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

NAME

sgeqrf - compute a QR factorization of a real M-by-N matrix A

SYNOPSIS

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

  SUBROUTINE SGEQRF_64( M, N, A, LDA, TAU, WORK, LDWORK, INFO)
  INTEGER*8 M, N, LDA, LDWORK, INFO
  REAL A(LDA,*), TAU(*), WORK(*)

F95 INTERFACE

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

  SUBROUTINE GEQRF_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 sgeqrf(int m, int n, float *a, int lda, float *tau, int *info);

void sgeqrf_64(long m, long n, float *a, long lda, float *tau, long *info);

PURPOSE

sgeqrf computes a QR factorization of a real M-by-N matrix A: A = Q * R.

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, 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 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,N). For optimum performance LDWORK > = N*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(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).