348 lines
13 KiB
C#
348 lines
13 KiB
C#
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/*
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* BSD Licence:
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* Copyright (c) 2001, 2002 Ben Houston [ ben@exocortex.org ]
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* Exocortex Technologies [ www.exocortex.org ]
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* All rights reserved.
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions are met:
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*
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* 1. Redistributions of source code must retain the above copyright notice,
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* this list of conditions and the following disclaimer.
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* 2. Redistributions in binary form must reproduce the above copyright
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* notice, this list of conditions and the following disclaimer in the
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* documentation and/or other materials provided with the distribution.
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* 3. Neither the name of the <ORGANIZATION> nor the names of its contributors
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* may be used to endorse or promote products derived from this software
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* without specific prior written permission.
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*
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* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
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* AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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* ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE FOR
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* ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
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* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
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* SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
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* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
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* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH
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* DAMAGE.
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*/
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using System;
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using System.Diagnostics;
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namespace Exocortex.DSP
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{
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// Comments? Questions? Bugs? Tell Ben Houston at ben@exocortex.org
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// Version: May 4, 2002
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/// <summary>
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/// <p>A set of statistical utilities for complex number arrays</p>
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/// </summary>
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public class ComplexStats
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{
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//---------------------------------------------------------------------------------------------
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private ComplexStats()
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{
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}
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//---------------------------------------------------------------------------------------------
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//--------------------------------------------------------------------------------------------
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/// <summary>
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/// Calculate the sum
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/// </summary>
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/// <param name="data"></param>
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/// <returns></returns>
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static public ComplexF Sum(ComplexF[] data)
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{
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Debug.Assert(data != null);
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return SumRecursion(data, 0, data.Length);
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}
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static private ComplexF SumRecursion(ComplexF[] data, int start, int end)
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{
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Debug.Assert(0 <= start, "start = " + start);
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Debug.Assert(start < end, "start = " + start + " and end = " + end);
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Debug.Assert(end <= data.Length, "end = " + end + " and data.Length = " + data.Length);
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if ((end - start) <= 1000)
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{
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ComplexF sum = ComplexF.Zero;
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for (int i = start; i < end; i++)
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{
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sum += data[i];
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}
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return sum;
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}
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else
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{
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int middle = (start + end) >> 1;
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return SumRecursion(data, start, middle) + SumRecursion(data, middle, end);
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}
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}
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/// <summary>
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/// Calculate the sum
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/// </summary>
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/// <param name="data"></param>
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/// <returns></returns>
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static public Complex Sum(Complex[] data)
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{
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Debug.Assert(data != null);
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return SumRecursion(data, 0, data.Length);
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}
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static private Complex SumRecursion(Complex[] data, int start, int end)
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{
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Debug.Assert(0 <= start, "start = " + start);
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Debug.Assert(start < end, "start = " + start + " and end = " + end);
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Debug.Assert(end <= data.Length, "end = " + end + " and data.Length = " + data.Length);
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if ((end - start) <= 1000)
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{
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Complex sum = Complex.Zero;
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for (int i = start; i < end; i++)
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{
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sum += data[i];
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}
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return sum;
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}
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else
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{
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int middle = (start + end) >> 1;
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return SumRecursion(data, start, middle) + SumRecursion(data, middle, end);
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}
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}
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//--------------------------------------------------------------------------------------------
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//--------------------------------------------------------------------------------------------
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/// <summary>
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/// Calculate the sum of squares
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/// </summary>
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/// <param name="data"></param>
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/// <returns></returns>
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static public ComplexF SumOfSquares(ComplexF[] data)
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{
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Debug.Assert(data != null);
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return SumOfSquaresRecursion(data, 0, data.Length);
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}
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static private ComplexF SumOfSquaresRecursion(ComplexF[] data, int start, int end)
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{
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Debug.Assert(0 <= start, "start = " + start);
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Debug.Assert(start < end, "start = " + start + " and end = " + end);
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Debug.Assert(end <= data.Length, "end = " + end + " and data.Length = " + data.Length);
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if ((end - start) <= 1000)
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{
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ComplexF sumOfSquares = ComplexF.Zero;
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for (int i = start; i < end; i++)
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{
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sumOfSquares += data[i] * data[i];
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}
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return sumOfSquares;
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}
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else
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{
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int middle = (start + end) >> 1;
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return SumOfSquaresRecursion(data, start, middle) + SumOfSquaresRecursion(data, middle, end);
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}
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}
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/// <summary>
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/// Calculate the sum of squares
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/// </summary>
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/// <param name="data"></param>
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/// <returns></returns>
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static public Complex SumOfSquares(Complex[] data)
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{
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Debug.Assert(data != null);
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return SumOfSquaresRecursion(data, 0, data.Length);
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}
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static private Complex SumOfSquaresRecursion(Complex[] data, int start, int end)
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{
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Debug.Assert(0 <= start, "start = " + start);
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Debug.Assert(start < end, "start = " + start + " and end = " + end);
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Debug.Assert(end <= data.Length, "end = " + end + " and data.Length = " + data.Length);
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if ((end - start) <= 1000)
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{
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Complex sumOfSquares = Complex.Zero;
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for (int i = start; i < end; i++)
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{
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sumOfSquares += data[i] * data[i];
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}
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return sumOfSquares;
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}
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else
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{
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int middle = (start + end) >> 1;
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return SumOfSquaresRecursion(data, start, middle) + SumOfSquaresRecursion(data, middle, end);
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}
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}
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//--------------------------------------------------------------------------------------------
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//--------------------------------------------------------------------------------------------
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/// <summary>
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/// Calculate the mean (average)
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/// </summary>
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/// <param name="data"></param>
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/// <returns></returns>
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static public ComplexF Mean(ComplexF[] data)
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{
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return ComplexStats.Sum(data) / data.Length;
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}
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/// <summary>
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/// Calculate the mean (average)
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/// </summary>
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/// <param name="data"></param>
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/// <returns></returns>
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static public Complex Mean(Complex[] data)
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{
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return ComplexStats.Sum(data) / data.Length;
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}
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/// <summary>
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/// Calculate the variance
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/// </summary>
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/// <param name="data"></param>
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/// <returns></returns>
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static public ComplexF Variance(ComplexF[] data)
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{
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Debug.Assert(data != null);
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if (data.Length == 0)
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{
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throw new DivideByZeroException("length of data is zero");
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}
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return ComplexStats.SumOfSquares(data) / data.Length - ComplexStats.Sum(data);
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}
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/// <summary>
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/// Calculate the variance
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/// </summary>
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/// <param name="data"></param>
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/// <returns></returns>
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static public Complex Variance(Complex[] data)
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{
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Debug.Assert(data != null);
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if (data.Length == 0)
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{
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throw new DivideByZeroException("length of data is zero");
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}
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return ComplexStats.SumOfSquares(data) / data.Length - ComplexStats.Sum(data);
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}
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/// <summary>
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/// Calculate the standard deviation
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/// </summary>
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/// <param name="data"></param>
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/// <returns></returns>
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static public ComplexF StdDev(ComplexF[] data)
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{
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Debug.Assert(data != null);
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if (data.Length == 0)
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{
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throw new DivideByZeroException("length of data is zero");
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}
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return ComplexMath.Sqrt(ComplexStats.Variance(data));
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}
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/// <summary>
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/// Calculate the standard deviation
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/// </summary>
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/// <param name="data"></param>
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/// <returns></returns>
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static public Complex StdDev(Complex[] data)
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{
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Debug.Assert(data != null);
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if (data.Length == 0)
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{
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throw new DivideByZeroException("length of data is zero");
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}
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return ComplexMath.Sqrt(ComplexStats.Variance(data));
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}
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//--------------------------------------------------------------------------------------------
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//--------------------------------------------------------------------------------------------
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/// <summary>
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/// Calculate the root mean squared (RMS) error between two sets of data.
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/// </summary>
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/// <param name="alpha"></param>
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/// <param name="beta"></param>
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/// <returns></returns>
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static public float RMSError(ComplexF[] alpha, ComplexF[] beta)
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{
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Debug.Assert(alpha != null);
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Debug.Assert(beta != null);
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Debug.Assert(beta.Length == alpha.Length);
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return (float)Math.Sqrt(SumOfSquaredErrorRecursion(alpha, beta, 0, alpha.Length));
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}
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static private float SumOfSquaredErrorRecursion(ComplexF[] alpha, ComplexF[] beta, int start, int end)
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{
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Debug.Assert(0 <= start, "start = " + start);
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Debug.Assert(start < end, "start = " + start + " and end = " + end);
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Debug.Assert(end <= alpha.Length, "end = " + end + " and alpha.Length = " + alpha.Length);
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Debug.Assert(beta.Length == alpha.Length);
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if ((end - start) <= 1000)
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{
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float sumOfSquaredError = 0;
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for (int i = start; i < end; i++)
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{
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ComplexF delta = beta[i] - alpha[i];
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sumOfSquaredError += (delta.Re * delta.Re) + (delta.Im * delta.Im);
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}
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return sumOfSquaredError;
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}
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else
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{
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int middle = (start + end) >> 1;
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return SumOfSquaredErrorRecursion(alpha, beta, start, middle) + SumOfSquaredErrorRecursion(alpha, beta, middle, end);
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}
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}
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/// <summary>
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/// Calculate the root mean squared (RMS) error between two sets of data.
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/// </summary>
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/// <param name="alpha"></param>
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/// <param name="beta"></param>
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/// <returns></returns>
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static public double RMSError(Complex[] alpha, Complex[] beta)
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{
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Debug.Assert(alpha != null);
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Debug.Assert(beta != null);
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Debug.Assert(beta.Length == alpha.Length);
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return Math.Sqrt(SumOfSquaredErrorRecursion(alpha, beta, 0, alpha.Length));
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}
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static private double SumOfSquaredErrorRecursion(Complex[] alpha, Complex[] beta, int start, int end)
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{
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Debug.Assert(0 <= start, "start = " + start);
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Debug.Assert(start < end, "start = " + start + " and end = " + end);
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Debug.Assert(end <= alpha.Length, "end = " + end + " and alpha.Length = " + alpha.Length);
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Debug.Assert(beta.Length == alpha.Length);
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if ((end - start) <= 1000)
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{
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double sumOfSquaredError = 0;
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for (int i = start; i < end; i++)
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{
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Complex delta = beta[i] - alpha[i];
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sumOfSquaredError += (delta.Re * delta.Re) + (delta.Im * delta.Im);
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}
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return sumOfSquaredError;
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}
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else
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{
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int middle = (start + end) >> 1;
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return SumOfSquaredErrorRecursion(alpha, beta, start, middle) + SumOfSquaredErrorRecursion(alpha, beta, middle, end);
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}
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}
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}
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}
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