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---
:name: stgexc
:md5sum: 5d3e5cea4ba4800679b5eae4b7a67cc3
:category: :subroutine
:arguments:
- wantq:
:type: logical
:intent: input
- wantz:
:type: logical
:intent: input
- n:
:type: integer
:intent: input
- a:
:type: real
:intent: input/output
:dims:
- lda
- n
- lda:
:type: integer
:intent: input
- b:
:type: real
:intent: input/output
:dims:
- ldb
- n
- ldb:
:type: integer
:intent: input
- q:
:type: real
:intent: input/output
:dims:
- ldz
- n
- ldq:
:type: integer
:intent: input
- z:
:type: real
:intent: input/output
:dims:
- ldz
- n
- ldz:
:type: integer
:intent: input
- ifst:
:type: integer
:intent: input/output
- ilst:
:type: integer
:intent: input/output
- work:
:type: real
:intent: output
:dims:
- MAX(1,lwork)
- lwork:
:type: integer
:intent: input
:option: true
:default: "n<=1 ? 1 : 4*n+16"
- info:
:type: integer
:intent: output
:substitutions: {}
:fortran_help: " SUBROUTINE STGEXC( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z, LDZ, IFST, ILST, WORK, LWORK, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* STGEXC reorders the generalized real Schur decomposition of a real\n\
* matrix pair (A,B) using an orthogonal equivalence transformation\n\
*\n\
* (A, B) = Q * (A, B) * Z',\n\
*\n\
* so that the diagonal block of (A, B) with row index IFST is moved\n\
* to row ILST.\n\
*\n\
* (A, B) must be in generalized real Schur canonical form (as returned\n\
* by SGGES), i.e. A is block upper triangular with 1-by-1 and 2-by-2\n\
* diagonal blocks. B is 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\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) REAL array, dimension (LDA,N)\n\
* On entry, the matrix A in generalized real Schur canonical\n\
* form.\n\
* On exit, the updated matrix A, again in generalized\n\
* real Schur canonical form.\n\
*\n\
* LDA (input) INTEGER\n\
* The leading dimension of the array A. LDA >= max(1,N).\n\
*\n\
* B (input/output) REAL array, dimension (LDB,N)\n\
* On entry, the matrix B in generalized real Schur canonical\n\
* form (A,B).\n\
* On exit, the updated matrix B, again in generalized\n\
* real Schur canonical form (A,B).\n\
*\n\
* LDB (input) INTEGER\n\
* The leading dimension of the array B. LDB >= max(1,N).\n\
*\n\
* Q (input/output) REAL array, dimension (LDZ,N)\n\
* On entry, if WANTQ = .TRUE., the orthogonal 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) REAL array, dimension (LDZ,N)\n\
* On entry, if WANTZ = .TRUE., the orthogonal 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/output) 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\
* On exit, if IFST pointed on entry to the second row of\n\
* a 2-by-2 block, it is changed to point to the first row;\n\
* ILST always points to the first row of the block in its\n\
* final position (which may differ from its input value by\n\
* +1 or -1). 1 <= IFST, ILST <= N.\n\
*\n\
* WORK (workspace/output) REAL array, dimension (MAX(1,LWORK))\n\
* On exit, if INFO = 0, WORK(1) returns the optimal LWORK.\n\
*\n\
* LWORK (input) INTEGER\n\
* The dimension of the array WORK.\n\
* LWORK >= 1 when N <= 1, otherwise LWORK >= 4*N + 16.\n\
*\n\
* If LWORK = -1, then a workspace query is assumed; the routine\n\
* only calculates the optimal size of the WORK array, returns\n\
* this value as the first entry of the WORK array, and no error\n\
* message related to LWORK is issued by XERBLA.\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\
* 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\
* =====================================================================\n\
*\n"
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