Page MenuHomeHEPForge
Files F19244852

test_gegenbauerSeriesSum.cc
No OneTemporary
Actions

Size
3 KB
Referenced Files
None
Subscribers
None

test_gegenbauerSeriesSum.cc
View Options

#include <cmath>
#include "UnitTest++.h"
#include "test_utils.hh"
#include "npstat/nm/MathUtils.hh"
using namespace npstat;
using namespace std;
namespace {
double poly0(const double /* x */, double /* lambda */)
{
return 1.0;
}
double poly1(const double x, const double lambda)
{
return 2.0*lambda*x;
}
double poly2(const double x, const double lambda)
{
return -lambda + 2*lambda*(1 + lambda)*x*x;
}
double poly3(const double x, const double lambda)
{
return -2*lambda*(1 + lambda)*x +
(4*lambda*(1 + lambda)*(2 + lambda)*x*x*x)/3.0;
}
double poly4(const double x, const double lambda)
{
const double xsq = x*x;
return (lambda*(1 + lambda))/2. -
2*lambda*(1 + lambda)*(2 + lambda)*x*x +
(2*lambda*(1 + lambda)*(2 + lambda)*(3 + lambda)*xsq*xsq)/3.0;
}
TEST(gegenbauerSeriesSum_1)
{
typedef double (*Poly)(double, double);
const unsigned nscan = 100;
Poly polys[] = {poly0, poly1, poly2, poly3, poly4};
double coeffs[sizeof(polys)/sizeof(polys[0])] = {0.0,};
const unsigned nset[] = {1, 2, 3, 4};
for (unsigned in = 0; in < sizeof(nset)/sizeof(nset[0]); ++in)
{
const double lambda = nset[in] + 0.5;
for (unsigned icycle=0; icycle<sizeof(polys)/sizeof(polys[0]);
++icycle)
{
for (unsigned i=0; i<icycle; ++i)
coeffs[i] = 0.0;
coeffs[icycle] = 1.0;
for (unsigned i=0; i<nscan; ++i)
{
const double x = -1.0 + (i + 0.5)*2.0/nscan;
const double vexpected = polys[icycle](x, lambda);
const double vcalc = gegenbauerSeriesSum(
coeffs, icycle, lambda, x);
CHECK_CLOSE(vexpected, vcalc, 1.0e-12);
}
}
coeffs[0] = 2.0;
coeffs[1] = 3.0;
coeffs[2] = 5.0;
coeffs[3] = 7.0;
coeffs[4] = 11.0;
double xset[] = {0.0, 0.1, 0.2, 0.3, 0.4, 0.5};
for (unsigned icycle=0; icycle<sizeof(xset)/sizeof(xset[0]); ++icycle)
{
const double x = xset[icycle];
const double vcalc = gegenbauerSeriesSum(coeffs, 4, lambda, x);
long double sum = 0.0L;
for (unsigned i=0; i<5; ++i)
sum += coeffs[i]*polys[i](x, lambda);
const double vexpected = sum;
CHECK_CLOSE(vexpected, vcalc, 1.0e-12);
}
}
}
TEST(gegenbauerSeriesSum_2)
{
// Test that Gegenbauer series are reduced to Legendre
// series for lambda = 1/2
const unsigned ncycles = 100;
const unsigned degree = 10;
const unsigned nintervals = 51;
const double eps = 1.0e-12;
const double step = 2.0/nintervals;
double coeffs[degree + 1];
for (unsigned icycle=0; icycle<ncycles; ++icycle)
{
for (unsigned i=0; i<=degree; ++i)
coeffs[i] = 2.0*test_rng() - 1.0;
for (unsigned i=0; i<nintervals; ++i)
{
const double x = -1.0 + (i + 0.5)*step;
const double gsum = gegenbauerSeriesSum(coeffs, degree, 0.5, x);
const double lsum = legendreSeriesSum(coeffs, degree, x);
CHECK_CLOSE(lsum, gsum, eps);
}
}
}
}

File Metadata

Mime Type
text/x-c
Expires
Tue, Sep 30, 4:45 AM (15 h, 46 m)
Storage Engine
blob
Storage Format
Raw Data
Storage Handle
6540737
Default Alt Text
test_gegenbauerSeriesSum.cc (3 KB)

Event Timeline

HEPForge.org · .