ZTGEX2(3)

💖 NAME 💖

okay so this is the ztgex2.f(3) page from the Library Functions Manual, bestie 💅. The file it’s repping is:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/ztgex2.f

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✨ SYNOPSIS ✨

🌸 Functions/Subroutines 🌸

Here’s the subroutine vibe check:

subroutine ZTGEX2 (wantq, wantz, n, a, lda, b, ldb, q, ldq, z, ldz, j1,
    info)

ZTGEX2 swaps adjacent diagonal blocks in an upper (quasi) triangular matrix pair by an unitary equivalence transformation. periodt 💫

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🎀 Function/Subroutine Documentation 🎀

The full signature situation is literally this:

subroutine ZTGEX2 (logical wantq, logical wantz, integer n, complex*16,
    dimension( lda, * ) a, integer lda, complex*16, dimension( ldb, * ) b,
    integer ldb, complex*16, dimension( ldq, * ) q, integer ldq, complex*16,
    dimension( ldz, * ) z, integer ldz, integer j1, integer info)

ZTGEX2 swaps adjacent diagonal blocks in an upper (quasi) triangular matrix pair by an unitary equivalence transformation. iconic ✨

🌸 Purpose: 🌸

okay so the purpose is literally this, no cap:

• ZTGEX2 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.

And the equations it keeps are:

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

🍓 Parameters 🍓

• WANTQ — WANTQ is LOGICAL. .TRUE.: update the left transformation matrix Q; .FALSE.: do not update Q.
• WANTZ — WANTZ is LOGICAL. .TRUE.: update the right transformation matrix Z; .FALSE.: do not update Z.
• N — N is INTEGER. The order of the matrices A and B. N >= 0.
• A — A is COMPLEX*16 array, dimensions (LDA,N). On entry, the matrix A in the pair (A, B). On exit, the updated matrix A.
• LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,N).
• B — B is COMPLEX*16 array, dimensions (LDB,N). On entry, the matrix B in the pair (A, B). On exit, the updated matrix B.
• LDB — LDB is INTEGER. The leading dimension of the array B. LDB >= max(1,N).
• Q — Q is COMPLEX*16 array, dimension (LDQ,N). If WANTQ = .TRUE, on entry, the unitary matrix Q. On exit, the updated matrix Q. Not referenced if WANTQ = .FALSE..
• LDQ — LDQ is INTEGER. The leading dimension of the array Q. LDQ >= 1; If WANTQ = .TRUE., LDQ >= N.
• Z — Z is COMPLEX*16 array, dimension (LDZ,N). If WANTZ = .TRUE, on entry, the unitary matrix Z. On exit, the updated matrix Z. Not referenced if WANTZ = .FALSE..
• 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).
• INFO — INFO is INTEGER. =0: Successful exit. =1: The transformed matrix pair (A, B) would be too far from generalized Schur form; the problem is ill-conditioned.

🫶 Author 🫶

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

💜 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.

📚 References: 📚

1. [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. [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.

Definition at line 188 of file ztgex2.f.

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🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

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Cute sign-off: this page’s footer says LAPACK Version 3.12.0 and points back to /home/abui...RC/ztgex2.f(3). No date is listed up in here, so we’re not inventing one 💅✨🫶