LAMSWLQ - 5.2 English - 68552

LAMSWLQ overwrites the general real M-by-N matrix C.

Purpose:

 LAMSWLQ 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 (LASWLQ)

Parameters:

• SIDE – [in]

  SIDE is CHARACTER*1

  = ‘L’: apply Q or Q**T from the Left;

  = ‘R’: apply Q or Q**T from the Right.

• TRANS – [in]

  TRANS is CHARACTER*1

  = ‘N’: No transpose, apply Q;

  = ‘T’: Transpose, apply Q**T.

• M – [in]

  M is INTEGER

  The number of rows of the matrix C. M >=0.

• N – [in]

  N is INTEGER

  The number of columns of the matrix C. N >= M.

• K – [in]

  K is INTEGER

  The number of elementary reflectors whose product defines the matrix Q. M >= K >= 0;

• MB – [in]

  MB is INTEGER

  The row block size to be used in the blocked QR. M >= MB >= 1

• NB – [in]

  NB is INTEGER

  The column block size to be used in the blocked QR. NB > M.

• NB – [in]

  NB is INTEGER

  The block size to be used in the blocked QR. MB > M.

• A – [in]

  A is REAL array, dimension

  (LDA,M) if SIDE = ‘L’,

  (LDA,N) if SIDE = ‘R’

  The i-th row must contain the vector which defines the blocked elementary reflector H(i), for i = 1,2,…,k, as returned by SLASWLQ in the first k rows of its array argument A.

• LDA – [in]

  LDA is INTEGER

  The leading dimension of the array A.

  If SIDE = ‘L’, LDA >= fla_max(1,M);

  if SIDE = ‘R’, LDA >= fla_max(1,N).

• T – [in]

  T is REAL array, dimension

  (M * Number of blocks(CEIL(N-K/NB-K)),

  The blocked upper triangular block reflectors stored in compact form as a sequence of upper triangular blocks. See below for further details.

• LDT – [in]

  LDT is INTEGER

  The leading dimension of the array T. LDT >= MB.

• C – [inout]

  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 – [in]

  LDC is INTEGER

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

• WORK – [out] (workspace) REAL array, dimension (MAX(1,LWORK))

• LWORK – [in]

  LWORK is INTEGER

  The dimension of the array WORK.

  If SIDE = ‘L’, LWORK >= fla_max(1,NB) * MB;

  if SIDE = ‘R’, LWORK >= fla_max(1,M) * MB.

  If LWORK = -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 LWORK is issued by XERBLA.

• INFO – [out]

  INFO is INTEGER

  = 0: successful exit

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