method

determinant

v1_9_3_125 - Show latest stable - Class: Matrix

determinant()

public

Returns the determinant of the matrix.

Beware that using Float values can yield erroneous results because of their lack of precision. Consider using exact types like Rational or BigDecimal instead.

Matrix[[7,6], [3,9]].determinant
  => 45

# File lib/matrix.rb, line 1006
  def determinant
    Matrix.Raise ErrDimensionMismatch unless square?
    m = @rows
    case row_size
      # Up to 4x4, give result using Laplacian expansion by minors.
      # This will typically be faster, as well as giving good results
      # in case of Floats
    when 0
      +1
    when 1
      + m[0][0]
    when 2
      + m[0][0] * m[1][1] - m[0][1] * m[1][0]
    when 3
      m0, m1, m2 = m
      + m0[0] * m1[1] * m2[2] - m0[0] * m1[2] * m2[1]        - m0[1] * m1[0] * m2[2] + m0[1] * m1[2] * m2[0]        + m0[2] * m1[0] * m2[1] - m0[2] * m1[1] * m2[0]
    when 4
      m0, m1, m2, m3 = m
      + m0[0] * m1[1] * m2[2] * m3[3] - m0[0] * m1[1] * m2[3] * m3[2]        - m0[0] * m1[2] * m2[1] * m3[3] + m0[0] * m1[2] * m2[3] * m3[1]        + m0[0] * m1[3] * m2[1] * m3[2] - m0[0] * m1[3] * m2[2] * m3[1]        - m0[1] * m1[0] * m2[2] * m3[3] + m0[1] * m1[0] * m2[3] * m3[2]        + m0[1] * m1[2] * m2[0] * m3[3] - m0[1] * m1[2] * m2[3] * m3[0]        - m0[1] * m1[3] * m2[0] * m3[2] + m0[1] * m1[3] * m2[2] * m3[0]        + m0[2] * m1[0] * m2[1] * m3[3] - m0[2] * m1[0] * m2[3] * m3[1]        - m0[2] * m1[1] * m2[0] * m3[3] + m0[2] * m1[1] * m2[3] * m3[0]        + m0[2] * m1[3] * m2[0] * m3[1] - m0[2] * m1[3] * m2[1] * m3[0]        - m0[3] * m1[0] * m2[1] * m3[2] + m0[3] * m1[0] * m2[2] * m3[1]        + m0[3] * m1[1] * m2[0] * m3[2] - m0[3] * m1[1] * m2[2] * m3[0]        - m0[3] * m1[2] * m2[0] * m3[1] + m0[3] * m1[2] * m2[1] * m3[0]
    else
      # For bigger matrices, use an efficient and general algorithm.
      # Currently, we use the Gauss-Bareiss algorithm
      determinant_bareiss
    end
  end

determinant

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