zgerqf(3S)

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( * )

IMPLEMENTATION
     These routines are part of the SCSL Scientific Library and can be loaded
     using either the -lscs or the -lscs_mp option.  The -lscs_mp option
     directs the linker to use the multi-processor version of the library.

     When linking to SCSL with -lscs or -lscs_mp, the default integer size is
     4 bytes (32 bits). Another version of SCSL is available in which integers
     are 8 bytes (64 bits).  This version allows the user access to larger
     memory sizes and helps when porting legacy Cray codes.  It can be loaded
     by using the -lscs_i8 option or the -lscs_i8_mp option. A program may use
     only one of the two versions; 4-byte integer and 8-byte integer library
     calls cannot be mixed.

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 trapezoidal 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.

             If LWORK = -1, then a workspace query is assumed; the routine
             only calculates the optimal size of the WORK array, returns this
             value as the first entry of the WORK array, and no error message
             related to LWORK is issued by XERBLA.

     INFO    (output) INTEGER
             = 0:  successful exit
             < 0:  if INFO = -i, the i-th argument had an illegal 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).


SEE ALSO
     INTRO_LAPACK(3S), INTRO_SCSL(3S)

     This man page is available only online.