DTGEX2(3)

💅 DTGEX2(3) — Library Functions Manual 💅

Library Functions Manual, bestie. Let’s get into it. ✨

💖 NAME 💖

DTGEX2 is the LAPACK subroutine that swaps adjacent diagonal blocks in an upper (quasi) triangular matrix pair by an orthogonal equivalence transformation. The source file is /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dtgex2.f. This page is from the Library Functions Manual.

🦋 SYNOPSIS 🦋

Functions/Subroutines

subroutine DTGEX2 (wantq, wantz, n, a, lda, b, ldb, q, ldq, z, ldz, j1,
    n1, n2, work, lwork, info)

One-liner vibe: DTGEX2 swaps adjacent diagonal blocks in an upper (quasi) triangular matrix pair by an orthogonal equivalence transformation.

🫶 FUNCTION/SUBROUTINE DOCUMENTATION 🫶

subroutine DTGEX2 (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 j1, integer n1, integer n2, double precision, dimension( * )
    work, integer lwork, integer info)

Same one-liner again, because it’s iconic: DTGEX2 swaps adjacent diagonal blocks in an upper (quasi) triangular matrix pair by an orthogonal equivalence transformation.

✨ PURPOSE ✨

Okay so here’s the tea: DTGEX2 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 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 — LOGICAL. .TRUE. : update the left transformation matrix Q; .FALSE.: do not update Q. 🫶
• WANTZ — LOGICAL. .TRUE. : update the right transformation matrix Z; .FALSE.: do not update Z. 🫶
• N — INTEGER. The order of the matrices A and B. N >= 0.
• A — DOUBLE PRECISION array, dimensions (LDA,N). On entry, the matrix A in the pair (A, B). On exit, the updated matrix A.
• LDA — INTEGER. The leading dimension of the array A. LDA >= max(1,N).
• B — DOUBLE PRECISION array, dimensions (LDB,N). On entry, the matrix B in the pair (A, B). On exit, the updated matrix B.
• LDB — INTEGER. The leading dimension of the array B. LDB >= max(1,N).
• Q — DOUBLE PRECISION 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 — INTEGER. The leading dimension of the array Q. LDQ >= 1. If WANTQ = .TRUE., LDQ >= N.
• Z — DOUBLE PRECISION 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 — INTEGER. The leading dimension of the array Z. LDZ >= 1. If WANTZ = .TRUE., LDZ >= N.
• J1 — INTEGER. The index to the first block (A11, B11). 1 <= J1 <= N.
• N1 — INTEGER. The order of the first block (A11, B11). N1 = 0, 1 or 2.
• N2 — INTEGER. The order of the second block (A22, B22). N2 = 0, 1 or 2.
• WORK — DOUBLE PRECISION array, dimension (MAX(1,LWORK)).
• LWORK — INTEGER. The dimension of the array WORK. LWORK >= MAX( 1, N*(N2+N1), (N2+N1)*(N2+N1)*2 ).
• INFO — 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] 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] 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 📍

Definition at line 219 of file dtgex2.f.

👑 AUTHOR (GENERATED ONE) 👑

Generated automatically by Doxygen for LAPACK from the source code.

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