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



894
895
896
897
898
899
900
901
902
903
904
905
 
# File 'lib/extendmatrix.rb', line 894

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)



912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
 
# File 'lib/extendmatrix.rb', line 912

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