source: branches/3022-FastFunctionExtraction/FFX/SimpleBasisFunction.cs @ 18215

using HeuristicLab.Collections;
using HeuristicLab.Common;
using HeuristicLab.Problems.DataAnalysis;
using System;
using System.Globalization;
using System.Linq;

namespace HeuristicLab.Algorithms.DataAnalysis.FastFunctionExtraction {

    internal struct SimpleBasisFunction : ISimpleBasisFunction {
        public double Exponent { get; set; }
        public NonlinearOperator Operator { get; set; }
        public bool IsDenominator { get; set; }
        public string Feature { get; set; }
        public double Threshold { get; set; } // only relevant for hinge function 
        public bool HasExponent => !(Exponent == 1.0);
        public bool HasOperator => Operator != NonlinearOperator.None;
        public int Complexity => Operator == NonlinearOperator.GT_Hinge || Operator == NonlinearOperator.LT_Hinge ? 3 : 1;

        public SimpleBasisFunction(string feature, double exponent = 1, NonlinearOperator op = NonlinearOperator.None, bool isNominator = true, double threshold = 0) {
            Feature = feature ?? throw new ArgumentNullException(nameof(feature));
            Exponent = exponent;
            Operator = op;
            IsDenominator = isNominator;
            Threshold = threshold;
        }

        public IBasisFunction DeepCopy() {
            return new SimpleBasisFunction(Feature, Exponent, Operator, IsDenominator, Threshold);
        }

        public override string ToString() {
            var culture = new CultureInfo("en-US");
            string str = $"\"{Feature}\"";

            if (HasExponent) {
                if (Exponent.IsAlmost((double)-1 / 2)) str = $"1 / SQRT({str})";
                else if (Exponent.IsAlmost((double)1 / 2)) str = $"SQRT({str})";
                else if (Exponent.IsAlmost(1)) str = $"1 / {str}";
                else if (Exponent.IsAlmost(2)) str = $"SQR({str})";
                else if (Exponent.IsAlmost(3)) str = $"CUBE({str})";
                else str = $"({str}) ^ ({Exponent.ToString(culture)})";
            }

            if (!HasOperator) return str;

            var thr = Threshold.ToString(culture);
            if (Operator == NonlinearOperator.LT_Hinge) {
                var expr = $"{str} {((Threshold >= 0) ? " - " + Math.Abs(Threshold).ToString(culture) : " + " + Math.Abs(Threshold).ToString(culture))}";
                str = $"IF(GT(0, {expr}), 0, {expr})";
            } else if (Operator == NonlinearOperator.GT_Hinge) {
                var expr = $"{thr} - {str}";
                str = $"IF(GT(0, {expr}), 0, {expr})";
            } else {
                str = $"{opToStr.GetByFirst(Operator)}({str})";
            }
            return str;
        }

        public double[] Evaluate(IRegressionProblemData data) {
            var exp = Exponent;
            // exponentVals : e.g. "x3^2"
            var exponentVals = data.Dataset.GetDoubleValues(Feature)
                .Select(val => Math.Pow(val, exp))
                .ToArray();
            // vals: e.g. "log(x3^2)
            var vals = Eval(exponentVals);

            if (!IsDenominator) {
                var y = data.TargetVariableValues;
                vals = vals.Zip(y, (a, b) => -a * b).ToArray();
            }
            return vals;
        }

        private double[] Eval(double[] x) {
            var thr = this.Threshold;
            switch (Operator) {
                case NonlinearOperator.None:
                    return x;
                case NonlinearOperator.Abs:
                    return x.Select(val => Math.Abs(val)).ToArray();
                case NonlinearOperator.Log:
                    return x.Select(val => Math.Log(val)).ToArray();
                case NonlinearOperator.Sin:
                    return x.Select(val => Math.Sin(val)).ToArray();
                case NonlinearOperator.Cos:
                    return x.Select(val => Math.Cos(val)).ToArray();
                case NonlinearOperator.GT_Hinge:
                    return x.Select(val => Math.Max(0, thr - val)).ToArray();
                case NonlinearOperator.LT_Hinge:
                    return x.Select(val => Math.Max(0, val - thr)).ToArray();
                default:
                    throw new Exception("Unimplemented operator: " + Operator.ToString());
            }
        }

        private static readonly BidirectionalDictionary<NonlinearOperator, string> opToStr = new BidirectionalDictionary<NonlinearOperator, string>() {
            { NonlinearOperator.Abs, "ABS"},
            { NonlinearOperator.Log, "LOG"},
            { NonlinearOperator.Sin, "SIN"},
            { NonlinearOperator.Cos, "COS"}
        };
    }
}