/*

* Copyright (c) NM LTD.

* https://nm.dev/

*

* THIS SOFTWARE IS LICENSED, NOT SOLD.

*

* YOU MAY USE THIS SOFTWARE ONLY AS DESCRIBED IN THE LICENSE.

* IF YOU ARE NOT AWARE OF AND/OR DO NOT AGREE TO THE TERMS OF THE LICENSE,

* DO NOT USE THIS SOFTWARE.

*

* THE SOFTWARE IS PROVIDED "AS IS", WITH NO WARRANTY WHATSOEVER,

* EITHER EXPRESS OR IMPLIED, INCLUDING, WITHOUT LIMITATION,

* ANY WARRANTIES OF ACCURACY, ACCESSIBILITY, COMPLETENESS,

* FITNESS FOR A PARTICULAR PURPOSE, MERCHANTABILITY, NON-INFRINGEMENT,

* TITLE AND USEFULNESS.

*

* IN NO EVENT AND UNDER NO LEGAL THEORY,

* WHETHER IN ACTION, CONTRACT, NEGLIGENCE, TORT, OR OTHERWISE,

* SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR

* ANY CLAIMS, DAMAGES OR OTHER LIABILITIES,

* ARISING AS A RESULT OF USING OR OTHER DEALINGS IN THE SOFTWARE.

*/

package dev.nm.nmj;

import dev.nm.algebra.linear.vector.doubles.Vector;

import dev.nm.algebra.linear.vector.doubles.dense.DenseVector;

import dev.nm.analysis.function.rn2r1.AbstractBivariateRealFunction;

import dev.nm.analysis.function.rn2r1.AbstractRealScalarFunction;

import dev.nm.analysis.function.rn2r1.AbstractTrivariateRealFunction;

import dev.nm.analysis.function.rn2r1.BivariateRealFunction;

import dev.nm.analysis.function.rn2r1.RealScalarFunction;

import dev.nm.analysis.function.rn2r1.TrivariateRealFunction;

import dev.nm.analysis.function.rn2rm.AbstractRealVectorFunction;

import dev.nm.analysis.function.rn2rm.RealVectorFunction;

import dev.nm.analysis.root.multivariate.NewtonSystemRoot;

import dev.nm.analysis.root.univariate.NoRootFoundException;

import java.util.Arrays;

/**

* Numerical Methods Using Java: For Data Science, Analysis, and Engineering

*

* @author haksunli

* @see

* https://www.amazon.com/Numerical-Methods-Using-Java-Engineering/dp/1484267966

* https://nm.dev/

*/

public class Chapter4 {

public static void main(String[] args) throws Exception {

System.out.println("Chapter 4 demos");

Chapter4 chapter4 = new Chapter4();

chapter4.define_multivariate_functions();

chapter4.define_multivariate_vector_function();

chapter4.solve_system_of_two_equations();

chapter4.solve_system_of_equations();

}

public void define_multivariate_functions() {

System.out.println("define multivariate functions");

RealScalarFunction f1 = new AbstractRealScalarFunction(3) {

@Override

public Double evaluate(Vector x) {

double x1 = x.get(1);

double x2 = x.get(2);

double x3 = x.get(3);

return 2 * x1 * x1 + x2 * x2 - x3;

}

};

System.out.println("f1(1,2,3) = " + f1.evaluate(new DenseVector(1, 2, 3)));

TrivariateRealFunction f2 = new AbstractTrivariateRealFunction() {

@Override

public double evaluate(double x1, double x2, double x3) {

return 2 * x1 * x1 + x2 * x2 - x3;

}

};

System.out.println("f2(1,2,3) = " + f2.evaluate(new DenseVector(1, 2, 3)));

}

public void define_multivariate_vector_function() {

System.out.println("define multivariate vector function");

TrivariateRealFunction f1 = new AbstractTrivariateRealFunction() {

@Override

public double evaluate(double x, double y, double z) {

return Math.pow(x, 2) + Math.pow(y, 3) - z - 6;

}

};

TrivariateRealFunction f2 = new AbstractTrivariateRealFunction() {

@Override

public double evaluate(double x, double y, double z) {

return 2 * x + 9 * y - z - 17;

}

};

TrivariateRealFunction f3 = new AbstractTrivariateRealFunction() {

@Override

public double evaluate(double x, double y, double z) {

return Math.pow(x, 4) + 5 * y + 6 * z - 29;

}

};

RealScalarFunction[] F = new TrivariateRealFunction[]{f1, f2, f3};

Vector x = new DenseVector(1.5, 2.5, 3.5);

double f1_x = F[0].evaluate(x);

double f2_x = F[1].evaluate(x);

double f3_x = F[2].evaluate(x);

double[] F_x = new double[]{f1_x, f2_x, f3_x};

System.out.println("F(x) = " + Arrays.toString(F_x));

RealVectorFunction G = new AbstractRealVectorFunction(3, 3) {

@Override

public Vector evaluate(Vector v) {

double x = v.get(1);

double y = v.get(2);

double z = v.get(3);

double g1 = Math.pow(x, 2) + Math.pow(y, 3) - z - 6;

double g2 = 2 * x + 9 * y - z - 17;

double g3 = Math.pow(x, 4) + 5 * y + 6 * z - 29;

Vector g = new DenseVector(g1, g2, g3);

return g;

}

};

Vector Gx = G.evaluate(x);

System.out.println("G(x) = " + Gx);

}

public void solve_system_of_two_equations() throws NoRootFoundException {

System.out.println("solve a system of two equations");

BivariateRealFunction f1 = new AbstractBivariateRealFunction() {

@Override

public double evaluate(double x, double y) {

return 3 * x + y * y - 12;

}

};

BivariateRealFunction f2 = new AbstractBivariateRealFunction() {

@Override

public double evaluate(double x, double y) {

return x * x + y - 4;

}

};

BivariateRealFunction[] F = new BivariateRealFunction[]{f1, f2};

NewtonSystemRoot solver = new NewtonSystemRoot(1e-8, 10);

Vector initial = new DenseVector(new double[]{0, 0}); // (0, 0)

Vector root = solver.solve(F, initial);

System.out.println(String.format("f(%s) = (%f, %f)", root.toString(), f1.evaluate(root), f2.evaluate(root)));

}

public void solve_system_of_equations() throws NoRootFoundException {

System.out.println("solve a system of equations");

RealVectorFunction G = new AbstractRealVectorFunction(3, 3) {

@Override

public Vector evaluate(Vector v) {

double x = v.get(1);

double y = v.get(2);

double z = v.get(3);

double g1 = Math.pow(x, 2) + Math.pow(y, 3) - z - 6;

double g2 = 2 * x + 9 * y - z - 17;

double g3 = Math.pow(x, 4) + 5 * y + 6 * z - 29;

Vector g = new DenseVector(g1, g2, g3);

return g;

}

};

NewtonSystemRoot solver = new NewtonSystemRoot(1e-8, 15);

Vector initial = new DenseVector(new double[]{0, 0, 0}); // (0, 0, 0)

Vector root = solver.solve(G, initial);

System.out.println(String.format("f(%s) = %s", root.toString(), G.evaluate(root).toString()));

}

}