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