//Set up the nodes (x) and weights (w) of Gaussian quadrature, using the Golub Welsch algorithm
//coeffs and vectors are allocated arrays which are required only for solving the tridiagonal matrix equation
void gauss_integration_setup(int datapoints, double *weights, double *x)
{ int idx; double *coeffs, *vectors;
coeffs=(double*)malloc((datapoints-1)*sizeof(double));
vectors=(double*)malloc(datapoints*datapoints*sizeof(double));
x[0]=0.0;
for (idx=1;idx<datapoints;idx++)
{
x[idx]=0.0;
coeffs[idx-1]=0.5/sqrt(1.0-1.0/(4.0*idx*idx));
}
//dstev finds the eigenvalues and vectors of a symmetric matrix
LAPACKE_dstev(LAPACK_ROW_MAJOR,'v', datapoints, x, coeffs, vectors, datapoints);
for (idx=0;idx<datapoints;idx++)
{
x[idx]=0.5*(x[idx]+1.0); //This leads to nodes in the range (0,1)
weights[idx]=vectors[idx]*vectors[idx];
}
free(coeffs);
free(vectors);
}
template <> inline
int stev(const char order, const char job, const int N, double *D, double *E, double *Z, const int LDZ)
{
return LAPACKE_dstev(order, job, N, D, E, Z, LDZ);
}
