STGEX2(3)

💅 NAME 💅

This is the manual page for stgex2.f(3) — bestie, it's the glow-up page for /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/stgex2.f. We're swapping blocks, not vibes. Periodt. ✨

🦋 SYNOPSIS 🦋

✨ Functions/Subroutines ✨

• subroutine STGEX2 (wantq, wantz, n, a, lda, b, ldb, q, ldq, z, ldz, j1, n1, n2, work, lwork, info) — STGEX2 swaps adjacent diagonal blocks in an upper (quasi) triangular matrix pair by an orthogonal equivalence transformation. It's giving very serious math main character energy. 🔥

🌸 Function/Subroutine Documentation 🌸

subroutine STGEX2 (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 j1, integer n1, integer n2, real, dimension( * ) work,
    integer lwork, integer info)

STGEX2 swaps adjacent diagonal blocks in an upper (quasi) triangular matrix pair by an orthogonal equivalence transformation. No cap, that's the whole assignment. 💖

💖 Purpose 💖

STGEX2 swaps adjacent diagonal blocks (A11, B11) and (A22, B22) of size 1-by-1 or 2-by-2 in an upper (quasi) triangular matrix pair (A, B) by an orthogonal equivalence transformation.

(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. Slay. 🫶

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.
• 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 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 REAL array, dimension (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 REAL array, dimension (LDQ,N). On entry, if WANTQ = .TRUE., the orthogonal 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 REAL array, dimension (LDZ,N). On entry, if WANTZ = .TRUE., the orthogonal 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). 1 <= J1 <= N.
• N1 — N1 is INTEGER. The order of the first block (A11, B11). N1 = 0, 1 or 2.
• N2 — N2 is INTEGER. The order of the second block (A22, B22). N2 = 0, 1 or 2.
• WORK — WORK is REAL array, dimension (MAX(1,LWORK)).
• LWORK — LWORK is INTEGER. The dimension of the array WORK. LWORK >= MAX( N*(N2+N1), (N2+N1)*(N2+N1)*2 ).
• INFO — INFO is INTEGER
  • =0: Successful exit
  • >0: If INFO = 1, the transformed matrix (A, B) would be too far from generalized Schur form; the blocks are not swapped and (A, B) and (Q, Z) are unchanged. The problem of swapping is too ill-conditioned.
  • <0: If INFO = -16: LWORK is too small. Appropriate value for LWORK is returned in WORK(1).

👑 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.

🌈 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 219 of file stgex2.f.

✨ Author ✨

Generated automatically by Doxygen for LAPACK from the source code.

---

Okay bye bestie! 💖 This page is LAPACK Version 3.12.0, with footer path /home/abui...RC/stgex2.f(3) — and the original footer doesn't hand me an explicit date, so I'm not inventing one 😭 no cap, that's the whole vibe check. 🎀