Module: Matrix::Givens

Defined in:
lib/extendmatrix.rb

Class Method Summary collapse

Class Method Details

.givens(a, b) ⇒ Object

Returns the values “c and s” of a Given rotation MC, Golub, pg 216, Alghorithm 5.1.3



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# File 'lib/extendmatrix.rb', line 860

def self.givens(a, b)
  if b == 0
    c = 0; s = 0
  else
    if b.abs > a.abs
      tau = Float(-a)/b; s = 1/Math.sqrt(1+tau**2); c = s * tau
    else
      tau = Float(-b)/a; c = 1/Math.sqrt(1+tau**2); s = c * tau
    end
  end
  return c, s
end

.QR(mat) ⇒ Object

a QR factorization using Givens rotation Computes the upper triangular matrix R and the orthogonal matrix Q where Q^t A = R (MC, Golub, p227 algorithm 5.2.2)



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# File 'lib/extendmatrix.rb', line 878

def self.QR(mat)
r = mat.clone
m = r.row_size
n = r.column_size
q = Matrix.I(m)
n.times{|j|
  m-1.downto(j+1){|i|
    c, s = givens(r[i - 1, j], r[i, j])
    qt = Matrix.I(m); qt[i-1..i, i-1..i] = Matrix[[c, s],[-s, c]]
    q *= qt
  r[i-1..i, j..n-1] = Matrix[[c, -s],[s, c]] * r[i-1..i, j..n-1]}}
  return r, q
end