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::BlankLineo; ;[ 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[i0o;;[; 0; 0[@I" Matrix;TcRDoc::NormalClass