• NAME
• SYNOPSIS
• F95 INTERFACE
• C INTERFACE
• PURPOSE
• ARGUMENTS
• FURTHER DETAILS

NAME

sgerqf - compute an RQ factorization of a real M-by-N matrix A

SYNOPSIS

  SUBROUTINE SGERQF( M, N, A, LDA, TAU, WORK, LDWORK, INFO)
  INTEGER M, N, LDA, LDWORK, INFO
  REAL A(LDA,*), TAU(*), WORK(*)

  SUBROUTINE SGERQF_64( M, N, A, LDA, TAU, WORK, LDWORK, INFO)
  INTEGER*8 M, N, LDA, LDWORK, INFO
  REAL A(LDA,*), TAU(*), WORK(*)

F95 INTERFACE

  SUBROUTINE GERQF( [M], [N], A, [LDA], TAU, [WORK], [LDWORK], [INFO])
  INTEGER :: M, N, LDA, LDWORK, INFO
  REAL, DIMENSION(:) :: TAU, WORK
  REAL, DIMENSION(:,:) :: A

  SUBROUTINE GERQF_64( [M], [N], A, [LDA], TAU, [WORK], [LDWORK], 
 *       [INFO])
  INTEGER(8) :: M, N, LDA, LDWORK, INFO
  REAL, DIMENSION(:) :: TAU, WORK
  REAL, DIMENSION(:,:) :: A

C INTERFACE

#include <sunperf.h>

void sgerqf(int m, int n, float *a, int lda, float *tau, int *info);

void sgerqf_64(long m, long n, float *a, long lda, float *tau, long *info);

PURPOSE

sgerqf computes an RQ factorization of a real M-by-N matrix A: A = R * Q.

ARGUMENTS

• M (input)
  The number of rows of the matrix A. M > = 0.

• N (input)
  The number of columns of the matrix A. N > = 0.

• A (input/output)
  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 min(m,n) elementary reflectors (see Further Details).

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

• TAU (output)
  The scalar factors of the elementary reflectors (see Further Details).

• 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)
  

   = 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'

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).