/* slasy2.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__4 = 4;
static integer c__1 = 1;
static integer c__16 = 16;
static integer c__0 = 0;
/* Subroutine */ int slasy2_(logical *ltranl, logical *ltranr, integer *isgn,
integer *n1, integer *n2, real *tl, integer *ldtl, real *tr, integer *
ldtr, real *b, integer *ldb, real *scale, real *x, integer *ldx, real
*xnorm, integer *info)
{
/* Initialized data */
static integer locu12[4] = { 3,4,1,2 };
static integer locl21[4] = { 2,1,4,3 };
static integer locu22[4] = { 4,3,2,1 };
static logical xswpiv[4] = { FALSE_,FALSE_,TRUE_,TRUE_ };
static 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;
real r__1, r__2, r__3, r__4, r__5, r__6, r__7, r__8;
/* Local variables */
integer i__, j, k;
real x2[2], l21, u11, u12;
integer ip, jp;
real u22, t16[16] /* was [4][4] */, gam, bet, eps, sgn, tmp[4], tau1,
btmp[4], smin;
integer ipiv;
real temp;
integer jpiv[4];
real xmax;
integer ipsv, jpsv;
logical bswap;
extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *,
integer *), sswap_(integer *, real *, integer *, real *, integer *
);
logical xswap;
extern doublereal slamch_(char *);
extern integer isamax_(integer *, real *, integer *);
real smlnum;
/* -- LAPACK auxiliary routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* SLASY2 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', where T' denotes the transpose of T. */
/* Arguments */
/* ========= */
/* LTRANL (input) LOGICAL */
/* On entry, LTRANL specifies the op(TL): */
/* = .FALSE., op(TL) = TL, */
/* = .TRUE., op(TL) = TL'. */
/* LTRANR (input) LOGICAL */
/* On entry, LTRANR specifies the op(TR): */
/* = .FALSE., op(TR) = TR, */
/* = .TRUE., op(TR) = TR'. */
/* ISGN (input) INTEGER */
/* On entry, ISGN specifies the sign of the equation */
/* as described before. ISGN may only be 1 or -1. */
/* N1 (input) INTEGER */
/* On entry, N1 specifies the order of matrix TL. */
/* N1 may only be 0, 1 or 2. */
/* N2 (input) INTEGER */
/* On entry, N2 specifies the order of matrix TR. */
/* N2 may only be 0, 1 or 2. */
/* TL (input) REAL array, dimension (LDTL,2) */
/* On entry, TL contains an N1 by N1 matrix. */
/* LDTL (input) INTEGER */
/* The leading dimension of the matrix TL. LDTL >= max(1,N1). */
/* TR (input) REAL array, dimension (LDTR,2) */
/* On entry, TR contains an N2 by N2 matrix. */
/* LDTR (input) INTEGER */
/* The leading dimension of the matrix TR. LDTR >= max(1,N2). */
/* B (input) REAL array, dimension (LDB,2) */
/* On entry, the N1 by N2 matrix B contains the right-hand */
/* side of the equation. */
/* LDB (input) INTEGER */
/* The leading dimension of the matrix B. LDB >= max(1,N1). */
/* SCALE (output) REAL */
/* On exit, SCALE contains the scale factor. SCALE is chosen */
/* less than or equal to 1 to prevent the solution overflowing. */
/* X (output) REAL array, dimension (LDX,2) */
/* On exit, X contains the N1 by N2 solution. */
/* LDX (input) INTEGER */
/* The leading dimension of the matrix X. LDX >= max(1,N1). */
/* XNORM (output) REAL */
/* On exit, XNORM is the infinity-norm of the solution. */
/* INFO (output) 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. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Data statements .. */
/* 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 */
/* .. */
/* .. Executable Statements .. */
/* 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 = slamch_("P");
smlnum = slamch_("S") / eps;
sgn = (real) (*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 = dabs(tau1);
if (bet <= smlnum) {
tau1 = smlnum;
bet = smlnum;
*info = 1;
}
*scale = 1.f;
gam = (r__1 = b[b_dim1 + 1], dabs(r__1));
if (smlnum * gam > bet) {
*scale = 1.f / gam;
}
x[x_dim1 + 1] = b[b_dim1 + 1] * *scale / tau1;
*xnorm = (r__1 = x[x_dim1 + 1], dabs(r__1));
return 0;
/* 1 by 2: */
/* TL11*[X11 X12] + ISGN*[X11 X12]*op[TR11 TR12] = [B11 B12] */
/* [TR21 TR22] */
L20:
/* Computing MAX */
/* Computing MAX */
r__7 = (r__1 = tl[tl_dim1 + 1], dabs(r__1)), r__8 = (r__2 = tr[tr_dim1 +
1], dabs(r__2)), r__7 = max(r__7,r__8), r__8 = (r__3 = tr[(
tr_dim1 << 1) + 1], dabs(r__3)), r__7 = max(r__7,r__8), r__8 = (
r__4 = tr[tr_dim1 + 2], dabs(r__4)), r__7 = max(r__7,r__8), r__8 =
(r__5 = tr[(tr_dim1 << 1) + 2], dabs(r__5));
r__6 = eps * dmax(r__7,r__8);
smin = dmax(r__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 */
r__7 = (r__1 = tr[tr_dim1 + 1], dabs(r__1)), r__8 = (r__2 = tl[tl_dim1 +
1], dabs(r__2)), r__7 = max(r__7,r__8), r__8 = (r__3 = tl[(
tl_dim1 << 1) + 1], dabs(r__3)), r__7 = max(r__7,r__8), r__8 = (
r__4 = tl[tl_dim1 + 2], dabs(r__4)), r__7 = max(r__7,r__8), r__8 =
(r__5 = tl[(tl_dim1 << 1) + 2], dabs(r__5));
r__6 = eps * dmax(r__7,r__8);
smin = dmax(r__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 = isamax_(&c__4, tmp, &c__1);
u11 = tmp[ipiv - 1];
if (dabs(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 (dabs(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.f;
if (smlnum * 2.f * dabs(btmp[1]) > dabs(u22) || smlnum * 2.f * dabs(btmp[
0]) > dabs(u11)) {
/* Computing MAX */
r__1 = dabs(btmp[0]), r__2 = dabs(btmp[1]);
*scale = .5f / dmax(r__1,r__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 = (r__1 = x[x_dim1 + 1], dabs(r__1)) + (r__2 = x[(x_dim1 << 1)
+ 1], dabs(r__2));
} else {
x[x_dim1 + 2] = x2[1];
/* Computing MAX */
r__3 = (r__1 = x[x_dim1 + 1], dabs(r__1)), r__4 = (r__2 = x[x_dim1 +
2], dabs(r__2));
*xnorm = dmax(r__3,r__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 */
r__5 = (r__1 = tr[tr_dim1 + 1], dabs(r__1)), r__6 = (r__2 = tr[(tr_dim1 <<
1) + 1], dabs(r__2)), r__5 = max(r__5,r__6), r__6 = (r__3 = tr[
tr_dim1 + 2], dabs(r__3)), r__5 = max(r__5,r__6), r__6 = (r__4 =
tr[(tr_dim1 << 1) + 2], dabs(r__4));
smin = dmax(r__5,r__6);
/* Computing MAX */
r__5 = smin, r__6 = (r__1 = tl[tl_dim1 + 1], dabs(r__1)), r__5 = max(r__5,
r__6), r__6 = (r__2 = tl[(tl_dim1 << 1) + 1], dabs(r__2)), r__5 =
max(r__5,r__6), r__6 = (r__3 = tl[tl_dim1 + 2], dabs(r__3)), r__5
= max(r__5,r__6), r__6 = (r__4 = tl[(tl_dim1 << 1) + 2], dabs(
r__4));
smin = dmax(r__5,r__6);
/* Computing MAX */
r__1 = eps * smin;
smin = dmax(r__1,smlnum);
btmp[0] = 0.f;
scopy_(&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.f;
for (ip = i__; ip <= 4; ++ip) {
for (jp = i__; jp <= 4; ++jp) {
if ((r__1 = t16[ip + (jp << 2) - 5], dabs(r__1)) >= xmax) {
xmax = (r__1 = t16[ip + (jp << 2) - 5], dabs(r__1));
ipsv = ip;
jpsv = jp;
}
/* L60: */
}
/* L70: */
}
if (ipsv != i__) {
sswap_(&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__) {
sswap_(&c__4, &t16[(jpsv << 2) - 4], &c__1, &t16[(i__ << 2) - 4],
&c__1);
}
jpiv[i__ - 1] = jpsv;
if ((r__1 = t16[i__ + (i__ << 2) - 5], dabs(r__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 (dabs(t16[15]) < smin) {
t16[15] = smin;
}
*scale = 1.f;
if (smlnum * 8.f * dabs(btmp[0]) > dabs(t16[0]) || smlnum * 8.f * dabs(
btmp[1]) > dabs(t16[5]) || smlnum * 8.f * dabs(btmp[2]) > dabs(
t16[10]) || smlnum * 8.f * dabs(btmp[3]) > dabs(t16[15])) {
/* Computing MAX */
r__1 = dabs(btmp[0]), r__2 = dabs(btmp[1]), r__1 = max(r__1,r__2),
r__2 = dabs(btmp[2]), r__1 = max(r__1,r__2), r__2 = dabs(btmp[
3]);
*scale = .125f / dmax(r__1,r__2);
btmp[0] *= *scale;
btmp[1] *= *scale;
btmp[2] *= *scale;
btmp[3] *= *scale;
}
for (i__ = 1; i__ <= 4; ++i__) {
k = 5 - i__;
temp = 1.f / 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 */
r__1 = dabs(tmp[0]) + dabs(tmp[2]), r__2 = dabs(tmp[1]) + dabs(tmp[3]);
*xnorm = dmax(r__1,r__2);
return 0;
/* End of SLASY2 */
} /* slasy2_ */