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<h1 class="type-name">
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<span class="kind">class</span> Apatite::LinearAlgebra::Matrix::LupDecomposition
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</h1>
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<ul class="superclass-hierarchy"><li class="superclass"><a href="../../../Apatite/LinearAlgebra/Matrix/LupDecomposition.html">Apatite::LinearAlgebra::Matrix::LupDecomposition</a></li><li class="superclass">Reference</li><li class="superclass">Object</li></ul>
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<h2>Overview</h2>
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<p>For an m-by-n matrix A with m >= n, the LU decomposition is an m-by-n
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unit lower triangular matrix L, an n-by-n upper triangular matrix U,
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and a m-by-m permutation matrix P so that L<em>U = P</em>A.
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If m < n, then L is m-by-m and U is m-by-n.</p>
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<p>The LUP decomposition with pivoting always exists, even if the matrix is
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singular, so the constructor will never fail. The primary use of the
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LU decomposition is in the solution of square systems of simultaneous
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linear equations. This will fail if singular? returns true.</p>
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<h2>Defined in:</h2>
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<a href="https://github.com/watzon/apatite/blob/c7bc6f4f5ec3f4b2725b0b6bdf03d9524007e864/src/apatite/linear_algebra/matrix/lup_decomposition.cr#L12" target="_blank">
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apatite/linear_algebra/matrix/lup_decomposition.cr
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</a>
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<br/>
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<h2>Constructors</h2>
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<ul class="list-summary">
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<li class="entry-summary">
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<a href="#new(matrix)-class-method" class="signature"><strong>.new</strong>(matrix)</a>
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</li>
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</ul>
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<div class="methods-inherited">
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</div>
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<h2>Constructor Detail</h2>
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<div class="entry-detail" id="new(matrix)-class-method">
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<div class="signature">
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def self.<strong>new</strong>(matrix)
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<a class="method-permalink" href="#new(matrix)-class-method">#</a>
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</div>
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<br/>
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<div>
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[<a href="https://github.com/watzon/apatite/blob/c7bc6f4f5ec3f4b2725b0b6bdf03d9524007e864/src/apatite/linear_algebra/matrix/lup_decomposition.cr#L13" target="_blank">View source</a>]
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</div>
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</div>
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