void deriv_yy(const ScalarField<T, S>& f, ScalarField<S, S>& out) {
const GridParams& p = f.grid_params();
assert(p == out.grid_params());
assert(p.ny >= 3);
const double d = 1./(p.eps_y*p.eps_y);
for (int i = 0; i < p.nx; ++i) {
for (int j = 0; j < p.ny; ++j) {
T a, b, c;
if (j == 0) {
a = f(i,j);
b = f(i,j+1);
c = f(i,j+2);
} else if (j == p.ny-1) {
a = f(i,j-2);
b = f(i,j-1);
c = f(i,j);
} else {
a = f(i,j-1);
b = f(i,j);
c = f(i,j+1);
}
out(i,j) = (a - 2.*b + c) * d;
}
}
}
void deriv_xx(const ScalarField<T, S>& f, ScalarField<S, S>& out) {
const GridParams& p = f.grid_params();
assert(p == out.grid_params());
assert(p.nx >= 3);
const double d = 1./(p.eps_x*p.eps_x);
for (int i = 0; i < p.nx; ++i) {
for (int j = 0; j < p.ny; ++j) {
T a, b, c;
if (i == 0) {
a = f(i,j);
b = f(i+1,j);
c = f(i+2,j);
} else if (i == p.nx-1) {
a = f(i-2,j);
b = f(i-1,j);
c = f(i,j);
} else {
a = f(i-1,j);
b = f(i,j);
c = f(i+1,j);
}
out(i,j) = (a - 2.*b + c) * d;
}
}
}
void apply_flow(const ScalarField<ElemT, ExprT>& phi, const DoubleField& u_x, const DoubleField& u_y, ScalarField<ExprT, ExprT>& out) {
const GridParams& gp = phi.grid_params();
assert(u_x.grid_params() == gp && u_y.grid_params() == gp && out.grid_params() == gp);
for (int i = 0; i < gp.nx; ++i) {
for (int j = 0; j < gp.ny; ++j) {
auto xy = gp.to_xy(i, j);
out(i,j) = phi.eval_xy(xy.first - u_x(i,j), xy.second - u_y(i,j));
}
}
}
void deriv_y(const ScalarField<T, S>& f, ScalarField<S, S>& g_y) {
const GridParams& p = f.grid_params();
assert(p == g_y.grid_params());
// derivatives in y direction
for (int i = 0; i < p.nx; ++i) {
for (int j = 0; j < p.ny - 1; ++j) {
g_y(i,j) = (f(i,j+1) - f(i,j)) * (1./p.eps_y);
}
// copy over last column
g_y(i,p.ny-1) = g_y(i,p.ny-2);
}
}
void deriv_x(const ScalarField<T, S>& f, ScalarField<S, S>& g_x) {
const GridParams& p = f.grid_params();
assert(p == g_x.grid_params());
// derivatives in x direction
for (int i = 0; i < p.nx - 1; ++i) {
for (int j = 0; j < p.ny; ++j) {
g_x(i,j) = (f(i+1,j) - f(i,j)) * (1./p.eps_x);
}
}
// copy over last row
for (int j = 0; j < p.ny; ++j) {
g_x(p.nx-1,j) = g_x(p.nx-2,j);
}
}
void deriv_y_central(const ScalarField<T, S>& f, ScalarField<S, S>& g_y) {
const GridParams& p = f.grid_params();
assert(p == g_y.grid_params());
// derivatives in y direction
// forward/backward differences for edges, central for everything else
for (int i = 0; i < p.nx; ++i) {
for (int j = 0; j < p.ny; ++j) {
if (j == 0) {
g_y(i,j) = (f(i,j+1) - f(i,j)) * (1./p.eps_y);
} else if (j == p.ny-1) {
g_y(i,j) = (f(i,j) - f(i,j-1)) * (1./p.eps_y);
} else {
g_y(i,j) = (f(i,j+1) - f(i,j-1)) * (1./(2.*p.eps_y));
}
}
}
}
