/* stgsy2.f -- translated by f2c (version 20061008).
You must link the resulting object file with libf2c:
on Microsoft Windows system, link with libf2c.lib;
on Linux or Unix systems, link with .../path/to/libf2c.a -lm
or, if you install libf2c.a in a standard place, with -lf2c -lm
-- in that order, at the end of the command line, as in
cc *.o -lf2c -lm
Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
http://www.netlib.org/f2c/libf2c.zip
*/
#include "f2c.h"
#include "blaswrap.h"
/* Table of constant values */
static integer c__8 = 8;
static integer c__1 = 1;
static real c_b27 = -1.f;
static real c_b42 = 1.f;
static real c_b56 = 0.f;
/* Subroutine */ int stgsy2_(char *trans, integer *ijob, integer *m, integer *
n, real *a, integer *lda, real *b, integer *ldb, real *c__, integer *
ldc, real *d__, integer *ldd, real *e, integer *lde, real *f, integer
*ldf, real *scale, real *rdsum, real *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;
real z__[64] /* was [8][8] */;
integer ie, je, mb, nb, ii, jj, is, js;
real rhs[8];
integer isp1, jsp1;
extern /* Subroutine */ int sger_(integer *, integer *, real *, real *,
integer *, real *, integer *, real *, integer *);
integer ierr, zdim, ipiv[8], jpiv[8];
real alpha;
extern logical lsame_(char *, char *);
extern /* Subroutine */ int sscal_(integer *, real *, real *, integer *),
sgemm_(char *, char *, integer *, integer *, integer *, real *,
real *, integer *, real *, integer *, real *, real *, integer *), sgemv_(char *, integer *, integer *, real *,
real *, integer *, real *, integer *, real *, real *, integer *), scopy_(integer *, real *, integer *, real *, integer *),
saxpy_(integer *, real *, real *, integer *, real *, integer *),
sgesc2_(integer *, real *, integer *, real *, integer *, integer *
, real *), sgetc2_(integer *, real *, integer *, integer *,
integer *, integer *);
real scaloc;
extern /* Subroutine */ int slatdf_(integer *, integer *, real *, integer
*, real *, real *, real *, integer *, integer *), xerbla_(char *,
integer *), slaset_(char *, integer *, integer *, real *,
real *, real *, integer *);
logical notran;
/* -- LAPACK auxiliary routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* January 2007 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* STGSY2 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 SLACON. */
/* STGSY2 also (IJOB >= 1) contributes to the computation in STGSYL */
/* 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 */
/* STGSYL. See STGSYL 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. (SGECON 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) REAL 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) REAL 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) REAL 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) REAL 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) REAL 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) REAL 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) REAL */
/* 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) REAL */
/* On entry, the sum of squares of computed contributions to */
/* the Dif-estimate under computation by STGSYL, 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 STGSY2 is called by STGSYL. */
/* RDSCAL (input/output) REAL */
/* 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 STGSY2 is called by */
/* STGSYL. */
/* 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 SCOPY by calls to SLASET. */
/* 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_("STGSY2", &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.f) {
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.f) {
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.f;
scaloc = 1.f;
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 */
sgetc2_(&zdim, z__, &c__8, ipiv, jpiv, &ierr);
if (ierr > 0) {
*info = ierr;
}
if (*ijob == 0) {
sgesc2_(&zdim, z__, &c__8, rhs, ipiv, jpiv, &scaloc);
if (scaloc != 1.f) {
i__2 = *n;
for (k = 1; k <= i__2; ++k) {
sscal_(m, &scaloc, &c__[k * c_dim1 + 1], &
c__1);
sscal_(m, &scaloc, &f[k * f_dim1 + 1], &c__1);
/* L50: */
}
*scale *= scaloc;
}
} else {
slatdf_(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;
saxpy_(&i__2, &alpha, &a[is * a_dim1 + 1], &c__1, &
c__[js * c_dim1 + 1], &c__1);
i__2 = is - 1;
saxpy_(&i__2, &alpha, &d__[is * d_dim1 + 1], &c__1, &
f[js * f_dim1 + 1], &c__1);
}
if (j < q) {
i__2 = *n - je;
saxpy_(&i__2, &rhs[1], &b[js + (je + 1) * b_dim1],
ldb, &c__[is + (je + 1) * c_dim1], ldc);
i__2 = *n - je;
saxpy_(&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.f;
z__[2] = d__[is + is * d_dim1];
z__[3] = 0.f;
z__[8] = 0.f;
z__[9] = a[is + is * a_dim1];
z__[10] = 0.f;
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.f;
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 */
sgetc2_(&zdim, z__, &c__8, ipiv, jpiv, &ierr);
if (ierr > 0) {
*info = ierr;
}
if (*ijob == 0) {
sgesc2_(&zdim, z__, &c__8, rhs, ipiv, jpiv, &scaloc);
if (scaloc != 1.f) {
i__2 = *n;
for (k = 1; k <= i__2; ++k) {
sscal_(m, &scaloc, &c__[k * c_dim1 + 1], &
c__1);
sscal_(m, &scaloc, &f[k * f_dim1 + 1], &c__1);
/* L60: */
}
*scale *= scaloc;
}
} else {
slatdf_(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;
sger_(&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;
sger_(&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;
saxpy_(&i__2, &rhs[2], &b[js + (je + 1) * b_dim1],
ldb, &c__[is + (je + 1) * c_dim1], ldc);
i__2 = *n - je;
saxpy_(&i__2, &rhs[2], &e[js + (je + 1) * e_dim1],
lde, &f[is + (je + 1) * f_dim1], ldf);
i__2 = *n - je;
saxpy_(&i__2, &rhs[3], &b[jsp1 + (je + 1) * b_dim1],
ldb, &c__[is + (je + 1) * c_dim1], ldc);
i__2 = *n - je;
saxpy_(&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.f;
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.f;
z__[18] = -e[js + js * e_dim1];
z__[19] = 0.f;
z__[24] = 0.f;
z__[25] = -b[js + js * b_dim1];
z__[26] = 0.f;
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 */
sgetc2_(&zdim, z__, &c__8, ipiv, jpiv, &ierr);
if (ierr > 0) {
*info = ierr;
}
if (*ijob == 0) {
sgesc2_(&zdim, z__, &c__8, rhs, ipiv, jpiv, &scaloc);
if (scaloc != 1.f) {
i__2 = *n;
for (k = 1; k <= i__2; ++k) {
sscal_(m, &scaloc, &c__[k * c_dim1 + 1], &
c__1);
sscal_(m, &scaloc, &f[k * f_dim1 + 1], &c__1);
/* L70: */
}
*scale *= scaloc;
}
} else {
slatdf_(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;
sgemv_("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;
sgemv_("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;
sger_(&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;
sger_(&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 */
slaset_("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) {
scopy_(&mb, &c__[is + (js + jj) * c_dim1], &c__1, &
rhs[k - 1], &c__1);
scopy_(&mb, &f[is + (js + jj) * f_dim1], &c__1, &rhs[
ii - 1], &c__1);
k += mb;
ii += mb;
/* L80: */
}
/* Solve Z * x = RHS */
sgetc2_(&zdim, z__, &c__8, ipiv, jpiv, &ierr);
if (ierr > 0) {
*info = ierr;
}
if (*ijob == 0) {
sgesc2_(&zdim, z__, &c__8, rhs, ipiv, jpiv, &scaloc);
if (scaloc != 1.f) {
i__2 = *n;
for (k = 1; k <= i__2; ++k) {
sscal_(m, &scaloc, &c__[k * c_dim1 + 1], &
c__1);
sscal_(m, &scaloc, &f[k * f_dim1 + 1], &c__1);
/* L90: */
}
*scale *= scaloc;
}
} else {
slatdf_(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) {
scopy_(&mb, &rhs[k - 1], &c__1, &c__[is + (js + jj) *
c_dim1], &c__1);
scopy_(&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;
sgemm_("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;
sgemm_("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;
sgemm_("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;
sgemm_("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.f;
scaloc = 1.f;
i__1 = p;
for (i__ = 1; i__ <= i__1; ++i__) {
is = iwork[i__];
isp1 = is + 1;
ie = iwork[i__ + 1] - 1;
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 */
sgetc2_(&zdim, z__, &c__8, ipiv, jpiv, &ierr);
if (ierr > 0) {
*info = ierr;
}
sgesc2_(&zdim, z__, &c__8, rhs, ipiv, jpiv, &scaloc);
if (scaloc != 1.f) {
i__3 = *n;
for (k = 1; k <= i__3; ++k) {
sscal_(m, &scaloc, &c__[k * c_dim1 + 1], &c__1);
sscal_(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;
saxpy_(&i__3, &alpha, &b[js * b_dim1 + 1], &c__1, &f[
is + f_dim1], ldf);
alpha = rhs[1];
i__3 = js - 1;
saxpy_(&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;
saxpy_(&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;
saxpy_(&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.f;
z__[2] = -b[js + js * b_dim1];
z__[3] = -b[jsp1 + js * b_dim1];
z__[8] = 0.f;
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.f;
z__[18] = -e[js + js * e_dim1];
z__[19] = 0.f;
z__[24] = 0.f;
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 */
sgetc2_(&zdim, z__, &c__8, ipiv, jpiv, &ierr);
if (ierr > 0) {
*info = ierr;
}
sgesc2_(&zdim, z__, &c__8, rhs, ipiv, jpiv, &scaloc);
if (scaloc != 1.f) {
i__3 = *n;
for (k = 1; k <= i__3; ++k) {
sscal_(m, &scaloc, &c__[k * c_dim1 + 1], &c__1);
sscal_(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;
saxpy_(&i__3, rhs, &b[js * b_dim1 + 1], &c__1, &f[is
+ f_dim1], ldf);
i__3 = js - 1;
saxpy_(&i__3, &rhs[1], &b[jsp1 * b_dim1 + 1], &c__1, &
f[is + f_dim1], ldf);
i__3 = js - 1;
saxpy_(&i__3, &rhs[2], &e[js * e_dim1 + 1], &c__1, &f[
is + f_dim1], ldf);
i__3 = js - 1;
saxpy_(&i__3, &rhs[3], &e[jsp1 * e_dim1 + 1], &c__1, &
f[is + f_dim1], ldf);
}
if (i__ < p) {
i__3 = *m - ie;
sger_(&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;
sger_(&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.f;
z__[8] = a[isp1 + is * a_dim1];
z__[9] = a[isp1 + isp1 * a_dim1];
z__[10] = 0.f;
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.f;
z__[24] = 0.f;
z__[25] = d__[isp1 + isp1 * d_dim1];
z__[26] = 0.f;
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 */
sgetc2_(&zdim, z__, &c__8, ipiv, jpiv, &ierr);
if (ierr > 0) {
*info = ierr;
}
sgesc2_(&zdim, z__, &c__8, rhs, ipiv, jpiv, &scaloc);
if (scaloc != 1.f) {
i__3 = *n;
for (k = 1; k <= i__3; ++k) {
sscal_(m, &scaloc, &c__[k * c_dim1 + 1], &c__1);
sscal_(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;
sger_(&mb, &i__3, &c_b42, rhs, &c__1, &b[js * b_dim1
+ 1], &c__1, &f[is + f_dim1], ldf);
i__3 = js - 1;
sger_(&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;
sgemv_("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;
sgemv_("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 */
slaset_("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) {
scopy_(&mb, &c__[is + (js + jj) * c_dim1], &c__1, &
rhs[k - 1], &c__1);
scopy_(&mb, &f[is + (js + jj) * f_dim1], &c__1, &rhs[
ii - 1], &c__1);
k += mb;
ii += mb;
/* L160: */
}
/* Solve Z' * x = RHS */
sgetc2_(&zdim, z__, &c__8, ipiv, jpiv, &ierr);
if (ierr > 0) {
*info = ierr;
}
sgesc2_(&zdim, z__, &c__8, rhs, ipiv, jpiv, &scaloc);
if (scaloc != 1.f) {
i__3 = *n;
for (k = 1; k <= i__3; ++k) {
sscal_(m, &scaloc, &c__[k * c_dim1 + 1], &c__1);
sscal_(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) {
scopy_(&mb, &rhs[k - 1], &c__1, &c__[is + (js + jj) *
c_dim1], &c__1);
scopy_(&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;
sgemm_("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;
sgemm_("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;
sgemm_("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;
sgemm_("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 STGSY2 */
} /* stgsy2_ */