TPRFB - 5.2 English - 68552

AOCL API Guide (68552)

Document ID
68552
Release Date
2025-12-29
Version
5.2 English
template<typename T>
void tprfb(char *side, char *trans, char *direct, char *storev, integer *m, integer *n, integer *k, integer *l, T *v, integer *ldv, T *t, integer *ldt, T *a, integer *lda, T *b, integer *ldb, T *work, integer *ldwork)#

TPRFB applies a real or complex “triangular-pentagonal” blocked

reflector to a real or complex matrix, which is composed of two blocks.

Purpose:

  TPRFB applies a real "triangular-pentagonal" block reflector H or its
  conjugate transpose H^H to a real matrix C, which is composed of two
  blocks A and B, either from the left or right.
Parameters:
  • SIDE[in]

    SIDE is CHARACTER*1

    = ‘L’: apply H or H^H from the Left

    = ‘R’: apply H or H^H from the Right
  • TRANS[in]

    TRANS is CHARACTER*1

    = ‘N’: apply H (No transpose)

    = ‘C’: apply H^H (Conjugate transpose)
  • DIRECT[in]

    DIRECT is CHARACTER*1

    Indicates how H is formed from a product of elementary reflectors

    = ‘F’: H = H(1) H(2) … H(k) (Forward)

    = ‘B’: H = H(k) … H(2) H(1) (Backward)

  • STOREV[in]

    STOREV is CHARACTER*1

    Indicates how the vectors which define the elementary reflectors are stored:

    = ‘C’: Columns

    = ‘R’: Rows

  • M[in]

    M is INTEGER

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

  • N[in]

    N is INTEGER

    The number of columns of the matrix B. N >= 0.

  • K[in]

    K is INTEGER

    The order of the matrix T, i.e. the number of elementary reflectors whose product defines the block reflector. K >= 0.

  • L[in]

    L is INTEGER

    The order of the trapezoidal part of V. K >= L >= 0. See Further Details.

  • V[in]

    V is REAL array, dimension

    (LDV,K) if STOREV = ‘C’

    (LDV,M) if STOREV = ‘R’ and SIDE = ‘L’

    (LDV,N) if STOREV = ‘R’ and SIDE = ‘R’

    The pentagonal matrix V, which contains the elementary reflectors H(1), H(2), …, H(K). See Further Details.
  • LDV[in]

    LDV is INTEGER

    The leading dimension of the array V.

    If STOREV = ‘C’ and SIDE = ‘L’, LDV >= fla_max(1,M);

    if STOREV = ‘C’ and SIDE = ‘R’, LDV >= fla_max(1,N);

    if STOREV = ‘R’, LDV >= K.
  • T[in]

    T is REAL array, dimension (LDT,K)

    The triangular K-by-K matrix T in the representation of the block reflector.

  • LDT[in]

    LDT is INTEGER

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

  • A[inout]

    A is REAL array, dimension (LDA,N) if SIDE = ‘L’ or (LDA,K) if SIDE = ‘R’

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

    On exit, A is overwritten by the corresponding block of H*C or H^H*C or C*H or C*H^H. See Further Details.
  • LDA[in]

    LDA is INTEGER

    The leading dimension of the array A.

    If SIDE = ‘L’, LDA >= fla_max(1,K);

    If SIDE = ‘R’, LDA >= fla_max(1,M).

  • B[inout]

    B is REAL array, dimension (LDB,N)

    On entry, the M-by-N matrix B. On exit, B is overwritten by the corresponding block of H*C or H^H*C or C*H or C*H^H. See Further Details.

  • LDB[in]

    LDB is INTEGER

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

  • WORK[out]

    WORK is REAL array, dimension

    (LDWORK,N) if SIDE = ‘L’,

    (LDWORK,K) if SIDE = ‘R’.
  • LDWORK[in]

    LDWORK is INTEGER

    The leading dimension of the array WORK.

    If SIDE = ‘L’, LDWORK >= K;

    if SIDE = ‘R’, LDWORK >= M.