Examples of UnivariateDifferentiableFunction

org.apache.commons.math3.analysis.differentiation.UnivariateDifferentiableFunction
Interface for univariate functions derivatives.
This interface represents a simple function which computes both the value and the first derivative of a mathematical function. The derivative is computed with respect to the input variable.
@see UnivariateDifferentiableFunction @see UnivariateFunctionDifferentiator @since 3.1

Examples of org.apache.commons.math3.analysis.differentiation.UnivariateDifferentiableFunction

     * @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);
            }

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Examples of org.apache.commons.math3.analysis.differentiation.UnivariateDifferentiableFunction

        Assert.assertEquals(81, FunctionUtils.compose(pow, pow).value(3), EPS);
    }


    @Test
    public void testComposeDifferentiable() {
        UnivariateDifferentiableFunction id = new Identity();
        Assert.assertEquals(1, FunctionUtils.compose(id, id, id).value(new DerivativeStructure(1, 1, 0, 3)).getPartialDerivative(1), EPS);


        UnivariateDifferentiableFunction c = new Constant(4);
        Assert.assertEquals(0, FunctionUtils.compose(id, c).value(new DerivativeStructure(1, 1, 0, 3)).getPartialDerivative(1), EPS);
        Assert.assertEquals(0, FunctionUtils.compose(c, id).value(new DerivativeStructure(1, 1, 0, 3)).getPartialDerivative(1), EPS);


        UnivariateDifferentiableFunction m = new Minus();
        Assert.assertEquals(-1, FunctionUtils.compose(m).value(new DerivativeStructure(1, 1, 0, 3)).getPartialDerivative(1), EPS);
        Assert.assertEquals(1, FunctionUtils.compose(m, m).value(new DerivativeStructure(1, 1, 0, 3)).getPartialDerivative(1), EPS);


        UnivariateDifferentiableFunction inv = new Inverse();
        Assert.assertEquals(0.25, FunctionUtils.compose(inv, m, id).value(new DerivativeStructure(1, 1, 0, 2)).getPartialDerivative(1), EPS);


        UnivariateDifferentiableFunction pow = new Power(2);
        Assert.assertEquals(108, FunctionUtils.compose(pow, pow).value(new DerivativeStructure(1, 1, 0, 3)).getPartialDerivative(1), EPS);


        UnivariateDifferentiableFunction log = new Log();
        double a = 9876.54321;
        Assert.assertEquals(pow.value(new DerivativeStructure(1, 1, 0, a)).getPartialDerivative(1) / pow.value(a),
                            FunctionUtils.compose(log, pow).value(new DerivativeStructure(1, 1, 0, a)).getPartialDerivative(1), EPS);
    }

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Examples of org.apache.commons.math3.analysis.differentiation.UnivariateDifferentiableFunction

        Assert.assertEquals(4 - 2, FunctionUtils.add(c, FunctionUtils.compose(m, id)).value(2), EPS);
    }


    @Test
    public void testAddDifferentiable() {
        UnivariateDifferentiableFunction sin = new Sin();
        UnivariateDifferentiableFunction c = new Constant(4);
        UnivariateDifferentiableFunction m = new Minus();
        UnivariateDifferentiableFunction inv = new Inverse();


        final double a = 123.456;
        Assert.assertEquals(- 1 / (a * a) -1 + FastMath.cos(a),
                            FunctionUtils.add(inv, m, c, sin).value(new DerivativeStructure(1, 1, 0, a)).getPartialDerivative(1),
                            EPS);

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Examples of org.apache.commons.math3.analysis.differentiation.UnivariateDifferentiableFunction

        Assert.assertEquals(1, FunctionUtils.multiply(FunctionUtils.compose(inv, pow), pow).value(3.5), EPS);
    }


    @Test
    public void testMultiplyDifferentiable() {
        UnivariateDifferentiableFunction c = new Constant(4);
        UnivariateDifferentiableFunction id = new Identity();
        final double a = 1.2345678;
        Assert.assertEquals(8 * a, FunctionUtils.multiply(c, id, id).value(new DerivativeStructure(1, 1, 0, a)).getPartialDerivative(1), EPS);


        UnivariateDifferentiableFunction inv = new Inverse();
        UnivariateDifferentiableFunction pow = new Power(2.5);
        UnivariateDifferentiableFunction cos = new Cos();
        Assert.assertEquals(1.5 * FastMath.sqrt(a) * FastMath.cos(a) - FastMath.pow(a, 1.5) * FastMath.sin(a),
                            FunctionUtils.multiply(inv, pow, cos).value(new DerivativeStructure(1, 1, 0, a)).getPartialDerivative(1), EPS);


        UnivariateDifferentiableFunction cosh = new Cosh();
        Assert.assertEquals(1.5 * FastMath.sqrt(a) * FastMath.cosh(a) + FastMath.pow(a, 1.5) * FastMath.sinh(a),
                            FunctionUtils.multiply(inv, pow, cosh).value(new DerivativeStructure(1, 1, 0, a)).getPartialDerivative(1), 8 * EPS);
    }

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Examples of org.apache.commons.math3.analysis.differentiation.UnivariateDifferentiableFunction

    @Deprecated
    public void testToUnivariateDifferential() {


        // Sin implements both UnivariateDifferentiableFunction and DifferentiableUnivariateFunction
        Sin sin = new Sin();
        UnivariateDifferentiableFunction converted = FunctionUtils.toUnivariateDifferential(sin);
        for (double x = 0.1; x < 0.5; x += 0.01) {
            DerivativeStructure t = new DerivativeStructure(2, 1, x, 1.0, 2.0);
            Assert.assertEquals(sin.value(t).getValue(), converted.value(t).getValue(), 1.0e-10);
            Assert.assertEquals(sin.value(t).getPartialDerivative(1, 0),
                                converted.value(t).getPartialDerivative(1, 0),
                                1.0e-10);
            Assert.assertEquals(sin.value(t).getPartialDerivative(0, 1),
                                converted.value(t).getPartialDerivative(0, 1),
                                1.0e-10);
        }


    }

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Examples of org.apache.commons.math3.analysis.differentiation.UnivariateDifferentiableFunction

       }
   }


   @Test
   public void testDerivativeComparison() {
       final UnivariateDifferentiableFunction sPrime = new Sqrt();
       final UnivariateFunction f = new UnivariateFunction() {
               public double value(double x) {
                   return 1 / (2 * FastMath.sqrt(x));
               }
           };


       for (double x = 1e-30; x < 1e10; x *= 2) {
           final double fX = f.value(x);
           final double sX = sPrime.value(new DerivativeStructure(1, 1, 0, x)).getPartialDerivative(1);
           Assert.assertEquals("x=" + x, fX, sX, FastMath.ulp(fX));
       }
   }

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Examples of org.apache.commons.math3.analysis.differentiation.UnivariateDifferentiableFunction

     * @param f List of functions.
     * @return the composite function.
     * @since 3.1
     */
    public static UnivariateDifferentiableFunction compose(final UnivariateDifferentiableFunction ... f) {
        return new UnivariateDifferentiableFunction() {


            /** {@inheritDoc} */
            public double value(final double t) {
                double r = t;
                for (int i = f.length - 1; i >= 0; i--) {

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Examples of org.apache.commons.math3.analysis.differentiation.UnivariateDifferentiableFunction

     * @param f List of functions.
     * @return a function that computes the sum of the functions.
     * @since 3.1
     */
    public static UnivariateDifferentiableFunction add(final UnivariateDifferentiableFunction ... f) {
        return new UnivariateDifferentiableFunction() {


            /** {@inheritDoc} */
            public double value(final double t) {
                double r = f[0].value(t);
                for (int i = 1; i < f.length; i++) {

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Examples of org.apache.commons.math3.analysis.differentiation.UnivariateDifferentiableFunction

     * @param f List of functions.
     * @return a function that computes the product of the functions.
     * @since 3.1
     */
    public static UnivariateDifferentiableFunction multiply(final UnivariateDifferentiableFunction ... f) {
        return new UnivariateDifferentiableFunction() {


            /** {@inheritDoc} */
            public double value(final double t) {
                double r = f[0].value(t);
                for (int i = 1; i < f.length; i++) {

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Examples of org.apache.commons.math3.analysis.differentiation.UnivariateDifferentiableFunction

     * @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);
            }

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