method

determinant_bareiss

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determinant_bareiss() private

Returns the determinant of the matrix, using Bareiss’ multistep integer-preserving gaussian elimination. It has the same computational cost order O(n^3) as standard Gaussian elimination. Intermediate results are fraction free and of lower complexity. A matrix of Integers will have thus intermediate results that are also Integers, with smaller bignums (if any), while a matrix of Float will usually have intermediate results with better precision.

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# File lib/matrix.rb, line 1214
  def determinant_bareiss
    size = row_count
    last = size - 1
    a = to_a
    no_pivot = Proc.new{ return 0 }
    sign = +1
    pivot = 1
    size.times do |k|
      previous_pivot = pivot
      if (pivot = a[k][k]) == 0
        switch = (k+1 ... size).find(no_pivot) {|row|
          a[row][k] != 0
        }
        a[switch], a[k] = a[k], a[switch]
        pivot = a[k][k]
        sign = -sign
      end
      (k+1).upto(last) do |i|
        ai = a[i]
        (k+1).upto(last) do |j|
          ai[j] =  (pivot * ai[j] - ai[k] * a[k][j]) / previous_pivot
        end
      end
    end
    sign * pivot
  end

determinant_bareiss

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