of the vector.\n\nRaises `IndexError` if the starting index is out of range.\n\n```\nv = Vector{1.0, 2.0, 3.0, 4.0, 5.0}\nv[1..3]  # => Vector{2.0, 3.0, 4.0}\nv[6..10] # raise IndexError\n```","summary":"<p>Returns all elements that are within the given range.</p>","abstract":false,"args":[{"name":"range","doc":null,"default_value":"","external_name":"range","restriction":"Range(Int, Int)"}],"args_string":"(range : Range(Int, Int))","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L173","def":{"name":"[]","args":[{"name":"range","doc":null,"default_value":"","external_name":"range","restriction":"Range(Int, Int)"}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"self[*Indexable.range_to_index_and_count(range, size)]"}},{"id":"[]=(index:Int,count:Int,values:Vector)-instance-method","html_id":"[]=(index:Int,count:Int,values:Vector)-instance-method","name":"[]=","doc":"Replaces a subrange with the elements of the given vector.\n\n```\nvec = Vector{1.0, 2.0, 3.0, 4.0, 5.0}\nvec[1, 3] = Vector{6.0, 7.0, 8.0}\nvec # = Vector{1.0, 6.0, 7.0, 8.0, 5.0}\n\nvec = Vector{1.0, 2.0, 3.0, 4.0, 5.0}\nvec[1, 3] = Vector{6.0, 7.0}\nvec # = Vector{1.0, 6.0, 7.0, 5.0}\n```","summary":"<p>Replaces a subrange with the elements of the given vector.</p>","abstract":false,"args":[{"name":"index","doc":null,"default_value":"","external_name":"index","restriction":"Int"},{"name":"count","doc":null,"default_value":"","external_name":"count","restriction":"Int"},{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":"Vector"}],"args_string":"(index : Int, count : Int, values : Vector)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L297","def":{"name":"[]=","args":[{"name":"index","doc":null,"default_value":"","external_name":"index","restriction":"Int"},{"name":"count","doc":null,"default_value":"","external_name":"count","restriction":"Int"},{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":"Vector"}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"if count < 0\n  raise(ArgumentError.new(\"Negative count: #{count}\"))\nend\nindex = check_index_out_of_bounds(index)\ncount = ((index + count) <= size) ? count : size - index\ndiff = values.size - count\nif diff == 0\n  (@buffer + index).copy_from(values.to_unsafe, values.size)\nelse\n  if diff < 0\n    diff = -diff\n    (@buffer + index).copy_from(values.to_unsafe, values.size)\n    ((@buffer + index) + values.size).move_from((@buffer + index) + count, (size - index) - count)\n    ((@buffer + @size) - diff).clear(diff)\n    @size = @size - diff\n  else\n    resize_to_capacity(Math.pw2ceil(@size + diff))\n    ((@buffer + index) + values.size).move_from((@buffer + index) + count, (size - index) - count)\n    (@buffer + index).copy_from(values.to_unsafe, values.size)\n    @size = @size + diff\n  end\nend\nvalues\n"}},{"id":"[]=(index:Int,count:Int,value)-instance-method","html_id":"[]=(index:Int,count:Int,value)-instance-method","name":"[]=","doc":"Replaces a subrange with a single value. All elements in the range\n`index...index+count` are removed and replaced by a single element\n*value*.\n\nIf *count* is zero, *value* is inserted at *index*.\n\nNegative values of *index* count from the end of the vector.\n\n```\nvec = Vector{1.0, 2.0, 3.0, 4.0, 5.0}\nvec[1, 3] = 6.0\nvec # => Vector{1.0, 6.0, 5.0}\n\nvec = Vector{1.0, 2.0, 3.0, 4.0, 5.0}\nvec[1, 0] = 6.0\nvec # => Vector{1.0, 6.0, 2.0, 3.0, 4.0, 5.0}\n```","summary":"<p>Replaces a subrange with a single value.</p>","abstract":false,"args":[{"name":"index","doc":null,"default_value":"","external_name":"index","restriction":"Int"},{"name":"count","doc":null,"default_value":"","external_name":"count","restriction":"Int"},{"name":"value","doc":null,"default_value":"","external_name":"value","restriction":""}],"args_string":"(index : Int, count : Int, value)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L248","def":{"name":"[]=","args":[{"name":"index","doc":null,"default_value":"","external_name":"index","restriction":"Int"},{"name":"count","doc":null,"default_value":"","external_name":"count","restriction":"Int"},{"name":"value","doc":null,"default_value":"","external_name":"value","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"if count < 0\n  raise(ArgumentError.new(\"Negative count: #{count}\"))\nend\nvalue = value.to_f64\nindex = check_index_out_of_bounds(index)\ncount = ((index + count) <= size) ? count : size - index\ncase count\nwhen 0\n  insert(index, value)\nwhen 1\n  @buffer[index] = value\nelse\n  diff = count - 1\n  ((@buffer + index) + 1).move_from((@buffer + index) + count, (size - index) - count)\n  ((@buffer + @size) - diff).clear(diff)\n  @buffer[index] = value\n  @size = @size - diff\nend\nvalue\n"}},{"id":"[]=(index:Int,value)-instance-method","html_id":"[]=(index:Int,value)-instance-method","name":"[]=","doc":"Sets the given value at the given index.\n\nNegative indices can be used to start counting from the end of the array.\nRaises `IndexError` if trying to set an element outside the array's range.\n\n```\nvec = Vector{1.0, 2.0, 3.0}\nvec[0] = 5.0\np vec # => Vec{5.0, 2.0, 3.0}\n\nvec[3] = 5.0 # raises IndexError\n```","summary":"<p>Sets the given value at the given index.</p>","abstract":false,"args":[{"name":"index","doc":null,"default_value":"","external_name":"index","restriction":"Int"},{"name":"value","doc":null,"default_value":"","external_name":"value","restriction":""}],"args_string":"(index : Int, value)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L226","def":{"name":"[]=","args":[{"name":"index","doc":null,"default_value":"","external_name":"index","restriction":"Int"},{"name":"value","doc":null,"default_value":"","external_name":"value","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"index = check_index_out_of_bounds(index)\n@buffer[index] = value.to_f64\n"}},{"id":"[]=(range:Range(Int,Int),value)-instance-method","html_id":"[]=(range:Range(Int,Int),value)-instance-method","name":"[]=","doc":"Replaces a subrange with a single value.\n\n```\nvec = Vector{1.0, 2.0, 3.0, 4.0, 5.0}\nvec[1..3] = 6.0\nvec # = Vector{1.0, 6.0, 5.0}\n\nvec = Vector{1.0, 2.0, 3.0, 4.0, 5.0}\nvec[1...1] = 6\nvec # = Vector{1.0, 6.0, 2.0, 3.0, 4.0, 5.0}\n```","summary":"<p>Replaces a subrange with a single value.</p>","abstract":false,"args":[{"name":"range","doc":null,"default_value":"","external_name":"range","restriction":"Range(Int, Int)"},{"name":"value","doc":null,"default_value":"","external_name":"value","restriction":""}],"args_string":"(range : Range(Int, Int), value)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L282","def":{"name":"[]=","args":[{"name":"range","doc":null,"default_value":"","external_name":"range","restriction":"Range(Int, Int)"},{"name":"value","doc":null,"default_value":"","external_name":"value","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"self[*Indexable.range_to_index_and_count(range, size)] = value.to_f64"}},{"id":"add(value)-instance-method","html_id":"add(value)-instance-method","name":"add","doc":"When the input is a number, this returns the result of adding\nit to all vector elements. When it's a vector, the vectors\nwill be added together.","summary":"<p>When the input is a number, this returns the result of adding it to all vector elements.</p>","abstract":false,"args":[{"name":"value","doc":null,"default_value":"","external_name":"value","restriction":""}],"args_string":"(value)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L476","def":{"name":"add","args":[{"name":"value","doc":null,"default_value":"","external_name":"value","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"run_binary_op(value) do |a, b|\n  a + b\nend"}},{"id":"angle_from(vector)-instance-method","html_id":"angle_from(vector)-instance-method","name":"angle_from","doc":"Returns the angle between this vector and another in radians.\nIf the vectors are mirrored across their axes this will return `nil`.","summary":"<p>Returns the angle between this vector and another in radians.</p>","abstract":false,"args":[{"name":"vector","doc":null,"default_value":"","external_name":"vector","restriction":""}],"args_string":"(vector)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L449","def":{"name":"angle_from","args":[{"name":"vector","doc":null,"default_value":"","external_name":"vector","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"Apatite.angle_from(self, vector)"}},{"id":"antiparallel_to?(vector)-instance-method","html_id":"antiparallel_to?(vector)-instance-method","name":"antiparallel_to?","doc":"Returns whether the vectors are antiparallel to each other.","summary":"<p>Returns whether the vectors are antiparallel to each other.</p>","abstract":false,"args":[{"name":"vector","doc":null,"default_value":"","external_name":"vector","restriction":""}],"args_string":"(vector)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L464","def":{"name":"antiparallel_to?","args":[{"name":"vector","doc":null,"default_value":"","external_name":"vector","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"Apatite.antiparallel_to?(self, vector)"}},{"id":"augment(elements)-instance-method","html_id":"augment(elements)-instance-method","name":"augment","doc":"Returns a new vector with the provided `elements` concatenated\non the end.","summary":"<p>Returns a new vector with the provided <code>elements</code> concatenated on the end.</p>","abstract":false,"args":[{"name":"elements","doc":null,"default_value":"","external_name":"elements","restriction":""}],"args_string":"(elements)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L551","def":{"name":"augment","args":[{"name":"elements","doc":null,"default_value":"","external_name":"elements","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"elements = elements.is_a?(Vector) ? elements : Vector.create(elements)\nconcat(elements)\n"}},{"id":"chomp(n)-instance-method","html_id":"chomp(n)-instance-method","name":"chomp","doc":"Returns a new vector with the first `n` elements removed from\nthe beginning.","summary":"<p>Returns a new vector with the first <code>n</code> elements removed from the beginning.</p>","abstract":false,"args":[{"name":"n","doc":null,"default_value":"","external_name":"n","restriction":""}],"args_string":"(n)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L536","def":{"name":"chomp","args":[{"name":"n","doc":null,"default_value":"","external_name":"n","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"elements = [] of Float64\neach_with_index do |e, i|\n  if i >= n\n    elements << e\n  end\nend\nVector.create(elements)\n"}},{"id":"clear-instance-method","html_id":"clear-instance-method","name":"clear","doc":"Removes all elements from self.\n\n```\nvec = Vector{1.0, 2.0, 3.0}\nvec.clear # => Vector{}\n```","summary":"<p>Removes all elements from self.</p>","abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L768","def":{"name":"clear","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"@buffer.clear(@size)\n@size = 0\nself\n"}},{"id":"clone-instance-method","html_id":"clone-instance-method","name":"clone","doc":null,"summary":null,"abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L378","def":{"name":"clone","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"Vector.create(@elements.clone)"}},{"id":"concat(other:Vector)-instance-method","html_id":"concat(other:Vector)-instance-method","name":"concat","doc":null,"summary":null,"abstract":false,"args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":"Vector"}],"args_string":"(other : Vector)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L717","def":{"name":"concat","args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":"Vector"}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"other_size = other.size\nnew_size = size + other_size\nif new_size > @capacity\n  resize_to_capacity(Math.pw2ceil(new_size))\nend\n(@buffer + @size).copy_from(other.to_unsafe, other_size)\n@size = new_size\nself\n"}},{"id":"covector-instance-method","html_id":"covector-instance-method","name":"covector","doc":"Creates a single-row matrix from this vector.","summary":"<p>Creates a single-row matrix from this vector.</p>","abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L587","def":{"name":"covector","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"Matrix.row_vector(self)"}},{"id":"cross(*vs)-instance-method","html_id":"cross(*vs)-instance-method","name":"cross","doc":"Returns the cross product of this vector with the others.\n\n```\nv1 = Vector{1.0, 0.0, 0.0}\nv2 = Vector{0.0, 1.0, 0.0}\nv1.cross(v2) => Vector{0.0, 0.0, 1.0}\n```","summary":"<p>Returns the cross product of this vector with the others.</p>","abstract":false,"args":[{"name":"vs","doc":null,"default_value":"","external_name":"vs","restriction":""}],"args_string":"(*vs)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L513","def":{"name":"cross","args":[{"name":"vs","doc":null,"default_value":"","external_name":"vs","restriction":""}],"double_splat":null,"splat_index":0,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"if size >= 2\nelse\n  raise(\"cross product is not defined on vectors of dimension #{size}\")\nend\nif vs.size == (size - 2)\nelse\n  raise(ArgumentError.new(\"wrong number of arguments (#{vs.size} for #{size - 2})\"))\nend\nvs.each do |v|\n  if v.size == size\n  else\n    raise(\"Dimension mismatch. Vectors not all the same size.\")\n  end\nend\ncase size\nwhen 2\n  Vector[-@buffer[1], @buffer[0]]\nwhen 3\n  v = vs[0]\n  Vector[(v[2] * @buffer[1]) - (v[1] * @buffer[2]), (v[0] * @buffer[2]) - (v[2] * @buffer[0]), (v[1] * @buffer[0]) - (v[0] * @buffer[1])]\nelse\nend\n"}},{"id":"distance_from(obj)-instance-method","html_id":"distance_from(obj)-instance-method","name":"distance_from","doc":"Gets this vector's distance from the argument, when considered\na point in space.","summary":"<p>Gets this vector's distance from the argument, when considered a point in space.</p>","abstract":false,"args":[{"name":"obj","doc":null,"default_value":"","external_name":"obj","restriction":""}],"args_string":"(obj)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L615","def":{"name":"distance_from","args":[{"name":"obj","doc":null,"default_value":"","external_name":"obj","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"if object.is_a?(Plane) || object.is_a?(Line)\n  return object.distance_from(self)\nend\nv = elements.is_a?(Vector) ? elements.elements : elements\nif v.size == @elements.size\nelse\n  return nil\nend\nsum = 0\npart = 0\neach_with_index do |x, i|\n  part = x - v[i - 1]\n  sum = sum + (part * part)\nend\nMath.sqrt(sum)\n"}},{"id":"divide(value)-instance-method","html_id":"divide(value)-instance-method","name":"divide","doc":"When the input is a number, this returns the result of dividing\nit to all vector elements. When it's a vector, the vectors\nwill be element-wise divided.","summary":"<p>When the input is a number, this returns the result of dividing it to all vector elements.</p>","abstract":false,"args":[{"name":"value","doc":null,"default_value":"","external_name":"value","restriction":""}],"args_string":"(value)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L497","def":{"name":"divide","args":[{"name":"value","doc":null,"default_value":"","external_name":"value","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"run_binary_op(value) do |a, b|\n  a / b\nend"}},{"id":"dot(other)-instance-method","html_id":"dot(other)-instance-method","name":"dot","doc":"Get the scalar (dot) product of this vector with `vector`.\n\n[https://en.wikipedia.org/wiki/Scalar_product](https://en.wikipedia.org/wiki/Scalar_product)","summary":"<p>Get the scalar (dot) product of this vector with <code>vector</code>.</p>","abstract":false,"args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":""}],"args_string":"(other)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L569","def":{"name":"dot","args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"other = other.is_a?(Vector) ? other : Vector.create(other)\nApatite.dot(self, other)\n"}},{"id":"e(i)-instance-method","html_id":"e(i)-instance-method","name":"e","doc":"Returns the `ith` element of the vector. Returns `nil` if `i`\nis out of bounds. Indexing starts from 1.","summary":"<p>Returns the <code>ith</code> element of the vector.</p>","abstract":false,"args":[{"name":"i","doc":null,"default_value":"","external_name":"i","restriction":""}],"args_string":"(i)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L430","def":{"name":"e","args":[{"name":"i","doc":null,"default_value":"","external_name":"i","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"(i < 1 || i > @size) ? nil : self[i - 1]"}},{"id":"independent?(*vs)-instance-method","html_id":"independent?(*vs)-instance-method","name":"independent?","doc":"Returns true if all vectors are linearly independent.","summary":"<p>Returns true if all vectors are linearly independent.</p>","abstract":false,"args":[{"name":"vs","doc":null,"default_value":"","external_name":"vs","restriction":""}],"args_string":"(*vs)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L388","def":{"name":"independent?","args":[{"name":"vs","doc":null,"default_value":"","external_name":"vs","restriction":""}],"double_splat":null,"splat_index":0,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"vs.each do |v|\n  if v.size == vs.first.size\n  else\n    raise(\"Dimension mismatch. Vectors not all the same size.\")\n  end\nend\nif vs.size > sv.first.size\n  return false\nend\nMatrix[*vs].rank.equal?(vs.count)\n"}},{"id":"lies_in(plane)-instance-method","html_id":"lies_in(plane)-instance-method","name":"lies_in","doc":"Returns true if the vector is a point on the given plane.","summary":"<p>Returns true if the vector is a point on the given plane.</p>","abstract":false,"args":[{"name":"plane","doc":null,"default_value":"","external_name":"plane","restriction":""}],"args_string":"(plane)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L640","def":{"name":"lies_in","args":[{"name":"plane","doc":null,"default_value":"","external_name":"plane","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"plane.contains(self)"}},{"id":"lies_on(line)-instance-method","html_id":"lies_on(line)-instance-method","name":"lies_on","doc":"Returns true if the vector is a point on the given line","summary":"<p>Returns true if the vector is a point on the given line</p>","abstract":false,"args":[{"name":"line","doc":null,"default_value":"","external_name":"line","restriction":""}],"args_string":"(line)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L635","def":{"name":"lies_on","args":[{"name":"line","doc":null,"default_value":"","external_name":"line","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"line.contains(self)"}},{"id":"log-instance-method","html_id":"log-instance-method","name":"log","doc":"Return a new `Vector` with the log of every item in `self`.","summary":"<p>Return a new <code><a href=\"../../Apatite/LinearAlgebra/Vector.html\">Vector</a></code> with the log of every item in <code>self</code>.</p>","abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L557","def":{"name":"log","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"map do |x|\n  Math.log(x)\nend"}},{"id":"magnitude-instance-method","html_id":"magnitude-instance-method","name":"magnitude","doc":"Returns the magnitude/euclidian norm of this vector.\n\n[https://en.wikipedia.org/wiki/Euclidean_distance](https://en.wikipedia.org/wiki/Euclidean_distance)","summary":"<p>Returns the magnitude/euclidian norm of this vector.</p>","abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L423","def":{"name":"magnitude","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"sum = reduce(0.0) do |acc, e|\n  acc = acc + (e * e)\nend\nMath.sqrt(sum)\n"}},{"id":"map(&block)-instance-method","html_id":"map(&amp;block)-instance-method","name":"map","doc":"Invokes the given block for each element of `self`.","summary":"<p>Invokes the given block for each element of <code>self</code>.</p>","abstract":false,"args":[],"args_string":"(&block)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L383","def":{"name":"map","args":[],"double_splat":null,"splat_index":null,"yields":1,"block_arg":null,"return_type":"","visibility":"Public","body":"Vector.new(size) do |i|\n  yield @buffer[i]\nend"}},{"id":"map!(&block)-instance-method","html_id":"map!(&amp;block)-instance-method","name":"map!","doc":"Invokes the given block for each element of `self`, replacing the element\nwith the value returned by the block. Returns `self`.\n\n```\nvec = Vector{1.0, 2.0, 3.0}\nvec.map! { |x| x * x }\na # => Vector{1.0, 4.0, 9.0}\n```","summary":"<p>Invokes the given block for each element of <code>self</code>, replacing the element with the value returned by the block.</p>","abstract":false,"args":[],"args_string":"(&block)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L404","def":{"name":"map!","args":[],"double_splat":null,"splat_index":null,"yields":1,"block_arg":null,"return_type":"","visibility":"Public","body":"@buffer.map!(size) do |e|\n  yield e\nend\nself\n"}},{"id":"map_with_index(&block)-instance-method","html_id":"map_with_index(&amp;block)-instance-method","name":"map_with_index","doc":"Optimized version of `Enumerable#map_with_index`.","summary":"<p>Optimized version of <code>Enumerable#map_with_index</code>.</p>","abstract":false,"args":[],"args_string":"(&block)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L410","def":{"name":"map_with_index","args":[],"double_splat":null,"splat_index":null,"yields":2,"block_arg":null,"return_type":"","visibility":"Public","body":"Vector.new(size) do |i|\n  yield @buffer[i], i\nend"}},{"id":"map_with_index!(&block)-instance-method","html_id":"map_with_index!(&amp;block)-instance-method","name":"map_with_index!","doc":"Like `map_with_index`, but mutates `self` instead of allocating a new object.","summary":"<p>Like <code><a href=\"../../Apatite/LinearAlgebra/Vector.html#map_with_index%28%26block%29-instance-method\">#map_with_index</a></code>, but mutates <code>self</code> instead of allocating a new object.</p>","abstract":false,"args":[],"args_string":"(&block)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L415","def":{"name":"map_with_index!","args":[],"double_splat":null,"splat_index":null,"yields":2,"block_arg":null,"return_type":"","visibility":"Public","body":"to_unsafe.map_with_index!(size) do |e, i|\n  yield e, i\nend\nself\n"}},{"id":"max-instance-method","html_id":"max-instance-method","name":"max","doc":"Returns the (absolute) largest element in this vector.","summary":"<p>Returns the (absolute) largest element in this vector.</p>","abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L575","def":{"name":"max","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"reduce do |acc, i|\n  i.abs > acc.abs ? i : acc\nend"}},{"id":"max_index-instance-method","html_id":"max_index-instance-method","name":"max_index","doc":"Gets the index of the largest element in this vector.","summary":"<p>Gets the index of the largest element in this vector.</p>","abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L580","def":{"name":"max_index","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"idx = 0\neach_with_index do |e, i|\n  idx = e.abs > self[idx].abs ? i : idx\nend\nidx\n"}},{"id":"multiply(value)-instance-method","html_id":"multiply(value)-instance-method","name":"multiply","doc":"When the input is a number, this returns the result of multiplying\nit to all vector elements. When it's a vector, the vectors\nwill be element-wise multiplied.","summary":"<p>When the input is a number, this returns the result of multiplying it to all vector elements.</p>","abstract":false,"args":[{"name":"value","doc":null,"default_value":"","external_name":"value","restriction":""}],"args_string":"(value)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L490","def":{"name":"multiply","args":[{"name":"value","doc":null,"default_value":"","external_name":"value","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"run_binary_op(value) do |a, b|\n  a * b\nend"}},{"id":"normalize-instance-method","html_id":"normalize-instance-method","name":"normalize","doc":"Returns a new vector created by normalizing this one\nto have a magnitude of `1`. If the vector is a zero\nvector, it will not be modified.","summary":"<p>Returns a new vector created by normalizing this one to have a magnitude of <code>1</code>.</p>","abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L443","def":{"name":"normalize","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"to_unit_vector"}},{"id":"parallel_to?(vector)-instance-method","html_id":"parallel_to?(vector)-instance-method","name":"parallel_to?","doc":"Returns whether the vectors are parallel to each other.","summary":"<p>Returns whether the vectors are parallel to each other.</p>","abstract":false,"args":[{"name":"vector","doc":null,"default_value":"","external_name":"vector","restriction":""}],"args_string":"(vector)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L459","def":{"name":"parallel_to?","args":[{"name":"vector","doc":null,"default_value":"","external_name":"vector","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"Apatite.parallel_to?(self, vector)"}},{"id":"perpendicular_to?(vector)-instance-method","html_id":"perpendicular_to?(vector)-instance-method","name":"perpendicular_to?","doc":"Returns whether the vectors are perpendicular to each other.","summary":"<p>Returns whether the vectors are perpendicular to each other.</p>","abstract":false,"args":[{"name":"vector","doc":null,"default_value":"","external_name":"vector","restriction":""}],"args_string":"(vector)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L469","def":{"name":"perpendicular_to?","args":[{"name":"vector","doc":null,"default_value":"","external_name":"vector","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"Apatite.perpendicular_to?(self, vector)"}},{"id":"pretty_print(pp):Nil-instance-method","html_id":"pretty_print(pp):Nil-instance-method","name":"pretty_print","doc":null,"summary":null,"abstract":false,"args":[{"name":"pp","doc":null,"default_value":"","external_name":"pp","restriction":""}],"args_string":"(pp) : Nil","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L740","def":{"name":"pretty_print","args":[{"name":"pp","doc":null,"default_value":"","external_name":"pp","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"Nil","visibility":"Public","body":"pp.list(\"Vector{\", self, \"}\")"}},{"id":"product-instance-method","html_id":"product-instance-method","name":"product","doc":"Get the product of all elements in this vector.","summary":"<p>Get the product of all elements in this vector.</p>","abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L562","def":{"name":"product","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"reduce do |acc, v|\n  acc = acc * v\nend"}},{"id":"push(value:Float64)-instance-method","html_id":"push(value:Float64)-instance-method","name":"push","doc":null,"summary":null,"abstract":false,"args":[{"name":"value","doc":null,"default_value":"","external_name":"value","restriction":"Float64"}],"args_string":"(value : Float64)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L644","def":{"name":"push","args":[{"name":"value","doc":null,"default_value":"","external_name":"value","restriction":"Float64"}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"check_needs_resize\n@buffer[@size] = value\n@size = @size + 1\nself\n"}},{"id":"push(*values:Float64)-instance-method","html_id":"push(*values:Float64)-instance-method","name":"push","doc":null,"summary":null,"abstract":false,"args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":"Float64"}],"args_string":"(*values : Float64)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L651","def":{"name":"push","args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":"Float64"}],"double_splat":null,"splat_index":0,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"new_size = @size + values.size\nif new_size > @capacity\n  resize_to_capacity(Math.pw2ceil(new_size))\nend\nvalues.each_with_index do |value, i|\n  @buffer[@size + i] = value\nend\n@size = new_size\nself\n"}},{"id":"reflection_in(object)-instance-method","html_id":"reflection_in(object)-instance-method","name":"reflection_in","doc":"Returns the result of reflecting the point in the given `object`\n(point, line, or plane).","summary":"<p>Returns the result of reflecting the point in the given <code>object</code> (point, line, or plane).</p>","abstract":false,"args":[{"name":"object","doc":null,"default_value":"","external_name":"object","restriction":""}],"args_string":"(object)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L670","def":{"name":"reflection_in","args":[{"name":"object","doc":null,"default_value":"","external_name":"object","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"if object.is_a?(Plane) || object.is_a?(Line)\n  p = @elements.dup\n  c = (object.point_closest_to(p)).elements\n  return Vector.create([C[0] + (C[0] - P[0]), C[1] + (C[1] - P[1]), C[2] + (C[2] - (P[2] || 0))])\nend\nq = object.is_a?(Vector) ? object.elements : object\nif @elements.size == q.size\nelse\n  return nil\nend\nmap_with_index do |x, i|\n  q[i - 1] + (q[i - 1] - x)\nend\n"}},{"id":"rotate(t,object)-instance-method","html_id":"rotate(t,object)-instance-method","name":"rotate","doc":"Rotates the vector about the given `object`. The object should\nbe a point if the vector is 2D, and a line if it is 3D. Be\ncareful with line directions!","summary":"<p>Rotates the vector about the given <code>object</code>.</p>","abstract":false,"args":[{"name":"t","doc":null,"default_value":"","external_name":"t","restriction":""},{"name":"object","doc":null,"default_value":"","external_name":"object","restriction":""}],"args_string":"(t, object)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L664","def":{"name":"rotate","args":[{"name":"t","doc":null,"default_value":"","external_name":"t","restriction":""},{"name":"object","doc":null,"default_value":"","external_name":"object","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":""}},{"id":"round-instance-method","html_id":"round-instance-method","name":"round","doc":"Gets the result of rounding the elements of the vector.","summary":"<p>Gets the result of rounding the elements of the vector.</p>","abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L598","def":{"name":"round","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"map do |x|\n  x.round\nend"}},{"id":"set_elements(elements)-instance-method","html_id":"set_elements(elements)-instance-method","name":"set_elements","doc":null,"summary":null,"abstract":false,"args":[{"name":"elements","doc":null,"default_value":"","external_name":"elements","restriction":""}],"args_string":"(elements)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L712","def":{"name":"set_elements","args":[{"name":"elements","doc":null,"default_value":"","external_name":"elements","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"@elements = elements.is_a?(Vector) ? elements.elements : elements\nself\n"}},{"id":"sigmoid-instance-method","html_id":"sigmoid-instance-method","name":"sigmoid","doc":"Sums the numbers in the vector and returns a sigmoid value\nacross the whole vector.","summary":"<p>Sums the numbers in the vector and returns a sigmoid value across the whole vector.</p>","abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L693","def":{"name":"sigmoid","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"LinearAlgebra.sigmoid(sum)"}},{"id":"similarity(other)-instance-method","html_id":"similarity(other)-instance-method","name":"similarity","doc":"Compute the cosine similarity between this vector and another.","summary":"<p>Compute the cosine similarity between this vector and another.</p>","abstract":false,"args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":""}],"args_string":"(other)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L454","def":{"name":"similarity","args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"Apatite.similarity(self, other)"}},{"id":"size:Int32-instance-method","html_id":"size:Int32-instance-method","name":"size","doc":"Returns the number of elements in the vector","summary":"<p>Returns the number of elements in the vector</p>","abstract":false,"args":[],"args_string":" : Int32","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L24","def":{"name":"size","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"Int32","visibility":"Public","body":"@size"}},{"id":"snap_to(value)-instance-method","html_id":"snap_to(value)-instance-method","name":"snap_to","doc":"Returns a copy of the vector with elements set to `value` if\nthey differ from it by less than `Apetite.precision`","summary":"<p>Returns a copy of the vector with elements set to <code>value</code> if they differ from it by less than <code>Apetite.precision</code></p>","abstract":false,"args":[{"name":"value","doc":null,"default_value":"","external_name":"value","restriction":""}],"args_string":"(value)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L609","def":{"name":"snap_to","args":[{"name":"value","doc":null,"default_value":"","external_name":"value","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"map do |y|\n  (y - x).abs <= Apetite.precision ? 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When it's a vector, the vectors\nwill be subtracted.","summary":"<p>When the input is a number, this returns the result of subtracting it to all vector elements.</p>","abstract":false,"args":[{"name":"value","doc":null,"default_value":"","external_name":"value","restriction":""}],"args_string":"(value)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L483","def":{"name":"subtract","args":[{"name":"value","doc":null,"default_value":"","external_name":"value","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"run_binary_op(value) do |a, b|\n  a - b\nend"}},{"id":"sum-instance-method","html_id":"sum-instance-method","name":"sum","doc":"Returns the sum of all elements in the vector.","summary":"<p>Returns the sum of all elements in the vector.</p>","abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L502","def":{"name":"sum","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"reduce(0) do |acc, i|\n  acc + i\nend"}},{"id":"to_3d-instance-method","html_id":"to_3d-instance-method","name":"to_3d","doc":"Utility to make sure vectors are 3D. If they are 2D, a zero\nz-component is added.","summary":"<p>Utility to make sure vectors are 3D.</p>","abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L699","def":{"name":"to_3d","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"v = dup\ncase v.elements.size\nwhen 3\n  break\nwhen 2\n  v.elements.push(0)\nelse\n  return nil\nend\nreturn v\n"}},{"id":"to_a-instance-method","html_id":"to_a-instance-method","name":"to_a","doc":null,"summary":null,"abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L730","def":{"name":"to_a","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"Array(Float64).new(size) do |i|\n  self[i]\nend"}},{"id":"to_diagonal_matrix-instance-method","html_id":"to_diagonal_matrix-instance-method","name":"to_diagonal_matrix","doc":"Returns a diagonal `Matrix` with the vectors elements as its\ndiagonal elements.","summary":"<p>Returns a diagonal <code><a href=\"../../Apatite/LinearAlgebra/Matrix.html\">Matrix</a></code> with the vectors elements as its diagonal elements.</p>","abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L593","def":{"name":"to_diagonal_matrix","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"Matrix::Diagonal.new(elements)"}},{"id":"to_s(io)-instance-method","html_id":"to_s(io)-instance-method","name":"to_s","doc":null,"summary":null,"abstract":false,"args":[{"name":"io","doc":null,"default_value":"","external_name":"io","restriction":""}],"args_string":"(io)","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L734","def":{"name":"to_s","args":[{"name":"io","doc":null,"default_value":"","external_name":"io","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"io << \"{\"\njoin(\", \", io, &.inspect(io))\nio << \"}\"\n"}},{"id":"to_unit_vector-instance-method","html_id":"to_unit_vector-instance-method","name":"to_unit_vector","doc":"Returns a new vector created by normalizing this one\nto have a magnitude of `1`. If the vector is a zero\nvector, it will not be modified.","summary":"<p>Returns a new vector created by normalizing this one to have a magnitude of <code>1</code>.</p>","abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/linear_algebra/vector.cr#L437","def":{"name":"to_unit_vector","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"r = magnitude\nr == 0 ? dup : map do |x|\n  x.to_f64 / r\nend\n"}},{"id":"to_unsafe:Pointer(Float64)-instance-method","html_id":"to_unsafe:Pointer(Float64)-instance-method","name":"to_unsafe","doc":"Returns a pointer to the internal buffer where `self`'s elements are stored.\n\nThis method is **unsafe** because it returns a pointer, and the pointed might eventually\nnot be that of `self` if the array grows and its internal buffer is reallocated.\n\n```\nvec = Vector{1.0, 2.0, 3.0}\nvec.to_unsafe[0] # 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A negative index is assumed to be\nrelative to the end of the array: -1 indicates the last element,\n-2 is the next to last element, and so on.\n\nAn `Array` can be created using the usual `new` method (several are provided), or with an array literal:\n\n```\nArray(Int32).new  # => []\n[1, 2, 3]         # Array(Int32)\n[1, \"hello\", 'x'] # Array(Int32 | String | Char)\n```\n\nAn `Array` can have mixed types, meaning T will be a union of types, but these are determined\nwhen the array is created, either by specifying T or by using an array literal. In the latter\ncase, T will be set to the union of the array literal elements' types.\n\nWhen creating an empty array you must always specify T:\n\n```\n[] of Int32 # same as Array(Int32)\n[]          # syntax error\n```\n\nAn `Array` is implemented using an internal buffer of some capacity\nand is reallocated when elements are pushed to it when more capacity\nis needed. This is normally known as a [dynamic array](http://en.wikipedia.org/wiki/Dynamic_array).\n\nYou can use a special array literal syntax with other types too, as long as they define an argless\n`new` method and a `<<` method. `Set` is one such type:\n\n```\nset = Set{1, 2, 3} # => Set{1, 2, 3}\nset.class          # => Set(Int32)\n```\n\nThe above is the same as this:\n\n```\nset = Set(typeof(1, 2, 3)).new\nset << 1\nset << 2\nset << 3\n```","summary":"<p>An <code><a href=\"Array.html\">Array</a></code> is an ordered, integer-indexed collection of objects of type T.</p>","class_methods":[],"constructors":[],"instance_methods":[{"id":"all?-instance-method","html_id":"all?-instance-method","name":"all?","doc":"Tests whether all elements evaluate to true","summary":"<p>Tests whether all elements evaluate to true</p>","abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/core_ext/array.cr#L3","def":{"name":"all?","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"each do |i|\n  if (!(!i)) == false\n    return false\n  end\nend\ntrue\n"}},{"id":"any?-instance-method","html_id":"any?-instance-method","name":"any?","doc":"Tests whether any of the elements evaluate to true","summary":"<p>Tests whether any of the elements evaluate to true</p>","abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/core_ext/array.cr#L11","def":{"name":"any?","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"each do |i|\n  if (!(!i)) == true\n    return true\n  end\nend\nfalse\n"}},{"id":"shape-instance-method","html_id":"shape-instance-method","name":"shape","doc":"Get the array's dimensions","summary":"<p>Get the array's dimensions</p>","abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/ef28e84ecc4b7dc21e66c18464fec0892633d420/src/apatite/core_ext/array.cr#L19","def":{"name":"shape","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"max = max_by do |i|\n  i.is_a?(Array) ? i.size : i\nend\nmax.is_a?(Array) ? 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