cgerq2 (3p)

Name

cgerq2 - computes the RQ factorization of a general rectangular matrix using an unblocked algorithm

Synopsis

SUBROUTINE CGERQ2(M, N, A, LDA, TAU, WORK, INFO)


INTEGER INFO, LDA, M, N

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


SUBROUTINE CGERQ2_64(M, N, A, LDA, TAU, WORK, INFO)


INTEGER*8 INFO, LDA, M, N

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


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


INTEGER :: M, N, LDA, INFO

COMPLEX, DIMENSION(:) :: TAU, WORK

COMPLEX, DIMENSION(:,:) :: A


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


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

COMPLEX, DIMENSION(:) :: TAU, WORK

COMPLEX, DIMENSION(:,:) :: A


C INTERFACE
#include <sunperf.h>

void cgerq2 (int m, int n, floatcomplex *a, int lda, floatcomplex *tau,
int *info);


void cgerq2_64 (long m, long n, floatcomplex *a, long lda, floatcomplex
*tau, long *info);

Description

Oracle Solaris Studio Performance Library                           cgerq2(3P)



NAME
       cgerq2  - computes the RQ factorization of a general rectangular matrix
       using an unblocked algorithm


SYNOPSIS
       SUBROUTINE CGERQ2(M, N, A, LDA, TAU, WORK, INFO)


       INTEGER INFO, LDA, M, N

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


       SUBROUTINE CGERQ2_64(M, N, A, LDA, TAU, WORK, INFO)


       INTEGER*8 INFO, LDA, M, N

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


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


       INTEGER :: M, N, LDA, INFO

       COMPLEX, DIMENSION(:) :: TAU, WORK

       COMPLEX, DIMENSION(:,:) :: A


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


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

       COMPLEX, DIMENSION(:) :: TAU, WORK

       COMPLEX, DIMENSION(:,:) :: A


   C INTERFACE
       #include <sunperf.h>

       void cgerq2 (int m, int n, floatcomplex *a, int lda, floatcomplex *tau,
                 int *info);


       void cgerq2_64 (long m, long n, floatcomplex *a, long lda, floatcomplex
                 *tau, long *info);


PURPOSE
       cgerq2 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 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 array, dimension (min(M,N))
                 The  scalar factors of the elementary reflectors (see Further
                 Details).


       WORK (output)
                 WORK is COMPLEX 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                        cgerq2(3P)