test_chebyshevSeriesSum.cc
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test_chebyshevSeriesSum.cc
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	#include <cmath>
	#include "UnitTest++.h"

	#include "test_utils.hh"
	#include "npstat/nm/MathUtils.hh"
	#include "npstat/nm/SimpleFunctors.hh"

	using namespace npstat;
	using namespace std;

	namespace {
	double poly0(const double /* x */)
	{
	return 1.0;
	}

	double poly1(const double x)
	{
	return x;
	}

	double poly2(const double x)
	{
	return 2.0xx - 1.0;
	}

	double poly3(const double x)
	{
	return 4.0xxx - 3.0x;
	}

	double poly4(const double x)
	{
	const double xsq = x*x;
	return 8.0xsqxsq - 8.0*xsq + 1.0;
	}

	TEST(chebyshevSeriesSum)
	{
	typedef double (*Poly)(double);
	const unsigned nscan = 100;

	Poly polys[] = {poly0, poly1, poly2, poly3, poly4};
	double coeffs[sizeof(polys)/sizeof(polys[0])] = {0.0,};

	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);
	const double vcalc = chebyshevSeriesSum(coeffs, icycle, 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 = chebyshevSeriesSum(coeffs, 4, x);
	long double sum = 0.0L;
	for (unsigned i=0; i<5; ++i)
	sum += coeffs[i]*polys[i](x);
	const double vexpected = sum;
	CHECK_CLOSE(vexpected, vcalc, 1.0e-12);
	}
	}

	TEST(chebyshevSeriesCoeffs)
	{
	const unsigned deg = 20;
	double coeffs[deg + 1];
	double xmin = 0.0;
	double xmax = 2.0*M_PI;
	const unsigned nscan = 100;

	chebyshevSeriesCoeffs(FcnFunctor1<long double,long double>(sinl),
	xmin, xmax, deg, coeffs);

	double h = (xmax - xmin)/nscan;
	for (unsigned i=0; i<nscan; ++i)
	{
	double x = xmin + i*h;
	const double ref = sin(x);
	x = 2.0*(x - xmin)/(xmax - xmin) - 1.0;
	double fval = chebyshevSeriesSum(coeffs, deg, x);
	CHECK_CLOSE(ref, fval, 1.0e-15);
	}
	}
	}

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