hmatrix-gsl-0.18.2.0: Numerical computation

Numeric.GSL.SimulatedAnnealing

Description

Simulated annealing routines.

https://www.gnu.org/software/gsl/manual/html_node/Simulated-Annealing.html#Simulated-Annealing

Here is a translation of the simple example given in the GSL manual:

import Numeric.GSL.SimulatedAnnealing
import Numeric.LinearAlgebra.HMatrix

main = print $simanSolve 0 1 exampleParams 15.5 exampleE exampleM exampleS (Just show) exampleParams = SimulatedAnnealingParams 200 1000 1.0 1.0 0.008 1.003 2.0e-6 exampleE x = exp (-(x - 1)**2) * sin (8 * x) exampleM x y = abs$ x - y

exampleS rands stepSize current = (rands ! 0) * 2 * stepSize - stepSize + current

The manual states:

    The first example, in one dimensional Cartesian space, sets up an
energy function which is a damped sine wave; this has many local
minima, but only one global minimum, somewhere between 1.0 and
1.5. The initial guess given is 15.5, which is several local minima
away from the global minimum.

This global minimum is around 1.36.

Synopsis

# Searching for minima

Arguments

 :: Int Seed for the random number generator -> Int nrand, the number of random Doubles the step function requires -> SimulatedAnnealingParams Parameters to configure the solver -> a Initial configuration x0 -> (a -> Double) Energy functional e -> (a -> a -> Double) Metric definition m -> (Vector Double -> Double -> a -> a) Stepping function step -> Maybe (a -> String) Optional printing function -> a Best configuration the solver has found

Calling

simanSolve seed nrand params x0 e m step print

performs a simulated annealing search through a given space. So that any configuration type may be used, the space is specified by providing the functions e (the energy functional) and m (the metric definition). x0 is the initial configuration of the system. The simulated annealing steps are generated using the user-provided function step, which should randomly construct a new system configuration.

If Nothing is passed instead of a printing function, no incremental output will be generated. Otherwise, the GSL-formatted output, including the configuration description the user function generates, will be printed to stdout.

Each time the step function is called, it is supplied with a random vector containing nrand Double values, uniformly distributed in [0, 1). It should use these values to generate its new configuration.

# Configuring the annealing process

SimulatedAnnealingParams is a translation of the gsl_siman_params_t structure documented in the GSL manual, which controls the simulated annealing algorithm.

The annealing process is parameterized by the Boltzmann distribution and the cooling schedule. For more details, see the relevant section of the manual.

Constructors

 SimulatedAnnealingParams Fieldsn_tries :: CIntThe number of points to try for each step.iters_fixed_T :: CIntThe number of iterations at each temperaturestep_size :: DoubleThe maximum step size in the random walkboltzmann_k :: DoubleBoltzmann distribution parametercooling_t_initial :: DoubleInitial temperaturecooling_mu_t :: DoubleCooling rate parametercooling_t_min :: DoubleFinal temperature

Instances

 Source # Methods Source # Source # Methods Source # MethodspokeByteOff :: Ptr b -> Int -> SimulatedAnnealingParams -> IO () #