Java Code Examples for org.apache.commons.math3.analysis.differentiation.DerivativeStructure#getPartialDerivative()
The following examples show how to use
org.apache.commons.math3.analysis.differentiation.DerivativeStructure#getPartialDerivative() .
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Example 1
| Source File: NewtonRaphsonSolver.java From astor with GNU General Public License v2.0 | 6 votes |
|
/**
* {@inheritDoc}
*/
@Override
protected double doSolve()
throws TooManyEvaluationsException {
final double startValue = getStartValue();
final double absoluteAccuracy = getAbsoluteAccuracy();
double x0 = startValue;
double x1;
while (true) {
final DerivativeStructure y0 = computeObjectiveValueAndDerivative(x0);
x1 = x0 - (y0.getValue() / y0.getPartialDerivative(1));
if (FastMath.abs(x1 - x0) <= absoluteAccuracy) {
return x1;
}
x0 = x1;
}
}
Example 2
| Source File: NewtonRaphsonSolver.java From astor with GNU General Public License v2.0 | 6 votes |
|
/**
* {@inheritDoc}
*/
@Override
protected double doSolve()
throws TooManyEvaluationsException {
final double startValue = getStartValue();
final double absoluteAccuracy = getAbsoluteAccuracy();
double x0 = startValue;
double x1;
while (true) {
final DerivativeStructure y0 = computeObjectiveValueAndDerivative(x0);
x1 = x0 - (y0.getValue() / y0.getPartialDerivative(1));
if (FastMath.abs(x1 - x0) <= absoluteAccuracy) {
return x1;
}
x0 = x1;
}
}
Example 3
| Source File: NewtonRaphsonSolver.java From astor with GNU General Public License v2.0 | 6 votes |
|
/**
* {@inheritDoc}
*/
@Override
protected double doSolve()
throws TooManyEvaluationsException {
final double startValue = getStartValue();
final double absoluteAccuracy = getAbsoluteAccuracy();
double x0 = startValue;
double x1;
while (true) {
final DerivativeStructure y0 = computeObjectiveValueAndDerivative(x0);
x1 = x0 - (y0.getValue() / y0.getPartialDerivative(1));
if (FastMath.abs(x1 - x0) <= absoluteAccuracy) {
return x1;
}
x0 = x1;
}
}
Example 4
| Source File: NewtonRaphsonSolver.java From astor with GNU General Public License v2.0 | 6 votes |
|
/**
* {@inheritDoc}
*/
@Override
protected double doSolve()
throws TooManyEvaluationsException {
final double startValue = getStartValue();
final double absoluteAccuracy = getAbsoluteAccuracy();
double x0 = startValue;
double x1;
while (true) {
final DerivativeStructure y0 = computeObjectiveValueAndDerivative(x0);
x1 = x0 - (y0.getValue() / y0.getPartialDerivative(1));
if (FastMath.abs(x1 - x0) <= absoluteAccuracy) {
return x1;
}
x0 = x1;
}
}
Example 5
| Source File: NewtonRaphsonSolver.java From astor with GNU General Public License v2.0 | 6 votes |
|
/**
* {@inheritDoc}
*/
@Override
protected double doSolve()
throws TooManyEvaluationsException {
final double startValue = getStartValue();
final double absoluteAccuracy = getAbsoluteAccuracy();
double x0 = startValue;
double x1;
while (true) {
final DerivativeStructure y0 = computeObjectiveValueAndDerivative(x0);
x1 = x0 - (y0.getValue() / y0.getPartialDerivative(1));
if (FastMath.abs(x1 - x0) <= absoluteAccuracy) {
return x1;
}
x0 = x1;
}
}
Example 6
| Source File: NewtonRaphsonSolver.java From astor with GNU General Public License v2.0 | 6 votes |
|
/**
* {@inheritDoc}
*/
@Override
protected double doSolve()
throws TooManyEvaluationsException {
final double startValue = getStartValue();
final double absoluteAccuracy = getAbsoluteAccuracy();
double x0 = startValue;
double x1;
while (true) {
final DerivativeStructure y0 = computeObjectiveValueAndDerivative(x0);
x1 = x0 - (y0.getValue() / y0.getPartialDerivative(1));
if (FastMath.abs(x1 - x0) <= absoluteAccuracy) {
return x1;
}
x0 = x1;
}
}
Example 7
| Source File: FunctionUtils.java From astor with GNU General Public License v2.0 | 5 votes |
|
/** Convert a {@link DifferentiableUnivariateFunction} into a {@link UnivariateDifferentiableFunction}.
* <p>
* Note that the converted function is able to handle {@link DerivativeStructure} up to order one.
* If the function is called with higher order, a {@link NumberIsTooLargeException} will be thrown.
* </p>
* @param f function to convert
* @return converted function
* @deprecated this conversion method is temporary in version 3.1, as the {@link
* DifferentiableUnivariateFunction} interface itself is deprecated
*/
@Deprecated
public static UnivariateDifferentiableFunction toUnivariateDifferential(final DifferentiableUnivariateFunction f) {
return new UnivariateDifferentiableFunction() {
/** {@inheritDoc} */
public double value(final double x) {
return f.value(x);
}
/** {@inheritDoc}
* @exception NumberIsTooLargeException if derivation order is greater than 1
*/
public DerivativeStructure value(final DerivativeStructure t)
throws NumberIsTooLargeException {
switch (t.getOrder()) {
case 0 :
return new DerivativeStructure(t.getFreeParameters(), 0, f.value(t.getValue()));
case 1 : {
final int parameters = t.getFreeParameters();
final double[] derivatives = new double[parameters + 1];
derivatives[0] = f.value(t.getValue());
final double fPrime = f.derivative().value(t.getValue());
int[] orders = new int[parameters];
for (int i = 0; i < parameters; ++i) {
orders[i] = 1;
derivatives[i + 1] = fPrime * t.getPartialDerivative(orders);
orders[i] = 0;
}
return new DerivativeStructure(parameters, 1, derivatives);
}
default :
throw new NumberIsTooLargeException(t.getOrder(), 1, true);
}
}
};
}
Example 8
| Source File: SphericalCoordinatesTest.java From astor with GNU General Public License v2.0 | 5 votes |
|
@Test
public void testGradient() {
for (double r = 0.2; r < 10; r += 0.5) {
for (double theta = 0; theta < 2 * FastMath.PI; theta += 0.1) {
for (double phi = 0.1; phi < FastMath.PI; phi += 0.1) {
SphericalCoordinates sc = new SphericalCoordinates(r, theta, phi);
DerivativeStructure svalue = valueSpherical(new DerivativeStructure(3, 1, 0, r),
new DerivativeStructure(3, 1, 1, theta),
new DerivativeStructure(3, 1, 2, phi));
double[] sGradient = new double[] {
svalue.getPartialDerivative(1, 0, 0),
svalue.getPartialDerivative(0, 1, 0),
svalue.getPartialDerivative(0, 0, 1),
};
DerivativeStructure cvalue = valueCartesian(new DerivativeStructure(3, 1, 0, sc.getCartesian().getX()),
new DerivativeStructure(3, 1, 1, sc.getCartesian().getY()),
new DerivativeStructure(3, 1, 2, sc.getCartesian().getZ()));
Vector3D refCGradient = new Vector3D(cvalue.getPartialDerivative(1, 0, 0),
cvalue.getPartialDerivative(0, 1, 0),
cvalue.getPartialDerivative(0, 0, 1));
Vector3D testCGradient = new Vector3D(sc.toCartesianGradient(sGradient));
Assert.assertEquals(0, testCGradient.distance(refCGradient) / refCGradient.getNorm(), 5.0e-14);
}
}
}
}
Example 9
| Source File: SphericalCoordinatesTest.java From astor with GNU General Public License v2.0 | 5 votes |
|
@Test
public void testGradient() {
for (double r = 0.2; r < 10; r += 0.5) {
for (double theta = 0; theta < 2 * FastMath.PI; theta += 0.1) {
for (double phi = 0.1; phi < FastMath.PI; phi += 0.1) {
SphericalCoordinates sc = new SphericalCoordinates(r, theta, phi);
DerivativeStructure svalue = valueSpherical(new DerivativeStructure(3, 1, 0, r),
new DerivativeStructure(3, 1, 1, theta),
new DerivativeStructure(3, 1, 2, phi));
double[] sGradient = new double[] {
svalue.getPartialDerivative(1, 0, 0),
svalue.getPartialDerivative(0, 1, 0),
svalue.getPartialDerivative(0, 0, 1),
};
DerivativeStructure cvalue = valueCartesian(new DerivativeStructure(3, 1, 0, sc.getCartesian().getX()),
new DerivativeStructure(3, 1, 1, sc.getCartesian().getY()),
new DerivativeStructure(3, 1, 2, sc.getCartesian().getZ()));
Vector3D refCGradient = new Vector3D(cvalue.getPartialDerivative(1, 0, 0),
cvalue.getPartialDerivative(0, 1, 0),
cvalue.getPartialDerivative(0, 0, 1));
Vector3D testCGradient = new Vector3D(sc.toCartesianGradient(sGradient));
Assert.assertEquals(0, testCGradient.distance(refCGradient) / refCGradient.getNorm(), 5.0e-14);
}
}
}
}
Example 10
| Source File: FunctionUtils.java From astor with GNU General Public License v2.0 | 5 votes |
|
/** Convert a {@link DifferentiableUnivariateFunction} into a {@link UnivariateDifferentiableFunction}.
* <p>
* Note that the converted function is able to handle {@link DerivativeStructure} up to order one.
* If the function is called with higher order, a {@link NumberIsTooLargeException} will be thrown.
* </p>
* @param f function to convert
* @return converted function
* @deprecated this conversion method is temporary in version 3.1, as the {@link
* DifferentiableUnivariateFunction} interface itself is deprecated
*/
@Deprecated
public static UnivariateDifferentiableFunction toUnivariateDifferential(final DifferentiableUnivariateFunction f) {
return new UnivariateDifferentiableFunction() {
/** {@inheritDoc} */
public double value(final double x) {
return f.value(x);
}
/** {@inheritDoc}
* @exception NumberIsTooLargeException if derivation order is greater than 1
*/
public DerivativeStructure value(final DerivativeStructure t)
throws NumberIsTooLargeException {
switch (t.getOrder()) {
case 0 :
return new DerivativeStructure(t.getFreeParameters(), 0, f.value(t.getValue()));
case 1 : {
final int parameters = t.getFreeParameters();
final double[] derivatives = new double[parameters + 1];
derivatives[0] = f.value(t.getValue());
final double fPrime = f.derivative().value(t.getValue());
int[] orders = new int[parameters];
for (int i = 0; i < parameters; ++i) {
orders[i] = 1;
derivatives[i + 1] = fPrime * t.getPartialDerivative(orders);
orders[i] = 0;
}
return new DerivativeStructure(parameters, 1, derivatives);
}
default :
throw new NumberIsTooLargeException(t.getOrder(), 1, true);
}
}
};
}
Example 11
| Source File: SphericalCoordinatesTest.java From astor with GNU General Public License v2.0 | 5 votes |
|
@Test
public void testGradient() {
for (double r = 0.2; r < 10; r += 0.5) {
for (double theta = 0; theta < 2 * FastMath.PI; theta += 0.1) {
for (double phi = 0.1; phi < FastMath.PI; phi += 0.1) {
SphericalCoordinates sc = new SphericalCoordinates(r, theta, phi);
DerivativeStructure svalue = valueSpherical(new DerivativeStructure(3, 1, 0, r),
new DerivativeStructure(3, 1, 1, theta),
new DerivativeStructure(3, 1, 2, phi));
double[] sGradient = new double[] {
svalue.getPartialDerivative(1, 0, 0),
svalue.getPartialDerivative(0, 1, 0),
svalue.getPartialDerivative(0, 0, 1),
};
DerivativeStructure cvalue = valueCartesian(new DerivativeStructure(3, 1, 0, sc.getCartesian().getX()),
new DerivativeStructure(3, 1, 1, sc.getCartesian().getY()),
new DerivativeStructure(3, 1, 2, sc.getCartesian().getZ()));
Vector3D refCGradient = new Vector3D(cvalue.getPartialDerivative(1, 0, 0),
cvalue.getPartialDerivative(0, 1, 0),
cvalue.getPartialDerivative(0, 0, 1));
Vector3D testCGradient = new Vector3D(sc.toCartesianGradient(sGradient));
Assert.assertEquals(0, testCGradient.distance(refCGradient) / refCGradient.getNorm(), 5.0e-14);
}
}
}
}
Example 12
| Source File: SphericalCoordinatesTest.java From astor with GNU General Public License v2.0 | 5 votes |
|
@Test
public void testGradient() {
for (double r = 0.2; r < 10; r += 0.5) {
for (double theta = 0; theta < 2 * FastMath.PI; theta += 0.1) {
for (double phi = 0.1; phi < FastMath.PI; phi += 0.1) {
SphericalCoordinates sc = new SphericalCoordinates(r, theta, phi);
DerivativeStructure svalue = valueSpherical(new DerivativeStructure(3, 1, 0, r),
new DerivativeStructure(3, 1, 1, theta),
new DerivativeStructure(3, 1, 2, phi));
double[] sGradient = new double[] {
svalue.getPartialDerivative(1, 0, 0),
svalue.getPartialDerivative(0, 1, 0),
svalue.getPartialDerivative(0, 0, 1),
};
DerivativeStructure cvalue = valueCartesian(new DerivativeStructure(3, 1, 0, sc.getCartesian().getX()),
new DerivativeStructure(3, 1, 1, sc.getCartesian().getY()),
new DerivativeStructure(3, 1, 2, sc.getCartesian().getZ()));
Vector3D refCGradient = new Vector3D(cvalue.getPartialDerivative(1, 0, 0),
cvalue.getPartialDerivative(0, 1, 0),
cvalue.getPartialDerivative(0, 0, 1));
Vector3D testCGradient = new Vector3D(sc.toCartesianGradient(sGradient));
Assert.assertEquals(0, testCGradient.distance(refCGradient) / refCGradient.getNorm(), 5.0e-14);
}
}
}
}
Example 13
| Source File: FunctionUtils.java From astor with GNU General Public License v2.0 | 5 votes |
|
/** Convert a {@link DifferentiableUnivariateFunction} into a {@link UnivariateDifferentiableFunction}.
* <p>
* Note that the converted function is able to handle {@link DerivativeStructure} up to order one.
* If the function is called with higher order, a {@link NumberIsTooLargeException} will be thrown.
* </p>
* @param f function to convert
* @return converted function
* @deprecated this conversion method is temporary in version 3.1, as the {@link
* DifferentiableUnivariateFunction} interface itself is deprecated
*/
@Deprecated
public static UnivariateDifferentiableFunction toUnivariateDifferential(final DifferentiableUnivariateFunction f) {
return new UnivariateDifferentiableFunction() {
/** {@inheritDoc} */
public double value(final double x) {
return f.value(x);
}
/** {@inheritDoc}
* @exception NumberIsTooLargeException if derivation order is greater than 1
*/
public DerivativeStructure value(final DerivativeStructure t)
throws NumberIsTooLargeException {
switch (t.getOrder()) {
case 0 :
return new DerivativeStructure(t.getFreeParameters(), 0, f.value(t.getValue()));
case 1 : {
final int parameters = t.getFreeParameters();
final double[] derivatives = new double[parameters + 1];
derivatives[0] = f.value(t.getValue());
final double fPrime = f.derivative().value(t.getValue());
int[] orders = new int[parameters];
for (int i = 0; i < parameters; ++i) {
orders[i] = 1;
derivatives[i + 1] = fPrime * t.getPartialDerivative(orders);
orders[i] = 0;
}
return new DerivativeStructure(parameters, 1, derivatives);
}
default :
throw new NumberIsTooLargeException(t.getOrder(), 1, true);
}
}
};
}
Example 14
| Source File: SphericalCoordinatesTest.java From astor with GNU General Public License v2.0 | 5 votes |
|
@Test
public void testGradient() {
for (double r = 0.2; r < 10; r += 0.5) {
for (double theta = 0; theta < 2 * FastMath.PI; theta += 0.1) {
for (double phi = 0.1; phi < FastMath.PI; phi += 0.1) {
SphericalCoordinates sc = new SphericalCoordinates(r, theta, phi);
DerivativeStructure svalue = valueSpherical(new DerivativeStructure(3, 1, 0, r),
new DerivativeStructure(3, 1, 1, theta),
new DerivativeStructure(3, 1, 2, phi));
double[] sGradient = new double[] {
svalue.getPartialDerivative(1, 0, 0),
svalue.getPartialDerivative(0, 1, 0),
svalue.getPartialDerivative(0, 0, 1),
};
DerivativeStructure cvalue = valueCartesian(new DerivativeStructure(3, 1, 0, sc.getCartesian().getX()),
new DerivativeStructure(3, 1, 1, sc.getCartesian().getY()),
new DerivativeStructure(3, 1, 2, sc.getCartesian().getZ()));
Vector3D refCGradient = new Vector3D(cvalue.getPartialDerivative(1, 0, 0),
cvalue.getPartialDerivative(0, 1, 0),
cvalue.getPartialDerivative(0, 0, 1));
Vector3D testCGradient = new Vector3D(sc.toCartesianGradient(sGradient));
Assert.assertEquals(0, testCGradient.distance(refCGradient) / refCGradient.getNorm(), 5.0e-14);
}
}
}
}
Example 15
| Source File: FunctionUtils.java From astor with GNU General Public License v2.0 | 5 votes |
|
/** Convert a {@link DifferentiableUnivariateFunction} into a {@link UnivariateDifferentiableFunction}.
* <p>
* Note that the converted function is able to handle {@link DerivativeStructure} up to order one.
* If the function is called with higher order, a {@link NumberIsTooLargeException} will be thrown.
* </p>
* @param f function to convert
* @return converted function
* @deprecated this conversion method is temporary in version 3.1, as the {@link
* DifferentiableUnivariateFunction} interface itself is deprecated
*/
@Deprecated
public static UnivariateDifferentiableFunction toUnivariateDifferential(final DifferentiableUnivariateFunction f) {
return new UnivariateDifferentiableFunction() {
/** {@inheritDoc} */
public double value(final double x) {
return f.value(x);
}
/** {@inheritDoc}
* @exception NumberIsTooLargeException if derivation order is greater than 1
*/
public DerivativeStructure value(final DerivativeStructure t)
throws NumberIsTooLargeException {
switch (t.getOrder()) {
case 0 :
return new DerivativeStructure(t.getFreeParameters(), 0, f.value(t.getValue()));
case 1 : {
final int parameters = t.getFreeParameters();
final double[] derivatives = new double[parameters + 1];
derivatives[0] = f.value(t.getValue());
final double fPrime = f.derivative().value(t.getValue());
int[] orders = new int[parameters];
for (int i = 0; i < parameters; ++i) {
orders[i] = 1;
derivatives[i + 1] = fPrime * t.getPartialDerivative(orders);
orders[i] = 0;
}
return new DerivativeStructure(parameters, 1, derivatives);
}
default :
throw new NumberIsTooLargeException(t.getOrder(), 1, true);
}
}
};
}
Example 16
| Source File: SphericalCoordinatesTest.java From astor with GNU General Public License v2.0 | 4 votes |
|
@Test
public void testHessian() {
for (double r = 0.2; r < 10; r += 0.5) {
for (double theta = 0; theta < 2 * FastMath.PI; theta += 0.2) {
for (double phi = 0.1; phi < FastMath.PI; phi += 0.2) {
SphericalCoordinates sc = new SphericalCoordinates(r, theta, phi);
DerivativeStructure svalue = valueSpherical(new DerivativeStructure(3, 2, 0, r),
new DerivativeStructure(3, 2, 1, theta),
new DerivativeStructure(3, 2, 2, phi));
double[] sGradient = new double[] {
svalue.getPartialDerivative(1, 0, 0),
svalue.getPartialDerivative(0, 1, 0),
svalue.getPartialDerivative(0, 0, 1),
};
double[][] sHessian = new double[3][3];
sHessian[0][0] = svalue.getPartialDerivative(2, 0, 0); // d2F/dR2
sHessian[1][0] = svalue.getPartialDerivative(1, 1, 0); // d2F/dRdTheta
sHessian[2][0] = svalue.getPartialDerivative(1, 0, 1); // d2F/dRdPhi
sHessian[0][1] = Double.NaN; // just to check upper-right part is not used
sHessian[1][1] = svalue.getPartialDerivative(0, 2, 0); // d2F/dTheta2
sHessian[2][1] = svalue.getPartialDerivative(0, 1, 1); // d2F/dThetadPhi
sHessian[0][2] = Double.NaN; // just to check upper-right part is not used
sHessian[1][2] = Double.NaN; // just to check upper-right part is not used
sHessian[2][2] = svalue.getPartialDerivative(0, 0, 2); // d2F/dPhi2
DerivativeStructure cvalue = valueCartesian(new DerivativeStructure(3, 2, 0, sc.getCartesian().getX()),
new DerivativeStructure(3, 2, 1, sc.getCartesian().getY()),
new DerivativeStructure(3, 2, 2, sc.getCartesian().getZ()));
double[][] refCHessian = new double[3][3];
refCHessian[0][0] = cvalue.getPartialDerivative(2, 0, 0); // d2F/dX2
refCHessian[1][0] = cvalue.getPartialDerivative(1, 1, 0); // d2F/dXdY
refCHessian[2][0] = cvalue.getPartialDerivative(1, 0, 1); // d2F/dXdZ
refCHessian[0][1] = refCHessian[1][0];
refCHessian[1][1] = cvalue.getPartialDerivative(0, 2, 0); // d2F/dY2
refCHessian[2][1] = cvalue.getPartialDerivative(0, 1, 1); // d2F/dYdZ
refCHessian[0][2] = refCHessian[2][0];
refCHessian[1][2] = refCHessian[2][1];
refCHessian[2][2] = cvalue.getPartialDerivative(0, 0, 2); // d2F/dZ2
double norm = 0;
for (int i = 0; i < 3; ++i) {
for (int j = 0; j < 3; ++j) {
norm = FastMath.max(norm, FastMath.abs(refCHessian[i][j]));
}
}
double[][] testCHessian = sc.toCartesianHessian(sHessian, sGradient);
for (int i = 0; i < 3; ++i) {
for (int j = 0; j < 3; ++j) {
Assert.assertEquals("" + FastMath.abs((refCHessian[i][j] - testCHessian[i][j]) / norm),
refCHessian[i][j], testCHessian[i][j], 1.0e-14 * norm);
}
}
}
}
}
}
Example 17
| Source File: SphericalCoordinatesTest.java From astor with GNU General Public License v2.0 | 4 votes |
|
@Test
public void testHessian() {
for (double r = 0.2; r < 10; r += 0.5) {
for (double theta = 0; theta < 2 * FastMath.PI; theta += 0.2) {
for (double phi = 0.1; phi < FastMath.PI; phi += 0.2) {
SphericalCoordinates sc = new SphericalCoordinates(r, theta, phi);
DerivativeStructure svalue = valueSpherical(new DerivativeStructure(3, 2, 0, r),
new DerivativeStructure(3, 2, 1, theta),
new DerivativeStructure(3, 2, 2, phi));
double[] sGradient = new double[] {
svalue.getPartialDerivative(1, 0, 0),
svalue.getPartialDerivative(0, 1, 0),
svalue.getPartialDerivative(0, 0, 1),
};
double[][] sHessian = new double[3][3];
sHessian[0][0] = svalue.getPartialDerivative(2, 0, 0); // d2F/dR2
sHessian[1][0] = svalue.getPartialDerivative(1, 1, 0); // d2F/dRdTheta
sHessian[2][0] = svalue.getPartialDerivative(1, 0, 1); // d2F/dRdPhi
sHessian[0][1] = Double.NaN; // just to check upper-right part is not used
sHessian[1][1] = svalue.getPartialDerivative(0, 2, 0); // d2F/dTheta2
sHessian[2][1] = svalue.getPartialDerivative(0, 1, 1); // d2F/dThetadPhi
sHessian[0][2] = Double.NaN; // just to check upper-right part is not used
sHessian[1][2] = Double.NaN; // just to check upper-right part is not used
sHessian[2][2] = svalue.getPartialDerivative(0, 0, 2); // d2F/dPhi2
DerivativeStructure cvalue = valueCartesian(new DerivativeStructure(3, 2, 0, sc.getCartesian().getX()),
new DerivativeStructure(3, 2, 1, sc.getCartesian().getY()),
new DerivativeStructure(3, 2, 2, sc.getCartesian().getZ()));
double[][] refCHessian = new double[3][3];
refCHessian[0][0] = cvalue.getPartialDerivative(2, 0, 0); // d2F/dX2
refCHessian[1][0] = cvalue.getPartialDerivative(1, 1, 0); // d2F/dXdY
refCHessian[2][0] = cvalue.getPartialDerivative(1, 0, 1); // d2F/dXdZ
refCHessian[0][1] = refCHessian[1][0];
refCHessian[1][1] = cvalue.getPartialDerivative(0, 2, 0); // d2F/dY2
refCHessian[2][1] = cvalue.getPartialDerivative(0, 1, 1); // d2F/dYdZ
refCHessian[0][2] = refCHessian[2][0];
refCHessian[1][2] = refCHessian[2][1];
refCHessian[2][2] = cvalue.getPartialDerivative(0, 0, 2); // d2F/dZ2
double norm = 0;
for (int i = 0; i < 3; ++i) {
for (int j = 0; j < 3; ++j) {
norm = FastMath.max(norm, FastMath.abs(refCHessian[i][j]));
}
}
double[][] testCHessian = sc.toCartesianHessian(sHessian, sGradient);
for (int i = 0; i < 3; ++i) {
for (int j = 0; j < 3; ++j) {
Assert.assertEquals("" + FastMath.abs((refCHessian[i][j] - testCHessian[i][j]) / norm),
refCHessian[i][j], testCHessian[i][j], 1.0e-14 * norm);
}
}
}
}
}
}
Example 18
| Source File: SphericalCoordinatesTest.java From astor with GNU General Public License v2.0 | 4 votes |
|
@Test
public void testHessian() {
for (double r = 0.2; r < 10; r += 0.5) {
for (double theta = 0; theta < 2 * FastMath.PI; theta += 0.2) {
for (double phi = 0.1; phi < FastMath.PI; phi += 0.2) {
SphericalCoordinates sc = new SphericalCoordinates(r, theta, phi);
DerivativeStructure svalue = valueSpherical(new DerivativeStructure(3, 2, 0, r),
new DerivativeStructure(3, 2, 1, theta),
new DerivativeStructure(3, 2, 2, phi));
double[] sGradient = new double[] {
svalue.getPartialDerivative(1, 0, 0),
svalue.getPartialDerivative(0, 1, 0),
svalue.getPartialDerivative(0, 0, 1),
};
double[][] sHessian = new double[3][3];
sHessian[0][0] = svalue.getPartialDerivative(2, 0, 0); // d2F/dR2
sHessian[1][0] = svalue.getPartialDerivative(1, 1, 0); // d2F/dRdTheta
sHessian[2][0] = svalue.getPartialDerivative(1, 0, 1); // d2F/dRdPhi
sHessian[0][1] = Double.NaN; // just to check upper-right part is not used
sHessian[1][1] = svalue.getPartialDerivative(0, 2, 0); // d2F/dTheta2
sHessian[2][1] = svalue.getPartialDerivative(0, 1, 1); // d2F/dThetadPhi
sHessian[0][2] = Double.NaN; // just to check upper-right part is not used
sHessian[1][2] = Double.NaN; // just to check upper-right part is not used
sHessian[2][2] = svalue.getPartialDerivative(0, 0, 2); // d2F/dPhi2
DerivativeStructure cvalue = valueCartesian(new DerivativeStructure(3, 2, 0, sc.getCartesian().getX()),
new DerivativeStructure(3, 2, 1, sc.getCartesian().getY()),
new DerivativeStructure(3, 2, 2, sc.getCartesian().getZ()));
double[][] refCHessian = new double[3][3];
refCHessian[0][0] = cvalue.getPartialDerivative(2, 0, 0); // d2F/dX2
refCHessian[1][0] = cvalue.getPartialDerivative(1, 1, 0); // d2F/dXdY
refCHessian[2][0] = cvalue.getPartialDerivative(1, 0, 1); // d2F/dXdZ
refCHessian[0][1] = refCHessian[1][0];
refCHessian[1][1] = cvalue.getPartialDerivative(0, 2, 0); // d2F/dY2
refCHessian[2][1] = cvalue.getPartialDerivative(0, 1, 1); // d2F/dYdZ
refCHessian[0][2] = refCHessian[2][0];
refCHessian[1][2] = refCHessian[2][1];
refCHessian[2][2] = cvalue.getPartialDerivative(0, 0, 2); // d2F/dZ2
double norm = 0;
for (int i = 0; i < 3; ++i) {
for (int j = 0; j < 3; ++j) {
norm = FastMath.max(norm, FastMath.abs(refCHessian[i][j]));
}
}
double[][] testCHessian = sc.toCartesianHessian(sHessian, sGradient);
for (int i = 0; i < 3; ++i) {
for (int j = 0; j < 3; ++j) {
Assert.assertEquals("" + FastMath.abs((refCHessian[i][j] - testCHessian[i][j]) / norm),
refCHessian[i][j], testCHessian[i][j], 1.0e-14 * norm);
}
}
}
}
}
}
Example 19
| Source File: SphericalCoordinatesTest.java From astor with GNU General Public License v2.0 | 4 votes |
|
@Test
public void testHessian() {
for (double r = 0.2; r < 10; r += 0.5) {
for (double theta = 0; theta < 2 * FastMath.PI; theta += 0.2) {
for (double phi = 0.1; phi < FastMath.PI; phi += 0.2) {
SphericalCoordinates sc = new SphericalCoordinates(r, theta, phi);
DerivativeStructure svalue = valueSpherical(new DerivativeStructure(3, 2, 0, r),
new DerivativeStructure(3, 2, 1, theta),
new DerivativeStructure(3, 2, 2, phi));
double[] sGradient = new double[] {
svalue.getPartialDerivative(1, 0, 0),
svalue.getPartialDerivative(0, 1, 0),
svalue.getPartialDerivative(0, 0, 1),
};
double[][] sHessian = new double[3][3];
sHessian[0][0] = svalue.getPartialDerivative(2, 0, 0); // d2F/dR2
sHessian[1][0] = svalue.getPartialDerivative(1, 1, 0); // d2F/dRdTheta
sHessian[2][0] = svalue.getPartialDerivative(1, 0, 1); // d2F/dRdPhi
sHessian[0][1] = Double.NaN; // just to check upper-right part is not used
sHessian[1][1] = svalue.getPartialDerivative(0, 2, 0); // d2F/dTheta2
sHessian[2][1] = svalue.getPartialDerivative(0, 1, 1); // d2F/dThetadPhi
sHessian[0][2] = Double.NaN; // just to check upper-right part is not used
sHessian[1][2] = Double.NaN; // just to check upper-right part is not used
sHessian[2][2] = svalue.getPartialDerivative(0, 0, 2); // d2F/dPhi2
DerivativeStructure cvalue = valueCartesian(new DerivativeStructure(3, 2, 0, sc.getCartesian().getX()),
new DerivativeStructure(3, 2, 1, sc.getCartesian().getY()),
new DerivativeStructure(3, 2, 2, sc.getCartesian().getZ()));
double[][] refCHessian = new double[3][3];
refCHessian[0][0] = cvalue.getPartialDerivative(2, 0, 0); // d2F/dX2
refCHessian[1][0] = cvalue.getPartialDerivative(1, 1, 0); // d2F/dXdY
refCHessian[2][0] = cvalue.getPartialDerivative(1, 0, 1); // d2F/dXdZ
refCHessian[0][1] = refCHessian[1][0];
refCHessian[1][1] = cvalue.getPartialDerivative(0, 2, 0); // d2F/dY2
refCHessian[2][1] = cvalue.getPartialDerivative(0, 1, 1); // d2F/dYdZ
refCHessian[0][2] = refCHessian[2][0];
refCHessian[1][2] = refCHessian[2][1];
refCHessian[2][2] = cvalue.getPartialDerivative(0, 0, 2); // d2F/dZ2
double norm = 0;
for (int i = 0; i < 3; ++i) {
for (int j = 0; j < 3; ++j) {
norm = FastMath.max(norm, FastMath.abs(refCHessian[i][j]));
}
}
double[][] testCHessian = sc.toCartesianHessian(sHessian, sGradient);
for (int i = 0; i < 3; ++i) {
for (int j = 0; j < 3; ++j) {
Assert.assertEquals("" + FastMath.abs((refCHessian[i][j] - testCHessian[i][j]) / norm),
refCHessian[i][j], testCHessian[i][j], 1.0e-14 * norm);
}
}
}
}
}
}
Example 20
| Source File: SphericalCoordinatesTest.java From astor with GNU General Public License v2.0 | 4 votes |
|
@Test
public void testHessian() {
for (double r = 0.2; r < 10; r += 0.5) {
for (double theta = 0; theta < 2 * FastMath.PI; theta += 0.2) {
for (double phi = 0.1; phi < FastMath.PI; phi += 0.2) {
SphericalCoordinates sc = new SphericalCoordinates(r, theta, phi);
DerivativeStructure svalue = valueSpherical(new DerivativeStructure(3, 2, 0, r),
new DerivativeStructure(3, 2, 1, theta),
new DerivativeStructure(3, 2, 2, phi));
double[] sGradient = new double[] {
svalue.getPartialDerivative(1, 0, 0),
svalue.getPartialDerivative(0, 1, 0),
svalue.getPartialDerivative(0, 0, 1),
};
double[][] sHessian = new double[3][3];
sHessian[0][0] = svalue.getPartialDerivative(2, 0, 0); // d2F/dR2
sHessian[1][0] = svalue.getPartialDerivative(1, 1, 0); // d2F/dRdTheta
sHessian[2][0] = svalue.getPartialDerivative(1, 0, 1); // d2F/dRdPhi
sHessian[0][1] = Double.NaN; // just to check upper-right part is not used
sHessian[1][1] = svalue.getPartialDerivative(0, 2, 0); // d2F/dTheta2
sHessian[2][1] = svalue.getPartialDerivative(0, 1, 1); // d2F/dThetadPhi
sHessian[0][2] = Double.NaN; // just to check upper-right part is not used
sHessian[1][2] = Double.NaN; // just to check upper-right part is not used
sHessian[2][2] = svalue.getPartialDerivative(0, 0, 2); // d2F/dPhi2
DerivativeStructure cvalue = valueCartesian(new DerivativeStructure(3, 2, 0, sc.getCartesian().getX()),
new DerivativeStructure(3, 2, 1, sc.getCartesian().getY()),
new DerivativeStructure(3, 2, 2, sc.getCartesian().getZ()));
double[][] refCHessian = new double[3][3];
refCHessian[0][0] = cvalue.getPartialDerivative(2, 0, 0); // d2F/dX2
refCHessian[1][0] = cvalue.getPartialDerivative(1, 1, 0); // d2F/dXdY
refCHessian[2][0] = cvalue.getPartialDerivative(1, 0, 1); // d2F/dXdZ
refCHessian[0][1] = refCHessian[1][0];
refCHessian[1][1] = cvalue.getPartialDerivative(0, 2, 0); // d2F/dY2
refCHessian[2][1] = cvalue.getPartialDerivative(0, 1, 1); // d2F/dYdZ
refCHessian[0][2] = refCHessian[2][0];
refCHessian[1][2] = refCHessian[2][1];
refCHessian[2][2] = cvalue.getPartialDerivative(0, 0, 2); // d2F/dZ2
double norm = 0;
for (int i = 0; i < 3; ++i) {
for (int j = 0; j < 3; ++j) {
norm = FastMath.max(norm, FastMath.abs(refCHessian[i][j]));
}
}
double[][] testCHessian = sc.toCartesianHessian(sHessian, sGradient);
for (int i = 0; i < 3; ++i) {
for (int j = 0; j < 3; ++j) {
Assert.assertEquals("" + FastMath.abs((refCHessian[i][j] - testCHessian[i][j]) / norm),
refCHessian[i][j], testCHessian[i][j], 1.0e-14 * norm);
}
}
}
}
}
}
