Method: Stick::Matrix#determinant_e

Defined in:
lib/stick/matrix/core.rb

#determinant_e ⇒ Object Also known as: det_e

Returns the determinant of the matrix. If the matrix is not square, the result is 0. This method’s algorism is Gaussian elimination method. This method uses Euclidean algorism. If all elements are integer, really exact value. But, if an element is a float, can’t return exact value.

Matrix[[7,6], [3,9]].determinant
  => 63



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# File 'lib/stick/matrix/core.rb', line 738

def determinant_e
  return 0 unless square?

  size = row_size - 1
  a = to_a

  det = 1
  k = 0
  begin
    if a[k][k].zero?
      i = k
      begin
        return 0 if (i += 1) > size
      end while a[i][k].zero?
      a[i], a[k] = a[k], a[i]
      det *= -1
    end
    (k + 1).upto(size) do |i|
      q = a[i][k].quo(a[k][k])
      k.upto(size) do |j|
        a[i][j] -= a[k][j] * q
      end
      unless a[i][k].zero?
        a[i], a[k] = a[k], a[i]
        det *= -1
        redo
      end
    end
    det *= a[k][k]
  end while (k += 1) <= size
  det
end