sgelqf (3p)

Name

sgelqf - N matrix A

Synopsis

SUBROUTINE SGELQF(M, N, A, LDA, TAU, WORK, LDWORK, INFO)

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

SUBROUTINE SGELQF_64(M, N, A, LDA, TAU, WORK, LDWORK, INFO)

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




F95 INTERFACE
SUBROUTINE GELQF(M, N, A, LDA, TAU, WORK, LDWORK, INFO)

INTEGER :: M, N, LDA, LDWORK, INFO
REAL, DIMENSION(:) :: TAU, WORK
REAL, DIMENSION(:,:) :: A

SUBROUTINE GELQF_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 sgelqf(int m, int n, float *a, int lda, float *tau, int *info);

void  sgelqf_64(long  m,  long  n, float *a, long lda, float *tau, long
*info);

Description

Oracle Solaris Studio Performance Library                           sgelqf(3P)



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


SYNOPSIS
       SUBROUTINE SGELQF(M, N, A, LDA, TAU, WORK, LDWORK, INFO)

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

       SUBROUTINE SGELQF_64(M, N, A, LDA, TAU, WORK, LDWORK, INFO)

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




   F95 INTERFACE
       SUBROUTINE GELQF(M, N, A, LDA, TAU, WORK, LDWORK, INFO)

       INTEGER :: M, N, LDA, LDWORK, INFO
       REAL, DIMENSION(:) :: TAU, WORK
       REAL, DIMENSION(:,:) :: A

       SUBROUTINE GELQF_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 sgelqf(int m, int n, float *a, int lda, float *tau, int *info);

       void  sgelqf_64(long  m,  long  n, float *a, long lda, float *tau, long
                 *info);



PURPOSE
       sgelqf 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,  repre-
                 sent  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 rou-
                 tine 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).




                                  7 Nov 2015                        sgelqf(3P)