cgeqlf (3p)

Name

cgeqlf - N matrix A

Synopsis

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

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

SUBROUTINE CGEQLF_64(M, N, A, LDA, TAU, WORK, LDWORK, INFO)

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




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

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

SUBROUTINE GEQLF_64(M, N, A, LDA, TAU, WORK, LDWORK, INFO)

COMPLEX, DIMENSION(:) :: TAU, WORK
COMPLEX, DIMENSION(:,:) :: A
INTEGER(8) :: M, N, LDA, LDWORK, INFO




C INTERFACE
#include <sunperf.h>

void  cgeqlf(int  m,  int  n,  complex  *a,  int lda, complex *tau, int
*info);

void cgeqlf_64(long m, long n, complex *a, long lda, complex *tau, long
*info);

Description

Oracle Solaris Studio Performance Library                           cgeqlf(3P)



NAME
       cgeqlf - compute a QL factorization of a complex M-by-N matrix A


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

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

       SUBROUTINE CGEQLF_64(M, N, A, LDA, TAU, WORK, LDWORK, INFO)

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




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

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

       SUBROUTINE GEQLF_64(M, N, A, LDA, TAU, WORK, LDWORK, INFO)

       COMPLEX, DIMENSION(:) :: TAU, WORK
       COMPLEX, DIMENSION(:,:) :: A
       INTEGER(8) :: M, N, LDA, LDWORK, INFO




   C INTERFACE
       #include <sunperf.h>

       void  cgeqlf(int  m,  int  n,  complex  *a,  int lda, complex *tau, int
                 *info);

       void cgeqlf_64(long m, long n, complex *a, long lda, complex *tau, long
                 *info);



PURPOSE
       cgeqlf  computes a QL factorization of a complex 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 unitary matrix Q as a product of elemen-
                 tary 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 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                        cgeqlf(3P)