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zgeqr2 (3)
  • >> zgeqr2 (3) ( Solaris man: Библиотечные вызовы )
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    NAME
         zgeqr2 - compute a QR factorization of  a  complex  m  by  n
         matrix A
    
    SYNOPSIS
         SUBROUTINE ZGEQR2( M, N, A, LDA, TAU, WORK, INFO )
    
         INTEGER INFO, LDA, M, N
    
         COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
    
    
    
         #include <sunperf.h>
    
         void zgeqr2(int m, int n, doublecomplex *za, int lda,  doub-
                   lecomplex *tau, int *info) ;
    
    PURPOSE
         ZGEQR2 computes a QR factorization  of  a  complex  m  by  n
         matrix A:  A = Q * R.
    
    
    ARGUMENTS
         M         (input) INTEGER
                   The number of rows of the matrix A.  M >= 0.
    
         N         (input) INTEGER
                   The number of columns of the matrix A.  N >= 0.
    
         A         (input/output) COMPLEX*16 array, dimension (LDA,N)
                   On entry, the m by n matrix A.  On exit, the  ele-
                   ments  on and above the diagonal of the array con-
                   tain the min(m,n) by n upper trapezoidal matrix  R
                   (R  is  upper  triangular if m >= n); the elements
                   below the diagonal, with the array TAU,  represent
                   the  unitary  matrix  Q as a product of elementary
                   reflectors (see Further Details).  LDA     (input)
                   INTEGER The leading dimension of the array A.  LDA
                   >= max(1,M).
    
         TAU       (output) COMPLEX*16 array, dimension (min(M,N))
                   The scalar factors of  the  elementary  reflectors
                   (see Further Details).
    
         WORK      (workspace) COMPLEX*16 array, dimension (N)
    
         INFO      (output) INTEGER
                   = 0: successful exit
                   < 0: if INFO = -i, the i-th argument had an  ille-
                   gal value
    
    FURTHER DETAILS
         The matrix Q is  represented  as  a  product  of  elementary
         reflectors
    
            Q = H(1) H(2) . . . H(k), where k = min(m,n).
    
         Each H(i) has the form
    
            H(i) = I - tau * v * v'
    
         where tau is a complex scalar, and v  is  a  complex  vector
         with  v(1:i-1)  = 0 and v(i) = 1; v(i+1:m) is stored on exit
         in A(i+1:m,i), and tau in TAU(i).
    
    
    
    


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