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/* -- translated by f2c (version 20240504).
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__4 = 4;
static integer c__1 = 1;
static integer c__16 = 16;
static integer c__0 = 0;
/* > \brief \b DLASY2 solves the Sylvester matrix equation where the matrices are of order 1 or 2.
=========== DOCUMENTATION ===========
Online html documentation available at
http://www.netlib.org/lapack/explore-html/
> \htmlonly
> Download DLASY2 + dependencies
> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlasy2.
f">
> [TGZ]</a>
> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlasy2.
f">
> [ZIP]</a>
> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlasy2.
f">
> [TXT]</a>
> \endhtmlonly
Definition:
===========
SUBROUTINE DLASY2( LTRANL, LTRANR, ISGN, N1, N2, TL, LDTL, TR,
LDTR, B, LDB, SCALE, X, LDX, XNORM, INFO )
LOGICAL LTRANL, LTRANR
INTEGER INFO, ISGN, LDB, LDTL, LDTR, LDX, N1, N2
DOUBLE PRECISION SCALE, XNORM
DOUBLE PRECISION B( LDB, * ), TL( LDTL, * ), TR( LDTR, * ),
$ X( LDX, * )
> \par Purpose:
=============
>
> \verbatim
>
> DLASY2 solves for the N1 by N2 matrix X, 1 <= N1,N2 <= 2, in
>
> op(TL)*X + ISGN*X*op(TR) = SCALE*B,
>
> where TL is N1 by N1, TR is N2 by N2, B is N1 by N2, and ISGN = 1 or
> -1. op(T) = T or T**T, where T**T denotes the transpose of T.
> \endverbatim
Arguments:
==========
> \param[in] LTRANL
> \verbatim
> LTRANL is LOGICAL
> On entry, LTRANL specifies the op(TL):
> = .FALSE., op(TL) = TL,
> = .TRUE., op(TL) = TL**T.
> \endverbatim
>
> \param[in] LTRANR
> \verbatim
> LTRANR is LOGICAL
> On entry, LTRANR specifies the op(TR):
> = .FALSE., op(TR) = TR,
> = .TRUE., op(TR) = TR**T.
> \endverbatim
>
> \param[in] ISGN
> \verbatim
> ISGN is INTEGER
> On entry, ISGN specifies the sign of the equation
> as described before. ISGN may only be 1 or -1.
> \endverbatim
>
> \param[in] N1
> \verbatim
> N1 is INTEGER
> On entry, N1 specifies the order of matrix TL.
> N1 may only be 0, 1 or 2.
> \endverbatim
>
> \param[in] N2
> \verbatim
> N2 is INTEGER
> On entry, N2 specifies the order of matrix TR.
> N2 may only be 0, 1 or 2.
> \endverbatim
>
> \param[in] TL
> \verbatim
> TL is DOUBLE PRECISION array, dimension (LDTL,2)
> On entry, TL contains an N1 by N1 matrix.
> \endverbatim
>
> \param[in] LDTL
> \verbatim
> LDTL is INTEGER
> The leading dimension of the matrix TL. LDTL >= max(1,N1).
> \endverbatim
>
> \param[in] TR
> \verbatim
> TR is DOUBLE PRECISION array, dimension (LDTR,2)
> On entry, TR contains an N2 by N2 matrix.
> \endverbatim
>
> \param[in] LDTR
> \verbatim
> LDTR is INTEGER
> The leading dimension of the matrix TR. LDTR >= max(1,N2).
> \endverbatim
>
> \param[in] B
> \verbatim
> B is DOUBLE PRECISION array, dimension (LDB,2)
> On entry, the N1 by N2 matrix B contains the right-hand
> side of the equation.
> \endverbatim
>
> \param[in] LDB
> \verbatim
> LDB is INTEGER
> The leading dimension of the matrix B. LDB >= max(1,N1).
> \endverbatim
>
> \param[out] SCALE
> \verbatim
> SCALE is DOUBLE PRECISION
> On exit, SCALE contains the scale factor. SCALE is chosen
> less than or equal to 1 to prevent the solution overflowing.
> \endverbatim
>
> \param[out] X
> \verbatim
> X is DOUBLE PRECISION array, dimension (LDX,2)
> On exit, X contains the N1 by N2 solution.
> \endverbatim
>
> \param[in] LDX
> \verbatim
> LDX is INTEGER
> The leading dimension of the matrix X. LDX >= max(1,N1).
> \endverbatim
>
> \param[out] XNORM
> \verbatim
> XNORM is DOUBLE PRECISION
> On exit, XNORM is the infinity-norm of the solution.
> \endverbatim
>
> \param[out] INFO
> \verbatim
> INFO is INTEGER
> On exit, INFO is set to
> 0: successful exit.
> 1: TL and TR have too close eigenvalues, so TL or
> TR is perturbed to get a nonsingular equation.
> NOTE: In the interests of speed, this routine does not
> check the inputs for errors.
> \endverbatim
Authors:
========
> \author Univ. of Tennessee
> \author Univ. of California Berkeley
> \author Univ. of Colorado Denver
> \author NAG Ltd.
> \date September 2012
> \ingroup doubleSYauxiliary
=====================================================================
Subroutine */ int igraphdlasy2_(logical *ltranl, logical *ltranr, integer *isgn,
integer *n1, integer *n2, doublereal *tl, integer *ldtl, doublereal *
tr, integer *ldtr, doublereal *b, integer *ldb, doublereal *scale,
doublereal *x, integer *ldx, doublereal *xnorm, integer *info)
{
/* Initialized data */
IGRAPH_F77_SAVE integer locu12[4] = { 3,4,1,2 };
IGRAPH_F77_SAVE integer locl21[4] = { 2,1,4,3 };
IGRAPH_F77_SAVE integer locu22[4] = { 4,3,2,1 };
IGRAPH_F77_SAVE logical xswpiv[4] = { FALSE_,FALSE_,TRUE_,TRUE_ };
IGRAPH_F77_SAVE logical bswpiv[4] = { FALSE_,TRUE_,FALSE_,TRUE_ };
/* System generated locals */
integer b_dim1, b_offset, tl_dim1, tl_offset, tr_dim1, tr_offset, x_dim1,
x_offset;
doublereal d__1, d__2, d__3, d__4, d__5, d__6, d__7, d__8;
/* Local variables */
integer i__, j, k;
doublereal x2[2], l21, u11, u12;
integer ip, jp;
doublereal u22, t16[16] /* was [4][4] */, gam, bet, eps, sgn, tmp[4],
tau1, btmp[4], smin;
integer ipiv;
doublereal temp;
integer jpiv[4];
doublereal xmax;
integer ipsv, jpsv;
logical bswap;
extern /* Subroutine */ int igraphdcopy_(integer *, doublereal *, integer *,
doublereal *, integer *), igraphdswap_(integer *, doublereal *, integer
*, doublereal *, integer *);
logical xswap;
extern doublereal igraphdlamch_(char *);
extern integer igraphidamax_(integer *, doublereal *, integer *);
doublereal smlnum;
/* -- LAPACK auxiliary routine (version 3.4.2) --
-- LAPACK is a software package provided by Univ. of Tennessee, --
-- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
September 2012
=====================================================================
Parameter adjustments */
tl_dim1 = *ldtl;
tl_offset = 1 + tl_dim1;
tl -= tl_offset;
tr_dim1 = *ldtr;
tr_offset = 1 + tr_dim1;
tr -= tr_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
x_dim1 = *ldx;
x_offset = 1 + x_dim1;
x -= x_offset;
/* Function Body
Do not check the input parameters for errors */
*info = 0;
/* Quick return if possible */
if (*n1 == 0 || *n2 == 0) {
return 0;
}
/* Set constants to control overflow */
eps = igraphdlamch_("P");
smlnum = igraphdlamch_("S") / eps;
sgn = (doublereal) (*isgn);
k = *n1 + *n1 + *n2 - 2;
switch (k) {
case 1: goto L10;
case 2: goto L20;
case 3: goto L30;
case 4: goto L50;
}
/* 1 by 1: TL11*X + SGN*X*TR11 = B11 */
L10:
tau1 = tl[tl_dim1 + 1] + sgn * tr[tr_dim1 + 1];
bet = abs(tau1);
if (bet <= smlnum) {
tau1 = smlnum;
bet = smlnum;
*info = 1;
}
*scale = 1.;
gam = (d__1 = b[b_dim1 + 1], abs(d__1));
if (smlnum * gam > bet) {
*scale = 1. / gam;
}
x[x_dim1 + 1] = b[b_dim1 + 1] * *scale / tau1;
*xnorm = (d__1 = x[x_dim1 + 1], abs(d__1));
return 0;
/* 1 by 2:
TL11*[X11 X12] + ISGN*[X11 X12]*op[TR11 TR12] = [B11 B12]
[TR21 TR22] */
L20:
/* Computing MAX
Computing MAX */
d__7 = (d__1 = tl[tl_dim1 + 1], abs(d__1)), d__8 = (d__2 = tr[tr_dim1 + 1]
, abs(d__2)), d__7 = max(d__7,d__8), d__8 = (d__3 = tr[(tr_dim1 <<
1) + 1], abs(d__3)), d__7 = max(d__7,d__8), d__8 = (d__4 = tr[
tr_dim1 + 2], abs(d__4)), d__7 = max(d__7,d__8), d__8 = (d__5 =
tr[(tr_dim1 << 1) + 2], abs(d__5));
d__6 = eps * max(d__7,d__8);
smin = max(d__6,smlnum);
tmp[0] = tl[tl_dim1 + 1] + sgn * tr[tr_dim1 + 1];
tmp[3] = tl[tl_dim1 + 1] + sgn * tr[(tr_dim1 << 1) + 2];
if (*ltranr) {
tmp[1] = sgn * tr[tr_dim1 + 2];
tmp[2] = sgn * tr[(tr_dim1 << 1) + 1];
} else {
tmp[1] = sgn * tr[(tr_dim1 << 1) + 1];
tmp[2] = sgn * tr[tr_dim1 + 2];
}
btmp[0] = b[b_dim1 + 1];
btmp[1] = b[(b_dim1 << 1) + 1];
goto L40;
/* 2 by 1:
op[TL11 TL12]*[X11] + ISGN* [X11]*TR11 = [B11]
[TL21 TL22] [X21] [X21] [B21] */
L30:
/* Computing MAX
Computing MAX */
d__7 = (d__1 = tr[tr_dim1 + 1], abs(d__1)), d__8 = (d__2 = tl[tl_dim1 + 1]
, abs(d__2)), d__7 = max(d__7,d__8), d__8 = (d__3 = tl[(tl_dim1 <<
1) + 1], abs(d__3)), d__7 = max(d__7,d__8), d__8 = (d__4 = tl[
tl_dim1 + 2], abs(d__4)), d__7 = max(d__7,d__8), d__8 = (d__5 =
tl[(tl_dim1 << 1) + 2], abs(d__5));
d__6 = eps * max(d__7,d__8);
smin = max(d__6,smlnum);
tmp[0] = tl[tl_dim1 + 1] + sgn * tr[tr_dim1 + 1];
tmp[3] = tl[(tl_dim1 << 1) + 2] + sgn * tr[tr_dim1 + 1];
if (*ltranl) {
tmp[1] = tl[(tl_dim1 << 1) + 1];
tmp[2] = tl[tl_dim1 + 2];
} else {
tmp[1] = tl[tl_dim1 + 2];
tmp[2] = tl[(tl_dim1 << 1) + 1];
}
btmp[0] = b[b_dim1 + 1];
btmp[1] = b[b_dim1 + 2];
L40:
/* Solve 2 by 2 system using complete pivoting.
Set pivots less than SMIN to SMIN. */
ipiv = igraphidamax_(&c__4, tmp, &c__1);
u11 = tmp[ipiv - 1];
if (abs(u11) <= smin) {
*info = 1;
u11 = smin;
}
u12 = tmp[locu12[ipiv - 1] - 1];
l21 = tmp[locl21[ipiv - 1] - 1] / u11;
u22 = tmp[locu22[ipiv - 1] - 1] - u12 * l21;
xswap = xswpiv[ipiv - 1];
bswap = bswpiv[ipiv - 1];
if (abs(u22) <= smin) {
*info = 1;
u22 = smin;
}
if (bswap) {
temp = btmp[1];
btmp[1] = btmp[0] - l21 * temp;
btmp[0] = temp;
} else {
btmp[1] -= l21 * btmp[0];
}
*scale = 1.;
if (smlnum * 2. * abs(btmp[1]) > abs(u22) || smlnum * 2. * abs(btmp[0]) >
abs(u11)) {
/* Computing MAX */
d__1 = abs(btmp[0]), d__2 = abs(btmp[1]);
*scale = .5 / max(d__1,d__2);
btmp[0] *= *scale;
btmp[1] *= *scale;
}
x2[1] = btmp[1] / u22;
x2[0] = btmp[0] / u11 - u12 / u11 * x2[1];
if (xswap) {
temp = x2[1];
x2[1] = x2[0];
x2[0] = temp;
}
x[x_dim1 + 1] = x2[0];
if (*n1 == 1) {
x[(x_dim1 << 1) + 1] = x2[1];
*xnorm = (d__1 = x[x_dim1 + 1], abs(d__1)) + (d__2 = x[(x_dim1 << 1)
+ 1], abs(d__2));
} else {
x[x_dim1 + 2] = x2[1];
/* Computing MAX */
d__3 = (d__1 = x[x_dim1 + 1], abs(d__1)), d__4 = (d__2 = x[x_dim1 + 2]
, abs(d__2));
*xnorm = max(d__3,d__4);
}
return 0;
/* 2 by 2:
op[TL11 TL12]*[X11 X12] +ISGN* [X11 X12]*op[TR11 TR12] = [B11 B12]
[TL21 TL22] [X21 X22] [X21 X22] [TR21 TR22] [B21 B22]
Solve equivalent 4 by 4 system using complete pivoting.
Set pivots less than SMIN to SMIN. */
L50:
/* Computing MAX */
d__5 = (d__1 = tr[tr_dim1 + 1], abs(d__1)), d__6 = (d__2 = tr[(tr_dim1 <<
1) + 1], abs(d__2)), d__5 = max(d__5,d__6), d__6 = (d__3 = tr[
tr_dim1 + 2], abs(d__3)), d__5 = max(d__5,d__6), d__6 = (d__4 =
tr[(tr_dim1 << 1) + 2], abs(d__4));
smin = max(d__5,d__6);
/* Computing MAX */
d__5 = smin, d__6 = (d__1 = tl[tl_dim1 + 1], abs(d__1)), d__5 = max(d__5,
d__6), d__6 = (d__2 = tl[(tl_dim1 << 1) + 1], abs(d__2)), d__5 =
max(d__5,d__6), d__6 = (d__3 = tl[tl_dim1 + 2], abs(d__3)), d__5 =
max(d__5,d__6), d__6 = (d__4 = tl[(tl_dim1 << 1) + 2], abs(d__4))
;
smin = max(d__5,d__6);
/* Computing MAX */
d__1 = eps * smin;
smin = max(d__1,smlnum);
btmp[0] = 0.;
igraphdcopy_(&c__16, btmp, &c__0, t16, &c__1);
t16[0] = tl[tl_dim1 + 1] + sgn * tr[tr_dim1 + 1];
t16[5] = tl[(tl_dim1 << 1) + 2] + sgn * tr[tr_dim1 + 1];
t16[10] = tl[tl_dim1 + 1] + sgn * tr[(tr_dim1 << 1) + 2];
t16[15] = tl[(tl_dim1 << 1) + 2] + sgn * tr[(tr_dim1 << 1) + 2];
if (*ltranl) {
t16[4] = tl[tl_dim1 + 2];
t16[1] = tl[(tl_dim1 << 1) + 1];
t16[14] = tl[tl_dim1 + 2];
t16[11] = tl[(tl_dim1 << 1) + 1];
} else {
t16[4] = tl[(tl_dim1 << 1) + 1];
t16[1] = tl[tl_dim1 + 2];
t16[14] = tl[(tl_dim1 << 1) + 1];
t16[11] = tl[tl_dim1 + 2];
}
if (*ltranr) {
t16[8] = sgn * tr[(tr_dim1 << 1) + 1];
t16[13] = sgn * tr[(tr_dim1 << 1) + 1];
t16[2] = sgn * tr[tr_dim1 + 2];
t16[7] = sgn * tr[tr_dim1 + 2];
} else {
t16[8] = sgn * tr[tr_dim1 + 2];
t16[13] = sgn * tr[tr_dim1 + 2];
t16[2] = sgn * tr[(tr_dim1 << 1) + 1];
t16[7] = sgn * tr[(tr_dim1 << 1) + 1];
}
btmp[0] = b[b_dim1 + 1];
btmp[1] = b[b_dim1 + 2];
btmp[2] = b[(b_dim1 << 1) + 1];
btmp[3] = b[(b_dim1 << 1) + 2];
/* Perform elimination */
for (i__ = 1; i__ <= 3; ++i__) {
xmax = 0.;
for (ip = i__; ip <= 4; ++ip) {
for (jp = i__; jp <= 4; ++jp) {
if ((d__1 = t16[ip + (jp << 2) - 5], abs(d__1)) >= xmax) {
xmax = (d__1 = t16[ip + (jp << 2) - 5], abs(d__1));
ipsv = ip;
jpsv = jp;
}
/* L60: */
}
/* L70: */
}
if (ipsv != i__) {
igraphdswap_(&c__4, &t16[ipsv - 1], &c__4, &t16[i__ - 1], &c__4);
temp = btmp[i__ - 1];
btmp[i__ - 1] = btmp[ipsv - 1];
btmp[ipsv - 1] = temp;
}
if (jpsv != i__) {
igraphdswap_(&c__4, &t16[(jpsv << 2) - 4], &c__1, &t16[(i__ << 2) - 4],
&c__1);
}
jpiv[i__ - 1] = jpsv;
if ((d__1 = t16[i__ + (i__ << 2) - 5], abs(d__1)) < smin) {
*info = 1;
t16[i__ + (i__ << 2) - 5] = smin;
}
for (j = i__ + 1; j <= 4; ++j) {
t16[j + (i__ << 2) - 5] /= t16[i__ + (i__ << 2) - 5];
btmp[j - 1] -= t16[j + (i__ << 2) - 5] * btmp[i__ - 1];
for (k = i__ + 1; k <= 4; ++k) {
t16[j + (k << 2) - 5] -= t16[j + (i__ << 2) - 5] * t16[i__ + (
k << 2) - 5];
/* L80: */
}
/* L90: */
}
/* L100: */
}
if (abs(t16[15]) < smin) {
t16[15] = smin;
}
*scale = 1.;
if (smlnum * 8. * abs(btmp[0]) > abs(t16[0]) || smlnum * 8. * abs(btmp[1])
> abs(t16[5]) || smlnum * 8. * abs(btmp[2]) > abs(t16[10]) ||
smlnum * 8. * abs(btmp[3]) > abs(t16[15])) {
/* Computing MAX */
d__1 = abs(btmp[0]), d__2 = abs(btmp[1]), d__1 = max(d__1,d__2), d__2
= abs(btmp[2]), d__1 = max(d__1,d__2), d__2 = abs(btmp[3]);
*scale = .125 / max(d__1,d__2);
btmp[0] *= *scale;
btmp[1] *= *scale;
btmp[2] *= *scale;
btmp[3] *= *scale;
}
for (i__ = 1; i__ <= 4; ++i__) {
k = 5 - i__;
temp = 1. / t16[k + (k << 2) - 5];
tmp[k - 1] = btmp[k - 1] * temp;
for (j = k + 1; j <= 4; ++j) {
tmp[k - 1] -= temp * t16[k + (j << 2) - 5] * tmp[j - 1];
/* L110: */
}
/* L120: */
}
for (i__ = 1; i__ <= 3; ++i__) {
if (jpiv[4 - i__ - 1] != 4 - i__) {
temp = tmp[4 - i__ - 1];
tmp[4 - i__ - 1] = tmp[jpiv[4 - i__ - 1] - 1];
tmp[jpiv[4 - i__ - 1] - 1] = temp;
}
/* L130: */
}
x[x_dim1 + 1] = tmp[0];
x[x_dim1 + 2] = tmp[1];
x[(x_dim1 << 1) + 1] = tmp[2];
x[(x_dim1 << 1) + 2] = tmp[3];
/* Computing MAX */
d__1 = abs(tmp[0]) + abs(tmp[2]), d__2 = abs(tmp[1]) + abs(tmp[3]);
*xnorm = max(d__1,d__2);
return 0;
/* End of DLASY2 */
} /* igraphdlasy2_ */
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