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zgerqf (3)
  • >> zgerqf (3) ( Solaris man: Библиотечные вызовы )
  • 
    NAME
         zgerqf - compute an RQ factorization  of  a  complex  M-by-N
         matrix A
    
    SYNOPSIS
         SUBROUTINE ZGERQF( M, N, A, LDA, TAU, WORK, LWORK, INFO )
    
         INTEGER INFO, LDA, LWORK, M, N
    
         COMPLEX*16 A( LDA, * ), TAU( * ), WORK( LWORK )
    
    
    
         #include <sunperf.h>
    
         void zgerqf(int m, int n, doublecomplex *za, int lda,  doub-
                   lecomplex *tau, int *info) ;
    
    PURPOSE
         ZGERQF computes an RQ  factorization  of  a  complex  M-by-N
         matrix A:  A = R * Q.
    
    
    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, if  m  <=
                   n,  the  upper  triangle  of the subarray A(1:m,n-
                   m+1:n) contains the M-by-M upper triangular matrix
                   R;  if  m  >= n, the elements on and above the (m-
                   n)-th subdiagonal contain the  M-by-N  upper  tra-
                   pezoidal  matrix  R;  the remaining elements, with
                   the array TAU, represent the unitary matrix Q as a
                   product  of  min(m,n)  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/output)  COMPLEX*16  array,   dimension
                   (LWORK)
                   On exit, if INFO = 0, WORK(1) returns the  optimal
                   LWORK.
    
         LWORK     (input) INTEGER
                   The  dimension  of  the  array  WORK.   LWORK   >=
                   max(1,M).   For optimum performance LWORK >= M*NB,
                   where NB is the optimal blocksize.
    
         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(n-k+i+1:n) = 0 and v(n-k+i) = 1; conjg(v(1:n-k+i-1))
         is stored on exit in A(m-k+i,1:n-k+i-1), and tau in TAU(i).
    
    
    
    


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