#include "f2c.h" #include "blaswrap.h" /* Table of constant values */ static integer c__8 = 8; static integer c__1 = 1; static doublereal c_b27 = -1.; static doublereal c_b42 = 1.; static doublereal c_b56 = 0.; /* Subroutine */ int dtgsy2_(char *trans, integer *ijob, integer *m, integer * n, doublereal *a, integer *lda, doublereal *b, integer *ldb, doublereal *c__, integer *ldc, doublereal *d__, integer *ldd, doublereal *e, integer *lde, doublereal *f, integer *ldf, doublereal * scale, doublereal *rdsum, doublereal *rdscal, integer *iwork, integer *pq, integer *info) { /* System generated locals */ integer a_dim1, a_offset, b_dim1, b_offset, c_dim1, c_offset, d_dim1, d_offset, e_dim1, e_offset, f_dim1, f_offset, i__1, i__2, i__3; /* Local variables */ integer i__, j, k, p, q; doublereal z__[64] /* was [8][8] */; integer ie, je, mb, nb, ii, jj, is, js; doublereal rhs[8]; integer isp1, jsp1; extern /* Subroutine */ int dger_(integer *, integer *, doublereal *, doublereal *, integer *, doublereal *, integer *, doublereal *, integer *); integer ierr, zdim, ipiv[8], jpiv[8]; doublereal alpha; extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, integer *), dgemm_(char *, char *, integer *, integer *, integer * , doublereal *, doublereal *, integer *, doublereal *, integer *, doublereal *, doublereal *, integer *); extern logical lsame_(char *, char *); extern /* Subroutine */ int dgemv_(char *, integer *, integer *, doublereal *, doublereal *, integer *, doublereal *, integer *, doublereal *, doublereal *, integer *), dcopy_(integer *, doublereal *, integer *, doublereal *, integer *), daxpy_(integer *, doublereal *, doublereal *, integer *, doublereal *, integer *) , dgesc2_(integer *, doublereal *, integer *, doublereal *, integer *, integer *, doublereal *), dgetc2_(integer *, doublereal *, integer *, integer *, integer *, integer *), dlatdf_(integer *, integer *, doublereal *, integer *, doublereal *, doublereal *, doublereal *, integer *, integer *); doublereal scaloc; extern /* Subroutine */ int dlaset_(char *, integer *, integer *, doublereal *, doublereal *, doublereal *, integer *), xerbla_(char *, integer *); logical notran; /* -- LAPACK auxiliary routine (version 3.1.1) -- */ /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ /* January 2007 */ /* .. Scalar Arguments .. */ /* .. */ /* .. Array Arguments .. */ /* .. */ /* Purpose */ /* ======= */ /* DTGSY2 solves the generalized Sylvester equation: */ /* A * R - L * B = scale * C (1) */ /* D * R - L * E = scale * F, */ /* using Level 1 and 2 BLAS. where R and L are unknown M-by-N matrices, */ /* (A, D), (B, E) and (C, F) are given matrix pairs of size M-by-M, */ /* N-by-N and M-by-N, respectively, with real entries. (A, D) and (B, E) */ /* must be in generalized Schur canonical form, i.e. A, B are upper */ /* quasi triangular and D, E are upper triangular. The solution (R, L) */ /* overwrites (C, F). 0 <= SCALE <= 1 is an output scaling factor */ /* chosen to avoid overflow. */ /* In matrix notation solving equation (1) corresponds to solve */ /* Z*x = scale*b, where Z is defined as */ /* Z = [ kron(In, A) -kron(B', Im) ] (2) */ /* [ kron(In, D) -kron(E', Im) ], */ /* Ik is the identity matrix of size k and X' is the transpose of X. */ /* kron(X, Y) is the Kronecker product between the matrices X and Y. */ /* In the process of solving (1), we solve a number of such systems */ /* where Dim(In), Dim(In) = 1 or 2. */ /* If TRANS = 'T', solve the transposed system Z'*y = scale*b for y, */ /* which is equivalent to solve for R and L in */ /* A' * R + D' * L = scale * C (3) */ /* R * B' + L * E' = scale * -F */ /* This case is used to compute an estimate of Dif[(A, D), (B, E)] = */ /* sigma_min(Z) using reverse communicaton with DLACON. */ /* DTGSY2 also (IJOB >= 1) contributes to the computation in DTGSYL */ /* of an upper bound on the separation between to matrix pairs. Then */ /* the input (A, D), (B, E) are sub-pencils of the matrix pair in */ /* DTGSYL. See DTGSYL for details. */ /* Arguments */ /* ========= */ /* TRANS (input) CHARACTER*1 */ /* = 'N', solve the generalized Sylvester equation (1). */ /* = 'T': solve the 'transposed' system (3). */ /* IJOB (input) INTEGER */ /* Specifies what kind of functionality to be performed. */ /* = 0: solve (1) only. */ /* = 1: A contribution from this subsystem to a Frobenius */ /* norm-based estimate of the separation between two matrix */ /* pairs is computed. (look ahead strategy is used). */ /* = 2: A contribution from this subsystem to a Frobenius */ /* norm-based estimate of the separation between two matrix */ /* pairs is computed. (DGECON on sub-systems is used.) */ /* Not referenced if TRANS = 'T'. */ /* M (input) INTEGER */ /* On entry, M specifies the order of A and D, and the row */ /* dimension of C, F, R and L. */ /* N (input) INTEGER */ /* On entry, N specifies the order of B and E, and the column */ /* dimension of C, F, R and L. */ /* A (input) DOUBLE PRECISION array, dimension (LDA, M) */ /* On entry, A contains an upper quasi triangular matrix. */ /* LDA (input) INTEGER */ /* The leading dimension of the matrix A. LDA >= max(1, M). */ /* B (input) DOUBLE PRECISION array, dimension (LDB, N) */ /* On entry, B contains an upper quasi triangular matrix. */ /* LDB (input) INTEGER */ /* The leading dimension of the matrix B. LDB >= max(1, N). */ /* C (input/output) DOUBLE PRECISION array, dimension (LDC, N) */ /* On entry, C contains the right-hand-side of the first matrix */ /* equation in (1). */ /* On exit, if IJOB = 0, C has been overwritten by the */ /* solution R. */ /* LDC (input) INTEGER */ /* The leading dimension of the matrix C. LDC >= max(1, M). */ /* D (input) DOUBLE PRECISION array, dimension (LDD, M) */ /* On entry, D contains an upper triangular matrix. */ /* LDD (input) INTEGER */ /* The leading dimension of the matrix D. LDD >= max(1, M). */ /* E (input) DOUBLE PRECISION array, dimension (LDE, N) */ /* On entry, E contains an upper triangular matrix. */ /* LDE (input) INTEGER */ /* The leading dimension of the matrix E. LDE >= max(1, N). */ /* F (input/output) DOUBLE PRECISION array, dimension (LDF, N) */ /* On entry, F contains the right-hand-side of the second matrix */ /* equation in (1). */ /* On exit, if IJOB = 0, F has been overwritten by the */ /* solution L. */ /* LDF (input) INTEGER */ /* The leading dimension of the matrix F. LDF >= max(1, M). */ /* SCALE (output) DOUBLE PRECISION */ /* On exit, 0 <= SCALE <= 1. If 0 < SCALE < 1, the solutions */ /* R and L (C and F on entry) will hold the solutions to a */ /* slightly perturbed system but the input matrices A, B, D and */ /* E have not been changed. If SCALE = 0, R and L will hold the */ /* solutions to the homogeneous system with C = F = 0. Normally, */ /* SCALE = 1. */ /* RDSUM (input/output) DOUBLE PRECISION */ /* On entry, the sum of squares of computed contributions to */ /* the Dif-estimate under computation by DTGSYL, where the */ /* scaling factor RDSCAL (see below) has been factored out. */ /* On exit, the corresponding sum of squares updated with the */ /* contributions from the current sub-system. */ /* If TRANS = 'T' RDSUM is not touched. */ /* NOTE: RDSUM only makes sense when DTGSY2 is called by DTGSYL. */ /* RDSCAL (input/output) DOUBLE PRECISION */ /* On entry, scaling factor used to prevent overflow in RDSUM. */ /* On exit, RDSCAL is updated w.r.t. the current contributions */ /* in RDSUM. */ /* If TRANS = 'T', RDSCAL is not touched. */ /* NOTE: RDSCAL only makes sense when DTGSY2 is called by */ /* DTGSYL. */ /* IWORK (workspace) INTEGER array, dimension (M+N+2) */ /* PQ (output) INTEGER */ /* On exit, the number of subsystems (of size 2-by-2, 4-by-4 and */ /* 8-by-8) solved by this routine. */ /* INFO (output) INTEGER */ /* On exit, if INFO is set to */ /* =0: Successful exit */ /* <0: If INFO = -i, the i-th argument had an illegal value. */ /* >0: The matrix pairs (A, D) and (B, E) have common or very */ /* close eigenvalues. */ /* Further Details */ /* =============== */ /* Based on contributions by */ /* Bo Kagstrom and Peter Poromaa, Department of Computing Science, */ /* Umea University, S-901 87 Umea, Sweden. */ /* ===================================================================== */ /* Replaced various illegal calls to DCOPY by calls to DLASET. */ /* Sven Hammarling, 27/5/02. */ /* .. Parameters .. */ /* .. */ /* .. Local Scalars .. */ /* .. */ /* .. Local Arrays .. */ /* .. */ /* .. External Functions .. */ /* .. */ /* .. External Subroutines .. */ /* .. */ /* .. Intrinsic Functions .. */ /* .. */ /* .. Executable Statements .. */ /* Decode and test input parameters */ /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; b_dim1 = *ldb; b_offset = 1 + b_dim1; b -= b_offset; c_dim1 = *ldc; c_offset = 1 + c_dim1; c__ -= c_offset; d_dim1 = *ldd; d_offset = 1 + d_dim1; d__ -= d_offset; e_dim1 = *lde; e_offset = 1 + e_dim1; e -= e_offset; f_dim1 = *ldf; f_offset = 1 + f_dim1; f -= f_offset; --iwork; /* Function Body */ *info = 0; ierr = 0; notran = lsame_(trans, "N"); if (! notran && ! lsame_(trans, "T")) { *info = -1; } else if (notran) { if (*ijob < 0 || *ijob > 2) { *info = -2; } } if (*info == 0) { if (*m <= 0) { *info = -3; } else if (*n <= 0) { *info = -4; } else if (*lda < max(1,*m)) { *info = -5; } else if (*ldb < max(1,*n)) { *info = -8; } else if (*ldc < max(1,*m)) { *info = -10; } else if (*ldd < max(1,*m)) { *info = -12; } else if (*lde < max(1,*n)) { *info = -14; } else if (*ldf < max(1,*m)) { *info = -16; } } if (*info != 0) { i__1 = -(*info); xerbla_("DTGSY2", &i__1); return 0; } /* Determine block structure of A */ *pq = 0; p = 0; i__ = 1; L10: if (i__ > *m) { goto L20; } ++p; iwork[p] = i__; if (i__ == *m) { goto L20; } if (a[i__ + 1 + i__ * a_dim1] != 0.) { i__ += 2; } else { ++i__; } goto L10; L20: iwork[p + 1] = *m + 1; /* Determine block structure of B */ q = p + 1; j = 1; L30: if (j > *n) { goto L40; } ++q; iwork[q] = j; if (j == *n) { goto L40; } if (b[j + 1 + j * b_dim1] != 0.) { j += 2; } else { ++j; } goto L30; L40: iwork[q + 1] = *n + 1; *pq = p * (q - p - 1); if (notran) { /* Solve (I, J) - subsystem */ /* A(I, I) * R(I, J) - L(I, J) * B(J, J) = C(I, J) */ /* D(I, I) * R(I, J) - L(I, J) * E(J, J) = F(I, J) */ /* for I = P, P - 1, ..., 1; J = 1, 2, ..., Q */ *scale = 1.; scaloc = 1.; i__1 = q; for (j = p + 2; j <= i__1; ++j) { js = iwork[j]; jsp1 = js + 1; je = iwork[j + 1] - 1; nb = je - js + 1; for (i__ = p; i__ >= 1; --i__) { is = iwork[i__]; isp1 = is + 1; ie = iwork[i__ + 1] - 1; mb = ie - is + 1; zdim = mb * nb << 1; if (mb == 1 && nb == 1) { /* Build a 2-by-2 system Z * x = RHS */ z__[0] = a[is + is * a_dim1]; z__[1] = d__[is + is * d_dim1]; z__[8] = -b[js + js * b_dim1]; z__[9] = -e[js + js * e_dim1]; /* Set up right hand side(s) */ rhs[0] = c__[is + js * c_dim1]; rhs[1] = f[is + js * f_dim1]; /* Solve Z * x = RHS */ dgetc2_(&zdim, z__, &c__8, ipiv, jpiv, &ierr); if (ierr > 0) { *info = ierr; } if (*ijob == 0) { dgesc2_(&zdim, z__, &c__8, rhs, ipiv, jpiv, &scaloc); if (scaloc != 1.) { i__2 = *n; for (k = 1; k <= i__2; ++k) { dscal_(m, &scaloc, &c__[k * c_dim1 + 1], & c__1); dscal_(m, &scaloc, &f[k * f_dim1 + 1], &c__1); /* L50: */ } *scale *= scaloc; } } else { dlatdf_(ijob, &zdim, z__, &c__8, rhs, rdsum, rdscal, ipiv, jpiv); } /* Unpack solution vector(s) */ c__[is + js * c_dim1] = rhs[0]; f[is + js * f_dim1] = rhs[1]; /* Substitute R(I, J) and L(I, J) into remaining */ /* equation. */ if (i__ > 1) { alpha = -rhs[0]; i__2 = is - 1; daxpy_(&i__2, &alpha, &a[is * a_dim1 + 1], &c__1, & c__[js * c_dim1 + 1], &c__1); i__2 = is - 1; daxpy_(&i__2, &alpha, &d__[is * d_dim1 + 1], &c__1, & f[js * f_dim1 + 1], &c__1); } if (j < q) { i__2 = *n - je; daxpy_(&i__2, &rhs[1], &b[js + (je + 1) * b_dim1], ldb, &c__[is + (je + 1) * c_dim1], ldc); i__2 = *n - je; daxpy_(&i__2, &rhs[1], &e[js + (je + 1) * e_dim1], lde, &f[is + (je + 1) * f_dim1], ldf); } } else if (mb == 1 && nb == 2) { /* Build a 4-by-4 system Z * x = RHS */ z__[0] = a[is + is * a_dim1]; z__[1] = 0.; z__[2] = d__[is + is * d_dim1]; z__[3] = 0.; z__[8] = 0.; z__[9] = a[is + is * a_dim1]; z__[10] = 0.; z__[11] = d__[is + is * d_dim1]; z__[16] = -b[js + js * b_dim1]; z__[17] = -b[js + jsp1 * b_dim1]; z__[18] = -e[js + js * e_dim1]; z__[19] = -e[js + jsp1 * e_dim1]; z__[24] = -b[jsp1 + js * b_dim1]; z__[25] = -b[jsp1 + jsp1 * b_dim1]; z__[26] = 0.; z__[27] = -e[jsp1 + jsp1 * e_dim1]; /* Set up right hand side(s) */ rhs[0] = c__[is + js * c_dim1]; rhs[1] = c__[is + jsp1 * c_dim1]; rhs[2] = f[is + js * f_dim1]; rhs[3] = f[is + jsp1 * f_dim1]; /* Solve Z * x = RHS */ dgetc2_(&zdim, z__, &c__8, ipiv, jpiv, &ierr); if (ierr > 0) { *info = ierr; } if (*ijob == 0) { dgesc2_(&zdim, z__, &c__8, rhs, ipiv, jpiv, &scaloc); if (scaloc != 1.) { i__2 = *n; for (k = 1; k <= i__2; ++k) { dscal_(m, &scaloc, &c__[k * c_dim1 + 1], & c__1); dscal_(m, &scaloc, &f[k * f_dim1 + 1], &c__1); /* L60: */ } *scale *= scaloc; } } else { dlatdf_(ijob, &zdim, z__, &c__8, rhs, rdsum, rdscal, ipiv, jpiv); } /* Unpack solution vector(s) */ c__[is + js * c_dim1] = rhs[0]; c__[is + jsp1 * c_dim1] = rhs[1]; f[is + js * f_dim1] = rhs[2]; f[is + jsp1 * f_dim1] = rhs[3]; /* Substitute R(I, J) and L(I, J) into remaining */ /* equation. */ if (i__ > 1) { i__2 = is - 1; dger_(&i__2, &nb, &c_b27, &a[is * a_dim1 + 1], &c__1, rhs, &c__1, &c__[js * c_dim1 + 1], ldc); i__2 = is - 1; dger_(&i__2, &nb, &c_b27, &d__[is * d_dim1 + 1], & c__1, rhs, &c__1, &f[js * f_dim1 + 1], ldf); } if (j < q) { i__2 = *n - je; daxpy_(&i__2, &rhs[2], &b[js + (je + 1) * b_dim1], ldb, &c__[is + (je + 1) * c_dim1], ldc); i__2 = *n - je; daxpy_(&i__2, &rhs[2], &e[js + (je + 1) * e_dim1], lde, &f[is + (je + 1) * f_dim1], ldf); i__2 = *n - je; daxpy_(&i__2, &rhs[3], &b[jsp1 + (je + 1) * b_dim1], ldb, &c__[is + (je + 1) * c_dim1], ldc); i__2 = *n - je; daxpy_(&i__2, &rhs[3], &e[jsp1 + (je + 1) * e_dim1], lde, &f[is + (je + 1) * f_dim1], ldf); } } else if (mb == 2 && nb == 1) { /* Build a 4-by-4 system Z * x = RHS */ z__[0] = a[is + is * a_dim1]; z__[1] = a[isp1 + is * a_dim1]; z__[2] = d__[is + is * d_dim1]; z__[3] = 0.; z__[8] = a[is + isp1 * a_dim1]; z__[9] = a[isp1 + isp1 * a_dim1]; z__[10] = d__[is + isp1 * d_dim1]; z__[11] = d__[isp1 + isp1 * d_dim1]; z__[16] = -b[js + js * b_dim1]; z__[17] = 0.; z__[18] = -e[js + js * e_dim1]; z__[19] = 0.; z__[24] = 0.; z__[25] = -b[js + js * b_dim1]; z__[26] = 0.; z__[27] = -e[js + js * e_dim1]; /* Set up right hand side(s) */ rhs[0] = c__[is + js * c_dim1]; rhs[1] = c__[isp1 + js * c_dim1]; rhs[2] = f[is + js * f_dim1]; rhs[3] = f[isp1 + js * f_dim1]; /* Solve Z * x = RHS */ dgetc2_(&zdim, z__, &c__8, ipiv, jpiv, &ierr); if (ierr > 0) { *info = ierr; } if (*ijob == 0) { dgesc2_(&zdim, z__, &c__8, rhs, ipiv, jpiv, &scaloc); if (scaloc != 1.) { i__2 = *n; for (k = 1; k <= i__2; ++k) { dscal_(m, &scaloc, &c__[k * c_dim1 + 1], & c__1); dscal_(m, &scaloc, &f[k * f_dim1 + 1], &c__1); /* L70: */ } *scale *= scaloc; } } else { dlatdf_(ijob, &zdim, z__, &c__8, rhs, rdsum, rdscal, ipiv, jpiv); } /* Unpack solution vector(s) */ c__[is + js * c_dim1] = rhs[0]; c__[isp1 + js * c_dim1] = rhs[1]; f[is + js * f_dim1] = rhs[2]; f[isp1 + js * f_dim1] = rhs[3]; /* Substitute R(I, J) and L(I, J) into remaining */ /* equation. */ if (i__ > 1) { i__2 = is - 1; dgemv_("N", &i__2, &mb, &c_b27, &a[is * a_dim1 + 1], lda, rhs, &c__1, &c_b42, &c__[js * c_dim1 + 1] , &c__1); i__2 = is - 1; dgemv_("N", &i__2, &mb, &c_b27, &d__[is * d_dim1 + 1], ldd, rhs, &c__1, &c_b42, &f[js * f_dim1 + 1], &c__1); } if (j < q) { i__2 = *n - je; dger_(&mb, &i__2, &c_b42, &rhs[2], &c__1, &b[js + (je + 1) * b_dim1], ldb, &c__[is + (je + 1) * c_dim1], ldc); i__2 = *n - je; dger_(&mb, &i__2, &c_b42, &rhs[2], &c__1, &e[js + (je + 1) * e_dim1], lde, &f[is + (je + 1) * f_dim1], ldf); } } else if (mb == 2 && nb == 2) { /* Build an 8-by-8 system Z * x = RHS */ dlaset_("F", &c__8, &c__8, &c_b56, &c_b56, z__, &c__8); z__[0] = a[is + is * a_dim1]; z__[1] = a[isp1 + is * a_dim1]; z__[4] = d__[is + is * d_dim1]; z__[8] = a[is + isp1 * a_dim1]; z__[9] = a[isp1 + isp1 * a_dim1]; z__[12] = d__[is + isp1 * d_dim1]; z__[13] = d__[isp1 + isp1 * d_dim1]; z__[18] = a[is + is * a_dim1]; z__[19] = a[isp1 + is * a_dim1]; z__[22] = d__[is + is * d_dim1]; z__[26] = a[is + isp1 * a_dim1]; z__[27] = a[isp1 + isp1 * a_dim1]; z__[30] = d__[is + isp1 * d_dim1]; z__[31] = d__[isp1 + isp1 * d_dim1]; z__[32] = -b[js + js * b_dim1]; z__[34] = -b[js + jsp1 * b_dim1]; z__[36] = -e[js + js * e_dim1]; z__[38] = -e[js + jsp1 * e_dim1]; z__[41] = -b[js + js * b_dim1]; z__[43] = -b[js + jsp1 * b_dim1]; z__[45] = -e[js + js * e_dim1]; z__[47] = -e[js + jsp1 * e_dim1]; z__[48] = -b[jsp1 + js * b_dim1]; z__[50] = -b[jsp1 + jsp1 * b_dim1]; z__[54] = -e[jsp1 + jsp1 * e_dim1]; z__[57] = -b[jsp1 + js * b_dim1]; z__[59] = -b[jsp1 + jsp1 * b_dim1]; z__[63] = -e[jsp1 + jsp1 * e_dim1]; /* Set up right hand side(s) */ k = 1; ii = mb * nb + 1; i__2 = nb - 1; for (jj = 0; jj <= i__2; ++jj) { dcopy_(&mb, &c__[is + (js + jj) * c_dim1], &c__1, & rhs[k - 1], &c__1); dcopy_(&mb, &f[is + (js + jj) * f_dim1], &c__1, &rhs[ ii - 1], &c__1); k += mb; ii += mb; /* L80: */ } /* Solve Z * x = RHS */ dgetc2_(&zdim, z__, &c__8, ipiv, jpiv, &ierr); if (ierr > 0) { *info = ierr; } if (*ijob == 0) { dgesc2_(&zdim, z__, &c__8, rhs, ipiv, jpiv, &scaloc); if (scaloc != 1.) { i__2 = *n; for (k = 1; k <= i__2; ++k) { dscal_(m, &scaloc, &c__[k * c_dim1 + 1], & c__1); dscal_(m, &scaloc, &f[k * f_dim1 + 1], &c__1); /* L90: */ } *scale *= scaloc; } } else { dlatdf_(ijob, &zdim, z__, &c__8, rhs, rdsum, rdscal, ipiv, jpiv); } /* Unpack solution vector(s) */ k = 1; ii = mb * nb + 1; i__2 = nb - 1; for (jj = 0; jj <= i__2; ++jj) { dcopy_(&mb, &rhs[k - 1], &c__1, &c__[is + (js + jj) * c_dim1], &c__1); dcopy_(&mb, &rhs[ii - 1], &c__1, &f[is + (js + jj) * f_dim1], &c__1); k += mb; ii += mb; /* L100: */ } /* Substitute R(I, J) and L(I, J) into remaining */ /* equation. */ if (i__ > 1) { i__2 = is - 1; dgemm_("N", "N", &i__2, &nb, &mb, &c_b27, &a[is * a_dim1 + 1], lda, rhs, &mb, &c_b42, &c__[js * c_dim1 + 1], ldc); i__2 = is - 1; dgemm_("N", "N", &i__2, &nb, &mb, &c_b27, &d__[is * d_dim1 + 1], ldd, rhs, &mb, &c_b42, &f[js * f_dim1 + 1], ldf); } if (j < q) { k = mb * nb + 1; i__2 = *n - je; dgemm_("N", "N", &mb, &i__2, &nb, &c_b42, &rhs[k - 1], &mb, &b[js + (je + 1) * b_dim1], ldb, &c_b42, &c__[is + (je + 1) * c_dim1], ldc); i__2 = *n - je; dgemm_("N", "N", &mb, &i__2, &nb, &c_b42, &rhs[k - 1], &mb, &e[js + (je + 1) * e_dim1], lde, &c_b42, &f[is + (je + 1) * f_dim1], ldf); } } /* L110: */ } /* L120: */ } } else { /* Solve (I, J) - subsystem */ /* A(I, I)' * R(I, J) + D(I, I)' * L(J, J) = C(I, J) */ /* R(I, I) * B(J, J) + L(I, J) * E(J, J) = -F(I, J) */ /* for I = 1, 2, ..., P, J = Q, Q - 1, ..., 1 */ *scale = 1.; scaloc = 1.; i__1 = p; for (i__ = 1; i__ <= i__1; ++i__) { is = iwork[i__]; isp1 = is + 1; ie = i__; mb = ie - is + 1; i__2 = p + 2; for (j = q; j >= i__2; --j) { js = iwork[j]; jsp1 = js + 1; je = iwork[j + 1] - 1; nb = je - js + 1; zdim = mb * nb << 1; if (mb == 1 && nb == 1) { /* Build a 2-by-2 system Z' * x = RHS */ z__[0] = a[is + is * a_dim1]; z__[1] = -b[js + js * b_dim1]; z__[8] = d__[is + is * d_dim1]; z__[9] = -e[js + js * e_dim1]; /* Set up right hand side(s) */ rhs[0] = c__[is + js * c_dim1]; rhs[1] = f[is + js * f_dim1]; /* Solve Z' * x = RHS */ dgetc2_(&zdim, z__, &c__8, ipiv, jpiv, &ierr); if (ierr > 0) { *info = ierr; } dgesc2_(&zdim, z__, &c__8, rhs, ipiv, jpiv, &scaloc); if (scaloc != 1.) { i__3 = *n; for (k = 1; k <= i__3; ++k) { dscal_(m, &scaloc, &c__[k * c_dim1 + 1], &c__1); dscal_(m, &scaloc, &f[k * f_dim1 + 1], &c__1); /* L130: */ } *scale *= scaloc; } /* Unpack solution vector(s) */ c__[is + js * c_dim1] = rhs[0]; f[is + js * f_dim1] = rhs[1]; /* Substitute R(I, J) and L(I, J) into remaining */ /* equation. */ if (j > p + 2) { alpha = rhs[0]; i__3 = js - 1; daxpy_(&i__3, &alpha, &b[js * b_dim1 + 1], &c__1, &f[ is + f_dim1], ldf); alpha = rhs[1]; i__3 = js - 1; daxpy_(&i__3, &alpha, &e[js * e_dim1 + 1], &c__1, &f[ is + f_dim1], ldf); } if (i__ < p) { alpha = -rhs[0]; i__3 = *m - ie; daxpy_(&i__3, &alpha, &a[is + (ie + 1) * a_dim1], lda, &c__[ie + 1 + js * c_dim1], &c__1); alpha = -rhs[1]; i__3 = *m - ie; daxpy_(&i__3, &alpha, &d__[is + (ie + 1) * d_dim1], ldd, &c__[ie + 1 + js * c_dim1], &c__1); } } else if (mb == 1 && nb == 2) { /* Build a 4-by-4 system Z' * x = RHS */ z__[0] = a[is + is * a_dim1]; z__[1] = 0.; z__[2] = -b[js + js * b_dim1]; z__[3] = -b[jsp1 + js * b_dim1]; z__[8] = 0.; z__[9] = a[is + is * a_dim1]; z__[10] = -b[js + jsp1 * b_dim1]; z__[11] = -b[jsp1 + jsp1 * b_dim1]; z__[16] = d__[is + is * d_dim1]; z__[17] = 0.; z__[18] = -e[js + js * e_dim1]; z__[19] = 0.; z__[24] = 0.; z__[25] = d__[is + is * d_dim1]; z__[26] = -e[js + jsp1 * e_dim1]; z__[27] = -e[jsp1 + jsp1 * e_dim1]; /* Set up right hand side(s) */ rhs[0] = c__[is + js * c_dim1]; rhs[1] = c__[is + jsp1 * c_dim1]; rhs[2] = f[is + js * f_dim1]; rhs[3] = f[is + jsp1 * f_dim1]; /* Solve Z' * x = RHS */ dgetc2_(&zdim, z__, &c__8, ipiv, jpiv, &ierr); if (ierr > 0) { *info = ierr; } dgesc2_(&zdim, z__, &c__8, rhs, ipiv, jpiv, &scaloc); if (scaloc != 1.) { i__3 = *n; for (k = 1; k <= i__3; ++k) { dscal_(m, &scaloc, &c__[k * c_dim1 + 1], &c__1); dscal_(m, &scaloc, &f[k * f_dim1 + 1], &c__1); /* L140: */ } *scale *= scaloc; } /* Unpack solution vector(s) */ c__[is + js * c_dim1] = rhs[0]; c__[is + jsp1 * c_dim1] = rhs[1]; f[is + js * f_dim1] = rhs[2]; f[is + jsp1 * f_dim1] = rhs[3]; /* Substitute R(I, J) and L(I, J) into remaining */ /* equation. */ if (j > p + 2) { i__3 = js - 1; daxpy_(&i__3, rhs, &b[js * b_dim1 + 1], &c__1, &f[is + f_dim1], ldf); i__3 = js - 1; daxpy_(&i__3, &rhs[1], &b[jsp1 * b_dim1 + 1], &c__1, & f[is + f_dim1], ldf); i__3 = js - 1; daxpy_(&i__3, &rhs[2], &e[js * e_dim1 + 1], &c__1, &f[ is + f_dim1], ldf); i__3 = js - 1; daxpy_(&i__3, &rhs[3], &e[jsp1 * e_dim1 + 1], &c__1, & f[is + f_dim1], ldf); } if (i__ < p) { i__3 = *m - ie; dger_(&i__3, &nb, &c_b27, &a[is + (ie + 1) * a_dim1], lda, rhs, &c__1, &c__[ie + 1 + js * c_dim1], ldc); i__3 = *m - ie; dger_(&i__3, &nb, &c_b27, &d__[is + (ie + 1) * d_dim1] , ldd, &rhs[2], &c__1, &c__[ie + 1 + js * c_dim1], ldc); } } else if (mb == 2 && nb == 1) { /* Build a 4-by-4 system Z' * x = RHS */ z__[0] = a[is + is * a_dim1]; z__[1] = a[is + isp1 * a_dim1]; z__[2] = -b[js + js * b_dim1]; z__[3] = 0.; z__[8] = a[isp1 + is * a_dim1]; z__[9] = a[isp1 + isp1 * a_dim1]; z__[10] = 0.; z__[11] = -b[js + js * b_dim1]; z__[16] = d__[is + is * d_dim1]; z__[17] = d__[is + isp1 * d_dim1]; z__[18] = -e[js + js * e_dim1]; z__[19] = 0.; z__[24] = 0.; z__[25] = d__[isp1 + isp1 * d_dim1]; z__[26] = 0.; z__[27] = -e[js + js * e_dim1]; /* Set up right hand side(s) */ rhs[0] = c__[is + js * c_dim1]; rhs[1] = c__[isp1 + js * c_dim1]; rhs[2] = f[is + js * f_dim1]; rhs[3] = f[isp1 + js * f_dim1]; /* Solve Z' * x = RHS */ dgetc2_(&zdim, z__, &c__8, ipiv, jpiv, &ierr); if (ierr > 0) { *info = ierr; } dgesc2_(&zdim, z__, &c__8, rhs, ipiv, jpiv, &scaloc); if (scaloc != 1.) { i__3 = *n; for (k = 1; k <= i__3; ++k) { dscal_(m, &scaloc, &c__[k * c_dim1 + 1], &c__1); dscal_(m, &scaloc, &f[k * f_dim1 + 1], &c__1); /* L150: */ } *scale *= scaloc; } /* Unpack solution vector(s) */ c__[is + js * c_dim1] = rhs[0]; c__[isp1 + js * c_dim1] = rhs[1]; f[is + js * f_dim1] = rhs[2]; f[isp1 + js * f_dim1] = rhs[3]; /* Substitute R(I, J) and L(I, J) into remaining */ /* equation. */ if (j > p + 2) { i__3 = js - 1; dger_(&mb, &i__3, &c_b42, rhs, &c__1, &b[js * b_dim1 + 1], &c__1, &f[is + f_dim1], ldf); i__3 = js - 1; dger_(&mb, &i__3, &c_b42, &rhs[2], &c__1, &e[js * e_dim1 + 1], &c__1, &f[is + f_dim1], ldf); } if (i__ < p) { i__3 = *m - ie; dgemv_("T", &mb, &i__3, &c_b27, &a[is + (ie + 1) * a_dim1], lda, rhs, &c__1, &c_b42, &c__[ie + 1 + js * c_dim1], &c__1); i__3 = *m - ie; dgemv_("T", &mb, &i__3, &c_b27, &d__[is + (ie + 1) * d_dim1], ldd, &rhs[2], &c__1, &c_b42, &c__[ie + 1 + js * c_dim1], &c__1); } } else if (mb == 2 && nb == 2) { /* Build an 8-by-8 system Z' * x = RHS */ dlaset_("F", &c__8, &c__8, &c_b56, &c_b56, z__, &c__8); z__[0] = a[is + is * a_dim1]; z__[1] = a[is + isp1 * a_dim1]; z__[4] = -b[js + js * b_dim1]; z__[6] = -b[jsp1 + js * b_dim1]; z__[8] = a[isp1 + is * a_dim1]; z__[9] = a[isp1 + isp1 * a_dim1]; z__[13] = -b[js + js * b_dim1]; z__[15] = -b[jsp1 + js * b_dim1]; z__[18] = a[is + is * a_dim1]; z__[19] = a[is + isp1 * a_dim1]; z__[20] = -b[js + jsp1 * b_dim1]; z__[22] = -b[jsp1 + jsp1 * b_dim1]; z__[26] = a[isp1 + is * a_dim1]; z__[27] = a[isp1 + isp1 * a_dim1]; z__[29] = -b[js + jsp1 * b_dim1]; z__[31] = -b[jsp1 + jsp1 * b_dim1]; z__[32] = d__[is + is * d_dim1]; z__[33] = d__[is + isp1 * d_dim1]; z__[36] = -e[js + js * e_dim1]; z__[41] = d__[isp1 + isp1 * d_dim1]; z__[45] = -e[js + js * e_dim1]; z__[50] = d__[is + is * d_dim1]; z__[51] = d__[is + isp1 * d_dim1]; z__[52] = -e[js + jsp1 * e_dim1]; z__[54] = -e[jsp1 + jsp1 * e_dim1]; z__[59] = d__[isp1 + isp1 * d_dim1]; z__[61] = -e[js + jsp1 * e_dim1]; z__[63] = -e[jsp1 + jsp1 * e_dim1]; /* Set up right hand side(s) */ k = 1; ii = mb * nb + 1; i__3 = nb - 1; for (jj = 0; jj <= i__3; ++jj) { dcopy_(&mb, &c__[is + (js + jj) * c_dim1], &c__1, & rhs[k - 1], &c__1); dcopy_(&mb, &f[is + (js + jj) * f_dim1], &c__1, &rhs[ ii - 1], &c__1); k += mb; ii += mb; /* L160: */ } /* Solve Z' * x = RHS */ dgetc2_(&zdim, z__, &c__8, ipiv, jpiv, &ierr); if (ierr > 0) { *info = ierr; } dgesc2_(&zdim, z__, &c__8, rhs, ipiv, jpiv, &scaloc); if (scaloc != 1.) { i__3 = *n; for (k = 1; k <= i__3; ++k) { dscal_(m, &scaloc, &c__[k * c_dim1 + 1], &c__1); dscal_(m, &scaloc, &f[k * f_dim1 + 1], &c__1); /* L170: */ } *scale *= scaloc; } /* Unpack solution vector(s) */ k = 1; ii = mb * nb + 1; i__3 = nb - 1; for (jj = 0; jj <= i__3; ++jj) { dcopy_(&mb, &rhs[k - 1], &c__1, &c__[is + (js + jj) * c_dim1], &c__1); dcopy_(&mb, &rhs[ii - 1], &c__1, &f[is + (js + jj) * f_dim1], &c__1); k += mb; ii += mb; /* L180: */ } /* Substitute R(I, J) and L(I, J) into remaining */ /* equation. */ if (j > p + 2) { i__3 = js - 1; dgemm_("N", "T", &mb, &i__3, &nb, &c_b42, &c__[is + js * c_dim1], ldc, &b[js * b_dim1 + 1], ldb, & c_b42, &f[is + f_dim1], ldf); i__3 = js - 1; dgemm_("N", "T", &mb, &i__3, &nb, &c_b42, &f[is + js * f_dim1], ldf, &e[js * e_dim1 + 1], lde, & c_b42, &f[is + f_dim1], ldf); } if (i__ < p) { i__3 = *m - ie; dgemm_("T", "N", &i__3, &nb, &mb, &c_b27, &a[is + (ie + 1) * a_dim1], lda, &c__[is + js * c_dim1], ldc, &c_b42, &c__[ie + 1 + js * c_dim1], ldc); i__3 = *m - ie; dgemm_("T", "N", &i__3, &nb, &mb, &c_b27, &d__[is + ( ie + 1) * d_dim1], ldd, &f[is + js * f_dim1], ldf, &c_b42, &c__[ie + 1 + js * c_dim1], ldc); } } /* L190: */ } /* L200: */ } } return 0; /* End of DTGSY2 */ } /* dtgsy2_ */