SRC/sgelq.f(3)

NAME
SRC/sgelq.f

SYNOPSIS

  Functions/Subroutines
subroutine sgelq (m, n, a, lda, t, tsize, work, lwork, info)
SGELQ

Function/Subroutine Documentation

  subroutine sgelq (integer m, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( * ) t, integer tsize, real, dimension( * ) work, integer lwork, integer info)

SGELQ

Purpose:

     SGELQ computes an LQ factorization of a real M-by-N matrix A:
        A = ( L 0 ) *  Q
     where:
        Q is a N-by-N orthogonal matrix;
        L is a lower-triangular M-by-M matrix;
        0 is a M-by-(N-M) zero matrix, if M < N.

Parameters
    M

              M is INTEGER
              The number of rows of the matrix A.  M >= 0.

    N

              N is INTEGER
              The number of columns of the matrix A.  N >= 0.

    A

              A is REAL array, dimension (LDA,N)
              On entry, the M-by-N matrix A.
              On exit, the elements on and below the diagonal of the array
              contain the M-by-min(M,N) lower trapezoidal matrix L
              (L is lower triangular if M <= N);
              the elements above the diagonal are used to store part of the
              data structure to represent Q.

    LDA

              LDA is INTEGER
              The leading dimension of the array A.  LDA >= max(1,M).

    T

              T is REAL array, dimension (MAX(5,TSIZE))
              On exit, if INFO = 0, T(1) returns optimal (or either minimal
              or optimal, if query is assumed) TSIZE. See TSIZE for details.
              Remaining T contains part of the data structure used to represent Q.
              If one wants to apply or construct Q, then one needs to keep T
              (in addition to A) and pass it to further subroutines.

    TSIZE

              TSIZE is INTEGER
              If TSIZE >= 5, the dimension of the array T.
              If TSIZE = -1 or -2, then a workspace query is assumed. The routine
              only calculates the sizes of the T and WORK arrays, returns these
              values as the first entries of the T and WORK arrays, and no error
              message related to T or WORK is issued by XERBLA.
              If TSIZE = -1, the routine calculates optimal size of T for the
              optimum performance and returns this value in T(1).
              If TSIZE = -2, the routine calculates minimal size of T and
              returns this value in T(1).

    WORK

              (workspace) REAL array, dimension (MAX(1,LWORK))
              On exit, if INFO = 0, WORK(1) contains optimal (or either minimal
              or optimal, if query was assumed) LWORK.
              See LWORK for details.

    LWORK

              LWORK is INTEGER
              The dimension of the array WORK.
              If LWORK = -1 or -2, then a workspace query is assumed. The routine
              only calculates the sizes of the T and WORK arrays, returns these
              values as the first entries of the T and WORK arrays, and no error
              message related to T or WORK is issued by XERBLA.
              If LWORK = -1, the routine calculates optimal size of WORK for the
              optimal performance and returns this value in WORK(1).
              If LWORK = -2, the routine calculates minimal size of WORK and
              returns this value in WORK(1).

    INFO

              INFO is INTEGER
              = 0:  successful exit
              < 0:  if INFO = -i, the i-th argument had an illegal value

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Further Details

     The goal of the interface is to give maximum freedom to the developers for
     creating any LQ factorization algorithm they wish. The triangular
     (trapezoidal) L has to be stored in the lower part of A. The lower part of A
     and the array T can be used to store any relevant information for applying or
     constructing the Q factor. The WORK array can safely be discarded after exit.
     Caution: One should not expect the sizes of T and WORK to be the same from one
     LAPACK implementation to the other, or even from one execution to the other.
     A workspace query (for T and WORK) is needed at each execution. However,
     for a given execution, the size of T and WORK are fixed and will not change
     from one query to the next.

Further Details particular to this LAPACK implementation:

     These details are particular for this LAPACK implementation. Users should not
     take them for granted. These details may change in the future, and are not likely
     true for another LAPACK implementation. These details are relevant if one wants
     to try to understand the code. They are not part of the interface.
     In this version,
              T(2): row block size (MB)
              T(3): column block size (NB)
              T(6:TSIZE): data structure needed for Q, computed by
                               SLASWLQ or SGELQT
      Depending on the matrix dimensions M and N, and row and column
      block sizes MB and NB returned by ILAENV, SGELQ will use either
      SLASWLQ (if the matrix is short-and-wide) or SGELQT to compute
      the LQ factorization.

Definition at line 172 of file sgelq.f.

Author

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