@Test
public void test() {
final int n = 12;
final GaussianQuadratureData f1 = GAUSS_LEGENDRE.generate(n);
final GaussianQuadratureData f2 = GAUSS_JACOBI_GL_EQUIV.generate(n);
final GaussianQuadratureData f3 = GAUSS_JACOBI_CHEBYSHEV_EQUIV.generate(n);
final double[] w1 = f1.getWeights();
final double[] w2 = f2.getWeights();
final double[] x1 = f1.getAbscissas();
final double[] x2 = f2.getAbscissas();
assertTrue(w1.length == w2.length);
assertTrue(x1.length == x2.length);
for (int i = 0; i < n; i++) {
assertEquals(w1[i], w2[i], EPS);
assertEquals(x1[i], -x2[i], EPS);
}
final double[] w3 = f3.getWeights();
final double[] x3 = f3.getAbscissas();
final double chebyshevWeight = Math.PI / n;
final Function1D<Integer, Double> chebyshevAbscissa =
new Function1D<Integer, Double>() {
@Override
public Double evaluate(final Integer x) {
return -Math.cos(Math.PI * (x + 0.5) / n);
}
};
for (int i = 0; i < n; i++) {
assertEquals(chebyshevWeight, w3[i], EPS);
assertEquals(chebyshevAbscissa.evaluate(i), -x3[i], EPS);
}
}
/** {@inheritDoc} */
@Override
public Double integrate(
final Function1D<Double, Double> function, final Double lower, final Double upper) {
Validate.notNull(function);
Validate.notNull(lower);
Validate.notNull(upper);
final Function1D<Double, Double> integral = getIntegralFunction(function, lower, upper);
final GaussianQuadratureData quadrature = _generator.generate(_n);
final double[] abscissas = quadrature.getAbscissas();
final int n = abscissas.length;
final double[] weights = quadrature.getWeights();
double sum = 0;
for (int i = 0; i < n; i++) {
sum += integral.evaluate(abscissas[i]) * weights[i];
}
return sum;
}