dgeql2 (3p)

Name

dgeql2 - compute the QL factorization of a general rectangular matrix using an unblocked algorithm

Synopsis

SUBROUTINE DGEQL2(M, N, A, LDA, TAU, WORK, INFO)


INTEGER INFO, LDA, M, N

DOUBLE PRECISION A(LDA,*), TAU(*), WORK(*)


SUBROUTINE DGEQL2_64(M, N, A, LDA, TAU, WORK, INFO)


INTEGER*8 INFO, LDA, M, N

DOUBLE PRECISION A(LDA,*), TAU(*), WORK(*)


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


INTEGER :: M, N, LDA, INFO

REAL(8), DIMENSION(:,:) :: A

REAL(8), DIMENSION(:) :: TAU, WORK


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


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

REAL(8), DIMENSION(:,:) :: A

REAL(8), DIMENSION(:) :: TAU, WORK


C INTERFACE
#include <sunperf.h>

void dgeql2 (int m, int n, double *a, int lda, double *tau, int *info);


void  dgeql2_64 (long m, long n, double *a, long lda, double *tau, long
*info);

Description

Oracle Solaris Studio Performance Library                           dgeql2(3P)



NAME
       dgeql2  -  compute the QL factorization of a general rectangular matrix
       using an unblocked algorithm


SYNOPSIS
       SUBROUTINE DGEQL2(M, N, A, LDA, TAU, WORK, INFO)


       INTEGER INFO, LDA, M, N

       DOUBLE PRECISION A(LDA,*), TAU(*), WORK(*)


       SUBROUTINE DGEQL2_64(M, N, A, LDA, TAU, WORK, INFO)


       INTEGER*8 INFO, LDA, M, N

       DOUBLE PRECISION A(LDA,*), TAU(*), WORK(*)


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


       INTEGER :: M, N, LDA, INFO

       REAL(8), DIMENSION(:,:) :: A

       REAL(8), DIMENSION(:) :: TAU, WORK


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


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

       REAL(8), DIMENSION(:,:) :: A

       REAL(8), DIMENSION(:) :: TAU, WORK


   C INTERFACE
       #include <sunperf.h>

       void dgeql2 (int m, int n, double *a, int lda, double *tau, int *info);


       void  dgeql2_64 (long m, long n, double *a, long lda, double *tau, long
                 *info);


PURPOSE
       dgeql2 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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (min(M,N))
                 The scalar factors of the elementary reflectors (see  Further
                 Details).


       WORK (output)
                 WORK is DOUBLE PRECISION 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                        dgeql2(3P)