mirror of https://github.com/davisking/dlib.git
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
|
|
/*
|
|
|
|
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 lets 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, lets 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 lets 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
|
|
*/
|