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

NAME

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

SYNOPSIS

  SUBROUTINE DGEQRF( M, N, A, LDA, TAU, WORK, LDWORK, INFO)
  INTEGER M, N, LDA, LDWORK, INFO
  DOUBLE PRECISION A(LDA,*), TAU(*), WORK(*)

  SUBROUTINE DGEQRF_64( M, N, A, LDA, TAU, WORK, LDWORK, INFO)
  INTEGER*8 M, N, LDA, LDWORK, INFO
  DOUBLE PRECISION A(LDA,*), TAU(*), WORK(*)

F95 INTERFACE

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

  SUBROUTINE GEQRF_64( [M], [N], A, [LDA], TAU, [WORK], [LDWORK], 
 *       [INFO])
  INTEGER(8) :: M, N, LDA, LDWORK, INFO
  REAL(8), DIMENSION(:) :: TAU, WORK
  REAL(8), DIMENSION(:,:) :: A

C INTERFACE

#include <sunperf.h>

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

void dgeqrf_64(long m, long n, double *a, long lda, double *tau, long *info);

PURPOSE

dgeqrf 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).