ok
Direktori : /proc/thread-self/root/proc/self/root/opt/alt/ruby24/lib64/ruby/2.4.0/matrix/ |
Current File : //proc/thread-self/root/proc/self/root/opt/alt/ruby24/lib64/ruby/2.4.0/matrix/lup_decomposition.rb |
# frozen_string_literal: false class Matrix # Adapted from JAMA: http://math.nist.gov/javanumerics/jama/ # # For an m-by-n matrix A with m >= n, the LU decomposition is an m-by-n # unit lower triangular matrix L, an n-by-n upper triangular matrix U, # and a m-by-m permutation matrix P so that L*U = P*A. # If m < n, then L is m-by-m and U is m-by-n. # # The LUP decomposition with pivoting always exists, even if the matrix is # singular, so the constructor will never fail. The primary use of the # LU decomposition is in the solution of square systems of simultaneous # linear equations. This will fail if singular? returns true. # class LUPDecomposition # Returns the lower triangular factor +L+ include Matrix::ConversionHelper def l Matrix.build(@row_count, [@column_count, @row_count].min) do |i, j| if (i > j) @lu[i][j] elsif (i == j) 1 else 0 end end end # Returns the upper triangular factor +U+ def u Matrix.build([@column_count, @row_count].min, @column_count) do |i, j| if (i <= j) @lu[i][j] else 0 end end end # Returns the permutation matrix +P+ def p rows = Array.new(@row_count){Array.new(@row_count, 0)} @pivots.each_with_index{|p, i| rows[i][p] = 1} Matrix.send :new, rows, @row_count end # Returns +L+, +U+, +P+ in an array def to_ary [l, u, p] end alias_method :to_a, :to_ary # Returns the pivoting indices attr_reader :pivots # Returns +true+ if +U+, and hence +A+, is singular. def singular? @column_count.times do |j| if (@lu[j][j] == 0) return true end end false end # Returns the determinant of +A+, calculated efficiently # from the factorization. def det if (@row_count != @column_count) Matrix.Raise Matrix::ErrDimensionMismatch end d = @pivot_sign @column_count.times do |j| d *= @lu[j][j] end d end alias_method :determinant, :det # Returns +m+ so that <tt>A*m = b</tt>, # or equivalently so that <tt>L*U*m = P*b</tt> # +b+ can be a Matrix or a Vector def solve b if (singular?) Matrix.Raise Matrix::ErrNotRegular, "Matrix is singular." end if b.is_a? Matrix if (b.row_count != @row_count) Matrix.Raise Matrix::ErrDimensionMismatch end # Copy right hand side with pivoting nx = b.column_count m = @pivots.map{|row| b.row(row).to_a} # Solve L*Y = P*b @column_count.times do |k| (k+1).upto(@column_count-1) do |i| nx.times do |j| m[i][j] -= m[k][j]*@lu[i][k] end end end # Solve U*m = Y (@column_count-1).downto(0) do |k| nx.times do |j| m[k][j] = m[k][j].quo(@lu[k][k]) end k.times do |i| nx.times do |j| m[i][j] -= m[k][j]*@lu[i][k] end end end Matrix.send :new, m, nx else # same algorithm, specialized for simpler case of a vector b = convert_to_array(b) if (b.size != @row_count) Matrix.Raise Matrix::ErrDimensionMismatch end # Copy right hand side with pivoting m = b.values_at(*@pivots) # Solve L*Y = P*b @column_count.times do |k| (k+1).upto(@column_count-1) do |i| m[i] -= m[k]*@lu[i][k] end end # Solve U*m = Y (@column_count-1).downto(0) do |k| m[k] = m[k].quo(@lu[k][k]) k.times do |i| m[i] -= m[k]*@lu[i][k] end end Vector.elements(m, false) end end def initialize a raise TypeError, "Expected Matrix but got #{a.class}" unless a.is_a?(Matrix) # Use a "left-looking", dot-product, Crout/Doolittle algorithm. @lu = a.to_a @row_count = a.row_count @column_count = a.column_count @pivots = Array.new(@row_count) @row_count.times do |i| @pivots[i] = i end @pivot_sign = 1 lu_col_j = Array.new(@row_count) # Outer loop. @column_count.times do |j| # Make a copy of the j-th column to localize references. @row_count.times do |i| lu_col_j[i] = @lu[i][j] end # Apply previous transformations. @row_count.times do |i| lu_row_i = @lu[i] # Most of the time is spent in the following dot product. kmax = [i, j].min s = 0 kmax.times do |k| s += lu_row_i[k]*lu_col_j[k] end lu_row_i[j] = lu_col_j[i] -= s end # Find pivot and exchange if necessary. p = j (j+1).upto(@row_count-1) do |i| if (lu_col_j[i].abs > lu_col_j[p].abs) p = i end end if (p != j) @column_count.times do |k| t = @lu[p][k]; @lu[p][k] = @lu[j][k]; @lu[j][k] = t end k = @pivots[p]; @pivots[p] = @pivots[j]; @pivots[j] = k @pivot_sign = -@pivot_sign end # Compute multipliers. if (j < @row_count && @lu[j][j] != 0) (j+1).upto(@row_count-1) do |i| @lu[i][j] = @lu[i][j].quo(@lu[j][j]) end end end end end end