int main()
{
void *cpode_mem;
N_Vector yy, yp, ctols;
realtype reltol, abstol, t, tout, Tout;
realtype x, y, xd, yd, g;
int iout, Nout, flag;
printf("double %d\n",(int)sizeof(double));
printf("long double %d\n",(int)sizeof(long double));
printf("float %d\n",(int)sizeof(float));
printf("realtype %d\n",(int)sizeof(realtype));
yy = N_VNew_Serial(4);
yp = N_VNew_Serial(4);
/* Initialize y */
Ith(yy,1) = 1.0; /* x */
Ith(yy,2) = 0.0; /* y */
Ith(yy,3) = 0.0; /* xd */
Ith(yy,4) = 0.0; /* yd */
/* Set tolerances */
reltol = RTOL;
abstol = ATOL;
Nout = 30;
Tout = Nout*1.0;
/* Initialize solver */
cpode_mem = CPodeCreate(CP_EXPL, CP_BDF, CP_NEWTON);
flag = CPodeInit(cpode_mem, f, NULL, 0.0, yy, yp, CP_SS, reltol, &abstol);
flag = CPodeSetMaxNumSteps(cpode_mem, 5000);
flag = CPodeSetStopTime(cpode_mem, Tout);
flag = CPDense(cpode_mem, 4);
/* USER-PROVIDED PROJECTION FUNCTION */
/*
flag = CPodeProjDefine(cpode_mem, proj, NULL);
*/
/* INTERNAL PROJECTION FUNCTION */
ctols = N_VNew_Serial(2);
Ith(ctols,1) = 1.0e-8;
Ith(ctols,2) = 1.0e-8;
flag = CPodeProjInit(cpode_mem, CP_PROJ_L2NORM, CP_CNSTR_NONLIN, cfun, NULL, ctols);
flag = CPodeSetProjTestCnstr(cpode_mem, TRUE);
flag = CPDenseProj(cpode_mem, 2, 4, CPDIRECT_LU);
flag = CPodeSetProjUpdateErrEst(cpode_mem, FALSE);
/* DISABLE PROJECTION */
/*
CPodeSetProjFrequency(cpode_mem, 0);
*/
/* INTEGRATE TO FINAL TIME */
/*
flag = CPode(cpode_mem, Tout, &t, yy, yp, CP_NORMAL_TSTOP);
x = Ith(yy,1);
y = Ith(yy,2);
xd = Ith(yy,3);
yd = Ith(yy,4);
g = x*x + y*y - 1.0;
Ith(yy,1) = x - 1.0;
Ith(yy,2) = y - 0.0;
Ith(yy,3) = xd - 0.0;
Ith(yy,4) = yd - 0.0;
printf("%14.10e %14.10e %14.10e %14.10e | %14.10e\n",
Ith(yy,1),Ith(yy,2),Ith(yy,3),Ith(yy,4),g);
*/
/* INTEGRATE THROUGH A SEQUENCE OF TIMES */
t = 0.0;
for(iout=1; iout<=Nout; iout++) {
tout = iout*1.0;
flag = CPode(cpode_mem, tout, &t, yy, yp, CP_NORMAL_TSTOP);
if (flag < 0) break;
x = Ith(yy,1);
y = Ith(yy,2);
xd = Ith(yy,3);
yd = Ith(yy,4);
g = x*x + y*y - 1.0;
printf(" -------------- %lf %14.10lf %14.10lf %14.10lf %14.10lf %14.10lf\n", t, x,y,xd,yd,g);
}
PrintFinalStats(cpode_mem);
N_VDestroy_Serial(yy);
N_VDestroy_Serial(yp);
N_VDestroy_Serial(ctols);
CPodeFree(&cpode_mem);
return(0);
}
int main()
{
PbData data;
realtype R, L, m, g, V0;
void *cpode_mem;
N_Vector yy, yp, ctols;
realtype reltol, abstol;
realtype t0, tf, t;
realtype x1, y1, x2, y2;
realtype vx1, vy1, vx2, vy2;
int flag, Neq, Nc;
int rdir[1], iroots[1];
FILE *fout;
/* --------------------------------
* INITIALIZATIONS
* -------------------------------- */
R = 0.1; /* ball radius */
L = 1.0; /* pendulum length */
m = 1.0; /* pendulum mass */
g = 9.8; /* gravitational acc. */
V0 = 3.0; /* initial velocity for pendulum 1 */
/* Set-up user data structure */
data = (PbData)malloc(sizeof *data);
data->R = R;
data->L = L;
data->m = m;
data->g = g;
/* Problem dimensions */
Neq = 2*2*2;
Nc = 2*2;
/* Solution vectors */
yy = N_VNew_Serial(Neq);
yp = N_VNew_Serial(Neq);
/* Integration limits */
t0 = 0.0;
tf = 6.0;
/* Integration and projection tolerances */
reltol = 1.0e-8;
abstol = 1.0e-8;
ctols = N_VNew_Serial(Nc);
N_VConst(1.0e-8, ctols);
/* Direction of monitored events
* (only zero-crossing with decreasing even function) */
rdir[0] = -1;
/* --------------------------------
* CASE 1
* -------------------------------- */
fout = fopen("newton1.out","w");
/* Initial conditions */
NV_Ith_S(yy,0) = R; NV_Ith_S(yy,4) = -R;
NV_Ith_S(yy,1) = -L; NV_Ith_S(yy,5) = -L;
NV_Ith_S(yy,2) = V0; NV_Ith_S(yy,6) = 0.0;
NV_Ith_S(yy,3) = 0.0; NV_Ith_S(yy,7) = 0.0;
/* Initialize solver */
cpode_mem = CPodeCreate(CP_EXPL, CP_BDF, CP_NEWTON);
flag = CPodeInit(cpode_mem, ffun1, data, t0, yy, yp, CP_SS, reltol, &abstol);
flag = CPDense(cpode_mem, Neq);
flag = CPodeRootInit(cpode_mem, 1, gfun, data);
flag = CPodeSetRootDirection(cpode_mem, rdir);
/* Set-up the internal projection */
flag = CPodeProjInit(cpode_mem, CP_PROJ_L2NORM, CP_CNSTR_NONLIN, cfun, data, ctols);
flag = CPodeSetProjTestCnstr(cpode_mem, TRUE);
flag = CPDenseProj(cpode_mem, Nc, Neq, CPDIRECT_LU);
/* Integrate in ONE_STEP mode, while monitoring events */
t = t0;
while(t<tf) {
flag = CPode(cpode_mem, tf, &t, yy, yp, CP_ONE_STEP);
if (flag < 0) break;
x1 = NV_Ith_S(yy,0); x2 = NV_Ith_S(yy,4);
y1 = NV_Ith_S(yy,1); y2 = NV_Ith_S(yy,5);
vx1 = NV_Ith_S(yy,2); vx2 = NV_Ith_S(yy,6);
vy1 = NV_Ith_S(yy,3); vy2 = NV_Ith_S(yy,7);
fprintf(fout, "%lf %14.10lf %14.10lf %14.10lf %14.10lf %14.10lf %14.10lf %14.10lf %14.10lf",
t, x1, y1, x2, y2, vx1, vy1, vx2, vy2);
if (flag == CP_ROOT_RETURN) {
CPodeGetRootInfo(cpode_mem, iroots);
fprintf(fout, " %d\n", iroots[0]);
/* Note: the test iroots[0]<0 is really needed ONLY if not using rdir */
if (iroots[0] < 0) {
/* Update velocities in yy */
contact(yy, data);
/* reinitialize CPODES solver */
flag = CPodeReInit(cpode_mem, ffun1, data, t, yy, yp, CP_SS, reltol, &abstol);
}
} else {
fprintf(fout, " 0\n");
}
}
PrintFinalStats(cpode_mem);
CPodeFree(&cpode_mem);
fclose(fout);
/* --------------------------------
* CASE 2
* -------------------------------- */
fout = fopen("newton2.out","w");
/* Initial conditions */
NV_Ith_S(yy,0) = R; NV_Ith_S(yy,4) = -R;
NV_Ith_S(yy,1) = -L; NV_Ith_S(yy,5) = -L;
NV_Ith_S(yy,2) = 0.0; NV_Ith_S(yy,6) = 0.0;
NV_Ith_S(yy,3) = 0.0; NV_Ith_S(yy,7) = 0.0;
/* Initialize solver */
cpode_mem = CPodeCreate(CP_EXPL, CP_BDF, CP_NEWTON);
flag = CPodeInit(cpode_mem, ffun2, data, t0, yy, yp, CP_SS, reltol, &abstol);
flag = CPDense(cpode_mem, Neq);
flag = CPodeRootInit(cpode_mem, 1, gfun, data);
flag = CPodeSetRootDirection(cpode_mem, rdir);
/* Set-up the internal projection */
flag = CPodeProjInit(cpode_mem, CP_PROJ_L2NORM, CP_CNSTR_NONLIN, cfun, data, ctols);
flag = CPodeSetProjTestCnstr(cpode_mem, TRUE);
flag = CPDenseProj(cpode_mem, Nc, Neq, CPDIRECT_LU);
/* Integrate in ONE_STEP mode, while monitoring events */
t = t0;
while(t<tf) {
flag = CPode(cpode_mem, tf, &t, yy, yp, CP_ONE_STEP);
if (flag < 0) break;
x1 = NV_Ith_S(yy,0); x2 = NV_Ith_S(yy,4);
y1 = NV_Ith_S(yy,1); y2 = NV_Ith_S(yy,5);
vx1 = NV_Ith_S(yy,2); vx2 = NV_Ith_S(yy,6);
vy1 = NV_Ith_S(yy,3); vy2 = NV_Ith_S(yy,7);
fprintf(fout, "%lf %14.10lf %14.10lf %14.10lf %14.10lf %14.10lf %14.10lf %14.10lf %14.10lf",
t, x1, y1, x2, y2, vx1, vy1, vx2, vy2);
if (flag == CP_ROOT_RETURN) {
CPodeGetRootInfo(cpode_mem, iroots);
fprintf(fout, " %d\n", iroots[0]);
/* Note: the test iroots[0]<0 is really needed ONLY if not using rdir */
if (iroots[0] < 0) {
/* Update velocities in yy */
contact(yy, data);
/* reinitialize CPODES solver */
flag = CPodeReInit(cpode_mem, ffun2, data, t, yy, yp, CP_SS, reltol, &abstol);
}
} else {
fprintf(fout, " 0\n");
}
}
PrintFinalStats(cpode_mem);
CPodeFree(&cpode_mem);
fclose(fout);
/* --------------------------------
* CLEAN-UP
* -------------------------------- */
free(data);
N_VDestroy_Serial(yy);
N_VDestroy_Serial(yp);
N_VDestroy_Serial(ctols);
return(0);
}