SRC/stgex2.f(3)

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version 3.12.1 · 4 versions
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💅 SRC/stgex2.f(3) — Library Functions Manual 💅

okay so bestie, this is the SRC/stgex2.f glow-up page from the Library Functions Manual. It’s giving “linear algebra but make it iconic,” and yes, every flag-situation and condition is still here. No cap. ✨

🎀 NAME 🎀

SRC/stgex2.f

✨ SYNOPSIS ✨

Functions/Subroutines

Here’s the callable bestie, exactly as it shows up:

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.

📚 Function/Subroutine Documentation 📚

The whole signature, in all its Fortran-realness:

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.

💡 Purpose 💡

So the main-character move here: 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. Obsessed. 🦋

(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 — 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 👑

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