TPQRT2 - 5.2 English - 68552

AOCL API Guide (68552)

Document ID
68552
Release Date
2025-12-29
Version
5.2 English
template<typename T>
void tpqrt2(integer *m, integer *n, integer *l, T *a, integer *lda, T *b, integer *ldb, T *t, integer *ldt, integer *info)#

TPQRT2 computes a QR factorization of a real or complex

”triangular-pentagonal” matrix, which is composed of a triangular block

and a pentagonal block, using the compact WY representation for Q.

Purpose:

  TPQRT2 computes a QR factorization of a real "triangular-pentagonal"
  matrix C, which is composed of a triangular block A and pentagonal block B,
  using the compact WY representation for Q.
Parameters:
  • M[in]

    M is INTEGER

    The total number of rows of the matrix B. M >= 0.

  • N[in]

    N is INTEGER

    The number of columns of the matrix B, and the order of the triangular matrix A. N >= 0.

  • L[in]

    L is INTEGER

    The number of rows of the upper trapezoidal part of B. MIN(M,N) >= L >= 0. See Further Details.

  • A[inout]

    A is REAL array, dimension (LDA,N)

    On entry, the upper triangular N-by-N matrix A. On exit, the elements on and above the diagonal of the array contain the upper triangular matrix R.

  • LDA[in]

    LDA is INTEGER

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

  • B[inout]

    B is REAL array, dimension (LDB,N)

    On entry, the pentagonal M-by-N matrix B. The first M-L rows are rectangular, and the last L rows are upper trapezoidal. On exit, B contains the pentagonal matrix V. See Further Details.

  • LDB[in]

    LDB is INTEGER

    The leading dimension of the array B. LDB >= fla_max(1,M).

  • T[out]

    T is REAL array, dimension (LDT,N)

    The N-by-N upper triangular factor T of the block reflector. See Further Details.

  • LDT[in]

    LDT is INTEGER

    The leading dimension of the array T. LDT >= fla_max(1,N)

  • INFO[out]

    INFO is INTEGER

    = 0: successful exit

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