Loading...
Searching...
No Matches

## sgemlq()

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

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

  [in]

  SIDE

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

  [in]

  TRANS

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

  [in]

  M

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

  [in]

  N

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

  [in]

  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.
      !>

  [in]

  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 SGELQ.
      !>

  [in]

  LDA

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

  [in]

  T

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

  [in]

  TSIZE

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

  [in,out]

  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.
      !>

  [in]

  LDC

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

  [out]

  WORK

      !>          (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK))
      !>          On exit, if INFO = 0, WORK(1) returns the minimal LWORK.
      !>

  [in]

  LWORK

      !>          LWORK is INTEGER
      !>          The dimension of the array WORK. LWORK >= 1.
      !>          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.
      !>

  [out]

  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 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.
      !>