共轭梯度优化算法的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 */ /***************************************************************************** * conjgrad.h * * Conjugate gradient optimal method. * * This class is designed for finding the minimum value of objective function * in one dimension or multidimension. Inexact line search and PRP (Polak- * Ribiere-Polyak) formula are used to get the step size and conjgate * coefficient "beta" in each iteration. * * Zhang Ming, 2010-03, Xi'an Jiaotong University. *****************************************************************************/ #ifndef CONJGRAD_H #define CONJGRAD_H #include <linesearch.h> #include <utilities.h> namespace splab { template <typename Dtype, typename Ftype> class ConjGrad : public LineSearch<Dtype, Ftype> { public: ConjGrad(); ~ConjGrad(); void optimize( Ftype &func, Vector<Dtype> &x0, int reLen, Dtype tol=Dtype(1.0e-6), int maxItr=100 ); Vector<Dtype> getOptValue() const; Vector<Dtype> getGradNorm() const; Dtype getFuncMin() const; int getItrNum() const; private: // iteration number int itrNum; // minimum value of objective function Dtype fMin; // optimal solution Vector<Dtype> xOpt; // gradient norm for each iteration Vector<Dtype> gradNorm; }; // class ConjGrad #include <conjgrad-impl.h> } // namespace splab #endif // CONJGRAD_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 */ /***************************************************************************** * conjgrad-impl.h * * Implementation for ConjGrad class. * * Zhang Ming, 2010-03, Xi'an Jiaotong University. *****************************************************************************/ /** * constructors and destructor */ template <typename Dtype, typename Ftype> ConjGrad<Dtype, Ftype>::ConjGrad() : LineSearch<Dtype, Ftype>() { } template <typename Dtype, typename Ftype> ConjGrad<Dtype, Ftype>::~ConjGrad() { } /** * Finding the optimal solution. The default tolerance error and maximum * iteratin number are "tol=1.0e-6" and "maxItr=100", respectively. */ template <typename Dtype, typename Ftype> void ConjGrad<Dtype, Ftype>::optimize( Ftype &func, Vector<Dtype> &x0, int reLen, Dtype tol, int maxItr ) { // initialize parameters. int k = 0, cnt = 0; Vector<Dtype> x(x0); Dtype fx = func(x); this->funcNum++; Vector<Dtype> gnorm(maxItr); Vector<Dtype> g = func.grad(x); gnorm[k++]= norm(g); Dtype alpha, beta; Vector<Dtype> d(x0.dim()), dPrev(x0.dim()), gPrev(x0.dim()); while( ( gnorm(k) > tol ) && ( k < maxItr ) ) { // descent direction if( mod(k,reLen) == 1 ) d = - g; else { beta = dotProd(g,g-gPrev) / dotProd(gPrev,gPrev); d = beta*dPrev - g ; } // one dimension searching alpha = this->getStep( func, x, d ); if( !this->success ) { dPrev = 0; cnt++; if( cnt == maxItr ) break; } else { // update x += alpha*d; fx = func(x); this->funcNum++; dPrev = d; gPrev = g; g = func.grad(x); gnorm[k++] = norm(g); } } xOpt = x; fMin = fx; gradNorm.resize(k); for( int i=0; i<k; ++i ) gradNorm[i] = gnorm[i]; if( gradNorm(k) > tol ) this->success = false; } /** * Get the optimum point. */ template <typename Dtype, typename Ftype> inline Vector<Dtype> ConjGrad<Dtype, Ftype>::getOptValue() const { return xOpt; } /** * Get the norm of gradient in each iteration. */ template <typename Dtype, typename Ftype> inline Vector<Dtype> ConjGrad<Dtype, Ftype>::getGradNorm() const { return gradNorm; } /** * Get the minimum value of objective function. */ template <typename Dtype, typename Ftype> inline Dtype ConjGrad<Dtype, Ftype>::getFuncMin() const { return fMin; } /** * Get the iteration number. */ template <typename Dtype, typename Ftype> inline int ConjGrad<Dtype, Ftype>::getItrNum() const { return gradNorm.dim()-1; }
测试代码：
/*****************************************************************************
* conjgrad_test.cpp
*
* Conjugate gradient optimal method testing.
*
* Zhang Ming, 2010-03, Xi'an Jiaotong University.
*****************************************************************************/
#define BOUNDS_CHECK
#include <iostream>
#include <iomanip>
#include <objfunc.h>
#include <conjgrad.h>
using namespace std;
using namespace splab;
typedef double Type;
int main()
{
Type a = 1.0,
b = -1.0,
c = -1.0;
ObjFunc<Type> f( a, b, c );
Vector<Type> x0(2);
x0(1) = 0.5;
x0(2) = 0.5;
Type tolErr = 1.0e-6;
ConjGrad< Type, ObjFunc<Type> > prp;
prp.optimize( f, x0, x0.dim(), tolErr );
if( prp.isSuccess() )
{
Vector<Type> xmin = prp.getOptValue();
int N = prp.getItrNum();
cout << "The iterative number is: " << N << endl << endl;
cout << "The number of function calculation is: "
<< prp.getFuncNum() << endl << endl;
cout << setiosflags(ios::fixed) << setprecision(4);
cout << "The optimal value of x is: " << xmin << endl;
cout << "The minimum value of f(x) is: " << f(xmin) << endl << endl;
cout << "The gradient's norm at x is: "
<< prp.getGradNorm()[N] << endl << endl;
}
else
cout << "The optimal solution cann't be found!" << endl;
return 0;
}
运行结果：
The iterative number is: 29 The number of function calculation is: 207 The optimal value of x is: size: 2 by 1 -0.7071 -0.0000 The minimum value of f(x) is: -0.4289 The gradient's norm at x is: 0.0000 Process returned 0 (0x0) execution time : 0.078 s Press any key to continue.