/* -- translated by f2c (version 20100827).
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"
/* Table of constant values */
static integer c__1 = 1;
static logical c_false = FALSE_;
static integer c__2 = 2;
static doublereal c_b26 = 1.;
static doublereal c_b30 = 0.;
static logical c_true = TRUE_;
/* > \brief \b DTRSYL
=========== DOCUMENTATION ===========
Online html documentation available at
http://www.netlib.org/lapack/explore-html/
> \htmlonly
> Download DTRSYL + dependencies
> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dtrsyl.
f">
> [TGZ]</a>
> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dtrsyl.
f">
> [ZIP]</a>
> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dtrsyl.
f">
> [TXT]</a>
> \endhtmlonly
Definition:
===========
SUBROUTINE DTRSYL( TRANA, TRANB, ISGN, M, N, A, LDA, B, LDB, C,
LDC, SCALE, INFO )
CHARACTER TRANA, TRANB
INTEGER INFO, ISGN, LDA, LDB, LDC, M, N
DOUBLE PRECISION SCALE
DOUBLE PRECISION A( LDA, * ), B( LDB, * ), C( LDC, * )
> \par Purpose:
=============
>
> \verbatim
>
> DTRSYL solves the real 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**T, and A and B are both upper quasi-
> 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.
>
> A and B must be in Schur canonical form (as returned by DHSEQR), that
> is, block upper triangular with 1-by-1 and 2-by-2 diagonal blocks;
> each 2-by-2 diagonal block has its diagonal elements equal and its
> off-diagonal elements of opposite sign.
> \endverbatim
Arguments:
==========
> \param[in] TRANA
> \verbatim
> TRANA is CHARACTER*1
> Specifies the option op(A):
> = 'N': op(A) = A (No transpose)
> = 'T': op(A) = A**T (Transpose)
> = 'C': op(A) = A**H (Conjugate transpose = Transpose)
> \endverbatim
>
> \param[in] TRANB
> \verbatim
> TRANB is CHARACTER*1
> Specifies the option op(B):
> = 'N': op(B) = B (No transpose)
> = 'T': op(B) = B**T (Transpose)
> = 'C': op(B) = B**H (Conjugate transpose = Transpose)
> \endverbatim
>
> \param[in] ISGN
> \verbatim
> ISGN is 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
> \endverbatim
>
> \param[in] M
> \verbatim
> M is INTEGER
> The order of the matrix A, and the number of rows in the
> matrices X and C. M >= 0.
> \endverbatim
>
> \param[in] N
> \verbatim
> N is INTEGER
> The order of the matrix B, and the number of columns in the
> matrices X and C. N >= 0.
> \endverbatim
>
> \param[in] A
> \verbatim
> A is DOUBLE PRECISION array, dimension (LDA,M)
> The upper quasi-triangular matrix A, in Schur canonical form.
> \endverbatim
>
> \param[in] LDA
> \verbatim
> LDA is INTEGER
> The leading dimension of the array A. LDA >= max(1,M).
> \endverbatim
>
> \param[in] B
> \verbatim
> B is DOUBLE PRECISION array, dimension (LDB,N)
> The upper quasi-triangular matrix B, in Schur canonical form.
> \endverbatim
>
> \param[in] LDB
> \verbatim
> LDB is INTEGER
> The leading dimension of the array B. LDB >= max(1,N).
> \endverbatim
>
> \param[in,out] C
> \verbatim
> C is DOUBLE PRECISION 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.
> \endverbatim
>
> \param[in] LDC
> \verbatim
> LDC is INTEGER
> The leading dimension of the array C. LDC >= max(1,M)
> \endverbatim
>
> \param[out] SCALE
> \verbatim
> SCALE is DOUBLE PRECISION
> The scale factor, scale, set <= 1 to avoid overflow in X.
> \endverbatim
>
> \param[out] INFO
> \verbatim
> INFO is 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).
> \endverbatim
Authors:
========
> \author Univ. of Tennessee
> \author Univ. of California Berkeley
> \author Univ. of Colorado Denver
> \author NAG Ltd.
> \date November 2011
> \ingroup doubleSYcomputational
=====================================================================
Subroutine */ int igraphdtrsyl_(char *trana, char *tranb, integer *isgn, integer
*m, integer *n, doublereal *a, integer *lda, doublereal *b, integer *
ldb, doublereal *c__, integer *ldc, doublereal *scale, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, c_dim1, c_offset, i__1, i__2,
i__3, i__4;
doublereal d__1, d__2;
/* Local variables */
integer j, k, l;
doublereal x[4] /* was [2][2] */;
integer k1, k2, l1, l2;
doublereal a11, db, da11, vec[4] /* was [2][2] */, dum[1], eps, sgn;
extern doublereal igraphddot_(integer *, doublereal *, integer *, doublereal *,
integer *);
integer ierr;
doublereal smin, suml, sumr;
extern /* Subroutine */ int igraphdscal_(integer *, doublereal *, doublereal *,
integer *);
extern logical igraphlsame_(char *, char *);
integer knext, lnext;
doublereal xnorm;
extern /* Subroutine */ int igraphdlaln2_(logical *, integer *, integer *,
doublereal *, doublereal *, doublereal *, integer *, doublereal *,
doublereal *, doublereal *, integer *, doublereal *, doublereal *
, doublereal *, integer *, doublereal *, doublereal *, integer *),
igraphdlasy2_(logical *, logical *, integer *, integer *, integer *,
doublereal *, integer *, doublereal *, integer *, doublereal *,
integer *, doublereal *, doublereal *, integer *, doublereal *,
integer *), igraphdlabad_(doublereal *, doublereal *);
extern doublereal igraphdlamch_(char *), igraphdlange_(char *, integer *,
integer *, doublereal *, integer *, doublereal *);
doublereal scaloc;
extern /* Subroutine */ int igraphxerbla_(char *, integer *, ftnlen);
doublereal bignum;
logical notrna, notrnb;
doublereal smlnum;
/* -- LAPACK computational routine (version 3.4.0) --
-- LAPACK is a software package provided by Univ. of Tennessee, --
-- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
November 2011
=====================================================================
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;
/* Function Body */
notrna = igraphlsame_(trana, "N");
notrnb = igraphlsame_(tranb, "N");
*info = 0;
if (! notrna && ! igraphlsame_(trana, "T") && ! igraphlsame_(
trana, "C")) {
*info = -1;
} else if (! notrnb && ! igraphlsame_(tranb, "T") && !
igraphlsame_(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);
igraphxerbla_("DTRSYL", &i__1, (ftnlen)6);
return 0;
}
/* Quick return if possible */
*scale = 1.;
if (*m == 0 || *n == 0) {
return 0;
}
/* Set constants to control overflow */
eps = igraphdlamch_("P");
smlnum = igraphdlamch_("S");
bignum = 1. / smlnum;
igraphdlabad_(&smlnum, &bignum);
smlnum = smlnum * (doublereal) (*m * *n) / eps;
bignum = 1. / smlnum;
/* Computing MAX */
d__1 = smlnum, d__2 = eps * igraphdlange_("M", m, m, &a[a_offset], lda, dum), d__1 = max(d__1,d__2), d__2 = eps * igraphdlange_("M", n, n,
&b[b_offset], ldb, dum);
smin = max(d__1,d__2);
sgn = (doublereal) (*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
Start column loop (index = L)
L1 (L2) : column index of the first (first) row of X(K,L). */
lnext = 1;
i__1 = *n;
for (l = 1; l <= i__1; ++l) {
if (l < lnext) {
goto L60;
}
if (l == *n) {
l1 = l;
l2 = l;
} else {
if (b[l + 1 + l * b_dim1] != 0.) {
l1 = l;
l2 = l + 1;
lnext = l + 2;
} else {
l1 = l;
l2 = l;
lnext = l + 1;
}
}
/* Start row loop (index = K)
K1 (K2): row index of the first (last) row of X(K,L). */
knext = *m;
for (k = *m; k >= 1; --k) {
if (k > knext) {
goto L50;
}
if (k == 1) {
k1 = k;
k2 = k;
} else {
if (a[k + (k - 1) * a_dim1] != 0.) {
k1 = k - 1;
k2 = k;
knext = k - 2;
} else {
k1 = k;
k2 = k;
knext = k - 1;
}
}
if (l1 == l2 && k1 == k2) {
i__2 = *m - k1;
/* Computing MIN */
i__3 = k1 + 1;
/* Computing MIN */
i__4 = k1 + 1;
suml = igraphddot_(&i__2, &a[k1 + min(i__3,*m) * a_dim1], lda, &
c__[min(i__4,*m) + l1 * c_dim1], &c__1);
i__2 = l1 - 1;
sumr = igraphddot_(&i__2, &c__[k1 + c_dim1], ldc, &b[l1 *
b_dim1 + 1], &c__1);
vec[0] = c__[k1 + l1 * c_dim1] - (suml + sgn * sumr);
scaloc = 1.;
a11 = a[k1 + k1 * a_dim1] + sgn * b[l1 + l1 * b_dim1];
da11 = abs(a11);
if (da11 <= smin) {
a11 = smin;
da11 = smin;
*info = 1;
}
db = abs(vec[0]);
if (da11 < 1. && db > 1.) {
if (db > bignum * da11) {
scaloc = 1. / db;
}
}
x[0] = vec[0] * scaloc / a11;
if (scaloc != 1.) {
i__2 = *n;
for (j = 1; j <= i__2; ++j) {
igraphdscal_(m, &scaloc, &c__[j * c_dim1 + 1], &c__1);
/* L10: */
}
*scale *= scaloc;
}
c__[k1 + l1 * c_dim1] = x[0];
} else if (l1 == l2 && k1 != k2) {
i__2 = *m - k2;
/* Computing MIN */
i__3 = k2 + 1;
/* Computing MIN */
i__4 = k2 + 1;
suml = igraphddot_(&i__2, &a[k1 + min(i__3,*m) * a_dim1], lda, &
c__[min(i__4,*m) + l1 * c_dim1], &c__1);
i__2 = l1 - 1;
sumr = igraphddot_(&i__2, &c__[k1 + c_dim1], ldc, &b[l1 *
b_dim1 + 1], &c__1);
vec[0] = c__[k1 + l1 * c_dim1] - (suml + sgn * sumr);
i__2 = *m - k2;
/* Computing MIN */
i__3 = k2 + 1;
/* Computing MIN */
i__4 = k2 + 1;
suml = igraphddot_(&i__2, &a[k2 + min(i__3,*m) * a_dim1], lda, &
c__[min(i__4,*m) + l1 * c_dim1], &c__1);
i__2 = l1 - 1;
sumr = igraphddot_(&i__2, &c__[k2 + c_dim1], ldc, &b[l1 *
b_dim1 + 1], &c__1);
vec[1] = c__[k2 + l1 * c_dim1] - (suml + sgn * sumr);
d__1 = -sgn * b[l1 + l1 * b_dim1];
igraphdlaln2_(&c_false, &c__2, &c__1, &smin, &c_b26, &a[k1 + k1
* a_dim1], lda, &c_b26, &c_b26, vec, &c__2, &d__1,
&c_b30, x, &c__2, &scaloc, &xnorm, &ierr);
if (ierr != 0) {
*info = 1;
}
if (scaloc != 1.) {
i__2 = *n;
for (j = 1; j <= i__2; ++j) {
igraphdscal_(m, &scaloc, &c__[j * c_dim1 + 1], &c__1);
/* L20: */
}
*scale *= scaloc;
}
c__[k1 + l1 * c_dim1] = x[0];
c__[k2 + l1 * c_dim1] = x[1];
} else if (l1 != l2 && k1 == k2) {
i__2 = *m - k1;
/* Computing MIN */
i__3 = k1 + 1;
/* Computing MIN */
i__4 = k1 + 1;
suml = igraphddot_(&i__2, &a[k1 + min(i__3,*m) * a_dim1], lda, &
c__[min(i__4,*m) + l1 * c_dim1], &c__1);
i__2 = l1 - 1;
sumr = igraphddot_(&i__2, &c__[k1 + c_dim1], ldc, &b[l1 *
b_dim1 + 1], &c__1);
vec[0] = sgn * (c__[k1 + l1 * c_dim1] - (suml + sgn *
sumr));
i__2 = *m - k1;
/* Computing MIN */
i__3 = k1 + 1;
/* Computing MIN */
i__4 = k1 + 1;
suml = igraphddot_(&i__2, &a[k1 + min(i__3,*m) * a_dim1], lda, &
c__[min(i__4,*m) + l2 * c_dim1], &c__1);
i__2 = l1 - 1;
sumr = igraphddot_(&i__2, &c__[k1 + c_dim1], ldc, &b[l2 *
b_dim1 + 1], &c__1);
vec[1] = sgn * (c__[k1 + l2 * c_dim1] - (suml + sgn *
sumr));
d__1 = -sgn * a[k1 + k1 * a_dim1];
igraphdlaln2_(&c_true, &c__2, &c__1, &smin, &c_b26, &b[l1 + l1 *
b_dim1], ldb, &c_b26, &c_b26, vec, &c__2, &d__1,
&c_b30, x, &c__2, &scaloc, &xnorm, &ierr);
if (ierr != 0) {
*info = 1;
}
if (scaloc != 1.) {
i__2 = *n;
for (j = 1; j <= i__2; ++j) {
igraphdscal_(m, &scaloc, &c__[j * c_dim1 + 1], &c__1);
/* L30: */
}
*scale *= scaloc;
}
c__[k1 + l1 * c_dim1] = x[0];
c__[k1 + l2 * c_dim1] = x[1];
} else if (l1 != l2 && k1 != k2) {
i__2 = *m - k2;
/* Computing MIN */
i__3 = k2 + 1;
/* Computing MIN */
i__4 = k2 + 1;
suml = igraphddot_(&i__2, &a[k1 + min(i__3,*m) * a_dim1], lda, &
c__[min(i__4,*m) + l1 * c_dim1], &c__1);
i__2 = l1 - 1;
sumr = igraphddot_(&i__2, &c__[k1 + c_dim1], ldc, &b[l1 *
b_dim1 + 1], &c__1);
vec[0] = c__[k1 + l1 * c_dim1] - (suml + sgn * sumr);
i__2 = *m - k2;
/* Computing MIN */
i__3 = k2 + 1;
/* Computing MIN */
i__4 = k2 + 1;
suml = igraphddot_(&i__2, &a[k1 + min(i__3,*m) * a_dim1], lda, &
c__[min(i__4,*m) + l2 * c_dim1], &c__1);
i__2 = l1 - 1;
sumr = igraphddot_(&i__2, &c__[k1 + c_dim1], ldc, &b[l2 *
b_dim1 + 1], &c__1);
vec[2] = c__[k1 + l2 * c_dim1] - (suml + sgn * sumr);
i__2 = *m - k2;
/* Computing MIN */
i__3 = k2 + 1;
/* Computing MIN */
i__4 = k2 + 1;
suml = igraphddot_(&i__2, &a[k2 + min(i__3,*m) * a_dim1], lda, &
c__[min(i__4,*m) + l1 * c_dim1], &c__1);
i__2 = l1 - 1;
sumr = igraphddot_(&i__2, &c__[k2 + c_dim1], ldc, &b[l1 *
b_dim1 + 1], &c__1);
vec[1] = c__[k2 + l1 * c_dim1] - (suml + sgn * sumr);
i__2 = *m - k2;
/* Computing MIN */
i__3 = k2 + 1;
/* Computing MIN */
i__4 = k2 + 1;
suml = igraphddot_(&i__2, &a[k2 + min(i__3,*m) * a_dim1], lda, &
c__[min(i__4,*m) + l2 * c_dim1], &c__1);
i__2 = l1 - 1;
sumr = igraphddot_(&i__2, &c__[k2 + c_dim1], ldc, &b[l2 *
b_dim1 + 1], &c__1);
vec[3] = c__[k2 + l2 * c_dim1] - (suml + sgn * sumr);
igraphdlasy2_(&c_false, &c_false, isgn, &c__2, &c__2, &a[k1 +
k1 * a_dim1], lda, &b[l1 + l1 * b_dim1], ldb, vec,
&c__2, &scaloc, x, &c__2, &xnorm, &ierr);
if (ierr != 0) {
*info = 1;
}
if (scaloc != 1.) {
i__2 = *n;
for (j = 1; j <= i__2; ++j) {
igraphdscal_(m, &scaloc, &c__[j * c_dim1 + 1], &c__1);
/* L40: */
}
*scale *= scaloc;
}
c__[k1 + l1 * c_dim1] = x[0];
c__[k1 + l2 * c_dim1] = x[2];
c__[k2 + l1 * c_dim1] = x[1];
c__[k2 + l2 * c_dim1] = x[3];
}
L50:
;
}
L60:
;
}
} else if (! notrna && notrnb) {
/* Solve A**T *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)**T*X(K,L) + ISGN*X(K,L)*B(L,L) = C(K,L) - R(K,L)
Where
K-1 T L-1
R(K,L) = SUM [A(I,K)**T*X(I,L)] +ISGN*SUM [X(K,J)*B(J,L)]
I=1 J=1
Start column loop (index = L)
L1 (L2): column index of the first (last) row of X(K,L) */
lnext = 1;
i__1 = *n;
for (l = 1; l <= i__1; ++l) {
if (l < lnext) {
goto L120;
}
if (l == *n) {
l1 = l;
l2 = l;
} else {
if (b[l + 1 + l * b_dim1] != 0.) {
l1 = l;
l2 = l + 1;
lnext = l + 2;
} else {
l1 = l;
l2 = l;
lnext = l + 1;
}
}
/* Start row loop (index = K)
K1 (K2): row index of the first (last) row of X(K,L) */
knext = 1;
i__2 = *m;
for (k = 1; k <= i__2; ++k) {
if (k < knext) {
goto L110;
}
if (k == *m) {
k1 = k;
k2 = k;
} else {
if (a[k + 1 + k * a_dim1] != 0.) {
k1 = k;
k2 = k + 1;
knext = k + 2;
} else {
k1 = k;
k2 = k;
knext = k + 1;
}
}
if (l1 == l2 && k1 == k2) {
i__3 = k1 - 1;
suml = igraphddot_(&i__3, &a[k1 * a_dim1 + 1], &c__1, &c__[l1 *
c_dim1 + 1], &c__1);
i__3 = l1 - 1;
sumr = igraphddot_(&i__3, &c__[k1 + c_dim1], ldc, &b[l1 *
b_dim1 + 1], &c__1);
vec[0] = c__[k1 + l1 * c_dim1] - (suml + sgn * sumr);
scaloc = 1.;
a11 = a[k1 + k1 * a_dim1] + sgn * b[l1 + l1 * b_dim1];
da11 = abs(a11);
if (da11 <= smin) {
a11 = smin;
da11 = smin;
*info = 1;
}
db = abs(vec[0]);
if (da11 < 1. && db > 1.) {
if (db > bignum * da11) {
scaloc = 1. / db;
}
}
x[0] = vec[0] * scaloc / a11;
if (scaloc != 1.) {
i__3 = *n;
for (j = 1; j <= i__3; ++j) {
igraphdscal_(m, &scaloc, &c__[j * c_dim1 + 1], &c__1);
/* L70: */
}
*scale *= scaloc;
}
c__[k1 + l1 * c_dim1] = x[0];
} else if (l1 == l2 && k1 != k2) {
i__3 = k1 - 1;
suml = igraphddot_(&i__3, &a[k1 * a_dim1 + 1], &c__1, &c__[l1 *
c_dim1 + 1], &c__1);
i__3 = l1 - 1;
sumr = igraphddot_(&i__3, &c__[k1 + c_dim1], ldc, &b[l1 *
b_dim1 + 1], &c__1);
vec[0] = c__[k1 + l1 * c_dim1] - (suml + sgn * sumr);
i__3 = k1 - 1;
suml = igraphddot_(&i__3, &a[k2 * a_dim1 + 1], &c__1, &c__[l1 *
c_dim1 + 1], &c__1);
i__3 = l1 - 1;
sumr = igraphddot_(&i__3, &c__[k2 + c_dim1], ldc, &b[l1 *
b_dim1 + 1], &c__1);
vec[1] = c__[k2 + l1 * c_dim1] - (suml + sgn * sumr);
d__1 = -sgn * b[l1 + l1 * b_dim1];
igraphdlaln2_(&c_true, &c__2, &c__1, &smin, &c_b26, &a[k1 + k1 *
a_dim1], lda, &c_b26, &c_b26, vec, &c__2, &d__1,
&c_b30, x, &c__2, &scaloc, &xnorm, &ierr);
if (ierr != 0) {
*info = 1;
}
if (scaloc != 1.) {
i__3 = *n;
for (j = 1; j <= i__3; ++j) {
igraphdscal_(m, &scaloc, &c__[j * c_dim1 + 1], &c__1);
/* L80: */
}
*scale *= scaloc;
}
c__[k1 + l1 * c_dim1] = x[0];
c__[k2 + l1 * c_dim1] = x[1];
} else if (l1 != l2 && k1 == k2) {
i__3 = k1 - 1;
suml = igraphddot_(&i__3, &a[k1 * a_dim1 + 1], &c__1, &c__[l1 *
c_dim1 + 1], &c__1);
i__3 = l1 - 1;
sumr = igraphddot_(&i__3, &c__[k1 + c_dim1], ldc, &b[l1 *
b_dim1 + 1], &c__1);
vec[0] = sgn * (c__[k1 + l1 * c_dim1] - (suml + sgn *
sumr));
i__3 = k1 - 1;
suml = igraphddot_(&i__3, &a[k1 * a_dim1 + 1], &c__1, &c__[l2 *
c_dim1 + 1], &c__1);
i__3 = l1 - 1;
sumr = igraphddot_(&i__3, &c__[k1 + c_dim1], ldc, &b[l2 *
b_dim1 + 1], &c__1);
vec[1] = sgn * (c__[k1 + l2 * c_dim1] - (suml + sgn *
sumr));
d__1 = -sgn * a[k1 + k1 * a_dim1];
igraphdlaln2_(&c_true, &c__2, &c__1, &smin, &c_b26, &b[l1 + l1 *
b_dim1], ldb, &c_b26, &c_b26, vec, &c__2, &d__1,
&c_b30, x, &c__2, &scaloc, &xnorm, &ierr);
if (ierr != 0) {
*info = 1;
}
if (scaloc != 1.) {
i__3 = *n;
for (j = 1; j <= i__3; ++j) {
igraphdscal_(m, &scaloc, &c__[j * c_dim1 + 1], &c__1);
/* L90: */
}
*scale *= scaloc;
}
c__[k1 + l1 * c_dim1] = x[0];
c__[k1 + l2 * c_dim1] = x[1];
} else if (l1 != l2 && k1 != k2) {
i__3 = k1 - 1;
suml = igraphddot_(&i__3, &a[k1 * a_dim1 + 1], &c__1, &c__[l1 *
c_dim1 + 1], &c__1);
i__3 = l1 - 1;
sumr = igraphddot_(&i__3, &c__[k1 + c_dim1], ldc, &b[l1 *
b_dim1 + 1], &c__1);
vec[0] = c__[k1 + l1 * c_dim1] - (suml + sgn * sumr);
i__3 = k1 - 1;
suml = igraphddot_(&i__3, &a[k1 * a_dim1 + 1], &c__1, &c__[l2 *
c_dim1 + 1], &c__1);
i__3 = l1 - 1;
sumr = igraphddot_(&i__3, &c__[k1 + c_dim1], ldc, &b[l2 *
b_dim1 + 1], &c__1);
vec[2] = c__[k1 + l2 * c_dim1] - (suml + sgn * sumr);
i__3 = k1 - 1;
suml = igraphddot_(&i__3, &a[k2 * a_dim1 + 1], &c__1, &c__[l1 *
c_dim1 + 1], &c__1);
i__3 = l1 - 1;
sumr = igraphddot_(&i__3, &c__[k2 + c_dim1], ldc, &b[l1 *
b_dim1 + 1], &c__1);
vec[1] = c__[k2 + l1 * c_dim1] - (suml + sgn * sumr);
i__3 = k1 - 1;
suml = igraphddot_(&i__3, &a[k2 * a_dim1 + 1], &c__1, &c__[l2 *
c_dim1 + 1], &c__1);
i__3 = l1 - 1;
sumr = igraphddot_(&i__3, &c__[k2 + c_dim1], ldc, &b[l2 *
b_dim1 + 1], &c__1);
vec[3] = c__[k2 + l2 * c_dim1] - (suml + sgn * sumr);
igraphdlasy2_(&c_true, &c_false, isgn, &c__2, &c__2, &a[k1 + k1
* a_dim1], lda, &b[l1 + l1 * b_dim1], ldb, vec, &
c__2, &scaloc, x, &c__2, &xnorm, &ierr);
if (ierr != 0) {
*info = 1;
}
if (scaloc != 1.) {
i__3 = *n;
for (j = 1; j <= i__3; ++j) {
igraphdscal_(m, &scaloc, &c__[j * c_dim1 + 1], &c__1);
/* L100: */
}
*scale *= scaloc;
}
c__[k1 + l1 * c_dim1] = x[0];
c__[k1 + l2 * c_dim1] = x[2];
c__[k2 + l1 * c_dim1] = x[1];
c__[k2 + l2 * c_dim1] = x[3];
}
L110:
;
}
L120:
;
}
} else if (! notrna && ! notrnb) {
/* Solve A**T*X + ISGN*X*B**T = scale*C.
The (K,L)th block of X is determined starting from
top-right corner column by column by
A(K,K)**T*X(K,L) + ISGN*X(K,L)*B(L,L)**T = C(K,L) - R(K,L)
Where
K-1 N
R(K,L) = SUM [A(I,K)**T*X(I,L)] + ISGN*SUM [X(K,J)*B(L,J)**T].
I=1 J=L+1
Start column loop (index = L)
L1 (L2): column index of the first (last) row of X(K,L) */
lnext = *n;
for (l = *n; l >= 1; --l) {
if (l > lnext) {
goto L180;
}
if (l == 1) {
l1 = l;
l2 = l;
} else {
if (b[l + (l - 1) * b_dim1] != 0.) {
l1 = l - 1;
l2 = l;
lnext = l - 2;
} else {
l1 = l;
l2 = l;
lnext = l - 1;
}
}
/* Start row loop (index = K)
K1 (K2): row index of the first (last) row of X(K,L) */
knext = 1;
i__1 = *m;
for (k = 1; k <= i__1; ++k) {
if (k < knext) {
goto L170;
}
if (k == *m) {
k1 = k;
k2 = k;
} else {
if (a[k + 1 + k * a_dim1] != 0.) {
k1 = k;
k2 = k + 1;
knext = k + 2;
} else {
k1 = k;
k2 = k;
knext = k + 1;
}
}
if (l1 == l2 && k1 == k2) {
i__2 = k1 - 1;
suml = igraphddot_(&i__2, &a[k1 * a_dim1 + 1], &c__1, &c__[l1 *
c_dim1 + 1], &c__1);
i__2 = *n - l1;
/* Computing MIN */
i__3 = l1 + 1;
/* Computing MIN */
i__4 = l1 + 1;
sumr = igraphddot_(&i__2, &c__[k1 + min(i__3,*n) * c_dim1], ldc,
&b[l1 + min(i__4,*n) * b_dim1], ldb);
vec[0] = c__[k1 + l1 * c_dim1] - (suml + sgn * sumr);
scaloc = 1.;
a11 = a[k1 + k1 * a_dim1] + sgn * b[l1 + l1 * b_dim1];
da11 = abs(a11);
if (da11 <= smin) {
a11 = smin;
da11 = smin;
*info = 1;
}
db = abs(vec[0]);
if (da11 < 1. && db > 1.) {
if (db > bignum * da11) {
scaloc = 1. / db;
}
}
x[0] = vec[0] * scaloc / a11;
if (scaloc != 1.) {
i__2 = *n;
for (j = 1; j <= i__2; ++j) {
igraphdscal_(m, &scaloc, &c__[j * c_dim1 + 1], &c__1);
/* L130: */
}
*scale *= scaloc;
}
c__[k1 + l1 * c_dim1] = x[0];
} else if (l1 == l2 && k1 != k2) {
i__2 = k1 - 1;
suml = igraphddot_(&i__2, &a[k1 * a_dim1 + 1], &c__1, &c__[l1 *
c_dim1 + 1], &c__1);
i__2 = *n - l2;
/* Computing MIN */
i__3 = l2 + 1;
/* Computing MIN */
i__4 = l2 + 1;
sumr = igraphddot_(&i__2, &c__[k1 + min(i__3,*n) * c_dim1], ldc,
&b[l1 + min(i__4,*n) * b_dim1], ldb);
vec[0] = c__[k1 + l1 * c_dim1] - (suml + sgn * sumr);
i__2 = k1 - 1;
suml = igraphddot_(&i__2, &a[k2 * a_dim1 + 1], &c__1, &c__[l1 *
c_dim1 + 1], &c__1);
i__2 = *n - l2;
/* Computing MIN */
i__3 = l2 + 1;
/* Computing MIN */
i__4 = l2 + 1;
sumr = igraphddot_(&i__2, &c__[k2 + min(i__3,*n) * c_dim1], ldc,
&b[l1 + min(i__4,*n) * b_dim1], ldb);
vec[1] = c__[k2 + l1 * c_dim1] - (suml + sgn * sumr);
d__1 = -sgn * b[l1 + l1 * b_dim1];
igraphdlaln2_(&c_true, &c__2, &c__1, &smin, &c_b26, &a[k1 + k1 *
a_dim1], lda, &c_b26, &c_b26, vec, &c__2, &d__1,
&c_b30, x, &c__2, &scaloc, &xnorm, &ierr);
if (ierr != 0) {
*info = 1;
}
if (scaloc != 1.) {
i__2 = *n;
for (j = 1; j <= i__2; ++j) {
igraphdscal_(m, &scaloc, &c__[j * c_dim1 + 1], &c__1);
/* L140: */
}
*scale *= scaloc;
}
c__[k1 + l1 * c_dim1] = x[0];
c__[k2 + l1 * c_dim1] = x[1];
} else if (l1 != l2 && k1 == k2) {
i__2 = k1 - 1;
suml = igraphddot_(&i__2, &a[k1 * a_dim1 + 1], &c__1, &c__[l1 *
c_dim1 + 1], &c__1);
i__2 = *n - l2;
/* Computing MIN */
i__3 = l2 + 1;
/* Computing MIN */
i__4 = l2 + 1;
sumr = igraphddot_(&i__2, &c__[k1 + min(i__3,*n) * c_dim1], ldc,
&b[l1 + min(i__4,*n) * b_dim1], ldb);
vec[0] = sgn * (c__[k1 + l1 * c_dim1] - (suml + sgn *
sumr));
i__2 = k1 - 1;
suml = igraphddot_(&i__2, &a[k1 * a_dim1 + 1], &c__1, &c__[l2 *
c_dim1 + 1], &c__1);
i__2 = *n - l2;
/* Computing MIN */
i__3 = l2 + 1;
/* Computing MIN */
i__4 = l2 + 1;
sumr = igraphddot_(&i__2, &c__[k1 + min(i__3,*n) * c_dim1], ldc,
&b[l2 + min(i__4,*n) * b_dim1], ldb);
vec[1] = sgn * (c__[k1 + l2 * c_dim1] - (suml + sgn *
sumr));
d__1 = -sgn * a[k1 + k1 * a_dim1];
igraphdlaln2_(&c_false, &c__2, &c__1, &smin, &c_b26, &b[l1 + l1
* b_dim1], ldb, &c_b26, &c_b26, vec, &c__2, &d__1,
&c_b30, x, &c__2, &scaloc, &xnorm, &ierr);
if (ierr != 0) {
*info = 1;
}
if (scaloc != 1.) {
i__2 = *n;
for (j = 1; j <= i__2; ++j) {
igraphdscal_(m, &scaloc, &c__[j * c_dim1 + 1], &c__1);
/* L150: */
}
*scale *= scaloc;
}
c__[k1 + l1 * c_dim1] = x[0];
c__[k1 + l2 * c_dim1] = x[1];
} else if (l1 != l2 && k1 != k2) {
i__2 = k1 - 1;
suml = igraphddot_(&i__2, &a[k1 * a_dim1 + 1], &c__1, &c__[l1 *
c_dim1 + 1], &c__1);
i__2 = *n - l2;
/* Computing MIN */
i__3 = l2 + 1;
/* Computing MIN */
i__4 = l2 + 1;
sumr = igraphddot_(&i__2, &c__[k1 + min(i__3,*n) * c_dim1], ldc,
&b[l1 + min(i__4,*n) * b_dim1], ldb);
vec[0] = c__[k1 + l1 * c_dim1] - (suml + sgn * sumr);
i__2 = k1 - 1;
suml = igraphddot_(&i__2, &a[k1 * a_dim1 + 1], &c__1, &c__[l2 *
c_dim1 + 1], &c__1);
i__2 = *n - l2;
/* Computing MIN */
i__3 = l2 + 1;
/* Computing MIN */
i__4 = l2 + 1;
sumr = igraphddot_(&i__2, &c__[k1 + min(i__3,*n) * c_dim1], ldc,
&b[l2 + min(i__4,*n) * b_dim1], ldb);
vec[2] = c__[k1 + l2 * c_dim1] - (suml + sgn * sumr);
i__2 = k1 - 1;
suml = igraphddot_(&i__2, &a[k2 * a_dim1 + 1], &c__1, &c__[l1 *
c_dim1 + 1], &c__1);
i__2 = *n - l2;
/* Computing MIN */
i__3 = l2 + 1;
/* Computing MIN */
i__4 = l2 + 1;
sumr = igraphddot_(&i__2, &c__[k2 + min(i__3,*n) * c_dim1], ldc,
&b[l1 + min(i__4,*n) * b_dim1], ldb);
vec[1] = c__[k2 + l1 * c_dim1] - (suml + sgn * sumr);
i__2 = k1 - 1;
suml = igraphddot_(&i__2, &a[k2 * a_dim1 + 1], &c__1, &c__[l2 *
c_dim1 + 1], &c__1);
i__2 = *n - l2;
/* Computing MIN */
i__3 = l2 + 1;
/* Computing MIN */
i__4 = l2 + 1;
sumr = igraphddot_(&i__2, &c__[k2 + min(i__3,*n) * c_dim1], ldc,
&b[l2 + min(i__4,*n) * b_dim1], ldb);
vec[3] = c__[k2 + l2 * c_dim1] - (suml + sgn * sumr);
igraphdlasy2_(&c_true, &c_true, isgn, &c__2, &c__2, &a[k1 + k1 *
a_dim1], lda, &b[l1 + l1 * b_dim1], ldb, vec, &
c__2, &scaloc, x, &c__2, &xnorm, &ierr);
if (ierr != 0) {
*info = 1;
}
if (scaloc != 1.) {
i__2 = *n;
for (j = 1; j <= i__2; ++j) {
igraphdscal_(m, &scaloc, &c__[j * c_dim1 + 1], &c__1);
/* L160: */
}
*scale *= scaloc;
}
c__[k1 + l1 * c_dim1] = x[0];
c__[k1 + l2 * c_dim1] = x[2];
c__[k2 + l1 * c_dim1] = x[1];
c__[k2 + l2 * c_dim1] = x[3];
}
L170:
;
}
L180:
;
}
} else if (notrna && ! notrnb) {
/* Solve A*X + ISGN*X*B**T = scale*C.
The (K,L)th block of X is determined starting from
bottom-right corner column by column by
A(K,K)*X(K,L) + ISGN*X(K,L)*B(L,L)**T = 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)**T].
I=K+1 J=L+1
Start column loop (index = L)
L1 (L2): column index of the first (last) row of X(K,L) */
lnext = *n;
for (l = *n; l >= 1; --l) {
if (l > lnext) {
goto L240;
}
if (l == 1) {
l1 = l;
l2 = l;
} else {
if (b[l + (l - 1) * b_dim1] != 0.) {
l1 = l - 1;
l2 = l;
lnext = l - 2;
} else {
l1 = l;
l2 = l;
lnext = l - 1;
}
}
/* Start row loop (index = K)
K1 (K2): row index of the first (last) row of X(K,L) */
knext = *m;
for (k = *m; k >= 1; --k) {
if (k > knext) {
goto L230;
}
if (k == 1) {
k1 = k;
k2 = k;
} else {
if (a[k + (k - 1) * a_dim1] != 0.) {
k1 = k - 1;
k2 = k;
knext = k - 2;
} else {
k1 = k;
k2 = k;
knext = k - 1;
}
}
if (l1 == l2 && k1 == k2) {
i__1 = *m - k1;
/* Computing MIN */
i__2 = k1 + 1;
/* Computing MIN */
i__3 = k1 + 1;
suml = igraphddot_(&i__1, &a[k1 + min(i__2,*m) * a_dim1], lda, &
c__[min(i__3,*m) + l1 * c_dim1], &c__1);
i__1 = *n - l1;
/* Computing MIN */
i__2 = l1 + 1;
/* Computing MIN */
i__3 = l1 + 1;
sumr = igraphddot_(&i__1, &c__[k1 + min(i__2,*n) * c_dim1], ldc,
&b[l1 + min(i__3,*n) * b_dim1], ldb);
vec[0] = c__[k1 + l1 * c_dim1] - (suml + sgn * sumr);
scaloc = 1.;
a11 = a[k1 + k1 * a_dim1] + sgn * b[l1 + l1 * b_dim1];
da11 = abs(a11);
if (da11 <= smin) {
a11 = smin;
da11 = smin;
*info = 1;
}
db = abs(vec[0]);
if (da11 < 1. && db > 1.) {
if (db > bignum * da11) {
scaloc = 1. / db;
}
}
x[0] = vec[0] * scaloc / a11;
if (scaloc != 1.) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
igraphdscal_(m, &scaloc, &c__[j * c_dim1 + 1], &c__1);
/* L190: */
}
*scale *= scaloc;
}
c__[k1 + l1 * c_dim1] = x[0];
} else if (l1 == l2 && k1 != k2) {
i__1 = *m - k2;
/* Computing MIN */
i__2 = k2 + 1;
/* Computing MIN */
i__3 = k2 + 1;
suml = igraphddot_(&i__1, &a[k1 + min(i__2,*m) * a_dim1], lda, &
c__[min(i__3,*m) + l1 * c_dim1], &c__1);
i__1 = *n - l2;
/* Computing MIN */
i__2 = l2 + 1;
/* Computing MIN */
i__3 = l2 + 1;
sumr = igraphddot_(&i__1, &c__[k1 + min(i__2,*n) * c_dim1], ldc,
&b[l1 + min(i__3,*n) * b_dim1], ldb);
vec[0] = c__[k1 + l1 * c_dim1] - (suml + sgn * sumr);
i__1 = *m - k2;
/* Computing MIN */
i__2 = k2 + 1;
/* Computing MIN */
i__3 = k2 + 1;
suml = igraphddot_(&i__1, &a[k2 + min(i__2,*m) * a_dim1], lda, &
c__[min(i__3,*m) + l1 * c_dim1], &c__1);
i__1 = *n - l2;
/* Computing MIN */
i__2 = l2 + 1;
/* Computing MIN */
i__3 = l2 + 1;
sumr = igraphddot_(&i__1, &c__[k2 + min(i__2,*n) * c_dim1], ldc,
&b[l1 + min(i__3,*n) * b_dim1], ldb);
vec[1] = c__[k2 + l1 * c_dim1] - (suml + sgn * sumr);
d__1 = -sgn * b[l1 + l1 * b_dim1];
igraphdlaln2_(&c_false, &c__2, &c__1, &smin, &c_b26, &a[k1 + k1
* a_dim1], lda, &c_b26, &c_b26, vec, &c__2, &d__1,
&c_b30, x, &c__2, &scaloc, &xnorm, &ierr);
if (ierr != 0) {
*info = 1;
}
if (scaloc != 1.) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
igraphdscal_(m, &scaloc, &c__[j * c_dim1 + 1], &c__1);
/* L200: */
}
*scale *= scaloc;
}
c__[k1 + l1 * c_dim1] = x[0];
c__[k2 + l1 * c_dim1] = x[1];
} else if (l1 != l2 && k1 == k2) {
i__1 = *m - k1;
/* Computing MIN */
i__2 = k1 + 1;
/* Computing MIN */
i__3 = k1 + 1;
suml = igraphddot_(&i__1, &a[k1 + min(i__2,*m) * a_dim1], lda, &
c__[min(i__3,*m) + l1 * c_dim1], &c__1);
i__1 = *n - l2;
/* Computing MIN */
i__2 = l2 + 1;
/* Computing MIN */
i__3 = l2 + 1;
sumr = igraphddot_(&i__1, &c__[k1 + min(i__2,*n) * c_dim1], ldc,
&b[l1 + min(i__3,*n) * b_dim1], ldb);
vec[0] = sgn * (c__[k1 + l1 * c_dim1] - (suml + sgn *
sumr));
i__1 = *m - k1;
/* Computing MIN */
i__2 = k1 + 1;
/* Computing MIN */
i__3 = k1 + 1;
suml = igraphddot_(&i__1, &a[k1 + min(i__2,*m) * a_dim1], lda, &
c__[min(i__3,*m) + l2 * c_dim1], &c__1);
i__1 = *n - l2;
/* Computing MIN */
i__2 = l2 + 1;
/* Computing MIN */
i__3 = l2 + 1;
sumr = igraphddot_(&i__1, &c__[k1 + min(i__2,*n) * c_dim1], ldc,
&b[l2 + min(i__3,*n) * b_dim1], ldb);
vec[1] = sgn * (c__[k1 + l2 * c_dim1] - (suml + sgn *
sumr));
d__1 = -sgn * a[k1 + k1 * a_dim1];
igraphdlaln2_(&c_false, &c__2, &c__1, &smin, &c_b26, &b[l1 + l1
* b_dim1], ldb, &c_b26, &c_b26, vec, &c__2, &d__1,
&c_b30, x, &c__2, &scaloc, &xnorm, &ierr);
if (ierr != 0) {
*info = 1;
}
if (scaloc != 1.) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
igraphdscal_(m, &scaloc, &c__[j * c_dim1 + 1], &c__1);
/* L210: */
}
*scale *= scaloc;
}
c__[k1 + l1 * c_dim1] = x[0];
c__[k1 + l2 * c_dim1] = x[1];
} else if (l1 != l2 && k1 != k2) {
i__1 = *m - k2;
/* Computing MIN */
i__2 = k2 + 1;
/* Computing MIN */
i__3 = k2 + 1;
suml = igraphddot_(&i__1, &a[k1 + min(i__2,*m) * a_dim1], lda, &
c__[min(i__3,*m) + l1 * c_dim1], &c__1);
i__1 = *n - l2;
/* Computing MIN */
i__2 = l2 + 1;
/* Computing MIN */
i__3 = l2 + 1;
sumr = igraphddot_(&i__1, &c__[k1 + min(i__2,*n) * c_dim1], ldc,
&b[l1 + min(i__3,*n) * b_dim1], ldb);
vec[0] = c__[k1 + l1 * c_dim1] - (suml + sgn * sumr);
i__1 = *m - k2;
/* Computing MIN */
i__2 = k2 + 1;
/* Computing MIN */
i__3 = k2 + 1;
suml = igraphddot_(&i__1, &a[k1 + min(i__2,*m) * a_dim1], lda, &
c__[min(i__3,*m) + l2 * c_dim1], &c__1);
i__1 = *n - l2;
/* Computing MIN */
i__2 = l2 + 1;
/* Computing MIN */
i__3 = l2 + 1;
sumr = igraphddot_(&i__1, &c__[k1 + min(i__2,*n) * c_dim1], ldc,
&b[l2 + min(i__3,*n) * b_dim1], ldb);
vec[2] = c__[k1 + l2 * c_dim1] - (suml + sgn * sumr);
i__1 = *m - k2;
/* Computing MIN */
i__2 = k2 + 1;
/* Computing MIN */
i__3 = k2 + 1;
suml = igraphddot_(&i__1, &a[k2 + min(i__2,*m) * a_dim1], lda, &
c__[min(i__3,*m) + l1 * c_dim1], &c__1);
i__1 = *n - l2;
/* Computing MIN */
i__2 = l2 + 1;
/* Computing MIN */
i__3 = l2 + 1;
sumr = igraphddot_(&i__1, &c__[k2 + min(i__2,*n) * c_dim1], ldc,
&b[l1 + min(i__3,*n) * b_dim1], ldb);
vec[1] = c__[k2 + l1 * c_dim1] - (suml + sgn * sumr);
i__1 = *m - k2;
/* Computing MIN */
i__2 = k2 + 1;
/* Computing MIN */
i__3 = k2 + 1;
suml = igraphddot_(&i__1, &a[k2 + min(i__2,*m) * a_dim1], lda, &
c__[min(i__3,*m) + l2 * c_dim1], &c__1);
i__1 = *n - l2;
/* Computing MIN */
i__2 = l2 + 1;
/* Computing MIN */
i__3 = l2 + 1;
sumr = igraphddot_(&i__1, &c__[k2 + min(i__2,*n) * c_dim1], ldc,
&b[l2 + min(i__3,*n) * b_dim1], ldb);
vec[3] = c__[k2 + l2 * c_dim1] - (suml + sgn * sumr);
igraphdlasy2_(&c_false, &c_true, isgn, &c__2, &c__2, &a[k1 + k1
* a_dim1], lda, &b[l1 + l1 * b_dim1], ldb, vec, &
c__2, &scaloc, x, &c__2, &xnorm, &ierr);
if (ierr != 0) {
*info = 1;
}
if (scaloc != 1.) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
igraphdscal_(m, &scaloc, &c__[j * c_dim1 + 1], &c__1);
/* L220: */
}
*scale *= scaloc;
}
c__[k1 + l1 * c_dim1] = x[0];
c__[k1 + l2 * c_dim1] = x[2];
c__[k2 + l1 * c_dim1] = x[1];
c__[k2 + l2 * c_dim1] = x[3];
}
L230:
;
}
L240:
;
}
}
return 0;
/* End of DTRSYL */
} /* igraphdtrsyl_ */