Contents


NAME

     cgelqf - compute an LQ factorization  of  a  complex  M-by-N
     matrix A

SYNOPSIS

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

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

     SUBROUTINE CGELQF_64(M, N, A, LDA, TAU, WORK, LDWORK, INFO)

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

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

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

     SUBROUTINE GELQF_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 cgelqf(int m, int n, complex *a, int lda, complex *tau,
               int *info);

     void cgelqf_64(long m, long n, complex *a, long lda, complex
               *tau, long *info);

PURPOSE

     cgelqf computes an LQ  factorization  of  a  complex  M-by-N
     matrix A:  A = L * Q.

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, the  ele-
               ments  on and below the diagonal of the array con-
               tain the m-by-min(m,n) lower trapezoidal matrix  L
               (L  is  lower  triangular if m <= n); the elements
               above the diagonal, 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,M).  For optimum performance LDWORK >= M*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 complex scalar, and v  is  a  complex  vector
     with v(1:i-1) = 0 and v(i) = 1; conjg(v(i+1:n)) is stored on
     exit in A(i,i+1:n), and tau in TAU(i).