相关及其快速算法的C++实现
头文件：
/* * Copyright (c) 2008-2011 Zhang Ming (M. Zhang), [email protected] * * This program is free software; you can redistribute it and/or modify it * under the terms of the GNU General Public License as published by the * Free Software Foundation, either version 2 or any later version. * * 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. * * This program is distributed in the hope that it will be useful, but WITHOUT * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for * more details. A copy of the GNU General Public License is available at: * http://www.fsf.org/licensing/licenses */ /***************************************************************************** * correlation.h * * The routines in this file estimate the cross-correlation sequence of a * random process. Autocorrelation is handled as a special case. * * c = corr(x,y,opt) returns the cross-correlation sequence in a length * 2*N-1 vector, where x and y are length N vectors (N>1). If x and y are * not the same length, the shorter vector is zero-padded to the length of * the longer vector. * * The parameter "opt" specifies a normalization option for the cross- * correlation, where 'opt' is * "none" : to use the raw, unscaled cross-correlations (default); * "biased" : biased estimate of the cross-correlation function; * "unbiased" : unbiased estimate of the cross-correlation function. * * We use FFT computing the auto-corelation and cross-corelation functions * based on fallowing facts: for real functions, * R1[x(t),y(t)] = sum{ x(u)*y(u-t) } = Conv[x(t),y(-t)] * R2[x(t),y(t)] = sum{ x(u)*y(u+t) } = Conv[x(-t),y(t)] * And here we use the first defination. * * Zhang Ming, 2010-10, Xi'an Jiaotong University. *****************************************************************************/ #ifndef CORRELATION_H #define CORRELATION_H #include <convolution.h> #include <utilities.h> namespace splab { template<typename Type> Vector<Type> corr( const Vector<Type>&, const string &opt="none" ); template<typename Type> Vector<Type> corr( const Vector<Type>&, const Vector<Type>&, const string &opt="none" ); template<typename Type> Vector<Type> fastCorr( const Vector<Type>&, const string &opt="none" ); template<typename Type> Vector<Type> fastCorr( const Vector<Type>&, const Vector<Type>&, const string &opt="none" ); template<typename Type> static void biasedProcessing( Vector<Type> &, const string &opt ); #include <correlation-impl.h> } // namespace splab #endif // CORRELATION_H
实现文件：
/* * Copyright (c) 2008-2011 Zhang Ming (M. Zhang), [email protected] * * This program is free software; you can redistribute it and/or modify it * under the terms of the GNU General Public License as published by the * Free Software Foundation, either version 2 or any later version. * * 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. * * This program is distributed in the hope that it will be useful, but WITHOUT * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for * more details. A copy of the GNU General Public License is available at: * http://www.fsf.org/licensing/licenses */ /***************************************************************************** * correlation-impl.h * * Implementation for linear correlation. * * Zhang Ming, 2010-10, Xi'an Jiaotong University. *****************************************************************************/ /** * Auto-correlation by defination in time domain. */ template<typename Type> inline Vector<Type> corr( const Vector<Type> &xn, const string &opt ) { Vector<Type> rn = conv( xn, reverse(xn) ); biasedProcessing( rn, opt ); return rn; } /** * Cross-correlation by defination in time domain. */ template<typename Type> inline Vector<Type> corr( const Vector<Type> &xn, const Vector<Type> &yn, const string &opt ) { int N = xn.size(), d = N - yn.size(); Vector<Type> rn; if( d > 0 ) rn = conv( xn, reverse(wextend(yn,d,"right","zpd")) ); else if( d < 0 ) { N -= d; rn = conv( wextend(xn,-d,"right","zpd"), reverse(yn) ); } else rn = conv( xn, reverse(yn) ); biasedProcessing( rn, opt ); return rn; } /** * Fast auto-correlation by using FFT. */ template<typename Type> inline Vector<Type> fastCorr( const Vector<Type> &xn, const string &opt ) { Vector<Type> rn = fastConv( xn, reverse(xn) ); biasedProcessing( rn, opt ); return rn; } /** * Fast cross-correlation by using FFT. */ template<typename Type> inline Vector<Type> fastCorr( const Vector<Type> &xn, const Vector<Type> &yn, const string &opt ) { int N = xn.size(), d = N - yn.size(); Vector<Type> rn; if( d > 0 ) rn = fastConv( xn, reverse(wextend(yn,d,"right","zpd")) ); else if( d < 0 ) { N -= d; rn = fastConv( wextend(xn,-d,"right","zpd"), reverse(yn) ); } else rn = fastConv( xn, reverse(yn) ); biasedProcessing( rn, opt ); return rn; } /** * Biase processing for correlation. */ template<typename Type> static void biasedProcessing( Vector<Type> &rn, const string &opt ) { int N = (rn.size()+1) / 2; if( opt == "biased" ) rn /= Type(N); else if( opt == "unbiased" ) { int mid = N-1; rn[mid] /= N; for( int i=1; i<N; ++i ) { rn[mid+i] /= (N-i); rn[mid-i] /= (N-i); } } }
测试代码：
/*****************************************************************************
* correlation_test.cpp
*
* Correlation testing.
*
* Zhang Ming, 2010-10, Xi'an Jiaotong University.
*****************************************************************************/
#define BOUNDS_CHECK
#include <iostream>
#include <iomanip>
#include <correlation.h>
using namespace std;
using namespace splab;
typedef double Type;
const int M = 3;
const int N = 5;
int main()
{
Vector<Type> xn( M ), yn( N );
for( int i=0; i<M; ++i )
xn[i] = i;
for( int i=0; i<N; ++i )
yn[i] = i-N/2;
cout << setiosflags(ios::fixed) << setprecision(4);
cout << "xn: " << xn << endl;
cout << "yn: " << yn << endl;
// auto and cross correlation functions
cout << "auto-correlation of xn: " << corr(xn) << endl;
cout << "biased auto-correlation of xn: " << corr(xn,"biased") << endl;
cout << "unbiased auto-correlation of xn: " << corr(xn,"unbiased") << endl;
cout << "cross-correlation of xn and yn: " << corr(xn,yn) << endl;
cout << "cross-correlation of yn and xn: " << corr(yn,xn) << endl;
cout << "biased cross-correlation of xn and yn: "
<< corr(xn,yn,"biased") << endl;
cout << "biased cross-correlation of yn and xn: "
<< corr(yn,xn,"biased") << endl;
cout << "unbiased cross-correlation of xn and yn: "
<< corr(xn,yn,"unbiased") << endl;
cout << "unbiased cross-correlation of yn and xn: "
<< corr(yn,xn,"unbiased") << endl;
// fast auto and cross correlation functions
cout << "fast auto-correlation of xn: " << fastCorr(xn) << endl;
cout << "fast biased auto-correlation of xn: " << fastCorr(xn,"biased") << endl;
cout << "fast unbiased auto-correlation of xn: " << fastCorr(xn,"unbiased") << endl;
cout << "fast cross-correlation of xn and yn: " << fastCorr(xn,yn) << endl;
cout << "fast cross-correlation of yn and xn: " << fastCorr(yn,xn) << endl;
cout << "fast biased cross-correlation of xn and yn: "
<< fastCorr(xn,yn,"biased") << endl;
cout << "fast biased cross-correlation of yn and xn: "
<< fastCorr(yn,xn,"biased") << endl;
cout << "fast unbiased cross-correlation of xn and yn: "
<< fastCorr(xn,yn,"unbiased") << endl;
cout << "fast unbiased cross-correlation of yn and xn: "
<< fastCorr(yn,xn,"unbiased") << endl;
return 0;
}
运行结果：
xn: size: 3 by 1 0.0000 1.0000 2.0000 yn: size: 5 by 1 -2.0000 -1.0000 0.0000 1.0000 2.0000 auto-correlation of xn: size: 5 by 1 0.0000 2.0000 5.0000 2.0000 0.0000 biased auto-correlation of xn: size: 5 by 1 0.0000 0.6667 1.6667 0.6667 0.0000 unbiased auto-correlation of xn: size: 5 by 1 0.0000 1.0000 1.6667 1.0000 0.0000 cross-correlation of xn and yn: size: 9 by 1 0.0000 2.0000 5.0000 2.0000 -1.0000 -4.0000 -4.0000 0.0000 0.0000 cross-correlation of yn and xn: size: 9 by 1 0.0000 0.0000 -4.0000 -4.0000 -1.0000 2.0000 5.0000 2.0000 0.0000 biased cross-correlation of xn and yn: size: 9 by 1 0.0000 0.4000 1.0000 0.4000 -0.2000 -0.8000 -0.8000 0.0000 0.0000 biased cross-correlation of yn and xn: size: 9 by 1 0.0000 0.0000 -0.8000 -0.8000 -0.2000 0.4000 1.0000 0.4000 0.0000 unbiased cross-correlation of xn and yn: size: 9 by 1 0.0000 1.0000 1.6667 0.5000 -0.2000 -1.0000 -1.3333 0.0000 0.0000 unbiased cross-correlation of yn and xn: size: 9 by 1 0.0000 0.0000 -1.3333 -1.0000 -0.2000 0.5000 1.6667 1.0000 0.0000 fast auto-correlation of xn: size: 5 by 1 0.0000 2.0000 5.0000 2.0000 -0.0000 fast biased auto-correlation of xn: size: 5 by 1 0.0000 0.6667 1.6667 0.6667 -0.0000 fast unbiased auto-correlation of xn: size: 5 by 1 0.0000 1.0000 1.6667 1.0000 -0.0000 fast cross-correlation of xn and yn: size: 9 by 1 -0.0000 2.0000 5.0000 2.0000 -1.0000 -4.0000 -4.0000 -0.0000 -0.0000 fast cross-correlation of yn and xn: size: 9 by 1 -0.0000 -0.0000 -4.0000 -4.0000 -1.0000 2.0000 5.0000 2.0000 0.0000 fast biased cross-correlation of xn and yn: size: 9 by 1 -0.0000 0.4000 1.0000 0.4000 -0.2000 -0.8000 -0.8000 -0.0000 -0.0000 fast biased cross-correlation of yn and xn: size: 9 by 1 -0.0000 -0.0000 -0.8000 -0.8000 -0.2000 0.4000 1.0000 0.4000 0.0000 fast unbiased cross-correlation of xn and yn: size: 9 by 1 -0.0000 1.0000 1.6667 0.5000 -0.2000 -1.0000 -1.3333 -0.0000 -0.0000 fast unbiased cross-correlation of yn and xn: size: 9 by 1 -0.0000 -0.0000 -1.3333 -1.0000 -0.2000 0.5000 1.6667 1.0000 0.0000 Process returned 0 (0x0) execution time : 0.187 s Press any key to continue.