Contents


NAME

     dgeqlf - compute a QL factorization of a real M-by-N  matrix
     A

SYNOPSIS

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

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

     SUBROUTINE DGEQLF_64(M, N, A, LDA, TAU, WORK, LDWORK, INFO)

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

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

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

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

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

  C INTERFACE
     #include <sunperf.h>

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

     void dgeqlf_64(long m, long n, double *a, long  lda,  double
               *tau, long *info);

PURPOSE

     dgeqlf computes a QL factorization of a real  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 orthogonal  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 ille-
               gal 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 real scalar, and v is a real 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).