sgemlq.f - Man Page



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)



     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)


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


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


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


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


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


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


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


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


         (workspace) REAL array, dimension (MAX(1,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 is INTEGER
          = 0:  successful exit
          < 0:  if INFO = -i, the i-th argument had an illegal value

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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 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 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 168 of file sgemlq.f.


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Referenced By

The man page sgemlq(3) is an alias of sgemlq.f(3).

Mon Jun 28 2021 Version 3.10.0 LAPACK