void MFAUTONRegionFreeData(void *d, MFErrorHandler e)
{
struct MFAUTONRegionData *data;
data=(struct MFAUTONRegionData*)d;
MFFreeNSpace(data->space,e);
free(data->RL0);
free(data->RL1);
free(data);
}
void MFAUTONSpaceFreeData(void *d, MFErrorHandler e)
{
double *par;
struct MFAUTONRegionData *data;
data=(struct MFAUTONRegionData*)d;
MFFreeNSpace(data->space,e);
free(data->RL0);
free(data->RL1);
free(data);
return;
}
/*! \fn MFImplicitMF MFIMFCreateSphere(double x,double y,double z,double R, MFErrorHandler e);
* \brief Creates an implicitly defined manifold for a 2-sphere embedded in 3-space, centered at (x,y,z) with
* radius R.
*
* \param x The x coordinate of the center of the sphere
* \param y The y coordinate of the center of the sphere
* \param z The z coordinate of the center of the sphere
* \param R The radius.
* \param e An error handler.
* \returns An implicitly defined manifold.
*/
MFImplicitMF MFIMFCreateSphere(double x,double y,double z,double R, MFErrorHandler e)
{
static char RoutineName[]={"MFIMFCreateSphere"};
MFImplicitMF sphere;
MFNSpace space;
double *data;
sphere=MFIMFCreateBaseClass(3,2,"Sphere",e);
space=MFCreateNSpace(3,e);
MFIMFSetSpace(sphere,space,e);
MFFreeNSpace(space,e);
data=(double*)malloc(4*sizeof(double));
#ifndef MFNPOSAFETYNET
if(data==NULL)
{
sprintf(MFSphereMFErrorHandlerMsg,"Out of memory, trying to allocate %d bytes",4*sizeof(double));
MFSetError(e,12,RoutineName,MFSphereMFErrorHandlerMsg,__LINE__,__FILE__);
MFErrorHandlerOutOfMemory(e);
free(sphere);
return NULL;
}
#endif
data[0]=x;
data[1]=y;
data[2]=z;
data[3]=R;
MFIMFSetData(sphere,(void*)data,e);
MFIMFSetFreeData(sphere,MFFreeSphereData,e);
MFIMFSetProject(sphere,MFProjectSphere,e);
MFIMFSetTangent(sphere,MFTangentSphere,e);
MFIMFSetR(sphere,-1.,e);
MFIMFSetScale(sphere,MFScaleSphere,e);
MFIMFSetWriteData(sphere,MFWriteSphereData,e);
MFIMFSetProjectForSave(sphere,MFSphereProjectToSave,e);
MFIMFSetProjectForDraw(sphere,MFSphereProjectToDraw,e);
MFIMFSetProjectForBB(sphere,MFSphereProjectForBB,e);
MFIMFSetVectorFactory(sphere,MFNVectorFactory,e);
MFIMFSetMatrixFactory(sphere,MFNKMatrixFactory,e);
return sphere;
}
/*! \fn MFImplicitMF MFIMFCreateCircle(double x,double y,double R, MFErrorHandler e);
* \brief Creates an implicitly defined manifold for a circle embedded in the plane, centered at (x,y) with
* radius R.
*
* \param x The x coordinate of the center of the circle
* \param y The y coordinate of the center of the circle
* \param R The radius.
* \param e An error handler.
* \returns An implicitly defined manifold.
*/
MFImplicitMF MFIMFCreateCircle(double x,double y,double R, MFErrorHandler e)
{
static char RoutineName[]={"MFIMFCreateCircle"};
MFImplicitMF circle;
MFNSpace space;
double *data;
circle=MFIMFCreateBaseClass(2,1,"Circle",e);
space=MFCreateNSpace(2,e);
MFIMFSetSpace(circle,space,e);
MFFreeNSpace(space,e);
data=(double*)malloc(3*sizeof(double));
#ifndef MFNOSAFETYNET
if(data==NULL)
{
sprintf(MFCircleMFErrorHandlerMsg,"Out of memory, trying to allocate %d bytes",3*sizeof(double));
MFSetError(e,12,RoutineName,MFCircleMFErrorHandlerMsg,__LINE__,__FILE__);
free(circle);
return NULL;
}
#endif
data[0]=x;
data[1]=y;
data[2]=R;
MFIMFSetData(circle,data,e);
MFIMFSetFreeData(circle,MFFreeCircleData,e);
MFIMFSetProject(circle,MFProjectCircle,e);
MFIMFSetTangent(circle,MFTangentCircle,e);
MFIMFSetScale(circle,MFScaleCircle,e);
MFIMFSetWriteData(circle,MFWriteCircleData,e);
MFIMFSetProjectForSave(circle,MFCircleProjectToSave,e);
MFIMFSetProjectForDraw(circle,MFCircleProjectToDraw,e);
MFIMFSetProjectForBB(circle,MFCircleProjectForBB,e);
MFIMFSetVectorFactory(circle,MFNVectorFactory,e);
MFIMFSetMatrixFactory(circle,MFNKMatrixFactory,e);
return circle;
}
MFImplicitMF MFIMFCreateLOCA(LOCAData* data)
{
MFImplicitMF loca;
MFNSpace space;
loca=MFIMFCreateBaseClass(-1, data->np, "LOCA", data->mfErrorHandler);
space=MFCreateLOCANSpace(data);
MFIMFSetSpace(loca,space, data->mfErrorHandler);
MFFreeNSpace(space, data->mfErrorHandler);
MFIMFSetData(loca,(void*)data, data->mfErrorHandler);
data->space=space;
MFRefNSpace(space, data->mfErrorHandler);
MFIMFSetFreeData(loca,MFLOCAFreeData, data->mfErrorHandler);
MFIMFSetProject(loca,MFProjectLOCA, data->mfErrorHandler);
MFIMFSetTangent(loca,MFTangentLOCA, data->mfErrorHandler);
MFIMFSetScale(loca,MFScaleLOCA, data->mfErrorHandler);
MFIMFSetProjectForSave(loca,MFLOCAProjectToDraw, data->mfErrorHandler);
MFIMFSetProjectForDraw(loca,MFLOCAProjectToDraw, data->mfErrorHandler);
MFIMFSetProjectForBB(loca,MFLOCAProjectToDraw, data->mfErrorHandler);
return loca;
}
int main(int argc,char *argv[])
{
MFAUTOTPBVP tpbvp;
MFNSpace space;
MFNRegion Omega;
MFImplicitMF M;
MFContinuationMethod H;
MFNVector u0;
MFNKMatrix Phi0;
MFAtlas S;
MFErrorHandler e;
double epsilon=1.00;
int through=10;
doublereal rl0[1]={0.};
doublereal rl1[1]={20.};
doublereal a0=0.;
doublereal a1=100.;
doublereal ds=0.1;
integer npar=3;
integer nicp=1;
integer icp[1]={0};
doublereal par[3];
doublereal thu[2]={1.,1.};
doublereal thl[3]={1.,1.,1.};
integer k=1;
integer jac=1;
integer ntst=5,ncol=4,ndim=2;
integer nbc=1,nic=1;
e=MFCreateErrorHandler();
tpbvp=MFCreateAUTOTPBVP(k,ndim,f,jac,nbc,a,nic,ic,npar,nicp,icp,ntst,ncol,plt,e);
space=MFCreateAUTONSpace(tpbvp,thu,thl,e);
M=MFCreateAUTOBV(tpbvp,space,e);
MFAUTOBVSetRealParameter(M,"dlmin",0.0001,e);
MFAUTOBVSetRealParameter(M,"dsmax",2.0,e);
MFAUTOBVSetRealParameter(M,"ds0",0.1,e);
MFAUTOBVSetRealParameter(M,"epsl",1.e-4,e);
MFAUTOBVSetRealParameter(M,"epsu",1.e-4,e);
MFAUTOBVSetIntegerParameter(M,"iid",0,e);
/*MFAUTOAddUserZero(M,0,1.,e);
MFAUTOAddUserZero(M,0,3.,e);
MFAUTODetectLimitPoints(M,e);*/
Omega=MFNRegionCreateAUTO(space,k,icp,rl0,rl1,a0,a1,e);
H=MFCreateMultifariosMethod(e);
MFMultifarioSetRealParameter(H,"minR",0.0001,e);
MFMultifarioSetRealParameter(H,"maxR",2.0,e);
MFMultifarioSetRealParameter(H,"epsilon",epsilon,e);
MFMultifarioSetIntegerParameter(H,"maxCharts",-1,e);
MFMultifarioSetIntegerParameter(H,"verbose",1,e);
MFMultifarioSetIntegerParameter(H,"page",1,e);
MFMultifarioSetIntegerParameter(H,"branchSwitch",1,e);
MFMultifarioSetIntegerParameter(H,"dumpToPlotFile",1,e);
MFMultifarioSetIntegerParameter(H,"dumpToCenterFile",0,e);
MFMultifarioSetFilename(H,"AUTINTMultifario",e);
par[0]=0.;
par[1]=0.;
par[2]=0.;
MFAUTOGetStartPoint(M,tpbvp,stpnt,par,&u0,&Phi0,e);
S=MFComputeAtlasWithTangent(H,M,Omega,u0,Phi0,e);
MFCloseAtlas(H,S,e);
MFFreeNRegion(Omega,e);
MFFreeNSpace(space,e);
MFFreeNVector(u0,e);
if(Phi0!=(MFNKMatrix)NULL)MFFreeNKMatrix(Phi0,e);
MFFreeImplicitMF(M,e);
MFFreeContinuationMethod(H,e);
MFFreeAtlas(S,e);
MFFreeErrorHandler(e);
return 0;
}
/*! \fn MFImplicitMF MFIMFCreatePolygonIn3SpaceWithRadius(int nv,double *v,double R, MFErrorHandler e);
* \brief Creates a Euclidean plane which contains the given polygon (which is assumed to be flat).
*
* \param nv The number of vertices.
* \param v The vertices stored as (v[0+3*iv],v[1+3*iv],v[2+3*iv]).
* \param R A radius to use for charts on the manifold.
* \param e An error handler.
* \returns An implicitly defined manifold.
*/
MFImplicitMF MFIMFCreatePolygonIn3SpaceWithRadius(int n,double *v,double R, MFErrorHandler e)
{
static char RoutineName[]={"MFIMFCreatePolygonIn3SpaceWithRadius"};
MFImplicitMF polygon;
MFNSpace space;
struct MFPolygonIn3SpaceData *p;
double d;
int verbose=0;
int i;
#ifdef MFALLOWVERBOSE
if(verbose)
{
printf("%s\n",RoutineName);
printf("%d\n",n);
for(i=0;i<n;i++)
printf(" %d (%lf,%lf,%lf)\n",i,v[3*i],v[3*i+1],v[3*i+2]);
fflush(stdout);
}
#endif
polygon=MFIMFCreateBaseClass(3,2,"PolygonIn3Space",e);
space=MFCreateNSpace(3,e);
MFIMFSetSpace(polygon,space,e);
MFFreeNSpace(space,e);
p=(struct MFPolygonIn3SpaceData*)malloc(sizeof(struct MFPolygonIn3SpaceData));
#ifndef MFNOSAFETYNET
if(p==NULL)
{
sprintf(MFPolygonMFErrorHandlerMsg,"Out of memory, trying to allocate %d bytes",sizeof(struct MFPolygonIn3SpaceData));
MFSetError(e,12,RoutineName,MFPolygonMFErrorHandlerMsg,__LINE__,__FILE__);
MFErrorHandlerOutOfMemory(e);
return NULL;
}
#endif
p->r=R;
p->ox=v[0];
p->oy=v[1];
p->oz=v[2];
#ifdef MFALLOWVERBOSE
if(verbose){printf(" o=(%lf,%lf,%lf)\n",p->ox,p->oy,p->oz);fflush(stdout);}
#endif
p->ax=v[3]-v[0];
p->ay=v[4]-v[1];
p->az=v[5]-v[2];
d=1./sqrt(p->ax*p->ax+p->ay*p->ay+p->az*p->az);
p->ax=p->ax*d;
p->ay=p->ay*d;
p->az=p->az*d;
#ifdef MFALLOWVERBOSE
if(verbose){printf(" a=(%lf,%lf,%lf)\n",p->ax,p->ay,p->az);fflush(stdout);}
#endif
p->bx=v[6]-v[0];
p->by=v[7]-v[1];
p->bz=v[8]-v[2];
d=p->ax*p->bx+p->ay*p->by+p->az*p->bz;
p->bx-=p->ax*d;
p->by-=p->ay*d;
p->bz-=p->az*d;
d=1./sqrt(p->bx*p->bx+p->by*p->by+p->bz*p->bz);
p->bx=p->bx*d;
p->by=p->by*d;
p->bz=p->bz*d;
#ifdef MFALLOWVERBOSE
if(verbose){printf(" b=(%lf,%lf,%lf)\n",p->bx,p->by,p->bz);fflush(stdout);}
#endif
p->nx=p->ay*p->bz-p->az*p->by;
p->ny=p->az*p->bx-p->ax*p->bz;
p->nz=p->ax*p->by-p->ay*p->bx;
#ifdef MFALLOWVERBOSE
if(verbose){printf(" n=(%lf,%lf,%lf)\n",p->nx,p->ny,p->nz);fflush(stdout);}
#endif
MFIMFSetData(polygon,(void*)p,e);
MFIMFSetFreeData(polygon,MFFreePolygonIn3SpaceData,e);
MFIMFSetProject(polygon,MFProjectPolygonIn3Space,e);
MFIMFSetTangent(polygon,MFTangentPolygonIn3Space,e);
MFIMFSetScale(polygon,MFScalePolygonIn3Space,e);
MFIMFSetR(polygon,R,e);
MFIMFSetProjectForBB(polygon,MFPolygonIn3SpaceProjectForBB,e);
MFIMFSetProjectForDraw(polygon,MFPolygonIn3SpaceProjectForBB,e);
MFIMFSetWriteData(polygon,MFWritePolygonIn3SpaceData,e);
MFIMFSetVectorFactory(polygon,MFNVectorFactory,e);
MFIMFSetMatrixFactory(polygon,MFNKMatrixFactory,e);
/* Test */
#ifdef MFALLOWVERBOSE
if(verbose)
{
printf("Tangent [ %lf %lf %lf ]\n",
(p->ax*p->ax+p->ay*p->ay+p->az*p->az),
(p->ax*p->bx+p->ay*p->by+p->az*p->bz),
(p->ax*p->nx+p->ay*p->ny+p->az*p->nz));
printf(" [ %lf %lf %lf ]\n",
(p->bx*p->ax+p->by*p->ay+p->bz*p->az),
(p->bx*p->bx+p->by*p->by+p->bz*p->bz),
(p->bx*p->nx+p->by*p->ny+p->bz*p->nz));
printf(" [ %lf %lf %lf ]\n",
(p->nx*p->ax+p->ny*p->ay+p->nz*p->az),
(p->nx*p->bx+p->ny*p->by+p->nz*p->bz),
(p->nx*p->nx+p->ny*p->ny+p->nz*p->nz));
for(i=1;i<n;i++)
{
d=(p->nx*(v[3*i]-v[0])+p->ny*(v[3*i+1]-v[1])+p->nz*(v[3*i+2]-v[2]));
printf(" (x[%d]-x[0]).n=%lf\n",i,d);
}
printf("done %s\n",RoutineName);fflush(stdout);
}
#endif
return polygon;
}
/*! \fn MFImplicitMF MFIMFCreateEdgeIn3SpaceWithRadius(double *o,double *d,double R, MFErrorHandler e);
* \brief Creates a Euclidean line which contains the segment between the points l and r (left and right).
*
* \param o An array of length at least 3, with the coordinates of the left end point of the interval.
* \param d An array of length at least 3, with the coordinates of the right end point of the interval.
* \param R A radius to use for charts on the manifold.
* \param e An error handler.
* \returns An implicitly defined manifold.
*/
MFImplicitMF MFIMFCreateEdgeIn3SpaceWithRadius(double *v0, double *v1,double R, MFErrorHandler e)
{
static char RoutineName[]={"MFIMFCreateEdgeIn3SpaceWithRadius"};
MFImplicitMF edge;
MFNSpace space;
struct MFEdgeIn3SpaceData *p;
double d;
int verbose=0;
int i;
#ifdef MFALLOWVERBOSE
if(verbose)printf("%s\n",RoutineName);
#endif
edge=MFIMFCreateBaseClass(3,1,"EdgeIn3Space",e);
space=MFCreateNSpace(3,e);
MFIMFSetSpace(edge,space,e);
MFFreeNSpace(space,e);
p=(struct MFEdgeIn3SpaceData*)malloc(sizeof(struct MFEdgeIn3SpaceData));
#ifndef MFNOSAFETYNET
if(p==NULL)
{
sprintf(MFEdgeMFErrorHandlerMsg,"Out of memory, trying to allocate %d bytes",sizeof(struct MFEdgeIn3SpaceData));
MFSetError(e,12,RoutineName,MFEdgeMFErrorHandlerMsg,__LINE__,__FILE__);
MFErrorHandlerOutOfMemory(e);
return NULL;
}
#endif
p->r=R;
p->ox=v0[0];
p->oy=v0[1];
p->oz=v0[2];
p->ax=v1[0]-v0[0];
p->ay=v1[1]-v0[1];
p->az=v1[2]-v0[2];
d=1./sqrt(p->ax*p->ax+p->ay*p->ay+p->az*p->az);
p->ax=p->ax*d;
p->ay=p->ay*d;
p->az=p->az*d;
#ifdef MFALLOWVERBOSE
if(verbose){printf("%s, data=0x%8.8x, o=(%lf,%lf,%lf), n=(%lf,%lf,%lf)\n",RoutineName,p,p->ox,p->oy,p->oz,p->ax,p->ay,p->az);fflush(stdout);}
#endif
MFIMFSetData(edge,(void*)p,e);
MFIMFSetFreeData(edge,MFFreeEdgeIn3SpaceData,e);
MFIMFSetProject(edge,MFProjectEdgeIn3Space,e);
MFIMFSetProjectForBB(edge,MFEdgeIn3SpaceProjectForBB,e);
MFIMFSetProjectForDraw(edge,MFEdgeIn3SpaceProjectForBB,e);
MFIMFSetTangent(edge,MFTangentEdgeIn3Space,e);
MFIMFSetScale(edge,MFScaleEdgeIn3Space,e);
MFIMFSetR(edge,R,e);
MFIMFSetWriteData(edge,MFWriteEdgeIn3SpaceData,e);
MFIMFSetVectorFactory(edge,MFNVectorFactory,e);
MFIMFSetMatrixFactory(edge,MFNKMatrixFactory,e);
#ifdef MFALLOWVERBOSE
if(verbose){printf("done %s\n",RoutineName);fflush(stdout);}
#endif
return edge;
}
