#include "blaswrap.h" #include "f2c.h" /* Subroutine */ int ctgexc_(logical *wantq, logical *wantz, integer *n, complex *a, integer *lda, complex *b, integer *ldb, complex *q, integer *ldq, complex *z__, integer *ldz, integer *ifst, integer * ilst, integer *info) { /* -- LAPACK routine (version 3.1) -- Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. November 2006 Purpose ======= CTGEXC reorders the generalized Schur decomposition of a complex matrix pair (A,B), using an unitary equivalence transformation (A, B) := Q * (A, B) * Z', so that the diagonal block of (A, B) with row index IFST is moved to row ILST. (A, B) must be in generalized Schur canonical form, that is, A and B are both upper triangular. Optionally, the matrices Q and Z of generalized Schur vectors are updated. Q(in) * A(in) * Z(in)' = Q(out) * A(out) * Z(out)' Q(in) * B(in) * Z(in)' = Q(out) * B(out) * Z(out)' Arguments ========= WANTQ (input) LOGICAL .TRUE. : update the left transformation matrix Q; .FALSE.: do not update Q. WANTZ (input) LOGICAL .TRUE. : update the right transformation matrix Z; .FALSE.: do not update Z. N (input) INTEGER The order of the matrices A and B. N >= 0. A (input/output) COMPLEX array, dimension (LDA,N) On entry, the upper triangular matrix A in the pair (A, B). On exit, the updated matrix A. LDA (input) INTEGER The leading dimension of the array A. LDA >= max(1,N). B (input/output) COMPLEX array, dimension (LDB,N) On entry, the upper triangular matrix B in the pair (A, B). On exit, the updated matrix B. LDB (input) INTEGER The leading dimension of the array B. LDB >= max(1,N). Q (input/output) COMPLEX array, dimension (LDZ,N) On entry, if WANTQ = .TRUE., the unitary matrix Q. On exit, the updated matrix Q. If WANTQ = .FALSE., Q is not referenced. LDQ (input) INTEGER The leading dimension of the array Q. LDQ >= 1; If WANTQ = .TRUE., LDQ >= N. Z (input/output) COMPLEX array, dimension (LDZ,N) On entry, if WANTZ = .TRUE., the unitary matrix Z. On exit, the updated matrix Z. If WANTZ = .FALSE., Z is not referenced. LDZ (input) INTEGER The leading dimension of the array Z. LDZ >= 1; If WANTZ = .TRUE., LDZ >= N. IFST (input) INTEGER ILST (input/output) INTEGER Specify the reordering of the diagonal blocks of (A, B). The block with row index IFST is moved to row ILST, by a sequence of swapping between adjacent blocks. INFO (output) INTEGER =0: Successful exit. <0: if INFO = -i, the i-th argument had an illegal value. =1: The transformed matrix pair (A, B) would be too far from generalized Schur form; the problem is ill- conditioned. (A, B) may have been partially reordered, and ILST points to the first row of the current position of the block being moved. Further Details =============== Based on contributions by Bo Kagstrom and Peter Poromaa, Department of Computing Science, Umea University, S-901 87 Umea, Sweden. [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. [3] B. Kagstrom and P. Poromaa, LAPACK-Style Algorithms and Software for Solving the Generalized Sylvester Equation and Estimating the Separation between Regular Matrix Pairs, Report UMINF - 93.23, Department of Computing Science, Umea University, S-901 87 Umea, Sweden, December 1993, Revised April 1994, Also as LAPACK working Note 75. To appear in ACM Trans. on Math. Software, Vol 22, No 1, 1996. ===================================================================== Decode and test input arguments. Parameter adjustments */ /* System generated locals */ integer a_dim1, a_offset, b_dim1, b_offset, q_dim1, q_offset, z_dim1, z_offset, i__1; /* Local variables */ static integer here; extern /* Subroutine */ int ctgex2_(logical *, logical *, integer *, complex *, integer *, complex *, integer *, complex *, integer *, complex *, integer *, integer *, integer *), xerbla_(char *, integer *); a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; b_dim1 = *ldb; b_offset = 1 + b_dim1; b -= b_offset; q_dim1 = *ldq; q_offset = 1 + q_dim1; q -= q_offset; z_dim1 = *ldz; z_offset = 1 + z_dim1; z__ -= z_offset; /* Function Body */ *info = 0; if (*n < 0) { *info = -3; } else if (*lda < max(1,*n)) { *info = -5; } else if (*ldb < max(1,*n)) { *info = -7; } else if (*ldq < 1 || *wantq && *ldq < max(1,*n)) { *info = -9; } else if (*ldz < 1 || *wantz && *ldz < max(1,*n)) { *info = -11; } else if (*ifst < 1 || *ifst > *n) { *info = -12; } else if (*ilst < 1 || *ilst > *n) { *info = -13; } if (*info != 0) { i__1 = -(*info); xerbla_("CTGEXC", &i__1); return 0; } /* Quick return if possible */ if (*n <= 1) { return 0; } if (*ifst == *ilst) { return 0; } if (*ifst < *ilst) { here = *ifst; L10: /* Swap with next one below */ ctgex2_(wantq, wantz, n, &a[a_offset], lda, &b[b_offset], ldb, &q[ q_offset], ldq, &z__[z_offset], ldz, &here, info); if (*info != 0) { *ilst = here; return 0; } ++here; if (here < *ilst) { goto L10; } --here; } else { here = *ifst - 1; L20: /* Swap with next one above */ ctgex2_(wantq, wantz, n, &a[a_offset], lda, &b[b_offset], ldb, &q[ q_offset], ldq, &z__[z_offset], ldz, &here, info); if (*info != 0) { *ilst = here; return 0; } --here; if (here >= *ilst) { goto L20; } ++here; } *ilst = here; return 0; /* End of CTGEXC */ } /* ctgexc_ */