LATSQR - 5.2 English - 68552

AOCL API Guide (68552)

Document ID
68552
Release Date
2025-12-29
Version
5.2 English
template<typename T>
void latsqr(integer *m, integer *n, integer *mb, integer *nb, T *a, integer *lda, T *t, integer *ldt, T *work, integer *lwork, integer *info)#

LATSQR computes a blocked Tall-Skinny QR factorization of a real M-by-N matrix A for M >= N.

Purpose:

   LATSQR computes a blocked Tall-Skinny QR factorization of
   a real M-by-N matrix A for M >= N:

      A = Q * (R),
              (0)

   where:

      Q is a M-by-M orthogonal matrix, stored on exit in an implicit
      form in the elements below the digonal of the array A and in
      the elemenst of the array T;

      R is an upper-triangular N-by-N matrix, stored on exit in
      the elements on and above the diagonal of the array A.

      0 is a (M-N)-by-N zero matrix, and is not stored.
Parameters:
  • 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 A. M >= N >= 0.

  • MB[in]

    MB is INTEGER

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

  • NB[in]

    NB is INTEGER

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

  • A[inout]

    A is REAL array, dimension (LDA,N)

    On entry, the M-by-N matrix A.

    On exit, the elements on and above the diagonal of the array contain the N-by-N upper triangular matrix R; the elements below the diagonal represent Q by the columns of blocked V (see Further Details).
  • LDA[in]

    LDA is INTEGER

    The leading dimension of the array A. LDA >= fla_max(1,M).

  • T[out]

    T is REAL array, dimension (LDT, N * Number_of_row_blocks)

    where Number_of_row_blocks = CEIL((M-N)/(MB-N))

    The blocked upper triangular block reflectors stored in compact form as a sequence of upper triangular blocks. See Further Details below.
  • LDT[in]

    LDT is INTEGER

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

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

  • LWORK[in]

    The dimension of the array WORK. LWORK >= NB*N.

    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