dorgrq

NAME

dorgrq - generate an M-by-N real matrix Q with orthonormal rows,

SYNOPSIS 

  SUBROUTINE DORGRQ( M, N, K, A, LDA, TAU, WORK, LDWORK, INFO)
  INTEGER M, N, K, LDA, LDWORK, INFO
  DOUBLE PRECISION A(LDA,*), TAU(*), WORK(*)
 
  SUBROUTINE DORGRQ_64( M, N, K, A, LDA, TAU, WORK, LDWORK, INFO)
  INTEGER*8 M, N, K, LDA, LDWORK, INFO
  DOUBLE PRECISION A(LDA,*), TAU(*), WORK(*)

F95 INTERFACE 

  SUBROUTINE ORGRQ( M, [N], [K], A, [LDA], TAU, [WORK], [LDWORK], 
 *       [INFO])
  INTEGER :: M, N, K, LDA, LDWORK, INFO
  REAL(8), DIMENSION(:) :: TAU, WORK
  REAL(8), DIMENSION(:,:) :: A
 
  SUBROUTINE ORGRQ_64( M, [N], [K], A, [LDA], TAU, [WORK], [LDWORK], 
 *       [INFO])
  INTEGER(8) :: M, N, K, LDA, LDWORK, INFO
  REAL(8), DIMENSION(:) :: TAU, WORK
  REAL(8), DIMENSION(:,:) :: A

C INTERFACE

#include <sunperf.h>

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

void dorgrq_64(long m, long n, long k, double *a, long lda, double *tau, long *info);

PURPOSE

dorgrq generates an M-by-N real matrix Q with orthonormal rows, which is defined as the last M rows of a product of K elementary reflectors of order N 

      Q  =  H(1) H(2) . . . H(k)

as returned by SGERQF.

ARGUMENTS

* M (input)
The number of rows of the matrix Q. M >= 0.

* N (input)
The number of columns of the matrix Q. N >= M.

* K (input)
The number of elementary reflectors whose product defines the matrix Q. M >= K >= 0.

* A (input/output)
On entry, the (m-k+i)-th row must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by SGERQF in the last k rows of its array argument A. On exit, the M-by-N matrix Q.

* LDA (input)
The first dimension of the array A. LDA >= max(1,M).

* TAU (input)
TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by SGERQF.

* WORK (workspace)
On exit, if INFO = 0, WORK(1) returns the optimal LDWORK.

* LDWORK (input)
The dimension of the array WORK. LDWORK >= max(1,M). For optimum performance LDWORK >= M*NB, where NB is the optimal blocksize.

If LDWORK = -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 LDWORK is issued by XERBLA.

* INFO (output)