SRC/ctgex2.f(3)

📦
version 3.12.1 · 4 versions
, in arch rolling

🦋 SRC/ctgex2.f 💅

okay so bestie, this is a page from the LAPACK Library Functions Manual — yes the whole manual, the header line was SRC/ctgex2.f(3) and I'm folding that in here bc we're cute like that 🎀

✨ NAME ✨

SRC/ctgex2.f — the file, the icon, the moment. 🌟

🫶 SYNOPSIS 🫶

Functions/Subroutines

subroutine ctgex2 (wantq, wantz, n, a, lda, b, ldb, q, ldq, z, ldz, j1,
    info)

CTGEX2 swaps adjacent diagonal blocks in an upper (quasi) triangular matrix pair by an unitary equivalence transformation. literally its whole personality 💫

👑 Function/Subroutine Documentation 👑

subroutine ctgex2 (logical wantq, logical wantz, integer n, complex,
    dimension( lda, * ) a, integer lda, complex, dimension( ldb, * ) b,
    integer ldb, complex, dimension( ldq, * ) q, integer ldq, complex,
    dimension( ldz, * ) z, integer ldz, integer j1, integer info)

CTGEX2 swaps adjacent diagonal blocks in an upper (quasi) triangular matrix pair by an unitary equivalence transformation. no cap, that's the whole gig 🔥

🌸 Purpose 🌸

CTGEX2 swaps adjacent diagonal 1 by 1 blocks (A11,B11) and (A22,B22) in an upper triangular matrix pair (A, B) by an unitary equivalence transformation.
(A, B) must be in generalized Schur canonical form, that is, A and B are both upper triangular.
Optionally, the matrices Q and Z of generalized Schur vectors are updated.
Q(in) * A(in) * Z(in)**H = Q(out) * A(out) * Z(out)**H
Q(in) * B(in) * Z(in)**H = Q(out) * B(out) * Z(out)**H

like, the vibe check is: swap those two diagonal blocks and keep everything equivalent 💜

🎀 Parameters 🎀

  • WANTQ — WANTQ is LOGICAL. .TRUE. : update the left transformation matrix Q; .FALSE.: do not update Q. bestie gets to choose 🙈
  • WANTZ — WANTZ is LOGICAL. .TRUE. : update the right transformation matrix Z; .FALSE.: do not update Z. same energy, other side 🦋
  • N — N is INTEGER. The order of the matrices A and B. N >= 0. main character dimension ✨
  • A — A is COMPLEX array, dimension (LDA,N). On entry, the matrix A in the pair (A, B). On exit, the updated matrix A. glow-up confirmed 💅
  • LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,N). respect the leading dimension pls 🫶
  • B — B is COMPLEX array, dimension (LDB,N). On entry, the matrix B in the pair (A, B). On exit, the updated matrix B. also slaying 🌈
  • LDB — LDB is INTEGER. The leading dimension of the array B. LDB >= max(1,N). 👑
  • Q — Q is COMPLEX array, dimension (LDQ,N). If WANTQ = .TRUE, on entry, the unitary matrix Q. On exit, the updated matrix Q. Not referenced if WANTQ = .FALSE.. she only shows up when invited 🎀
  • LDQ — LDQ is INTEGER. The leading dimension of the array Q. LDQ >= 1; if WANTQ = .TRUE., LDQ >= N. 🧚
  • Z — Z is COMPLEX array, dimension (LDZ,N). If WANTZ = .TRUE, on entry, the unitary matrix Z. On exit, the updated matrix Z. Not referenced if WANTZ = .FALSE.. she's lowkey optional too 💫
  • LDZ — LDZ is INTEGER. The leading dimension of the array Z. LDZ >= 1; if WANTZ = .TRUE., LDZ >= N. ⭐
  • J1 — J1 is INTEGER. The index to the first block (A11, B11). it's giving "start here" 📍
  • INFO — INFO is INTEGER. Exit status, and it is not subtle:
    • =0: Successful exit. we love a win 💖
    • =1: The transformed matrix pair (A, B) would be too far from generalized Schur form; the problem is ill-conditioned. 😭 yeah that one hurts

💀 Author 💀

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

the whole squad showed up fr fr 🫶

🔍 Further Details 🔍

In the current code both weak and strong stability tests are performed. The user can omit the strong stability test by changing the internal logical parameter WANDS to .FALSE.. See ref. [2] for details. iykyk 👀

🌟 Contributors 🌟

Bo Kagstrom and Peter Poromaa, Department of Computing Science, Umea University, S-901 87 Umea, Sweden. legends, honestly 👑

📚 References 📚

  1. B. Kagstrom; A Direct Method for Reordering Eigenvalues in the Generalized Real Schur Form of a Regular Matrix Pair (A, B), in M.S. Moonen et al (eds), Linear Algebra for Large Scale and Real-Time Applications, Kluwer Academic Publ. 1993, pp 195-218.
  2. B. Kagstrom and P. Poromaa; Computing Eigenspaces with Specified Eigenvalues of a Regular Matrix Pair (A, B) and Condition Estimation: Theory, Algorithms and Software, Report UMINF-94.04, Department of Computing Science, Umea University, S-901 87 Umea, Sweden, 1994. Also as LAPACK Working Note 87. To appear in Numerical Algorithms, 1996.

required reading bestie, sorry not sorry 🍓

Definition at line 188 of file ctgex2.f. that's the exact line, don't come for me 💅

🌸 Author 🌸

Generated automatically by Doxygen for LAPACK from the source code. the bot did its thing, we respect it 🤖✨

aaaand scene — LAPACK Version 3.12.0, page SRC/ctgex2.f(3), that's a wrap bestie 💖🎀🦋

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