int main (void)
{
static int i;
int n;
printf("Please enter the maximum degree of the polynomial:\n");
scanf("%d", &n);
printf("Please enter the coefficients:\n");
for(i=n; i>=0; i--){
scanf("%d", &a[i]);
}
printf("The polynomial is ");
poly(n);
printf("\nIts derivative is ");
deri(n);
}
int main (void)
{
static int i;
int n;
printf("Please enter the maximum degree of the polynomial:\n");
scanf("%d", &n);
if(n>=0){ //run the program when n>= 0
a = (int *)calloc(n+1, sizeof(int));
printf("Please enter the coefficients:\n");
if (a != NULL)
{
for(i=n; i>=0; i--)
{
scanf("%d", &a[i]);
}
printf("The polynomial is ");
poly(n);
printf("\nIts derivative is ");
deri(n);
free(a);
}
}
else //do nothing when n<0
{
}
}
void KNDdeTorusCollocation::jacobian(KNSparseMatrix& A, KNArray1D< KNVector* > Avar, KNVector& rhs, KNVector& par, KNVector& /*sol*/, KNArray1D<size_t>& var)
{
A.clear();
rhs.clear();
for (size_t r = 0; r < var.size(); r++) Avar(r)->clear();
// rhs doesn't need to be cleared
// creates kk, ee, rr & interpolates p_xx & gets p_tau
// init(sol, par);
// builds up the structure of the sparse matrix
for (size_t idx = 0; idx < time1.size(); ++idx)
{
const size_t lend = NDIM * (rr(ee((NTAU+1)*(ndeg1+1)*(ndeg2+1)-1,idx),idx) + 1);
for (size_t p = 0; p < NDIM; p++) A.newLine(lend);
}
// the right-hand side
sys->p_rhs(p_fx, time1, p_xx, par, 0);
for (size_t idx = 0; idx < time1.size(); ++idx)
{
for (size_t p = 0; p < NDIM; p++)
{
rhs(p + NDIM*idx) = par(0) * p_fx(p,idx) - p_xx(p, NTAU, idx) - par(RHO) * p_xx(p, NTAU + 1, idx);
}
}
// derivatives w.r.t the parameters
for (size_t r = 0; r < var.size(); r++)
{
KNVector& deri = *Avar(r);
deri.clear();
//!!!!!!!!!!!!!!!!!
//!BEGIN w.r.t the period
//!!!!!!!!!!!!!!!!!
if (var(r) == 0)
{
for (size_t idx = 0; idx < time1.size(); ++idx)
{
for (size_t p = 0; p < NDIM; p++) deri(p + NDIM*idx) = -p_fx(p,idx);
}
sys->p_dtau(p_dtau, time1, par, 0);
for (size_t k = 0; k < NTAU; k++)
{
size_t nx = 1, vx = k, np = 0, vp = 0;
sys->p_deri(p_dfx, time1, p_xx, par, 0, nx, &vx, np, &vp, p_dummy);
for (size_t idx = 0; idx < time1.size(); ++idx)
{
for (size_t p = 0; p < NDIM; p++)
{
for (size_t q = 0; q < NDIM; q++)
{
const double d = p_tau(k,idx) / par(0) - p_dtau(k,idx);
deri(p + NDIM*idx) -= p_dfx(p, q, idx) * d * (p_xx(q, NTAU + 2 * (k + 1), idx) + par(RHO) * p_xx(q, NTAU + 2 * (k + 1) + 1, idx));
}
}
}
}
}
else
//!!!!!!!!!!!!!!!!!
//!END w.r.t the period
//!!!!!!!!!!!!!!!!!
//
//!!!!!!!!!!!!!!!!!
//!BEGIN w.r.t the ordinary parameters
//!!!!!!!!!!!!!!!!!
// derivatives w.r.t. the real parameters
if (var(r) < NPAR)
{
size_t nx = 0, vx = 0, np = 1, vp = var(r);
sys->p_deri(p_dfp, time1, p_xx, par, 0, nx, &vx, np, &vp, p_dummy);
for (size_t idx = 0; idx < time1.size(); ++idx)
{
for (size_t p = 0; p < NDIM; p++) deri(p + NDIM*idx) = - par(0) * p_dfp(p, 0, idx);
}
}
else
//!!!!!!!!!!!!!!!!!
//!END w.r.t the ordinary parameters
//!!!!!!!!!!!!!!!!!
//
//!!!!!!!!!!!!!!!!!
//!BEGIN w.r.t the rotation number
//!!!!!!!!!!!!!!!!!
if (var(r) == RHO)
{
for (size_t idx = 0; idx < time1.size(); ++idx)
{
for (size_t p = 0; p < NDIM; p++) deri(p + NDIM*idx) = p_xx(p, NTAU + 1, idx);
}
sys->p_dtau(p_dtau, time1, par, 0);
for (size_t k = 0; k < NTAU; k++)
{
const size_t nx = 1, vx = k, np = 0, vp = 0;
sys->p_deri(p_dfx, time1, p_xx, par, 0, nx, &vx, np, &vp, p_dummy);
for (size_t idx = 0; idx < time1.size(); ++idx)
{
const double d = -p_tau(k, idx);
for (size_t p = 0; p < NDIM; p++)
{
for (size_t q = 0; q < NDIM; q++)
{
deri(p + NDIM*idx) -= p_dfx(p, q, idx) * d * p_xx(q, NTAU + 2 * (k + 1) + 1, idx);
}
}
}
}
}
//!!!!!!!!!!!!!!!!!
//!END w.r.t the rotation number
//!!!!!!!!!!!!!!!!!
else std::cout << "Jac:NNN\n";
}
// fill the matrix
for (size_t k = 0; k < NTAU + 1; k++)
{
if (k != 0)
{
// evaluate the solution
const size_t nx = 1, vx = k - 1, np = 0, vp = 0;
sys->p_deri(p_dfx, time1, p_xx, par, 0, nx, &vx, np, &vp, p_dummy);
}
for (size_t idx = 0; idx < time1.size(); ++idx)
{
double tk1, tk2;
if (k != 0)
{
tk1 = time1(idx) - p_tau(k-1,idx) / par(0);
tk2 = time2(idx) - par(RHO) * p_tau(k-1,idx) / par(0);
} else
{
tk1 = time1(idx);
tk2 = time2(idx);
}
const double c1 = nint1 * tk1 - floor(nint1 * tk1);
const double c2 = nint2 * tk2 - floor(nint2 * tk2);
// the real jacobian
for (size_t l2 = 0; l2 < ndeg2 + 1; l2++)
{
for (size_t l1 = 0; l1 < ndeg1 + 1; l1++)
{
const size_t idxK = idxkk(l1, l2, k);
if (k != 0)
{
const double cf = poly_lgr_eval(mesh1, l1, c1) * poly_lgr_eval(mesh2, l2, c2);
for (size_t p = 0; p < NDIM; p++)
{
for (size_t q = 0; q < NDIM; q++)
{
// jacobian of rhs
A.writeIndex(p + NDIM*idx, q + NDIM*rr(idxK, idx)) = static_cast<int>(q + NDIM * kk(idxK, idx));
A.writeData(p + NDIM*idx, q + NDIM*rr(idxK, idx)) -= cf * par(0) * p_dfx(p, q, idx);
}
}
}
else
{
const double cf1 = poly_dlg_eval(mesh1, l1, c1) * nint1 * poly_lgr_eval(mesh2, l2, c2);
const double cf2 = poly_lgr_eval(mesh1, l1, c1) * poly_dlg_eval(mesh2, l2, c2) * nint2;
for (size_t p = 0; p < NDIM; p++)
{
for (size_t q = 0; q < NDIM; q++)
{
// derivative part of the jacobian
A.writeIndex(p + NDIM*idx, q + NDIM*rr(idxK, idx)) = static_cast<int>(q + NDIM * kk(idxK, idx));
if (p == q)
A.writeData(p + NDIM*idx, q + NDIM*rr(idxK, idx)) += cf1 + par(RHO) * cf2;
}
}
}
// error check
if (kk(idxK, idx) > (ndeg1*nint1)*(ndeg2*nint2)) std::cout << "D" << kk(idxK, idx);
}
}
}
}
}
