SRC/stgexc.f(3)

💖 NAME 💖

SRC/stgexc.f — that’s the name, bestie, and it’s giving “we are deep in LAPACK land” 💅

This page lives in the Library Functions Manual 🌸

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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 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

🎀 Parameters 🎀

• WANTQ — is LOGICAL. .TRUE. : update the left transformation matrix Q; .FALSE.: do not update Q.
• WANTZ — is LOGICAL. .TRUE. : update the right transformation matrix Z; .FALSE.: do not update Z.
• N — is INTEGER. The order of the matrices A and B. N >= 0.
• 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 — is INTEGER. The leading dimension of the array A. LDA >= max(1,N).
• 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 — is INTEGER. The leading dimension of the array B. LDB >= max(1,N).
• 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 — is INTEGER. The leading dimension of the array Q. LDQ >= 1. If WANTQ = .TRUE., LDQ >= N.
• 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 — is INTEGER. The leading dimension of the array Z. LDZ >= 1. If WANTZ = .TRUE., LDZ >= N.
• IFST — is INTEGER.
• 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 — is REAL array, dimension (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the optimal 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 — 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.

bestie, that INFO = 1 case is the “it’s giving ill-conditioned, proceed with emotional support” moment 😭💀

🌟 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 stgexc.f.

🌟 Author 🌟

Generated automatically by Doxygen for LAPACK from the source code.

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okay that’s the whole page, bestie — bye! 💖✨ This one is from LAPACK, Version 3.12.0, and the footer says SRC/stgexc.f(3) 🫶👑