using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using Azimuth;
using Azimuth.DenseLinearAlgebra;
using Azimuth.Approximation;

namespace Azimuth.UnitTests.Approximation
{
    public class ChebyshevTests : UnitTestSharp.TestFixture
    {
        private static Func<Scalar, Scalar> cheby_4 = x => ((8 * x * x) - 8) * x * x + 1;
        private static Func<Scalar, Scalar> cheby_3 = x => (4 * x * x - 3) * x;
        private static Func<Scalar, Scalar> cheby_2 = x => 2 * x * x - 1;
        private static Func<Scalar, Scalar> cheby_1 = x => x;
        private static Func<Scalar, Scalar> cheby_0 = x => 1;

        public class CtorTests : UnitTestSharp.TestFixture
        {
            public void Chebyshev_0()
            {            
                var window = new Interval(-1, 1);

                var cheby = new Chebyshev(cheby_0, window);

                CheckEqual(new DenseVector(new Scalar[] { 2, }), cheby.Coefficients);
            }

            public void Chebyshev_1()
            {            
                var window = new Interval(-1, 1);

                var cheby = new Chebyshev(cheby_1, window);

                CheckEqual(new DenseVector(new Scalar[] { 0, 1, }), cheby.Coefficients);
            }

            public void Chebyshev_2()
            {
                var window = new Interval(-1, 1);

                var cheby = new Chebyshev(cheby_2, window);

                CheckEqual(new DenseVector(new Scalar[] { 0, 0, 1, }), cheby.Coefficients);
            }

            public void Chebyshev_3()
            {
                var window = new Interval(-1, 1);

                var cheby = new Chebyshev(cheby_3, window);

                CheckEqual(new DenseVector(new Scalar[] { 0, 0, 0, 1, }), cheby.Coefficients);
            }
        
            public void Chebyshev_4()
            {            
                var window = new Interval(-1, 1);

                var cheby = new Chebyshev(cheby_4, window);

                CheckEqual(new DenseVector(new Scalar[] { 0, 0, 0, 0, 1, }), cheby.Coefficients);
            }

            public void x54321()
            {            
                var window = new Interval(-1, 1);

                var cheby = new Chebyshev(x => cheby_4(x) + 2 * cheby_3(x) + 3 * cheby_2(x) + 4 * cheby_1(x) + 2.5 * cheby_0(x), window);

                CheckEqual(new DenseVector(new Scalar[] { 5, 4, 3, 2, 1, }), cheby.Coefficients);
            }

            public void Chebyshev_0_Window()
            {            
                var window = new Interval(3, 7);

                var cheby = new Chebyshev(x => cheby_0(x*2+5), window);

                CheckEqual(new DenseVector(new Scalar[] { 2, }), cheby.Coefficients);
            }

            public void Chebyshev_1_Window()
            {
                var window = new Interval(-1, 4);

                var cheby = new Chebyshev(x => cheby_1((x-1.5)/2.5), window);

                CheckEqual(new DenseVector(new Scalar[] { 0, 1, }), cheby.Coefficients);
            }

            public void Chebyshev_2_Window()
            {
                var window = new Interval(3, 6);

                var cheby = new Chebyshev(x => cheby_2((x-4.5)/1.5), window);

                CheckEqual(new DenseVector(new Scalar[] { 0, 0, 1, }), cheby.Coefficients);
            }

            public void Chebyshev_3_Window()
            {
                var window = new Interval(-2, 11);

                var cheby = new Chebyshev(x => cheby_3((x-4.5)/6.5), window);

                CheckEqual(new DenseVector(new Scalar[] { 0, 0, 0, 1, }), cheby.Coefficients);
            }

            public void Chebyshev_4_Window()
            {            
                var window = new Interval(2.5, 3.5);

                var cheby = new Chebyshev(x => cheby_4((x-3)/0.5), window);

                CheckEqual(new DenseVector(new Scalar[] { 0, 0, 0, 0, 1, }), cheby.Coefficients);
            }

            public void x54321_Window()
            {            
                var window = new Interval(-1, 0);

                var cheby = new Chebyshev(x => 
                {
                    x = ((x + 0.5) * 2);
                    return cheby_4(x) + 2 * cheby_3(x) + 3 * cheby_2(x) + 4 * cheby_1(x) + 2.5 * cheby_0(x);
                }, window);

                CheckEqual(new DenseVector(new Scalar[] { 5, 4, 3, 2, 1, }), cheby.Coefficients);
            }
        }

        public class EvaluateTests : UnitTestSharp.TestFixture
        {
            public void Basic()
            {
                Func<Scalar, Scalar> func = x => Math.Cos(10 * Math.PI * x) + 2 * Math.Sin(3 * Math.PI * x + 1) * x + 1;
                var window = new Interval(0, 2);

                var cheby = new Chebyshev(func, window);

                Scalar t = 0.25;
                var expected = func(t);
                CheckEqual(expected, cheby.Evaluate(t));
            }

            public void Chebyshev_0()
            {
                var window = new Interval(-1, 1);

                var func = cheby_0;
                var cheby = new Chebyshev(func, window);

                int max = 13;
                for(int i = 0; i < max; ++i)
                {
                    Scalar t = (Scalar)i / (Scalar)max * (window.Max - window.Min) + window.Min;
                    CheckEqual(func(t), cheby.Evaluate(t));
                }
            }

            public void Chebyshev_1()
            {
                var window = new Interval(-1, 1);

                var func = cheby_1;
                var cheby = new Chebyshev(func, window);

                int max = 13;
                for (int i = 0; i < max; ++i)
                {
                    Scalar t = (Scalar)i / (Scalar)max * (window.Max - window.Min) + window.Min;
                    CheckEqual(func(t), cheby.Evaluate(t));
                }
            }

            public void Chebyshev_2()
            {
                var window = new Interval(-1, 1);

                var func = cheby_2;
                var cheby = new Chebyshev(func, window);

                int max = 13;
                for (int i = 0; i < max; ++i)
                {
                    Scalar t = (Scalar)i / (Scalar)max * (window.Max - window.Min) + window.Min;
                    CheckEqual(func(t), cheby.Evaluate(t));
                }
            }

            public void Chebyshev_3()
            {
                var window = new Interval(-1, 1);

                var func = cheby_3;
                var cheby = new Chebyshev(func, window);

                int max = 13;
                for (int i = 0; i < max; ++i)
                {
                    Scalar t = (Scalar)i / (Scalar)max * (window.Max - window.Min) + window.Min;
                    CheckEqual(func(t), cheby.Evaluate(t));
                }
            }

            public void Chebyshev_4()
            {
                var window = new Interval(-1, 1);

                var func = cheby_4;
                var cheby = new Chebyshev(func, window);

                int max = 13;
                for (int i = 0; i < max; ++i)
                {
                    Scalar t = (Scalar)i / (Scalar)max * (window.Max - window.Min) + window.Min;
                    CheckEqual(func(t), cheby.Evaluate(t));
                }
            }

            public void x54321()
            {
                var window = new Interval(-1, 1);

                Func<Scalar, Scalar> func = x => cheby_4(x) + 2 * cheby_3(x) + 3 * cheby_2(x) + 4 * cheby_1(x) + 2.5 * cheby_0(x);
                var cheby = new Chebyshev(func, window);

                int max = 13;
                for (int i = 0; i < max; ++i)
                {
                    Scalar t = (Scalar)i / (Scalar)max * (window.Max - window.Min) + window.Min;
                    CheckEqual(func(t), cheby.Evaluate(t));
                }
            }

            public void Chebyshev_0_Window()
            {            
                var window = new Interval(3, 7);

                Func<Scalar, Scalar> func = x => cheby_0(x * 2 + 5);
                var cheby = new Chebyshev(func, window);

                int max = 13;
                for (int i = 0; i < max; ++i)
                {
                    Scalar t = (Scalar)i / (Scalar)max * (window.Max - window.Min) + window.Min;
                    CheckEqual(func(t), cheby.Evaluate(t));
                }
            }

            public void Chebyshev_1_Window()
            {
                var window = new Interval(-1, 4);

                Func<Scalar, Scalar> func = x => cheby_1((x - 1.5) / 2.5);
                var cheby = new Chebyshev(func, window);

                int max = 13;
                for (int i = 0; i < max; ++i)
                {
                    Scalar t = (Scalar)i / (Scalar)max * (window.Max - window.Min) + window.Min;
                    CheckEqual(func(t), cheby.Evaluate(t));
                }
            }

            public void Chebyshev_2_Window()
            {
                var window = new Interval(3, 6);

                Func<Scalar, Scalar> func = x => cheby_2((x - 4.5) / 1.5);
                var cheby = new Chebyshev(func, window);

                int max = 13;
                for (int i = 0; i < max; ++i)
                {
                    Scalar t = (Scalar)i / (Scalar)max * (window.Max - window.Min) + window.Min;
                    CheckEqual(func(t), cheby.Evaluate(t));
                }
            }

            public void Chebyshev_3_Window()
            {
                var window = new Interval(-2, 11);

                Func<Scalar, Scalar> func = x => cheby_3((x - 4.5) / 6.5);
                var cheby = new Chebyshev(func, window);

                int max = 13;
                for (int i = 0; i < max; ++i)
                {
                    Scalar t = (Scalar)i / (Scalar)max * (window.Max - window.Min) + window.Min;
                    CheckEqual(func(t), cheby.Evaluate(t));
                }
            }

            public void Chebyshev_4_Window()
            {            
                var window = new Interval(2.5, 3.5);

                Func<Scalar, Scalar> func = x => cheby_4((x - 3) / 0.5);
                var cheby = new Chebyshev(func, window);

                int max = 13;
                for (int i = 0; i < max; ++i)
                {
                    Scalar t = (Scalar)i / (Scalar)max * (window.Max - window.Min) + window.Min;
                    CheckEqual(func(t), cheby.Evaluate(t));
                }
            }

            public void x54321_Window()
            {            
                var window = new Interval(-1, 0);

                Func<Scalar, Scalar> func = x =>
                {
                    x = ((x + 0.5) * 2);
                    return cheby_4(x) + 2 * cheby_3(x) + 3 * cheby_2(x) + 4 * cheby_1(x) + 2.5 * cheby_0(x);
                };

                var cheby = new Chebyshev(func, window);

                int max = 13;
                for (int i = 0; i < max; ++i)
                {
                    Scalar t = (Scalar)i / (Scalar)max * (window.Max - window.Min) + window.Min;
                    CheckEqual(func(t), cheby.Evaluate(t));
                }
            }
        }
    }
}