* lib/matrix: Add LUP decomposition
git-svn-id: svn+ssh://ci.ruby-lang.org/ruby/trunk@32353 b2dd03c8-39d4-4d8f-98ff-823fe69b080e
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@ -1,3 +1,7 @@
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Fri Jul 1 15:23:00 2011 Marc-Andre Lafortune <ruby-core@marc-andre.ca>
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* lib/matrix: Add LUP decomposition
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Fri Jul 1 15:21:14 2011 Marc-Andre Lafortune <ruby-core@marc-andre.ca>
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Fri Jul 1 15:21:14 2011 Marc-Andre Lafortune <ruby-core@marc-andre.ca>
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* lib/matrix.rb: Allow non integer exponents for Matrix#**
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* lib/matrix.rb: Allow non integer exponents for Matrix#**
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3
NEWS
3
NEWS
@ -159,12 +159,15 @@ with all sufficient information, see the ChangeLog file.
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* matrix
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* matrix
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* new classes:
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* new classes:
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* Matrix::EigenvalueDecomposition
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* Matrix::EigenvalueDecomposition
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* Matrix::LUPDecomposition
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* new methods:
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* new methods:
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* Matrix#diagonal?
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* Matrix#diagonal?
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* Matrix#eigen
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* Matrix#eigen
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* Matrix#eigensystem
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* Matrix#eigensystem
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* Matrix#hermitian?
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* Matrix#hermitian?
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* Matrix#lower_triangular?
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* Matrix#lower_triangular?
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* Matrix#lup
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* Matrix#lup_decomposition
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* Matrix#normal?
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* Matrix#normal?
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* Matrix#orthogonal?
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* Matrix#orthogonal?
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* Matrix#permutation?
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* Matrix#permutation?
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@ -98,6 +98,8 @@ end
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# Matrix decompositions:
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# Matrix decompositions:
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# * <tt> #eigen </tt>
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# * <tt> #eigen </tt>
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# * <tt> #eigensystem </tt>
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# * <tt> #eigensystem </tt>
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# * <tt> #lup </tt>
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# * <tt> #lup_decomposition </tt>
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#
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#
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# Complex arithmetic:
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# Complex arithmetic:
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# * <tt> conj </tt>
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# * <tt> conj </tt>
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@ -122,6 +124,7 @@ class Matrix
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include Enumerable
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include Enumerable
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include ExceptionForMatrix
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include ExceptionForMatrix
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autoload :EigenvalueDecomposition, "matrix/eigenvalue_decomposition"
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autoload :EigenvalueDecomposition, "matrix/eigenvalue_decomposition"
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autoload :LUPDecomposition, "matrix/lup_decomposition"
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# instance creations
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# instance creations
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private_class_method :new
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private_class_method :new
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@ -1187,6 +1190,21 @@ class Matrix
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end
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end
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alias eigen eigensystem
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alias eigen eigensystem
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#
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# Returns the LUP decomposition of the matrix; see +LUPDecomposition+.
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# a = Matrix[[1, 2], [3, 4]]
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# l, u, p = a.lup
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# l.lower_triangular? # => true
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# u.upper_triangular? # => true
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# p.permutation? # => true
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# l * u == a * p # => true
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# a.lup.solve([2, 5]) # => Vector[(1/1), (1/2)]
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#
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def lup
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LUPDecomposition.new(self)
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end
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alias lup_decomposition lup
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#--
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#--
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# COMPLEX ARITHMETIC -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
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# COMPLEX ARITHMETIC -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
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#++
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#++
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218
lib/matrix/lup_decomposition.rb
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218
lib/matrix/lup_decomposition.rb
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@ -0,0 +1,218 @@
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class Matrix
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# Adapted from JAMA: http://math.nist.gov/javanumerics/jama/
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#
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# 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*U = P*A.
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# If m < n, then L is m-by-m and U is m-by-n.
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#
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# 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.
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#
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class LUPDecomposition
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# Returns the lower triangular factor +L+
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include Matrix::ConversionHelper
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def l
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Matrix.build(@row_size, @col_size) do |i, j|
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if (i > j)
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@lu[i][j]
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elsif (i == j)
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1
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else
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0
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end
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end
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end
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# Returns the upper triangular factor +U+
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def u
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Matrix.build(@col_size, @col_size) do |i, j|
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if (i <= j)
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@lu[i][j]
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else
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0
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end
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end
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end
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# Returns the permutation matrix +P+
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def p
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rows = Array.new(@row_size){Array.new(@col_size, 0)}
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@pivots.each_with_index{|p, i| rows[i][p] = 1}
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Matrix.send :new, rows, @col_size
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end
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# Returns +L+, +U+, +P+ in an array
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def to_ary
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[l, u, p]
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end
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alias_method :to_a, :to_ary
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# Returns the pivoting indices
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attr_reader :pivots
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# Returns +true+ if +U+, and hence +A+, is singular.
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def singular? ()
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@col_size.times do |j|
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if (@lu[j][j] == 0)
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return true
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end
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end
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false
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end
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# Returns the determinant of +A+, calculated efficiently
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# from the factorization.
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def det
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if (@row_size != @col_size)
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Matrix.Raise Matrix::ErrDimensionMismatch unless square?
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end
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d = @pivot_sign
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@col_size.times do |j|
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d *= @lu[j][j]
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end
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d
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end
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alias_method :determinant, :det
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# Returns +m+ so that <tt>A*m = b</tt>,
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# or equivalently so that <tt>L*U*m = P*b</tt>
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# +b+ can be a Matrix or a Vector
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def solve b
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if (singular?)
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Matrix.Raise Matrix::ErrNotRegular, "Matrix is singular."
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end
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if b.is_a? Matrix
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if (b.row_size != @row_size)
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Matrix.Raise Matrix::ErrDimensionMismatch
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end
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# Copy right hand side with pivoting
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nx = b.column_size
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m = @pivots.map{|row| b.row(row).to_a}
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# Solve L*Y = P*b
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@col_size.times do |k|
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(k+1).upto(@col_size-1) do |i|
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nx.times do |j|
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m[i][j] -= m[k][j]*@lu[i][k]
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end
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end
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end
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# Solve U*m = Y
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(@col_size-1).downto(0) do |k|
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nx.times do |j|
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m[k][j] = m[k][j].quo(@lu[k][k])
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end
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k.times do |i|
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nx.times do |j|
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m[i][j] -= m[k][j]*@lu[i][k]
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end
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end
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end
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Matrix.send :new, m, nx
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else # same algorithm, specialized for simpler case of a vector
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b = convert_to_array(b)
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if (b.size != @row_size)
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Matrix.Raise Matrix::ErrDimensionMismatch
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end
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# Copy right hand side with pivoting
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m = b.values_at(*@pivots)
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# Solve L*Y = P*b
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@col_size.times do |k|
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(k+1).upto(@col_size-1) do |i|
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m[i] -= m[k]*@lu[i][k]
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end
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end
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# Solve U*m = Y
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(@col_size-1).downto(0) do |k|
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m[k] = m[k].quo(@lu[k][k])
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k.times do |i|
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m[i] -= m[k]*@lu[i][k]
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end
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end
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Vector.elements(m, false)
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end
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end
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def initialize a
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raise TypeError, "Expected Matrix but got #{a.class}" unless a.is_a?(Matrix)
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# Use a "left-looking", dot-product, Crout/Doolittle algorithm.
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@lu = a.to_a
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@row_size = a.row_size
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@col_size = a.column_size
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@pivots = Array.new(@row_size)
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@row_size.times do |i|
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@pivots[i] = i
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end
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@pivot_sign = 1
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lu_col_j = Array.new(@row_size)
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# Outer loop.
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@col_size.times do |j|
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# Make a copy of the j-th column to localize references.
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@row_size.times do |i|
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lu_col_j[i] = @lu[i][j]
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end
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# Apply previous transformations.
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@row_size.times do |i|
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lu_row_i = @lu[i]
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# Most of the time is spent in the following dot product.
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kmax = [i, j].min
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s = 0
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kmax.times do |k|
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s += lu_row_i[k]*lu_col_j[k]
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end
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lu_row_i[j] = lu_col_j[i] -= s
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end
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# Find pivot and exchange if necessary.
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p = j
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(j+1).upto(@row_size-1) do |i|
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if (lu_col_j[i].abs > lu_col_j[p].abs)
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p = i
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end
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end
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if (p != j)
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@col_size.times do |k|
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t = @lu[p][k]; @lu[p][k] = @lu[j][k]; @lu[j][k] = t
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end
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k = @pivots[p]; @pivots[p] = @pivots[j]; @pivots[j] = k
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@pivot_sign = -@pivot_sign
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end
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# Compute multipliers.
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if (j < @row_size && @lu[j][j] != 0)
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(j+1).upto(@row_size-1) do |i|
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@lu[i][j] = @lu[i][j].quo(@lu[j][j])
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end
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end
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end
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end
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end
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end
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