zgerq2 (3p)

Name

zgerq2 - computes the RQ factorization of a general rectangular matrix using an unblocked algorithm

Synopsis

SUBROUTINE ZGERQ2(M, N, A, LDA, TAU, WORK, INFO)


INTEGER INFO, LDA, M, N

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


SUBROUTINE ZGERQ2_64(M, N, A, LDA, TAU, WORK, INFO)


INTEGER*8 INFO, LDA, M, N

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


F95 INTERFACE
SUBROUTINE GERQ2(M, N, A, LDA, TAU, WORK, INFO)


INTEGER :: M, N, LDA, INFO

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

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


SUBROUTINE GERQ2_64(M, N, A, LDA, TAU, WORK, INFO)


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

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

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


C INTERFACE
#include <sunperf.h>

void zgerq2 (int m, int n, doublecomplex  *a,  int  lda,  doublecomplex
*tau, int *info);


void  zgerq2_64 (long m, long n, doublecomplex *a, long lda, doublecom-
plex *tau, long *info);

Description

Oracle Solaris Studio Performance Library                           zgerq2(3P)



NAME
       zgerq2  - computes the RQ factorization of a general rectangular matrix
       using an unblocked algorithm


SYNOPSIS
       SUBROUTINE ZGERQ2(M, N, A, LDA, TAU, WORK, INFO)


       INTEGER INFO, LDA, M, N

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


       SUBROUTINE ZGERQ2_64(M, N, A, LDA, TAU, WORK, INFO)


       INTEGER*8 INFO, LDA, M, N

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


   F95 INTERFACE
       SUBROUTINE GERQ2(M, N, A, LDA, TAU, WORK, INFO)


       INTEGER :: M, N, LDA, INFO

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

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


       SUBROUTINE GERQ2_64(M, N, A, LDA, TAU, WORK, INFO)


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

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

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


   C INTERFACE
       #include <sunperf.h>

       void zgerq2 (int m, int n, doublecomplex  *a,  int  lda,  doublecomplex
                 *tau, int *info);


       void  zgerq2_64 (long m, long n, doublecomplex *a, long lda, doublecom-
                 plex *tau, long *info);


PURPOSE
       zgerq2 computes an RQ factorization of a complex m by n matrix A: A = R
       * Q.


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,  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 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 (M)


       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 H(2)**H . . . H(k)**H, 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(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).



                                  7 Nov 2015                        zgerq2(3P)