sgeqlf (3p)

Name

sgeqlf - N matrix A

Synopsis

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

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

SUBROUTINE SGEQLF_64(M, N, A, LDA, TAU, WORK, LDWORK, INFO)

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




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

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

SUBROUTINE GEQLF_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 sgeqlf(int m, int n, float *a, int lda, float *tau, int *info);

void  sgeqlf_64(long  m,  long  n, float *a, long lda, float *tau, long
*info);

Description

Oracle Solaris Studio Performance Library                           sgeqlf(3P)



NAME
       sgeqlf - compute a QL factorization of a real M-by-N matrix A


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

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

       SUBROUTINE SGEQLF_64(M, N, A, LDA, TAU, WORK, LDWORK, INFO)

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




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

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

       SUBROUTINE GEQLF_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 sgeqlf(int m, int n, float *a, int lda, float *tau, int *info);

       void  sgeqlf_64(long  m,  long  n, float *a, long lda, float *tau, long
                 *info);



PURPOSE
       sgeqlf computes a QL factorization of a real M-by-N matrix A: A =  Q  *
       L.


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 lower
                 triangle of the subarray A(m-n+1:m,1:n) contains  the  N-by-N
                 lower  triangular  matrix  L;  if m <= n, the elements on and
                 below the (n-m)-th superdiagonal  contain  the  M-by-N  lower
                 trapezoidal  matrix L; the remaining elements, with the array
                 TAU, represent the orthogonal matrix Q as a product  of  ele-
                 mentary 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  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(m-k+i+1:m)  =  0  and v(m-k+i) = 1; v(1:m-k+i-1) is stored on exit in
       A(1:m-k+i-1,n-k+i), and tau in TAU(i).




                                  7 Nov 2015                        sgeqlf(3P)