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Class: LUPDecomposition
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# File lib/matrix/lup_decomposition.rb, line 154 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