/* ctgsy2.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__2 = 2;
static integer c__1 = 1;
/* Subroutine */ int ctgsy2_(char *trans, integer *ijob, integer *m, integer *
n, complex *a, integer *lda, complex *b, integer *ldb, complex *c__,
integer *ldc, complex *d__, integer *ldd, complex *e, integer *lde,
complex *f, integer *ldf, real *scale, real *rdsum, real *rdscal,
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,
i__4;
complex q__1, q__2, q__3, q__4, q__5, q__6;
/* Builtin functions */
void r_cnjg(complex *, complex *);
/* Local variables */
integer i__, j, k;
complex z__[4] /* was [2][2] */, rhs[2];
integer ierr, ipiv[2], jpiv[2];
complex alpha;
extern /* Subroutine */ int cscal_(integer *, complex *, complex *,
integer *);
extern logical lsame_(char *, char *);
extern /* Subroutine */ int caxpy_(integer *, complex *, complex *,
integer *, complex *, integer *), cgesc2_(integer *, complex *,
integer *, complex *, integer *, integer *, real *), cgetc2_(
integer *, complex *, integer *, integer *, integer *, integer *),
clatdf_(integer *, integer *, complex *, integer *, complex *,
real *, real *, integer *, integer *);
real scaloc;
extern /* Subroutine */ int xerbla_(char *, integer *);
logical notran;
/* -- LAPACK auxiliary routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* CTGSY2 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. A, B, D and E are upper triangular */
/* (i.e., (A,D) and (B,E) in generalized Schur form). */
/* 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 */
/* Zx = 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. */
/* If TRANS = 'C', y in the conjugate transposed system Z'y = scale*b */
/* is solved for, 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 CLACON. */
/* CTGSY2 also (IJOB >= 1) contributes to the computation in CTGSYL */
/* of an upper bound on the separation between to matrix pairs. Then */
/* the input (A, D), (B, E) are sub-pencils of two matrix pairs in */
/* CTGSYL. */
/* 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) COMPLEX array, dimension (LDA, M) */
/* On entry, A contains an upper triangular matrix. */
/* LDA (input) INTEGER */
/* The leading dimension of the matrix A. LDA >= max(1, M). */
/* B (input) COMPLEX array, dimension (LDB, N) */
/* On entry, B contains an upper triangular matrix. */
/* LDB (input) INTEGER */
/* The leading dimension of the matrix B. LDB >= max(1, N). */
/* C (input/output) COMPLEX 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) COMPLEX 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) COMPLEX 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) COMPLEX 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 CTGSYL, 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 CTGSY2 is called by */
/* CTGSYL. */
/* 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 CTGSY2 is called by */
/* CTGSYL. */
/* INFO (output) INTEGER */
/* On exit, if INFO is set to */
/* =0: Successful exit */
/* <0: If INFO = -i, input argument number i is illegal. */
/* >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. */
/* ===================================================================== */
/* .. 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;
/* Function Body */
*info = 0;
ierr = 0;
notran = lsame_(trans, "N");
if (! notran && ! lsame_(trans, "C")) {
*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_("CTGSY2", &i__1);
return 0;
}
if (notran) {
/* Solve (I, J) - system */
/* 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 = M, M - 1, ..., 1; J = 1, 2, ..., N */
*scale = 1.f;
scaloc = 1.f;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
for (i__ = *m; i__ >= 1; --i__) {
/* Build 2 by 2 system */
i__2 = i__ + i__ * a_dim1;
z__[0].r = a[i__2].r, z__[0].i = a[i__2].i;
i__2 = i__ + i__ * d_dim1;
z__[1].r = d__[i__2].r, z__[1].i = d__[i__2].i;
i__2 = j + j * b_dim1;
q__1.r = -b[i__2].r, q__1.i = -b[i__2].i;
z__[2].r = q__1.r, z__[2].i = q__1.i;
i__2 = j + j * e_dim1;
q__1.r = -e[i__2].r, q__1.i = -e[i__2].i;
z__[3].r = q__1.r, z__[3].i = q__1.i;
/* Set up right hand side(s) */
i__2 = i__ + j * c_dim1;
rhs[0].r = c__[i__2].r, rhs[0].i = c__[i__2].i;
i__2 = i__ + j * f_dim1;
rhs[1].r = f[i__2].r, rhs[1].i = f[i__2].i;
/* Solve Z * x = RHS */
cgetc2_(&c__2, z__, &c__2, ipiv, jpiv, &ierr);
if (ierr > 0) {
*info = ierr;
}
if (*ijob == 0) {
cgesc2_(&c__2, z__, &c__2, rhs, ipiv, jpiv, &scaloc);
if (scaloc != 1.f) {
i__2 = *n;
for (k = 1; k <= i__2; ++k) {
q__1.r = scaloc, q__1.i = 0.f;
cscal_(m, &q__1, &c__[k * c_dim1 + 1], &c__1);
q__1.r = scaloc, q__1.i = 0.f;
cscal_(m, &q__1, &f[k * f_dim1 + 1], &c__1);
/* L10: */
}
*scale *= scaloc;
}
} else {
clatdf_(ijob, &c__2, z__, &c__2, rhs, rdsum, rdscal, ipiv,
jpiv);
}
/* Unpack solution vector(s) */
i__2 = i__ + j * c_dim1;
c__[i__2].r = rhs[0].r, c__[i__2].i = rhs[0].i;
i__2 = i__ + j * f_dim1;
f[i__2].r = rhs[1].r, f[i__2].i = rhs[1].i;
/* Substitute R(I, J) and L(I, J) into remaining equation. */
if (i__ > 1) {
q__1.r = -rhs[0].r, q__1.i = -rhs[0].i;
alpha.r = q__1.r, alpha.i = q__1.i;
i__2 = i__ - 1;
caxpy_(&i__2, &alpha, &a[i__ * a_dim1 + 1], &c__1, &c__[j
* c_dim1 + 1], &c__1);
i__2 = i__ - 1;
caxpy_(&i__2, &alpha, &d__[i__ * d_dim1 + 1], &c__1, &f[j
* f_dim1 + 1], &c__1);
}
if (j < *n) {
i__2 = *n - j;
caxpy_(&i__2, &rhs[1], &b[j + (j + 1) * b_dim1], ldb, &
c__[i__ + (j + 1) * c_dim1], ldc);
i__2 = *n - j;
caxpy_(&i__2, &rhs[1], &e[j + (j + 1) * e_dim1], lde, &f[
i__ + (j + 1) * f_dim1], ldf);
}
/* L20: */
}
/* L30: */
}
} else {
/* Solve transposed (I, J) - system: */
/* 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, ..., M, J = N, N - 1, ..., 1 */
*scale = 1.f;
scaloc = 1.f;
i__1 = *m;
for (i__ = 1; i__ <= i__1; ++i__) {
for (j = *n; j >= 1; --j) {
/* Build 2 by 2 system Z' */
r_cnjg(&q__1, &a[i__ + i__ * a_dim1]);
z__[0].r = q__1.r, z__[0].i = q__1.i;
r_cnjg(&q__2, &b[j + j * b_dim1]);
q__1.r = -q__2.r, q__1.i = -q__2.i;
z__[1].r = q__1.r, z__[1].i = q__1.i;
r_cnjg(&q__1, &d__[i__ + i__ * d_dim1]);
z__[2].r = q__1.r, z__[2].i = q__1.i;
r_cnjg(&q__2, &e[j + j * e_dim1]);
q__1.r = -q__2.r, q__1.i = -q__2.i;
z__[3].r = q__1.r, z__[3].i = q__1.i;
/* Set up right hand side(s) */
i__2 = i__ + j * c_dim1;
rhs[0].r = c__[i__2].r, rhs[0].i = c__[i__2].i;
i__2 = i__ + j * f_dim1;
rhs[1].r = f[i__2].r, rhs[1].i = f[i__2].i;
/* Solve Z' * x = RHS */
cgetc2_(&c__2, z__, &c__2, ipiv, jpiv, &ierr);
if (ierr > 0) {
*info = ierr;
}
cgesc2_(&c__2, z__, &c__2, rhs, ipiv, jpiv, &scaloc);
if (scaloc != 1.f) {
i__2 = *n;
for (k = 1; k <= i__2; ++k) {
q__1.r = scaloc, q__1.i = 0.f;
cscal_(m, &q__1, &c__[k * c_dim1 + 1], &c__1);
q__1.r = scaloc, q__1.i = 0.f;
cscal_(m, &q__1, &f[k * f_dim1 + 1], &c__1);
/* L40: */
}
*scale *= scaloc;
}
/* Unpack solution vector(s) */
i__2 = i__ + j * c_dim1;
c__[i__2].r = rhs[0].r, c__[i__2].i = rhs[0].i;
i__2 = i__ + j * f_dim1;
f[i__2].r = rhs[1].r, f[i__2].i = rhs[1].i;
/* Substitute R(I, J) and L(I, J) into remaining equation. */
i__2 = j - 1;
for (k = 1; k <= i__2; ++k) {
i__3 = i__ + k * f_dim1;
i__4 = i__ + k * f_dim1;
r_cnjg(&q__4, &b[k + j * b_dim1]);
q__3.r = rhs[0].r * q__4.r - rhs[0].i * q__4.i, q__3.i =
rhs[0].r * q__4.i + rhs[0].i * q__4.r;
q__2.r = f[i__4].r + q__3.r, q__2.i = f[i__4].i + q__3.i;
r_cnjg(&q__6, &e[k + j * e_dim1]);
q__5.r = rhs[1].r * q__6.r - rhs[1].i * q__6.i, q__5.i =
rhs[1].r * q__6.i + rhs[1].i * q__6.r;
q__1.r = q__2.r + q__5.r, q__1.i = q__2.i + q__5.i;
f[i__3].r = q__1.r, f[i__3].i = q__1.i;
/* L50: */
}
i__2 = *m;
for (k = i__ + 1; k <= i__2; ++k) {
i__3 = k + j * c_dim1;
i__4 = k + j * c_dim1;
r_cnjg(&q__4, &a[i__ + k * a_dim1]);
q__3.r = q__4.r * rhs[0].r - q__4.i * rhs[0].i, q__3.i =
q__4.r * rhs[0].i + q__4.i * rhs[0].r;
q__2.r = c__[i__4].r - q__3.r, q__2.i = c__[i__4].i -
q__3.i;
r_cnjg(&q__6, &d__[i__ + k * d_dim1]);
q__5.r = q__6.r * rhs[1].r - q__6.i * rhs[1].i, q__5.i =
q__6.r * rhs[1].i + q__6.i * rhs[1].r;
q__1.r = q__2.r - q__5.r, q__1.i = q__2.i - q__5.i;
c__[i__3].r = q__1.r, c__[i__3].i = q__1.i;
/* L60: */
}
/* L70: */
}
/* L80: */
}
}
return 0;
/* End of CTGSY2 */
} /* ctgsy2_ */
