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---
:name: ctgexc
:md5sum: 28615b111bd89941edff51027b6ac193
:category: :subroutine
:arguments:
- wantq:
:type: logical
:intent: input
- wantz:
:type: logical
:intent: input
- n:
:type: integer
:intent: input
- a:
:type: complex
:intent: input/output
:dims:
- lda
- n
- lda:
:type: integer
:intent: input
- b:
:type: complex
:intent: input/output
:dims:
- ldb
- n
- ldb:
:type: integer
:intent: input
- q:
:type: complex
:intent: input/output
:dims:
- ldz
- n
- ldq:
:type: integer
:intent: input
- z:
:type: complex
:intent: input/output
:dims:
- ldz
- n
- ldz:
:type: integer
:intent: input
- ifst:
:type: integer
:intent: input
- ilst:
:type: integer
:intent: input/output
- info:
:type: integer
:intent: output
:substitutions: {}
:fortran_help: " SUBROUTINE CTGEXC( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z, LDZ, IFST, ILST, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* CTGEXC reorders the generalized Schur decomposition of a complex\n\
* matrix pair (A,B), using an unitary equivalence transformation\n\
* (A, B) := Q * (A, B) * Z', so that the diagonal block of (A, B) with\n\
* row index IFST is moved to row ILST.\n\
*\n\
* (A, B) must be in generalized Schur canonical form, that is, A and\n\
* B are both upper triangular.\n\
*\n\
* Optionally, the matrices Q and Z of generalized Schur vectors are\n\
* updated.\n\
*\n\
* Q(in) * A(in) * Z(in)' = Q(out) * A(out) * Z(out)'\n\
* Q(in) * B(in) * Z(in)' = Q(out) * B(out) * Z(out)'\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* WANTQ (input) LOGICAL\n\
* .TRUE. : update the left transformation matrix Q;\n\
* .FALSE.: do not update Q.\n\
*\n\
* WANTZ (input) LOGICAL\n\
* .TRUE. : update the right transformation matrix Z;\n\
* .FALSE.: do not update Z.\n\
*\n\
* N (input) INTEGER\n\
* The order of the matrices A and B. N >= 0.\n\
*\n\
* A (input/output) COMPLEX array, dimension (LDA,N)\n\
* On entry, the upper triangular matrix A in the pair (A, B).\n\
* On exit, the updated matrix A.\n\
*\n\
* LDA (input) INTEGER\n\
* The leading dimension of the array A. LDA >= max(1,N).\n\
*\n\
* B (input/output) COMPLEX array, dimension (LDB,N)\n\
* On entry, the upper triangular matrix B in the pair (A, B).\n\
* On exit, the updated matrix B.\n\
*\n\
* LDB (input) INTEGER\n\
* The leading dimension of the array B. LDB >= max(1,N).\n\
*\n\
* Q (input/output) COMPLEX array, dimension (LDZ,N)\n\
* On entry, if WANTQ = .TRUE., the unitary matrix Q.\n\
* On exit, the updated matrix Q.\n\
* If WANTQ = .FALSE., Q is not referenced.\n\
*\n\
* LDQ (input) INTEGER\n\
* The leading dimension of the array Q. LDQ >= 1;\n\
* If WANTQ = .TRUE., LDQ >= N.\n\
*\n\
* Z (input/output) COMPLEX array, dimension (LDZ,N)\n\
* On entry, if WANTZ = .TRUE., the unitary matrix Z.\n\
* On exit, the updated matrix Z.\n\
* If WANTZ = .FALSE., Z is not referenced.\n\
*\n\
* LDZ (input) INTEGER\n\
* The leading dimension of the array Z. LDZ >= 1;\n\
* If WANTZ = .TRUE., LDZ >= N.\n\
*\n\
* IFST (input) INTEGER\n\
* ILST (input/output) INTEGER\n\
* Specify the reordering of the diagonal blocks of (A, B).\n\
* The block with row index IFST is moved to row ILST, by a\n\
* sequence of swapping between adjacent blocks.\n\
*\n\
* INFO (output) INTEGER\n\
* =0: Successful exit.\n\
* <0: if INFO = -i, the i-th argument had an illegal value.\n\
* =1: The transformed matrix pair (A, B) would be too far\n\
* from generalized Schur form; the problem is ill-\n\
* conditioned. (A, B) may have been partially reordered,\n\
* and ILST points to the first row of the current\n\
* position of the block being moved.\n\
*\n\
*\n\n\
* Further Details\n\
* ===============\n\
*\n\
* Based on contributions by\n\
* Bo Kagstrom and Peter Poromaa, Department of Computing Science,\n\
* Umea University, S-901 87 Umea, Sweden.\n\
*\n\
* [1] B. Kagstrom; A Direct Method for Reordering Eigenvalues in the\n\
* Generalized Real Schur Form of a Regular Matrix Pair (A, B), in\n\
* M.S. Moonen et al (eds), Linear Algebra for Large Scale and\n\
* Real-Time Applications, Kluwer Academic Publ. 1993, pp 195-218.\n\
*\n\
* [2] B. Kagstrom and P. Poromaa; Computing Eigenspaces with Specified\n\
* Eigenvalues of a Regular Matrix Pair (A, B) and Condition\n\
* Estimation: Theory, Algorithms and Software, Report\n\
* UMINF - 94.04, Department of Computing Science, Umea University,\n\
* S-901 87 Umea, Sweden, 1994. Also as LAPACK Working Note 87.\n\
* To appear in Numerical Algorithms, 1996.\n\
*\n\
* [3] B. Kagstrom and P. Poromaa, LAPACK-Style Algorithms and Software\n\
* for Solving the Generalized Sylvester Equation and Estimating the\n\
* Separation between Regular Matrix Pairs, Report UMINF - 93.23,\n\
* Department of Computing Science, Umea University, S-901 87 Umea,\n\
* Sweden, December 1993, Revised April 1994, Also as LAPACK working\n\
* Note 75. To appear in ACM Trans. on Math. Software, Vol 22, No 1,\n\
* 1996.\n\
*\n\
* =====================================================================\n\
*\n\
* .. Local Scalars ..\n INTEGER HERE\n\
* ..\n\
* .. External Subroutines ..\n EXTERNAL CTGEX2, XERBLA\n\
* ..\n\
* .. Intrinsic Functions ..\n INTRINSIC MAX\n\
* ..\n"
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