//Compute the force in the z direction
double SCFPotentialzforce(double R,double Z, double phi,
double t,
struct potentialArg * potentialArgs)
{
double r;
double theta;
cyl_to_spher(R, Z,&r, &theta);
double dr_dz = Z/r;
double dtheta_dz = -R/(r*r);
double dphi_dz = 0;
double F[3];
computeForce(R, Z, phi, t,potentialArgs, &F[0]) ;
return *(F + 0)*dr_dz + *(F + 1)*dtheta_dz + *(F + 2)*dphi_dz;
}
//Compute the force in the phi direction
double SCFPotentialphiforce(double R,double Z, double phi,
double t,
struct potentialArg * potentialArgs)
{
double r;
double theta;
cyl_to_spher(R, Z, &r, &theta);
double dr_dphi = 0;
double dtheta_dphi = 0;
double dphi_dphi = 1;
double F[3];
computeForce(R, Z, phi, t,potentialArgs, &F) ;
return *(F + 0)*dr_dphi + *(F + 1)*dtheta_dphi + *(F + 2)*dphi_dphi;
}
//Compute the force in the R direction
double SCFPotentialRforce(double R,double Z, double phi,
double t,
struct potentialArg * potentialArgs)
{
double r;
double theta;
cyl_to_spher(R, Z, &r, &theta);
// The derivatives
double dr_dR = R/r;
double dtheta_dR = Z/(r*r);
double dphi_dR = 0;
double F[3];
computeForce(R, Z, phi, t,potentialArgs, &F[0]) ;
return *(F + 0)*dr_dR + *(F + 1)*dtheta_dR + *(F + 2)*dphi_dR;
}
//Compute the Potential
double SCFPotentialEval(double R,double Z, double phi,
double t,
struct potentialArg * potentialArgs)
{
double * args= potentialArgs->args;
//Get args
double a = *args++;
int isNonAxi = (int)*args++;
int N = *args++;
int L = *args++;
int M = *args++;
double* Acos = args;
double* Asin;
if (isNonAxi==1) //LCOV_EXCL_START
{
Asin = args + N*L*M;
} //LCOV_EXCL_STOP
//convert R,Z to r, theta
double r;
double theta;
cyl_to_spher(R, Z,&r, &theta);
double xi;
calculateXi(r, a, &xi);
//Compute the gegenbauer polynomials and its derivative.
double C[N*L];
compute_C(xi, N, L, &C[0]);
//Compute phiTilde and its derivative
double phiTilde[L*N];
compute_phiTilde(r, a, N, L, &C[0], &phiTilde[0]);
//Compute Associated Legendre Polynomials
int M_eff = M;
int size = 0;
if (isNonAxi==0)
{
M_eff = 1;
size = L;
} else{ //LCOV_EXCL_START
size = L*L - L*(L-1)/2;
} //LCOV_EXCL_STOP
double P[size];
compute_P(cos(theta), L,M_eff, &P[0]);
double potential;
double (*PhiTilde_Pointer[1]) = {&phiTilde[0]};
double (*P_Pointer[1]) = {&P[0]};
double Constant[1] = {1.};
if (isNonAxi==1) //LCOV_EXCL_START
{
double (*Eq[1])(double, double, double, double, double, double, int) = {&computePhi};
equations e = {Eq,&PhiTilde_Pointer[0],&P_Pointer[0],&Constant[0]};
computeNonAxi(a, N, L, M,r, theta, phi, Acos, Asin, 1, e, &potential);
} //LCOV_EXCL_STOP
else
{
double (*Eq[1])(double, double, double) = {&computeAxiPhi};
axi_equations e = {Eq,&PhiTilde_Pointer[0],&P_Pointer[0],&Constant[0]};
compute(a, N, L, M,r, theta, phi, Acos, 1, e, &potential);
}
return potential;
}
//Compute the Derivatives
void computeDeriv(double R,double Z, double phi,
double t,
struct potentialArg * potentialArgs, double * F)
{
double * args= potentialArgs->args;
//Get args
double a = *args++;
int isNonAxi = (int)*args++;
int N = *args++;
int L = *args++;
int M = *args++;
double* Acos = args;
double * caching_i = (args + (isNonAxi + 1)*N*L*M);
double *Asin;
if (isNonAxi == 1)
{
Asin = args + N*L*M;
}
double *cached_type = caching_i;
double * cached_coords = (caching_i+ 1);
double * cached_values = (caching_i + 4);
if ((int)*cached_type==DERIV)
{
if (*cached_coords == R && *(cached_coords + 1) == Z && *(cached_coords + 2) == phi)
{
*F = *cached_values;
*(F + 1) = *(cached_values + 1);
*(F + 2) = *(cached_values + 2);
return;
}
}
double r;
double theta;
cyl_to_spher(R, Z, &r, &theta);
double xi;
calculateXi(r, a, &xi);
//Compute the gegenbauer polynomials and its derivative.
double C[N*L];
double dC[N*L];
double d2C[N*L];
compute_C(xi, N, L, &C[0]);
compute_dC(xi, N, L, &dC[0]);
compute_d2C(xi, N, L, &d2C[0]);
//Compute phiTilde and its derivative
double phiTilde[L*N];
compute_phiTilde(r, a, N, L, &C[0], &phiTilde[0]);
double dphiTilde[L*N];
compute_dphiTilde(r, a, N, L, &C[0], &dC[0], &dphiTilde[0]);
double d2phiTilde[L*N];
compute_d2phiTilde(r, a, N, L, &C[0], &dC[0], &d2C[0], &d2phiTilde[0]);
//Compute Associated Legendre Polynomials
int M_eff = M;
int size = 0;
if (isNonAxi==0)
{
M_eff = 1;
size = L;
} else{
size = L*L - L*(L-1)/2;
}
double P[size];
compute_P(cos(theta), L,M_eff, &P[0]);
double (*PhiTilde_Pointer[3])= {&d2phiTilde[0],&phiTilde[0],&dphiTilde[0]};
double (*P_Pointer[3]) = {&P[0], &P[0], &P[0]};
double Constant[3] = {1., 1., 1.};
if (isNonAxi==1)
{
double (*Eq[3])(double, double, double, double, double, double, int) = {&computeF_rr, &computeF_phiphi, &computeF_rphi};
equations e = {Eq,&PhiTilde_Pointer[0],&P_Pointer[0],&Constant[0]};
computeNonAxi(a, N, L, M,r, theta, phi, Acos, Asin, 3, e, F);
}
else
{
double (*Eq[3])(double, double, double) = {&computeAxiF_rr, &computeAxiF_phiphi, &computeAxiF_rphi};
axi_equations e = {Eq,&PhiTilde_Pointer[0],&P_Pointer[0],&Constant[0]};
compute(a, N, L, M,r, theta, phi, Acos, 3, e, F);
}
//Caching
*cached_type = (double)DERIV;
* cached_coords = R;
* (cached_coords + 1) = Z;
* (cached_coords + 2) = phi;
* (cached_values) = *F;
* (cached_values + 1) = *(F + 1);
* (cached_values + 2) = *(F + 2);
}