sgeql2 (3p)

Name

sgeql2 - compute the QL factorization of a general rectangular matrix using an unblocked algorithm

Synopsis

SUBROUTINE SGEQL2(M, N, A, LDA, TAU, WORK, INFO)


INTEGER INFO, LDA, M, N

REAL A(LDA,*), TAU(*), WORK(*)


SUBROUTINE SGEQL2_64(M, N, A, LDA, TAU, WORK, INFO)


INTEGER*8 INFO, LDA, M, N

REAL A(LDA,*), TAU(*), WORK(*)


F95 INTERFACE
SUBROUTINE GEQL2(M, N, A, LDA, TAU, WORK, INFO)


REAL, DIMENSION(:,:) :: A

INTEGER :: M, N, LDA, INFO

REAL, DIMENSION(:) :: TAU, WORK


SUBROUTINE GEQL2_64(M, N, A, LDA, TAU, WORK, INFO)


REAL, DIMENSION(:,:) :: A

INTEGER(8) :: M, N, LDA, INFO

REAL, DIMENSION(:) :: TAU, WORK


C INTERFACE
#include <sunperf.h>

void sgeql2 (int m, int n, float *a, int lda, float *tau, int *info);


void sgeql2_64 (long m, long n, float *a, long lda,  float  *tau,  long
*info);

Description

Oracle Solaris Studio Performance Library                           sgeql2(3P)



NAME
       sgeql2  -  compute the QL factorization of a general rectangular matrix
       using an unblocked algorithm


SYNOPSIS
       SUBROUTINE SGEQL2(M, N, A, LDA, TAU, WORK, INFO)


       INTEGER INFO, LDA, M, N

       REAL A(LDA,*), TAU(*), WORK(*)


       SUBROUTINE SGEQL2_64(M, N, A, LDA, TAU, WORK, INFO)


       INTEGER*8 INFO, LDA, M, N

       REAL A(LDA,*), TAU(*), WORK(*)


   F95 INTERFACE
       SUBROUTINE GEQL2(M, N, A, LDA, TAU, WORK, INFO)


       REAL, DIMENSION(:,:) :: A

       INTEGER :: M, N, LDA, INFO

       REAL, DIMENSION(:) :: TAU, WORK


       SUBROUTINE GEQL2_64(M, N, A, LDA, TAU, WORK, INFO)


       REAL, DIMENSION(:,:) :: A

       INTEGER(8) :: M, N, LDA, INFO

       REAL, DIMENSION(:) :: TAU, WORK


   C INTERFACE
       #include <sunperf.h>

       void sgeql2 (int m, int n, float *a, int lda, float *tau, int *info);


       void sgeql2_64 (long m, long n, float *a, long lda,  float  *tau,  long
                 *info);


PURPOSE
       sgeql2 computes a QL factorization of a real m by n matrix A: A=Q*L.


ARGUMENTS
       M (input)
                 M is INTEGER
                 The number of rows of the matrix A. M >= 0.


       N (input)
                 N is INTEGER
                 The number of columns of the matrix A. N >= 0.


       A (input/output)
                 A is REAL array, dimension (LDA,N)
                 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  elementary  reflectors  (see   Further
                 Details).


       LDA (input)
                 LDA is INTEGER
                 The leading dimension of the array A. LDA >= max(1,M).


       TAU (output)
                 TAU is REAL array, dimension (min(M,N))
                 The  scalar factors of the elementary reflectors (see Further
                 Details).


       WORK (output)
                 WORK is REAL array, dimension (N)


       INFO (output)
                 INFO is INTEGER
                 = 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**T

       where tau is a complex scalar, and v is a complex 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                        sgeql2(3P)