dgerq2 (3p)

Name

dgerq2 - computes the RQ factorization of a general rectangular matrix using an unblocked algorithm

Synopsis

SUBROUTINE DGERQ2(M, N, A, LDA, TAU, WORK, INFO)


INTEGER INFO, LDA, M, N

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


SUBROUTINE DGERQ2_64( M, N, A, LDA, TAU, WORK, INFO )


INTEGER*8 INFO, LDA, M, N

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


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


INTEGER :: M, N, LDA, INFO

REAL(8), DIMENSION(:,:) :: A

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


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


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

REAL(8), DIMENSION(:,:) :: A

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


C INTERFACE
#include <sunperf.h>

void dgerq2 (int m, int n, double *a, int lda, double *tau, int *info);


void  dgerq2_64 (long m, long n, double *a, long lda, double *tau, long
*info);

Description

Oracle Solaris Studio Performance Library                           dgerq2(3P)



NAME
       dgerq2  - computes the RQ factorization of a general rectangular matrix
       using an unblocked algorithm


SYNOPSIS
       SUBROUTINE DGERQ2(M, N, A, LDA, TAU, WORK, INFO)


       INTEGER INFO, LDA, M, N

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


       SUBROUTINE DGERQ2_64( M, N, A, LDA, TAU, WORK, INFO )


       INTEGER*8 INFO, LDA, M, N

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


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


       INTEGER :: M, N, LDA, INFO

       REAL(8), DIMENSION(:,:) :: A

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


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


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

       REAL(8), DIMENSION(:,:) :: A

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


   C INTERFACE
       #include <sunperf.h>

       void dgerq2 (int m, int n, double *a, int lda, double *tau, int *info);


       void  dgerq2_64 (long m, long n, double *a, long lda, double *tau, long
                 *info);


PURPOSE
       dgerq2 computes an RQ factorization of a real 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 DOUBLE PRECISION 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 orthogonal 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 DOUBLE PRECISION array, dimension (min(M,N))
                 The  scalar factors of the elementary reflectors (see Further
                 Details).


       WORK (output)
                 WORK is DOUBLE PRECISION 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(2) . . . H(k), where k = min(m,n).

       Each H(i) has the form

       H(i) = I - tau * v * v**T

       where tau is a real scalar, and v is a real vector with
       v(n-k+i+1:n) = 0 and v(n-k+i) = 1; 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                        dgerq2(3P)