2019獨角獸企業重金招聘Python工程師標準>>>

頭文件：

/** Copyright (c) 2008-2011 Zhang Ming (M. Zhang), zmjerry@163.com** 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

實現文件：

/** Copyright (c) 2008-2011 Zhang Ming (M. Zhang), zmjerry@163.com** 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) );}elsern = 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) );}elsern = 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);}} }

測試代碼：

/****************************************************************************** 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 functionscout << "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 functionscout << "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; }

運行結果：

xn: size: 3 by 1 0.0000 1.0000 2.0000yn: size: 5 by 1 -2.0000 -1.0000 0.0000 1.0000 2.0000auto-correlation of xn: size: 5 by 1 0.0000 2.0000 5.0000 2.0000 0.0000biased auto-correlation of xn: size: 5 by 1 0.0000 0.6667 1.6667 0.6667 0.0000unbiased auto-correlation of xn: size: 5 by 1 0.0000 1.0000 1.6667 1.0000 0.0000cross-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 0.0000cross-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 0.0000biased 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 0.0000biased 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 0.0000unbiased 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 0.0000unbiased 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 0.0000fast auto-correlation of xn: size: 5 by 1 0.0000 2.0000 5.0000 2.0000 -0.0000fast biased auto-correlation of xn: size: 5 by 1 0.0000 0.6667 1.6667 0.6667 -0.0000fast unbiased auto-correlation of xn: size: 5 by 1 0.0000 1.0000 1.6667 1.0000 -0.0000fast 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 -0.0000fast 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 0.0000fast 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 -0.0000fast 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 0.0000fast 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 -0.0000fast 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 0.0000Process returned 0 (0x0) execution time : 0.187 s Press any key to continue.

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