sgemlq.f(3)

NAME
sgemlq.f

SYNOPSIS

  Functions/Subroutines
subroutine sgemlq (SIDE, TRANS, M, N, K, A, LDA, T, TSIZE, C, LDC, WORK, LWORK, INFO)

Function/Subroutine Documentation

  subroutine sgemlq (character SIDE, character TRANS, integer M, integer N, integer K, real, dimension( lda, * ) A, integer LDA, real, dimension( * ) T, integer TSIZE, real, dimension( ldc, * ) C, integer LDC, real, dimension( * ) WORK, integer LWORK, integer INFO)

Purpose:

SGEMLQ overwrites the general real M-by-N matrix C with

SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * C C * Q TRANS = 'T': Q**T * C C * Q**T where Q is a real orthogonal matrix defined as the product of blocked elementary reflectors computed by short wide LQ factorization (SGELQ)

Parameters:
    SIDE

              SIDE is CHARACTER*1
              = 'L': apply Q or Q**T from the Left;
              = 'R': apply Q or Q**T from the Right.

    TRANS

              TRANS is CHARACTER*1
              = 'N':  No transpose, apply Q;
              = 'T':  Transpose, apply Q**T.

    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 C. N >= 0.

    K

              K is INTEGER
              The number of elementary reflectors whose product defines
              the matrix Q.
              If SIDE = 'L', M >= K >= 0;
              if SIDE = 'R', N >= K >= 0.

    A

              A is REAL array, dimension
                                   (LDA,M) if SIDE = 'L',
                                   (LDA,N) if SIDE = 'R'
              Part of the data structure to represent Q as returned by DGELQ.

    LDA

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

    T

              T is REAL array, dimension (MAX(5,TSIZE)).
              Part of the data structure to represent Q as returned by SGELQ.

    TSIZE

              TSIZE is INTEGER
              The dimension of the array T. TSIZE >= 5.

    C

              C is REAL array, dimension (LDC,N)
              On entry, the M-by-N matrix C.
              On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.

    LDC

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

    WORK

             (workspace) REAL array, dimension (MAX(1,LWORK))

    LWORK

              LWORK is INTEGER
              The dimension of the array WORK.
              If LWORK = -1, then a workspace query is assumed. The routine
              only calculates the size of the WORK array, returns this
              value as WORK(1), and no error message related to WORK
              is issued by XERBLA.

    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

These details are particular for this LAPACK implementation. Users should not take them for granted. These details may change in the future, and are unlikely not 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 wide-and-short) or SGELQT to compute the LQ factorization. This version of SGEMLQ will use either SLAMSWLQ or SGEMLQT to multiply matrix Q by another matrix. Further Details in SLAMSWLQ or SGEMLQT.

Definition at line 169 of file sgemlq.f.

Author

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