// Generate the rational approximation x^(pnum/pden)
void AlgRemez::generateApprox()
{
char *fname = "generateApprox()";
Float time = -dclock();
iter = 0;
spread = 1.0e37;
if (approx_type == RATIONAL_APPROX_ZERO_POLE) {
n--;
neq--;
}
initialGuess();
stpini(step);
while (spread > tolerance) { //iterate until convergance
if (iter++%100==0)
VRB.Result(cname,fname,"Iteration %d, spread %e delta %e\n", iter-1,(Float)spread,(Float)delta);
equations();
if (delta < tolerance)
ERR.General(cname, fname,"Delta too small, try increasing precision\n");
search(step);
}
int sign;
Float error = (Float)getErr(mm[0],&sign);
VRB.Result(cname,fname,"Converged at %d iterations, error = %e\n",
iter,error);
//!< Once the approximation has been generated, calculate the roots
if(!root()) ERR.General(cname,fname,"Root finding failed\n");
if (approx_type == RATIONAL_APPROX_ZERO_POLE) {
roots[n] = (bigfloat)0.0;
n++;
neq++;
}
//!< Now find the partial fraction expansions
if (remez_arg->field_type == BOSON) {
getPFE(remez_arg->residue, remez_arg->pole, &(remez_arg->norm));
getIPFE(remez_arg->residue_inv, remez_arg->pole_inv, &(remez_arg->norm_inv));
} else {
getIPFE(remez_arg->residue, remez_arg->pole, &(remez_arg->norm));
getPFE(remez_arg->residue_inv, remez_arg->pole_inv, &(remez_arg->norm_inv));
}
remez_arg->error = error;
time += dclock();
print_time(cname,fname,time);
}
// Generate the rational approximation x^(pnum/pden)
double AlgRemez::generateApprox(int num_degree, int den_degree,
unsigned long pnum, unsigned long pden,
int a_len, double *a_param, int *a_pow)
{
char *fname = "generateApprox(int, unsigned long, unsigned long)";
printf("Degree of the approximation is (%d,%d)\n", num_degree, den_degree);
printf("Approximating the function x^(%d/%d)\n", pnum, pden);
// Reallocate arrays, since degree has changed
if (num_degree != n || den_degree != d) allocate(num_degree,den_degree);
if (a_len > SUM_MAX) {
printf("Error: a_length > SUM_MAX");
exit(0);
}
step = new bigfloat[num_degree+den_degree+2];
a_length = a_len;
for (int j=0; j<a_len; j++) {
a[j]= a_param[j];
a_power[j] = a_pow[j];
}
power_num = pnum;
power_den = pden;
spread = 1.0e37;
iter = 0;
n = num_degree;
d = den_degree;
neq = n + d + 1;
initialGuess();
stpini(step);
while (spread > tolerance) { //iterate until convergance
if (iter++%100==0)
printf("Iteration %d, spread %e delta %e\n",
iter-1,(double)spread,(double)delta);
equations();
if (delta < tolerance) {
printf("Delta too small, try increasing precision\n");
exit(0);
}
search(step);
}
int sign;
double error = (double)getErr(mm[0],&sign);
printf("Converged at %d iterations, error = %e\n",iter,error);
// Once the approximation has been generated, calculate the roots
if(!root()) {
printf("Root finding failed\n");
} else {
foundRoots = 1;
}
delete [] step;
// Return the maximum error in the approximation
return error;
}
