/*
 * Java Genetic Algorithm Library (jenetics-7.0.0).
 * Copyright (c) 2007-2022 Franz Wilhelmstötter
 *
 * Licensed 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
 *
 *      http://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.
 *
 * Author:
 *    Franz Wilhelmstötter (franz.wilhelmstoetter@gmail.com)
 */
package io.jenetics.prog.regression;

import static java.lang.Math.pow;
import static java.lang.String.format;
import static java.util.Objects.requireNonNull;

import java.util.ArrayList;
import java.util.List;
import java.util.function.Function;
import java.util.function.Predicate;
import java.util.stream.Collectors;

import io.jenetics.Genotype;
import io.jenetics.engine.Codec;
import io.jenetics.engine.Problem;
import io.jenetics.util.ISeq;

import io.jenetics.ext.util.Tree;

import io.jenetics.prog.ProgramChromosome;
import io.jenetics.prog.ProgramGene;
import io.jenetics.prog.op.Op;
import io.jenetics.prog.regression.Sampling.Result;

/**
 * This class implements a <em>symbolic</em> regression problem. The example
 * below shows a typical usage of the {@code Regression} class.
 *
 * <pre>{@code
 * public class SymbolicRegression {
 *     private static final ISeq<Op<Double>> OPERATIONS =
 *         ISeq.of(MathOp.ADD, MathOp.SUB, MathOp.MUL);
 *
 *     private static final ISeq<Op<Double>> TERMINALS = ISeq.of(
 *         Var.of("x", 0),
 *         EphemeralConst.of(() -> (double)RandomRegistry.random().nextInt(10))
 *     );
 *
 *     private static final Regression<Double> REGRESSION = Regression.of(
 *         Regression.codecOf(OPERATIONS, TERMINALS, 5),
 *         Error.of(LossFunction::mse),
 *         Sample.ofDouble(-1.0, -8.0000),
 *         // ...
 *         Sample.ofDouble(0.9, 1.3860),
 *         Sample.ofDouble(1.0, 2.0000)
 *     );
 *
 *     public static void main(final String[] args) {
 *         final Engine<ProgramGene<Double>, Double> engine = Engine
 *             .builder(REGRESSION)
 *             .minimizing()
 *             .alterers(
 *                 new SingleNodeCrossover<>(0.1),
 *                 new Mutator<>())
 *             .build();
 *
 *         final EvolutionResult<ProgramGene<Double>, Double> result = engine.stream()
 *             .limit(Limits.byFitnessThreshold(0.01))
 *             .collect(EvolutionResult.toBestEvolutionResult());
 *
 *         final ProgramGene<Double> program = result.bestPhenotype()
 *             .genotype()
 *             .gene();
 *
 *         final TreeNode<Op<Double>> tree = program.toTreeNode();
 *         MathExpr.rewrite(tree); // Simplify result program.
 *         System.out.println("Generations: " + result.totalGenerations());
 *         System.out.println("Function:    " + new MathExpr(tree));
 *         System.out.println("Error:       " + REGRESSION.error(tree));
 *     }
 * }
 * }</pre>
 *
 * @see SampleBuffer
 * @see Sampling
 *
 * @param <T> the operation type
 *
 * @author <a href="mailto:franz.wilhelmstoetter@gmail.com">Franz Wilhelmstötter</a>
 * @version 6.0
 * @since 5.0
 */
public final class Regression<T>
        implements Problem<Tree<Op<T>, ?>, ProgramGene<T>, Double>
{

        private final Codec<Tree<Op<T>, ?>, ProgramGene<T>> _codec;
        private final Error<T> _error;
        private final Sampling<T> _sampling;


        /**
         * Create a new <em>symbolic</em> regression problem with the given data.
         *
         * @param codec the codec used for the problem
         * @param error the error function
         * @param sampling the sample values used for finding a regression.
         */
        private Regression(
                final Codec<Tree<Op<T>, ?>, ProgramGene<T>> codec,
                final Error<T> error,
                final Sampling<T> sampling
        ) {
                _codec = requireNonNull(codec);
                _error = requireNonNull(error);
                _sampling = requireNonNull(sampling);
        }

        @Override
        public Function<Tree<Op<T>, ?>, Double> fitness() {
                return this::error;
        }

        @Override
        public Codec<Tree<Op<T>, ?>, ProgramGene<T>> codec() {
                return _codec;
        }

        /**
         * Calculates the actual error for the given {@code program}.
         *
         * @param program the program to calculate the error value for
         * @return the overall error value of the program
         */
        public double error(final Tree<? extends Op<T>, ?> program) {
                final Result<T> result = _sampling.eval(program);
                return result != null
                        ? _error.apply(program, result.calculated(), result.expected())
                        : Double.MAX_VALUE;
        }

        /* *************************************************************************
         * Factory methods.
         * ************************************************************************/

        /**
         * Create a new regression problem instance with the given parameters.
         *
         * @see #codecOf(ISeq, ISeq, int)
         * @see #codecOf(ISeq, ISeq, int, Predicate)
         *
         * @param <T> the operation type
         * @param codec the problem codec to use
         * @param error the error function
         * @param sampling the sampling function
         * @return a new regression problem instance
         * @throws NullPointerException if on of the arguments is {@code null}
         */
        public static <T> Regression<T> of(
                final Codec<Tree<Op<T>, ?>, ProgramGene<T>> codec,
                final Error<T> error,
                final Sampling<T> sampling
        ) {
                return new Regression<>(codec, error, sampling);
        }

        /**
         * Create a new regression problem instance with the given parameters.
         *
         * @see #codecOf(ISeq, ISeq, int)
         * @see #codecOf(ISeq, ISeq, int, Predicate)
         *
         * @param <T> the operation type
         * @param codec the problem codec to use
         * @param error the error function
         * @param samples the sample points used for regression analysis
         * @return a new regression problem instance
         * @throws IllegalArgumentException if the given {@code samples} is empty
         * @throws NullPointerException if on of the arguments is {@code null}
         */
        public static <T> Regression<T> of(
                final Codec<Tree<Op<T>, ?>, ProgramGene<T>> codec,
                final Error<T> error,
                final Iterable<? extends Sample<T>> samples
        ) {
                if (!samples.iterator().hasNext()) {
                        throw new IllegalArgumentException("Sample list must not be empty.");
                }

                final List<Sample<T>> s = new ArrayList<>();
                samples.forEach(s::add);

                return new Regression<>(codec, error, new SampleList<>(s));
        }

        /**
         * Create a new regression problem instance with the given parameters.
         *
         * @see #codecOf(ISeq, ISeq, int)
         * @see #codecOf(ISeq, ISeq, int, Predicate)
         *
         * @param <T> the operation type
         * @param codec the problem codec to use
         * @param error the error function
         * @param samples the sample points used for regression analysis
         * @return a new regression problem instance
         * @throws IllegalArgumentException if the given {@code samples} is empty
         * @throws NullPointerException if on of the arguments is {@code null}
         */
        @SafeVarargs
        public static <T> Regression<T> of(
                final Codec<Tree<Op<T>, ?>, ProgramGene<T>> codec,
                final Error<T> error,
                final Sample<T>... samples
        ) {
                return of(codec, error, List.of(samples));
        }


        /* *************************************************************************
         * Codec factory methods.
         * ************************************************************************/

        /**
         * Create a new <em>codec</em>, usable for <em>symbolic regression</em>
         * problems, with the given parameters.
         *
         * @param <T> the operation type
         * @param operations the operations used for the symbolic regression
         * @param terminals the terminal operations of the program tree
         * @param depth the maximal tree depth (height) of newly created program
         *        trees
         * @param validator the chromosome validator. A typical validator would
         *        check the size of the tree and if the tree is too large, mark it
         *        at <em>invalid</em>. The <em>validator</em> may be {@code null}.
         * @return a new codec, usable for symbolic regression
         * @throws IllegalArgumentException if the tree {@code depth} is not in the
         *         valid range of {@code [0, 30)}
         * @throws NullPointerException if the {@code operations} or {@code terminals}
         *         are {@code null}
         */
        public static <T> Codec<Tree<Op<T>, ?>, ProgramGene<T>>
        codecOf(
                final ISeq<Op<T>> operations,
                final ISeq<Op<T>> terminals,
                final int depth,
                final Predicate<? super ProgramChromosome<T>> validator
        ) {
                if (depth >= 30 || depth < 0) {
                        throw new IllegalArgumentException(format(
                                "Tree depth out of range [0, 30): %d", depth
                        ));
                }

                return Codec.of(
                        Genotype.of(
                                ProgramChromosome.of(
                                        depth,
                                        validator,
                                        operations,
                                        terminals
                                )
                        ),
                        Genotype::gene
                );
        }

        /**
         * Create a new <em>codec</em>, usable for <em>symbolic regression</em>
         * problems, with the given parameters.
         *
         * @param <T> the operation type
         * @param operations the operations used for the symbolic regression
         * @param terminals the terminal operations of the program tree
         * @param depth the maximal tree depth (height) of newly created program
         *        trees
         * @return a new codec, usable for symbolic regression
         * @throws IllegalArgumentException if the tree {@code depth} is not in the
         *         valid range of {@code [0, 30)}
         * @throws NullPointerException if the {@code operations} or {@code terminals}
         *         are {@code null}
         */
        public static <T> Codec<Tree<Op<T>, ?>, ProgramGene<T>>
        codecOf(
                final ISeq<Op<T>> operations,
                final ISeq<Op<T>> terminals,
                final int depth
        ) {
                // Average arity of tree nodes.
                final double k = operations.stream()
                        .collect(Collectors.averagingDouble(Op::arity));

                // The average node count between treeDepth and treeDepth + 1.
                // 2^(k + 1) - 1 + 2^(k + 2) - 1)/2 == 3*2^k - 1
                final int max = (int)(3*pow(k, depth) - 1);

                return codecOf(
                        operations,
                        terminals,
                        depth,
                        ch -> ch.root().size() <= max
                );
        }

}