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autlib3.c
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autlib3.c
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/* autlib3.f -- translated by f2c (version 19970805).
You must link the resulting object file with the libraries:
-lf2c -lm (in that order)
*/
#include "auto_f2c.h"
#include "auto_c.h"
/* The memory for these are taken care of in main, and setubv for the
mpi parallel case. These are global since the they are used many times
in the wrapper functions in autlib3.c (and autlib5.c) and the cost
of allocating and deallocating them is prohibitive. */
extern struct {
doublereal *dfu, *dfp, *uu1, *uu2, *ff1, *ff2;
} global_scratch;
/* The memory for these are taken care of in main, and setubv for the
mpi parallel case. These are global since they only need to be
computed once for an entire run, so we do them at the
beginning to save the cost later on. */
extern struct {
integer irtn;
integer *nrtn;
} global_rotations;
/* ----------------------------------------------------------------------- */
/* ----------------------------------------------------------------------- */
/* Subroutines for the Continuation of Folds (Algebraic Problems) */
/* ----------------------------------------------------------------------- */
/* ----------------------------------------------------------------------- */
/* ---------- ---- */
/* Subroutine */ int
fnlp(const iap_type *iap, const rap_type *rap, integer ndim, const doublereal *u, const doublereal *uold, const integer *icp, doublereal *par, integer ijac, doublereal *f, doublereal *dfdu, doublereal *dfdp)
{
/* System generated locals */
integer dfdu_dim1, dfdp_dim1;
/* Local variables */
doublereal rtmp;
integer i, j;
doublereal ep;
integer ndm;
doublereal umx;
/* Generates the equations for the 2-par continuation of folds. */
/* Local */
/* Parameter adjustments */
dfdp_dim1 = ndim;
dfdu_dim1 = ndim;
ndm = iap->ndm;
/* Generate the function. */
fflp(iap, rap, ndim, u, uold, icp, par, f, ndm,
global_scratch.dfu, global_scratch.dfp);
if (ijac == 0) {
return 0;
}
/* Generate the Jacobian. */
umx = 0.;
for (i = 0; i < ndim; ++i) {
if (fabs(u[i]) > umx) {
umx = fabs(u[i]);
}
}
rtmp = HMACH;
ep = rtmp * (umx + 1);
for (i = 0; i < ndim; ++i) {
for (j = 0; j < ndim; ++j) {
global_scratch.uu1[j] = u[j];
global_scratch.uu2[j] = u[j];
}
global_scratch.uu1[i] -= ep;
global_scratch.uu2[i] += ep;
fflp(iap, rap, ndim, global_scratch.uu1, uold, icp, par,
global_scratch.ff1, ndm, global_scratch.dfu, global_scratch.dfp);
fflp(iap, rap, ndim, global_scratch.uu2, uold, icp, par,
global_scratch.ff2, ndm, global_scratch.dfu, global_scratch.dfp);
for (j = 0; j < ndim; ++j) {
ARRAY2D(dfdu, j, i) = (global_scratch.ff2[j] - global_scratch.ff1[j]) / (ep * 2);
}
}
par[icp[0]] += ep;
fflp(iap, rap, ndim, u, uold, icp, par, global_scratch.ff1, ndm, global_scratch.dfu, global_scratch.dfp);
for (j = 0; j < ndim; ++j) {
ARRAY2D(dfdp, j, (icp[0])) = (global_scratch.ff1[j] - f[j]) / ep;
}
par[icp[0]] -= ep;
return 0;
} /* fnlp_ */
/* ---------- ---- */
/* Subroutine */ int
fflp(const iap_type *iap, const rap_type *rap, integer ndim, const doublereal *u, const doublereal *uold, const integer *icp, doublereal *par, doublereal *f, integer ndm, doublereal *dfdu, doublereal *dfdp)
{
/* System generated locals */
integer dfdu_dim1, dfdp_dim1;
/* Local variables */
integer i, j, ips;
/* Parameter adjustments */
dfdp_dim1 = ndm;
dfdu_dim1 = ndm;
ips = iap->ips;
par[icp[1]] = u[-1 + ndim];
if (ips == -1) {
fnds(iap, rap, ndm, u, uold, icp, par, 1, f, dfdu, dfdp);
} else {
funi(iap, rap, ndm, u, uold, icp, par, 1, f, dfdu, dfdp);
}
for (i = 0; i < ndm; ++i) {
f[ndm + i] = 0.;
for (j = 0; j < ndm; ++j) {
f[ndm + i] += ARRAY2D(dfdu, i, j) * u[ndm + j];
}
}
f[-1 + ndim] = -1.;
for (i = 0; i < ndm; ++i) {
f[-1 + ndim] += u[ndm + i] * u[ndm + i];
}
return 0;
} /* fflp_ */
/* ---------- ------ */
/* Subroutine */ int
stpnlp(iap_type *iap, rap_type *rap, doublereal *par, integer *icp, doublereal *u)
{
/* Local variables */
integer ndim;
doublereal uold;
integer nfpr1;
doublereal *f;
integer i;
doublereal *v;
logical found;
integer ndm, ips, irs;
f = (doublereal *)malloc(sizeof(doublereal)*(iap->ndim));
v = (doublereal *)malloc(sizeof(doublereal)*(iap->ndim));
/* Generates starting data for the continuation of folds. */
/* Local */
/* Parameter adjustments */
ndim = iap->ndim;
ips = iap->ips;
irs = iap->irs;
ndm = iap->ndm;
findlb(iap, rap, irs, &nfpr1, &found);
readlb(iap, rap, u, par);
if (ips == -1) {
fnds(iap, rap, ndm, u, &uold, icp, par, 1, f,
global_scratch.dfu, global_scratch.dfp);
} else {
funi(iap, rap, ndm, u, &uold, icp, par, 1, f,
global_scratch.dfu, global_scratch.dfp);
}
nlvc(ndm, ndm, 1, global_scratch.dfu, v);
nrmlz(&ndm, v);
for (i = 0; i < ndm; ++i) {
u[ndm + i] = v[i];
}
u[-1 + ndim] = par[icp[1]];
free(f);
free(v);
return 0;
} /* stpnlp_ */
/* ----------------------------------------------------------------------- */
/* ----------------------------------------------------------------------- */
/* Subroutines for the Optimization of Algebraic Systems */
/* ----------------------------------------------------------------------- */
/* ----------------------------------------------------------------------- */
/* ---------- ---- */
/* Subroutine */ int
fnc1(const iap_type *iap, const rap_type *rap, integer ndim, const doublereal *u, const doublereal *uold, const integer *icp, doublereal *par, integer ijac, doublereal *f, doublereal *dfdu, doublereal *dfdp)
{
/* System generated locals */
integer dfdu_dim1, dfdp_dim1;
/* Local variables */
integer i, j;
doublereal ddp[NPARX], *ddu;
integer ndm;
ddu = (doublereal *)malloc(sizeof(doublereal)*(iap->ndim));
/* Generate the equations for the continuation scheme used for */
/* the optimization of algebraic systems (one parameter). */
/* Local */
/* Parameter adjustments */
dfdp_dim1 = ndim;
dfdu_dim1 = ndim;
ndm = iap->ndm;
par[icp[1]] = u[-1 + ndim];
funi(iap, rap, ndm, u, uold, icp, par, ijac, f, dfdu, dfdp);
/* Rearrange (Since dimensions in FNC1 and FUNI differ). */
if (ijac != 0) {
for (j = ndm - 1; j >= 0; --j) {
for (i = ndm - 1; i >= 0; --i) {
ARRAY2D(dfdu, i, j) = dfdu[j * ndm + i];
}
}
for (j = NPARX - 1; j >= 0; --j) {
for (i = ndm - 1; i >= 0; --i) {
ARRAY2D(dfdp, i, j) = dfdp[j * ndm + i];
}
}
}
fopi(iap, rap, ndm, u, icp, par, ijac, &f[-1 + ndim], ddu,
ddp);
f[-1 + ndim] = par[icp[0]] - f[-1 + ndim];
if (ijac != 0) {
for (i = 0; i < ndm; ++i) {
ARRAY2D(dfdu, (ndim - 1), i) = -ddu[i];
ARRAY2D(dfdu, i, (ndim - 1)) = ARRAY2D(dfdp, i, (icp[1]));
ARRAY2D(dfdp, i, (icp[0])) = 0.;
}
ARRAY2D(dfdu, (ndim - 1), (ndim - 1)) = -ddp[icp[1]];
ARRAY2D(dfdp, (ndim - 1), (icp[0])) = 1.;
}
free(ddu);
return 0;
} /* fnc1_ */
/* ---------- ------ */
/* Subroutine */ int
stpnc1(iap_type *iap, rap_type *rap, doublereal *par, integer *icp, doublereal *u)
{
integer ndim;
integer nfpr;
integer ndm;
doublereal fop, dum;
/* Generate starting data for optimization problems (one parameter). */
/* Parameter adjustments */
ndim = iap->ndim;
ndm = iap->ndm;
stpnt(ndim, 0.0, u, par);
nfpr = 2;
iap->nfpr = nfpr;
fopi(iap, rap, ndm, u, icp, par, 0, &fop, &dum, &
dum);
par[icp[0]] = fop;
u[-1 + ndim] = par[icp[1]];
return 0;
} /* stpnc1_ */
/* ---------- ---- */
/* Subroutine */ int
fnc2(const iap_type *iap, const rap_type *rap, integer ndim, const doublereal *u, const doublereal *uold, const integer *icp, doublereal *par, integer ijac, doublereal *f, doublereal *dfdu, doublereal *dfdp)
{
/* System generated locals */
integer dfdu_dim1, dfdp_dim1;
/* Local variables */
doublereal rtmp;
integer i, j;
doublereal ep;
integer ndm;
doublereal umx;
/* Generate the equations for the continuation scheme used for the */
/* optimization of algebraic systems (more than one parameter). */
/* Local */
/* Parameter adjustments */
dfdp_dim1 = ndim;
dfdu_dim1 = ndim;
ndm = iap->ndm;
/* Generate the function. */
ffc2(iap, rap, ndim, u, uold, icp, par, f, ndm,
global_scratch.dfu, global_scratch.dfp);
if (ijac == 0) {
return 0;
}
/* Generate the Jacobian. */
umx = 0.;
for (i = 0; i < ndim; ++i) {
if (fabs(u[i]) > umx) {
umx = fabs(u[i]);
}
}
rtmp = HMACH;
ep = rtmp * (umx + 1);
for (i = 0; i < ndim; ++i) {
for (j = 0; j < ndim; ++j) {
global_scratch.uu1[j] = u[j];
global_scratch.uu2[j] = u[j];
}
global_scratch.uu1[i] -= ep;
global_scratch.uu2[i] += ep;
ffc2(iap, rap, ndim, global_scratch.uu1, uold, icp, par,
global_scratch.ff1, ndm, global_scratch.dfu, global_scratch.dfp);
ffc2(iap, rap, ndim, global_scratch.uu2, uold, icp, par,
global_scratch.ff2, ndm, global_scratch.dfu, global_scratch.dfp);
for (j = 0; j < ndim; ++j) {
ARRAY2D(dfdu, j, i) = (global_scratch.ff2[j] - global_scratch.ff1[j]) / (ep * 2);
}
}
for (i = 0; i < ndim; ++i) {
ARRAY2D(dfdp, i, (icp[0])) = 0.;
}
ARRAY2D(dfdp, (ndim - 1), (icp[0])) = 1.;
return 0;
} /* fnc2_ */
/* ---------- ---- */
/* Subroutine */ int
ffc2(const iap_type *iap, const rap_type *rap, integer ndim, const doublereal *u, const doublereal *uold, const integer *icp, doublereal *par, doublereal *f, integer ndm, doublereal *dfdu, doublereal *dfdp)
{
/* System generated locals */
integer dfdu_dim1, dfdp_dim1;
/* Local variables */
integer icpm;
integer nfpr, i, j;
doublereal ddp[NPARX], *ddu, fop;
integer ndm2;
ddu = (doublereal *)malloc(sizeof(doublereal)*(iap->ndim));
/* Local */
/* Parameter adjustments */
dfdp_dim1 = ndm;
dfdu_dim1 = ndm;
nfpr = iap->nfpr;
for (i = 1; i < nfpr; ++i) {
par[icp[i]] = u[(ndm * 2) + i];
}
funi(iap, rap, ndm, u, uold, icp, par, 2, f, dfdu, dfdp);
fopi(iap, rap, ndm, u, icp, par, 2, &fop, ddu, ddp);
for (i = 0; i < ndm; ++i) {
f[ndm + i] = ddu[i] * u[(ndm * 2)];
for (j = 0; j < ndm; ++j) {
f[ndm + i] += ARRAY2D(dfdu, j, i) * u[ndm + j];
}
}
ndm2 = ndm * 2;
icpm = nfpr - 2;
for (i = 0; i < icpm; ++i) {
f[ndm2 + i] = ddp[icp[i + 1]] * u[ndm2];
}
for (i = 0; i < icpm; ++i) {
for (j = 0; j < ndm; ++j) {
f[ndm2 + i] += u[ndm + j] * ARRAY2D(dfdp, j, (icp[i + 1]));
}
}
f[ndim - 2] = u[ndm2] * u[ndm2] - 1;
for (j = 0; j < ndm; ++j) {
f[ndim - 2] += u[ndm + j] * u[ndm + j];
}
f[-1 + ndim] = par[icp[0]] - fop;
free(ddu);
return 0;
} /* ffc2_ */
/* ---------- ------ */
/* Subroutine */ int
stpnc2(iap_type *iap, rap_type *rap, doublereal *par, integer *icp, doublereal *u)
{
/* Local variables */
integer ndim;
doublereal uold;
integer nfpr;
doublereal *f;
integer i, j;
doublereal *v;
logical found;
doublereal *dd;
doublereal dp[NPARX], *du;
integer ndm;
doublereal fop;
integer irs;
f = (doublereal *)malloc(sizeof(doublereal)*(iap->ndim));
v = (doublereal *)malloc(sizeof(doublereal)*(iap->ndim));
dd = (doublereal *)malloc(sizeof(doublereal)*(iap->ndim)*(iap->ndim));
du = (doublereal *)malloc(sizeof(doublereal)*(iap->ndim));
/* Generates starting data for the continuation equations for */
/* optimization of algebraic systems (More than one parameter). */
/* Local */
/* Parameter adjustments */
ndim = iap->ndim;
irs = iap->irs;
ndm = iap->ndm;
findlb(iap, rap, irs, &nfpr, &found);
++nfpr;
iap->nfpr = nfpr;
readlb(iap, rap, u, par);
if (nfpr == 3) {
funi(iap, rap, ndm, u, &uold, icp, par, 2, f,
global_scratch.dfu, global_scratch.dfp);
fopi(iap, rap, ndm, u, icp, par, 2, &fop, du,
dp);
/* TRANSPOSE */
for (i = 0; i < ndm; ++i) {
for (j = 0; j < ndm; ++j) {
dd[i + j * ndim] = global_scratch.dfu[i * ndm + j];
}
}
for (i = 0; i < ndm; ++i) {
dd[i + ndm * ndim] = du[i];
dd[ndm + i * ndim] = global_scratch.dfp[(icp[1]) * ndm + i];
}
dd[ndm + ndm * ndim] = dp[icp[1]];
nlvc(ndm + 1, ndim, 1, dd, v);
{
integer tmp = ndm + 1;
nrmlz(&tmp, v);
}
for (i = 0; i < ndm + 1; ++i) {
u[ndm + i] = v[i];
}
par[icp[0]] = fop;
}
for (i = 0; i < nfpr - 1; ++i) {
u[ndim - nfpr + 1 + i] = par[icp[i + 1]];
}
free(f );
free(v );
free(dd );
free(du );
return 0;
} /* stpnc2_ */
/* ----------------------------------------------------------------------- */
/* ----------------------------------------------------------------------- */
/* Subroutines for Discrete Dynamical Systems */
/* ----------------------------------------------------------------------- */
/* ----------------------------------------------------------------------- */
/* ---------- ---- */
/* Subroutine */ int
fnds(const iap_type *iap, const rap_type *rap, integer ndim, const doublereal *u, const doublereal *uold, const integer *icp, doublereal *par, integer ijac, doublereal *f, doublereal *dfdu, doublereal *dfdp)
{
/* System generated locals */
integer dfdu_dim1, dfdp_dim1;
/* Local variables */
integer i;
/* Generate the equations for continuing fixed points. */
/* Parameter adjustments */
dfdp_dim1 = ndim;
dfdu_dim1 = ndim;
funi(iap, rap, ndim, u, uold, icp, par, ijac, f, dfdu, dfdp);
for (i = 0; i < ndim; ++i) {
f[i] -= u[i];
}
if (ijac == 0) {
return 0;
}
for (i = 0; i < ndim; ++i) {
--ARRAY2D(dfdu, i, i);
}
return 0;
} /* fnds_ */
/* ----------------------------------------------------------------------- */
/* ----------------------------------------------------------------------- */
/* Subroutines for Time Integration of ODEs */
/* ----------------------------------------------------------------------- */
/* ----------------------------------------------------------------------- */
/* ---------- ---- */
/* Subroutine */ int
fnti(const iap_type *iap, const rap_type *rap, integer ndim, const doublereal *u, const doublereal *uold, const integer *icp, doublereal *par, integer ijac, doublereal *f, doublereal *dfdu, doublereal *dfdp)
{
/* System generated locals */
integer dfdu_dim1, dfdp_dim1;
/* Local variables */
doublereal told;
integer i, j;
doublereal dt;
/* Generate the equations for continuing fixed points. */
/* Parameter adjustments */
dfdp_dim1 = ndim;
dfdu_dim1 = ndim;
funi(iap, rap, ndim, u, uold, icp, par, ijac, f,
dfdu, dfdp);
told = rap->tivp;
dt = par[icp[0]] - told;
for (i = 0; i < ndim; ++i) {
ARRAY2D(dfdp, i, (icp[0])) = f[i];
f[i] = dt * f[i] - u[i] + uold[i];
}
if (ijac == 0) {
return 0;
}
for (i = 0; i < ndim; ++i) {
for (j = 0; j < ndim; ++j) {
ARRAY2D(dfdu, i, j) = dt * ARRAY2D(dfdu, i, j);
}
ARRAY2D(dfdu, i, i) += -1.;
}
return 0;
} /* fnti */
/* ----------------------------------------------------------------------- */
/* ----------------------------------------------------------------------- */
/* Subroutines for the Continuation of Hopf Bifurcation Points (Maps) */
/* ----------------------------------------------------------------------- */
/* ----------------------------------------------------------------------- */
/* ---------- ---- */
/* Subroutine */ int
fnhd(const iap_type *iap, const rap_type *rap, integer ndim, const doublereal *u, const doublereal *uold, const integer *icp, doublereal *par, integer ijac, doublereal *f, doublereal *dfdu, doublereal *dfdp)
{
/* System generated locals */
integer dfdu_dim1, dfdp_dim1;
/* Local variables */
doublereal rtmp;
integer i, j;
doublereal ep;
integer ndm;
doublereal umx;
/* Generates the equations for the 2-parameter continuation of Hopf */
/* bifurcation points for maps. */
/* Local */
/* Parameter adjustments */
dfdp_dim1 = ndim;
dfdu_dim1 = ndim;
ndm = iap->ndm;
/* Generate the function. */
ffhd(iap, rap, ndim, u, uold, icp, par, f, ndm,
global_scratch.dfu, global_scratch.dfp);
if (ijac == 0) {
return 0;
}
/* Generate the Jacobian. */
umx = 0.;
for (i = 0; i < ndim; ++i) {
if (fabs(u[i]) > umx) {
umx = fabs(u[i]);
}
}
rtmp = HMACH;
ep = rtmp * (umx + 1);
for (i = 0; i < ndim; ++i) {
for (j = 0; j < ndim; ++j) {
global_scratch.uu1[j] = u[j];
global_scratch.uu2[j] = u[j];
}
global_scratch.uu1[i] -= ep;
global_scratch.uu2[i] += ep;
ffhd(iap, rap, ndim, global_scratch.uu1, uold, icp, par,
global_scratch.ff1, ndm, global_scratch.dfu, global_scratch.dfp);
ffhd(iap, rap, ndim, global_scratch.uu2, uold, icp, par,
global_scratch.ff2, ndm, global_scratch.dfu, global_scratch.dfp);
for (j = 0; j < ndim; ++j) {
ARRAY2D(dfdu, j, i) = (global_scratch.ff2[j] - global_scratch.ff1[j]) / (ep * 2);
}
}
par[icp[0]] += ep;
ffhd(iap, rap, ndim, u, uold, icp, par, global_scratch.ff1,
ndm, global_scratch.dfu, global_scratch.dfp);
for (j = 0; j < ndim; ++j) {
ARRAY2D(dfdp, j, icp[0]) = (global_scratch.ff1[j] - f[j]) / ep;
}
par[icp[0]] -= ep;
return 0;
} /* fnhd_ */
/* ---------- ---- */
/* Subroutine */ int
ffhd(const iap_type *iap, const rap_type *rap, integer ndim, const doublereal *u, const doublereal *uold, const integer *icp, doublereal *par, doublereal *f, integer ndm, doublereal *dfdu, doublereal *dfdp)
{
/* System generated locals */
integer dfdu_dim1, dfdp_dim1;
/* Local variables */
doublereal thta;
integer i, j;
doublereal c1, s1;
integer ndm2;
/* Parameter adjustments */
dfdp_dim1 = ndm;
dfdu_dim1 = ndm;
ndm2 = ndm * 2;
thta = u[-1 + ndim - 1];
s1 = sin(thta);
c1 = cos(thta);
par[icp[1]] = u[-1 + ndim];
funi(iap, rap, ndm, u, uold, icp, par, 1, f, dfdu, dfdp);
for (i = 0; i < ndm; ++i) {
f[i] -= u[i];
ARRAY2D(dfdu, i, i) -= c1;
}
for (i = 0; i < ndm; ++i) {
f[ndm + i] = s1 * u[ndm2 + i];
f[ndm2 + i] = -s1 * u[ndm + i];
for (j = 0; j < ndm; ++j) {
f[ndm + i] += ARRAY2D(dfdu, i, j) * u[ndm + j];
f[ndm2 + i] += ARRAY2D(dfdu, i, j) * u[ndm2 + j];
}
}
f[ndim - 2] = -1.;
for (i = 0; i < ndm; ++i) {
f[ndim - 2] = f[ndim - 2] + u[ndm + i] * u[ndm + i] + u[ndm2 + i] * u[ndm2 + i];
}
f[-1 + ndim] = 0.;
for (i = 0; i < ndm; ++i) {
f[-1 + ndim] = f[-1 + ndim] + uold[ndm2 + i] * u[ndm + i] - uold[ndm + i] * u[ndm2 + i];
}
return 0;
} /* ffhd_ */
/* ---------- ------ */
/* Subroutine */ int
stpnhd(iap_type *iap, rap_type *rap, doublereal *par, integer *icp, doublereal *u)
{
/* Local variables */
integer ndim;
doublereal thta;
doublereal uold, *smat;
integer nfpr1;
doublereal *f;
integer i, j;
doublereal *v;
logical found;
doublereal c1;
doublereal s1;
integer ndm, irs, ndm2;
f = (doublereal *)malloc(sizeof(doublereal)*(iap->ndim));
v = (doublereal *)malloc(sizeof(doublereal)*(iap->ndim));
smat = (doublereal *)malloc(sizeof(doublereal)*(iap->ndim * 2)*(iap->ndim * 2));
/* Generates starting data for the continuation of Hopf bifurcation */
/* points for maps. */
/* Local */
/* Parameter adjustments */
ndim = iap->ndim;
irs = iap->irs;
ndm = iap->ndm;
findlb(iap, rap, irs, &nfpr1, &found);
readlb(iap, rap, u, par);
thta = pi(2.0) / par[10];
s1 = sin(thta);
c1 = cos(thta);
funi(iap, rap, ndm, u, &uold, icp, par, 1, f,
global_scratch.dfu, global_scratch.dfp);
ndm2 = ndm * 2;
for (i = 0; i < ndm2; ++i) {
for (j = 0; j < ndm2; ++j) {
smat[i + j * (ndim*2)] = 0.;
}
}
for (i = 0; i < ndm; ++i) {
smat[i + (ndm + i) * (ndim*2)] = s1;
}
for (i = 0; i < ndm; ++i) {
smat[ndm + i + i * (ndim*2)] = -s1;
}
for (i = 0; i < ndm; ++i) {
for (j = 0; j < ndm; ++j) {
smat[i + j * (ndim*2)] = global_scratch.dfu[j * ndm + i];
smat[ndm + i + (ndm + j) * (ndim*2)] = global_scratch.dfu[j * ndm + i];
}
smat[i + i * (ndim*2)] -= c1;
smat[ndm + i + (ndm + i) * (ndim*2)] -= c1;
}
{
integer tmp=(ndim*2);
nlvc(ndm2, tmp, 2, smat, v);
}
nrmlz(&ndm2, v);
for (i = 0; i < ndm2; ++i) {
u[ndm + i] = v[i];
}
u[-1 + ndim - 1] = thta;
u[-1 + ndim] = par[icp[1]];
free(smat);
free(f);
free(v);
return 0;
} /* stpnhd_ */
/* ----------------------------------------------------------------------- */
/* ----------------------------------------------------------------------- */
/* Subroutines for the Continuation of Hopf Bifurcation Points (ODE) */
/* ----------------------------------------------------------------------- */
/* ----------------------------------------------------------------------- */
/* ---------- ---- */
/* Subroutine */ int
fnhb(const iap_type *iap, const rap_type *rap, integer ndim, const doublereal *u, const doublereal *uold, const integer *icp, doublereal *par, integer ijac, doublereal *f, doublereal *dfdu, doublereal *dfdp)
{
/* System generated locals */
integer dfdu_dim1, dfdp_dim1;
/* Local variables */
doublereal rtmp;
integer i, j;
doublereal ep;
integer ndm;
doublereal umx;
/* Generates the equations for the 2-parameter continuation of Hopf */
/* bifurcation points in ODE. */
/* Local */
/* Parameter adjustments */
dfdp_dim1 = ndim;
dfdu_dim1 = ndim;
ndm = iap->ndm;
/* Generate the function. */
ffhb(iap, rap, ndim, u, uold, icp, par, f, ndm,
global_scratch.dfu, global_scratch.dfp);
if (ijac == 0) {
return 0;
}
/* Generate the Jacobian. */
umx = 0.;
for (i = 0; i < ndim; ++i) {
if (fabs(u[i]) > umx) {
umx = fabs(u[i]);
}
}
rtmp = HMACH;
ep = rtmp * (umx + 1);
for (i = 0; i < ndim; ++i) {
for (j = 0; j < ndim; ++j) {
global_scratch.uu1[j] = u[j];
global_scratch.uu2[j] = u[j];
}
global_scratch.uu1[i] -= ep;
global_scratch.uu2[i] += ep;
ffhb(iap, rap, ndim, global_scratch.uu1, uold, icp, par,
global_scratch.ff1, ndm, global_scratch.dfu, global_scratch.dfp);
ffhb(iap, rap, ndim, global_scratch.uu2, uold, icp, par,
global_scratch.ff2, ndm, global_scratch.dfu, global_scratch.dfp);
for (j = 0; j < ndim; ++j) {
ARRAY2D(dfdu, j, i) = (global_scratch.ff2[j] - global_scratch.ff1[j]) / (ep * 2);
}
}
par[icp[0]] += ep;
ffhb(iap, rap, ndim, u, uold, icp, par, global_scratch.ff1,
ndm, global_scratch.dfu, global_scratch.dfp);
for (j = 0; j < ndim; ++j) {
ARRAY2D(dfdp, j, icp[0]) = (global_scratch.ff1[j] - f[j]) / ep;
}
par[icp[0]] -= ep;
return 0;
} /* fnhb_ */
/* ---------- ---- */
/* Subroutine */ int
ffhb(const iap_type *iap, const rap_type *rap, integer ndim, const doublereal *u, const doublereal *uold, const integer *icp, doublereal *par, doublereal *f, integer ndm, doublereal *dfdu, doublereal *dfdp)
{
/* System generated locals */
integer dfdu_dim1, dfdp_dim1;
/* Local variables */
integer i, j;
doublereal rom;
integer ndm2;
/* Parameter adjustments */
dfdp_dim1 = ndm;
dfdu_dim1 = ndm;
ndm2 = ndm * 2;
rom = u[ndim - 2];
par[10] = rom * pi(2.0);
par[icp[1]] = u[-1 + ndim];
funi(iap, rap, ndm, u, uold, icp, par, 1, f, dfdu, dfdp);
for (i = 0; i < ndm; ++i) {
f[ndm + i] = u[ndm2 + i];
f[ndm2 + i] = -u[ndm + i];
for (j = 0; j < ndm; ++j) {
f[ndm + i] += rom * ARRAY2D(dfdu, i, j) * u[ndm + j];
f[ndm2 + i] += rom * ARRAY2D(dfdu, i, j) * u[ndm2 + j];
}
}
f[ndim - 2] = -1.;
for (i = 0; i < ndm; ++i) {
f[ndim - 2] = f[ndim - 2] + u[ndm + i] * u[ndm + i] + u[ndm2 + i] * u[ndm2 + i];
}
f[-1 + ndim] = 0.;
for (i = 0; i < ndm; ++i) {
f[-1 + ndim] = f[-1 + ndim] + uold[ndm2 + i] * (u[ndm + i] - uold[ndm + i]) - uold[ndm + i] * (u[ndm2 + i] - uold[ndm2 + i]);