type(t_qr) mod_matrix::m_decompQR_GramSchimdt_Reortho ( type(matrix),intent(in)  m,
real*4,intent(in),optional  eps,
logical,intent(in),optional  is_permuted 
)

qr decomposition by Gram-Schmidt (reorthogonalization)

Author:
Abal-Kassim Cheik Ahamed <akcheik@gmail.com>
Parameters:
m : type(matrix)
is_permuted : with permutation matrix (optional)
eps : real*4 , tolerance error (optional)
Date:
03th of April, 2011
Remarks:
The Rayleigh Quotient Iteration is a natural union of the power and inverse power iterations algorithm of Yousef Saad (eig_book_2ndEd)
See also:
math_machine_eps()
 computes the QR decomposition using modified Gram-Schmidt 
 with reorthogonalization
 z is a vector that counts the reorthogonalization
 steps per column (source Ritzit) 

 A (m x n), if m>=n: 
         * Q (m x n) orthornormal (.tr.Q.Q=I)
         * R (n x n) upper triangular with nonnegative diagonal elements
 Algorithms for the QR-Decomposition (Walter Gander)
 
delete or save z vector

Definition at line 3620 of file matrix.f90.

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