// <copyright file="Sample.Equidistant.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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namespace MathNet.Numerics.Sampling
{
    using System;
    using System.Collections.Generic;

    /// <summary>
    /// Generic Function Sampling and Quantization Provider
    /// </summary>
    public static partial class Sample
    {
        /// <summary>
        /// Samples a function equidistant within the provided interval.
        /// </summary>
        /// <param name="function">The real-domain function to sample.</param>
        /// <param name="intervalBegin">The real domain interval begin where to start sampling.</param>
        /// <param name="intervalEnd">The real domain interval end where to stop sampling.</param>
        /// <param name="sampleCount">The number of samples to generate.</param>
        /// <typeparam name="T">The value type of the function to sample.</typeparam>
        /// <returns>The generated sample vector.</returns>
        /// <exception cref="ArgumentNullException" />
        /// <exception cref="ArgumentOutOfRangeException" />
        public static T[] EquidistantInterval<T>(
            Func<double, T> function,
            double intervalBegin,
            double intervalEnd,
            int sampleCount)
        {
            if (ReferenceEquals(function, null))
            {
                throw new ArgumentNullException("function");
            }

            if (sampleCount < 0)
            {
                throw new ArgumentOutOfRangeException("sampleCount");
            }

            if (sampleCount == 0)
            {
                return new T[0];
            }

            if (sampleCount == 1)
            {
                return new T[] { function(0.5 * (intervalBegin + intervalEnd)) };
            }

            var samples = new T[sampleCount];
            var step = (intervalEnd - intervalBegin) / (sampleCount - 1);
            var current = intervalBegin;

            for (int i = 0; i < samples.Length - 1; i++)
            {
                samples[i] = function(current);
                current += step;
            }

            samples[samples.Length - 1] = function(intervalEnd);

            return samples;
        }

        /// <summary>
        /// Samples a function equidistant within the provided interval.
        /// </summary>
        /// <param name="function">The real-domain function to sample.</param>
        /// <param name="intervalBegin">The real domain interval begin where to start sampling.</param>
        /// <param name="intervalEnd">The real domain interval end where to stop sampling.</param>
        /// <param name="sampleCount">The number of samples to generate.</param>
        /// <param name="samplePoints">The real domain points where the samples are taken at.</param>
        /// <typeparam name="T">The value type of the function to sample.</typeparam>
        /// <returns>The generated sample vector.</returns>
        /// <exception cref="ArgumentNullException" />
        /// <exception cref="ArgumentOutOfRangeException" />
        public static T[] EquidistantInterval<T>(
            Func<double, T> function,
            double intervalBegin,
            double intervalEnd,
            int sampleCount,
            out double[] samplePoints)
        {
            if (ReferenceEquals(function, null))
            {
                throw new ArgumentNullException("function");
            }

            if (sampleCount < 0)
            {
                throw new ArgumentOutOfRangeException("sampleCount");
            }
            
            if (sampleCount == 0)
            {
                samplePoints = new double[0];
                return new T[0];
            }

            if (sampleCount == 1)
            {
                samplePoints = new[] { 0.5 * (intervalBegin + intervalEnd) };
                return new T[] { function(samplePoints[0]) };
            }

            var samples = new T[sampleCount];
            samplePoints = new double[sampleCount];
            var step = (intervalEnd - intervalBegin) / (sampleCount - 1);
            var current = intervalBegin;

            for (int i = 0; i < samples.Length - 1; i++)
            {
                samplePoints[i] = current;
                samples[i] = function(current);
                current += step;
            }

            samplePoints[samplePoints.Length - 1] = intervalEnd;
            samples[samples.Length - 1] = function(intervalEnd);

            return samples;
        }

        /// <summary>
        /// Samples a periodic function equidistant within one period, but omits the last sample such that the sequence
        /// can be concatenated together.
        /// </summary>
        /// <param name="function">The real-domain function to sample.</param>
        /// <param name="periodLength">The real domain full period length.</param>
        /// <param name="periodOffset">The real domain offset where to start the sampling period.</param>
        /// <param name="sampleCount">The number of samples to generate.</param>
        /// <typeparam name="T">The value type of the function to sample.</typeparam>
        /// <returns>The generated sample vector.</returns>
        /// <exception cref="ArgumentNullException" />
        /// <exception cref="ArgumentOutOfRangeException"/>
        public static T[] EquidistantPeriodic<T>(
            Func<double, T> function,
            double periodLength,
            double periodOffset,
            int sampleCount)
        {
            if (ReferenceEquals(function, null))
            {
                throw new ArgumentNullException("function");
            }

            if (sampleCount < 1)
            {
                throw new ArgumentOutOfRangeException("sampleCount");
            }

            var samples = new T[sampleCount];
            var step = periodLength / sampleCount;
            var current = periodOffset;

            for (int i = 0; i < samples.Length; i++)
            {
                samples[i] = function(current);
                current += step;
            }

            return samples;
        }

        /// <summary>
        /// Samples a periodic function equidistant within one period, but omits the last sample such that the sequence
        /// can be concatenated together.
        /// </summary>
        /// <param name="function">The real-domain function to sample.</param>
        /// <param name="periodLength">The real domain full period length.</param>
        /// <param name="periodOffset">The real domain offset where to start the sampling period.</param>
        /// <param name="sampleCount">The number of samples to generate.</param>
        /// <param name="samplePoints">The real domain points where the samples are taken at.</param>
        /// <typeparam name="T">The value type of the function to sample.</typeparam>
        /// <returns>The generated sample vector.</returns>
        /// <exception cref="ArgumentNullException" />
        /// <exception cref="ArgumentOutOfRangeException"/>
        public static T[] EquidistantPeriodic<T>(
            Func<double, T> function,
            double periodLength,
            double periodOffset,
            int sampleCount,
            out double[] samplePoints)
        {
            if (ReferenceEquals(function, null))
            {
                throw new ArgumentNullException("function");
            }

            if (sampleCount < 1)
            {
                throw new ArgumentOutOfRangeException("sampleCount");
            }

            var samples = new T[sampleCount];
            samplePoints = new double[sampleCount];
            var step = periodLength / sampleCount;
            var current = periodOffset;

            for (int i = 0; i < samples.Length; i++)
            {
                samplePoints[i] = current;
                samples[i] = function(current);
                current += step;
            }

            return samples;
        }

        /// <summary>
        /// Samples a function equidistant starting from the provided location with a fixed step length.
        /// </summary>
        /// <param name="function">The real-domain function to sample.</param>
        /// <param name="start">The real domain location offset where to start sampling.</param>
        /// <param name="step">The real domain step length between the equidistant samples.</param>
        /// <param name="sampleCount">The number of samples to generate.</param>
        /// <typeparam name="T">The value type of the function to sample.</typeparam>
        /// <returns>The generated sample vector.</returns>
        /// <exception cref="ArgumentNullException" />
        /// <exception cref="ArgumentOutOfRangeException"/>
        public static T[] EquidistantStartingAt<T>(
            Func<double, T> function,
            double start,
            double step,
            int sampleCount)
        {
            if (ReferenceEquals(function, null))
            {
                throw new ArgumentNullException("function");
            }

            if (sampleCount < 0)
            {
                throw new ArgumentOutOfRangeException("sampleCount");
            }

            var samples = new T[sampleCount];
            var current = start;

            for (int i = 0; i < samples.Length; i++)
            {
                samples[i] = function(current);
                current += step;
            }

            return samples;
        }

        /// <summary>
        /// Samples a function equidistant starting from the provided location with a fixed step length.
        /// </summary>
        /// <param name="function">The real-domain function to sample.</param>
        /// <param name="start">The real domain location offset where to start sampling.</param>
        /// <param name="step">The real domain step length between the equidistant samples.</param>
        /// <param name="sampleCount">The number of samples to generate.</param>
        /// <param name="samplePoints">The real domain points where the samples are taken at.</param>
        /// <typeparam name="T">The value type of the function to sample.</typeparam>
        /// <returns>The generated sample vector.</returns>
        /// <exception cref="ArgumentNullException" />
        /// <exception cref="ArgumentOutOfRangeException"/>
        public static T[] EquidistantStartingAt<T>(
            Func<double, T> function,
            double start,
            double step,
            int sampleCount,
            out double[] samplePoints)
        {
            if (ReferenceEquals(function, null))
            {
                throw new ArgumentNullException("function");
            }

            if (sampleCount < 0)
            {
                throw new ArgumentOutOfRangeException("sampleCount");
            }

            var samples = new T[sampleCount];
            samplePoints = new double[sampleCount];
            var current = start;

            for (int i = 0; i < samples.Length; i++)
            {
                samplePoints[i] = current;
                samples[i] = function(current);
                current += step;
            }

            return samples;
        }

        /// <summary>
        /// Samples a function equidistant continuously starting from the provided location with a fixed step length.
        /// </summary>
        /// <param name="function">The real-domain function to sample.</param>
        /// <param name="start">The real domain location offset where to start sampling.</param>
        /// <param name="step">The real domain step length between the equidistant samples.</param>
        /// <typeparam name="T">The value type of the function to sample.</typeparam>
        /// <returns>The generated sample enumerator.</returns>
        /// <exception cref="ArgumentNullException" />
        public static IEnumerable<T> EquidistantContinuous<T>(
            Func<double, T> function,
            double start,
            double step)
        {
            if (ReferenceEquals(function, null))
            {
                throw new ArgumentNullException("function");
            }

            var current = start;

            while (true)
            {
                yield return function(current);
                current += step;
            }
        }

        /// <summary>
        /// Samples a function equidistant with the provided start and step length to an integer-domain function
        /// </summary>
        /// <param name="function">The real-domain function to sample.</param>
        /// <param name="start">The real domain location where to start sampling.</param>
        /// <param name="step">The real domain step length between the equidistant samples.</param>
        /// <typeparam name="T">The value type of the function to sample.</typeparam>
        /// <returns>The generated samples integer-domain function.</returns>
        /// <exception cref="ArgumentNullException" />
        public static Func<int, T> EquidistantToFunction<T>(
            Func<double, T> function,
            double start,
            double step)
        {
            if (ReferenceEquals(function, null))
            {
                throw new ArgumentNullException("function");
            }

            return k => function(start + k * step);
        }
    }
}