STGEXC(3)

💖 STGEXC(3) — Library Functions Manual 💖

okay so, bestie, this is the Library Functions Manual page for STGEXC(3). The header/footer path is /home/abui...RC/stgexc.f(3), and the full source path is chilling in NAME below. 💅

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💖 NAME 💖

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

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✨ SYNOPSIS ✨

💫 Functions/Subroutines 💫

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

STGEXC

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🦋 Function/Subroutine Documentation 🦋

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

STGEXC

✨ Purpose ✨

okay so here’s the main-character job of this routine: STGEXC 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 SGGES), 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

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🎀 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 REAL 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).
• B — B is REAL 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 REAL 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 REAL 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.
• 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 REAL 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.

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👑 Author 👑

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

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🌸 Contributors: 🌸

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

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📚 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 stgexc.f.

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🪄 Author 🪄

Generated automatically by Doxygen for LAPACK from the source code.

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okay that’s the whole manual page, bestie 🫶 — LAPACK Version 3.12.0, footer path /home/abui...RC/stgexc.f(3) included, Doxygen did its auto-generation thing, and yes, that’s the cute little source/version sign-off. periodt. 💅✨