zgeqrf (3p)

Name

zgeqrf - N matrix A

Synopsis

SUBROUTINE ZGEQRF(M, N, A, LDA, TAU, WORK, LDWORK, INFO)

DOUBLE COMPLEX A(LDA,*), TAU(*), WORK(*)
INTEGER M, N, LDA, LDWORK, INFO

SUBROUTINE ZGEQRF_64(M, N, A, LDA, TAU, WORK, LDWORK, INFO)

DOUBLE COMPLEX A(LDA,*), TAU(*), WORK(*)
INTEGER*8 M, N, LDA, LDWORK, INFO




F95 INTERFACE
SUBROUTINE GEQRF(M, N, A, LDA, TAU, WORK, LDWORK, INFO)

COMPLEX(8), DIMENSION(:) :: TAU, WORK
COMPLEX(8), DIMENSION(:,:) :: A
INTEGER :: M, N, LDA, LDWORK, INFO

SUBROUTINE GEQRF_64(M, N, A, LDA, TAU, WORK, LDWORK, INFO)

COMPLEX(8), DIMENSION(:) :: TAU, WORK
COMPLEX(8), DIMENSION(:,:) :: A
INTEGER(8) :: M, N, LDA, LDWORK, INFO




C INTERFACE
#include <sunperf.h>

void  zgeqrf(int  m,  int  n,  doublecomplex *a, int lda, doublecomplex
*tau, int *info);

void zgeqrf_64(long m, long n, doublecomplex *a, long  lda,  doublecom-
plex *tau, long *info);

Description

Oracle Solaris Studio Performance Library                           zgeqrf(3P)



NAME
       zgeqrf - compute a QR factorization of a complex M-by-N matrix A


SYNOPSIS
       SUBROUTINE ZGEQRF(M, N, A, LDA, TAU, WORK, LDWORK, INFO)

       DOUBLE COMPLEX A(LDA,*), TAU(*), WORK(*)
       INTEGER M, N, LDA, LDWORK, INFO

       SUBROUTINE ZGEQRF_64(M, N, A, LDA, TAU, WORK, LDWORK, INFO)

       DOUBLE COMPLEX A(LDA,*), TAU(*), WORK(*)
       INTEGER*8 M, N, LDA, LDWORK, INFO




   F95 INTERFACE
       SUBROUTINE GEQRF(M, N, A, LDA, TAU, WORK, LDWORK, INFO)

       COMPLEX(8), DIMENSION(:) :: TAU, WORK
       COMPLEX(8), DIMENSION(:,:) :: A
       INTEGER :: M, N, LDA, LDWORK, INFO

       SUBROUTINE GEQRF_64(M, N, A, LDA, TAU, WORK, LDWORK, INFO)

       COMPLEX(8), DIMENSION(:) :: TAU, WORK
       COMPLEX(8), DIMENSION(:,:) :: A
       INTEGER(8) :: M, N, LDA, LDWORK, INFO




   C INTERFACE
       #include <sunperf.h>

       void  zgeqrf(int  m,  int  n,  doublecomplex *a, int lda, doublecomplex
                 *tau, int *info);

       void zgeqrf_64(long m, long n, doublecomplex *a, long  lda,  doublecom-
                 plex *tau, long *info);



PURPOSE
       zgeqrf  computes a QR factorization of a complex M-by-N matrix A: A = Q
       * R.


ARGUMENTS
       M (input) The number of rows of the matrix A.  M >= 0.


       N (input) The number of columns of the matrix A.  N >= 0.


       A (input/output)
                 On entry, the M-by-N matrix A.  On exit, the elements on  and
                 above  the  diagonal  of  the array contain 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, repre-
                 sent the unitary matrix Q as a product of min(m,n) elementary
                 reflectors (see Further Details).


       LDA (input)
                 The leading dimension of the array A.  LDA >= max(1,M).


       TAU (output)
                 The  scalar factors of the elementary reflectors (see Further
                 Details).


       WORK (workspace)
                 On exit, if INFO = 0, WORK(1) returns the optimal LDWORK.


       LDWORK (input)
                 The dimension of the array WORK.  LDWORK  >=  max(1,N).   For
                 optimum  performance  LDWORK >= N*NB, where NB is the optimal
                 blocksize.

                 If LDWORK = -1, then a workspace query is assumed;  the  rou-
                 tine  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 LDWORK is issued by XERBLA.


       INFO (output)
                 = 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(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).




                                  7 Nov 2015                        zgeqrf(3P)