zgeqrfp (3p)

Name

zgeqrfp - N matrix A: A = Q * R

Synopsis

SUBROUTINE ZGEQRFP(M, N, A, LDA, TAU, WORK, LWORK, INFO)


INTEGER INFO, LDA, LWORK, M, N

DOUBLE COMPLEX A(LDA,*), TAU(*), WORK(*)


SUBROUTINE ZGEQRFP_64(M, N, A, LDA, TAU, WORK, LWORK, INFO)


INTEGER*8 INFO, LDA, LWORK, M, N

DOUBLE COMPLEX A(LDA,*), TAU(*), WORK(*)


F95 INTERFACE
SUBROUTINE GEQRFP(M, N, A, LDA, TAU, WORK, LWORK, INFO)


INTEGER :: M, N, LDA, LWORK, INFO

COMPLEX(8), DIMENSION(:,:) :: A

COMPLEX(8), DIMENSION(:) :: TAU, WORK


SUBROUTINE GEQRFP_64(M, N, A, LDA, TAU, WORK, LWORK, INFO)


INTEGER(8) :: M, N, LDA, LWORK, INFO

COMPLEX(8), DIMENSION(:,:) :: A

COMPLEX(8), DIMENSION(:) :: TAU, WORK


C INTERFACE
#include <sunperf.h>

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


void zgeqrfp_64 (long m, long n, doublecomplex *a, long lda, doublecom-
plex *tau, long *info);

Description

Oracle Solaris Studio Performance Library                          zgeqrfp(3P)



NAME
       zgeqrfp  - compute a QR factorization of a complex M-by-N matrix A: A =
       Q * R


SYNOPSIS
       SUBROUTINE ZGEQRFP(M, N, A, LDA, TAU, WORK, LWORK, INFO)


       INTEGER INFO, LDA, LWORK, M, N

       DOUBLE COMPLEX A(LDA,*), TAU(*), WORK(*)


       SUBROUTINE ZGEQRFP_64(M, N, A, LDA, TAU, WORK, LWORK, INFO)


       INTEGER*8 INFO, LDA, LWORK, M, N

       DOUBLE COMPLEX A(LDA,*), TAU(*), WORK(*)


   F95 INTERFACE
       SUBROUTINE GEQRFP(M, N, A, LDA, TAU, WORK, LWORK, INFO)


       INTEGER :: M, N, LDA, LWORK, INFO

       COMPLEX(8), DIMENSION(:,:) :: A

       COMPLEX(8), DIMENSION(:) :: TAU, WORK


       SUBROUTINE GEQRFP_64(M, N, A, LDA, TAU, WORK, LWORK, INFO)


       INTEGER(8) :: M, N, LDA, LWORK, INFO

       COMPLEX(8), DIMENSION(:,:) :: A

       COMPLEX(8), DIMENSION(:) :: TAU, WORK


   C INTERFACE
       #include <sunperf.h>

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


       void zgeqrfp_64 (long m, long n, doublecomplex *a, long lda, doublecom-
                 plex *tau, long *info);


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


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


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


       A (input/output)
                 A is COMPLEX*16 array, dimension (LDA,N)
                 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, represent the unitary matrix Q as a prod-
                 uct  of min(m,n) elementary reflectors (see Further Details).


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


       TAU (output)
                 TAU is COMPLEX*16 array, dimension (min(M,N))
                 The scalar factors of the elementary reflectors (see  Further
                 Details).


       WORK (output)
                 WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
                 On exit, if INFO = 0, WORK(1) returns the optimal LWORK.


       LWORK (input)
                 LWORK is INTEGER
                 The dimension of the array WORK.
                 LWORK >= max(1,N).
                 For  optimum performance LWORK >= N*NB, where NB is the opti-
                 mal 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)
                 INFO is 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**H

       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                       zgeqrfp(3P)