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

NAME

dgelqf - compute an LQ factorization of a real M-by-N matrix A

SYNOPSIS

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

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

  SUBROUTINE GELQF_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 dgelqf(int m, int n, double *a, int lda, double *tau, int *info);

void dgelqf_64(long m, long n, double *a, long lda, double *tau, long *info);

PURPOSE

dgelqf computes an LQ factorization of a real M-by-N matrix A: A = L * 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, the elements on and below the diagonal of the array contain the m-by-min(m,n) lower trapezoidal matrix L (L is lower triangular if m < = n); the elements above the diagonal, with the array TAU, represent the orthogonal matrix Q as a product of 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(k) . . . H(2) H(1), 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:n) is stored on exit in A(i,i+1:n), and tau in TAU(i).