DTGEXC(3)

✨ DTGEXC(3) — Library Functions Manual ✨

okay bestie, welcome to the DTGEXC page 💖 this is LAPACK’s little reordering queen: she moves diagonal blocks in a generalized real Schur decomposition and updates the transformation matrices if you ask nicely. The manual name is Library Functions Manual, and we’re about to go through every flag, constraint, and vibe check. No cap, nothing skipped. 🫶

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💅 NAME 💅

The NAME on this page is literally this file path — yes, bestie, it’s giving “who put the source path in the NAME section?” energy:

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

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🌸 SYNOPSIS 🌸

Functions/Subroutines

subroutine DTGEXC (wantq, wantz, n, a, lda, b, ldb, q, ldq, z, ldz,
    ifst, ilst, work, lwork, info)
    DTGEXC

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🦋 Function/Subroutine Documentation 🦋

Full signature, character for character:

subroutine DTGEXC (logical wantq, logical wantz, integer n, double
    precision, dimension( lda, * ) a, integer lda, double precision,
    dimension( ldb, * ) b, integer ldb, double precision, dimension( ldq, *
    ) q, integer ldq, double precision, dimension( ldz, * ) z, integer ldz,
    integer ifst, integer ilst, double precision, dimension( * ) work,
    integer lwork, integer info)
    DTGEXC

✨ Purpose ✨

okay so DTGEXC reorders the generalized real Schur decomposition of a real matrix pair (A,B) using an orthogonal equivalence transformation:

(A, B) = Q * (A, B) * Z**T,

so that the diagonal block of (A, B) with row index IFST is moved to row ILST. 💫

(A, B) must be in generalized real Schur canonical form (as returned by DGGES), i.e. A is block upper triangular with 1-by-1 and 2-by-2 diagonal blocks. B is upper triangular. 🫶

Optionally, the matrices Q and Z of generalized Schur vectors are updated:

Q(in) * A(in) * Z(in)**T = Q(out) * A(out) * Z(out)**T
Q(in) * B(in) * Z(in)**T = Q(out) * B(out) * Z(out)**T

🫶 Parameters 🫶

• WANTQ — WANTQ is LOGICAL. .TRUE. : update the left transformation matrix Q; .FALSE. : do not update Q. It’s literally the “do I touch Q?” switch. 🎀
• WANTZ — WANTZ is LOGICAL. .TRUE. : update the right transformation matrix Z; .FALSE. : do not update Z. Same energy for Z, bestie. ✨
• N — N is INTEGER. The order of the matrices A and B. N >= 0. No negative girlies allowed. 💅
• A — A is DOUBLE PRECISION array, dimension (LDA,N). On entry, the matrix A in generalized real Schur canonical form. On exit, the updated matrix A, again in generalized real Schur canonical form. 🦋
• LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,N). Respect the leading dimension, periodt. 🌸
• B — B is DOUBLE PRECISION array, dimension (LDB,N). On entry, the matrix B in generalized real Schur canonical form (A,B). On exit, the updated matrix B, again in generalized real Schur canonical form (A,B). 🧚
• LDB — LDB is INTEGER. The leading dimension of the array B. LDB >= max(1,N). 🎀
• Q — Q is DOUBLE PRECISION array, dimension (LDQ,N). On entry, if WANTQ = .TRUE., the orthogonal matrix Q. On exit, the updated matrix Q. If WANTQ = .FALSE., Q is not referenced. 🙈
• LDQ — LDQ is INTEGER. The leading dimension of the array Q. LDQ >= 1. If WANTQ = .TRUE., LDQ >= N. 📏
• Z — Z is DOUBLE PRECISION array, dimension (LDZ,N). On entry, if WANTZ = .TRUE., the orthogonal 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. That’s it — the rest of the reordering lore is under ILST below. 👀
• 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. On exit, if IFST pointed on entry to the second row of a 2-by-2 block, it is changed to point to the first row; ILST always points to the first row of the block in its final position (which may differ from its input value by +1 or -1). 1 <= IFST, ILST <= N. 🔥
• WORK — WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the optimal LWORK. ✨
• LWORK — LWORK is INTEGER. The dimension of the array WORK. LWORK >= 1 when N <= 1, otherwise LWORK >= 4*N + 16. If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA. 🫶
• 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. 😭

👑 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.

📚 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.

Definition at line 218 of file dtgexc.f.

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🤖 Author 🤖

Generated automatically by Doxygen for LAPACK from the source code.

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💖 That’s the whole page, bestie — LAPACK, Version 3.12.0, and the footer path /home/abui...RC/dtgexc.f(3). Stay slay, stay orthogonal, and may all your diagonal blocks land exactly where you want them. 💅✨