# stgex2.f man page

stgex2.f

## 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.

## 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.

**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. 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.

**Date:**June 2017

**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 at line 223 of file stgex2.f.

## Author

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## Referenced By

The man page stgex2(3) is an alias of stgex2.f(3).