module Matrix::Hessenberg

Public Class Methods

QR(mat) click to toggle source

the matrix must be an upper R^(n x n) Hessenberg matrix

# File lib/extendmatrix.rb, line 949
def self.QR(mat)
  r = mat.clone
  n = r.row_size
  q = Matrix.I(n)
  for j in (0...n-1)
    c, s = Givens.givens(r[j,j], r[j+1, j])
    cs = Matrix[[c, s], [-s, c]]
    q *= Matrix.diag(Matrix.robust_I(j), cs, Matrix.robust_I(n - j - 2))
    r[j..j+1, j..n-1] = cs.t * r[j..j+1, j..n-1]
  end
  return q, r
end