zgeqr2 (3p)

Name

zgeqr2 - computes the QR factorization of a general rectangular matrix using an unblocked algorithm.

Synopsis

SUBROUTINE ZGEQR2(M, N, A, LDA, TAU, WORK, INFO)


INTEGER INFO, LDA, M, N

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


SUBROUTINE ZGEQR2_64(M, N, A, LDA, TAU, WORK, INFO)


INTEGER*8 INFO, LDA, M, N

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


F95 INTERFACE
SUBROUTINE GEQR2(M, N, A, LDA, TAU, WORK, INFO)


INTEGER :: M, N, LDA, INFO

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

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


SUBROUTINE GEQR2_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 zgeqr2 (int m, int n, doublecomplex  *a,  int  lda,  doublecomplex
*tau, int *info);


void  zgeqr2_64 (long m, long n, doublecomplex *a, long lda, doublecom-
plex *tau, long *info);

Description

Oracle Solaris Studio Performance Library                           zgeqr2(3P)



NAME
       zgeqr2  - computes the QR factorization of a general rectangular matrix
       using an unblocked algorithm.


SYNOPSIS
       SUBROUTINE ZGEQR2(M, N, A, LDA, TAU, WORK, INFO)


       INTEGER INFO, LDA, M, N

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


       SUBROUTINE ZGEQR2_64(M, N, A, LDA, TAU, WORK, INFO)


       INTEGER*8 INFO, LDA, M, N

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


   F95 INTERFACE
       SUBROUTINE GEQR2(M, N, A, LDA, TAU, WORK, INFO)


       INTEGER :: M, N, LDA, INFO

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

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


       SUBROUTINE GEQR2_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 zgeqr2 (int m, int n, doublecomplex  *a,  int  lda,  doublecomplex
                 *tau, int *info);


       void  zgeqr2_64 (long m, long n, doublecomplex *a, long lda, doublecom-
                 plex *tau, long *info);


PURPOSE
       zgeqr2 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 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 (N)


       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                        zgeqr2(3P)