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