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Real Time Estimation and Prediction Using Optimistic Simulation and Control Theory Te
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stgex2.f(3) LAPACK stgex2.f(3) NAME
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 (logicalWANTQ, logicalWANTZ, integerN, real, dimension( lda, * )A, integerLDA, real, dimension( ldb, * )B, integerLDB, real, dimension( ldq, * )Q, integerLDQ, real, dimension( ldz, * )Z, integerLDZ, integerJ1, integerN1, integerN2, real, dimension( * )WORK, integerLWORK, integerINFO) 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 arrays, dimensions (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 arrays, dimensions (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 (LDZ,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: September 2012 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 221 of file stgex2.f. Author Generated automatically by Doxygen for LAPACK from the source code. Version 3.4.2 Tue Sep 25 2012 stgex2.f(3)
