@Test
public void linearAllTest() {
final double[] knots = new double[] {1., 4.};
final DoubleMatrix2D coefsMatrix = new DoubleMatrix2D(new double[][] {{0., 1., 1.}});
final double[] xKeys = new double[] {-2, 1., 2.5, 4.};
final double[] initials = new double[] {-0.5, 1., 2.5, 5.};
final int nKeys = xKeys.length;
final int nInit = initials.length;
final double[] valuesExp = new double[] {-2, 1, 2.5, 4.};
final double[][] integrateExp = new double[nInit][nKeys];
for (int i = 0; i < nInit; ++i) {
for (int j = 0; j < nKeys; ++j) {
integrateExp[i][j] = 0.5 * (xKeys[j] * xKeys[j] - initials[i] * initials[i]);
}
}
final double[] differentiateExp = new double[] {1., 1., 1., 1.};
PiecewisePolynomialResult result =
new PiecewisePolynomialResult(new DoubleMatrix1D(knots), coefsMatrix, 3, 1);
PiecewisePolynomialFunction1D function = new PiecewisePolynomialFunction1D();
final double[] values = function.evaluate(result, xKeys).getData()[0];
final double[] differentiate = function.differentiate(result, xKeys).getData()[0];
final double[][] integrate = new double[nInit][nKeys];
for (int i = 0; i < nInit; ++i) {
for (int j = 0; j < nKeys; ++j) {
integrate[i][j] = function.integrate(result, initials[i], xKeys).getData()[j];
}
}
for (int i = 0; i < nKeys; ++i) {
final double ref = valuesExp[i] == 0. ? 1. : Math.abs(valuesExp[i]);
assertEquals(values[i], valuesExp[i], ref * EPS);
}
for (int i = 0; i < nKeys; ++i) {
final double ref = differentiateExp[i] == 0. ? 1. : Math.abs(differentiateExp[i]);
assertEquals(differentiate[i], differentiateExp[i], ref * EPS);
}
for (int j = 0; j < nInit; ++j) {
for (int i = 0; i < nKeys; ++i) {
final double ref = integrateExp[j][i] == 0. ? 1. : Math.abs(integrateExp[j][i]);
assertEquals(integrate[j][i], integrateExp[j][i], ref * EPS);
}
}
}
@Test(expectedExceptions = IllegalArgumentException.class)
public void NaNxIntMultiTest() {
double[] xValues = new double[] {1, 2, 3, 4};
DoubleMatrix2D coefsMatrix =
new DoubleMatrix2D(new double[][] {{1., -3., 3., -1}, {1., 0., 0., 0.}, {1., 3., 3., 1.}});
double[] xKeys = new double[] {1.5, 7. / 3., 29. / 7., Double.NaN};
final int dim = 1;
final int nCoefs = 4;
PiecewisePolynomialResult pp =
new PiecewisePolynomialResult(new DoubleMatrix1D(xValues), coefsMatrix, nCoefs, dim);
PiecewisePolynomialFunction1D function = new PiecewisePolynomialFunction1D();
function.integrate(pp, 1., xKeys);
}
@Test(expectedExceptions = IllegalArgumentException.class)
public void nullpIntegrateTest() {
final double[] xValues = new double[] {1, 2, 3, 4};
final DoubleMatrix2D coefsMatrix =
new DoubleMatrix2D(new double[][] {{1., -3., 3., -1}, {1., 0., 0., 0.}, {1., 3., 3., 1.}});
final double[][] xKeys = new double[][] {{-2, 1, 2, 2.5}, {1.5, 7. / 3., 29. / 7., 5.}};
final int dim = 1;
final int nCoefs = 4;
PiecewisePolynomialResult pp =
new PiecewisePolynomialResult(new DoubleMatrix1D(xValues), coefsMatrix, nCoefs, dim);
pp = null;
PiecewisePolynomialFunction1D function = new PiecewisePolynomialFunction1D();
function.integrate(pp, 1., xKeys[0][0]);
}
@Test(expectedExceptions = IllegalArgumentException.class)
public void nullDimIntMultiTest() {
double[] xValues = new double[] {1, 2, 3, 4};
DoubleMatrix2D coefsMatrix =
new DoubleMatrix2D(
new double[][] {
{1., -3., 3., -1},
{0., 5., -20., 20},
{1., 0., 0., 0.},
{0., 5., -10., 5},
{1., 3., 3., 1.},
{0., 5., 0., 0.}
});
double[] xKeys = new double[] {-2, 1, 2, 2.5};
final int dim = 2;
final int nCoefs = 4;
PiecewisePolynomialResult pp =
new PiecewisePolynomialResult(new DoubleMatrix1D(xValues), coefsMatrix, nCoefs, dim);
PiecewisePolynomialFunction1D function = new PiecewisePolynomialFunction1D();
function.integrate(pp, 1., xKeys);
}
/** Sample function is f(x) = (x-1)^4 */
@Test
public void GeneralIntegrateDifferentiateTest() {
final double[] knots = new double[] {1., 2., 3., 4};
final double[][] coefMat =
new double[][] {{1., 0., 0., 0., 0.}, {1., 4., 6., 4., 1.}, {1., 8., 24., 32., 16.}};
final double[] xKeys = new double[] {-2, 1, 2.5, 4.};
final double[] initials = new double[] {1., 2.5, 23. / 7., 7.};
final int nKeys = xKeys.length;
final int nInit = initials.length;
final double[][] integrateExp = new double[nInit][nKeys];
for (int i = 0; i < nInit; ++i) {
for (int j = 0; j < nKeys; ++j) {
integrateExp[i][j] = Math.pow(xKeys[j] - 1., 5.) / 5. - Math.pow(initials[i] - 1., 5.) / 5.;
}
}
final double[] differentiateExp = new double[] {-108., 0., 27. / 2., 108.};
final double[] differentiateTwiceExp = new double[nKeys];
for (int i = 0; i < nKeys; ++i) {
differentiateTwiceExp[i] = 12. * (xKeys[i] - 1.) * (xKeys[i] - 1.);
}
PiecewisePolynomialFunction1D function = new PiecewisePolynomialFunction1D();
PiecewisePolynomialResult result =
new PiecewisePolynomialResult(new DoubleMatrix1D(knots), new DoubleMatrix2D(coefMat), 5, 1);
final double[] differentiate = function.differentiate(result, xKeys).getData()[0];
final double[] differentiateTwice = function.differentiateTwice(result, xKeys).getData()[0];
final double[][] integrate = new double[nInit][nKeys];
for (int i = 0; i < nInit; ++i) {
for (int j = 0; j < nKeys; ++j) {
integrate[i][j] = function.integrate(result, initials[i], xKeys).getData()[j];
}
}
for (int i = 0; i < nKeys; ++i) {
final double ref = differentiateExp[i] == 0. ? 1. : Math.abs(differentiateExp[i]);
assertEquals(differentiate[i], differentiateExp[i], ref * EPS);
}
for (int i = 0; i < nKeys; ++i) {
final double ref = differentiateTwiceExp[i] == 0. ? 1. : Math.abs(differentiateTwiceExp[i]);
assertEquals(differentiateTwice[i], differentiateTwiceExp[i], ref * EPS);
}
for (int j = 0; j < nInit; ++j) {
for (int i = 0; i < nKeys; ++i) {
final double ref = integrateExp[j][i] == 0. ? 1. : Math.abs(integrateExp[j][i]);
assertEquals(integrate[j][i], integrateExp[j][i], ref * EPS);
}
}
{
final double ref = differentiateExp[0] == 0. ? 1. : Math.abs(differentiateExp[0]);
assertEquals(
function.differentiate(result, xKeys[0]).getData()[0], differentiateExp[0], ref * EPS);
}
{
final double ref = differentiateExp[3] == 0. ? 1. : Math.abs(differentiateExp[3]);
assertEquals(
function.differentiate(result, xKeys[3]).getData()[0], differentiateExp[3], ref * EPS);
}
{
final double ref = differentiateTwiceExp[0] == 0. ? 1. : Math.abs(differentiateTwiceExp[0]);
assertEquals(
function.differentiateTwice(result, xKeys[0]).getData()[0],
differentiateTwiceExp[0],
ref * EPS);
}
{
final double ref = differentiateTwiceExp[3] == 0. ? 1. : Math.abs(differentiateTwiceExp[3]);
assertEquals(
function.differentiateTwice(result, xKeys[3]).getData()[0],
differentiateTwiceExp[3],
ref * EPS);
}
{
final double ref = integrateExp[0][0] == 0. ? 1. : Math.abs(integrateExp[0][0]);
assertEquals(
function.integrate(result, initials[0], xKeys[0]), integrateExp[0][0], ref * EPS);
}
{
final double ref = integrateExp[0][3] == 0. ? 1. : Math.abs(integrateExp[0][3]);
assertEquals(
function.integrate(result, initials[0], xKeys[3]), integrateExp[0][3], ref * EPS);
}
{
final double ref = integrateExp[3][0] == 0. ? 1. : Math.abs(integrateExp[3][0]);
assertEquals(
function.integrate(result, initials[3], xKeys[0]), integrateExp[3][0], ref * EPS);
}
{
final double ref = integrateExp[1][0] == 0. ? 1. : Math.abs(integrateExp[1][0]);
assertEquals(
function.integrate(result, initials[1], xKeys[0]), integrateExp[1][0], ref * EPS);
}
}