@Test
public void testChebyshevDifferentials() {
for (int k = 0; k < 12; ++k) {
PolynomialFunction Tk0 = PolynomialsUtils.createChebyshevPolynomial(k);
PolynomialFunction Tk1 = Tk0.polynomialDerivative();
PolynomialFunction Tk2 = Tk1.polynomialDerivative();
PolynomialFunction g0 = new PolynomialFunction(new double[] {k * k});
PolynomialFunction g1 = new PolynomialFunction(new double[] {0, -1});
PolynomialFunction g2 = new PolynomialFunction(new double[] {1, 0, -1});
PolynomialFunction Tk0g0 = Tk0.multiply(g0);
PolynomialFunction Tk1g1 = Tk1.multiply(g1);
PolynomialFunction Tk2g2 = Tk2.multiply(g2);
checkNullPolynomial(Tk0g0.add(Tk1g1.add(Tk2g2)));
}
}
@Test
public void testLaguerreDifferentials() {
for (int k = 0; k < 12; ++k) {
PolynomialFunction Lk0 = PolynomialsUtils.createLaguerrePolynomial(k);
PolynomialFunction Lk1 = Lk0.polynomialDerivative();
PolynomialFunction Lk2 = Lk1.polynomialDerivative();
PolynomialFunction g0 = new PolynomialFunction(new double[] {k});
PolynomialFunction g1 = new PolynomialFunction(new double[] {1, -1});
PolynomialFunction g2 = new PolynomialFunction(new double[] {0, 1});
PolynomialFunction Lk0g0 = Lk0.multiply(g0);
PolynomialFunction Lk1g1 = Lk1.multiply(g1);
PolynomialFunction Lk2g2 = Lk2.multiply(g2);
checkNullPolynomial(Lk0g0.add(Lk1g1.add(Lk2g2)));
}
}
@Test
public void testLegendreDifferentials() {
for (int k = 0; k < 12; ++k) {
PolynomialFunction Pk0 = PolynomialsUtils.createLegendrePolynomial(k);
PolynomialFunction Pk1 = Pk0.polynomialDerivative();
PolynomialFunction Pk2 = Pk1.polynomialDerivative();
PolynomialFunction g0 = new PolynomialFunction(new double[] {k * (k + 1)});
PolynomialFunction g1 = new PolynomialFunction(new double[] {0, -2});
PolynomialFunction g2 = new PolynomialFunction(new double[] {1, 0, -1});
PolynomialFunction Pk0g0 = Pk0.multiply(g0);
PolynomialFunction Pk1g1 = Pk1.multiply(g1);
PolynomialFunction Pk2g2 = Pk2.multiply(g2);
checkNullPolynomial(Pk0g0.add(Pk1g1.add(Pk2g2)));
}
}
@Test
public void testHermiteDifferentials() {
for (int k = 0; k < 12; ++k) {
PolynomialFunction Hk0 = PolynomialsUtils.createHermitePolynomial(k);
PolynomialFunction Hk1 = Hk0.polynomialDerivative();
PolynomialFunction Hk2 = Hk1.polynomialDerivative();
PolynomialFunction g0 = new PolynomialFunction(new double[] {2 * k});
PolynomialFunction g1 = new PolynomialFunction(new double[] {0, -2});
PolynomialFunction g2 = new PolynomialFunction(new double[] {1});
PolynomialFunction Hk0g0 = Hk0.multiply(g0);
PolynomialFunction Hk1g1 = Hk1.multiply(g1);
PolynomialFunction Hk2g2 = Hk2.multiply(g2);
checkNullPolynomial(Hk0g0.add(Hk1g1.add(Hk2g2)));
}
}