SRC/ctgexc.f(3)

📦
version 3.12.1 · 7 versions
, in arch rolling

✨ NAME ✨

SRC/ctgexc.f — bestie, this is the page for ctgexc, a LAPACK routine that literally just… reorders your generalized Schur decomposition. No cap. 🦋

✨ SYNOPSIS ✨

Functions/Subroutines

  • subroutine ctgexc (wantq, wantz, n, a, lda, b, ldb, q, ldq, z, ldz, ifst, ilst, info) — the one and only, CTGEXC herself 👑

💅 Function/Subroutine Documentation 💅

subroutine ctgexc 🎀

Here's the full signature, character for character, because we do not paraphrase arguments in this house:

subroutine ctgexc (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 ifst, integer ilst, integer
    info)

CTGEXC ✨

🎯 Purpose

Okay so boom — CTGEXC reorders the generalized Schur decomposition of a complex matrix pair (A,B), using an unitary equivalence transformation (A, B) := Q * (A, B) * Z**H, so that the diagonal block of (A, B) with row index IFST is moved to row ILST. Slay. 💅

(A, B) must be in generalized Schur canonical form, that is, A and B are both upper triangular. That part is not optional, bestie — it's the whole vibe check. 🧚

Optionally, the matrices Q and Z of generalized Schur vectors are updated. Cute, right?

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 decomposition is preserved exactly — that's the whole point, iykyk. 🫶

🌸 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 array, dimension (LDA,N) On entry, the upper triangular 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 array, dimension (LDB,N) On entry, the upper triangular 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 array, dimension (LDQ,N) On entry, if WANTQ = .TRUE., the unitary matrix Q. On exit, the updated matrix Q. If WANTQ = .FALSE., Q is not referenced. (She's literally not even invited to the function 💀)

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) On entry, if WANTZ = .TRUE., the unitary matrix Z. On exit, the updated matrix Z. If WANTZ = .FALSE., Z is not referenced.

LDZ

LDZ is INTEGER The leading dimension of the array Z. LDZ >= 1; If WANTZ = .TRUE., LDZ >= N.

IFST

IFST is INTEGER

ILST

ILST is INTEGER Specify the reordering of the diagonal blocks of (A, B). The block with row index IFST is moved to row ILST, by a sequence of swapping between adjacent blocks. 🔁

INFO

INFO is INTEGER

  • =0: Successful exit. 🎉
  • <0: if INFO = -i, the i-th argument had an illegal value.
  • =1: The transformed matrix pair (A, B) would be too far from generalized Schur form; the problem is ill-conditioned. (A, B) may have been partially reordered, and ILST points to the first row of the current position of the block being moved.
Okay so INFO = 1 is the situationship of exit codes — it's not a full-on error exactly, but it's not clean either. Things are ill-conditioned, (A, B) may have been partially reordered, and ILST is now pointing at the first row of wherever the block being moved currently is. Read it carefully, bestie. 😭

👑 Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

🍓 Contributors:

Bo Kagstrom and Peter Poromaa, Department of Computing Science, Umea University, S-901 87 Umea, Sweden. Absolute icons, both of them. 🌟

🌈 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.
  3. B. Kagstrom and P. Poromaa, LAPACK-Style Algorithms and Software for Solving the Generalized Sylvester Equation and Estimating the Separation between Regular Matrix Pairs, Report UMINF - 93.23, Department of Computing Science, Umea University, S-901 87 Umea, Sweden, December 1993, Revised April 1994, Also as LAPACK working Note 75. To appear in ACM Trans. on Math. Software, Vol 22, No 1, 1996.

Definition at line 198 of file ctgexc.f. 🎀

✨ Author ✨

Generated automatically by Doxygen for LAPACK from the source code. (Not a real person, just the robot doing her thing. Iconic behaviour, fr fr. 🤖💜)

That's the whole page, bestie — LAPACK Version 3.12.0, SRC/ctgexc.f(3). Go forth and reorder those diagonal blocks responsibly. 💖✨🦋

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