zgeql2 (3p)

Name

zgeql2 - compute the QL factorization of a general rectangular matrix using an unblocked algorithm

Synopsis

SUBROUTINE ZGEQL2(M, N, A, LDA, TAU, WORK, INFO)


INTEGER INFO, LDA, M, N

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


SUBROUTINE ZGEQL2_64(M, N, A, LDA, TAU, WORK, INFO)


INTEGER*8 INFO, LDA, M, N

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


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


INTEGER :: M, N, LDA, INFO

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

COMPLEX(8), DIMENSION(:,:) :: A


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


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

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

COMPLEX(8), DIMENSION(:,:) :: A


C INTERFACE
#include <sunperf.h>

void zgeql2 (int m, int n, doublecomplex  *a,  int  lda,  doublecomplex
*tau, int *info);


void  zgeql2_64 (long m, long n, doublecomplex *a, long lda, doublecom-
plex *tau, long *info);

Description

Oracle Solaris Studio Performance Library                           zgeql2(3P)



NAME
       zgeql2  -  compute the QL factorization of a general rectangular matrix
       using an unblocked algorithm


SYNOPSIS
       SUBROUTINE ZGEQL2(M, N, A, LDA, TAU, WORK, INFO)


       INTEGER INFO, LDA, M, N

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


       SUBROUTINE ZGEQL2_64(M, N, A, LDA, TAU, WORK, INFO)


       INTEGER*8 INFO, LDA, M, N

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


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


       INTEGER :: M, N, LDA, INFO

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

       COMPLEX(8), DIMENSION(:,:) :: A


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


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

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

       COMPLEX(8), DIMENSION(:,:) :: A


   C INTERFACE
       #include <sunperf.h>

       void zgeql2 (int m, int n, doublecomplex  *a,  int  lda,  doublecomplex
                 *tau, int *info);


       void  zgeql2_64 (long m, long n, doublecomplex *a, long lda, doublecom-
                 plex *tau, long *info);


PURPOSE
       zgeql2 computes a QL factorization of a complex 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 COMPLEX*16 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 unitary 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 COMPLEX*16 array, dimension (min(M,N))
                 The  scalar factors of the elementary reflectors (see Further
                 Details).


       WORK (output)
                 WORK is COMPLEX*16 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**H

       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                        zgeql2(3P)