ZTGEXC(3)

📦 version 3.12.0, in opensuse-leap 16.0

🦋 ZTGEXC(3) — Library Functions Manual 🦋

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✨ NAME ✨

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

🌟 SYNOPSIS 🌟

Functions/Subroutines

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

🫶 Function/Subroutine Documentation 🫶

subroutine ZTGEXC (logical wantq, logical wantz, integer n, complex*16,
    dimension( lda, * ) a, integer lda, complex*16, dimension( ldb, * ) b,
    integer ldb, complex*16, dimension( ldq, * ) q, integer ldq, complex*16,
    dimension( ldz, * ) z, integer ldz, integer ifst, integer ilst, integer
    info)
    ZTGEXC

🎯 Purpose 🎯

ZTGEXC reorders the generalized Schur decomposition of a complex matrix pair (A,B), using a unitary equivalence transformation (A, B) := Q * (A, B) * Z**H, so that the diagonal block of (A, B) with row index IFST is moved to row ILST. periodt. ✨

(A, B) must be in generalized Schur canonical form — that means A and B are both upper triangular. no cap. 💅

Optionally, the matrices Q and Z of generalized Schur vectors are updated. 🫶

Q(in) * A(in) * Z(in)**H = Q(out) * A(out) * Z(out)**H
Q(in) * B(in) * Z(in)**H = Q(out) * B(out) * Z(out)**H

🧾 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. It is the order of the matrices A and B. N >= 0.

A

A is COMPLEX*16 array, dimension (LDA,N).

On entry, the upper triangular 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 COMPLEX*16 array, dimension (LDB,N).

On entry, the upper triangular 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 COMPLEX*16 array, dimension (LDQ,N).

On entry, if WANTQ = .TRUE., the unitary 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 COMPLEX*16 array, dimension (LDZ,N).

On entry, if WANTZ = .TRUE., the unitary 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.

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.

👑 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.
  • [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.
  • [3] B. Kagstrom and P. Poromaa, LAPACK-Style Algorithms and Software for Solving the Generalized Sylvester Equation and Estimating the Separation between Regular Matrix Pairs, Report UMINF - 93.23, Department of Computing Science, Umea University, S-901 87 Umea, Sweden, December 1993, Revised April 1994, Also as LAPACK working Note 75. To appear in ACM Trans. on Math. Software, Vol 22, No 1, 1996.

Definition at line 198 of file ztgexc.f.

🤖 Author 🤖

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