DTPRFB(3)

💖 DTPRFB(3) — Library Functions Manual bestie 💖

okay so this is the Library Functions Manual page for DTPRFB(3), and it is lowkey a whole Fortran moment. ✨

🌸 NAME 🌸

The NAME field is literally this source file path, no cap:

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

✨ SYNOPSIS ✨

🫶 Functions/Subroutines 🫶

Here’s the synopsis exactly as it appears — yes, the spacing and quoting got a little feral, but that’s iconic:

subroutine DTPRFB (side, trans, direct, storev, m, n, k, l, v, ldv, t,
    ldt, a, lda, b, ldb, work, ldwork)
    DTPRFB applies a real triangular-
    pentagonal"blockreflectortoarealmatrix,whichiscomposedoftwoblocks.

💅 Function/Subroutine Documentation 💅

DTPRFB applies a real "triangular-pentagonal" block reflector to a real matrix, which is composed of two blocks. 🫶

Here’s the full signature, character for character:

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)

🎀 Purpose 🎀

okay so the purpose block is giving main character energy:

!>
!> 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.
!>
!>

💖 Parameters 💖

• SIDE — CHARACTER*1. This is the left/right vibe check:
  • = 'L': apply H or H**T from the Left
  • = 'R': apply H or H**T from the Right
• TRANS — CHARACTER*1. Transpose or no transpose, bestie:
  • = 'N': apply H (No transpose)
  • = 'T': apply H**T (Transpose)
• DIRECT — CHARACTER*1. Tells you 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 — CHARACTER*1. Tells you how the vectors that define the elementary reflectors are stored:
  • = 'C': Columns
  • = 'R': Rows
• M — INTEGER. The number of rows of the matrix B. M >= 0.
• N — INTEGER. The number of columns of the matrix B. N >= 0.
• K — INTEGER. The order of the matrix T, i.e. the number of elementary reflectors whose product defines the block reflector. K >= 0.
• L — INTEGER. The order of the trapezoidal part of V. K >= L >= 0. See Further Details.
• V — 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 — 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 — DOUBLE PRECISION array, dimension (LDT,K). The triangular K-by-K matrix T in the representation of the block reflector.
• LDT — INTEGER. The leading dimension of the array T. LDT >= K.
• A — 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 — INTEGER. The leading dimension of the array A.
  • If SIDE = 'L', LDA >= max(1,K);
  • If SIDE = 'R', LDA >= max(1,M).
• B — 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 — INTEGER. The leading dimension of the array B. LDB >= max(1,M).
• WORK — DOUBLE PRECISION array, dimension:
  • (LDWORK,N) if SIDE = 'L',
  • (LDWORK,K) if SIDE = 'R'.
• LDWORK — 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 🌟

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 dtprfb.f.

🦋 Author 🦋

Generated automatically by Doxygen for LAPACK from the source code.

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