SRC/dtprfb.f(3)

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🌸 NAME 🌸

SRC/dtprfb.f — yes bestie, that's the page name, and this whole thing comes from the Library Functions Manual ✨

✨ SYNOPSIS ✨

Functions/Subroutines

  • subroutine dtprfb — DTPRFB applies a real “triangular-pentagonal” block reflector to a real matrix, which is composed of two blocks. She's giving math-girlie main character energy 💅
       subroutine dtprfb (side, trans, direct, storev, m, n, k, l, v, ldv, t,
           ldt, a, lda, b, ldb, work, ldwork)

🦋 Function/Subroutine Documentation 🦋

Here's the full signature, bestie — yes it's long, but she ate 😭💖

   subroutine dtprfb (character side, character trans, character direct,
       character storev, integer m, integer n, integer k, integer l, double
       precision, dimension( ldv, * ) v, integer ldv, double precision,
       dimension( ldt, * ) t, integer ldt, double precision, dimension( lda, *
       ) a, integer lda, double precision, dimension( ldb, * ) b, integer ldb,
       double precision, dimension( ldwork, * ) work, integer ldwork)

DTPRFB applies a real “triangular-pentagonal” block reflector to a real matrix, which is composed of two blocks. No cap, that's the whole vibe 🫶

Purpose

!>
!> DTPRFB applies a real  block reflector H or its
!> transpose H**T to a real matrix C, which is composed of two
!> blocks A and B, either from the left or right.
!>
!>

So basically: real block reflector H or its transpose H**T gets applied to a real matrix C, and C is built out of two blocks, A and B, and it can come from the left or the right. Iconic 💫

Parameters

SIDE

SIDE is CHARACTER*1.

  • = 'L': apply H or H**T from the Left.
  • = 'R': apply H or H**T from the Right.

TRANS

TRANS is CHARACTER*1.

  • = 'N': apply H (No transpose).
  • = 'T': apply H**T (Transpose).

DIRECT

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

STOREV is CHARACTER*1. Indicates how the vectors which define the elementary reflectors are stored:

  • = 'C': Columns.
  • = 'R': Rows.

M

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

N

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

K

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

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

V

V is DOUBLE PRECISION 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

LDV is INTEGER. The leading dimension of the array V. If STOREV = 'C' and SIDE = 'L', LDV >= max(1,M); if STOREV = 'C' and SIDE = 'R', LDV >= max(1,N); if STOREV = 'R', LDV >= K.

T

T is DOUBLE PRECISION array, dimension (LDT,K). The triangular K-by-K matrix T in the representation of the block reflector.

LDT

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

A

A is DOUBLE PRECISION 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**T*C or C*H or C*H**T. See Further Details.

LDA

LDA is INTEGER. The leading dimension of the array A. If SIDE = 'L', LDA >= max(1,K); If SIDE = 'R', LDA >= max(1,M).

B

B is DOUBLE PRECISION 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**T*C or C*H or C*H**T. See Further Details.

LDB

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

WORK

WORK is DOUBLE PRECISION array, dimension

  • (LDWORK,N) if SIDE = 'L'
  • (LDWORK,K) if SIDE = 'R'

LDWORK

LDWORK is INTEGER. The leading dimension of the array WORK. If SIDE = 'L', LDWORK >= K; if SIDE = 'R', LDWORK >= M.

Author

  • Univ. of Tennessee
  • Univ. of California Berkeley
  • Univ. of Colorado Denver
  • NAG Ltd.

Further Details

Okay so here's the lore, bestie 💅 The matrix C is a composite matrix formed from blocks A and B. The block B is of size M-by-N; if SIDE = 'R', A is of size M-by-K, and if SIDE = 'L', A is of size K-by-N.

The C shapes are literally:

If SIDE = 'R' and DIRECT = 'F', C = [A B].

If SIDE = 'L' and DIRECT = 'F', C = [A]
                                     [B].

If SIDE = 'R' and DIRECT = 'B', C = [B A].

If SIDE = 'L' and DIRECT = 'B', C = [B]
                                     [A].

The pentagonal matrix V is composed of a rectangular block V1 and a trapezoidal block V2. The size of the trapezoidal block is determined by the parameter L, where 0<=L<=K. If L=K, the V2 block of V is triangular; if L=0, there is no trapezoidal block, thus V = V1 is rectangular.

The V block eras are giving:

If DIRECT = 'F' and STOREV = 'C':  V = [V1]
                                        [V2]
   - V2 is upper trapezoidal (first L rows of K-by-K upper triangular)

If DIRECT = 'F' and STOREV = 'R':  V = [V1 V2]

   - V2 is lower trapezoidal (first L columns of K-by-K lower triangular)

If DIRECT = 'B' and STOREV = 'C':  V = [V2]
                                        [V1]
   - V2 is lower trapezoidal (last L rows of K-by-K lower triangular)

If DIRECT = 'B' and STOREV = 'R':  V = [V2 V1]

   - V2 is upper trapezoidal (last L columns of K-by-K upper triangular)

And the size tea ☕:

  • If STOREV = 'C' and SIDE = 'L', V is M-by-K with V2 L-by-K.
  • If STOREV = 'C' and SIDE = 'R', V is N-by-K with V2 L-by-K.
  • If STOREV = 'R' and SIDE = 'L', V is K-by-M with V2 K-by-L.
  • If STOREV = 'R' and SIDE = 'R', V is K-by-N with V2 K-by-L.

Definition

Definition at line 249 of file dtprfb.f.

Author

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