#include "blaswrap.h"
#include "f2c.h"
/* Subroutine */ int ctrsyl_(char *trana, char *tranb, integer *isgn, integer
*m, integer *n, complex *a, integer *lda, complex *b, integer *ldb,
complex *c__, integer *ldc, real *scale, integer *info)
{
/* -- LAPACK routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
June 30, 1999
Purpose
=======
CTRSYL solves the complex Sylvester matrix equation:
op(A)*X + X*op(B) = scale*C or
op(A)*X - X*op(B) = scale*C,
where op(A) = A or A**H, and A and B are both upper triangular. A is
M-by-M and B is N-by-N; the right hand side C and the solution X are
M-by-N; and scale is an output scale factor, set <= 1 to avoid
overflow in X.
Arguments
=========
TRANA (input) CHARACTER*1
Specifies the option op(A):
= 'N': op(A) = A (No transpose)
= 'C': op(A) = A**H (Conjugate transpose)
TRANB (input) CHARACTER*1
Specifies the option op(B):
= 'N': op(B) = B (No transpose)
= 'C': op(B) = B**H (Conjugate transpose)
ISGN (input) INTEGER
Specifies the sign in the equation:
= +1: solve op(A)*X + X*op(B) = scale*C
= -1: solve op(A)*X - X*op(B) = scale*C
M (input) INTEGER
The order of the matrix A, and the number of rows in the
matrices X and C. M >= 0.
N (input) INTEGER
The order of the matrix B, and the number of columns in the
matrices X and C. N >= 0.
A (input) COMPLEX array, dimension (LDA,M)
The upper triangular matrix A.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,M).
B (input) COMPLEX array, dimension (LDB,N)
The upper triangular matrix B.
LDB (input) INTEGER
The leading dimension of the array B. LDB >= max(1,N).
C (input/output) COMPLEX array, dimension (LDC,N)
On entry, the M-by-N right hand side matrix C.
On exit, C is overwritten by the solution matrix X.
LDC (input) INTEGER
The leading dimension of the array C. LDC >= max(1,M)
SCALE (output) REAL
The scale factor, scale, set <= 1 to avoid overflow in X.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
= 1: A and B have common or very close eigenvalues; perturbed
values were used to solve the equation (but the matrices
A and B are unchanged).
=====================================================================
Decode and Test input parameters
Parameter adjustments */
/* Table of constant values */
static integer c__1 = 1;
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, c_dim1, c_offset, i__1, i__2,
i__3, i__4;
real r__1, r__2;
complex q__1, q__2, q__3, q__4;
/* Builtin functions */
double r_imag(complex *);
void r_cnjg(complex *, complex *);
/* Local variables */
static real smin;
static complex suml, sumr;
static integer j, k, l;
extern /* Complex */ VOID cdotc_(complex *, integer *, complex *, integer
*, complex *, integer *);
extern logical lsame_(char *, char *);
extern /* Complex */ VOID cdotu_(complex *, integer *, complex *, integer
*, complex *, integer *);
static complex a11;
static real db;
extern /* Subroutine */ int slabad_(real *, real *);
extern doublereal clange_(char *, integer *, integer *, complex *,
integer *, real *);
static complex x11;
extern /* Complex */ VOID cladiv_(complex *, complex *, complex *);
static real scaloc;
extern doublereal slamch_(char *);
extern /* Subroutine */ int csscal_(integer *, real *, complex *, integer
*), xerbla_(char *, integer *);
static real bignum;
static logical notrna, notrnb;
static real smlnum, da11;
static complex vec;
static real dum[1], eps, sgn;
#define a_subscr(a_1,a_2) (a_2)*a_dim1 + a_1
#define a_ref(a_1,a_2) a[a_subscr(a_1,a_2)]
#define b_subscr(a_1,a_2) (a_2)*b_dim1 + a_1
#define b_ref(a_1,a_2) b[b_subscr(a_1,a_2)]
#define c___subscr(a_1,a_2) (a_2)*c_dim1 + a_1
#define c___ref(a_1,a_2) c__[c___subscr(a_1,a_2)]
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1 * 1;
b -= b_offset;
c_dim1 = *ldc;
c_offset = 1 + c_dim1 * 1;
c__ -= c_offset;
/* Function Body */
notrna = lsame_(trana, "N");
notrnb = lsame_(tranb, "N");
*info = 0;
if (! notrna && ! lsame_(trana, "T") && ! lsame_(
trana, "C")) {
*info = -1;
} else if (! notrnb && ! lsame_(tranb, "T") && !
lsame_(tranb, "C")) {
*info = -2;
} else if (*isgn != 1 && *isgn != -1) {
*info = -3;
} else if (*m < 0) {
*info = -4;
} else if (*n < 0) {
*info = -5;
} else if (*lda < max(1,*m)) {
*info = -7;
} else if (*ldb < max(1,*n)) {
*info = -9;
} else if (*ldc < max(1,*m)) {
*info = -11;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("CTRSYL", &i__1);
return 0;
}
/* Quick return if possible */
if (*m == 0 || *n == 0) {
return 0;
}
/* Set constants to control overflow */
eps = slamch_("P");
smlnum = slamch_("S");
bignum = 1.f / smlnum;
slabad_(&smlnum, &bignum);
smlnum = smlnum * (real) (*m * *n) / eps;
bignum = 1.f / smlnum;
/* Computing MAX */
r__1 = smlnum, r__2 = eps * clange_("M", m, m, &a[a_offset], lda, dum), r__1 = max(r__1,r__2), r__2 = eps * clange_("M", n, n,
&b[b_offset], ldb, dum);
smin = dmax(r__1,r__2);
*scale = 1.f;
sgn = (real) (*isgn);
if (notrna && notrnb) {
/* Solve A*X + ISGN*X*B = scale*C.
The (K,L)th block of X is determined starting from
bottom-left corner column by column by
A(K,K)*X(K,L) + ISGN*X(K,L)*B(L,L) = C(K,L) - R(K,L)
Where
M L-1
R(K,L) = SUM [A(K,I)*X(I,L)] +ISGN*SUM [X(K,J)*B(J,L)].
I=K+1 J=1 */
i__1 = *n;
for (l = 1; l <= i__1; ++l) {
for (k = *m; k >= 1; --k) {
/* Computing MIN */
i__2 = k + 1;
/* Computing MIN */
i__3 = k + 1;
i__4 = *m - k;
cdotu_(&q__1, &i__4, &a_ref(k, min(i__2,*m)), lda, &c___ref(
min(i__3,*m), l), &c__1);
suml.r = q__1.r, suml.i = q__1.i;
i__2 = l - 1;
cdotu_(&q__1, &i__2, &c___ref(k, 1), ldc, &b_ref(1, l), &c__1)
;
sumr.r = q__1.r, sumr.i = q__1.i;
i__2 = c___subscr(k, l);
q__3.r = sgn * sumr.r, q__3.i = sgn * sumr.i;
q__2.r = suml.r + q__3.r, q__2.i = suml.i + q__3.i;
q__1.r = c__[i__2].r - q__2.r, q__1.i = c__[i__2].i - q__2.i;
vec.r = q__1.r, vec.i = q__1.i;
scaloc = 1.f;
i__2 = a_subscr(k, k);
i__3 = b_subscr(l, l);
q__2.r = sgn * b[i__3].r, q__2.i = sgn * b[i__3].i;
q__1.r = a[i__2].r + q__2.r, q__1.i = a[i__2].i + q__2.i;
a11.r = q__1.r, a11.i = q__1.i;
da11 = (r__1 = a11.r, dabs(r__1)) + (r__2 = r_imag(&a11),
dabs(r__2));
if (da11 <= smin) {
a11.r = smin, a11.i = 0.f;
da11 = smin;
*info = 1;
}
db = (r__1 = vec.r, dabs(r__1)) + (r__2 = r_imag(&vec), dabs(
r__2));
if (da11 < 1.f && db > 1.f) {
if (db > bignum * da11) {
scaloc = 1.f / db;
}
}
q__3.r = scaloc, q__3.i = 0.f;
q__2.r = vec.r * q__3.r - vec.i * q__3.i, q__2.i = vec.r *
q__3.i + vec.i * q__3.r;
cladiv_(&q__1, &q__2, &a11);
x11.r = q__1.r, x11.i = q__1.i;
if (scaloc != 1.f) {
i__2 = *n;
for (j = 1; j <= i__2; ++j) {
csscal_(m, &scaloc, &c___ref(1, j), &c__1);
/* L10: */
}
*scale *= scaloc;
}
i__2 = c___subscr(k, l);
c__[i__2].r = x11.r, c__[i__2].i = x11.i;
/* L20: */
}
/* L30: */
}
} else if (! notrna && notrnb) {
/* Solve A' *X + ISGN*X*B = scale*C.
The (K,L)th block of X is determined starting from
upper-left corner column by column by
A'(K,K)*X(K,L) + ISGN*X(K,L)*B(L,L) = C(K,L) - R(K,L)
Where
K-1 L-1
R(K,L) = SUM [A'(I,K)*X(I,L)] + ISGN*SUM [X(K,J)*B(J,L)]
I=1 J=1 */
i__1 = *n;
for (l = 1; l <= i__1; ++l) {
i__2 = *m;
for (k = 1; k <= i__2; ++k) {
i__3 = k - 1;
cdotc_(&q__1, &i__3, &a_ref(1, k), &c__1, &c___ref(1, l), &
c__1);
suml.r = q__1.r, suml.i = q__1.i;
i__3 = l - 1;
cdotu_(&q__1, &i__3, &c___ref(k, 1), ldc, &b_ref(1, l), &c__1)
;
sumr.r = q__1.r, sumr.i = q__1.i;
i__3 = c___subscr(k, l);
q__3.r = sgn * sumr.r, q__3.i = sgn * sumr.i;
q__2.r = suml.r + q__3.r, q__2.i = suml.i + q__3.i;
q__1.r = c__[i__3].r - q__2.r, q__1.i = c__[i__3].i - q__2.i;
vec.r = q__1.r, vec.i = q__1.i;
scaloc = 1.f;
r_cnjg(&q__2, &a_ref(k, k));
i__3 = b_subscr(l, l);
q__3.r = sgn * b[i__3].r, q__3.i = sgn * b[i__3].i;
q__1.r = q__2.r + q__3.r, q__1.i = q__2.i + q__3.i;
a11.r = q__1.r, a11.i = q__1.i;
da11 = (r__1 = a11.r, dabs(r__1)) + (r__2 = r_imag(&a11),
dabs(r__2));
if (da11 <= smin) {
a11.r = smin, a11.i = 0.f;
da11 = smin;
*info = 1;
}
db = (r__1 = vec.r, dabs(r__1)) + (r__2 = r_imag(&vec), dabs(
r__2));
if (da11 < 1.f && db > 1.f) {
if (db > bignum * da11) {
scaloc = 1.f / db;
}
}
q__3.r = scaloc, q__3.i = 0.f;
q__2.r = vec.r * q__3.r - vec.i * q__3.i, q__2.i = vec.r *
q__3.i + vec.i * q__3.r;
cladiv_(&q__1, &q__2, &a11);
x11.r = q__1.r, x11.i = q__1.i;
if (scaloc != 1.f) {
i__3 = *n;
for (j = 1; j <= i__3; ++j) {
csscal_(m, &scaloc, &c___ref(1, j), &c__1);
/* L40: */
}
*scale *= scaloc;
}
i__3 = c___subscr(k, l);
c__[i__3].r = x11.r, c__[i__3].i = x11.i;
/* L50: */
}
/* L60: */
}
} else if (! notrna && ! notrnb) {
/* Solve A'*X + ISGN*X*B' = C.
The (K,L)th block of X is determined starting from
upper-right corner column by column by
A'(K,K)*X(K,L) + ISGN*X(K,L)*B'(L,L) = C(K,L) - R(K,L)
Where
K-1
R(K,L) = SUM [A'(I,K)*X(I,L)] +
I=1
N
ISGN*SUM [X(K,J)*B'(L,J)].
J=L+1 */
for (l = *n; l >= 1; --l) {
i__1 = *m;
for (k = 1; k <= i__1; ++k) {
i__2 = k - 1;
cdotc_(&q__1, &i__2, &a_ref(1, k), &c__1, &c___ref(1, l), &
c__1);
suml.r = q__1.r, suml.i = q__1.i;
/* Computing MIN */
i__2 = l + 1;
/* Computing MIN */
i__3 = l + 1;
i__4 = *n - l;
cdotc_(&q__1, &i__4, &c___ref(k, min(i__2,*n)), ldc, &b_ref(l,
min(i__3,*n)), ldb);
sumr.r = q__1.r, sumr.i = q__1.i;
i__2 = c___subscr(k, l);
r_cnjg(&q__4, &sumr);
q__3.r = sgn * q__4.r, q__3.i = sgn * q__4.i;
q__2.r = suml.r + q__3.r, q__2.i = suml.i + q__3.i;
q__1.r = c__[i__2].r - q__2.r, q__1.i = c__[i__2].i - q__2.i;
vec.r = q__1.r, vec.i = q__1.i;
scaloc = 1.f;
i__2 = a_subscr(k, k);
i__3 = b_subscr(l, l);
q__3.r = sgn * b[i__3].r, q__3.i = sgn * b[i__3].i;
q__2.r = a[i__2].r + q__3.r, q__2.i = a[i__2].i + q__3.i;
r_cnjg(&q__1, &q__2);
a11.r = q__1.r, a11.i = q__1.i;
da11 = (r__1 = a11.r, dabs(r__1)) + (r__2 = r_imag(&a11),
dabs(r__2));
if (da11 <= smin) {
a11.r = smin, a11.i = 0.f;
da11 = smin;
*info = 1;
}
db = (r__1 = vec.r, dabs(r__1)) + (r__2 = r_imag(&vec), dabs(
r__2));
if (da11 < 1.f && db > 1.f) {
if (db > bignum * da11) {
scaloc = 1.f / db;
}
}
q__3.r = scaloc, q__3.i = 0.f;
q__2.r = vec.r * q__3.r - vec.i * q__3.i, q__2.i = vec.r *
q__3.i + vec.i * q__3.r;
cladiv_(&q__1, &q__2, &a11);
x11.r = q__1.r, x11.i = q__1.i;
if (scaloc != 1.f) {
i__2 = *n;
for (j = 1; j <= i__2; ++j) {
csscal_(m, &scaloc, &c___ref(1, j), &c__1);
/* L70: */
}
*scale *= scaloc;
}
i__2 = c___subscr(k, l);
c__[i__2].r = x11.r, c__[i__2].i = x11.i;
/* L80: */
}
/* L90: */
}
} else if (notrna && ! notrnb) {
/* Solve A*X + ISGN*X*B' = C.
The (K,L)th block of X is determined starting from
bottom-left corner column by column by
A(K,K)*X(K,L) + ISGN*X(K,L)*B'(L,L) = C(K,L) - R(K,L)
Where
M N
R(K,L) = SUM [A(K,I)*X(I,L)] + ISGN*SUM [X(K,J)*B'(L,J)]
I=K+1 J=L+1 */
for (l = *n; l >= 1; --l) {
for (k = *m; k >= 1; --k) {
/* Computing MIN */
i__1 = k + 1;
/* Computing MIN */
i__2 = k + 1;
i__3 = *m - k;
cdotu_(&q__1, &i__3, &a_ref(k, min(i__1,*m)), lda, &c___ref(
min(i__2,*m), l), &c__1);
suml.r = q__1.r, suml.i = q__1.i;
/* Computing MIN */
i__1 = l + 1;
/* Computing MIN */
i__2 = l + 1;
i__3 = *n - l;
cdotc_(&q__1, &i__3, &c___ref(k, min(i__1,*n)), ldc, &b_ref(l,
min(i__2,*n)), ldb);
sumr.r = q__1.r, sumr.i = q__1.i;
i__1 = c___subscr(k, l);
r_cnjg(&q__4, &sumr);
q__3.r = sgn * q__4.r, q__3.i = sgn * q__4.i;
q__2.r = suml.r + q__3.r, q__2.i = suml.i + q__3.i;
q__1.r = c__[i__1].r - q__2.r, q__1.i = c__[i__1].i - q__2.i;
vec.r = q__1.r, vec.i = q__1.i;
scaloc = 1.f;
i__1 = a_subscr(k, k);
r_cnjg(&q__3, &b_ref(l, l));
q__2.r = sgn * q__3.r, q__2.i = sgn * q__3.i;
q__1.r = a[i__1].r + q__2.r, q__1.i = a[i__1].i + q__2.i;
a11.r = q__1.r, a11.i = q__1.i;
da11 = (r__1 = a11.r, dabs(r__1)) + (r__2 = r_imag(&a11),
dabs(r__2));
if (da11 <= smin) {
a11.r = smin, a11.i = 0.f;
da11 = smin;
*info = 1;
}
db = (r__1 = vec.r, dabs(r__1)) + (r__2 = r_imag(&vec), dabs(
r__2));
if (da11 < 1.f && db > 1.f) {
if (db > bignum * da11) {
scaloc = 1.f / db;
}
}
q__3.r = scaloc, q__3.i = 0.f;
q__2.r = vec.r * q__3.r - vec.i * q__3.i, q__2.i = vec.r *
q__3.i + vec.i * q__3.r;
cladiv_(&q__1, &q__2, &a11);
x11.r = q__1.r, x11.i = q__1.i;
if (scaloc != 1.f) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
csscal_(m, &scaloc, &c___ref(1, j), &c__1);
/* L100: */
}
*scale *= scaloc;
}
i__1 = c___subscr(k, l);
c__[i__1].r = x11.r, c__[i__1].i = x11.i;
/* L110: */
}
/* L120: */
}
}
return 0;
/* End of CTRSYL */
} /* ctrsyl_ */
#undef c___ref
#undef c___subscr
#undef b_ref
#undef b_subscr
#undef a_ref
#undef a_subscr