FieldDerivativeStructure.java
/*
* Licensed to the Hipparchus project under one or more
* contributor license agreements. See the NOTICE file distributed with
* this work for additional information regarding copyright ownership.
* The Hipparchus project licenses this file to You under the Apache License, Version 2.0
* (the "License"); you may not use this file except in compliance with
* the License. You may obtain a copy of the License at
*
* https://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package org.hipparchus.analysis.differentiation;
import org.hipparchus.CalculusFieldElement;
import org.hipparchus.Field;
import org.hipparchus.exception.MathIllegalArgumentException;
import org.hipparchus.exception.MathRuntimeException;
import org.hipparchus.util.FieldSinCos;
import org.hipparchus.util.FieldSinhCosh;
import org.hipparchus.util.MathArrays;
import org.hipparchus.util.MathUtils;
/** Class representing both the value and the differentials of a function.
* <p>This class is similar to {@link DerivativeStructure} except function
* parameters and value can be any {@link CalculusFieldElement}.</p>
* <p>Instances of this class are guaranteed to be immutable.</p>
* @see DerivativeStructure
* @see FDSFactory
* @see DSCompiler
* @param <T> the type of the field elements
*/
public class FieldDerivativeStructure<T extends CalculusFieldElement<T>>
implements FieldDerivative<T, FieldDerivativeStructure<T>> {
/** Factory that built the instance. */
private final FDSFactory<T> factory;
/** Combined array holding all values. */
private final T[] data;
/** Build an instance with all values and derivatives set to 0.
* @param factory factory that built the instance
* @param data combined array holding all values
*/
FieldDerivativeStructure(final FDSFactory<T> factory, final T[] data) {
this.factory = factory;
this.data = data.clone();
}
/** Build an instance with all values and derivatives set to 0.
* @param factory factory that built the instance
* @since 1.4
*/
FieldDerivativeStructure(final FDSFactory<T> factory) {
this.factory = factory;
this.data = MathArrays.buildArray(factory.getValueField(), factory.getCompiler().getSize());
}
/** {@inheritDoc} */
@Override
public FieldDerivativeStructure<T> newInstance(final double value) {
return factory.constant(value);
}
/** {@inheritDoc} */
@Override
public FieldDerivativeStructure<T> newInstance(final T value) {
return factory.constant(value);
}
/** {@inheritDoc} */
@Override
public FieldDerivativeStructure<T> withValue(final T value) {
final FieldDerivativeStructure<T> ds = factory.build();
System.arraycopy(data, 1, ds.data, 1, data.length - 1);
ds.data[0] = value;
return ds;
}
/** Get the factory that built the instance.
* @return factory that built the instance
*/
public FDSFactory<T> getFactory() {
return factory;
}
@Override
/** {@inheritDoc} */
public int getFreeParameters() {
return getFactory().getCompiler().getFreeParameters();
}
@Override
/** {@inheritDoc} */
public int getOrder() {
return getFactory().getCompiler().getOrder();
}
/** Set a derivative component.
* <p>
* This method is package-private (no modifier specified), as it is intended
* to be used only by Hipparchus classes since it relied on the ordering of
* derivatives within the class. This allows avoiding checks on the index,
* for performance reasons.
* </p>
* @param index index of the derivative
* @param value of the derivative to set
* @since 1.4
*/
void setDerivativeComponent(final int index, final T value) {
data[index] = value;
}
/** Get a derivative component.
* <p>
* This method is package-private (no modifier specified), as it is intended
* to be used only by Hipparchus classes since it relied on the ordering of
* derivatives within the class. This allows avoiding checks on the index,
* for performance reasons.
* </p>
* @param index index of the derivative
* @return value of the derivative
* @since 2.2
*/
T getDerivativeComponent(final int index) {
return data[index];
}
/** Get the value part of the derivative structure.
* @return value part of the derivative structure
* @see #getPartialDerivative(int...)
*/
@Override
public T getValue() {
return data[0];
}
/** {@inheritDoc} */
@Override
public T getPartialDerivative(final int ... orders)
throws MathIllegalArgumentException {
return data[factory.getCompiler().getPartialDerivativeIndex(orders)];
}
/** Get all partial derivatives.
* @return a fresh copy of partial derivatives, in an array sorted according to
* {@link DSCompiler#getPartialDerivativeIndex(int...)}
*/
public T[] getAllDerivatives() {
return data.clone();
}
/** {@inheritDoc}
*/
@Override
public FieldDerivativeStructure<T> add(final double a) {
final FieldDerivativeStructure<T> ds = factory.build();
System.arraycopy(data, 0, ds.data, 0, data.length);
ds.data[0] = ds.data[0].add(a);
return ds;
}
/** {@inheritDoc}
* @exception MathIllegalArgumentException if number of free parameters
* or orders do not match
*/
@Override
public FieldDerivativeStructure<T> add(final FieldDerivativeStructure<T> a)
throws MathIllegalArgumentException {
factory.checkCompatibility(a.factory);
final FieldDerivativeStructure<T> ds = factory.build();
factory.getCompiler().add(data, 0, a.data, 0, ds.data, 0);
return ds;
}
/** {@inheritDoc}
*/
@Override
public FieldDerivativeStructure<T> subtract(final double a) {
final FieldDerivativeStructure<T> ds = factory.build();
System.arraycopy(data, 0, ds.data, 0, data.length);
ds.data[0] = ds.data[0].subtract(a);
return ds;
}
/** {@inheritDoc}
* @exception MathIllegalArgumentException if number of free parameters
* or orders do not match
*/
@Override
public FieldDerivativeStructure<T> subtract(final FieldDerivativeStructure<T> a)
throws MathIllegalArgumentException {
factory.checkCompatibility(a.factory);
final FieldDerivativeStructure<T> ds = factory.build();
factory.getCompiler().subtract(data, 0, a.data, 0, ds.data, 0);
return ds;
}
/** '×' operator.
* @param a right hand side parameter of the operator
* @return this×a
*/
public FieldDerivativeStructure<T> multiply(final T a) {
final FieldDerivativeStructure<T> ds = factory.build();
for (int i = 0; i < ds.data.length; ++i) {
ds.data[i] = data[i].multiply(a);
}
return ds;
}
/** {@inheritDoc}
*/
@Override
public FieldDerivativeStructure<T> multiply(final double a) {
final FieldDerivativeStructure<T> ds = factory.build();
for (int i = 0; i < ds.data.length; ++i) {
ds.data[i] = data[i].multiply(a);
}
return ds;
}
/** {@inheritDoc}
* @exception MathIllegalArgumentException if number of free parameters
* or orders do not match
*/
@Override
public FieldDerivativeStructure<T> multiply(final FieldDerivativeStructure<T> a)
throws MathIllegalArgumentException {
factory.checkCompatibility(a.factory);
final FieldDerivativeStructure<T> result = factory.build();
factory.getCompiler().multiply(data, 0, a.data, 0, result.data, 0);
return result;
}
/** {@inheritDoc} */
@Override
public FieldDerivativeStructure<T> square() {
return multiply(this);
}
/** '÷' operator.
* @param a right hand side parameter of the operator
* @return this÷a
*/
public FieldDerivativeStructure<T> divide(final T a) {
final FieldDerivativeStructure<T> ds = factory.build();
for (int i = 0; i < ds.data.length; ++i) {
ds.data[i] = data[i].divide(a);
}
return ds;
}
/** {@inheritDoc}
*/
@Override
public FieldDerivativeStructure<T> divide(final double a) {
final FieldDerivativeStructure<T> ds = factory.build();
for (int i = 0; i < ds.data.length; ++i) {
ds.data[i] = data[i].divide(a);
}
return ds;
}
/** {@inheritDoc}
* @exception MathIllegalArgumentException if number of free parameters
* or orders do not match
*/
@Override
public FieldDerivativeStructure<T> divide(final FieldDerivativeStructure<T> a)
throws MathIllegalArgumentException {
factory.checkCompatibility(a.factory);
final FieldDerivativeStructure<T> result = factory.build();
factory.getCompiler().divide(data, 0, a.data, 0, result.data, 0);
return result;
}
/** IEEE remainder operator.
* @param a right hand side parameter of the operator
* @return this - n × a where n is the closest integer to this/a
* (the even integer is chosen for n if this/a is halfway between two integers)
*/
public FieldDerivativeStructure<T> remainder(final T a) {
final FieldDerivativeStructure<T> ds = factory.build();
System.arraycopy(data, 0, ds.data, 0, data.length);
ds.data[0] = data[0].remainder(a);
return ds;
}
/** {@inheritDoc} */
@Override
public FieldDerivativeStructure<T> remainder(final double a) {
final FieldDerivativeStructure<T> ds = factory.build();
System.arraycopy(data, 0, ds.data, 0, data.length);
ds.data[0] = data[0].remainder(a);
return ds;
}
/** {@inheritDoc}
* @exception MathIllegalArgumentException if number of free parameters
* or orders do not match
*/
@Override
public FieldDerivativeStructure<T> remainder(final FieldDerivativeStructure<T> a)
throws MathIllegalArgumentException {
factory.checkCompatibility(a.factory);
final FieldDerivativeStructure<T> result = factory.build();
factory.getCompiler().remainder(data, 0, a.data, 0, result.data, 0);
return result;
}
/** {@inheritDoc} */
@Override
public FieldDerivativeStructure<T> negate() {
final FieldDerivativeStructure<T> ds = factory.build();
for (int i = 0; i < ds.data.length; ++i) {
ds.data[i] = data[i].negate();
}
return ds;
}
/** {@inheritDoc}
*/
@Override
public FieldDerivativeStructure<T> abs() {
if (Double.doubleToLongBits(data[0].getReal()) < 0) {
// we use the bits representation to also handle -0.0
return negate();
} else {
return this;
}
}
/**
* Returns the instance with the sign of the argument.
* A NaN {@code sign} argument is treated as positive.
*
* @param sign the sign for the returned value
* @return the instance with the same sign as the {@code sign} argument
*/
public FieldDerivativeStructure<T> copySign(final T sign) {
long m = Double.doubleToLongBits(data[0].getReal());
long s = Double.doubleToLongBits(sign.getReal());
if ((m >= 0 && s >= 0) || (m < 0 && s < 0)) { // Sign is currently OK
return this;
}
return negate(); // flip sign
}
/** {@inheritDoc}
*/
@Override
public FieldDerivativeStructure<T> copySign(final double sign) {
long m = Double.doubleToLongBits(data[0].getReal());
long s = Double.doubleToLongBits(sign);
if ((m >= 0 && s >= 0) || (m < 0 && s < 0)) { // Sign is currently OK
return this;
}
return negate(); // flip sign
}
/** {@inheritDoc}
*/
@Override
public FieldDerivativeStructure<T> copySign(final FieldDerivativeStructure<T> sign) {
long m = Double.doubleToLongBits(data[0].getReal());
long s = Double.doubleToLongBits(sign.data[0].getReal());
if ((m >= 0 && s >= 0) || (m < 0 && s < 0)) { // Sign is currently OK
return this;
}
return negate(); // flip sign
}
/** {@inheritDoc}
*/
@Override
public FieldDerivativeStructure<T> scalb(final int n) {
final FieldDerivativeStructure<T> ds = factory.build();
for (int i = 0; i < ds.data.length; ++i) {
ds.data[i] = data[i].scalb(n);
}
return ds;
}
/** {@inheritDoc}
* @exception MathIllegalArgumentException if number of free parameters
* or orders do not match
*/
@Override
public FieldDerivativeStructure<T> hypot(final FieldDerivativeStructure<T> y)
throws MathIllegalArgumentException {
factory.checkCompatibility(y.factory);
if (data[0].isInfinite() || y.data[0].isInfinite()) {
return factory.constant(Double.POSITIVE_INFINITY);
} else if (data[0].isNaN() || y.data[0].isNaN()) {
return factory.constant(Double.NaN);
} else {
final int expX = getExponent();
final int expY = y.getExponent();
if (expX > expY + 27) {
// y is negligible with respect to x
return abs();
} else if (expY > expX + 27) {
// x is negligible with respect to y
return y.abs();
} else {
// find an intermediate scale to avoid both overflow and underflow
final int middleExp = (expX + expY) / 2;
// scale parameters without losing precision
final FieldDerivativeStructure<T> scaledX = scalb(-middleExp);
final FieldDerivativeStructure<T> scaledY = y.scalb(-middleExp);
// compute scaled hypotenuse
final FieldDerivativeStructure<T> scaledH =
scaledX.multiply(scaledX).add(scaledY.multiply(scaledY)).sqrt();
// remove scaling
return scaledH.scalb(middleExp);
}
}
}
/**
* Returns the hypotenuse of a triangle with sides {@code x} and {@code y}
* - sqrt(<i>x</i><sup>2</sup> +<i>y</i><sup>2</sup>)
* avoiding intermediate overflow or underflow.
*
* <ul>
* <li> If either argument is infinite, then the result is positive infinity.</li>
* <li> else, if either argument is NaN then the result is NaN.</li>
* </ul>
*
* @param x a value
* @param y a value
* @return sqrt(<i>x</i><sup>2</sup> +<i>y</i><sup>2</sup>)
* @exception MathIllegalArgumentException if number of free parameters
* or orders do not match
* @param <T> the type of the field elements
*/
public static <T extends CalculusFieldElement<T>> FieldDerivativeStructure<T>
hypot(final FieldDerivativeStructure<T> x, final FieldDerivativeStructure<T> y)
throws MathIllegalArgumentException {
return x.hypot(y);
}
/** Compute composition of the instance by a univariate function.
* @param f array of value and derivatives of the function at
* the current point (i.e. [f({@link #getValue()}),
* f'({@link #getValue()}), f''({@link #getValue()})...]).
* @return f(this)
* @exception MathIllegalArgumentException if the number of derivatives
* in the array is not equal to {@link #getOrder() order} + 1
*/
@SafeVarargs
public final FieldDerivativeStructure<T> compose(final T ... f)
throws MathIllegalArgumentException {
MathUtils.checkDimension(f.length, getOrder() + 1);
final FieldDerivativeStructure<T> result = factory.build();
factory.getCompiler().compose(data, 0, f, result.data, 0);
return result;
}
/** Compute composition of the instance by a univariate function.
* @param f array of value and derivatives of the function at
* the current point (i.e. [f({@link #getValue()}),
* f'({@link #getValue()}), f''({@link #getValue()})...]).
* @return f(this)
* @exception MathIllegalArgumentException if the number of derivatives
* in the array is not equal to {@link #getOrder() order} + 1
*/
public FieldDerivativeStructure<T> compose(final double ... f)
throws MathIllegalArgumentException {
MathUtils.checkDimension(f.length, getOrder() + 1);
final FieldDerivativeStructure<T> result = factory.build();
factory.getCompiler().compose(data, 0, f, result.data, 0);
return result;
}
/** {@inheritDoc} */
@Override
public FieldDerivativeStructure<T> reciprocal() {
final FieldDerivativeStructure<T> result = factory.build();
factory.getCompiler().reciprocal(data, 0, result.data, 0);
return result;
}
/** {@inheritDoc}
*/
@Override
public FieldDerivativeStructure<T> sqrt() {
final FieldDerivativeStructure<T> result = factory.build();
factory.getCompiler().sqrt(data, 0, result.data, 0);
return result;
}
/** {@inheritDoc}
*/
@Override
public FieldDerivativeStructure<T> rootN(final int n) {
final FieldDerivativeStructure<T> result = factory.build();
factory.getCompiler().rootN(data, 0, n, result.data, 0);
return result;
}
/** {@inheritDoc} */
@Override
public Field<FieldDerivativeStructure<T>> getField() {
return factory.getDerivativeField();
}
/** Compute a<sup>x</sup> where a is a double and x a {@link FieldDerivativeStructure}
* @param a number to exponentiate
* @param x power to apply
* @param <T> the type of the field elements
* @return a<sup>x</sup>
*/
public static <T extends CalculusFieldElement<T>> FieldDerivativeStructure<T> pow(final double a, final FieldDerivativeStructure<T> x) {
final FieldDerivativeStructure<T> result = x.factory.build();
x.factory.getCompiler().pow(a, x.data, 0, result.data, 0);
return result;
}
/** {@inheritDoc}
*/
@Override
public FieldDerivativeStructure<T> pow(final double p) {
final FieldDerivativeStructure<T> result = factory.build();
factory.getCompiler().pow(data, 0, p, result.data, 0);
return result;
}
/** {@inheritDoc}
*/
@Override
public FieldDerivativeStructure<T> pow(final int n) {
final FieldDerivativeStructure<T> result = factory.build();
factory.getCompiler().pow(data, 0, n, result.data, 0);
return result;
}
/** {@inheritDoc}
* @exception MathIllegalArgumentException if number of free parameters
* or orders do not match
*/
@Override
public FieldDerivativeStructure<T> pow(final FieldDerivativeStructure<T> e)
throws MathIllegalArgumentException {
factory.checkCompatibility(e.factory);
final FieldDerivativeStructure<T> result = factory.build();
factory.getCompiler().pow(data, 0, e.data, 0, result.data, 0);
return result;
}
/** {@inheritDoc}
*/
@Override
public FieldDerivativeStructure<T> exp() {
final FieldDerivativeStructure<T> result = factory.build();
factory.getCompiler().exp(data, 0, result.data, 0);
return result;
}
/** {@inheritDoc}
*/
@Override
public FieldDerivativeStructure<T> expm1() {
final FieldDerivativeStructure<T> result = factory.build();
factory.getCompiler().expm1(data, 0, result.data, 0);
return result;
}
/** {@inheritDoc}
*/
@Override
public FieldDerivativeStructure<T> log() {
final FieldDerivativeStructure<T> result = factory.build();
factory.getCompiler().log(data, 0, result.data, 0);
return result;
}
/** {@inheritDoc}
*/
@Override
public FieldDerivativeStructure<T> log1p() {
final FieldDerivativeStructure<T> result = factory.build();
factory.getCompiler().log1p(data, 0, result.data, 0);
return result;
}
/** Base 10 logarithm.
* @return base 10 logarithm of the instance
*/
@Override
public FieldDerivativeStructure<T> log10() {
final FieldDerivativeStructure<T> result = factory.build();
factory.getCompiler().log10(data, 0, result.data, 0);
return result;
}
/** {@inheritDoc}
*/
@Override
public FieldDerivativeStructure<T> cos() {
final FieldDerivativeStructure<T> result = factory.build();
factory.getCompiler().cos(data, 0, result.data, 0);
return result;
}
/** {@inheritDoc}
*/
@Override
public FieldDerivativeStructure<T> sin() {
final FieldDerivativeStructure<T> result = factory.build();
factory.getCompiler().sin(data, 0, result.data, 0);
return result;
}
/** {@inheritDoc}
*/
@Override
public FieldSinCos<FieldDerivativeStructure<T>> sinCos() {
final FieldDerivativeStructure<T> sin = factory.build();
final FieldDerivativeStructure<T> cos = factory.build();
factory.getCompiler().sinCos(data, 0, sin.data, 0, cos.data, 0);
return new FieldSinCos<>(sin, cos);
}
/** {@inheritDoc}
*/
@Override
public FieldDerivativeStructure<T> tan() {
final FieldDerivativeStructure<T> result = factory.build();
factory.getCompiler().tan(data, 0, result.data, 0);
return result;
}
/** {@inheritDoc}
*/
@Override
public FieldDerivativeStructure<T> acos() {
final FieldDerivativeStructure<T> result = factory.build();
factory.getCompiler().acos(data, 0, result.data, 0);
return result;
}
/** {@inheritDoc}
*/
@Override
public FieldDerivativeStructure<T> asin() {
final FieldDerivativeStructure<T> result = factory.build();
factory.getCompiler().asin(data, 0, result.data, 0);
return result;
}
/** {@inheritDoc}
*/
@Override
public FieldDerivativeStructure<T> atan() {
final FieldDerivativeStructure<T> result = factory.build();
factory.getCompiler().atan(data, 0, result.data, 0);
return result;
}
/** {@inheritDoc}
*/
@Override
public FieldDerivativeStructure<T> atan2(final FieldDerivativeStructure<T> x)
throws MathIllegalArgumentException {
factory.checkCompatibility(x.factory);
final FieldDerivativeStructure<T> result = factory.build();
factory.getCompiler().atan2(data, 0, x.data, 0, result.data, 0);
return result;
}
/** Two arguments arc tangent operation.
* @param y first argument of the arc tangent
* @param x second argument of the arc tangent
* @param <T> the type of the field elements
* @return atan2(y, x)
* @exception MathIllegalArgumentException if number of free parameters
* or orders do not match
*/
public static <T extends CalculusFieldElement<T>> FieldDerivativeStructure<T> atan2(final FieldDerivativeStructure<T> y,
final FieldDerivativeStructure<T> x)
throws MathIllegalArgumentException {
return y.atan2(x);
}
/** {@inheritDoc}
*/
@Override
public FieldDerivativeStructure<T> cosh() {
final FieldDerivativeStructure<T> result = factory.build();
factory.getCompiler().cosh(data, 0, result.data, 0);
return result;
}
/** {@inheritDoc}
*/
@Override
public FieldDerivativeStructure<T> sinh() {
final FieldDerivativeStructure<T> result = factory.build();
factory.getCompiler().sinh(data, 0, result.data, 0);
return result;
}
/** {@inheritDoc}
*/
@Override
public FieldSinhCosh<FieldDerivativeStructure<T>> sinhCosh() {
final FieldDerivativeStructure<T> sinh = factory.build();
final FieldDerivativeStructure<T> cosh = factory.build();
factory.getCompiler().sinhCosh(data, 0, sinh.data, 0, cosh.data, 0);
return new FieldSinhCosh<>(sinh, cosh);
}
/** {@inheritDoc}
*/
@Override
public FieldDerivativeStructure<T> tanh() {
final FieldDerivativeStructure<T> result = factory.build();
factory.getCompiler().tanh(data, 0, result.data, 0);
return result;
}
/** {@inheritDoc}
*/
@Override
public FieldDerivativeStructure<T> acosh() {
final FieldDerivativeStructure<T> result = factory.build();
factory.getCompiler().acosh(data, 0, result.data, 0);
return result;
}
/** {@inheritDoc}
*/
@Override
public FieldDerivativeStructure<T> asinh() {
final FieldDerivativeStructure<T> result = factory.build();
factory.getCompiler().asinh(data, 0, result.data, 0);
return result;
}
/** {@inheritDoc}
*/
@Override
public FieldDerivativeStructure<T> atanh() {
final FieldDerivativeStructure<T> result = factory.build();
factory.getCompiler().atanh(data, 0, result.data, 0);
return result;
}
/** {@inheritDoc} */
@Override
public FieldDerivativeStructure<T> toDegrees() {
final FieldDerivativeStructure<T> ds = factory.build();
for (int i = 0; i < ds.data.length; ++i) {
ds.data[i] = data[i].toDegrees();
}
return ds;
}
/** {@inheritDoc} */
@Override
public FieldDerivativeStructure<T> toRadians() {
final FieldDerivativeStructure<T> ds = factory.build();
for (int i = 0; i < ds.data.length; ++i) {
ds.data[i] = data[i].toRadians();
}
return ds;
}
/** Integrate w.r.t. one independent variable.
* <p>
* Rigorously, if the derivatives of a function are known up to
* order N, the ones of its M-th integral w.r.t. a given variable
* (seen as a function itself) are actually known up to order N+M.
* However, this method still casts the output as a DerivativeStructure
* of order N. The integration constants are systematically set to zero.
* </p>
* @param varIndex Index of independent variable w.r.t. which integration is done.
* @param integrationOrder Number of times the integration operator must be applied. If non-positive, call the
* differentiation operator.
* @return DerivativeStructure on which integration operator has been applied a certain number of times.
* @since 2.2
*/
public FieldDerivativeStructure<T> integrate(final int varIndex, final int integrationOrder) {
// Deal first with trivial case
if (integrationOrder > getOrder()) {
return factory.constant(0.);
} else if (integrationOrder == 0) {
return factory.build(data);
}
// Call 'inverse' (not rigorously) operation if necessary
if (integrationOrder < 0) {
return differentiate(varIndex, -integrationOrder);
}
final T[] newData = MathArrays.buildArray(factory.getValueField(), data.length);
final DSCompiler dsCompiler = factory.getCompiler();
for (int i = 0; i < newData.length; i++) {
if (!data[i].isZero()) {
final int[] orders = dsCompiler.getPartialDerivativeOrders(i);
int sum = 0;
for (int order : orders) {
sum += order;
}
if (sum + integrationOrder <= getOrder()) {
final int saved = orders[varIndex];
orders[varIndex] += integrationOrder;
final int index = dsCompiler.getPartialDerivativeIndex(orders);
orders[varIndex] = saved;
newData[index] = data[i];
}
}
}
return factory.build(newData);
}
/** Differentiate w.r.t. one independent variable.
* <p>
* Rigorously, if the derivatives of a function are known up to
* order N, the ones of its M-th derivative w.r.t. a given variable
* (seen as a function itself) are only known up to order N-M.
* However, this method still casts the output as a DerivativeStructure
* of order N with zeroes for the higher order terms.
* </p>
* @param varIndex Index of independent variable w.r.t. which differentiation is done.
* @param differentiationOrder Number of times the differentiation operator must be applied. If non-positive, call
* the integration operator instead.
* @return DerivativeStructure on which differentiation operator has been applied a certain number of times
* @since 2.2
*/
public FieldDerivativeStructure<T> differentiate(final int varIndex, final int differentiationOrder) {
// Deal first with trivial case
if (differentiationOrder > getOrder()) {
return factory.constant(0.);
} else if (differentiationOrder == 0) {
return factory.build(data);
}
// Call 'inverse' (not rigorously) operation if necessary
if (differentiationOrder < 0) {
return integrate(varIndex, -differentiationOrder);
}
final T[] newData = MathArrays.buildArray(factory.getValueField(), data.length);
final DSCompiler dsCompiler = factory.getCompiler();
for (int i = 0; i < newData.length; i++) {
if (!data[i].isZero()) {
final int[] orders = dsCompiler.getPartialDerivativeOrders(i);
if (orders[varIndex] - differentiationOrder >= 0) {
final int saved = orders[varIndex];
orders[varIndex] -= differentiationOrder;
final int index = dsCompiler.getPartialDerivativeIndex(orders);
orders[varIndex] = saved;
newData[index] = data[i];
}
}
}
return factory.build(newData);
}
/** Evaluate Taylor expansion of a derivative structure.
* @param delta parameters offsets (Δx, Δy, ...)
* @return value of the Taylor expansion at x + Δx, y + Δy, ...
* @throws MathRuntimeException if factorials becomes too large
*/
@SafeVarargs
public final T taylor(final T ... delta) throws MathRuntimeException {
return factory.getCompiler().taylor(data, 0, delta);
}
/** Evaluate Taylor expansion of a derivative structure.
* @param delta parameters offsets (Δx, Δy, ...)
* @return value of the Taylor expansion at x + Δx, y + Δy, ...
* @throws MathRuntimeException if factorials becomes too large
*/
public T taylor(final double ... delta) throws MathRuntimeException {
return factory.getCompiler().taylor(data, 0, delta);
}
/** Rebase instance with respect to low level parameter functions.
* <p>
* The instance is considered to be a function of {@link #getFreeParameters()
* n free parameters} up to order {@link #getOrder() o} \(f(p_0, p_1, \ldots p_{n-1})\).
* Its {@link #getPartialDerivative(int...) partial derivatives} are therefore
* \(f, \frac{\partial f}{\partial p_0}, \frac{\partial f}{\partial p_1}, \ldots
* \frac{\partial^2 f}{\partial p_0^2}, \frac{\partial^2 f}{\partial p_0 p_1},
* \ldots \frac{\partial^o f}{\partial p_{n-1}^o}\). The free parameters
* \(p_0, p_1, \ldots p_{n-1}\) are considered to be functions of \(m\) lower
* level other parameters \(q_0, q_1, \ldots q_{m-1}\).
* </p>
* \( \begin{align}
* p_0 & = p_0(q_0, q_1, \ldots q_{m-1})\\
* p_1 & = p_1(q_0, q_1, \ldots q_{m-1})\\
* p_{n-1} & = p_{n-1}(q_0, q_1, \ldots q_{m-1})
* \end{align}\)
* <p>
* This method compute the composition of the partial derivatives of \(f\)
* and the partial derivatives of \(p_0, p_1, \ldots p_{n-1}\), i.e. the
* {@link #getPartialDerivative(int...) partial derivatives} of the value
* returned will be
* \(f, \frac{\partial f}{\partial q_0}, \frac{\partial f}{\partial q_1}, \ldots
* \frac{\partial^2 f}{\partial q_0^2}, \frac{\partial^2 f}{\partial q_0 q_1},
* \ldots \frac{\partial^o f}{\partial q_{m-1}^o}\).
* </p>
* <p>
* The number of parameters must match {@link #getFreeParameters()} and the
* derivation orders of the instance and parameters must also match.
* </p>
* @param p base parameters with respect to which partial derivatives
* were computed in the instance
* @return derivative structure with partial derivatives computed
* with respect to the lower level parameters used in the \(p_i\)
* @since 2.2
*/
public FieldDerivativeStructure<T> rebase(@SuppressWarnings("unchecked") final FieldDerivativeStructure<T>... p) {
MathUtils.checkDimension(getFreeParameters(), p.length);
// handle special case of no variables at all
if (p.length == 0) {
return this;
}
final int pSize = p[0].getFactory().getCompiler().getSize();
final T[] pData = MathArrays.buildArray(p[0].getFactory().getValueField(), p.length * pSize);
for (int i = 0; i < p.length; ++i) {
MathUtils.checkDimension(getOrder(), p[i].getOrder());
MathUtils.checkDimension(p[0].getFreeParameters(), p[i].getFreeParameters());
System.arraycopy(p[i].data, 0, pData, i * pSize, pSize);
}
final FieldDerivativeStructure<T> result = p[0].factory.build();
factory.getCompiler().rebase(data, 0, p[0].factory.getCompiler(), pData, result.data, 0);
return result;
}
/** {@inheritDoc}
* @exception MathIllegalArgumentException if number of free parameters
* or orders do not match
*/
@Override
public FieldDerivativeStructure<T> linearCombination(final FieldDerivativeStructure<T>[] a,
final FieldDerivativeStructure<T>[] b)
throws MathIllegalArgumentException {
// compute an accurate value, taking care of cancellations
final T[] aT = MathArrays.buildArray(factory.getValueField(), a.length);
for (int i = 0; i < a.length; ++i) {
aT[i] = a[i].getValue();
}
final T[] bT = MathArrays.buildArray(factory.getValueField(), b.length);
for (int i = 0; i < b.length; ++i) {
bT[i] = b[i].getValue();
}
final T accurateValue = aT[0].linearCombination(aT, bT);
// compute a simple value, with all partial derivatives
FieldDerivativeStructure<T> simpleValue = a[0].getField().getZero();
for (int i = 0; i < a.length; ++i) {
simpleValue = simpleValue.add(a[i].multiply(b[i]));
}
// create a result with accurate value and all derivatives (not necessarily as accurate as the value)
final T[] all = simpleValue.getAllDerivatives();
all[0] = accurateValue;
return factory.build(all);
}
/**
* Compute a linear combination.
* @param a Factors.
* @param b Factors.
* @return <code>Σ<sub>i</sub> a<sub>i</sub> b<sub>i</sub></code>.
* @throws MathIllegalArgumentException if arrays dimensions don't match
*/
public FieldDerivativeStructure<T> linearCombination(final T[] a, final FieldDerivativeStructure<T>[] b)
throws MathIllegalArgumentException {
// compute an accurate value, taking care of cancellations
final T[] bT = MathArrays.buildArray(factory.getValueField(), b.length);
for (int i = 0; i < b.length; ++i) {
bT[i] = b[i].getValue();
}
final T accurateValue = bT[0].linearCombination(a, bT);
// compute a simple value, with all partial derivatives
FieldDerivativeStructure<T> simpleValue = b[0].getField().getZero();
for (int i = 0; i < a.length; ++i) {
simpleValue = simpleValue.add(b[i].multiply(a[i]));
}
// create a result with accurate value and all derivatives (not necessarily as accurate as the value)
final T[] all = simpleValue.getAllDerivatives();
all[0] = accurateValue;
return factory.build(all);
}
/** {@inheritDoc}
* @exception MathIllegalArgumentException if number of free parameters
* or orders do not match
*/
@Override
public FieldDerivativeStructure<T> linearCombination(final double[] a, final FieldDerivativeStructure<T>[] b)
throws MathIllegalArgumentException {
// compute an accurate value, taking care of cancellations
final T[] bT = MathArrays.buildArray(factory.getValueField(), b.length);
for (int i = 0; i < b.length; ++i) {
bT[i] = b[i].getValue();
}
final T accurateValue = bT[0].linearCombination(a, bT);
// compute a simple value, with all partial derivatives
FieldDerivativeStructure<T> simpleValue = b[0].getField().getZero();
for (int i = 0; i < a.length; ++i) {
simpleValue = simpleValue.add(b[i].multiply(a[i]));
}
// create a result with accurate value and all derivatives (not necessarily as accurate as the value)
final T[] all = simpleValue.getAllDerivatives();
all[0] = accurateValue;
return factory.build(all);
}
/** {@inheritDoc}
* @exception MathIllegalArgumentException if number of free parameters
* or orders do not match
*/
@Override
public FieldDerivativeStructure<T> linearCombination(final FieldDerivativeStructure<T> a1, final FieldDerivativeStructure<T> b1,
final FieldDerivativeStructure<T> a2, final FieldDerivativeStructure<T> b2)
throws MathIllegalArgumentException {
// compute an accurate value, taking care of cancellations
final T accurateValue = a1.getValue().linearCombination(a1.getValue(), b1.getValue(),
a2.getValue(), b2.getValue());
// compute a simple value, with all partial derivatives
final FieldDerivativeStructure<T> simpleValue = a1.multiply(b1).add(a2.multiply(b2));
// create a result with accurate value and all derivatives (not necessarily as accurate as the value)
final T[] all = simpleValue.getAllDerivatives();
all[0] = accurateValue;
return factory.build(all);
}
/**
* Compute a linear combination.
* @param a1 first factor of the first term
* @param b1 second factor of the first term
* @param a2 first factor of the second term
* @param b2 second factor of the second term
* @return a<sub>1</sub>×b<sub>1</sub> +
* a<sub>2</sub>×b<sub>2</sub>
* @see #linearCombination(double, FieldDerivativeStructure, double, FieldDerivativeStructure)
* @see #linearCombination(double, FieldDerivativeStructure, double, FieldDerivativeStructure, double, FieldDerivativeStructure, double, FieldDerivativeStructure)
* @exception MathIllegalArgumentException if number of free parameters or orders are inconsistent
*/
public FieldDerivativeStructure<T> linearCombination(final T a1, final FieldDerivativeStructure<T> b1,
final T a2, final FieldDerivativeStructure<T> b2)
throws MathIllegalArgumentException {
factory.checkCompatibility(b1.factory);
factory.checkCompatibility(b2.factory);
final FieldDerivativeStructure<T> ds = factory.build();
factory.getCompiler().linearCombination(a1, b1.data, 0,
a2, b2.data, 0,
ds.data, 0);
return ds;
}
/** {@inheritDoc}
* @exception MathIllegalArgumentException if number of free parameters
* or orders do not match
*/
@Override
public FieldDerivativeStructure<T> linearCombination(final double a1, final FieldDerivativeStructure<T> b1,
final double a2, final FieldDerivativeStructure<T> b2)
throws MathIllegalArgumentException {
factory.checkCompatibility(b1.factory);
factory.checkCompatibility(b2.factory);
final FieldDerivativeStructure<T> ds = factory.build();
factory.getCompiler().linearCombination(a1, b1.data, 0,
a2, b2.data, 0,
ds.data, 0);
return ds;
}
/** {@inheritDoc}
* @exception MathIllegalArgumentException if number of free parameters
* or orders do not match
*/
@Override
public FieldDerivativeStructure<T> linearCombination(final FieldDerivativeStructure<T> a1, final FieldDerivativeStructure<T> b1,
final FieldDerivativeStructure<T> a2, final FieldDerivativeStructure<T> b2,
final FieldDerivativeStructure<T> a3, final FieldDerivativeStructure<T> b3)
throws MathIllegalArgumentException {
// compute an accurate value, taking care of cancellations
final T accurateValue = a1.getValue().linearCombination(a1.getValue(), b1.getValue(),
a2.getValue(), b2.getValue(),
a3.getValue(), b3.getValue());
// compute a simple value, with all partial derivatives
final FieldDerivativeStructure<T> simpleValue = a1.multiply(b1).add(a2.multiply(b2)).add(a3.multiply(b3));
// create a result with accurate value and all derivatives (not necessarily as accurate as the value)
final T[] all = simpleValue.getAllDerivatives();
all[0] = accurateValue;
return factory.build(all);
}
/**
* Compute a linear combination.
* @param a1 first factor of the first term
* @param b1 second factor of the first term
* @param a2 first factor of the second term
* @param b2 second factor of the second term
* @param a3 first factor of the third term
* @param b3 second factor of the third term
* @return a<sub>1</sub>×b<sub>1</sub> +
* a<sub>2</sub>×b<sub>2</sub> + a<sub>3</sub>×b<sub>3</sub>
* @see #linearCombination(double, FieldDerivativeStructure, double, FieldDerivativeStructure)
* @see #linearCombination(double, FieldDerivativeStructure, double, FieldDerivativeStructure, double, FieldDerivativeStructure, double, FieldDerivativeStructure)
* @exception MathIllegalArgumentException if number of free parameters or orders are inconsistent
*/
public FieldDerivativeStructure<T> linearCombination(final T a1, final FieldDerivativeStructure<T> b1,
final T a2, final FieldDerivativeStructure<T> b2,
final T a3, final FieldDerivativeStructure<T> b3)
throws MathIllegalArgumentException {
factory.checkCompatibility(b1.factory);
factory.checkCompatibility(b2.factory);
factory.checkCompatibility(b3.factory);
final FieldDerivativeStructure<T> ds = factory.build();
factory.getCompiler().linearCombination(a1, b1.data, 0,
a2, b2.data, 0,
a3, b3.data, 0,
ds.data, 0);
return ds;
}
/** {@inheritDoc}
* @exception MathIllegalArgumentException if number of free parameters
* or orders do not match
*/
@Override
public FieldDerivativeStructure<T> linearCombination(final double a1, final FieldDerivativeStructure<T> b1,
final double a2, final FieldDerivativeStructure<T> b2,
final double a3, final FieldDerivativeStructure<T> b3)
throws MathIllegalArgumentException {
factory.checkCompatibility(b1.factory);
factory.checkCompatibility(b2.factory);
factory.checkCompatibility(b3.factory);
final FieldDerivativeStructure<T> ds = factory.build();
factory.getCompiler().linearCombination(a1, b1.data, 0,
a2, b2.data, 0,
a3, b3.data, 0,
ds.data, 0);
return ds;
}
/** {@inheritDoc}
* @exception MathIllegalArgumentException if number of free parameters
* or orders do not match
*/
@Override
public FieldDerivativeStructure<T> linearCombination(final FieldDerivativeStructure<T> a1, final FieldDerivativeStructure<T> b1,
final FieldDerivativeStructure<T> a2, final FieldDerivativeStructure<T> b2,
final FieldDerivativeStructure<T> a3, final FieldDerivativeStructure<T> b3,
final FieldDerivativeStructure<T> a4, final FieldDerivativeStructure<T> b4)
throws MathIllegalArgumentException {
// compute an accurate value, taking care of cancellations
final T accurateValue = a1.getValue().linearCombination(a1.getValue(), b1.getValue(),
a2.getValue(), b2.getValue(),
a3.getValue(), b3.getValue(),
a4.getValue(), b4.getValue());
// compute a simple value, with all partial derivatives
final FieldDerivativeStructure<T> simpleValue = a1.multiply(b1).add(a2.multiply(b2)).add(a3.multiply(b3)).add(a4.multiply(b4));
// create a result with accurate value and all derivatives (not necessarily as accurate as the value)
final T[] all = simpleValue.getAllDerivatives();
all[0] = accurateValue;
return factory.build(all);
}
/**
* Compute a linear combination.
* @param a1 first factor of the first term
* @param b1 second factor of the first term
* @param a2 first factor of the second term
* @param b2 second factor of the second term
* @param a3 first factor of the third term
* @param b3 second factor of the third term
* @param a4 first factor of the third term
* @param b4 second factor of the third term
* @return a<sub>1</sub>×b<sub>1</sub> +
* a<sub>2</sub>×b<sub>2</sub> + a<sub>3</sub>×b<sub>3</sub> +
* a<sub>4</sub>×b<sub>4</sub>
* @see #linearCombination(double, FieldDerivativeStructure, double, FieldDerivativeStructure)
* @see #linearCombination(double, FieldDerivativeStructure, double, FieldDerivativeStructure, double, FieldDerivativeStructure)
* @exception MathIllegalArgumentException if number of free parameters or orders are inconsistent
*/
public FieldDerivativeStructure<T> linearCombination(final T a1, final FieldDerivativeStructure<T> b1,
final T a2, final FieldDerivativeStructure<T> b2,
final T a3, final FieldDerivativeStructure<T> b3,
final T a4, final FieldDerivativeStructure<T> b4)
throws MathIllegalArgumentException {
factory.checkCompatibility(b1.factory);
factory.checkCompatibility(b2.factory);
factory.checkCompatibility(b3.factory);
factory.checkCompatibility(b4.factory);
final FieldDerivativeStructure<T> ds = factory.build();
factory.getCompiler().linearCombination(a1, b1.data, 0,
a2, b2.data, 0,
a3, b3.data, 0,
a4, b4.data, 0,
ds.data, 0);
return ds;
}
/** {@inheritDoc}
* @exception MathIllegalArgumentException if number of free parameters
* or orders do not match
*/
@Override
public FieldDerivativeStructure<T> linearCombination(final double a1, final FieldDerivativeStructure<T> b1,
final double a2, final FieldDerivativeStructure<T> b2,
final double a3, final FieldDerivativeStructure<T> b3,
final double a4, final FieldDerivativeStructure<T> b4)
throws MathIllegalArgumentException {
factory.checkCompatibility(b1.factory);
factory.checkCompatibility(b2.factory);
factory.checkCompatibility(b3.factory);
factory.checkCompatibility(b4.factory);
final FieldDerivativeStructure<T> ds = factory.build();
factory.getCompiler().linearCombination(a1, b1.data, 0,
a2, b2.data, 0,
a3, b3.data, 0,
a4, b4.data, 0,
ds.data, 0);
return ds;
}
/** {@inheritDoc}
*/
@Override
public FieldDerivativeStructure<T> getPi() {
return factory.getDerivativeField().getPi();
}
}