#include "blaswrap.h" #include "f2c.h" /* Subroutine */ int dtgexc_(logical *wantq, logical *wantz, integer *n, doublereal *a, integer *lda, doublereal *b, integer *ldb, doublereal * q, integer *ldq, doublereal *z__, integer *ldz, integer *ifst, integer *ilst, doublereal *work, integer *lwork, integer *info) { /* -- LAPACK routine (version 3.1) -- Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. November 2006 Purpose ======= DTGEXC reorders the generalized real Schur decomposition of a real matrix pair (A,B) using an orthogonal 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 real Schur canonical form (as returned by DGGES), 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)' = 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) DOUBLE PRECISION array, dimension (LDA,N) On entry, the matrix A in generalized real Schur canonical form. On exit, the updated matrix A, again in generalized real Schur canonical form. LDA (input) INTEGER The leading dimension of the array A. LDA >= max(1,N). B (input/output) DOUBLE PRECISION array, dimension (LDB,N) On entry, the matrix B in generalized real Schur canonical form (A,B). On exit, the updated matrix B, again in generalized real Schur canonical form (A,B). LDB (input) INTEGER The leading dimension of the array B. LDB >= max(1,N). Q (input/output) DOUBLE PRECISION array, dimension (LDZ,N) On entry, if WANTQ = .TRUE., the orthogonal 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) DOUBLE PRECISION array, dimension (LDZ,N) On entry, if WANTZ = .TRUE., the orthogonal 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/output) 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. On exit, if IFST pointed on entry to the second row of a 2-by-2 block, it is changed to point to the first row; ILST always points to the first row of the block in its final position (which may differ from its input value by +1 or -1). 1 <= IFST, ILST <= N. WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK. LWORK (input) INTEGER The dimension of the array WORK. LWORK >= 1 when N <= 1, otherwise LWORK >= 4*N + 16. If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA. 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. ===================================================================== Decode and test input arguments. Parameter adjustments */ /* Table of constant values */ static integer c__1 = 1; static integer c__2 = 2; /* 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 nbf, nbl, here, lwmin; extern /* Subroutine */ int dtgex2_(logical *, logical *, integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, integer *, integer *, integer *, integer *, doublereal *, integer *, integer *), xerbla_(char *, integer *); static integer nbnext; static logical lquery; 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; --work; /* Function Body */ *info = 0; lquery = *lwork == -1; 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) { if (*n <= 1) { lwmin = 1; } else { lwmin = (*n << 2) + 16; } work[1] = (doublereal) lwmin; if (*lwork < lwmin && ! lquery) { *info = -15; } } if (*info != 0) { i__1 = -(*info); xerbla_("DTGEXC", &i__1); return 0; } else if (lquery) { return 0; } /* Quick return if possible */ if (*n <= 1) { return 0; } /* Determine the first row of the specified block and find out if it is 1-by-1 or 2-by-2. */ if (*ifst > 1) { if (a[*ifst + (*ifst - 1) * a_dim1] != 0.) { --(*ifst); } } nbf = 1; if (*ifst < *n) { if (a[*ifst + 1 + *ifst * a_dim1] != 0.) { nbf = 2; } } /* Determine the first row of the final block and find out if it is 1-by-1 or 2-by-2. */ if (*ilst > 1) { if (a[*ilst + (*ilst - 1) * a_dim1] != 0.) { --(*ilst); } } nbl = 1; if (*ilst < *n) { if (a[*ilst + 1 + *ilst * a_dim1] != 0.) { nbl = 2; } } if (*ifst == *ilst) { return 0; } if (*ifst < *ilst) { /* Update ILST. */ if (nbf == 2 && nbl == 1) { --(*ilst); } if (nbf == 1 && nbl == 2) { ++(*ilst); } here = *ifst; L10: /* Swap with next one below. */ if (nbf == 1 || nbf == 2) { /* Current block either 1-by-1 or 2-by-2. */ nbnext = 1; if (here + nbf + 1 <= *n) { if (a[here + nbf + 1 + (here + nbf) * a_dim1] != 0.) { nbnext = 2; } } dtgex2_(wantq, wantz, n, &a[a_offset], lda, &b[b_offset], ldb, &q[ q_offset], ldq, &z__[z_offset], ldz, &here, &nbf, &nbnext, &work[1], lwork, info); if (*info != 0) { *ilst = here; return 0; } here += nbnext; /* Test if 2-by-2 block breaks into two 1-by-1 blocks. */ if (nbf == 2) { if (a[here + 1 + here * a_dim1] == 0.) { nbf = 3; } } } else { /* Current block consists of two 1-by-1 blocks, each of which must be swapped individually. */ nbnext = 1; if (here + 3 <= *n) { if (a[here + 3 + (here + 2) * a_dim1] != 0.) { nbnext = 2; } } i__1 = here + 1; dtgex2_(wantq, wantz, n, &a[a_offset], lda, &b[b_offset], ldb, &q[ q_offset], ldq, &z__[z_offset], ldz, &i__1, &c__1, & nbnext, &work[1], lwork, info); if (*info != 0) { *ilst = here; return 0; } if (nbnext == 1) { /* Swap two 1-by-1 blocks. */ dtgex2_(wantq, wantz, n, &a[a_offset], lda, &b[b_offset], ldb, &q[q_offset], ldq, &z__[z_offset], ldz, &here, &c__1, &c__1, &work[1], lwork, info); if (*info != 0) { *ilst = here; return 0; } ++here; } else { /* Recompute NBNEXT in case of 2-by-2 split. */ if (a[here + 2 + (here + 1) * a_dim1] == 0.) { nbnext = 1; } if (nbnext == 2) { /* 2-by-2 block did not split. */ dtgex2_(wantq, wantz, n, &a[a_offset], lda, &b[b_offset], ldb, &q[q_offset], ldq, &z__[z_offset], ldz, & here, &c__1, &nbnext, &work[1], lwork, info); if (*info != 0) { *ilst = here; return 0; } here += 2; } else { /* 2-by-2 block did split. */ dtgex2_(wantq, wantz, n, &a[a_offset], lda, &b[b_offset], ldb, &q[q_offset], ldq, &z__[z_offset], ldz, & here, &c__1, &c__1, &work[1], lwork, info); if (*info != 0) { *ilst = here; return 0; } ++here; dtgex2_(wantq, wantz, n, &a[a_offset], lda, &b[b_offset], ldb, &q[q_offset], ldq, &z__[z_offset], ldz, & here, &c__1, &c__1, &work[1], lwork, info); if (*info != 0) { *ilst = here; return 0; } ++here; } } } if (here < *ilst) { goto L10; } } else { here = *ifst; L20: /* Swap with next one below. */ if (nbf == 1 || nbf == 2) { /* Current block either 1-by-1 or 2-by-2. */ nbnext = 1; if (here >= 3) { if (a[here - 1 + (here - 2) * a_dim1] != 0.) { nbnext = 2; } } i__1 = here - nbnext; dtgex2_(wantq, wantz, n, &a[a_offset], lda, &b[b_offset], ldb, &q[ q_offset], ldq, &z__[z_offset], ldz, &i__1, &nbnext, &nbf, &work[1], lwork, info); if (*info != 0) { *ilst = here; return 0; } here -= nbnext; /* Test if 2-by-2 block breaks into two 1-by-1 blocks. */ if (nbf == 2) { if (a[here + 1 + here * a_dim1] == 0.) { nbf = 3; } } } else { /* Current block consists of two 1-by-1 blocks, each of which must be swapped individually. */ nbnext = 1; if (here >= 3) { if (a[here - 1 + (here - 2) * a_dim1] != 0.) { nbnext = 2; } } i__1 = here - nbnext; dtgex2_(wantq, wantz, n, &a[a_offset], lda, &b[b_offset], ldb, &q[ q_offset], ldq, &z__[z_offset], ldz, &i__1, &nbnext, & c__1, &work[1], lwork, info); if (*info != 0) { *ilst = here; return 0; } if (nbnext == 1) { /* Swap two 1-by-1 blocks. */ dtgex2_(wantq, wantz, n, &a[a_offset], lda, &b[b_offset], ldb, &q[q_offset], ldq, &z__[z_offset], ldz, &here, & nbnext, &c__1, &work[1], lwork, info); if (*info != 0) { *ilst = here; return 0; } --here; } else { /* Recompute NBNEXT in case of 2-by-2 split. */ if (a[here + (here - 1) * a_dim1] == 0.) { nbnext = 1; } if (nbnext == 2) { /* 2-by-2 block did not split. */ i__1 = here - 1; dtgex2_(wantq, wantz, n, &a[a_offset], lda, &b[b_offset], ldb, &q[q_offset], ldq, &z__[z_offset], ldz, & i__1, &c__2, &c__1, &work[1], lwork, info); if (*info != 0) { *ilst = here; return 0; } here += -2; } else { /* 2-by-2 block did split. */ dtgex2_(wantq, wantz, n, &a[a_offset], lda, &b[b_offset], ldb, &q[q_offset], ldq, &z__[z_offset], ldz, & here, &c__1, &c__1, &work[1], lwork, info); if (*info != 0) { *ilst = here; return 0; } --here; dtgex2_(wantq, wantz, n, &a[a_offset], lda, &b[b_offset], ldb, &q[q_offset], ldq, &z__[z_offset], ldz, & here, &c__1, &c__1, &work[1], lwork, info); if (*info != 0) { *ilst = here; return 0; } --here; } } } if (here > *ilst) { goto L20; } } *ilst = here; work[1] = (doublereal) lwmin; return 0; /* End of DTGEXC */ } /* dtgexc_ */