LAMTSQR - 5.2 English - 68552

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

Purpose:

   LAMTSQR 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 tall skinny
  QR factorization (DLATSQR)

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 A. M >=0.

• N – [in]

  N is INTEGER

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

• K – [in]

  K is INTEGER

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

• MB – [in]

  MB is INTEGER

  The block size to be used in the blocked QR. MB > N. (must be the same as DLATSQR)

• NB – [in]

  NB is INTEGER

  The column block size to be used in the blocked QR. N >= NB >= 1.

• A – [in]

  A is REAL array, dimension (LDA,K)

  The i-th column must contain the vector which defines the blockedelementary reflector H(i), for i = 1,2,…,k, as returned by DLATSQR in the first k columns 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

  (N * Number of blocks(CEIL(M-K/MB-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 >= NB.

• 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,N)*NB;

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

  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