/home/abui.../ctpmqrt.f(3)

🌸 ctpmqrt.f — LAPACK Library Functions Manual 🌸

okay bestie, so this page lives at /home/abui.../ctpmqrt.f(3) in the LAPACK Library Functions Manual, and it's literally all about one single icon of a subroutine. she's giving main character energy and she does one thing: she applies a complex orthogonal matrix Q to a general complex matrix C. and C is actually two blocks, A and B. periodt. 💅

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✨ NAME ✨

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

like, that's the whole name. it's a whole path. she's not mysterious, she's just filed very specifically. 🎀

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🦋 SYNOPSIS 🦋

Functions/Subroutines

subroutine CTPMQRT (side, trans, m, n, k, l, nb, v, ldv, t, ldt, a, lda,
    b, ldb, work, info)

CTPMQRT

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👑 Function/Subroutine Documentation 👑

subroutine CTPMQRT (character side, character trans, integer m, integer n,
    integer k, integer l, integer nb, complex, dimension( ldv, * ) v,
    integer ldv, complex, dimension( ldt, * ) t, integer ldt, complex,
    dimension( lda, * ) a, integer lda, complex, dimension( ldb, * ) b,
    integer ldb, complex, dimension( * ) work, integer info)

CTPMQRT — yes, again. she said her name twice, she's confident, let her have it. ✨

🌈 Purpose 🌈

!> CTPMQRT applies a complex orthogonal matrix Q obtained from a !> complex block reflector H to a general !> complex matrix C, which consists of two blocks A and B. !>

translation: Q came from a complex block reflector H, and now she's getting applied to a general complex matrix C — which is lowkey just two blocks, A and B, living their lives stacked or side-by-side depending on the vibe. 🔥

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💖 Parameters 💖

• SIDE — SIDE is CHARACTER*1 🫶
  • = 'L': apply Q or Q**H from the Left;
  • = 'R': apply Q or Q**H from the Right.
• TRANS — TRANS is CHARACTER*1 🦋
  • = 'N': No transpose, apply Q;
  • = 'C': Conjugate transpose, apply Q**H.
• M — M is INTEGER. the number of rows of the matrix B. M >= 0. not me measuring the height of B 😭
• N — N is INTEGER. the number of columns of the matrix B. N >= 0. and this is her width. both non-negative, we respect that. 🎀
• K — K is INTEGER. the number of elementary reflectors whose product defines the matrix Q. it's giving "built from pieces" and honestly? iconic. 👑
• L — L is INTEGER. the order of the trapezoidal part of V. K >= L >= 0. see Further Details, babes, it's down there. 💜
• NB — NB is INTEGER. the block size used for the storage of T. K >= NB >= 1. 🚨 and listen: this must be the same value of NB used to generate T in CTPQRT. no cap, it has to match, do not freestyle this one.
• V — V is COMPLEX array, dimension (LDV,K). the i-th column must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by CTPQRT in B. see Further Details. 🌸
• LDV — LDV is INTEGER. the leading dimension of the array V.
  • If SIDE = 'L', LDV >= max(1,M);
  • if SIDE = 'R', LDV >= max(1,N).
• T — T is COMPLEX array, dimension (LDT,K). the upper triangular factors of the block reflectors as returned by CTPQRT, stored as a NB-by-K matrix. 💫
• LDT — LDT is INTEGER. the leading dimension of the array T. LDT >= NB.
• A — A is COMPLEX 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 Q*C or Q**H*C or C*Q or C*Q**H. See Further Details. 🪞 (yes she comes back different, that's the whole point)

• LDA — LDA is INTEGER. the leading dimension of the array A. ok so heads up, word for word from the source: If SIDE = 'L', LDC >= max(1,K); If SIDE = 'R', LDC >= max(1,M). 🫶 that's literally what it says, I'm not editing the queen's handwriting.
• B — B is COMPLEX array, dimension (LDB,N). On entry, the M-by-N matrix B. On exit, B is overwritten by the corresponding block of Q*C or Q**H*C or C*Q or C*Q**H. See Further Details. 🦋
• LDB — LDB is INTEGER. the leading dimension of the array B. LDB >= max(1,M). that's it, that's the rule.
• WORK — WORK is COMPLEX array. the dimension of WORK is N*NB if SIDE = 'L', or M*NB if SIDE = 'R'. ✨ size her correctly pls, she's working.
• INFO — INFO is INTEGER 📣
  • = 0: successful exit (slay)
  • < 0: if INFO = -i, the i-th argument had an illegal value (oop — go check argument number i)

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🌟 Author 🌟

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

the whole friend group co-signed this one. 🫶

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💅 Further Details: 💅

!> The columns of the pentagonal matrix V contain the elementary reflectors !> H(1), H(2), ..., H(K); V is composed of a rectangular block V1 and a !> trapezoidal block V2: > > V = [V1] > [V2]. > > The size of the trapezoidal block V2 is determined by the parameter L, > where 0 <= L <= K; V2 is upper trapezoidal, consisting of the first L > rows of a K-by-K upper triangular matrix. If L=K, V2 is upper triangular; > if L=0, there is no trapezoidal block, hence V = V1 is rectangular. > > If SIDE = 'L': C = [A] where A is K-by-N, B is M-by-N and V is M-by-K. > [B] > > If SIDE = 'R': C = [A B] where A is M-by-K, B is M-by-N and V is N-by-K. > > The complex orthogonal matrix Q is formed from V and T. > > If TRANS='N' and SIDE='L', C is on exit replaced with Q * C. > > If TRANS='C' and SIDE='L', C is on exit replaced with Q**H * C. > > If TRANS='N' and SIDE='R', C is on exit replaced with C * Q. > > If TRANS='C' and SIDE='R', C is on exit replaced with C * Q**H. >

so real quick, the shapes recap because I know you're a visual learner bestie 🧚

• SIDE = 'L' → C is stacked, A on top of B. A is K-by-N, B is M-by-N, V is M-by-K.
• SIDE = 'R' → C is side-by-side, [A B]. A is M-by-K, B is M-by-N, V is N-by-K.
• Q itself is formed from V and T. those two are a package deal, iykyk. 💜

and the four exit vibes, one more time so it's crystal:

• TRANS='N' + SIDE='L' → Q * C
• TRANS='C' + SIDE='L' → Q**H * C
• TRANS='N' + SIDE='R' → C * Q
• TRANS='C' + SIDE='R' → C * Q**H

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🔍 Definition 🔍

Definition at line 214 of file ctpmqrt.f. ⭐

Author (the meta one)

Generated automatically by Doxygen for LAPACK from the source code. 🤖 she was assembled by the robots, and she ate.

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🌈 that's the whole page, no crumbs left. shoutout to LAPACK, Version 3.12.0, and to the footer date stamp on /home/abui.../ctpmqrt.f(3) — mwah, go apply some matrices, bestie. 💖✨🎀