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229 lines
7.6 KiB
C++
229 lines
7.6 KiB
C++
// The contents of this file are in the public domain. See LICENSE_FOR_EXAMPLE_PROGRAMS.txt
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/*
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This is an example illustrating the use the general purpose non-linear
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least squares optimization routines from the dlib C++ Library.
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This example program will demonstrate how these routines can be used for data fitting.
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In particular, we will generate a set of data and then use the least squares
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routines to infer the parameters of the model which generated the data.
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*/
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#include <dlib/optimization.h>
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#include <iostream>
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#include <vector>
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using namespace std;
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using namespace dlib;
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// ----------------------------------------------------------------------------------------
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typedef matrix<double,2,1> input_vector;
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typedef matrix<double,3,1> parameter_vector;
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// ----------------------------------------------------------------------------------------
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// We will use this function to generate data. It represents a function of 2 variables
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// and 3 parameters. The least squares procedure will be used to infer the values of
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// the 3 parameters based on a set of input/output pairs.
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double model (
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const input_vector& input,
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const parameter_vector& params
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)
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{
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const double p0 = params(0);
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const double p1 = params(1);
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const double p2 = params(2);
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const double i0 = input(0);
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const double i1 = input(1);
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const double temp = p0*i0 + p1*i1 + p2;
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return temp*temp;
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}
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// ----------------------------------------------------------------------------------------
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// This function is the "residual" for a least squares problem. It takes an input/output
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// pair and compares it to the output of our model and returns the amount of error. The idea
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// is to find the set of parameters which makes the residual small on all the data pairs.
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double residual (
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const std::pair<input_vector, double>& data,
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const parameter_vector& params
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)
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{
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return model(data.first, params) - data.second;
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}
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// ----------------------------------------------------------------------------------------
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// This function is the derivative of the residual() function with respect to the parameters.
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parameter_vector residual_derivative (
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const std::pair<input_vector, double>& data,
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const parameter_vector& params
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)
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{
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parameter_vector der;
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const double p0 = params(0);
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const double p1 = params(1);
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const double p2 = params(2);
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const double i0 = data.first(0);
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const double i1 = data.first(1);
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const double temp = p0*i0 + p1*i1 + p2;
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der(0) = i0*2*temp;
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der(1) = i1*2*temp;
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der(2) = 2*temp;
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return der;
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}
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// ----------------------------------------------------------------------------------------
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int main()
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{
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try
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{
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// randomly pick a set of parameters to use in this example
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const parameter_vector params = 10*randm(3,1);
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cout << "params: " << trans(params) << endl;
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// Now lets generate a bunch of input/output pairs according to our model.
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std::vector<std::pair<input_vector, double> > data_samples;
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input_vector input;
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for (int i = 0; i < 1000; ++i)
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{
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input = 10*randm(2,1);
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const double output = model(input, params);
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// save the pair
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data_samples.push_back(make_pair(input, output));
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}
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// Before we do anything, lets make sure that our derivative function defined above matches
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// the approximate derivative computed using central differences (via derivative()).
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// If this value is big then it means we probably typed the derivative function incorrectly.
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cout << "derivative error: " << length(residual_derivative(data_samples[0], params) -
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derivative(&residual)(data_samples[0], params) ) << endl;
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// Now lets use the solve_least_squares_lm() routine to figure out what the
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// parameters are based on just the data_samples.
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parameter_vector x;
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x = 1;
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cout << "Use Levenberg-Marquardt" << endl;
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// Use the Levenberg-Marquardt method to determine the parameters which
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// minimize the sum of all squared residuals.
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solve_least_squares_lm(objective_delta_stop_strategy(1e-7).be_verbose(),
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&residual,
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&residual_derivative,
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data_samples,
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x);
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// Now x contains the solution. If everything worked it will be equal to params.
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cout << "inferred parameters: "<< trans(x) << endl;
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cout << "solution error: "<< length(x - params) << endl;
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cout << endl;
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x = 1;
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cout << "Use Levenberg-Marquardt, approximate derivatives" << endl;
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// If we didn't create the residual_derivative function then we could
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// have used this method which numerically approximates the derivatives for you.
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solve_least_squares_lm(objective_delta_stop_strategy(1e-7).be_verbose(),
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&residual,
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derivative(&residual),
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data_samples,
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x);
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// Now x contains the solution. If everything worked it will be equal to params.
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cout << "inferred parameters: "<< trans(x) << endl;
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cout << "solution error: "<< length(x - params) << endl;
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cout << endl;
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x = 1;
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cout << "Use Levenberg-Marquardt/quasi-newton hybrid" << endl;
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// This version of the solver uses a method which is appropriate for problems
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// where the residuals don't go to zero at the solution. So in these cases
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// it may provide a better answer.
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solve_least_squares(objective_delta_stop_strategy(1e-7).be_verbose(),
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&residual,
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&residual_derivative,
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data_samples,
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x);
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// Now x contains the solution. If everything worked it will be equal to params.
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cout << "inferred parameters: "<< trans(x) << endl;
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cout << "solution error: "<< length(x - params) << endl;
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}
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catch (std::exception& e)
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{
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cout << e.what() << endl;
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}
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}
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// Example output:
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/*
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params: 8.40188 3.94383 7.83099
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derivative error: 9.78267e-06
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Use Levenberg-Marquardt
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iteration: 0 objective: 2.14455e+10
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iteration: 1 objective: 1.96248e+10
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iteration: 2 objective: 1.39172e+10
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iteration: 3 objective: 1.57036e+09
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iteration: 4 objective: 2.66917e+07
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iteration: 5 objective: 4741.9
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iteration: 6 objective: 0.000238674
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iteration: 7 objective: 7.8815e-19
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iteration: 8 objective: 0
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inferred parameters: 8.40188 3.94383 7.83099
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solution error: 0
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Use Levenberg-Marquardt, approximate derivatives
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iteration: 0 objective: 2.14455e+10
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iteration: 1 objective: 1.96248e+10
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iteration: 2 objective: 1.39172e+10
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iteration: 3 objective: 1.57036e+09
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iteration: 4 objective: 2.66917e+07
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iteration: 5 objective: 4741.87
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iteration: 6 objective: 0.000238701
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iteration: 7 objective: 1.0571e-18
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iteration: 8 objective: 4.12469e-22
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inferred parameters: 8.40188 3.94383 7.83099
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solution error: 5.34754e-15
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Use Levenberg-Marquardt/quasi-newton hybrid
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iteration: 0 objective: 2.14455e+10
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iteration: 1 objective: 1.96248e+10
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iteration: 2 objective: 1.3917e+10
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iteration: 3 objective: 1.5572e+09
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iteration: 4 objective: 2.74139e+07
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iteration: 5 objective: 5135.98
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iteration: 6 objective: 0.000285539
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iteration: 7 objective: 1.15441e-18
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iteration: 8 objective: 3.38834e-23
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inferred parameters: 8.40188 3.94383 7.83099
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solution error: 1.77636e-15
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*/
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