• NAME
• SYNOPSIS
• F95 INTERFACE
• C INTERFACE
• PURPOSE
• ARGUMENTS
• FURTHER DETAILS

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 elementary 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 routine 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).