2019-06-13 02:23:54 +00:00
<!DOCTYPE html>
< html lang = "en" >
< head >
< meta charset = "utf-8" >
< meta http-equiv = "X-UA-Compatible" content = "IE=edge" >
< meta name = "generator" content = "Crystal Docs 0.29.0" >
< link href = "../../css/style.css" rel = "stylesheet" type = "text/css" >
< script type = "text/javascript" src = "../../js/doc.js" > < / script >
< script type = "text/javascript" >
CrystalDoc.base_path = "../../";
< / script >
< meta id = "repository-name" content = "github.com/watzon/apatite" >
2019-07-10 01:18:01 +00:00
< title > Apatite::LinearAlgebra::Matrix(T) - github.com/watzon/apatite< / title >
2019-06-13 02:23:54 +00:00
< / head >
< body >
< div class = "sidebar" >
< div class = "sidebar-header" >
< div class = "search-box" >
< input type = "search" class = "search-input" placeholder = "Search..." spellcheck = "false" aria-label = "Search" >
< / div >
< div class = "repository-links" >
< a href = "../../index.html" > README< / a >
< / div >
< / div >
< div class = "search-results" class = "hidden" >
< ul class = "search-list" > < / ul >
< / div >
< div class = "types-list" >
< ul >
< li class = "parent open current" data-id = "github.com/watzon/apatite/Apatite" data-name = "apatite" >
< a href = "../../Apatite.html" > Apatite< / a >
< ul >
< li class = "parent open current" data-id = "github.com/watzon/apatite/Apatite/LinearAlgebra" data-name = "apatite::linearalgebra" >
< a href = "../../Apatite/LinearAlgebra.html" > LinearAlgebra< / a >
< ul >
2019-07-10 01:18:01 +00:00
< li class = " " data-id = "github.com/watzon/apatite/Apatite/LinearAlgebra/ErrDimensionMismatch" data-name = "apatite::linearalgebra::errdimensionmismatch" >
< a href = "../../Apatite/LinearAlgebra/ErrDimensionMismatch.html" > ErrDimensionMismatch< / a >
< / li >
< li class = " " data-id = "github.com/watzon/apatite/Apatite/LinearAlgebra/ErrNotRegular" data-name = "apatite::linearalgebra::errnotregular" >
< a href = "../../Apatite/LinearAlgebra/ErrNotRegular.html" > ErrNotRegular< / a >
< / li >
< li class = " " data-id = "github.com/watzon/apatite/Apatite/LinearAlgebra/ErrOperationNotDefined" data-name = "apatite::linearalgebra::erroperationnotdefined" >
< a href = "../../Apatite/LinearAlgebra/ErrOperationNotDefined.html" > ErrOperationNotDefined< / a >
< / li >
< li class = " " data-id = "github.com/watzon/apatite/Apatite/LinearAlgebra/Error" data-name = "apatite::linearalgebra::error" >
< a href = "../../Apatite/LinearAlgebra/Error.html" > Error< / a >
< / li >
2019-07-10 02:08:46 +00:00
< li class = "parent open current" data-id = "github.com/watzon/apatite/Apatite/LinearAlgebra/Matrix" data-name = "apatite::linearalgebra::matrix(t)" >
2019-06-13 02:23:54 +00:00
< a href = "../../Apatite/LinearAlgebra/Matrix.html" > Matrix< / a >
2019-07-10 02:08:46 +00:00
< ul >
2019-06-13 02:23:54 +00:00
2019-07-10 02:08:46 +00:00
< li class = " " data-id = "github.com/watzon/apatite/Apatite/LinearAlgebra/Matrix/EigenvalueDecomposition" data-name = "apatite::linearalgebra::matrix::eigenvaluedecomposition" >
< a href = "../../Apatite/LinearAlgebra/Matrix/EigenvalueDecomposition.html" > EigenvalueDecomposition< / a >
2019-06-13 02:23:54 +00:00
< / li >
2019-07-10 02:08:46 +00:00
< li class = " " data-id = "github.com/watzon/apatite/Apatite/LinearAlgebra/Matrix/LupDecomposition" data-name = "apatite::linearalgebra::matrix::lupdecomposition" >
< a href = "../../Apatite/LinearAlgebra/Matrix/LupDecomposition.html" > LupDecomposition< / a >
2019-07-10 01:18:01 +00:00
< / li >
< / ul >
< / li >
2019-07-10 02:08:46 +00:00
< li class = " " data-id = "github.com/watzon/apatite/Apatite/LinearAlgebra/NDArray" data-name = "apatite::linearalgebra::ndarray" >
< a href = "../../Apatite/LinearAlgebra/NDArray.html" > NDArray< / a >
2019-07-10 01:18:01 +00:00
2019-07-10 02:08:46 +00:00
< / li >
2019-07-10 01:18:01 +00:00
2019-07-10 02:08:46 +00:00
< li class = " " data-id = "github.com/watzon/apatite/Apatite/LinearAlgebra/Vector" data-name = "apatite::linearalgebra::vector(t)" >
< a href = "../../Apatite/LinearAlgebra/Vector.html" > Vector< / a >
2019-07-10 01:18:01 +00:00
< / li >
2019-07-10 02:08:46 +00:00
< li class = " " data-id = "github.com/watzon/apatite/Apatite/LinearAlgebra/ZeroVectorError" data-name = "apatite::linearalgebra::zerovectorerror" >
< a href = "../../Apatite/LinearAlgebra/ZeroVectorError.html" > ZeroVectorError< / a >
2019-07-10 01:18:01 +00:00
< / li >
2019-06-13 02:23:54 +00:00
< / ul >
< / li >
< / ul >
< / li >
< li class = " " data-id = "github.com/watzon/apatite/Array" data-name = "array(t)" >
< a href = "../../Array.html" > Array< / a >
< / li >
< / ul >
< / div >
< / div >
< div class = "main-content" >
< h1 class = "type-name" >
2019-07-10 01:18:01 +00:00
< span class = "kind" > class< / span > Apatite::LinearAlgebra::Matrix(T)
2019-06-13 02:23:54 +00:00
< / h1 >
2019-07-10 01:18:01 +00:00
< ul class = "superclass-hierarchy" > < li class = "superclass" > < a href = "../../Apatite/LinearAlgebra/Matrix.html" > Apatite::LinearAlgebra::Matrix(T)< / a > < / li > < li class = "superclass" > Reference< / li > < li class = "superclass" > Object< / li > < / ul >
2019-06-13 02:23:54 +00:00
< h2 > Included Modules< / h2 >
< ul class = "other-types-list" >
2019-07-10 01:18:01 +00:00
< li class = "other-type" > Comparable(< a href = "../../Apatite/LinearAlgebra/Matrix.html" > Apatite::LinearAlgebra::Matrix(T)< / a > )< / li >
2019-06-13 02:23:54 +00:00
2019-07-10 01:18:01 +00:00
< li class = "other-type" > Enumerable(< a href = "../../Apatite/LinearAlgebra/Vector.html" > Apatite::LinearAlgebra::Vector(T)< / a > )< / li >
2019-06-13 02:23:54 +00:00
2019-07-10 01:18:01 +00:00
< li class = "other-type" > Indexable(< a href = "../../Apatite/LinearAlgebra/Vector.html" > Apatite::LinearAlgebra::Vector(T)< / a > )< / li >
2019-06-13 02:23:54 +00:00
< / ul >
< h2 > Defined in:< / h2 >
2019-07-10 02:22:15 +00:00
< a href = "https://github.com/watzon/apatite/blob/6e67ceb81b0b3c61d48b74e5ca5154866a9abd1a/src/apatite/linear_algebra/matrix/eigenvalue_decomposition.cr#L2" target = "_blank" >
2019-07-10 02:08:46 +00:00
apatite/linear_algebra/matrix/eigenvalue_decomposition.cr
< / a >
< br / >
2019-07-10 02:22:15 +00:00
< a href = "https://github.com/watzon/apatite/blob/6e67ceb81b0b3c61d48b74e5ca5154866a9abd1a/src/apatite/linear_algebra/matrix/lup_decomposition.cr#L2" target = "_blank" >
2019-07-10 02:08:46 +00:00
apatite/linear_algebra/matrix/lup_decomposition.cr
< / a >
< br / >
2019-07-10 02:22:15 +00:00
< a href = "https://github.com/watzon/apatite/blob/6e67ceb81b0b3c61d48b74e5ca5154866a9abd1a/src/apatite/linear_algebra/matrix.cr#L6" target = "_blank" >
2019-06-13 02:23:54 +00:00
apatite/linear_algebra/matrix.cr
< / a >
< br / >
2019-07-10 01:18:01 +00:00
< h2 > Constant Summary< / h2 >
< dl >
2019-06-13 02:23:54 +00:00
2019-07-10 01:18:01 +00:00
< dt class = "entry-const" id = "SELECTORS" >
< strong > SELECTORS< / strong > = < code > {all: < span class = "n" > true< / span > , diagonal: < span class = "n" > true< / span > , off_diagonal: < span class = "n" > true< / span > , lower: < span class = "n" > true< / span > , strict_lower: < span class = "n" > true< / span > , strict_upper: < span class = "n" > true< / span > , upper: < span class = "n" > true< / span > }< / code >
< / dt >
2019-06-13 02:23:54 +00:00
2019-07-10 01:18:01 +00:00
< / dl >
2019-06-13 02:23:54 +00:00
< h2 > Class Method Summary< / h2 >
< ul class = "list-summary" >
< li class = "entry-summary" >
< a href = "#%5B%5D%28%2Arows%29-class-method" class = "signature" > < strong > .[]< / strong > (*rows)< / a >
< div class = "summary" > < p > Creates a matrix where each argument is a row.< / p > < / div >
< / li >
< li class = "entry-summary" >
2019-07-10 01:18:01 +00:00
< a href = "#build%28row_count%2Ccolumn_count%3Drow_count%2C%26block%3AInt32%2CInt32-%3ET%29-class-method" class = "signature" > < strong > .build< / strong > (row_count, column_count = row_count, & block : Int32, Int32 -> T)< / a >
2019-06-13 02:23:54 +00:00
2019-07-10 01:18:01 +00:00
< div class = "summary" > < p > Creates a matrix of size +row_count+ x +column_count+.< / p > < / div >
2019-06-13 02:23:54 +00:00
< / li >
< li class = "entry-summary" >
2019-07-10 01:18:01 +00:00
< a href = "#column_vector%28column%29-class-method" class = "signature" > < strong > .column_vector< / strong > (column)< / a >
2019-06-13 02:23:54 +00:00
2019-07-10 02:22:15 +00:00
< div class = "summary" > < p > Creates a single-column matrix where the values of that column are as given in < code > < a href = "../../Apatite/LinearAlgebra/Matrix.html#column%28j%29-instance-method" > #column< / a > < / code > .< / p > < / div >
2019-06-13 02:23:54 +00:00
< / li >
< li class = "entry-summary" >
< a href = "#columns%28columns%29-class-method" class = "signature" > < strong > .columns< / strong > (columns)< / a >
2019-07-10 01:18:01 +00:00
< div class = "summary" > < p > Creates a matrix using +columns+ as an array of column vectors.< / p > < / div >
2019-06-13 02:23:54 +00:00
< / li >
< li class = "entry-summary" >
2019-07-10 01:18:01 +00:00
< a href = "#combine%28%2Amatrices%2C%26block%29-class-method" class = "signature" > < strong > .combine< / strong > (*matrices, & block)< / a >
2019-06-13 02:23:54 +00:00
2019-07-10 01:18:01 +00:00
< div class = "summary" > < p > Create a matrix by combining matrices entrywise, using the given block< / p > < / div >
2019-06-13 02:23:54 +00:00
< / li >
< li class = "entry-summary" >
2019-07-10 01:18:01 +00:00
< a href = "#diagonal%28values%3AIndexable%28T%29%2Cdummy%3Dnil%29-class-method" class = "signature" > < strong > .diagonal< / strong > (values : Indexable(T), dummy = < span class = "n" > nil< / span > )< / a >
2019-06-13 02:23:54 +00:00
< div class = "summary" > < p > Creates a matrix where the diagonal elements are composed of < code > values< / code > .< / p > < / div >
< / li >
< li class = "entry-summary" >
2019-07-10 01:18:01 +00:00
< a href = "#diagonal%28%2Avalues%3AT%29-class-method" class = "signature" > < strong > .diagonal< / strong > (*values : T)< / a >
2019-06-13 02:23:54 +00:00
2019-07-10 02:22:15 +00:00
< div class = "summary" > < p > Creates a matrix where the diagonal elements are composed of < code > values< / code > .< / p > < / div >
2019-06-13 02:23:54 +00:00
< / li >
2019-06-13 06:17:13 +00:00
< li class = "entry-summary" >
2019-07-10 01:18:01 +00:00
< a href = "#empty%28row_count%3D0%2Ccolumn_count%3D0%29-class-method" class = "signature" > < strong > .empty< / strong > (row_count = < span class = "n" > 0< / span > , column_count = < span class = "n" > 0< / span > )< / a >
2019-06-13 06:17:13 +00:00
2019-07-10 01:18:01 +00:00
< div class = "summary" > < p > Creates a empty matrix of < code > < a href = "../../Apatite/LinearAlgebra/Matrix.html#row_count-instance-method" > #row_count< / a > < / code > x < code > < a href = "../../Apatite/LinearAlgebra/Matrix.html#column_count%3AInt32-instance-method" > #column_count< / a > < / code > .< / p > < / div >
2019-06-13 06:17:13 +00:00
< / li >
2019-06-13 02:23:54 +00:00
< li class = "entry-summary" >
< a href = "#hstack%28x%2C%2Amatrices%29-class-method" class = "signature" > < strong > .hstack< / strong > (x, *matrices)< / a >
2019-07-10 01:18:01 +00:00
< div class = "summary" > < p > Create a matrix by stacking matrices horizontally< / p > < / div >
2019-06-13 02:23:54 +00:00
< / li >
< li class = "entry-summary" >
< a href = "#identity%28n%29-class-method" class = "signature" > < strong > .identity< / strong > (n)< / a >
2019-07-10 01:18:01 +00:00
< div class = "summary" > < p > Creates an < code > n< / code > by < code > n< / code > identity matrix.< / p > < / div >
2019-06-13 02:23:54 +00:00
< / li >
< li class = "entry-summary" >
< a href = "#row_vector%28row%29-class-method" class = "signature" > < strong > .row_vector< / strong > (row)< / a >
2019-07-10 01:18:01 +00:00
< div class = "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%3AVector-%3E%29-instance-method" > #row< / a > < / code > .< / p > < / div >
< / li >
< li class = "entry-summary" >
< a href = "#rows%28rows%3AIndexable%28Array%28T%29%29%2Ccopy%3Dtrue%29-class-method" class = "signature" > < strong > .rows< / strong > (rows : Indexable(Array(T)), copy = < span class = "n" > true< / span > )< / a >
< div class = "summary" > < p > Creates a matrix where +rows+ is an array of arrays, each of which is a row of the matrix.< / p > < / div >
2019-06-13 02:23:54 +00:00
< / li >
< li class = "entry-summary" >
2019-07-10 01:18:01 +00:00
< a href = "#scalar%28n%2Cvalue%3AT%29-class-method" class = "signature" > < strong > .scalar< / strong > (n, value : T)< / a >
2019-06-13 02:23:54 +00:00
2019-07-10 01:18:01 +00:00
< div class = "summary" > < p > Creates an +n+ by +n+ diagonal matrix where each diagonal element is < code > value< / code > .< / p > < / div >
2019-06-13 02:23:54 +00:00
< / li >
< li class = "entry-summary" >
2019-07-10 01:18:01 +00:00
< a href = "#unit%28n%3AT%29-class-method" class = "signature" > < strong > .unit< / strong > (n : T)< / a >
2019-06-13 02:23:54 +00:00
2019-07-10 01:18:01 +00:00
< div class = "summary" > < p > Creates an < code > n< / code > by < code > n< / code > identity matrix.< / p > < / div >
2019-06-13 02:23:54 +00:00
< / li >
< li class = "entry-summary" >
2019-07-10 01:18:01 +00:00
< a href = "#vstack%28x%2C%2Amatrices%29-class-method" class = "signature" > < strong > .vstack< / strong > (x, *matrices)< / a >
2019-06-13 02:23:54 +00:00
2019-07-10 01:18:01 +00:00
< div class = "summary" > < p > Create a matrix by stacking matrices vertically< / p > < / div >
2019-06-13 02:23:54 +00:00
< / li >
< li class = "entry-summary" >
< a href = "#zero%28row_count%2Ccolumn_count%3Drow_count%29-class-method" class = "signature" > < strong > .zero< / strong > (row_count, column_count = row_count)< / a >
< div class = "summary" > < p > Creates a zero matrix.< / p > < / div >
< / li >
< / ul >
< h2 > Instance Method Summary< / h2 >
< ul class = "list-summary" >
< li class = "entry-summary" >
2019-07-10 01:18:01 +00:00
< a href = "#%2A%28other%29-instance-method" class = "signature" > < strong > #*< / strong > (other)< / a >
< div class = "summary" > < p > Matrix multiplication< / p > < / div >
2019-06-13 02:23:54 +00:00
< / li >
< li class = "entry-summary" >
2019-07-10 01:18:01 +00:00
< a href = "#%2A%2A%28other%29-instance-method" class = "signature" > < strong > #**< / strong > (other)< / a >
< div class = "summary" > < p > Matrix exponentiation.< / p > < / div >
2019-06-13 02:23:54 +00:00
< / li >
< li class = "entry-summary" >
2019-07-10 01:18:01 +00:00
< a href = "#%2B%28other%3AMatrix%7CIndexable%29-instance-method" class = "signature" > < strong > #+< / strong > (other : Matrix | Indexable)< / a >
< div class = "summary" > < p > Matrix addition< / p > < / div >
2019-06-13 02:23:54 +00:00
< / li >
< li class = "entry-summary" >
2019-07-10 01:18:01 +00:00
< a href = "#-%28other%3AMatrix%7CIndexable%29-instance-method" class = "signature" > < strong > #-< / strong > (other : Matrix | Indexable)< / a >
< div class = "summary" > < p > Matrix subtraction< / p > < / div >
2019-06-13 02:23:54 +00:00
< / li >
< li class = "entry-summary" >
2019-07-10 01:18:01 +00:00
< a href = "#%2F%28other%29-instance-method" class = "signature" > < strong > #/< / strong > (other)< / a >
< div class = "summary" > < p > Matrix division (multiplication by the inverse).< / p > < / div >
2019-06-13 02:23:54 +00:00
< / li >
< li class = "entry-summary" >
2019-07-10 01:18:01 +00:00
< a href = "#%3D%3D%28other%3AMatrix%29-instance-method" class = "signature" > < strong > #==< / strong > (other : Matrix)< / a >
< div class = "summary" > < p > Equality operator< / p > < / div >
2019-06-13 02:23:54 +00:00
< / li >
< li class = "entry-summary" >
2019-07-10 02:22:15 +00:00
< a href = "#%5B%5D%28i%29-instance-method" class = "signature" > < strong > #[]< / strong > (i)< / a >
2019-07-10 01:18:01 +00:00
2019-07-10 02:22:15 +00:00
< div class = "summary" > < p > Returns row < code > i< / code > of the matrix as an Array.< / p > < / div >
2019-06-13 02:23:54 +00:00
< / li >
< li class = "entry-summary" >
2019-07-10 02:22:15 +00:00
< a href = "#%5B%5D%28i%2Cj%29-instance-method" class = "signature" > < strong > #[]< / strong > (i, j)< / a >
2019-07-10 01:18:01 +00:00
2019-07-10 02:22:15 +00:00
< div class = "summary" > < p > Returns element (< code > i< / code > , < code > j< / code > ) of the matrix.< / p > < / div >
2019-06-13 02:23:54 +00:00
< / li >
< li class = "entry-summary" >
2019-07-10 01:18:01 +00:00
< a href = "#%5B%5D%3D%28i%2Cj%2Cv%3AT%29-instance-method" class = "signature" > < strong > #[]=< / strong > (i, j, v : T)< / a >
< div class = "summary" > < p > Set the value at index (< code > i< / code > , < code > j< / code > ).< / p > < / div >
2019-06-13 02:23:54 +00:00
< / li >
< li class = "entry-summary" >
2019-07-10 02:22:15 +00:00
< a href = "#%5B%5D%3F%28i%29-instance-method" class = "signature" > < strong > #[]?< / strong > (i)< / a >
2019-07-10 01:18:01 +00:00
2019-07-10 02:22:15 +00:00
< div class = "summary" > < p > Returns row < code > i< / code > of the matrix as an Array.< / p > < / div >
2019-06-13 02:23:54 +00:00
< / li >
< li class = "entry-summary" >
2019-07-10 02:22:15 +00:00
< a href = "#%5B%5D%3F%28i%2Cj%29-instance-method" class = "signature" > < strong > #[]?< / strong > (i, j)< / a >
2019-07-10 01:18:01 +00:00
2019-07-10 02:22:15 +00:00
< div class = "summary" > < p > Returns element (< code > i< / code > , < code > j< / code > ) of the matrix.< / p > < / div >
2019-06-13 02:23:54 +00:00
< / li >
< li class = "entry-summary" >
2019-07-10 01:18:01 +00:00
< a href = "#adjugate-instance-method" class = "signature" > < strong > #adjugate< / strong > < / a >
2019-06-13 02:23:54 +00:00
2019-07-10 01:18:01 +00:00
< div class = "summary" > < p > Returns the adjugate of the matrix.< / p > < / div >
2019-06-13 02:23:54 +00:00
< / li >
< li class = "entry-summary" >
2019-07-10 01:18:01 +00:00
< a href = "#clone-instance-method" class = "signature" > < strong > #clone< / strong > < / a >
2019-06-13 02:23:54 +00:00
2019-07-10 01:18:01 +00:00
< div class = "summary" > < p > Returns a clone of the matrix, so that the contents of each do not reference identical objects.< / p > < / div >
2019-06-13 02:23:54 +00:00
< / li >
< li class = "entry-summary" >
2019-07-10 01:18:01 +00:00
< a href = "#coerce%28klass%29-instance-method" class = "signature" > < strong > #coerce< / strong > (klass)< / a >
2019-06-13 02:23:54 +00:00
2019-07-10 01:18:01 +00:00
< div class = "summary" > < p > Attempt to coerce the elements in the matrix to another type.< / p > < / div >
2019-06-13 02:23:54 +00:00
< / li >
< li class = "entry-summary" >
< a href = "#cofactor%28row%2Ccolumn%29-instance-method" class = "signature" > < strong > #cofactor< / strong > (row, column)< / a >
2019-07-10 01:18:01 +00:00
< div class = "summary" > < p > Returns the (row, column) cofactor which is obtained by multiplying the first minor by (-1)**(row + column).< / p > < / div >
2019-06-13 02:23:54 +00:00
< / li >
< li class = "entry-summary" >
2019-07-10 02:22:15 +00:00
< a href = "#column%28j%29-instance-method" class = "signature" > < strong > #column< / strong > (j)< / a >
2019-06-13 02:23:54 +00:00
2019-07-10 02:22:15 +00:00
< div class = "summary" > < p > Returns column vector < code > j< / code > of the Matrix as a Vector (starting at 0).< / p > < / div >
2019-06-13 02:23:54 +00:00
< / li >
< li class = "entry-summary" >
2019-07-10 02:22:15 +00:00
< a href = "#column%28j%2C%26block%3AT-%3E%29-instance-method" class = "signature" > < strong > #column< / strong > (j, & block : T -> )< / a >
2019-06-13 02:23:54 +00:00
2019-07-10 02:22:15 +00:00
< div class = "summary" > < p > Returns a block which yields every item in column < code > j< / code > of the Matrix.< / p > < / div >
2019-06-13 02:23:54 +00:00
< / li >
< li class = "entry-summary" >
< a href = "#column%3F%28j%29-instance-method" class = "signature" > < strong > #column?< / strong > (j)< / a >
2019-07-10 01:18:01 +00:00
< div class = "summary" > < p > Returns column vector < code > j< / code > of the Matrix as a Vector (starting at 0).< / p > < / div >
2019-06-13 02:23:54 +00:00
< / li >
< li class = "entry-summary" >
< a href = "#column_count%3AInt32-instance-method" class = "signature" > < strong > #column_count< / strong > : Int32< / a >
2019-07-10 01:18:01 +00:00
< div class = "summary" > < p > Returns the number of columns.< / p > < / div >
< / li >
2019-07-10 02:22:15 +00:00
< li class = "entry-summary" >
< a href = "#column_vectors-instance-method" class = "signature" > < strong > #column_vectors< / strong > < / a >
< div class = "summary" > < p > Returns an array of the column vectors of the matrix.< / p > < / div >
< / li >
2019-07-10 01:18:01 +00:00
< li class = "entry-summary" >
< a href = "#combine%28%2Amatrices%2C%26block%29-instance-method" class = "signature" > < strong > #combine< / strong > (*matrices, & block)< / a >
< div class = "summary" > < p > Create a matrix by combining matrices entrywise, using the given block< / p > < / div >
2019-06-13 02:23:54 +00:00
< / li >
< li class = "entry-summary" >
2019-07-10 01:18:01 +00:00
< a href = "#conj-instance-method" class = "signature" > < strong > #conj< / strong > < / a >
2019-06-13 02:23:54 +00:00
2019-07-10 01:18:01 +00:00
< div class = "summary" > < p > Returns the conjugate of the matrix.< / p > < / div >
2019-06-13 02:23:54 +00:00
< / li >
< li class = "entry-summary" >
< a href = "#determinant-instance-method" class = "signature" > < strong > #determinant< / strong > < / a >
2019-07-10 01:18:01 +00:00
< div class = "summary" > < p > Returns the determinant of the matrix.< / p > < / div >
< / li >
< li class = "entry-summary" >
< a href = "#diagonal%3F-instance-method" class = "signature" > < strong > #diagonal?< / strong > < / a >
< div class = "summary" > < p > Returns < code > true< / code > if this is a diagonal matrix.< / p > < / div >
< / li >
< li class = "entry-summary" >
< a href = "#each%28which%3D%3Aall%2C%26block%3AT-%3E%29-instance-method" class = "signature" > < strong > #each< / strong > (which = < span class = "n" > :all< / span > , & block : T -> )< / a >
< div class = "summary" > < p > Yields all elements of the matrix, starting with those of the first row, or returns an Enumerator if no block given.< / p > < / div >
< / li >
< li class = "entry-summary" >
< a href = "#each_with_index%28which%3D%3Aall%2C%26block%3AT%2CInt32%2CInt32-%3E%29-instance-method" class = "signature" > < strong > #each_with_index< / strong > (which = < span class = "n" > :all< / span > , & block : T, Int32, Int32 -> )< / a >
< div class = "summary" > < p > Same as #each, but the row index and column index in addition to the element< / p > < / div >
< / li >
< li class = "entry-summary" >
< a href = "#eigensystem-instance-method" class = "signature" > < strong > #eigensystem< / strong > < / a >
2019-07-10 02:08:46 +00:00
< div class = "summary" > < p > Returns the Eigensystem of the matrix See < code > < a href = "../../Apatite/LinearAlgebra/Matrix/EigenvalueDecomposition.html" > EigenvalueDecomposition< / a > < / code > .< / p > < / div >
2019-07-10 01:18:01 +00:00
< / li >
< li class = "entry-summary" >
< a href = "#empty%3F-instance-method" class = "signature" > < strong > #empty?< / strong > < / a >
< div class = "summary" > < p > Returns true if this matrix is empty.< / p > < / div >
2019-06-13 02:23:54 +00:00
< / li >
< li class = "entry-summary" >
< a href = "#first_minor%28row%2Ccolumn%29-instance-method" class = "signature" > < strong > #first_minor< / strong > (row, column)< / a >
2019-07-10 01:18:01 +00:00
< div class = "summary" > < p > Returns the submatrix obtained by deleting the specified row and column.< / p > < / div >
< / li >
< li class = "entry-summary" >
< a href = "#hadamard_product%28m%29-instance-method" class = "signature" > < strong > #hadamard_product< / strong > (m)< / a >
< div class = "summary" > < p > Hadamard product< / p > < / div >
< / li >
< li class = "entry-summary" >
< a href = "#hermitian%3F-instance-method" class = "signature" > < strong > #hermitian?< / strong > < / a >
< div class = "summary" > < p > Returns < code > true< / code > if this is an hermitian matrix.< / p > < / div >
< / li >
< li class = "entry-summary" >
< a href = "#hstack%28%2Amatrices%29-instance-method" class = "signature" > < strong > #hstack< / strong > (*matrices)< / a >
< div class = "summary" > < p > Returns a new matrix resulting by stacking horizontally the receiver with the given matrices< / p > < / div >
< / li >
< li class = "entry-summary" >
< a href = "#imag-instance-method" class = "signature" > < strong > #imag< / strong > < / a >
< div class = "summary" > < p > Returns the imaginary part of the matrix.< / p > < / div >
< / li >
< li class = "entry-summary" >
< a href = "#index%28i%2Cselector%3D%3Aall%29-instance-method" class = "signature" > < strong > #index< / strong > (i, selector = < span class = "n" > :all< / span > )< / a >
< div class = "summary" > < p > The index method is specialized to return the index as {row, column} It also accepts an optional < code > selector< / code > argument, see < code > < a href = "../../Apatite/LinearAlgebra/Matrix.html#each%28which%3D%3Aall%2C%26block%3AT-%3E%29-instance-method" > #each< / a > < / code > for details.< / p > < / div >
< / li >
< li class = "entry-summary" >
< a href = "#index%28selector%3D%3Aall%2C%26block%3AT-%3EBool%29-instance-method" class = "signature" > < strong > #index< / strong > (selector = < span class = "n" > :all< / span > , & block : T -> Bool)< / a >
< div class = "summary" > < p > Returns the index as {row, column}, using < code > & block< / code > to filter the result.< / p > < / div >
2019-06-13 02:23:54 +00:00
< / li >
< li class = "entry-summary" >
< a href = "#inverse-instance-method" class = "signature" > < strong > #inverse< / strong > < / a >
< div class = "summary" > < p > Returns the inverse of the matrix.< / p > < / div >
< / li >
< li class = "entry-summary" >
< a href = "#laplace_expansion%28%2A%2Crow%3Dnil%2Ccolumn%3Dnil%29-instance-method" class = "signature" > < strong > #laplace_expansion< / strong > (*, row = < span class = "n" > nil< / span > , column = < span class = "n" > nil< / span > )< / a >
< div class = "summary" > < p > Returns the Laplace expansion along given row or column.< / p > < / div >
< / li >
< li class = "entry-summary" >
2019-07-10 01:18:01 +00:00
< a href = "#lower_triangular%3F-instance-method" class = "signature" > < strong > #lower_triangular?< / strong > < / a >
< div class = "summary" > < p > Returns true if this matrix is a lower triangular matrix.< / p > < / div >
2019-06-13 02:23:54 +00:00
< / li >
< li class = "entry-summary" >
2019-07-10 01:18:01 +00:00
< a href = "#lup-instance-method" class = "signature" > < strong > #lup< / strong > < / a >
< div class = "summary" > < p > Returns the LUP decomposition of the matrix See +LUPDecomposition+.< / p > < / div >
2019-06-13 02:23:54 +00:00
< / li >
< li class = "entry-summary" >
2019-07-10 01:18:01 +00:00
< a href = "#map%28%26block%3AT-%3ET%29-instance-method" class = "signature" > < strong > #map< / strong > (& block : T -> T)< / a >
< div class = "summary" > < p > Returns a Matrix that is the result of iteration of the given block over all elements in the matrix.< / p > < / div >
2019-06-13 02:23:54 +00:00
< / li >
< li class = "entry-summary" >
2019-07-10 02:22:15 +00:00
< a href = "#minor%28from_row%3AInt%2Cnrows%3AInt%2Cfrom_col%3AInt%2Cncols%3AInt%29-instance-method" class = "signature" > < strong > #minor< / strong > (from_row : Int, nrows : Int, from_col : Int, ncols : Int)< / a >
2019-07-10 01:18:01 +00:00
< div class = "summary" > < p > Returns a section of the Matrix.< / p > < / div >
2019-06-13 02:23:54 +00:00
< / li >
< li class = "entry-summary" >
2019-07-10 02:22:15 +00:00
< a href = "#minor%28row_range%3ARange%2Ccol_range%3ARange%29-instance-method" class = "signature" > < strong > #minor< / strong > (row_range : Range, col_range : Range)< / a >
2019-07-10 01:18:01 +00:00
< div class = "summary" > < p > Returns a section of the Matrix.< / p > < / div >
2019-06-13 02:23:54 +00:00
< / li >
< li class = "entry-summary" >
2019-07-10 01:18:01 +00:00
< a href = "#normal%3F-instance-method" class = "signature" > < strong > #normal?< / strong > < / a >
< div class = "summary" > < p > Returns < code > true< / code > if this is a normal matrix.< / p > < / div >
2019-06-13 02:23:54 +00:00
< / li >
< li class = "entry-summary" >
2019-07-10 01:18:01 +00:00
< a href = "#orthogonal%3F-instance-method" class = "signature" > < strong > #orthogonal?< / strong > < / a >
< div class = "summary" > < p > Returns < code > true< / code > if this is an orthogonal matrix< / p > < / div >
2019-06-13 02:23:54 +00:00
< / li >
< li class = "entry-summary" >
2019-07-10 01:18:01 +00:00
< a href = "#permutation%3F-instance-method" class = "signature" > < strong > #permutation?< / strong > < / a >
< div class = "summary" > < p > Returns < code > true< / code > if this is a permutation matrix< / p > < / div >
2019-06-13 02:23:54 +00:00
< / li >
< li class = "entry-summary" >
2019-07-10 01:18:01 +00:00
< a href = "#pretty_print%28pp%29%3ANil-instance-method" class = "signature" > < strong > #pretty_print< / strong > (pp) : Nil< / a >
2019-06-13 02:23:54 +00:00
< / li >
2019-07-10 01:18:01 +00:00
< li class = "entry-summary" >
< a href = "#rank-instance-method" class = "signature" > < strong > #rank< / strong > < / a >
< div class = "summary" > < p > Returns the rank of the matrix.< / p > < / div >
< / li >
2019-06-13 02:23:54 +00:00
2019-07-10 01:18:01 +00:00
< li class = "entry-summary" >
< a href = "#real-instance-method" class = "signature" > < strong > #real< / strong > < / a >
< div class = "summary" > < p > Returns the real part of the matrix.< / p > < / div >
< / li >
2019-06-13 02:23:54 +00:00
2019-07-10 01:18:01 +00:00
< li class = "entry-summary" >
< a href = "#real%3F-instance-method" class = "signature" > < strong > #real?< / strong > < / a >
< div class = "summary" > < p > Returns < code > true< / code > if this matrix contains real numbers, i.e.< / p > < / div >
< / li >
2019-06-13 02:23:54 +00:00
2019-07-10 01:18:01 +00:00
< li class = "entry-summary" >
< a href = "#rect-instance-method" class = "signature" > < strong > #rect< / strong > < / a >
< div class = "summary" > < p > Returns an array containing matrices corresponding to the real and imaginary parts of the matrix< / p > < / div >
< / li >
2019-06-13 02:23:54 +00:00
2019-07-10 01:18:01 +00:00
< li class = "entry-summary" >
< a href = "#regular%3F-instance-method" class = "signature" > < strong > #regular?< / strong > < / a >
< div class = "summary" > < p > Returns < code > true< / code > if this is a regular (i.e.< / p > < / div >
< / li >
2019-06-13 02:23:54 +00:00
2019-07-10 01:18:01 +00:00
< li class = "entry-summary" >
< a href = "#round%28n%3D0%29-instance-method" class = "signature" > < strong > #round< / strong > (n = < span class = "n" > 0< / span > )< / a >
< div class = "summary" > < p > Returns a matrix with entries rounded to the given precision (see < code > Float#round< / code > )< / p > < / div >
< / li >
2019-06-13 02:23:54 +00:00
2019-07-10 01:18:01 +00:00
< li class = "entry-summary" >
< a href = "#row%28i%2C%26block%3AVector-%3E%29-instance-method" class = "signature" > < strong > #row< / strong > (i, & block : Vector -> )< / a >
< div class = "summary" > < p > Returns a block which yields every Vector in the row (starting at 0).< / p > < / div >
< / li >
2019-06-13 02:23:54 +00:00
2019-07-10 01:18:01 +00:00
< li class = "entry-summary" >
< a href = "#row%28i%29-instance-method" class = "signature" > < strong > #row< / strong > (i)< / a >
< div class = "summary" > < p > Returns row vector number < code > i< / code > of the Matrix as a Vector (starting at 0 like a good boy).< / p > < / div >
< / li >
2019-06-13 02:23:54 +00:00
2019-07-10 01:18:01 +00:00
< li class = "entry-summary" >
< a href = "#row%3F%28i%29-instance-method" class = "signature" > < strong > #row?< / strong > (i)< / a >
< div class = "summary" > < p > Returns row vector number < code > i< / code > of the Matrix as a Vector (starting at 0 like a good boy).< / p > < / div >
< / li >
2019-06-13 02:23:54 +00:00
2019-07-10 01:18:01 +00:00
< li class = "entry-summary" >
< a href = "#row_count-instance-method" class = "signature" > < strong > #row_count< / strong > < / a >
< div class = "summary" > < p > Returns the number of rows.< / p > < / div >
< / li >
2019-06-13 02:23:54 +00:00
2019-07-10 02:22:15 +00:00
< li class = "entry-summary" >
< a href = "#row_vectors-instance-method" class = "signature" > < strong > #row_vectors< / strong > < / a >
< div class = "summary" > < p > Returns an array of the row vectors of the matrix.< / p > < / div >
< / li >
2019-07-10 01:18:01 +00:00
< li class = "entry-summary" >
< a href = "#singular%3F-instance-method" class = "signature" > < strong > #singular?< / strong > < / a >
< div class = "summary" > < p > Returns < code > true< / code > if this is a singular matrix.< / p > < / div >
< / li >
2019-06-13 02:23:54 +00:00
2019-07-10 01:18:01 +00:00
< li class = "entry-summary" >
< a href = "#square%3F-instance-method" class = "signature" > < strong > #square?< / strong > < / a >
< div class = "summary" > < p > Returns < code > true< / code > if this is a square matrix.< / p > < / div >
< / li >
2019-06-13 02:23:54 +00:00
2019-07-10 01:18:01 +00:00
< li class = "entry-summary" >
< a href = "#swap_columns%28col1%2Ccol2%29-instance-method" class = "signature" > < strong > #swap_columns< / strong > (col1, col2)< / a >
< div class = "summary" > < p > Swaps < code > col1< / code > and < code > col2< / code > < / p > < / div >
< / li >
2019-06-13 02:23:54 +00:00
2019-07-10 01:18:01 +00:00
< li class = "entry-summary" >
< a href = "#swap_rows%28row1%2Crow2%29-instance-method" class = "signature" > < strong > #swap_rows< / strong > (row1, row2)< / a >
< div class = "summary" > < p > Swaps < code > row1< / code > and < code > row2< / code > < / p > < / div >
< / li >
2019-06-13 02:23:54 +00:00
2019-07-10 01:18:01 +00:00
< li class = "entry-summary" >
< a href = "#symmetric%3F-instance-method" class = "signature" > < strong > #symmetric?< / strong > < / a >
< div class = "summary" > < p > Returns +true+ if this is a symmetric matrix.< / p > < / div >
< / li >
2019-06-13 02:23:54 +00:00
2019-07-10 01:18:01 +00:00
< li class = "entry-summary" >
< a href = "#t-instance-method" class = "signature" > < strong > #t< / strong > < / a >
< div class = "summary" > < p > Returns the transpose of the matrix.< / p > < / div >
< / li >
< li class = "entry-summary" >
< a href = "#to_a-instance-method" class = "signature" > < strong > #to_a< / strong > < / a >
2019-07-10 02:22:15 +00:00
< div class = "summary" > < p > Returns an array of arrays that describe the rows of the matrix.< / p > < / div >
2019-07-10 01:18:01 +00:00
< / li >
< li class = "entry-summary" >
< a href = "#to_json%28json%3AJSON%3A%3ABuilder%29-instance-method" class = "signature" > < strong > #to_json< / strong > (json : JSON::Builder)< / a >
2019-07-10 02:22:15 +00:00
< div class = "summary" > < p > Convert the matrix to a json array< / p > < / div >
2019-07-10 01:18:01 +00:00
< / li >
< li class = "entry-summary" >
< a href = "#to_s%28io%29-instance-method" class = "signature" > < strong > #to_s< / strong > (io)< / a >
< / li >
< li class = "entry-summary" >
< a href = "#tr-instance-method" class = "signature" > < strong > #tr< / strong > < / a >
< div class = "summary" > < p > Returns the trace (sum of diagonal elements) of the matrix.< / p > < / div >
< / li >
< li class = "entry-summary" >
< a href = "#trace-instance-method" class = "signature" > < strong > #trace< / strong > < / a >
< div class = "summary" > < p > Returns the trace (sum of diagonal elements) of the matrix.< / p > < / div >
< / li >
< li class = "entry-summary" >
< a href = "#transpose-instance-method" class = "signature" > < strong > #transpose< / strong > < / a >
< div class = "summary" > < p > Returns the transpose of the matrix.< / p > < / div >
< / li >
< li class = "entry-summary" >
< a href = "#unitary%3F-instance-method" class = "signature" > < strong > #unitary?< / strong > < / a >
< div class = "summary" > < p > Returns < code > true< / code > if this is a unitary matrix< / p > < / div >
< / li >
< li class = "entry-summary" >
< a href = "#unsafe_fetch%28i%29-instance-method" class = "signature" > < strong > #unsafe_fetch< / strong > (i)< / a >
< / li >
< li class = "entry-summary" >
< a href = "#upper_triangular%3F-instance-method" class = "signature" > < strong > #upper_triangular?< / strong > < / a >
< div class = "summary" > < p > Returns true if this matrix is a upper triangular matrix.< / p > < / div >
< / li >
< li class = "entry-summary" >
< a href = "#vstack%28%2Amatrices%29-instance-method" class = "signature" > < strong > #vstack< / strong > (*matrices)< / a >
< div class = "summary" > < p > Returns a new matrix resulting by stacking vertically the receiver with the given matrices< / p > < / div >
< / li >
< li class = "entry-summary" >
< a href = "#zero%3F-instance-method" class = "signature" > < strong > #zero?< / strong > < / a >
< div class = "summary" > < p > Returns < code > true< / code > if this is a matrix with only zero elements< / p > < / div >
< / li >
< / ul >
< div class = "methods-inherited" >
2019-06-13 02:23:54 +00:00
2019-07-10 01:18:01 +00:00
< / div >
< h2 > Class Method Detail< / h2 >
< div class = "entry-detail" id = "[](*rows)-class-method" >
< div class = "signature" >
def self.< strong > []< / strong > (*rows)
< a class = "method-permalink" href = "#%5B%5D%28%2Arows%29-class-method" > #< / a >
< / div >
< div class = "doc" > < p > Creates a matrix where each argument is a row.< / p >
< pre > < code > < span class = "t" > Matrix< / span > [[< span class = "n" > 25< / span > , < span class = "n" > 93< / span > ], [< span class = "n" > -1< / span > , < span class = "n" > 66< / span > ]]
< span class = "c" > # => [ 25, 93,< / span >
< span class = "c" > # -1, 66 ]< / span > < / code > < / pre > < / div >
< br / >
< div >
2019-07-10 02:22:15 +00:00
[< a href = "https://github.com/watzon/apatite/blob/6e67ceb81b0b3c61d48b74e5ca5154866a9abd1a/src/apatite/linear_algebra/matrix.cr#L20" target = "_blank" > View source< / a > ]
2019-07-10 01:18:01 +00:00
< / div >
< / div >
< div class = "entry-detail" id = "build(row_count,column_count=row_count,&block:Int32,Int32->T)-class-method" >
< div class = "signature" >
def self.< strong > build< / strong > (row_count, column_count = row_count, & block : Int32, Int32 -> T)
< a class = "method-permalink" href = "#build%28row_count%2Ccolumn_count%3Drow_count%2C%26block%3AInt32%2CInt32-%3ET%29-class-method" > #< / a >
< / div >
< div class = "doc" > < p > Creates a matrix of size +row_count+ x +column_count+.
It fills the values by calling the given block,
passing the current row and column.
Returns an enumerator if no block is given.< / p >
< pre > < code > m < span class = "o" > =< / span > < span class = "t" > Matrix< / span > .build(< span class = "n" > 2< / span > , < span class = "n" > 4< / span > ) { < span class = "o" > |< / span > row, col< span class = "o" > |< / span > col < span class = "o" > -< / span > row }
< span class = "c" > # => Matrix[[0, 1, 2, 3], [-1, 0, 1, 2]]< / span >
m < span class = "o" > =< / span > < span class = "t" > Matrix< / span > .build(< span class = "n" > 3< / span > ) { rand }
< span class = "c" > # => a 3x3 matrix with random elements< / span > < / code > < / pre > < / div >
< br / >
< div >
2019-07-10 02:22:15 +00:00
[< a href = "https://github.com/watzon/apatite/blob/6e67ceb81b0b3c61d48b74e5ca5154866a9abd1a/src/apatite/linear_algebra/matrix.cr#L69" target = "_blank" > View source< / a > ]
2019-07-10 01:18:01 +00:00
< / div >
< / div >
< div class = "entry-detail" id = "column_vector(column)-class-method" >
< div class = "signature" >
def self.< strong > column_vector< / strong > (column)
< a class = "method-permalink" href = "#column_vector%28column%29-class-method" > #< / a >
< / div >
< div class = "doc" > < p > Creates a single-column matrix where the values of that column are as given
2019-07-10 02:22:15 +00:00
in < code > < a href = "../../Apatite/LinearAlgebra/Matrix.html#column%28j%29-instance-method" > #column< / a > < / code > .< / p >
2019-07-10 01:18:01 +00:00
< pre > < code > < span class = "t" > Matrix< / span > .column_vector([< span class = "n" > 4< / span > ,< span class = "n" > 5< / span > ,< span class = "n" > 6< / span > ])
< span class = "c" > # => [ 4,< / span >
< span class = "c" > # 5,< / span >
< span class = "c" > # 6 ]< / span > < / code > < / pre > < / div >
< br / >
< div >
2019-07-10 02:22:15 +00:00
[< a href = "https://github.com/watzon/apatite/blob/6e67ceb81b0b3c61d48b74e5ca5154866a9abd1a/src/apatite/linear_algebra/matrix.cr#L166" target = "_blank" > View source< / a > ]
2019-07-10 01:18:01 +00:00
< / div >
< / div >
< div class = "entry-detail" id = "columns(columns)-class-method" >
< div class = "signature" >
def self.< strong > columns< / strong > (columns)
< a class = "method-permalink" href = "#columns%28columns%29-class-method" > #< / a >
< / div >
< div class = "doc" > < p > Creates a matrix using +columns+ as an array of column vectors.< / p >
< pre > < code > < span class = "t" > Matrix< / span > .columns([[< span class = "n" > 25< / span > , < span class = "n" > 93< / span > ], [< span class = "n" > -1< / span > , < span class = "n" > 66< / span > ]])
< span class = "c" > # => [ 25, -1,< / span >
< span class = "c" > # 93, 66 ]< / span > < / code > < / pre > < / div >
< br / >
< div >
2019-07-10 02:22:15 +00:00
[< a href = "https://github.com/watzon/apatite/blob/6e67ceb81b0b3c61d48b74e5ca5154866a9abd1a/src/apatite/linear_algebra/matrix.cr#L54" target = "_blank" > View source< / a > ]
2019-07-10 01:18:01 +00:00
< / div >
< / div >
< div class = "entry-detail" id = "combine(*matrices,&block)-class-method" >
< div class = "signature" >
def self.< strong > combine< / strong > (*matrices, & block)
< a class = "method-permalink" href = "#combine%28%2Amatrices%2C%26block%29-class-method" > #< / a >
< / div >
< div class = "doc" > < p > Create a matrix by combining matrices entrywise, using the given block< / p >
< pre > < code > x < span class = "o" > =< / span > < span class = "t" > Matrix< / span > [[< span class = "n" > 6< / span > , < span class = "n" > 6< / span > ], [< span class = "n" > 4< / span > , < span class = "n" > 4< / span > ]]
y < span class = "o" > =< / span > < span class = "t" > Matrix< / span > [[< span class = "n" > 1< / span > , < span class = "n" > 2< / span > ], [< span class = "n" > 3< / span > , < span class = "n" > 4< / span > ]]
< span class = "t" > Matrix< / span > .combine(x, y) {< span class = "o" > |< / span > a, b< span class = "o" > |< / span > a < span class = "o" > -< / span > b}
< span class = "c" > # => Matrix[[5, 4], [1, 0]]< / span > < / code > < / pre > < / div >
< br / >
< div >
2019-07-10 02:22:15 +00:00
[< a href = "https://github.com/watzon/apatite/blob/6e67ceb81b0b3c61d48b74e5ca5154866a9abd1a/src/apatite/linear_algebra/matrix.cr#L245" target = "_blank" > View source< / a > ]
2019-07-10 01:18:01 +00:00
< / div >
< / div >
< div class = "entry-detail" id = "diagonal(values:Indexable(T),dummy=nil)-class-method" >
< div class = "signature" >
def self.< strong > diagonal< / strong > (values : Indexable(T), dummy = < span class = "n" > nil< / span > )
< a class = "method-permalink" href = "#diagonal%28values%3AIndexable%28T%29%2Cdummy%3Dnil%29-class-method" > #< / a >
< / div >
< div class = "doc" > < p > Creates a matrix where the diagonal elements are composed of < code > values< / code > .< / p >
< pre > < code > < span class = "t" > Matrix< / span > .diagonal(< span class = "n" > 9< / span > , < span class = "n" > 5< / span > , < span class = "n" > -3< / span > )
< span class = "c" > # => [ 9, 0, 0,< / span >
< span class = "c" > # 0, 5, 0,< / span >
< span class = "c" > # 0, 0, -3 ]< / span > < / code > < / pre > < / div >
< br / >
< div >
2019-07-10 02:22:15 +00:00
[< a href = "https://github.com/watzon/apatite/blob/6e67ceb81b0b3c61d48b74e5ca5154866a9abd1a/src/apatite/linear_algebra/matrix.cr#L89" target = "_blank" > View source< / a > ]
2019-07-10 01:18:01 +00:00
< / div >
< / div >
< div class = "entry-detail" id = "diagonal(*values:T)-class-method" >
< div class = "signature" >
def self.< strong > diagonal< / strong > (*values : T)
< a class = "method-permalink" href = "#diagonal%28%2Avalues%3AT%29-class-method" > #< / a >
< / div >
2019-07-10 02:22:15 +00:00
< div class = "doc" > < p > Creates a matrix where the diagonal elements are composed of < code > values< / code > .< / p >
< pre > < code > < span class = "t" > Matrix< / span > .diagonal(< span class = "n" > 9< / span > , < span class = "n" > 5< / span > , < span class = "n" > -3< / span > )
< span class = "c" > # => [ 9, 0, 0,< / span >
< span class = "c" > # 0, 5, 0,< / span >
< span class = "c" > # 0, 0, -3 ]< / span > < / code > < / pre > < / div >
2019-07-10 01:18:01 +00:00
< br / >
< div >
2019-07-10 02:22:15 +00:00
[< a href = "https://github.com/watzon/apatite/blob/6e67ceb81b0b3c61d48b74e5ca5154866a9abd1a/src/apatite/linear_algebra/matrix.cr#L101" target = "_blank" > View source< / a > ]
2019-07-10 01:18:01 +00:00
< / div >
< / div >
< div class = "entry-detail" id = "empty(row_count=0,column_count=0)-class-method" >
< div class = "signature" >
def self.< strong > empty< / strong > (row_count = < span class = "n" > 0< / span > , column_count = < span class = "n" > 0< / span > )
< a class = "method-permalink" href = "#empty%28row_count%3D0%2Ccolumn_count%3D0%29-class-method" > #< / a >
< / div >
< div class = "doc" > < p > Creates a empty matrix of < code > < a href = "../../Apatite/LinearAlgebra/Matrix.html#row_count-instance-method" > #row_count< / a > < / code > x < code > < a href = "../../Apatite/LinearAlgebra/Matrix.html#column_count%3AInt32-instance-method" > #column_count< / a > < / code > .
At least one of < code > < a href = "../../Apatite/LinearAlgebra/Matrix.html#row_count-instance-method" > #row_count< / a > < / code > or < code > < a href = "../../Apatite/LinearAlgebra/Matrix.html#column_count%3AInt32-instance-method" > #column_count< / a > < / code > must be 0.< / p >
< pre > < code > m < span class = "o" > =< / span > < span class = "t" > Matrix< / span > (< span class = "t" > Int32< / span > ).empty(< span class = "n" > 2< / span > , < span class = "n" > 0< / span > )
m < span class = "o" > ==< / span > < span class = "t" > Matrix< / span > [ < span class = "o" > []< / span > , < span class = "o" > []< / span > ]
< span class = "c" > # => true< / span >
n < span class = "o" > =< / span > < span class = "t" > Matrix< / span > (< span class = "t" > Int32< / span > ).empty(< span class = "n" > 0< / span > , < span class = "n" > 3< / span > )
m < span class = "o" > *< / span > n
< span class = "c" > # => Matrix[[0, 0, 0], [0, 0, 0]]< / span > < / code > < / pre > < / div >
< br / >
< div >
2019-07-10 02:22:15 +00:00
[< a href = "https://github.com/watzon/apatite/blob/6e67ceb81b0b3c61d48b74e5ca5154866a9abd1a/src/apatite/linear_algebra/matrix.cr#L182" target = "_blank" > View source< / a > ]
2019-07-10 01:18:01 +00:00
< / div >
< / div >
< div class = "entry-detail" id = "hstack(x,*matrices)-class-method" >
< div class = "signature" >
def self.< strong > hstack< / strong > (x, *matrices)
< a class = "method-permalink" href = "#hstack%28x%2C%2Amatrices%29-class-method" > #< / a >
< / div >
< div class = "doc" > < p > Create a matrix by stacking matrices horizontally< / p >
< pre > < code > x < span class = "o" > =< / span > < span class = "t" > Matrix< / span > [[< span class = "n" > 1< / span > , < span class = "n" > 2< / span > ], [< span class = "n" > 3< / span > , < span class = "n" > 4< / span > ]]
y < span class = "o" > =< / span > < span class = "t" > Matrix< / span > [[< span class = "n" > 5< / span > , < span class = "n" > 6< / span > ], [< span class = "n" > 7< / span > , < span class = "n" > 8< / span > ]]
< span class = "t" > Matrix< / span > .hstack(x, y)
< span class = "c" > # => Matrix[[1, 2, 5, 6], [3, 4, 7, 8]]< / span > < / code > < / pre > < / div >
< br / >
< div >
2019-07-10 02:22:15 +00:00
[< a href = "https://github.com/watzon/apatite/blob/6e67ceb81b0b3c61d48b74e5ca5154866a9abd1a/src/apatite/linear_algebra/matrix.cr#L217" target = "_blank" > View source< / a > ]
2019-07-10 01:18:01 +00:00
< / div >
< / div >
< div class = "entry-detail" id = "identity(n)-class-method" >
< div class = "signature" >
def self.< strong > identity< / strong > (n)
< a class = "method-permalink" href = "#identity%28n%29-class-method" > #< / a >
< / div >
< div class = "doc" > < p > Creates an < code > n< / code > by < code > n< / code > identity matrix.< / p >
< pre > < code > < span class = "t" > Matrix< / span > .identity(< span class = "n" > 2< / span > )
< span class = "c" > # => [ 1, 0,< / span >
< span class = "c" > # 0, 1 ]< / span > < / code > < / pre > < / div >
< br / >
< div >
2019-07-10 02:22:15 +00:00
[< a href = "https://github.com/watzon/apatite/blob/6e67ceb81b0b3c61d48b74e5ca5154866a9abd1a/src/apatite/linear_algebra/matrix.cr#L124" target = "_blank" > View source< / a > ]
2019-07-10 01:18:01 +00:00
< / div >
< / div >
< div class = "entry-detail" id = "row_vector(row)-class-method" >
< div class = "signature" >
def self.< strong > row_vector< / strong > (row)
< a class = "method-permalink" href = "#row_vector%28row%29-class-method" > #< / a >
< / div >
< div class = "doc" > < 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%3AVector-%3E%29-instance-method" > #row< / a > < / code > .< / p >
< pre > < code > < span class = "t" > Matrix< / span > .row_vector([< span class = "n" > 4< / span > ,< span class = "n" > 5< / span > ,< span class = "n" > 6< / span > ])
< span class = "c" > # => [ 4, 5, 6 ]< / span > < / code > < / pre > < / div >
< br / >
< div >
2019-07-10 02:22:15 +00:00
[< a href = "https://github.com/watzon/apatite/blob/6e67ceb81b0b3c61d48b74e5ca5154866a9abd1a/src/apatite/linear_algebra/matrix.cr#L152" target = "_blank" > View source< / a > ]
2019-07-10 01:18:01 +00:00
< / div >
< / div >
< div class = "entry-detail" id = "rows(rows:Indexable(Array(T)),copy=true)-class-method" >
< div class = "signature" >
def self.< strong > rows< / strong > (rows : Indexable(< a href = "../../Array.html" > Array< / a > (T)), copy = < span class = "n" > true< / span > )
< a class = "method-permalink" href = "#rows%28rows%3AIndexable%28Array%28T%29%29%2Ccopy%3Dtrue%29-class-method" > #< / a >
< / div >
< div class = "doc" > < p > Creates a matrix where +rows+ is an array of arrays, each of which is a row
of the matrix. If the optional argument +copy+ is false, use the given
arrays as the internal structure of the matrix without copying.< / p >
< pre > < code > < span class = "t" > Matrix< / span > .rows([[< span class = "n" > 25< / span > , < span class = "n" > 93< / span > ], [< span class = "n" > -1< / span > , < span class = "n" > 66< / span > ]])
< span class = "c" > # => [ 25, 93,< / span >
< span class = "c" > # -1, 66 ]< / span > < / code > < / pre > < / div >
< br / >
< div >
2019-07-10 02:22:15 +00:00
[< a href = "https://github.com/watzon/apatite/blob/6e67ceb81b0b3c61d48b74e5ca5154866a9abd1a/src/apatite/linear_algebra/matrix.cr#L33" target = "_blank" > View source< / a > ]
2019-07-10 01:18:01 +00:00
< / div >
< / div >
< div class = "entry-detail" id = "scalar(n,value:T)-class-method" >
< div class = "signature" >
def self.< strong > scalar< / strong > (n, value : T)
< a class = "method-permalink" href = "#scalar%28n%2Cvalue%3AT%29-class-method" > #< / a >
< / div >
< div class = "doc" > < p > Creates an +n+ by +n+ diagonal matrix where each diagonal element is
< code > value< / code > .< / p >
< pre > < code > < span class = "t" > Matrix< / span > .scalar(< span class = "n" > 2< / span > , < span class = "n" > 5< / span > )
< span class = "c" > # => [ 5, 0,< / span >
< span class = "c" > # 0, 5 ]< / span > < / code > < / pre > < / div >
< br / >
< div >
2019-07-10 02:22:15 +00:00
[< a href = "https://github.com/watzon/apatite/blob/6e67ceb81b0b3c61d48b74e5ca5154866a9abd1a/src/apatite/linear_algebra/matrix.cr#L113" target = "_blank" > View source< / a > ]
2019-07-10 01:18:01 +00:00
< / div >
< / div >
< div class = "entry-detail" id = "unit(n:T)-class-method" >
< div class = "signature" >
def self.< strong > unit< / strong > (n : T)
< a class = "method-permalink" href = "#unit%28n%3AT%29-class-method" > #< / a >
< / div >
< div class = "doc" > < p > Creates an < code > n< / code > by < code > n< / code > identity matrix.< / p >
< pre > < code > < span class = "t" > Matrix< / span > .identity(< span class = "n" > 2< / span > )
< span class = "c" > # => [ 1, 0,< / span >
< span class = "c" > # 0, 1 ]< / span > < / code > < / pre > < / div >
< br / >
< div >
2019-07-10 02:22:15 +00:00
[< a href = "https://github.com/watzon/apatite/blob/6e67ceb81b0b3c61d48b74e5ca5154866a9abd1a/src/apatite/linear_algebra/matrix.cr#L129" target = "_blank" > View source< / a > ]
2019-07-10 01:18:01 +00:00
< / div >
< / div >
< div class = "entry-detail" id = "vstack(x,*matrices)-class-method" >
< div class = "signature" >
def self.< strong > vstack< / strong > (x, *matrices)
< a class = "method-permalink" href = "#vstack%28x%2C%2Amatrices%29-class-method" > #< / a >
< / div >
< div class = "doc" > < p > Create a matrix by stacking matrices vertically< / p >
< pre > < code > x < span class = "o" > =< / span > < span class = "t" > Matrix< / span > [[< span class = "n" > 1< / span > , < span class = "n" > 2< / span > ], [< span class = "n" > 3< / span > , < span class = "n" > 4< / span > ]]
y < span class = "o" > =< / span > < span class = "t" > Matrix< / span > [[< span class = "n" > 5< / span > , < span class = "n" > 6< / span > ], [< span class = "n" > 7< / span > , < span class = "n" > 8< / span > ]]
< span class = "t" > Matrix< / span > .vstack(x, y)
< span class = "c" > # => Matrix[[1, 2], [3, 4], [5, 6], [7, 8]]< / span > < / code > < / pre > < / div >
< br / >
< div >
2019-07-10 02:22:15 +00:00
[< a href = "https://github.com/watzon/apatite/blob/6e67ceb81b0b3c61d48b74e5ca5154866a9abd1a/src/apatite/linear_algebra/matrix.cr#L197" target = "_blank" > View source< / a > ]
2019-07-10 01:18:01 +00:00
< / div >
< / div >
< div class = "entry-detail" id = "zero(row_count,column_count=row_count)-class-method" >
< div class = "signature" >
def self.< strong > zero< / strong > (row_count, column_count = row_count)
< a class = "method-permalink" href = "#zero%28row_count%2Ccolumn_count%3Drow_count%29-class-method" > #< / a >
< / div >
< div class = "doc" > < p > Creates a zero matrix.< / p >
< pre > < code > < span class = "t" > Matrix< / span > .zero(< span class = "n" > 2< / span > )
< span class = "c" > # => [ 0, 0,< / span >
< span class = "c" > # 0, 0 ]< / span > < / code > < / pre > < / div >
< br / >
< div >
2019-07-10 02:22:15 +00:00
[< a href = "https://github.com/watzon/apatite/blob/6e67ceb81b0b3c61d48b74e5ca5154866a9abd1a/src/apatite/linear_algebra/matrix.cr#L140" target = "_blank" > View source< / a > ]
2019-07-10 01:18:01 +00:00
< / div >
< / div >
< h2 > Instance Method Detail< / h2 >
< div class = "entry-detail" id = "*(other)-instance-method" >
< div class = "signature" >
def < strong > *< / strong > (other)
< a class = "method-permalink" href = "#%2A%28other%29-instance-method" > #< / a >
< / div >
< div class = "doc" > < p > Matrix multiplication< / p >
< pre > < code > < span class = "t" > Matrix< / span > [[< span class = "n" > 2< / span > ,< span class = "n" > 4< / span > ], [< span class = "n" > 6< / span > ,< span class = "n" > 8< / span > ]] < span class = "o" > *< / span > < span class = "t" > Matrix< / span > .identity(< span class = "n" > 2< / span > )
< span class = "c" > # => [ 2, 4,< / span >
< span class = "c" > # 6, 8 ]< / span > < / code > < / pre > < / div >
< br / >
< div >
2019-07-10 02:22:15 +00:00
[< a href = "https://github.com/watzon/apatite/blob/6e67ceb81b0b3c61d48b74e5ca5154866a9abd1a/src/apatite/linear_algebra/matrix.cr#L891" target = "_blank" > View source< / a > ]
2019-07-10 01:18:01 +00:00
< / div >
< / div >
< div class = "entry-detail" id = "**(other)-instance-method" >
< div class = "signature" >
def < strong > **< / strong > (other)
< a class = "method-permalink" href = "#%2A%2A%28other%29-instance-method" > #< / a >
< / div >
< div class = "doc" > < p > Matrix exponentiation.< / p >
< p > Equivalent to multiplying the matrix by itself N times.
Non integer exponents will be handled by diagonalizing the matrix.< / p >
< pre > < code > < span class = "t" > Matrix< / span > [[< span class = "n" > 7< / span > ,< span class = "n" > 6< / span > ], [< span class = "n" > 3< / span > ,< span class = "n" > 9< / span > ]] < span class = "o" > **< / span > < span class = "n" > 2< / span >
< span class = "c" > # => [ 67, 96,< / span >
< span class = "c" > # 48, 99 ]< / span > < / code > < / pre > < / div >
< br / >
< div >
2019-07-10 02:22:15 +00:00
[< a href = "https://github.com/watzon/apatite/blob/6e67ceb81b0b3c61d48b74e5ca5154866a9abd1a/src/apatite/linear_algebra/matrix.cr#L1061" target = "_blank" > View source< / a > ]
2019-07-10 01:18:01 +00:00
< / div >
< / div >
< div class = "entry-detail" id = "+(other:Matrix|Indexable)-instance-method" >
< div class = "signature" >
def < strong > +< / strong > (other : < a href = "../../Apatite/LinearAlgebra/Matrix.html" > Matrix< / a > | Indexable)
< a class = "method-permalink" href = "#%2B%28other%3AMatrix%7CIndexable%29-instance-method" > #< / a >
< / div >
< div class = "doc" > < p > Matrix addition< / p >
< pre > < code > < span class = "t" > Matrix< / span > .scalar(< span class = "n" > 2< / span > ,< span class = "n" > 5< / span > ) < span class = "o" > +< / span > < span class = "t" > Matrix< / span > [[< span class = "n" > 1< / span > ,< span class = "n" > 0< / span > ], [< span class = "n" > -4< / span > ,< span class = "n" > 7< / span > ]]
< span class = "c" > # => [ 6, 0,< / span >
< span class = "c" > # -4, 1 ]< / span > < / code > < / pre > < / div >
< br / >
< div >
2019-07-10 02:22:15 +00:00
[< a href = "https://github.com/watzon/apatite/blob/6e67ceb81b0b3c61d48b74e5ca5154866a9abd1a/src/apatite/linear_algebra/matrix.cr#L924" target = "_blank" > View source< / a > ]
2019-07-10 01:18:01 +00:00
< / div >
< / div >
< div class = "entry-detail" id = "-(other:Matrix|Indexable)-instance-method" >
< div class = "signature" >
def < strong > -< / strong > (other : < a href = "../../Apatite/LinearAlgebra/Matrix.html" > Matrix< / a > | Indexable)
< a class = "method-permalink" href = "#-%28other%3AMatrix%7CIndexable%29-instance-method" > #< / a >
< / div >
< div class = "doc" > < p > Matrix subtraction< / p >
< pre > < code > < span class = "t" > Matrix< / span > [[< span class = "n" > 1< / span > ,< span class = "n" > 5< / span > ], [< span class = "n" > 4< / span > ,< span class = "n" > 2< / span > ]] < span class = "o" > -< / span > < span class = "t" > Matrix< / span > [[< span class = "n" > 9< / span > ,< span class = "n" > 3< / span > ], [< span class = "n" > -4< / span > ,< span class = "n" > 1< / span > ]]
< span class = "c" > # => [-8, 2,< / span >
< span class = "c" > # 8, 1 ]< / span > < / code > < / pre > < / div >
< br / >
< div >
2019-07-10 02:22:15 +00:00
[< a href = "https://github.com/watzon/apatite/blob/6e67ceb81b0b3c61d48b74e5ca5154866a9abd1a/src/apatite/linear_algebra/matrix.cr#L951" target = "_blank" > View source< / a > ]
2019-07-10 01:18:01 +00:00
< / 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 >
< div class = "doc" > < p > Matrix division (multiplication by the inverse).< / p >
< pre > < code > < span class = "t" > Matrix< / span > [[< span class = "n" > 7< / span > ,< span class = "n" > 6< / span > ], [< span class = "n" > 3< / span > ,< span class = "n" > 9< / span > ]] < span class = "o" > /< / span > < span class = "t" > Matrix< / span > [[< span class = "n" > 2< / span > ,< span class = "n" > 9< / span > ], [< span class = "n" > 3< / span > ,< span class = "n" > 1< / span > ]]
< span class = "c" > # => [ -7, 1,< / span >
< span class = "c" > # -3, -6 ]< / span > < / code > < / pre > < / div >
< br / >
< div >
2019-07-10 02:22:15 +00:00
[< a href = "https://github.com/watzon/apatite/blob/6e67ceb81b0b3c61d48b74e5ca5154866a9abd1a/src/apatite/linear_algebra/matrix.cr#L978" target = "_blank" > View source< / a > ]
2019-07-10 01:18:01 +00:00
< / div >
< / div >
< div class = "entry-detail" id = "==(other:Matrix)-instance-method" >
< div class = "signature" >
def < strong > ==< / strong > (other : < a href = "../../Apatite/LinearAlgebra/Matrix.html" > Matrix< / a > )
< a class = "method-permalink" href = "#%3D%3D%28other%3AMatrix%29-instance-method" > #< / a >
< / div >
< div class = "doc" > < p > Equality operator< / p > < / div >
< br / >
< div >
2019-07-10 02:22:15 +00:00
[< a href = "https://github.com/watzon/apatite/blob/6e67ceb81b0b3c61d48b74e5ca5154866a9abd1a/src/apatite/linear_algebra/matrix.cr#L868" target = "_blank" > View source< / a > ]
2019-07-10 01:18:01 +00:00
< / div >
< / div >
2019-07-10 02:22:15 +00:00
< div class = "entry-detail" id = "[](i)-instance-method" >
2019-07-10 01:18:01 +00:00
< div class = "signature" >
2019-07-10 02:22:15 +00:00
def < strong > []< / strong > (i)
2019-07-10 01:18:01 +00:00
2019-07-10 02:22:15 +00:00
< a class = "method-permalink" href = "#%5B%5D%28i%29-instance-method" > #< / a >
2019-07-10 01:18:01 +00:00
< / div >
2019-07-10 02:22:15 +00:00
< div class = "doc" > < p > Returns row < code > i< / code > of the matrix as an Array. Raises if the
index is not found.< / p > < / div >
2019-07-10 01:18:01 +00:00
< br / >
< div >
2019-07-10 02:22:15 +00:00
[< a href = "https://github.com/watzon/apatite/blob/6e67ceb81b0b3c61d48b74e5ca5154866a9abd1a/src/apatite/linear_algebra/matrix.cr#L279" target = "_blank" > View source< / a > ]
2019-07-10 01:18:01 +00:00
< / div >
< / div >
2019-07-10 02:22:15 +00:00
< div class = "entry-detail" id = "[](i,j)-instance-method" >
2019-07-10 01:18:01 +00:00
< div class = "signature" >
2019-07-10 02:22:15 +00:00
def < strong > []< / strong > (i, j)
2019-07-10 01:18:01 +00:00
2019-07-10 02:22:15 +00:00
< a class = "method-permalink" href = "#%5B%5D%28i%2Cj%29-instance-method" > #< / a >
2019-07-10 01:18:01 +00:00
< / div >
2019-07-10 02:22:15 +00:00
< div class = "doc" > < p > Returns element (< code > i< / code > , < code > j< / code > ) of the matrix. That is: row < code > i< / code > , column < code > j< / code > .
Raises if either index is not found.< / p > < / div >
2019-07-10 01:18:01 +00:00
< br / >
< div >
2019-07-10 02:22:15 +00:00
[< a href = "https://github.com/watzon/apatite/blob/6e67ceb81b0b3c61d48b74e5ca5154866a9abd1a/src/apatite/linear_algebra/matrix.cr#L291" target = "_blank" > View source< / a > ]
2019-07-10 01:18:01 +00:00
< / div >
< / div >
< div class = "entry-detail" id = "[]=(i,j,v:T)-instance-method" >
< div class = "signature" >
def < strong > []=< / strong > (i, j, v : T)
< a class = "method-permalink" href = "#%5B%5D%3D%28i%2Cj%2Cv%3AT%29-instance-method" > #< / a >
< / div >
< div class = "doc" > < p > Set the value at index (< code > i< / code > , < code > j< / code > ). That is: row < code > i< / code > , column < code > j< / code > .< / p > < / div >
< br / >
< div >
2019-07-10 02:22:15 +00:00
[< a href = "https://github.com/watzon/apatite/blob/6e67ceb81b0b3c61d48b74e5ca5154866a9abd1a/src/apatite/linear_algebra/matrix.cr#L302" target = "_blank" > View source< / a > ]
2019-07-10 01:18:01 +00:00
< / div >
< / div >
2019-07-10 02:22:15 +00:00
< div class = "entry-detail" id = "[]?(i)-instance-method" >
2019-07-10 01:18:01 +00:00
< div class = "signature" >
2019-07-10 02:22:15 +00:00
def < strong > []?< / strong > (i)
2019-07-10 01:18:01 +00:00
2019-07-10 02:22:15 +00:00
< a class = "method-permalink" href = "#%5B%5D%3F%28i%29-instance-method" > #< / a >
2019-07-10 01:18:01 +00:00
< / div >
2019-07-10 02:22:15 +00:00
< div class = "doc" > < p > Returns row < code > i< / code > of the matrix as an Array. Returns nil if the
index is not found.< / p > < / div >
2019-07-10 01:18:01 +00:00
< br / >
< div >
2019-07-10 02:22:15 +00:00
[< a href = "https://github.com/watzon/apatite/blob/6e67ceb81b0b3c61d48b74e5ca5154866a9abd1a/src/apatite/linear_algebra/matrix.cr#L285" target = "_blank" > View source< / a > ]
2019-07-10 01:18:01 +00:00
< / div >
< / div >
2019-07-10 02:22:15 +00:00
< div class = "entry-detail" id = "[]?(i,j)-instance-method" >
2019-07-10 01:18:01 +00:00
< div class = "signature" >
2019-07-10 02:22:15 +00:00
def < strong > []?< / strong > (i, j)
2019-07-10 01:18:01 +00:00
2019-07-10 02:22:15 +00:00
< a class = "method-permalink" href = "#%5B%5D%3F%28i%2Cj%29-instance-method" > #< / a >
2019-07-10 01:18:01 +00:00
< / div >
2019-07-10 02:22:15 +00:00
< div class = "doc" > < p > Returns element (< code > i< / code > , < code > j< / code > ) of the matrix. That is: row < code > i< / code > , column < code > j< / code > .
Returns nil if either index is not found.< / p > < / div >
2019-07-10 01:18:01 +00:00
< br / >
< div >
2019-07-10 02:22:15 +00:00
[< a href = "https://github.com/watzon/apatite/blob/6e67ceb81b0b3c61d48b74e5ca5154866a9abd1a/src/apatite/linear_algebra/matrix.cr#L297" target = "_blank" > View source< / a > ]
2019-07-10 01:18:01 +00:00
< / div >
< / div >
< div class = "entry-detail" id = "adjugate-instance-method" >
< div class = "signature" >
def < strong > adjugate< / strong >
< a class = "method-permalink" href = "#adjugate-instance-method" > #< / a >
< / div >
< div class = "doc" > < p > Returns the adjugate of the matrix.< / p >
< p > Matrix[ [7,6],[3,9] ].adjugate< / p >
< h1 > => [ 9, -6,< / h1 >
< h1 > -3, 7 ]< / h1 >
< pre > < code > < / code > < / pre > < / div >
< br / >
< div >
2019-07-10 02:22:15 +00:00
[< a href = "https://github.com/watzon/apatite/blob/6e67ceb81b0b3c61d48b74e5ca5154866a9abd1a/src/apatite/linear_algebra/matrix.cr#L626" target = "_blank" > View source< / a > ]
2019-07-10 01:18:01 +00:00
< / div >
< / div >
< div class = "entry-detail" id = "clone-instance-method" >
< div class = "signature" >
def < strong > clone< / strong >
< a class = "method-permalink" href = "#clone-instance-method" > #< / a >
< / div >
< div class = "doc" > < p > Returns a clone of the matrix, so that the contents of each do not reference
identical objects.< / p >
< p > There should be no good reason to do this since Matrices are immutable.< / p > < / div >
< br / >
< div >
2019-07-10 02:22:15 +00:00
[< a href = "https://github.com/watzon/apatite/blob/6e67ceb81b0b3c61d48b74e5ca5154866a9abd1a/src/apatite/linear_algebra/matrix.cr#L876" target = "_blank" > View source< / a > ]
2019-07-10 01:18:01 +00:00
< / div >
< / div >
< div class = "entry-detail" id = "coerce(klass)-instance-method" >
< div class = "signature" >
def < strong > coerce< / strong > (klass)
< a class = "method-permalink" href = "#coerce%28klass%29-instance-method" > #< / a >
< / div >
< div class = "doc" > < p > Attempt to coerce the elements in the matrix to another type.< / p > < / div >
< br / >
< div >
2019-07-10 02:22:15 +00:00
[< a href = "https://github.com/watzon/apatite/blob/6e67ceb81b0b3c61d48b74e5ca5154866a9abd1a/src/apatite/linear_algebra/matrix.cr#L1365" target = "_blank" > View source< / a > ]
2019-07-10 01:18:01 +00:00
< / div >
< / div >
< div class = "entry-detail" id = "cofactor(row,column)-instance-method" >
< div class = "signature" >
def < strong > cofactor< / strong > (row, column)
< a class = "method-permalink" href = "#cofactor%28row%2Ccolumn%29-instance-method" > #< / a >
< / div >
< div class = "doc" > < p > Returns the (row, column) cofactor which is obtained by multiplying
the first minor by (-1)**(row + column).< / p >
< pre > < code > < span class = "t" > Matrix< / span > .diagonal(< span class = "n" > 9< / span > , < span class = "n" > 5< / span > , < span class = "n" > -3< / span > , < span class = "n" > 4< / span > ).cofactor(< span class = "n" > 1< / span > , < span class = "n" > 1< / span > )
< span class = "c" > # => -108< / span > < / code > < / pre > < / div >
< br / >
< div >
2019-07-10 02:22:15 +00:00
[< a href = "https://github.com/watzon/apatite/blob/6e67ceb81b0b3c61d48b74e5ca5154866a9abd1a/src/apatite/linear_algebra/matrix.cr#L612" target = "_blank" > View source< / a > ]
2019-07-10 01:18:01 +00:00
< / div >
< / div >
2019-07-10 02:22:15 +00:00
< div class = "entry-detail" id = "column(j)-instance-method" >
2019-07-10 01:18:01 +00:00
< div class = "signature" >
2019-07-10 02:22:15 +00:00
def < strong > column< / strong > (j)
2019-06-13 02:23:54 +00:00
2019-07-10 02:22:15 +00:00
< a class = "method-permalink" href = "#column%28j%29-instance-method" > #< / a >
2019-07-10 01:18:01 +00:00
< / div >
2019-07-10 02:22:15 +00:00
< div class = "doc" > < p > Returns column vector < code > j< / code > of the Matrix as a Vector (starting at 0).
Raises if the column doesn't exist.< / p > < / div >
2019-07-10 01:18:01 +00:00
< br / >
< div >
2019-07-10 02:22:15 +00:00
[< a href = "https://github.com/watzon/apatite/blob/6e67ceb81b0b3c61d48b74e5ca5154866a9abd1a/src/apatite/linear_algebra/matrix.cr#L336" target = "_blank" > View source< / a > ]
2019-07-10 01:18:01 +00:00
< / div >
< / div >
2019-07-10 02:22:15 +00:00
< div class = "entry-detail" id = "column(j,&block:T->)-instance-method" >
2019-07-10 01:18:01 +00:00
< div class = "signature" >
2019-07-10 02:22:15 +00:00
def < strong > column< / strong > (j, & block : T -> )
2019-06-13 02:23:54 +00:00
2019-07-10 02:22:15 +00:00
< a class = "method-permalink" href = "#column%28j%2C%26block%3AT-%3E%29-instance-method" > #< / a >
2019-07-10 01:18:01 +00:00
< / div >
2019-07-10 02:22:15 +00:00
< div class = "doc" > < p > Returns a block which yields every item in column < code > j< / code > of the Matrix.< / p > < / div >
2019-07-10 01:18:01 +00:00
< br / >
< div >
2019-07-10 02:22:15 +00:00
[< a href = "https://github.com/watzon/apatite/blob/6e67ceb81b0b3c61d48b74e5ca5154866a9abd1a/src/apatite/linear_algebra/matrix.cr#L353" target = "_blank" > View source< / a > ]
2019-07-10 01:18:01 +00:00
< / div >
< / div >
< div class = "entry-detail" id = "column?(j)-instance-method" >
< div class = "signature" >
def < strong > column?< / strong > (j)
2019-06-13 02:23:54 +00:00
2019-07-10 01:18:01 +00:00
< a class = "method-permalink" href = "#column%3F%28j%29-instance-method" > #< / a >
< / div >
< div class = "doc" > < p > Returns column vector < code > j< / code > of the Matrix as a Vector (starting at 0).
Returns nil if the column doesn't exist.< / p > < / div >
< br / >
< div >
2019-07-10 02:22:15 +00:00
[< a href = "https://github.com/watzon/apatite/blob/6e67ceb81b0b3c61d48b74e5ca5154866a9abd1a/src/apatite/linear_algebra/matrix.cr#L346" target = "_blank" > View source< / a > ]
2019-07-10 01:18:01 +00:00
< / div >
< / div >
< div class = "entry-detail" id = "column_count:Int32-instance-method" >
< div class = "signature" >
def < strong > column_count< / strong > : Int32
2019-06-13 02:23:54 +00:00
2019-07-10 01:18:01 +00:00
< a class = "method-permalink" href = "#column_count%3AInt32-instance-method" > #< / a >
< / div >
< div class = "doc" > < p > Returns the number of columns.< / p > < / div >
< br / >
< div >
2019-07-10 02:22:15 +00:00
[< a href = "https://github.com/watzon/apatite/blob/6e67ceb81b0b3c61d48b74e5ca5154866a9abd1a/src/apatite/linear_algebra/matrix.cr#L314" target = "_blank" > View source< / a > ]
< / div >
< / div >
< div class = "entry-detail" id = "column_vectors-instance-method" >
< div class = "signature" >
def < strong > column_vectors< / strong >
< a class = "method-permalink" href = "#column_vectors-instance-method" > #< / a >
< / div >
< div class = "doc" > < p > Returns an array of the column vectors of the matrix. See < code > < a href = "../../Apatite/LinearAlgebra/Vector.html" > Vector< / a > < / code > .< / p > < / div >
< br / >
< div >
[< a href = "https://github.com/watzon/apatite/blob/6e67ceb81b0b3c61d48b74e5ca5154866a9abd1a/src/apatite/linear_algebra/matrix.cr#L1378" target = "_blank" > View source< / a > ]
2019-07-10 01:18:01 +00:00
< / div >
< / div >
2019-06-13 02:23:54 +00:00
2019-07-10 01:18:01 +00:00
< div class = "entry-detail" id = "combine(*matrices,&block)-instance-method" >
< div class = "signature" >
def < strong > combine< / strong > (*matrices, & block)
2019-06-13 02:23:54 +00:00
2019-07-10 01:18:01 +00:00
< a class = "method-permalink" href = "#combine%28%2Amatrices%2C%26block%29-instance-method" > #< / a >
< / div >
< div class = "doc" > < p > Create a matrix by combining matrices entrywise, using the given block< / p >
2019-06-13 02:23:54 +00:00
2019-07-10 01:18:01 +00:00
< pre > < code > x < span class = "o" > =< / span > < span class = "t" > Matrix< / span > [[< span class = "n" > 6< / span > , < span class = "n" > 6< / span > ], [< span class = "n" > 4< / span > , < span class = "n" > 4< / span > ]]
y < span class = "o" > =< / span > < span class = "t" > Matrix< / span > [[< span class = "n" > 1< / span > , < span class = "n" > 2< / span > ], [< span class = "n" > 3< / span > , < span class = "n" > 4< / span > ]]
< span class = "t" > Matrix< / span > .combine(x, y) {< span class = "o" > |< / span > a, b< span class = "o" > |< / span > a < span class = "o" > -< / span > b}
< span class = "c" > # => Matrix[[5, 4], [1, 0]]< / span > < / code > < / pre > < / div >
< br / >
< div >
2019-07-10 02:22:15 +00:00
[< a href = "https://github.com/watzon/apatite/blob/6e67ceb81b0b3c61d48b74e5ca5154866a9abd1a/src/apatite/linear_algebra/matrix.cr#L264" target = "_blank" > View source< / a > ]
2019-07-10 01:18:01 +00:00
< / div >
< / div >
2019-06-13 02:23:54 +00:00
2019-07-10 01:18:01 +00:00
< div class = "entry-detail" id = "conj-instance-method" >
2019-06-13 02:23:54 +00:00
< div class = "signature" >
2019-07-10 01:18:01 +00:00
def < strong > conj< / strong >
2019-06-13 02:23:54 +00:00
2019-07-10 01:18:01 +00:00
< a class = "method-permalink" href = "#conj-instance-method" > #< / a >
2019-06-13 02:23:54 +00:00
< / div >
2019-07-10 01:18:01 +00:00
< div class = "doc" > < p > Returns the conjugate of the matrix.< / p >
< pre > < code > < span class = "t" > Matrix< / span > [[< span class = "t" > Complex< / span > (< span class = "n" > 1< / span > ,< span class = "n" > 2< / span > ), < span class = "t" > Complex< / span > (< span class = "n" > 0< / span > ,< span class = "n" > 1< / span > ), < span class = "n" > 0< / span > ], [< span class = "n" > 1< / span > , < span class = "n" > 2< / span > , < span class = "n" > 3< / span > ]]
< span class = "c" > # => 1+2i i 0< / span >
< span class = "c" > # 1 2 3< / span >
< span class = "t" > Matrix< / span > [[< span class = "t" > Complex< / span > (< span class = "n" > 1< / span > ,< span class = "n" > 2< / span > ), < span class = "t" > Complex< / span > (< span class = "n" > 0< / span > ,< span class = "n" > 1< / span > ), < span class = "n" > 0< / span > ], [< span class = "n" > 1< / span > , < span class = "n" > 2< / span > , < span class = "n" > 3< / span > ]].conj
< span class = "c" > # => 1-2i -i 0< / span >
< span class = "c" > # 1 2 3< / span > < / code > < / pre > < / div >
2019-06-13 02:23:54 +00:00
< br / >
< div >
2019-07-10 02:22:15 +00:00
[< a href = "https://github.com/watzon/apatite/blob/6e67ceb81b0b3c61d48b74e5ca5154866a9abd1a/src/apatite/linear_algebra/matrix.cr#L1313" target = "_blank" > View source< / a > ]
2019-06-13 02:23:54 +00:00
< / div >
< / div >
2019-07-10 01:18:01 +00:00
< div class = "entry-detail" id = "determinant-instance-method" >
< div class = "signature" >
def < strong > determinant< / strong >
2019-06-13 02:23:54 +00:00
2019-07-10 01:18:01 +00:00
< a class = "method-permalink" href = "#determinant-instance-method" > #< / a >
< / div >
< div class = "doc" > < p > Returns the determinant of the matrix.< / p >
2019-06-13 02:23:54 +00:00
2019-07-10 01:18:01 +00:00
< p > Beware that using Float values can yield erroneous results
because of their lack of precision.
Consider using exact types like Rational or BigDecimal instead.< / p >
2019-06-13 02:23:54 +00:00
2019-07-10 01:18:01 +00:00
< pre > < code > < span class = "t" > Matrix< / span > [[< span class = "n" > 7< / span > ,< span class = "n" > 6< / span > ], [< span class = "n" > 3< / span > ,< span class = "n" > 9< / span > ]].determinant
< span class = "c" > # => 45< / span > < / code > < / pre > < / div >
< br / >
< div >
2019-07-10 02:22:15 +00:00
[< a href = "https://github.com/watzon/apatite/blob/6e67ceb81b0b3c61d48b74e5ca5154866a9abd1a/src/apatite/linear_algebra/matrix.cr#L1079" target = "_blank" > View source< / a > ]
2019-07-10 01:18:01 +00:00
< / div >
< / div >
2019-06-13 02:23:54 +00:00
2019-07-10 01:18:01 +00:00
< div class = "entry-detail" id = "diagonal?-instance-method" >
2019-06-13 02:23:54 +00:00
< div class = "signature" >
2019-07-10 01:18:01 +00:00
def < strong > diagonal?< / strong >
2019-06-13 02:23:54 +00:00
2019-07-10 01:18:01 +00:00
< a class = "method-permalink" href = "#diagonal%3F-instance-method" > #< / a >
2019-06-13 02:23:54 +00:00
< / div >
2019-07-10 01:18:01 +00:00
< div class = "doc" > < p > Returns < code > true< / code > if this is a diagonal matrix.< / p > < / div >
2019-06-13 02:23:54 +00:00
< br / >
< div >
2019-07-10 02:22:15 +00:00
[< a href = "https://github.com/watzon/apatite/blob/6e67ceb81b0b3c61d48b74e5ca5154866a9abd1a/src/apatite/linear_algebra/matrix.cr#L697" target = "_blank" > View source< / a > ]
2019-06-13 02:23:54 +00:00
< / div >
< / div >
2019-07-10 01:18:01 +00:00
< div class = "entry-detail" id = "each(which=:all,&block:T->)-instance-method" >
2019-06-13 02:23:54 +00:00
< div class = "signature" >
2019-07-10 01:18:01 +00:00
def < strong > each< / strong > (which = < span class = "n" > :all< / span > , & block : T -> )
2019-06-13 02:23:54 +00:00
2019-07-10 01:18:01 +00:00
< a class = "method-permalink" href = "#each%28which%3D%3Aall%2C%26block%3AT-%3E%29-instance-method" > #< / a >
2019-06-13 02:23:54 +00:00
< / div >
2019-07-10 01:18:01 +00:00
< div class = "doc" > < p > Yields all elements of the matrix, starting with those of the first row,
or returns an Enumerator if no block given.
Elements can be restricted by passing an argument:< / p >
< ul > < li > :all (default): yields all elements< / li > < li > :diagonal: yields only elements on the diagonal< / li > < li > :off_diagonal: yields all elements except on the diagonal< / li > < li > :lower: yields only elements on or below the diagonal< / li > < li > :strict_lower: yields only elements below the diagonal< / li > < li > :strict_upper: yields only elements above the diagonal< / li > < li > :upper: yields only elements on or above the diagonal< / li > < / ul >
< pre > < code > < span class = "t" > Matrix< / span > [ [< span class = "n" > 1< / span > ,< span class = "n" > 2< / span > ], [< span class = "n" > 3< / span > ,< span class = "n" > 4< / span > ] ].each { < span class = "o" > |< / span > e< span class = "o" > |< / span > puts e }
< span class = "c" > # => prints the numbers 1 to 4< / span >
< span class = "t" > Matrix< / span > [ [< span class = "n" > 1< / span > ,< span class = "n" > 2< / span > ], [< span class = "n" > 3< / span > ,< span class = "n" > 4< / span > ] ].each(< span class = "n" > :strict_lower< / span > ).to_a < span class = "c" > # => [3]< / span > < / code > < / pre > < / div >
2019-06-13 02:23:54 +00:00
< br / >
< div >
2019-07-10 02:22:15 +00:00
[< a href = "https://github.com/watzon/apatite/blob/6e67ceb81b0b3c61d48b74e5ca5154866a9abd1a/src/apatite/linear_algebra/matrix.cr#L380" target = "_blank" > View source< / a > ]
2019-06-13 02:23:54 +00:00
< / div >
< / div >
2019-07-10 01:18:01 +00:00
< div class = "entry-detail" id = "each_with_index(which=:all,&block:T,Int32,Int32->)-instance-method" >
2019-06-13 02:23:54 +00:00
< div class = "signature" >
2019-07-10 01:18:01 +00:00
def < strong > each_with_index< / strong > (which = < span class = "n" > :all< / span > , & block : T, Int32, Int32 -> )
2019-06-13 02:23:54 +00:00
2019-07-10 01:18:01 +00:00
< a class = "method-permalink" href = "#each_with_index%28which%3D%3Aall%2C%26block%3AT%2CInt32%2CInt32-%3E%29-instance-method" > #< / a >
2019-06-13 02:23:54 +00:00
< / div >
2019-07-10 01:18:01 +00:00
< div class = "doc" > < p > Same as #each, but the row index and column index in addition to the element< / p >
< pre > < code > < span class = "t" > Matrix< / span > [ [< span class = "n" > 1< / span > ,< span class = "n" > 2< / span > ], [< span class = "n" > 3< / span > ,< span class = "n" > 4< / span > ] ].each_with_index < span class = "k" > do< / span > < span class = "o" > |< / span > e, row, col< span class = "o" > |< / span >
puts < span class = "s" > " < / span > < span class = "i" > #{< / span > e< span class = "i" > }< / span > < span class = "s" > at < / span > < span class = "i" > #{< / span > row< span class = "i" > }< / span > < span class = "s" > , < / span > < span class = "i" > #{< / span > col< span class = "i" > }< / span > < span class = "s" > " < / span >
< span class = "k" > end< / span >
< span class = "c" > # => Prints:< / span >
< span class = "c" > # 1 at 0, 0< / span >
< span class = "c" > # 2 at 0, 1< / span >
< span class = "c" > # 3 at 1, 0< / span >
< span class = "c" > # 4 at 1, 1< / span > < / code > < / pre > < / div >
2019-06-13 02:23:54 +00:00
< br / >
< div >
2019-07-10 02:22:15 +00:00
[< a href = "https://github.com/watzon/apatite/blob/6e67ceb81b0b3c61d48b74e5ca5154866a9abd1a/src/apatite/linear_algebra/matrix.cr#L438" target = "_blank" > View source< / a > ]
2019-06-13 02:23:54 +00:00
< / div >
< / div >
2019-07-10 01:18:01 +00:00
< div class = "entry-detail" id = "eigensystem-instance-method" >
2019-06-13 02:23:54 +00:00
< div class = "signature" >
2019-07-10 01:18:01 +00:00
def < strong > eigensystem< / strong >
2019-06-13 02:23:54 +00:00
2019-07-10 01:18:01 +00:00
< a class = "method-permalink" href = "#eigensystem-instance-method" > #< / a >
2019-06-13 02:23:54 +00:00
< / div >
2019-07-10 01:18:01 +00:00
< div class = "doc" > < p > Returns the Eigensystem of the matrix
2019-07-10 02:08:46 +00:00
See < code > < a href = "../../Apatite/LinearAlgebra/Matrix/EigenvalueDecomposition.html" > EigenvalueDecomposition< / a > < / code > .< / p >
2019-07-10 01:18:01 +00:00
< p > < span class = "flag purple" > NOTE< / span > Not working yet< / p >
< pre > < code > m < span class = "o" > =< / span > < span class = "t" > Matrix< / span > [[< span class = "n" > 1< / span > , < span class = "n" > 2< / span > ], [< span class = "n" > 3< / span > , < span class = "n" > 4< / span > ]]
v, d, v_inv < span class = "o" > =< / span > m.eigensystem
d.diagonal? < span class = "c" > # => true< / span >
v.inv < span class = "o" > ==< / span > v_inv < span class = "c" > # => true< / span >
(v < span class = "o" > *< / span > d < span class = "o" > *< / span > v_inv).round(< span class = "n" > 5< / span > ) < span class = "o" > ==< / span > m < span class = "c" > # => true< / span > < / code > < / pre > < / div >
2019-06-13 02:23:54 +00:00
< br / >
< div >
2019-07-10 02:22:15 +00:00
[< a href = "https://github.com/watzon/apatite/blob/6e67ceb81b0b3c61d48b74e5ca5154866a9abd1a/src/apatite/linear_algebra/matrix.cr#L1277" target = "_blank" > View source< / a > ]
2019-06-13 02:23:54 +00:00
< / div >
< / div >
2019-07-10 01:18:01 +00:00
< div class = "entry-detail" id = "empty?-instance-method" >
2019-06-13 02:23:54 +00:00
< div class = "signature" >
2019-07-10 01:18:01 +00:00
def < strong > empty?< / strong >
2019-06-13 02:23:54 +00:00
2019-07-10 01:18:01 +00:00
< a class = "method-permalink" href = "#empty%3F-instance-method" > #< / a >
2019-06-13 02:23:54 +00:00
< / div >
2019-07-10 01:18:01 +00:00
< div class = "doc" > < p > Returns true if this matrix is empty.< / p > < / div >
2019-06-13 02:23:54 +00:00
< br / >
< div >
2019-07-10 02:22:15 +00:00
[< a href = "https://github.com/watzon/apatite/blob/6e67ceb81b0b3c61d48b74e5ca5154866a9abd1a/src/apatite/linear_algebra/matrix.cr#L705" target = "_blank" > View source< / a > ]
2019-06-13 02:23:54 +00:00
< / div >
< / div >
2019-07-10 01:18:01 +00:00
< div class = "entry-detail" id = "first_minor(row,column)-instance-method" >
2019-06-13 02:23:54 +00:00
< div class = "signature" >
2019-07-10 01:18:01 +00:00
def < strong > first_minor< / strong > (row, column)
2019-06-13 02:23:54 +00:00
2019-07-10 01:18:01 +00:00
< a class = "method-permalink" href = "#first_minor%28row%2Ccolumn%29-instance-method" > #< / a >
2019-06-13 02:23:54 +00:00
< / div >
2019-07-10 01:18:01 +00:00
< div class = "doc" > < p > Returns the submatrix obtained by deleting the specified row and column.< / p >
< pre > < code > < span class = "t" > Matrix< / span > .diagonal(< span class = "n" > 9< / span > , < span class = "n" > 5< / span > , < span class = "n" > -3< / span > , < span class = "n" > 4< / span > ).first_minor(< span class = "n" > 1< / span > , < span class = "n" > 2< / span > )
< span class = "c" > # => [ 9, 0, 0,< / span >
< span class = "c" > # 0, 0, 0,< / span >
< span class = "c" > # 0, 0, 4 ]< / span > < / code > < / pre > < / div >
2019-06-13 02:23:54 +00:00
< br / >
< div >
2019-07-10 02:22:15 +00:00
[< a href = "https://github.com/watzon/apatite/blob/6e67ceb81b0b3c61d48b74e5ca5154866a9abd1a/src/apatite/linear_algebra/matrix.cr#L585" target = "_blank" > View source< / a > ]
2019-06-13 02:23:54 +00:00
< / div >
< / div >
2019-07-10 01:18:01 +00:00
< div class = "entry-detail" id = "hadamard_product(m)-instance-method" >
2019-06-13 02:23:54 +00:00
< div class = "signature" >
2019-07-10 01:18:01 +00:00
def < strong > hadamard_product< / strong > (m)
2019-06-13 02:23:54 +00:00
2019-07-10 01:18:01 +00:00
< a class = "method-permalink" href = "#hadamard_product%28m%29-instance-method" > #< / a >
2019-06-13 02:23:54 +00:00
< / div >
2019-07-10 01:18:01 +00:00
< div class = "doc" > < p > Hadamard product< / p >
< pre > < code > < span class = "t" > Matrix< / span > [[< span class = "n" > 1< / span > ,< span class = "n" > 2< / span > ], [< span class = "n" > 3< / span > ,< span class = "n" > 4< / span > ]].hadamard_product < span class = "t" > Matrix< / span > [[< span class = "n" > 1< / span > ,< span class = "n" > 2< / span > ], [< span class = "n" > 3< / span > ,< span class = "n" > 2< / span > ]]
< span class = "c" > # => [ 1, 4,< / span >
< span class = "c" > # 9, 8 ]< / span > < / code > < / pre > < / div >
2019-06-13 02:23:54 +00:00
< br / >
< div >
2019-07-10 02:22:15 +00:00
[< a href = "https://github.com/watzon/apatite/blob/6e67ceb81b0b3c61d48b74e5ca5154866a9abd1a/src/apatite/linear_algebra/matrix.cr#L999" target = "_blank" > View source< / a > ]
2019-06-13 06:17:13 +00:00
< / div >
< / div >
2019-07-10 01:18:01 +00:00
< div class = "entry-detail" id = "hermitian?-instance-method" >
2019-06-13 06:17:13 +00:00
< div class = "signature" >
2019-07-10 01:18:01 +00:00
def < strong > hermitian?< / strong >
2019-06-13 06:17:13 +00:00
2019-07-10 01:18:01 +00:00
< a class = "method-permalink" href = "#hermitian%3F-instance-method" > #< / a >
2019-06-13 06:17:13 +00:00
< / div >
2019-07-10 01:18:01 +00:00
< div class = "doc" > < p > Returns < code > true< / code > if this is an hermitian matrix.< / p > < / div >
2019-06-13 06:17:13 +00:00
< br / >
< div >
2019-07-10 02:22:15 +00:00
[< a href = "https://github.com/watzon/apatite/blob/6e67ceb81b0b3c61d48b74e5ca5154866a9abd1a/src/apatite/linear_algebra/matrix.cr#L710" target = "_blank" > View source< / a > ]
2019-06-13 02:23:54 +00:00
< / div >
< / div >
2019-07-10 01:18:01 +00:00
< div class = "entry-detail" id = "hstack(*matrices)-instance-method" >
2019-06-13 02:23:54 +00:00
< div class = "signature" >
2019-07-10 01:18:01 +00:00
def < strong > hstack< / strong > (*matrices)
2019-06-13 02:23:54 +00:00
2019-07-10 01:18:01 +00:00
< a class = "method-permalink" href = "#hstack%28%2Amatrices%29-instance-method" > #< / a >
2019-06-13 02:23:54 +00:00
< / div >
2019-07-10 01:18:01 +00:00
< div class = "doc" > < p > Returns a new matrix resulting by stacking horizontally
the receiver with the given matrices< / p >
< pre > < code > x < span class = "o" > =< / span > < span class = "t" > Matrix< / span > [[< span class = "n" > 1< / span > , < span class = "n" > 2< / span > ], [< span class = "n" > 3< / span > , < span class = "n" > 4< / span > ]]
y < span class = "o" > =< / span > < span class = "t" > Matrix< / span > [[< span class = "n" > 5< / span > , < span class = "n" > 6< / span > ], [< span class = "n" > 7< / span > , < span class = "n" > 8< / span > ]]
x.hstack(y) < span class = "c" > # => Matrix[[1, 2, 5, 6], [3, 4, 7, 8]]< / span > < / code > < / pre > < / div >
2019-06-13 02:23:54 +00:00
< br / >
< div >
2019-07-10 02:22:15 +00:00
[< a href = "https://github.com/watzon/apatite/blob/6e67ceb81b0b3c61d48b74e5ca5154866a9abd1a/src/apatite/linear_algebra/matrix.cr#L1161" target = "_blank" > View source< / a > ]
2019-06-13 02:23:54 +00:00
< / div >
< / div >
2019-07-10 01:18:01 +00:00
< div class = "entry-detail" id = "imag-instance-method" >
2019-06-13 02:23:54 +00:00
< div class = "signature" >
2019-07-10 01:18:01 +00:00
def < strong > imag< / strong >
2019-06-13 02:23:54 +00:00
2019-07-10 01:18:01 +00:00
< a class = "method-permalink" href = "#imag-instance-method" > #< / a >
2019-06-13 02:23:54 +00:00
< / div >
2019-07-10 01:18:01 +00:00
< div class = "doc" > < p > Returns the imaginary part of the matrix.< / p >
< pre > < code > < span class = "t" > Matrix< / span > [[< span class = "t" > Complex< / span > (< span class = "n" > 1< / span > ,< span class = "n" > 2< / span > ), < span class = "t" > Complex< / span > (< span class = "n" > 0< / span > ,< span class = "n" > 1< / span > ), < span class = "n" > 0< / span > ], [< span class = "n" > 1< / span > , < span class = "n" > 2< / span > , < span class = "n" > 3< / span > ]]
< span class = "c" > # => [ 1+2i, i, 0,< / span >
< span class = "c" > # 1, 2, 3 ]< / span >
< span class = "t" > Matrix< / span > [[< span class = "t" > Complex< / span > (< span class = "n" > 1< / span > ,< span class = "n" > 2< / span > ), < span class = "t" > Complex< / span > (< span class = "n" > 0< / span > ,< span class = "n" > 1< / span > ), < span class = "n" > 0< / span > ], [< span class = "n" > 1< / span > , < span class = "n" > 2< / span > , < span class = "n" > 3< / span > ]].imag
< span class = "c" > # => [ 2i, i, 0,< / span >
< span class = "c" > # 0, 0, 0 ]< / span > < / code > < / pre > < / div >
2019-06-13 02:23:54 +00:00
< br / >
< div >
2019-07-10 02:22:15 +00:00
[< a href = "https://github.com/watzon/apatite/blob/6e67ceb81b0b3c61d48b74e5ca5154866a9abd1a/src/apatite/linear_algebra/matrix.cr#L1328" target = "_blank" > View source< / a > ]
2019-06-13 02:23:54 +00:00
< / div >
< / div >
2019-07-10 01:18:01 +00:00
< div class = "entry-detail" id = "index(i,selector=:all)-instance-method" >
2019-06-13 02:23:54 +00:00
< div class = "signature" >
2019-07-10 01:18:01 +00:00
def < strong > index< / strong > (i, selector = < span class = "n" > :all< / span > )
2019-06-13 02:23:54 +00:00
2019-07-10 01:18:01 +00:00
< a class = "method-permalink" href = "#index%28i%2Cselector%3D%3Aall%29-instance-method" > #< / a >
2019-06-13 02:23:54 +00:00
< / div >
2019-07-10 01:18:01 +00:00
< div class = "doc" > < p > The index method is specialized to return the index as {row, column}
It also accepts an optional < code > selector< / code > argument, see < code > < a href = "../../Apatite/LinearAlgebra/Matrix.html#each%28which%3D%3Aall%2C%26block%3AT-%3E%29-instance-method" > #each< / a > < / code > for details.< / p >
< pre > < code > < span class = "t" > Matrix< / span > [ [< span class = "n" > 1< / span > ,< span class = "n" > 1< / span > ], [< span class = "n" > 1< / span > ,< span class = "n" > 1< / span > ] ].index(< span class = "n" > 1< / span > , < span class = "n" > :strict_lower< / span > )
< span class = "c" > # => {1, 0}< / span > < / code > < / pre > < / div >
2019-06-13 02:23:54 +00:00
< br / >
< div >
2019-07-10 02:22:15 +00:00
[< a href = "https://github.com/watzon/apatite/blob/6e67ceb81b0b3c61d48b74e5ca5154866a9abd1a/src/apatite/linear_algebra/matrix.cr#L495" target = "_blank" > View source< / a > ]
2019-06-13 02:23:54 +00:00
< / div >
< / div >
2019-07-10 01:18:01 +00:00
< div class = "entry-detail" id = "index(selector=:all,&block:T->Bool)-instance-method" >
2019-06-13 02:23:54 +00:00
< div class = "signature" >
2019-07-10 01:18:01 +00:00
def < strong > index< / strong > (selector = < span class = "n" > :all< / span > , & block : T -> Bool)
2019-06-13 02:23:54 +00:00
2019-07-10 01:18:01 +00:00
< a class = "method-permalink" href = "#index%28selector%3D%3Aall%2C%26block%3AT-%3EBool%29-instance-method" > #< / a >
2019-06-13 02:23:54 +00:00
< / div >
2019-07-10 01:18:01 +00:00
< div class = "doc" > < p > Returns the index as {row, column}, using < code > & block< / code > to filter the
result. It also accepts an optional < code > selector< / code > argument, see
< code > < a href = "../../Apatite/LinearAlgebra/Matrix.html#each%28which%3D%3Aall%2C%26block%3AT-%3E%29-instance-method" > #each< / a > < / code > for details.< / p >
< pre > < code > < span class = "t" > Matrix< / span > [ [< span class = "n" > 1< / span > ,< span class = "n" > 2< / span > ], [< span class = "n" > 3< / span > ,< span class = "n" > 4< / span > ] ].index(< span class = "o" > & < / span > .even?)
< span class = "c" > # => {0, 1}< / span > < / code > < / pre > < / div >
2019-06-13 02:23:54 +00:00
< br / >
< div >
2019-07-10 02:22:15 +00:00
[< a href = "https://github.com/watzon/apatite/blob/6e67ceb81b0b3c61d48b74e5ca5154866a9abd1a/src/apatite/linear_algebra/matrix.cr#L514" target = "_blank" > View source< / a > ]
2019-06-13 02:23:54 +00:00
< / div >
< / div >
2019-07-10 01:18:01 +00:00
< div class = "entry-detail" id = "inverse-instance-method" >
2019-06-13 02:23:54 +00:00
< div class = "signature" >
2019-07-10 01:18:01 +00:00
def < strong > inverse< / strong >
2019-06-13 02:23:54 +00:00
2019-07-10 01:18:01 +00:00
< a class = "method-permalink" href = "#inverse-instance-method" > #< / a >
2019-06-13 02:23:54 +00:00
< / div >
2019-07-10 01:18:01 +00:00
< div class = "doc" > < p > Returns the inverse of the matrix.< / p >
< p > < span class = "flag purple" > NOTE< / span > Always returns a < code > Float64< / code > regardless of < code > T< / code > s type. To coerce
back into an < code > Int< / code > , use < code > < a href = "../../Apatite/LinearAlgebra/Matrix.html#coerce%28klass%29-instance-method" > #coerce< / a > < / code > .< / p >
< pre > < code > < span class = "t" > Matrix< / span > [[< span class = "n" > -1< / span > , < span class = "n" > -1< / span > ], [< span class = "n" > 0< / span > , < span class = "n" > -1< / span > ]].inverse
< span class = "c" > # => [ -1.0, 1.0,< / span >
< span class = "c" > # 0.0, -1.0 ]< / span > < / code > < / pre > < / div >
2019-06-13 02:23:54 +00:00
< br / >
< div >
2019-07-10 02:22:15 +00:00
[< a href = "https://github.com/watzon/apatite/blob/6e67ceb81b0b3c61d48b74e5ca5154866a9abd1a/src/apatite/linear_algebra/matrix.cr#L1013" target = "_blank" > View source< / a > ]
2019-06-13 02:23:54 +00:00
< / div >
< / div >
2019-07-10 01:18:01 +00:00
< div class = "entry-detail" id = "laplace_expansion(*,row=nil,column=nil)-instance-method" >
2019-06-13 02:23:54 +00:00
< div class = "signature" >
2019-07-10 01:18:01 +00:00
def < strong > laplace_expansion< / strong > (*, row = < span class = "n" > nil< / span > , column = < span class = "n" > nil< / span > )
2019-06-13 02:23:54 +00:00
2019-07-10 01:18:01 +00:00
< a class = "method-permalink" href = "#laplace_expansion%28%2A%2Crow%3Dnil%2Ccolumn%3Dnil%29-instance-method" > #< / a >
2019-06-13 02:23:54 +00:00
< / div >
2019-07-10 01:18:01 +00:00
< div class = "doc" > < p > Returns the Laplace expansion along given row or column.< / p >
< pre > < code > < span class = "t" > Matrix< / span > [[< span class = "n" > 7< / span > ,< span class = "n" > 6< / span > ], [< span class = "n" > 3< / span > ,< span class = "n" > 9< / span > ]].laplace_expansion(column: < span class = "n" > 1< / span > )
< span class = "c" > # => 45< / span >
< span class = "t" > Matrix< / span > [[< span class = "t" > Vector< / span > [< span class = "n" > 1< / span > , < span class = "n" > 0< / span > ], < span class = "t" > Vector< / span > [< span class = "n" > 0< / span > , < span class = "n" > 1< / span > ]], [< span class = "n" > 2< / span > , < span class = "n" > 3< / span > ]].laplace_expansion(row: < span class = "n" > 0< / span > )
< span class = "c" > # => Vector[3, -2]< / span > < / code > < / pre > < / div >
2019-06-13 02:23:54 +00:00
< br / >
< div >
2019-07-10 02:22:15 +00:00
[< a href = "https://github.com/watzon/apatite/blob/6e67ceb81b0b3c61d48b74e5ca5154866a9abd1a/src/apatite/linear_algebra/matrix.cr#L642" target = "_blank" > View source< / a > ]
2019-06-13 02:23:54 +00:00
< / div >
< / div >
2019-07-10 01:18:01 +00:00
< div class = "entry-detail" id = "lower_triangular?-instance-method" >
2019-06-13 02:23:54 +00:00
< div class = "signature" >
2019-07-10 01:18:01 +00:00
def < strong > lower_triangular?< / strong >
2019-06-13 02:23:54 +00:00
2019-07-10 01:18:01 +00:00
< a class = "method-permalink" href = "#lower_triangular%3F-instance-method" > #< / a >
2019-06-13 02:23:54 +00:00
< / div >
2019-07-10 01:18:01 +00:00
< div class = "doc" > < p > Returns true if this matrix is a lower triangular matrix.< / p > < / div >
2019-06-13 02:23:54 +00:00
< br / >
< div >
2019-07-10 02:22:15 +00:00
[< a href = "https://github.com/watzon/apatite/blob/6e67ceb81b0b3c61d48b74e5ca5154866a9abd1a/src/apatite/linear_algebra/matrix.cr#L720" target = "_blank" > View source< / a > ]
2019-06-13 02:23:54 +00:00
< / div >
< / div >
2019-07-10 01:18:01 +00:00
< div class = "entry-detail" id = "lup-instance-method" >
< div class = "signature" >
def < strong > lup< / strong >
2019-06-13 02:23:54 +00:00
2019-07-10 01:18:01 +00:00
< a class = "method-permalink" href = "#lup-instance-method" > #< / a >
< / div >
< div class = "doc" > < p > Returns the LUP decomposition of the matrix
See +LUPDecomposition+.< / p >
2019-06-13 02:23:54 +00:00
2019-07-10 01:18:01 +00:00
< p > < span class = "flag purple" > NOTE< / span > Not working yet< / p >
2019-06-13 02:23:54 +00:00
2019-07-10 01:18:01 +00:00
< pre > < code > a < span class = "o" > =< / span > < span class = "t" > Matrix< / span > [[< span class = "n" > 1< / span > , < span class = "n" > 2< / span > ], [< span class = "n" > 3< / span > , < span class = "n" > 4< / span > ]]
l, u, p < span class = "o" > =< / span > a.lup
l.lower_triangular? < span class = "c" > # => true< / span >
u.upper_triangular? < span class = "c" > # => true< / span >
p.permutation? < span class = "c" > # => true< / span >
l < span class = "o" > *< / span > u < span class = "o" > ==< / span > p < span class = "o" > *< / span > a < span class = "c" > # => true< / span >
a.lup.solve([< span class = "n" > 2< / span > , < span class = "n" > 5< / span > ]) < span class = "c" > # => Vector[(1/1), (1/2)]< / span > < / code > < / pre > < / div >
< br / >
< div >
2019-07-10 02:22:15 +00:00
[< a href = "https://github.com/watzon/apatite/blob/6e67ceb81b0b3c61d48b74e5ca5154866a9abd1a/src/apatite/linear_algebra/matrix.cr#L1295" target = "_blank" > View source< / a > ]
2019-07-10 01:18:01 +00:00
< / div >
< / div >
2019-06-13 02:23:54 +00:00
2019-07-10 01:18:01 +00:00
< div class = "entry-detail" id = "map(&block:T->T)-instance-method" >
2019-06-13 02:23:54 +00:00
< div class = "signature" >
2019-07-10 01:18:01 +00:00
def < strong > map< / strong > (& block : T -> T)
2019-06-13 02:23:54 +00:00
2019-07-10 01:18:01 +00:00
< a class = "method-permalink" href = "#map%28%26block%3AT-%3ET%29-instance-method" > #< / a >
2019-06-13 02:23:54 +00:00
< / div >
2019-07-10 01:18:01 +00:00
< div class = "doc" > < p > Returns a Matrix that is the result of iteration of the given block
over all elements in the matrix.< / p > < / div >
2019-06-13 02:23:54 +00:00
< br / >
< div >
2019-07-10 02:22:15 +00:00
[< a href = "https://github.com/watzon/apatite/blob/6e67ceb81b0b3c61d48b74e5ca5154866a9abd1a/src/apatite/linear_algebra/matrix.cr#L359" target = "_blank" > View source< / a > ]
2019-06-13 02:23:54 +00:00
< / div >
< / div >
2019-07-10 02:22:15 +00:00
< div class = "entry-detail" id = "minor(from_row:Int,nrows:Int,from_col:Int,ncols:Int)-instance-method" >
2019-06-13 02:23:54 +00:00
< div class = "signature" >
2019-07-10 02:22:15 +00:00
def < strong > minor< / strong > (from_row : Int, nrows : Int, from_col : Int, ncols : Int)
2019-06-13 02:23:54 +00:00
2019-07-10 02:22:15 +00:00
< a class = "method-permalink" href = "#minor%28from_row%3AInt%2Cnrows%3AInt%2Cfrom_col%3AInt%2Cncols%3AInt%29-instance-method" > #< / a >
2019-06-13 02:23:54 +00:00
< / div >
2019-07-10 01:18:01 +00:00
< div class = "doc" > < p > Returns a section of the Matrix.< / p >
2019-07-10 02:22:15 +00:00
< pre > < code > < span class = "t" > Matrix< / span > .diagonal(< span class = "n" > 9< / span > , < span class = "n" > 5< / span > , < span class = "n" > -3< / span > ).minor(< span class = "n" > 0< / span > , < span class = "n" > 2< / span > , < span class = "n" > 0< / span > , < span class = "n" > 3< / span > )
2019-07-10 01:18:01 +00:00
< span class = "c" > # => [ 9, 0, 0,< / span >
< span class = "c" > # 0, 5, 0 ]< / span > < / code > < / pre > < / div >
2019-06-13 02:23:54 +00:00
< br / >
< div >
2019-07-10 02:22:15 +00:00
[< a href = "https://github.com/watzon/apatite/blob/6e67ceb81b0b3c61d48b74e5ca5154866a9abd1a/src/apatite/linear_algebra/matrix.cr#L563" target = "_blank" > View source< / a > ]
2019-06-13 02:23:54 +00:00
< / div >
< / div >
2019-07-10 02:22:15 +00:00
< div class = "entry-detail" id = "minor(row_range:Range,col_range:Range)-instance-method" >
2019-06-13 02:23:54 +00:00
< div class = "signature" >
2019-07-10 02:22:15 +00:00
def < strong > minor< / strong > (row_range : Range, col_range : Range)
2019-06-13 02:23:54 +00:00
2019-07-10 02:22:15 +00:00
< a class = "method-permalink" href = "#minor%28row_range%3ARange%2Ccol_range%3ARange%29-instance-method" > #< / a >
2019-06-13 02:23:54 +00:00
< / div >
2019-07-10 01:18:01 +00:00
< div class = "doc" > < p > Returns a section of the Matrix.< / p >
2019-07-10 02:22:15 +00:00
< pre > < code > < span class = "t" > Matrix< / span > .diagonal(< span class = "n" > 9< / span > , < span class = "n" > 5< / span > , < span class = "n" > -3< / span > ).minor(< span class = "n" > 0< / span > ..< span class = "n" > 1< / span > , < span class = "n" > 0< / span > ..< span class = "n" > 2< / span > )
2019-07-10 01:18:01 +00:00
< span class = "c" > # => [ 9, 0, 0,< / span >
< span class = "c" > # 0, 5, 0 ]< / span > < / code > < / pre > < / div >
2019-06-13 02:23:54 +00:00
< br / >
< div >
2019-07-10 02:22:15 +00:00
[< a href = "https://github.com/watzon/apatite/blob/6e67ceb81b0b3c61d48b74e5ca5154866a9abd1a/src/apatite/linear_algebra/matrix.cr#L532" target = "_blank" > View source< / a > ]
2019-06-13 02:23:54 +00:00
< / div >
< / div >
2019-07-10 01:18:01 +00:00
< div class = "entry-detail" id = "normal?-instance-method" >
2019-06-13 02:23:54 +00:00
< div class = "signature" >
2019-07-10 01:18:01 +00:00
def < strong > normal?< / strong >
2019-06-13 02:23:54 +00:00
2019-07-10 01:18:01 +00:00
< a class = "method-permalink" href = "#normal%3F-instance-method" > #< / a >
2019-06-13 02:23:54 +00:00
< / div >
2019-07-10 01:18:01 +00:00
< div class = "doc" > < p > Returns < code > true< / code > if this is a normal matrix.< / p >
< pre > < code > < span class = "t" > Matrix< / span > [[< span class = "n" > 1< / span > , < span class = "n" > 1< / span > , < span class = "n" > 0< / span > ], [< span class = "n" > 0< / span > , < span class = "n" > 1< / span > , < span class = "n" > 1< / span > ], [< span class = "n" > 1< / span > , < span class = "n" > 0< / span > , < span class = "n" > 1< / span > ]].normal?
< span class = "c" > # => true< / span > < / code > < / pre > < / div >
2019-06-13 02:23:54 +00:00
< br / >
< div >
2019-07-10 02:22:15 +00:00
[< a href = "https://github.com/watzon/apatite/blob/6e67ceb81b0b3c61d48b74e5ca5154866a9abd1a/src/apatite/linear_algebra/matrix.cr#L732" target = "_blank" > View source< / a > ]
2019-06-13 02:23:54 +00:00
< / div >
< / div >
2019-07-10 01:18:01 +00:00
< div class = "entry-detail" id = "orthogonal?-instance-method" >
2019-06-13 02:23:54 +00:00
< div class = "signature" >
2019-07-10 01:18:01 +00:00
def < strong > orthogonal?< / strong >
2019-06-13 02:23:54 +00:00
2019-07-10 01:18:01 +00:00
< a class = "method-permalink" href = "#orthogonal%3F-instance-method" > #< / a >
2019-06-13 02:23:54 +00:00
< / div >
2019-07-10 01:18:01 +00:00
< div class = "doc" > < p > Returns < code > true< / code > if this is an orthogonal matrix< / p >
< pre > < code > < span class = "t" > Matrix< / span > [[< span class = "n" > 1< / span > , < span class = "n" > 0< / span > ], [< span class = "n" > 0< / span > , < span class = "n" > 1< / span > ]].orthogonal?
< span class = "c" > # => true< / span > < / code > < / pre > < / div >
2019-06-13 02:23:54 +00:00
< br / >
< div >
2019-07-10 02:22:15 +00:00
[< a href = "https://github.com/watzon/apatite/blob/6e67ceb81b0b3c61d48b74e5ca5154866a9abd1a/src/apatite/linear_algebra/matrix.cr#L752" target = "_blank" > View source< / a > ]
2019-06-13 02:23:54 +00:00
< / div >
< / div >
2019-07-10 01:18:01 +00:00
< div class = "entry-detail" id = "permutation?-instance-method" >
2019-06-13 02:23:54 +00:00
< div class = "signature" >
2019-07-10 01:18:01 +00:00
def < strong > permutation?< / strong >
2019-06-13 02:23:54 +00:00
2019-07-10 01:18:01 +00:00
< a class = "method-permalink" href = "#permutation%3F-instance-method" > #< / a >
2019-06-13 02:23:54 +00:00
< / div >
2019-07-10 01:18:01 +00:00
< div class = "doc" > < p > Returns < code > true< / code > if this is a permutation matrix< / p >
< pre > < code > < span class = "t" > Matrix< / span > [[< span class = "n" > 1< / span > , < span class = "n" > 0< / span > ], [< span class = "n" > 0< / span > , < span class = "n" > 1< / span > ]].permutation?
< span class = "c" > # => true< / span > < / code > < / pre > < / div >
2019-06-13 02:23:54 +00:00
< br / >
< div >
2019-07-10 02:22:15 +00:00
[< a href = "https://github.com/watzon/apatite/blob/6e67ceb81b0b3c61d48b74e5ca5154866a9abd1a/src/apatite/linear_algebra/matrix.cr#L772" target = "_blank" > View source< / a > ]
2019-06-13 02:23:54 +00:00
< / div >
< / div >
2019-07-10 01:18:01 +00:00
< div class = "entry-detail" id = "pretty_print(pp):Nil-instance-method" >
2019-06-13 02:23:54 +00:00
< div class = "signature" >
2019-07-10 01:18:01 +00:00
def < strong > pretty_print< / strong > (pp) : Nil
2019-06-13 02:23:54 +00:00
2019-07-10 01:18:01 +00:00
< a class = "method-permalink" href = "#pretty_print%28pp%29%3ANil-instance-method" > #< / a >
2019-06-13 02:23:54 +00:00
< / div >
< br / >
< div >
2019-07-10 02:22:15 +00:00
[< a href = "https://github.com/watzon/apatite/blob/6e67ceb81b0b3c61d48b74e5ca5154866a9abd1a/src/apatite/linear_algebra/matrix.cr#L1414" target = "_blank" > View source< / a > ]
2019-06-13 02:23:54 +00:00
< / div >
< / div >
2019-07-10 01:18:01 +00:00
< div class = "entry-detail" id = "rank-instance-method" >
2019-06-13 02:23:54 +00:00
< div class = "signature" >
2019-07-10 01:18:01 +00:00
def < strong > rank< / strong >
2019-06-13 02:23:54 +00:00
2019-07-10 01:18:01 +00:00
< a class = "method-permalink" href = "#rank-instance-method" > #< / a >
2019-06-13 02:23:54 +00:00
< / div >
2019-07-10 01:18:01 +00:00
< div class = "doc" > < p > Returns the rank of the matrix.< / p >
< p > Beware that using Float values can yield erroneous results
because of their lack of precision.
Consider using exact types like Rational or BigDecimal instead.< / p >
< pre > < code > < span class = "t" > Matrix< / span > [[< span class = "n" > 7< / span > ,< span class = "n" > 6< / span > ], [< span class = "n" > 3< / span > ,< span class = "n" > 9< / span > ]].rank
< span class = "c" > # => 2< / span > < / code > < / pre > < / div >
2019-06-13 02:23:54 +00:00
< br / >
< div >
2019-07-10 02:22:15 +00:00
[< a href = "https://github.com/watzon/apatite/blob/6e67ceb81b0b3c61d48b74e5ca5154866a9abd1a/src/apatite/linear_algebra/matrix.cr#L1175" target = "_blank" > View source< / a > ]
2019-06-13 02:23:54 +00:00
< / div >
< / div >
2019-07-10 01:18:01 +00:00
< div class = "entry-detail" id = "real-instance-method" >
2019-06-13 02:23:54 +00:00
< div class = "signature" >
2019-07-10 01:18:01 +00:00
def < strong > real< / strong >
2019-06-13 02:23:54 +00:00
2019-07-10 01:18:01 +00:00
< a class = "method-permalink" href = "#real-instance-method" > #< / a >
2019-06-13 02:23:54 +00:00
< / div >
2019-07-10 01:18:01 +00:00
< div class = "doc" > < p > Returns the real part of the matrix.< / p >
< pre > < code > < span class = "t" > Matrix< / span > [[< span class = "t" > Complex< / span > (< span class = "n" > 1< / span > ,< span class = "n" > 2< / span > ), < span class = "t" > Complex< / span > (< span class = "n" > 0< / span > ,< span class = "n" > 1< / span > ), < span class = "n" > 0< / span > ], [< span class = "n" > 1< / span > , < span class = "n" > 2< / span > , < span class = "n" > 3< / span > ]]
< span class = "c" > # => [ 1+2i, i, 0,< / span >
< span class = "c" > # 1, 2, 3 ]< / span >
< span class = "t" > Matrix< / span > [[< span class = "t" > Complex< / span > (< span class = "n" > 1< / span > ,< span class = "n" > 2< / span > ), < span class = "t" > Complex< / span > (< span class = "n" > 0< / span > ,< span class = "n" > 1< / span > ), < span class = "n" > 0< / span > ], [< span class = "n" > 1< / span > , < span class = "n" > 2< / span > , < span class = "n" > 3< / span > ]].real
< span class = "c" > # => [ 1, 0, 0,< / span >
< span class = "c" > # 1, 2, 3 ]< / span > < / code > < / pre > < / div >
2019-06-13 02:23:54 +00:00
< br / >
< div >
2019-07-10 02:22:15 +00:00
[< a href = "https://github.com/watzon/apatite/blob/6e67ceb81b0b3c61d48b74e5ca5154866a9abd1a/src/apatite/linear_algebra/matrix.cr#L1343" target = "_blank" > View source< / a > ]
2019-06-13 02:23:54 +00:00
< / div >
< / div >
2019-07-10 01:18:01 +00:00
< div class = "entry-detail" id = "real?-instance-method" >
2019-06-13 02:23:54 +00:00
< div class = "signature" >
2019-07-10 01:18:01 +00:00
def < strong > real?< / strong >
2019-06-13 02:23:54 +00:00
2019-07-10 01:18:01 +00:00
< a class = "method-permalink" href = "#real%3F-instance-method" > #< / a >
2019-06-13 02:23:54 +00:00
< / div >
2019-07-10 01:18:01 +00:00
< div class = "doc" > < p > Returns < code > true< / code > if this matrix contains real numbers,
i.e. not < code > Complex< / code > .< / p >
< pre > < code > < span class = "k" > require< / span > < span class = "s" > " complex" < / span >
< span class = "t" > Matrix< / span > [[< span class = "t" > Complex< / span > .< span class = "k" > new< / span > (< span class = "n" > 1< / span > , < span class = "n" > 0< / span > )], [< span class = "t" > Complex< / span > .< span class = "k" > new< / span > (< span class = "n" > 0< / span > , < span class = "n" > 1< / span > )]].real?
< span class = "c" > # => false< / span > < / code > < / pre > < / div >
2019-06-13 02:23:54 +00:00
< br / >
< div >
2019-07-10 02:22:15 +00:00
[< a href = "https://github.com/watzon/apatite/blob/6e67ceb81b0b3c61d48b74e5ca5154866a9abd1a/src/apatite/linear_algebra/matrix.cr#L798" target = "_blank" > View source< / a > ]
2019-06-13 02:23:54 +00:00
< / div >
< / div >
2019-07-10 01:18:01 +00:00
< div class = "entry-detail" id = "rect-instance-method" >
2019-06-13 02:23:54 +00:00
< div class = "signature" >
2019-07-10 01:18:01 +00:00
def < strong > rect< / strong >
2019-06-13 02:23:54 +00:00
2019-07-10 01:18:01 +00:00
< a class = "method-permalink" href = "#rect-instance-method" > #< / a >
2019-06-13 02:23:54 +00:00
< / div >
2019-07-10 01:18:01 +00:00
< div class = "doc" > < p > Returns an array containing matrices corresponding to the real and imaginary
parts of the matrix< / p >
< pre > < code > m.rect < span class = "o" > ==< / span > [m.real, m.imag]
< span class = "c" > # ==> true for all matrices m< / span > < / code > < / pre > < / div >
2019-06-13 02:23:54 +00:00
< br / >
< div >
2019-07-10 02:22:15 +00:00
[< a href = "https://github.com/watzon/apatite/blob/6e67ceb81b0b3c61d48b74e5ca5154866a9abd1a/src/apatite/linear_algebra/matrix.cr#L1355" target = "_blank" > View source< / a > ]
2019-06-13 02:23:54 +00:00
< / div >
< / div >
2019-07-10 01:18:01 +00:00
< div class = "entry-detail" id = "regular?-instance-method" >
2019-06-13 02:23:54 +00:00
< div class = "signature" >
2019-07-10 01:18:01 +00:00
def < strong > regular?< / strong >
2019-06-13 02:23:54 +00:00
2019-07-10 01:18:01 +00:00
< a class = "method-permalink" href = "#regular%3F-instance-method" > #< / a >
2019-06-13 02:23:54 +00:00
< / div >
2019-07-10 01:18:01 +00:00
< div class = "doc" > < p > Returns < code > true< / code > if this is a regular (i.e. non-singular) matrix.< / p > < / div >
2019-06-13 02:23:54 +00:00
< br / >
< div >
2019-07-10 02:22:15 +00:00
[< a href = "https://github.com/watzon/apatite/blob/6e67ceb81b0b3c61d48b74e5ca5154866a9abd1a/src/apatite/linear_algebra/matrix.cr#L803" target = "_blank" > View source< / a > ]
2019-06-13 02:23:54 +00:00
< / div >
< / div >
2019-07-10 01:18:01 +00:00
< div class = "entry-detail" id = "round(n=0)-instance-method" >
2019-06-13 02:23:54 +00:00
< div class = "signature" >
2019-07-10 01:18:01 +00:00
def < strong > round< / strong > (n = < span class = "n" > 0< / span > )
2019-06-13 02:23:54 +00:00
2019-07-10 01:18:01 +00:00
< a class = "method-permalink" href = "#round%28n%3D0%29-instance-method" > #< / a >
2019-06-13 02:23:54 +00:00
< / div >
2019-07-10 01:18:01 +00:00
< div class = "doc" > < p > Returns a matrix with entries rounded to the given precision
(see < code > Float#round< / code > )< / p > < / div >
2019-06-13 02:23:54 +00:00
< br / >
< div >
2019-07-10 02:22:15 +00:00
[< a href = "https://github.com/watzon/apatite/blob/6e67ceb81b0b3c61d48b74e5ca5154866a9abd1a/src/apatite/linear_algebra/matrix.cr#L1205" target = "_blank" > View source< / a > ]
2019-06-13 02:23:54 +00:00
< / div >
< / div >
2019-07-10 01:18:01 +00:00
< div class = "entry-detail" id = "row(i,&block:Vector->)-instance-method" >
2019-06-13 02:23:54 +00:00
< div class = "signature" >
2019-07-10 01:18:01 +00:00
def < strong > row< / strong > (i, & block : < a href = "../../Apatite/LinearAlgebra/Vector.html" > Vector< / a > -> )
2019-06-13 02:23:54 +00:00
2019-07-10 01:18:01 +00:00
< a class = "method-permalink" href = "#row%28i%2C%26block%3AVector-%3E%29-instance-method" > #< / a >
2019-06-13 02:23:54 +00:00
< / div >
2019-07-10 01:18:01 +00:00
< div class = "doc" > < p > Returns a block which yields every Vector in the row (starting at 0).< / p > < / div >
2019-06-13 02:23:54 +00:00
< br / >
< div >
2019-07-10 02:22:15 +00:00
[< a href = "https://github.com/watzon/apatite/blob/6e67ceb81b0b3c61d48b74e5ca5154866a9abd1a/src/apatite/linear_algebra/matrix.cr#L322" target = "_blank" > View source< / a > ]
2019-06-13 02:23:54 +00:00
< / div >
< / div >
2019-07-10 01:18:01 +00:00
< div class = "entry-detail" id = "row(i)-instance-method" >
2019-06-13 02:23:54 +00:00
< div class = "signature" >
2019-07-10 01:18:01 +00:00
def < strong > row< / strong > (i)
2019-06-13 02:23:54 +00:00
2019-07-10 01:18:01 +00:00
< a class = "method-permalink" href = "#row%28i%29-instance-method" > #< / a >
2019-06-13 02:23:54 +00:00
< / div >
2019-07-10 01:18:01 +00:00
< div class = "doc" > < p > Returns row vector number < code > i< / code > of the Matrix as a Vector (starting
at 0 like a good boy). Raises if the row doesn't exist.< / p > < / div >
2019-06-13 02:23:54 +00:00
< br / >
< div >
2019-07-10 02:22:15 +00:00
[< a href = "https://github.com/watzon/apatite/blob/6e67ceb81b0b3c61d48b74e5ca5154866a9abd1a/src/apatite/linear_algebra/matrix.cr#L316" target = "_blank" > View source< / a > ]
2019-06-13 02:23:54 +00:00
< / div >
< / div >
2019-07-10 01:18:01 +00:00
< div class = "entry-detail" id = "row?(i)-instance-method" >
2019-06-13 02:23:54 +00:00
< div class = "signature" >
2019-07-10 01:18:01 +00:00
def < strong > row?< / strong > (i)
2019-06-13 02:23:54 +00:00
2019-07-10 01:18:01 +00:00
< a class = "method-permalink" href = "#row%3F%28i%29-instance-method" > #< / a >
2019-06-13 02:23:54 +00:00
< / div >
2019-07-10 01:18:01 +00:00
< div class = "doc" > < p > Returns row vector number < code > i< / code > of the Matrix as a Vector (starting
at 0 like a good boy). Returns nil if the row doesn't exist.< / p > < / div >
2019-06-13 02:23:54 +00:00
< br / >
< div >
2019-07-10 02:22:15 +00:00
[< a href = "https://github.com/watzon/apatite/blob/6e67ceb81b0b3c61d48b74e5ca5154866a9abd1a/src/apatite/linear_algebra/matrix.cr#L328" target = "_blank" > View source< / a > ]
2019-06-13 02:23:54 +00:00
< / div >
< / div >
2019-07-10 01:18:01 +00:00
< div class = "entry-detail" id = "row_count-instance-method" >
2019-06-13 02:23:54 +00:00
< div class = "signature" >
2019-07-10 01:18:01 +00:00
def < strong > row_count< / strong >
2019-06-13 02:23:54 +00:00
2019-07-10 01:18:01 +00:00
< a class = "method-permalink" href = "#row_count-instance-method" > #< / a >
2019-06-13 02:23:54 +00:00
< / div >
2019-07-10 01:18:01 +00:00
< div class = "doc" > < p > Returns the number of rows.< / p > < / div >
2019-06-13 02:23:54 +00:00
< br / >
< div >
2019-07-10 02:22:15 +00:00
[< a href = "https://github.com/watzon/apatite/blob/6e67ceb81b0b3c61d48b74e5ca5154866a9abd1a/src/apatite/linear_algebra/matrix.cr#L307" target = "_blank" > View source< / a > ]
< / div >
< / div >
< div class = "entry-detail" id = "row_vectors-instance-method" >
< div class = "signature" >
def < strong > row_vectors< / strong >
< a class = "method-permalink" href = "#row_vectors-instance-method" > #< / a >
< / div >
< div class = "doc" > < p > Returns an array of the row vectors of the matrix. See < code > < a href = "../../Apatite/LinearAlgebra/Vector.html" > Vector< / a > < / code > .< / p > < / div >
< br / >
< div >
[< a href = "https://github.com/watzon/apatite/blob/6e67ceb81b0b3c61d48b74e5ca5154866a9abd1a/src/apatite/linear_algebra/matrix.cr#L1371" target = "_blank" > View source< / a > ]
2019-06-13 02:23:54 +00:00
< / div >
< / div >
2019-07-10 01:18:01 +00:00
< div class = "entry-detail" id = "singular?-instance-method" >
2019-06-13 02:23:54 +00:00
< div class = "signature" >
2019-07-10 01:18:01 +00:00
def < strong > singular?< / strong >
2019-06-13 02:23:54 +00:00
2019-07-10 01:18:01 +00:00
< a class = "method-permalink" href = "#singular%3F-instance-method" > #< / a >
2019-06-13 02:23:54 +00:00
< / div >
2019-07-10 01:18:01 +00:00
< div class = "doc" > < p > Returns < code > true< / code > if this is a singular matrix.< / p > < / div >
2019-06-13 02:23:54 +00:00
< br / >
< div >
2019-07-10 02:22:15 +00:00
[< a href = "https://github.com/watzon/apatite/blob/6e67ceb81b0b3c61d48b74e5ca5154866a9abd1a/src/apatite/linear_algebra/matrix.cr#L808" target = "_blank" > View source< / a > ]
2019-06-13 02:23:54 +00:00
< / div >
< / div >
2019-07-10 01:18:01 +00:00
< div class = "entry-detail" id = "square?-instance-method" >
2019-06-13 02:23:54 +00:00
< div class = "signature" >
2019-07-10 01:18:01 +00:00
def < strong > square?< / strong >
2019-06-13 02:23:54 +00:00
2019-07-10 01:18:01 +00:00
< a class = "method-permalink" href = "#square%3F-instance-method" > #< / a >
2019-06-13 02:23:54 +00:00
< / div >
2019-07-10 01:18:01 +00:00
< div class = "doc" > < p > Returns < code > true< / code > if this is a square matrix.< / p > < / div >
2019-06-13 02:23:54 +00:00
< br / >
< div >
2019-07-10 02:22:15 +00:00
[< a href = "https://github.com/watzon/apatite/blob/6e67ceb81b0b3c61d48b74e5ca5154866a9abd1a/src/apatite/linear_algebra/matrix.cr#L813" target = "_blank" > View source< / a > ]
2019-06-13 02:23:54 +00:00
< / div >
< / div >
2019-07-10 01:18:01 +00:00
< div class = "entry-detail" id = "swap_columns(col1,col2)-instance-method" >
2019-06-13 02:23:54 +00:00
< div class = "signature" >
2019-07-10 01:18:01 +00:00
def < strong > swap_columns< / strong > (col1, col2)
2019-06-13 02:23:54 +00:00
2019-07-10 01:18:01 +00:00
< a class = "method-permalink" href = "#swap_columns%28col1%2Ccol2%29-instance-method" > #< / a >
2019-06-13 02:23:54 +00:00
< / div >
2019-07-10 01:18:01 +00:00
< div class = "doc" > < p > Swaps < code > col1< / code > and < code > col2< / code > < / p > < / div >
2019-06-13 02:23:54 +00:00
< br / >
< div >
2019-07-10 02:22:15 +00:00
[< a href = "https://github.com/watzon/apatite/blob/6e67ceb81b0b3c61d48b74e5ca5154866a9abd1a/src/apatite/linear_algebra/matrix.cr#L680" target = "_blank" > View source< / a > ]
2019-06-13 02:23:54 +00:00
< / div >
< / div >
2019-07-10 01:18:01 +00:00
< div class = "entry-detail" id = "swap_rows(row1,row2)-instance-method" >
2019-06-13 02:23:54 +00:00
< div class = "signature" >
2019-07-10 01:18:01 +00:00
def < strong > swap_rows< / strong > (row1, row2)
2019-06-13 02:23:54 +00:00
2019-07-10 01:18:01 +00:00
< a class = "method-permalink" href = "#swap_rows%28row1%2Crow2%29-instance-method" > #< / a >
2019-06-13 02:23:54 +00:00
< / div >
2019-07-10 01:18:01 +00:00
< div class = "doc" > < p > Swaps < code > row1< / code > and < code > row2< / code > < / p > < / div >
2019-06-13 02:23:54 +00:00
< br / >
< div >
2019-07-10 02:22:15 +00:00
[< a href = "https://github.com/watzon/apatite/blob/6e67ceb81b0b3c61d48b74e5ca5154866a9abd1a/src/apatite/linear_algebra/matrix.cr#L668" target = "_blank" > View source< / a > ]
2019-06-13 02:23:54 +00:00
< / div >
< / div >
2019-07-10 01:18:01 +00:00
< div class = "entry-detail" id = "symmetric?-instance-method" >
2019-06-13 02:23:54 +00:00
< div class = "signature" >
2019-07-10 01:18:01 +00:00
def < strong > symmetric?< / strong >
2019-06-13 02:23:54 +00:00
2019-07-10 01:18:01 +00:00
< a class = "method-permalink" href = "#symmetric%3F-instance-method" > #< / a >
2019-06-13 02:23:54 +00:00
< / div >
2019-07-10 01:18:01 +00:00
< div class = "doc" > < p > Returns +true+ if this is a symmetric matrix.
Raises an error if matrix is not square.< / p > < / div >
2019-06-13 02:23:54 +00:00
< br / >
< div >
2019-07-10 02:22:15 +00:00
[< a href = "https://github.com/watzon/apatite/blob/6e67ceb81b0b3c61d48b74e5ca5154866a9abd1a/src/apatite/linear_algebra/matrix.cr#L820" target = "_blank" > View source< / a > ]
2019-06-13 02:23:54 +00:00
< / div >
< / div >
2019-07-10 01:18:01 +00:00
< div class = "entry-detail" id = "t-instance-method" >
2019-06-13 02:23:54 +00:00
< div class = "signature" >
2019-07-10 01:18:01 +00:00
def < strong > t< / strong >
2019-06-13 02:23:54 +00:00
2019-07-10 01:18:01 +00:00
< a class = "method-permalink" href = "#t-instance-method" > #< / a >
2019-06-13 02:23:54 +00:00
< / div >
2019-07-10 01:18:01 +00:00
< div class = "doc" > < p > Returns the transpose of the matrix.< / p >
< pre > < code > < span class = "t" > Matrix< / span > [[< span class = "n" > 1< / span > ,< span class = "n" > 2< / span > ], [< span class = "n" > 3< / span > ,< span class = "n" > 4< / span > ], [< span class = "n" > 5< / span > ,< span class = "n" > 6< / span > ]]
< span class = "c" > # => [ 1, 2,< / span >
< span class = "c" > # 3, 4,< / span >
< span class = "c" > # 5, 6 ]< / span >
< span class = "t" > Matrix< / span > [[< span class = "n" > 1< / span > ,< span class = "n" > 2< / span > ], [< span class = "n" > 3< / span > ,< span class = "n" > 4< / span > ], [< span class = "n" > 5< / span > ,< span class = "n" > 6< / span > ]].transpose
< span class = "c" > # => [ 1, 3, 5,< / span >
< span class = "c" > # 2, 4, 6 ]< / span > < / code > < / pre > < / div >
2019-06-13 02:23:54 +00:00
< br / >
< div >
2019-07-10 02:22:15 +00:00
[< a href = "https://github.com/watzon/apatite/blob/6e67ceb81b0b3c61d48b74e5ca5154866a9abd1a/src/apatite/linear_algebra/matrix.cr#L1244" target = "_blank" > View source< / a > ]
2019-06-13 02:23:54 +00:00
< / div >
< / div >
2019-07-10 01:18:01 +00:00
< div class = "entry-detail" id = "to_a-instance-method" >
2019-06-13 02:23:54 +00:00
< div class = "signature" >
2019-07-10 01:18:01 +00:00
def < strong > to_a< / strong >
2019-06-13 02:23:54 +00:00
2019-07-10 01:18:01 +00:00
< a class = "method-permalink" href = "#to_a-instance-method" > #< / a >
2019-06-13 02:23:54 +00:00
< / div >
2019-07-10 02:22:15 +00:00
< div class = "doc" > < p > Returns an array of arrays that describe the rows of the matrix.< / p > < / div >
2019-06-13 02:23:54 +00:00
< br / >
< div >
2019-07-10 02:22:15 +00:00
[< a href = "https://github.com/watzon/apatite/blob/6e67ceb81b0b3c61d48b74e5ca5154866a9abd1a/src/apatite/linear_algebra/matrix.cr#L1385" target = "_blank" > View source< / a > ]
2019-06-13 02:23:54 +00:00
< / div >
< / div >
2019-07-10 01:18:01 +00:00
< div class = "entry-detail" id = "to_json(json:JSON::Builder)-instance-method" >
2019-06-13 02:23:54 +00:00
< div class = "signature" >
2019-07-10 01:18:01 +00:00
def < strong > to_json< / strong > (json : JSON::Builder)
2019-06-13 02:23:54 +00:00
2019-07-10 01:18:01 +00:00
< a class = "method-permalink" href = "#to_json%28json%3AJSON%3A%3ABuilder%29-instance-method" > #< / a >
2019-06-13 02:23:54 +00:00
< / div >
2019-07-10 02:22:15 +00:00
< div class = "doc" > < p > Convert the matrix to a json array< / p > < / div >
2019-06-13 02:23:54 +00:00
< br / >
< div >
2019-07-10 02:22:15 +00:00
[< a href = "https://github.com/watzon/apatite/blob/6e67ceb81b0b3c61d48b74e5ca5154866a9abd1a/src/apatite/linear_algebra/matrix.cr#L1390" target = "_blank" > View source< / a > ]
2019-06-13 02:23:54 +00:00
< / div >
< / div >
2019-07-10 01:18:01 +00:00
< div class = "entry-detail" id = "to_s(io)-instance-method" >
2019-06-13 02:23:54 +00:00
< div class = "signature" >
2019-07-10 01:18:01 +00:00
def < strong > to_s< / strong > (io)
2019-06-13 02:23:54 +00:00
2019-07-10 01:18:01 +00:00
< a class = "method-permalink" href = "#to_s%28io%29-instance-method" > #< / a >
2019-06-13 02:23:54 +00:00
< / div >
< br / >
< div >
2019-07-10 02:22:15 +00:00
[< a href = "https://github.com/watzon/apatite/blob/6e67ceb81b0b3c61d48b74e5ca5154866a9abd1a/src/apatite/linear_algebra/matrix.cr#L1400" target = "_blank" > View source< / a > ]
2019-06-13 02:23:54 +00:00
< / div >
< / div >
2019-07-10 01:18:01 +00:00
< div class = "entry-detail" id = "tr-instance-method" >
2019-06-13 02:23:54 +00:00
< div class = "signature" >
2019-07-10 01:18:01 +00:00
def < strong > tr< / strong >
2019-06-13 02:23:54 +00:00
2019-07-10 01:18:01 +00:00
< a class = "method-permalink" href = "#tr-instance-method" > #< / a >
< / div >
< div class = "doc" > < p > Returns the trace (sum of diagonal elements) of the matrix.< / p >
< pre > < code > < span class = "t" > Matrix< / span > [[< span class = "n" > 7< / span > ,< span class = "n" > 6< / span > ], [< span class = "n" > 3< / span > ,< span class = "n" > 9< / span > ]].trace
< span class = "c" > # => 16< / span > < / code > < / pre > < / div >
< br / >
< div >
2019-07-10 02:22:15 +00:00
[< a href = "https://github.com/watzon/apatite/blob/6e67ceb81b0b3c61d48b74e5ca5154866a9abd1a/src/apatite/linear_algebra/matrix.cr#L1223" target = "_blank" > View source< / a > ]
2019-07-10 01:18:01 +00:00
< / div >
< / div >
< div class = "entry-detail" id = "trace-instance-method" >
< div class = "signature" >
def < strong > trace< / strong >
< a class = "method-permalink" href = "#trace-instance-method" > #< / a >
2019-06-13 02:23:54 +00:00
< / div >
2019-07-10 01:18:01 +00:00
< div class = "doc" > < p > Returns the trace (sum of diagonal elements) of the matrix.< / p >
< pre > < code > < span class = "t" > Matrix< / span > [[< span class = "n" > 7< / span > ,< span class = "n" > 6< / span > ], [< span class = "n" > 3< / span > ,< span class = "n" > 9< / span > ]].trace
< span class = "c" > # => 16< / span > < / code > < / pre > < / div >
2019-06-13 02:23:54 +00:00
< br / >
< div >
2019-07-10 02:22:15 +00:00
[< a href = "https://github.com/watzon/apatite/blob/6e67ceb81b0b3c61d48b74e5ca5154866a9abd1a/src/apatite/linear_algebra/matrix.cr#L1215" target = "_blank" > View source< / a > ]
2019-06-13 02:23:54 +00:00
< / div >
< / div >
2019-07-10 01:18:01 +00:00
< div class = "entry-detail" id = "transpose-instance-method" >
2019-06-13 02:23:54 +00:00
< div class = "signature" >
2019-07-10 01:18:01 +00:00
def < strong > transpose< / strong >
2019-06-13 02:23:54 +00:00
2019-07-10 01:18:01 +00:00
< a class = "method-permalink" href = "#transpose-instance-method" > #< / a >
2019-06-13 02:23:54 +00:00
< / div >
2019-07-10 01:18:01 +00:00
< div class = "doc" > < p > Returns the transpose of the matrix.< / p >
< pre > < code > < span class = "t" > Matrix< / span > [[< span class = "n" > 1< / span > ,< span class = "n" > 2< / span > ], [< span class = "n" > 3< / span > ,< span class = "n" > 4< / span > ], [< span class = "n" > 5< / span > ,< span class = "n" > 6< / span > ]]
< span class = "c" > # => [ 1, 2,< / span >
< span class = "c" > # 3, 4,< / span >
< span class = "c" > # 5, 6 ]< / span >
< span class = "t" > Matrix< / span > [[< span class = "n" > 1< / span > ,< span class = "n" > 2< / span > ], [< span class = "n" > 3< / span > ,< span class = "n" > 4< / span > ], [< span class = "n" > 5< / span > ,< span class = "n" > 6< / span > ]].transpose
< span class = "c" > # => [ 1, 3, 5,< / span >
< span class = "c" > # 2, 4, 6 ]< / span > < / code > < / pre > < / div >
2019-06-13 02:23:54 +00:00
< br / >
< div >
2019-07-10 02:22:15 +00:00
[< a href = "https://github.com/watzon/apatite/blob/6e67ceb81b0b3c61d48b74e5ca5154866a9abd1a/src/apatite/linear_algebra/matrix.cr#L1238" target = "_blank" > View source< / a > ]
2019-06-13 02:23:54 +00:00
< / div >
< / div >
2019-07-10 01:18:01 +00:00
< div class = "entry-detail" id = "unitary?-instance-method" >
2019-06-13 02:23:54 +00:00
< div class = "signature" >
2019-07-10 01:18:01 +00:00
def < strong > unitary?< / strong >
2019-06-13 02:23:54 +00:00
2019-07-10 01:18:01 +00:00
< a class = "method-permalink" href = "#unitary%3F-instance-method" > #< / a >
2019-06-13 02:23:54 +00:00
< / div >
2019-07-10 01:18:01 +00:00
< div class = "doc" > < p > Returns < code > true< / code > if this is a unitary matrix< / p > < / div >
2019-06-13 02:23:54 +00:00
< br / >
< div >
2019-07-10 02:22:15 +00:00
[< a href = "https://github.com/watzon/apatite/blob/6e67ceb81b0b3c61d48b74e5ca5154866a9abd1a/src/apatite/linear_algebra/matrix.cr#L832" target = "_blank" > View source< / a > ]
2019-06-13 02:23:54 +00:00
< / div >
< / div >
2019-07-10 01:18:01 +00:00
< div class = "entry-detail" id = "unsafe_fetch(i)-instance-method" >
2019-06-13 02:23:54 +00:00
< div class = "signature" >
2019-07-10 01:18:01 +00:00
def < strong > unsafe_fetch< / strong > (i)
2019-06-13 02:23:54 +00:00
2019-07-10 01:18:01 +00:00
< a class = "method-permalink" href = "#unsafe_fetch%28i%29-instance-method" > #< / a >
2019-06-13 02:23:54 +00:00
< / div >
< br / >
< div >
2019-07-10 02:22:15 +00:00
[< a href = "https://github.com/watzon/apatite/blob/6e67ceb81b0b3c61d48b74e5ca5154866a9abd1a/src/apatite/linear_algebra/matrix.cr#L1423" target = "_blank" > View source< / a > ]
2019-06-13 02:23:54 +00:00
< / div >
< / div >
2019-07-10 01:18:01 +00:00
< div class = "entry-detail" id = "upper_triangular?-instance-method" >
2019-06-13 02:23:54 +00:00
< div class = "signature" >
2019-07-10 01:18:01 +00:00
def < strong > upper_triangular?< / strong >
2019-06-13 02:23:54 +00:00
2019-07-10 01:18:01 +00:00
< a class = "method-permalink" href = "#upper_triangular%3F-instance-method" > #< / a >
2019-06-13 02:23:54 +00:00
< / div >
2019-07-10 01:18:01 +00:00
< div class = "doc" > < p > Returns true if this matrix is a upper triangular matrix.< / p > < / div >
2019-06-13 02:23:54 +00:00
< br / >
< div >
2019-07-10 02:22:15 +00:00
[< a href = "https://github.com/watzon/apatite/blob/6e67ceb81b0b3c61d48b74e5ca5154866a9abd1a/src/apatite/linear_algebra/matrix.cr#L852" target = "_blank" > View source< / a > ]
2019-06-13 02:23:54 +00:00
< / div >
< / div >
2019-07-10 01:18:01 +00:00
< div class = "entry-detail" id = "vstack(*matrices)-instance-method" >
2019-06-13 02:23:54 +00:00
< div class = "signature" >
2019-07-10 01:18:01 +00:00
def < strong > vstack< / strong > (*matrices)
2019-06-13 02:23:54 +00:00
2019-07-10 01:18:01 +00:00
< a class = "method-permalink" href = "#vstack%28%2Amatrices%29-instance-method" > #< / a >
2019-06-13 02:23:54 +00:00
< / div >
2019-07-10 01:18:01 +00:00
< div class = "doc" > < p > Returns a new matrix resulting by stacking vertically
the receiver with the given matrices< / p >
< pre > < code > x < span class = "o" > =< / span > < span class = "t" > Matrix< / span > [[< span class = "n" > 1< / span > , < span class = "n" > 2< / span > ], [< span class = "n" > 3< / span > , < span class = "n" > 4< / span > ]]
y < span class = "o" > =< / span > < span class = "t" > Matrix< / span > [[< span class = "n" > 5< / span > , < span class = "n" > 6< / span > ], [< span class = "n" > 7< / span > , < span class = "n" > 8< / span > ]]
x.vstack(y)
< span class = "c" > # => Matrix[[1, 2], [3, 4], [5, 6], [7, 8]]< / span > < / code > < / pre > < / div >
2019-06-13 02:23:54 +00:00
< br / >
< div >
2019-07-10 02:22:15 +00:00
[< a href = "https://github.com/watzon/apatite/blob/6e67ceb81b0b3c61d48b74e5ca5154866a9abd1a/src/apatite/linear_algebra/matrix.cr#L1257" target = "_blank" > View source< / a > ]
2019-06-13 02:23:54 +00:00
< / div >
< / div >
2019-07-10 01:18:01 +00:00
< div class = "entry-detail" id = "zero?-instance-method" >
2019-06-13 02:23:54 +00:00
< div class = "signature" >
2019-07-10 01:18:01 +00:00
def < strong > zero?< / strong >
2019-06-13 02:23:54 +00:00
2019-07-10 01:18:01 +00:00
< a class = "method-permalink" href = "#zero%3F-instance-method" > #< / a >
2019-06-13 02:23:54 +00:00
< / div >
2019-07-10 01:18:01 +00:00
< div class = "doc" > < p > Returns < code > true< / code > if this is a matrix with only zero elements< / p > < / div >
2019-06-13 02:23:54 +00:00
< br / >
< div >
2019-07-10 02:22:15 +00:00
[< a href = "https://github.com/watzon/apatite/blob/6e67ceb81b0b3c61d48b74e5ca5154866a9abd1a/src/apatite/linear_algebra/matrix.cr#L859" target = "_blank" > View source< / a > ]
2019-06-13 02:23:54 +00:00
< / div >
< / div >
< / div >
< / body >
< / html >
