bool SingularPart::fillSigma(double* sigma) const {
// Set up the variables.
int nTheta = basis->getRank();
const double* u = basis->getAbscissas();
double* theta = new double[nTheta];
for (int i = 0; i < nTheta; i++) theta[i] = acos(-1.)*0.5*(u[i] + 1.);
double* beta = curvature.getBeta(theta, nTheta);
double p = getRegularityPower();
// Set sigma to the solution if beta were constant.
for (int i = 0; i < nTheta; i++) sigma[i] = p < 1. ?
pow(beta[i]*0.125/(p*(1.-p)), 0.125) :
pow(beta[i]*0.125/(p*(p - 1.)), 0.125) ;
double* lap = getOperator(theta);
bool converged = newtonRaphson(sigma, beta, lap);
if (!converged) {
std::clog << "Newton-Raphson did not converge.\n";
}
delete[] lap;
delete[] theta;
delete[] beta;
return converged;
}
double newtonRaphson ( // finds root f_(x_) = y_ in [p_, q_] with derivative y_'
double y_, // f_ (x_) = y_
double (*f_) (double x_), // function
double (*df_) (double x_), // derivative of function
double p_, // end-point
double x_, // initial guess : can be arbitrary
double q_, // end-point
double tol_, // absolute tolerance
double rtol_, // relative tolerance
Int4 *itmax_) // maximum # of permitted iterations
{
s_f = f_;
s_df = df_;
return newtonRaphson (y_, f, df, ZERO, p_, x_, q_, tol_, rtol_, itmax_);
}
