STPRFB(3)

💅 STPRFB(3) — Library Functions Manual 💅

okay bestie, you're in STPRFB(3), a Library Functions Manual page. Its header path is /home/abui...RC/stprfb.f(3). This is the group chat where a real block reflector gets applied to a real matrix, and the whole thing is composed of two blocks. It's giving "math but make it iconic." 💖

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✨ NAME ✨

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/stprfb.f

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🦋 SYNOPSIS 🦋

🌈 Functions/Subroutines

• subroutine STPRFB (side, trans, direct, storev, m, n, k, l, v, ldv, t, ldt, a, lda, b, ldb, work, ldwork) — the one and only. It applies a real "triangular-pentagonal" block reflector to a real matrix, and yes, that matrix is composed of two blocks. Slay.

The synopsis blurb is literally this:

STPRFB applies a real triangular-
pentagonal"blockreflectortoarealmatrix,whichiscomposedoftwoblocks.

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💖 Function/Subroutine Documentation 💖

👑 subroutine STPRFB

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

This icon does exactly one job: STPRFB applies a real "triangular-pentagonal" block reflector to a real matrix, which is composed of two blocks.

🎯 Purpose:

okay so the purpose is literally this:

STPRFB 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.

No cap, that's the whole vibe. 🫶

🧩 Parameters

• SIDE — SIDE is CHARACTER*1. This is the side switch, main-character energy only:
  • = 'L': apply H or H**T from the Left
  • = 'R': apply H or H**T from the Right
• TRANS — TRANS is CHARACTER*1. Transpose check, bestie:
  • = '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 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 — 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 REAL 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 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 HT*C or C*H or C*HT. 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 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 HT*C or C*H or C*HT. See Further Details.
• LDB — LDB is INTEGER. The leading dimension of the array B.
  • LDB >= max(1,M).
• WORK — WORK is REAL 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, this is the lore drop. 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 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.

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.

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)

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 at line 249 of file stprfb.f.

🫶 Author

Generated automatically by Doxygen for LAPACK from the source code.

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That's the whole page, bestie. Footer vibes: LAPACK Version 3.12.0, path /home/abui...RC/stprfb.f(3) — no extra date line on this one, iykyk. Stay legendary. 💖