#include <conjugate_gradient.h>
Public Member Functions | |
template<class Func, class Deriv> | |
ConjugateGradient (const Vector< Size > &start, const Func &func, const Deriv &deriv) | |
template<class Func> | |
void | find_next_point (const Func &func) |
bool | finished () |
template<class Deriv> | |
void | update_vectors_PR (const Deriv &deriv) |
template<class Func, class Deriv> | |
bool | iterate (const Func &func, const Deriv &deriv) |
Public Attributes | |
const int | size |
Vector< Size > | g |
Vector< Size > | h |
Vector< Size > | old_g |
Vector< Size > | old_h |
Vector< Size > | x |
Vector< Size > | old_x |
Precision | y |
Precision | old_y |
Precision | tolerance |
Precision | epsilon |
int | max_iterations |
Precision | bracket_initial_lambda |
Precision | linesearch_tolerance |
Precision | linesearch_epsilon |
int | linesearch_max_iterations |
int | iterations |
The following code snippet will perform an optimization on the Rosenbrock Bananna function in two dimensions:
double Rosenbrock(const Vector<2>& v) { return sq(1 - v[0]) + 100 * sq(v[1] - sq(v[0])); } Vector<2> RosenbrockDerivatives(const Vector<2>& v) { double x = v[0]; double y = v[1]; Vector<2> ret; ret[0] = -2+2*x-400*(y-sq(x))*x; ret[1] = 200*y-200*sq(x); return ret; } int main() { ConjugateGradient<2> cg(makeVector(0,0), Rosenbrock, RosenbrockDerivatives); while(!cg.iterate(Rosenbrock, RosenbrockDerivatives)) cout << "y_" << iteration << " = " << cg.y << endl; cout << "Optimal value: " << cg.y << endl; }
The chances are that you will want to read the documentation for ConjugateGradient::ConjugateGradient and ConjugateGradient::iterate.
Linesearch is currently performed using golden-section search and conjugate vector updates are performed using the Polak-Ribiere equations. There many tunable parameters, and the internals are readily accessible, so alternative termination conditions etc can easily be substituted. However, ususally these will not be necessary.
TooN::ConjugateGradient< Size, Precision >::ConjugateGradient | ( | const Vector< Size > & | start, | |
const Func & | func, | |||
const Deriv & | deriv | |||
) |
Initialize the ConjugateGradient class with sensible values.
start | Starting point, x | |
func | Function f to compute ![]() | |
deriv | Function to compute ![]() |
void TooN::ConjugateGradient< Size, Precision >::find_next_point | ( | const Func & | func | ) |
Perform a linesearch from the current point (x) along the current conjugate vector (h).
The linesearch does not make use of derivatives. You probably do not want to use this function. See iterate() instead. This function updates:
func | Functor returning the function value at a given point. |
bool TooN::ConjugateGradient< Size, Precision >::finished | ( | ) |
Check to see it iteration should stop.
You probably do not want to use this function. See iterate() instead. This function updates nothing.
void TooN::ConjugateGradient< Size, Precision >::update_vectors_PR | ( | const Deriv & | deriv | ) |
After an iteration, update the gradient and conjugate using the Polak-Ribiere equations.
/
deriv | Functor to compute derivatives at the specified point. This function updates:
|
bool TooN::ConjugateGradient< Size, Precision >::iterate | ( | const Func & | func, | |
const Deriv & | deriv | |||
) |
Use this function to iterate over the optimization.
Note that after iterate returns false, g, h, old_g and old_h will not have been updated. This function updates:
func | Functor returning the function value at a given point. | |
deriv | Functor to compute derivatives at the specified point. |
const int TooN::ConjugateGradient< Size, Precision >::size |
Dimensionality of the space.
Vector<Size> TooN::ConjugateGradient< Size, Precision >::g |
Gradient vector used by the next call to iterate().
Vector<Size> TooN::ConjugateGradient< Size, Precision >::h |
Conjugate vector to be searched along in the next call to iterate().
Vector<Size> TooN::ConjugateGradient< Size, Precision >::old_g |
Gradient vector used to compute $h$ in the last call to iterate().
Vector<Size> TooN::ConjugateGradient< Size, Precision >::old_h |
Conjugate vector searched along in the last call to iterate().
Vector<Size> TooN::ConjugateGradient< Size, Precision >::x |
Current position (best known point).
Vector<Size> TooN::ConjugateGradient< Size, Precision >::old_x |
Previous best known point (not set at construction).
Precision TooN::ConjugateGradient< Size, Precision >::y |
Function at .
Precision TooN::ConjugateGradient< Size, Precision >::old_y |
Function at old_x.
Precision TooN::ConjugateGradient< Size, Precision >::tolerance |
Tolerance used to determine if the optimization is complete. Defaults to square root of machine precision.
Precision TooN::ConjugateGradient< Size, Precision >::epsilon |
Additive term in tolerance to prevent excessive iterations if . Known as
ZEPS
in numerical recipies. Defaults to 1e-20.
int TooN::ConjugateGradient< Size, Precision >::max_iterations |
Maximum number of iterations. Defaults to size
.
Precision TooN::ConjugateGradient< Size, Precision >::bracket_initial_lambda |
Initial stepsize used in bracketing the minimum for the line search. Defaults to 1.
Precision TooN::ConjugateGradient< Size, Precision >::linesearch_tolerance |
Tolerance used to determine if the linesearch is complete. Defaults to square root of machine precision.
Precision TooN::ConjugateGradient< Size, Precision >::linesearch_epsilon |
Additive term in tolerance to prevent excessive iterations if . Known as
ZEPS
in numerical recipies. Defaults to 1e-20.
int TooN::ConjugateGradient< Size, Precision >::linesearch_max_iterations |
Maximum number of iterations in the linesearch. Defaults to 100.
int TooN::ConjugateGradient< Size, Precision >::iterations |
Number of iterations performed.