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U:RDoc::NormalClass[iI"LUPDecomposition:ETI" Matrix::LUPDecomposition;TI" Object;To:RDoc::Markup::Document: @parts[o;;[o: RDoc::Markup::Paragraph;[ I"KFor an m-by-n matrix A with m >= n, the LU decomposition is an m-by-n ;TI"Junit lower triangular matrix L, an n-by-n upper triangular matrix U, ;TI":and a m-by-m permutation matrix P so that L*U = P*A. ;TI"0If m < n, then L is m-by-m and U is m-by-n.;To: RDoc::Markup::BlankLine o; ;[ I"NThe LUP decomposition with pivoting always exists, even if the matrix is ;TI"Ksingular, so the constructor will never fail. The primary use of the ;TI"KLU decomposition is in the solution of square systems of simultaneous ;TI"Alinear equations. This will fail if singular? returns true.;T: @fileI"$lib/matrix/lup_decomposition.rb;T:0@omit_headings_from_table_of_contents_below0; 0; 0[[ I" pivots;TI"R;T: publicFI"$lib/matrix/lup_decomposition.rb;T[ [ [[I" class;T[[; [[I"new;T@ [:protected[ [: private[ [I" instance;T[[; [[I"det;F@ [I"determinant;T@ [I"l;F@ [I"p;F@ [I"singular?;F@ [I" solve;F@ [I" to_a;T@ [I" to_ary;F@ [I"u;F@ [;[ [;[ [ [U:RDoc::Context::Section[i 0o;;[ ; 0; 0[@I" Matrix;TcRDoc::NormalClass
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