cgeql2 (3p)

Name

cgeql2 - compute the QL factorization of a general rectangular matrix using an unblocked algorithm

Synopsis

SUBROUTINE CGEQL2(M, N, A, LDA, TAU, WORK, INFO)


INTEGER INFO, LDA, M, N

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


SUBROUTINE CGEQL2_64(M, N, A, LDA, TAU, WORK, INFO)


INTEGER*8 INFO, LDA, M, N

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


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


INTEGER :: M, N, LDA, INFO

COMPLEX, DIMENSION(:) :: TAU, WORK

COMPLEX, DIMENSION(:,:) :: A


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


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

COMPLEX, DIMENSION(:) :: TAU, WORK

COMPLEX, DIMENSION(:,:) :: A


C INTERFACE
#include <sunperf.h>

void cgeql2 (int m, int n, floatcomplex *a, int lda, floatcomplex *tau,
int *info);


void cgeql2_64 (long m, long n, floatcomplex *a, long lda, floatcomplex
*tau, long *info);

Description

Oracle Solaris Studio Performance Library                           cgeql2(3P)



NAME
       cgeql2  -  compute the QL factorization of a general rectangular matrix
       using an unblocked algorithm


SYNOPSIS
       SUBROUTINE CGEQL2(M, N, A, LDA, TAU, WORK, INFO)


       INTEGER INFO, LDA, M, N

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


       SUBROUTINE CGEQL2_64(M, N, A, LDA, TAU, WORK, INFO)


       INTEGER*8 INFO, LDA, M, N

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


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


       INTEGER :: M, N, LDA, INFO

       COMPLEX, DIMENSION(:) :: TAU, WORK

       COMPLEX, DIMENSION(:,:) :: A


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


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

       COMPLEX, DIMENSION(:) :: TAU, WORK

       COMPLEX, DIMENSION(:,:) :: A


   C INTERFACE
       #include <sunperf.h>

       void cgeql2 (int m, int n, floatcomplex *a, int lda, floatcomplex *tau,
                 int *info);


       void cgeql2_64 (long m, long n, floatcomplex *a, long lda, floatcomplex
                 *tau, long *info);


PURPOSE
       cgeql2 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 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 array, dimension (min(M,N))
                 The  scalar factors of the elementary reflectors (see Further
                 Details).


       WORK (output)
                 WORK is COMPLEX 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                        cgeql2(3P)