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template<typename T>
void tgex2(logical *wantq, logical *wantz, integer *n, T *a, integer *lda, T *b, integer *ldb, T *q, integer *ldq, T *z, integer *ldz, integer *j1, integer *n1, integer *n2, T *work, integer *lwork, integer *info)# TGEX2 swaps adjacent diagonal blocks in an upper (quasi) triangular matrix pair by an orthogonal equivalence transformation.
Purpose:
TGEX2 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 – [in]
WANTQ is LOGICAL
.TRUE. : update the left transformation matrix Q; .FALSE.: do not update Q.
WANTZ – [in]
WANTZ is LOGICAL
.TRUE. : update the right transformation matrix Z; .FALSE.: do not update Z.
N – [in]
N is INTEGER
The order of the matrices A and B. N >= 0.
A – [inout]
A is REAL array, dimension (LDA,N)
On entry, the matrix A in the pair (A, B). On exit, the updated matrix A.
LDA – [in]
LDA is INTEGER
The leading dimension of the array A. LDA >= fla_max(1,N).
B – [inout]
B is REAL array, dimension (LDB,N)
On entry, the matrix B in the pair (A, B). On exit, the updated matrix B.
LDB – [in]
LDB is INTEGER
The leading dimension of the array B. LDB >= fla_max(1,N).
Q – [inout]
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 – [in]
LDQ is INTEGER
The leading dimension of the array Q. LDQ >= 1. If WANTQ = .TRUE., LDQ >= N.
Z – [inout]
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 – [in]
LDZ is INTEGER
The leading dimension of the array Z. LDZ >= 1. If WANTZ = .TRUE., LDZ >= N.
J1 – [in]
J1 is INTEGER
The index to the first block (A11, B11). 1 <= J1 <= N.
N1 – [in]
N1 is INTEGER
The order of the first block (A11, B11). N1 = 0, 1 or 2.
N2 – [in]
N2 is INTEGER
The order of the second block (A22, B22). N2 = 0, 1 or 2.
WORK – [out] WORK is REAL array, dimension (MAX(1,LWORK)).
LWORK – [in]
LWORK is INTEGER
The dimension of the array WORK. LWORK >= MAX(N*(N2+N1), (N2+N1)*(N2+N1)*2)
INFO – [out]
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).