pygsti.optimize.optimize¶
Optimization (minimization) functions
Module Contents¶
Functions¶
|
Minimizes the function fn starting at x0. |
|
Minimize a function using repeated applications of the simplex algorithm. |
|
Minimizes a function using a custom simplex implmentation. |
|
A simple implementation of the Particle Swarm Optimization Algorithm. |
|
Minimize a function using an evolutionary algorithm. |
|
Create a callback function that prints the value of an objective function. |
|
|
|
Checks a jacobian function using finite differences. |
- pygsti.optimize.optimize.minimize(fn, x0, method='cg', callback=None, tol=1e-10, maxiter=1000000, maxfev=None, stopval=None, jac=None, verbosity=0, **addl_kwargs)¶
Minimizes the function fn starting at x0.
This is a gateway function to all other minimization routines within this module, providing a common interface to many different minimization methods (including and extending beyond those available from scipy.optimize).
- Parameters
fn (function) – The function to minimize.
x0 (numpy array) – The starting point (argument to fn).
method (string, optional) – Which minimization method to use. Allowed values are: “simplex” : uses _fmin_simplex “supersimplex” : uses _fmin_supersimplex “customcg” : uses fmax_cg (custom CG method) “brute” : uses scipy.optimize.brute “basinhopping” : uses scipy.optimize.basinhopping with L-BFGS-B “swarm” : uses _fmin_particle_swarm “evolve” : uses _fmin_evolutionary (which uses DEAP) < methods available from scipy.optimize.minimize >
callback (function, optional) – A callback function to be called in order to track optimizer progress. Should have signature: myCallback(x, f=None, accepted=None). Note that create_objfn_printer(…) function can be used to create a callback.
tol (float, optional) – Tolerance value used for all types of tolerances available in a given method.
maxiter (int, optional) – Maximum iterations.
maxfev (int, optional) – Maximum function evaluations; used only when available, and defaults to maxiter.
stopval (float, optional) – For basinhopping method only. When f <= stopval then basinhopping outer loop will terminate. Useful when a bound on the minimum is known.
jac (function) – Jacobian function.
verbosity (int) – Level of detail to print to stdout.
addl_kwargs (dict) – Additional arguments for the specific optimizer being used.
- Returns
scipy.optimize.Result object – Includes members ‘x’, ‘fun’, ‘success’, and ‘message’.
- pygsti.optimize.optimize._fmin_supersimplex(fn, x0, abs_outer_tol, rel_outer_tol, inner_tol, max_outer_iter, min_inner_maxiter, max_inner_maxiter, callback, printer)¶
Minimize a function using repeated applications of the simplex algorithm.
By varying the maximum number of iterations and repeatedly calling scipy’s Nelder-Mead simplex optimization, this function performs as a robust (but slow) minimization.
- Parameters
fn (function) – The function to minimize.
x0 (numpy array) – The starting point (argument to fn).
abs_outer_tol (float) – Absolute tolerance of outer loop
rel_outer_tol (float) – Relative tolerance of outer loop
inner_tol (float) – Tolerance fo inner loop
max_outer_iter (int) – Maximum number of outer-loop iterations
min_inner_maxiter (int) – Minimum number of inner-loop iterations
max_inner_maxiter (int) – Maxium number of outer-loop iterations
printer (VerbosityPrinter) – Printer for displaying output status messages.
- Returns
scipy.optimize.Result object – Includes members ‘x’, ‘fun’, ‘success’, and ‘message’.
- pygsti.optimize.optimize._fmin_simplex(fn, x0, slide=1.0, tol=1e-08, maxiter=1000)¶
Minimizes a function using a custom simplex implmentation.
This was used primarily to check scipy’s Nelder-Mead method and runs much slower, so there’s not much reason for using this method.
- Parameters
fn (function) – The function to minimize.
x0 (numpy array) – The starting point (argument to fn).
slide (float, optional) – Affects initial simplex point locations
tol (float, optional) – Relative tolerance as a convergence criterion.
maxiter (int, optional) – Maximum iterations.
- Returns
scipy.optimize.Result object – Includes members ‘x’, ‘fun’, ‘success’, and ‘message’.
- pygsti.optimize.optimize._fmin_particle_swarm(f, x0, err_crit, iter_max, printer, popsize=100, c1=2, c2=2)¶
A simple implementation of the Particle Swarm Optimization Algorithm.
(Pradeep Gowda 2009-03-16)
- Parameters
f (function) – The function to minimize.
x0 (numpy array) – The starting point (argument to fn).
err_crit (float) – Critical error (i.e. tolerance). Stops when error < err_crit.
iter_max (int) – Maximum iterations.
popsize (int, optional) – Population size. Larger populations are better at finding the global optimum but make the algorithm take longer to run.
c1 (float, optional) – Coefficient describing a particle’s affinity for it’s (local) maximum.
c2 (float, optional) – Coefficient describing a particle’s affinity for the best maximum any particle has seen (the current global max).
- Returns
scipy.optimize.Result object – Includes members ‘x’, ‘fun’, ‘success’, and ‘message’.
- pygsti.optimize.optimize._fmin_evolutionary(f, x0, num_generations, num_individuals, printer)¶
Minimize a function using an evolutionary algorithm.
Uses python’s deap package to perform an evolutionary algorithm to find a function’s global minimum.
- Parameters
f (function) – The function to minimize.
x0 (numpy array) – The starting point (argument to fn).
num_generations (int) – The number of generations to carry out. (similar to the number of iterations)
num_individuals (int) – The number of individuals in each generation. More individuals make finding the global optimum more likely, but take longer to run.
- Returns
scipy.optimize.Result object – Includes members ‘x’, ‘fun’, ‘success’, and ‘message’.
- pygsti.optimize.optimize.create_objfn_printer(obj_func, start_time=None)¶
Create a callback function that prints the value of an objective function.
- Parameters
obj_func (function) – The objective function to print.
start_time (float , optional) – A reference starting time to use when printing elapsed times. If None, then the system time when this function is called is used (which is often what you want).
- Returns
function – A callback function which prints obj_func.
- pygsti.optimize.optimize._fwd_diff_jacobian(f, x0, eps=1e-10)¶
- pygsti.optimize.optimize.check_jac(f, x0, jac_to_check, eps=1e-10, tol=1e-06, err_type='rel', verbosity=1)¶
Checks a jacobian function using finite differences.
- Parameters
f (function) – The function to check.
x0 (numpy array) – The point at which to check the jacobian.
jac_to_check (function) – A function which should compute the jacobian of f at x0.
eps (float, optional) – Epsilon to use in finite difference calculations of jacobian.
tol (float, optional) – The allowd tolerance on the relative differene between the values of the finite difference and jac_to_check jacobians if err_type == ‘rel’ or the absolute difference if err_type == ‘abs’.
err_type ({'rel', 'abs'), optional) – How to interpret tol (see above).
verbosity (int, optional) – Controls how much detail is printed to stdout.
- Returns
errSum (float) – The total error between the jacobians.
errs (list) – List of (row,col,err) tuples giving the error for each row and column.
ffd_jac (numpy array) – The computed forward-finite-difference jacobian.