## Feature #2772 » matrix_bareiss.diff

View differences:

lib/matrix.rb
#++
#
# Returns the determinant of the matrix. If the matrix is not square, the
# result is 0. This method's algorithm is Gaussian elimination method
# and using Numeric#quo(). Beware that using Float values, with their
# usual lack of precision, can affect the value returned by this method. Use
# Rational values or Matrix#det_e instead if this is important to you.
# Returns the determinant of the matrix.
# This method's algorithm is Bareiss algorithm, which has the nice properties
# of being exact for integers and minimizing the rounding error for floats.
#
# Matrix[[7,6], [3,9]].determinant
# => 45.0
# => 45
#
def determinant
return 0 unless square?
Matrix.Raise ErrDimensionMismatch unless square?
size = row_size
last = row_size - 1
a = to_a
det = 1
last_akk = 1
size.times do |k|
if (akk = a[k][k]) == 0
i = (k+1 ... size).find {|ii|
......
return 0 if i.nil?
a[i], a[k] = a[k], a[i]
akk = a[k][k]
det *= -1
det = -det
end
(k + 1 ... size).each do |ii|
q = a[ii][k].quo(akk)
(k + 1 ... size).each do |j|
a[ii][j] -= a[k][j] * q
(k+1).upto(last) do |ii|
last.downto(k) do |j|
a[ii][j] = (akk * a[ii][j] - a[ii][k] * a[k][j]) / last_akk
end
end
det *= akk
det = det / last_akk * akk
last_akk = akk
end
det
end
(1-1/3)