// <copyright file="Distance.cs" company="Math.NET">
// Math.NET Numerics, part of the Math.NET Project
// http://numerics.mathdotnet.com
// http://github.com/mathnet/mathnet-numerics
// http://mathnetnumerics.codeplex.com
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using System;
using MathNet.Numerics.LinearAlgebra;
using MathNet.Numerics.Properties;

namespace MathNet.Numerics
{
    public static class Distance
    {
        /// <summary>
        /// Sum of Absolute Difference (SAD), i.e. the L1-norm (Manhattan) of the difference.
        /// </summary>
        public static double SAD(Vector<double> a, Vector<double> b)
        {
            return (a - b).L1Norm();
        }

        /// <summary>
        /// Sum of Absolute Difference (SAD), i.e. the L1-norm (Manhattan) of the difference.
        /// </summary>
        public static double SAD(Vector<float> a, Vector<float> b)
        {
            return (a - b).L1Norm();
        }

        /// <summary>
        /// Sum of Absolute Difference (SAD), i.e. the L1-norm (Manhattan) of the difference.
        /// </summary>
        public static double SAD(double[] a, double[] b)
        {
            if (a.Length != b.Length) throw new ArgumentException(Resources.ArgumentVectorsSameLength);

            double sum = 0d;
            for (var i = 0; i < a.Length; i++)
            {
                sum += Math.Abs(a[i] - b[i]);
            }
            return sum;
        }

        /// <summary>
        /// Sum of Absolute Difference (SAD), i.e. the L1-norm (Manhattan) of the difference.
        /// </summary>
        public static float SAD(float[] a, float[] b)
        {
            if (a.Length != b.Length) throw new ArgumentException(Resources.ArgumentVectorsSameLength);

            float sum = 0f;
            for (var i = 0; i < a.Length; i++)
            {
                sum += Math.Abs(a[i] - b[i]);
            }
            return sum;
        }

        /// <summary>
        /// Mean-Absolute Error (MAE), i.e. the normalized L1-norm (Manhattan) of the difference.
        /// </summary>
        public static double MAE(Vector<double> a, Vector<double> b)
        {
            return (a - b).L1Norm()/a.Count;
        }

        /// <summary>
        /// Mean-Absolute Error (MAE), i.e. the normalized L1-norm (Manhattan) of the difference.
        /// </summary>
        public static double MAE(Vector<float> a, Vector<float> b)
        {
            return (a - b).L1Norm()/a.Count;
        }

        /// <summary>
        /// Mean-Absolute Error (MAE), i.e. the normalized L1-norm (Manhattan) of the difference.
        /// </summary>
        public static double MAE(double[] a, double[] b)
        {
            return SAD(a, b)/a.Length;
        }

        /// <summary>
        /// Mean-Absolute Error (MAE), i.e. the normalized L1-norm (Manhattan) of the difference.
        /// </summary>
        public static float MAE(float[] a, float[] b)
        {
            return SAD(a, b)/a.Length;
        }

        /// <summary>
        /// Sum of Squared Difference (SSD), i.e. the squared L2-norm (Euclidean) of the difference.
        /// </summary>
        public static double SSD(Vector<double> a, Vector<double> b)
        {
            var norm = (a - b).L2Norm();
            return norm*norm;
        }

        /// <summary>
        /// Sum of Squared Difference (SSD), i.e. the squared L2-norm (Euclidean) of the difference.
        /// </summary>
        public static double SSD(Vector<float> a, Vector<float> b)
        {
            var norm = (a - b).L2Norm();
            return norm*norm;
        }

        /// <summary>
        /// Sum of Squared Difference (SSD), i.e. the squared L2-norm (Euclidean) of the difference.
        /// </summary>
        public static double SSD(double[] a, double[] b)
        {
            var diff = new double[a.Length];
            Control.LinearAlgebraProvider.SubtractArrays(a, b, diff);
            return Control.LinearAlgebraProvider.DotProduct(diff, diff);
        }

        /// <summary>
        /// Sum of Squared Difference (SSD), i.e. the squared L2-norm (Euclidean) of the difference.
        /// </summary>
        public static float SSD(float[] a, float[] b)
        {
            var diff = new float[a.Length];
            Control.LinearAlgebraProvider.SubtractArrays(a, b, diff);
            return Control.LinearAlgebraProvider.DotProduct(diff, diff);
        }

        /// <summary>
        /// Mean-Squared Error (MSE), i.e. the normalized squared L2-norm (Euclidean) of the difference.
        /// </summary>
        public static double MSE(Vector<double> a, Vector<double> b)
        {
            var norm = (a - b).L2Norm();
            return norm*norm/a.Count;
        }

        /// <summary>
        /// Mean-Squared Error (MSE), i.e. the normalized squared L2-norm (Euclidean) of the difference.
        /// </summary>
        public static double MSE(Vector<float> a, Vector<float> b)
        {
            var norm = (a - b).L2Norm();
            return norm*norm/a.Count;
        }

        /// <summary>
        /// Mean-Squared Error (MSE), i.e. the normalized squared L2-norm (Euclidean) of the difference.
        /// </summary>
        public static double MSE(double[] a, double[] b)
        {
            return SSD(a, b)/a.Length;
        }

        /// <summary>
        /// Mean-Squared Error (MSE), i.e. the normalized squared L2-norm (Euclidean) of the difference.
        /// </summary>
        public static float MSE(float[] a, float[] b)
        {
            return SSD(a, b)/a.Length;
        }

        /// <summary>
        /// Euclidean Distance, i.e. the L2-norm of the difference.
        /// </summary>
        public static double Euclidean(Vector<double> a, Vector<double> b)
        {
            return (a - b).L2Norm();
        }

        /// <summary>
        /// Euclidean Distance, i.e. the L2-norm of the difference.
        /// </summary>
        public static double Euclidean(Vector<float> a, Vector<float> b)
        {
            return (a - b).L2Norm();
        }

        /// <summary>
        /// Euclidean Distance, i.e. the L2-norm of the difference.
        /// </summary>
        public static double Euclidean(double[] a, double[] b)
        {
            return Math.Sqrt(SSD(a, b));
        }

        /// <summary>
        /// Euclidean Distance, i.e. the L2-norm of the difference.
        /// </summary>
        public static float Euclidean(float[] a, float[] b)
        {
            return (float) Math.Sqrt(SSD(a, b));
        }

        /// <summary>
        /// Manhattan Distance, i.e. the L1-norm of the difference.
        /// </summary>
        public static double Manhattan(Vector<double> a, Vector<double> b)
        {
            return (a - b).L1Norm();
        }

        /// <summary>
        /// Manhattan Distance, i.e. the L1-norm of the difference.
        /// </summary>
        public static double Manhattan(Vector<float> a, Vector<float> b)
        {
            return (a - b).L1Norm();
        }

        /// <summary>
        /// Manhattan Distance, i.e. the L1-norm of the difference.
        /// </summary>
        public static double Manhattan(double[] a, double[] b)
        {
            return SAD(a, b);
        }

        /// <summary>
        /// Manhattan Distance, i.e. the L1-norm of the difference.
        /// </summary>
        public static float Manhattan(float[] a, float[] b)
        {
            return SAD(a, b);
        }

        /// <summary>
        /// Chebyshev Distance, i.e. the Infinity-norm of the difference.
        /// </summary>
        public static double Chebyshev(Vector<double> a, Vector<double> b)
        {
            return (a - b).InfinityNorm();
        }

        /// <summary>
        /// Chebyshev Distance, i.e. the Infinity-norm of the difference.
        /// </summary>
        public static double Chebyshev(Vector<float> a, Vector<float> b)
        {
            return (a - b).InfinityNorm();
        }

        /// <summary>
        /// Chebyshev Distance, i.e. the Infinity-norm of the difference.
        /// </summary>
        public static double Chebyshev(double[] a, double[] b)
        {
            if (a.Length != b.Length) throw new ArgumentOutOfRangeException("b");
            double max = Math.Abs(a[0] - b[0]);
            for (int i = 1; i < a.Length; i++)
            {
                var next = Math.Abs(a[i] - b[i]);
                if (next > max)
                {
                    max = next;
                }
            }
            return max;
        }

        /// <summary>
        /// Chebyshev Distance, i.e. the Infinity-norm of the difference.
        /// </summary>
        public static float Chebyshev(float[] a, float[] b)
        {
            if (a.Length != b.Length) throw new ArgumentOutOfRangeException("b");
            float max = Math.Abs(a[0] - b[0]);
            for (int i = 1; i < a.Length; i++)
            {
                var next = Math.Abs(a[i] - b[i]);
                if (next > max)
                {
                    max = next;
                }
            }
            return max;
        }

        /// <summary>
        /// Hamming Distance, i.e. the number of positions that have different values in the vectors.
        /// </summary>
        public static double Hamming(double[] a, double[] b)
        {
            if (a.Length != b.Length) throw new ArgumentOutOfRangeException("b");
            int count = 0;
            for (int i = 1; i < a.Length; i++)
            {
                if (a[i] != b[i])
                {
                    count++;
                }
            }
            return count;
        }

        /// <summary>
        /// Hamming Distance, i.e. the number of positions that have different values in the vectors.
        /// </summary>
        public static float Hamming(float[] a, float[] b)
        {
            if (a.Length != b.Length) throw new ArgumentOutOfRangeException("b");
            int count = 0;
            for (int i = 1; i < a.Length; i++)
            {
                if (a[i] != b[i])
                {
                    count++;
                }
            }
            return count;
        }
    }
}