shgpy.fformfit module

Fourier fitting module for fitting RA-SHG data in Fourier space.

This module provides two different methods (up to minor variations) for fitting RA-SHG data in Fourier space. The first is a simple least-square method (using scipy.optimize.least_squares) which is extremely fast and works well for simple problems. The second is a so-called basinhopping method (using scipy.optimize.basinhopping) which is proficient at finding the global minimum of complicated cost functions with many fitting parameters and local minima. See the relevant scipy documentation for more info.

shgpy.fformfit.basinhopping_fit(fform, fdat, guess_dict, niter, method='BFGS', args=(), stepsize=0.5, basinhopping_kwargs={}, chunk_cost_func=False, save_cost_func_filename=None, load_cost_func_filename=None)

Basinhopping fit of RA-SHG data.

Parameters:

fformfFormContainer

Instance of class fFormContainer. This is the (Fourier-transformed) fitting formula.

fdatfDataContainer

Instance of class fDataContainer. This is the (Fourier-transformed) data to fit.

guess_dictdict

Dict of form {sympy.Symbol:float}. This is the initial guess.

niterint

Number of basinhopping iterations (see scipy documentation)

methodstr, optional

Minimization method to use, defaults to ‘BFGS’. See scipy documentation for more information.

argstuple, optional

Additional arguments to give to the minimizer.

stepsizefloat, optional

Basinhopping stepsize, defaults to 0.5. See scipy documentation for more information.

basinhopping_kwargsdict, optional

Other options to pass to the basinhopping routine. See scipy documentation for more information.

chunk_cost_funcbool, optional

Whether to chunk the cost function generation into multiple parts. Default is False.

save_cost_func_filenamepath-like, optional

If provided, save the cost function (as a shared library) at this location.

load_cost_func_filenamepath-like, optional

If provided, load the cost function at this location.

Returns:

retscipy.optimize.OptimizeResult

Instance of class OptimizeResult. See scipy documentation for further description. Includes additional attribute ret.xdict which is a dict of {sympy.Symbol:float} indicating the final answer as a dictionary.

shgpy.fformfit.basinhopping_fit_jac(fform, fdat, guess_dict, niter, method='BFGS', args=(), stepsize=0.5, basinhopping_kwargs={}, chunk_cost_func=False, save_cost_func_filename=None, grad_save_cost_func_filename_prefix=None, load_cost_func_filename=None, load_grad_cost_func_filename_prefix=None)

Basinhopping fit of RA-SHG data.

Parameters:

fformfFormContainer

Instance of class fFormContainer. This is the (Fourier-transformed) fitting formula.

fdatfDataContainer

Instance of class fDataContainer. This is the (Fourier-transformed) data to fit.

guess_dictdict

Dict of form {sympy.Symbol:float}. This is the initial guess.

niterint

Number of basinhopping iterations (see scipy documentation)

methodstr, optional

Minimization method to use, defaults to ‘BFGS’. See scipy documentation for more information.

argstuple, optional

Additional arguments to give to the minimizer.

stepsizefloat, optional

Basinhopping stepsize, defaults to 0.5. See scipy documentation for more information.

basinhopping_kwargsdict, optional

Other options to pass to the basinhopping routine. See scipy documentation for more information.

chunk_cost_funcbool, optional

Whether to chunk the cost function generation into multiple parts. Default is False.

save_cost_func_filenamepath-like, optional

If provided, save the cost function (as a shared library) at this location.

grad_save_cos_func_filenamepath-like, optional

If provided, save the gradient cost functions as shared libraries at the locations defined by ...0.so, ...1.so, etc.

load_cost_func_filenamepath-like, optional

If provided, load the cost function at this location. Must be used in tandem with load_grad_cost_func_filename_prefix.

load_grad_cost_func_filename_prefixpath-like, optional

If provided, load the gradient functions defined by this prefix. Must be used in tandem with load_cost_func_filename.

Returns:

retscipy.optimize.OptimizeResult

Instance of class OptimizeResult. See scipy documentation for further description. Includes additional attribute ret.xdict which is a dict of {sympy.Symbol:float} indicating the final answer as a dictionary.

Notes

This function computes and supplies the gradient function to the scipy basinhopping algorithm. This requires some computational power up front but can speed up the minimization algorithm.

shgpy.fformfit.basinhopping_fit_jac_with_bounds(fform, fdat, guess_dict, bounds_dict, niter, method='L-BFGS-B', args=(), stepsize=0.5, basinhopping_kwargs={}, chunk_cost_func=False, save_cost_func_filename=None, grad_save_cost_func_filename_prefix=None, load_cost_func_filename=None, load_grad_cost_func_filename_prefix=None)

Basinhopping fit of RA-SHG data with bounds.

Parameters:

fformfFormContainer

Instance of class fFormContainer. This is the (Fourier-transformed) fitting formula.

fdatfDataContainer

Instance of class fDataContainer. This is the (Fourier-transformed) data to fit.

guess_dictdict

Dict of form {sympy.Symbol:float}. This is the initial guess.

bounds_dictdict

Dict of form {sympy.Symbol:tuple}. tuple should be of form (lower_bound, upper_bound).

niterint

Number of basinhopping iterations (see scipy documentation)

methodstr, optional

Minimization method to use, defaults to ‘L-BFGS-B’. See scipy documentation for more information.

argstuple, optional

Additional arguments to give to the minimizer.

stepsizefloat, optional

Basinhopping stepsize, defaults to 0.5. See scipy documentation for more information.

basinhopping_kwargsdict, optional

Other options to pass to the basinhopping routine. See scipy documentation for more information.

chunk_cost_funcbool, optional

Whether to chunk the cost function generation into multiple parts. Default is False.

save_cost_func_filenamepath-like, optional

If provided, save the cost function (as a shared library) at this location.

grad_save_cost_func_filename_prefixpath-like, optional

If provided, save the gradient cost functions as shared libraries at the locations defined by ...0.so, ...1.so, etc.

load_cost_func_filenamepath-like, optional

If provided, load the cost function at this location. Must be used in tandem with load_grad_cost_func_filename_prefix.

load_grad_cost_func_filename_prefixpath-like, optional

If provided, load the gradient functions defined by this prefix. Must be used in tandem with load_cost_func_filename.

Returns:

retscipy.optimize.OptimizeResult

Instance of class OptimizeResult. See scipy documentation for further description. Includes additional attribute ret.xdict which is a dict of {sympy.Symbol:float} indicating the final answer as a dictionary.

Notes

This function computes and supplies the gradient function to the scipy basinhopping algorithm. This requires some computational power up front but can speed up the minimization algorithm.

shgpy.fformfit.basinhopping_fit_with_bounds(fform, fdat, guess_dict, bounds_dict, niter, method='L-BFGS-B', args=(), stepsize=0.5, basinhopping_kwargs={}, chunk_cost_func=False, save_cost_func_filename=None, load_cost_func_filename=None)

Basinhopping fit of RA-SHG data with bounds.

Parameters:

fformfFormContainer

Instance of class fFormContainer. This is the (Fourier-transformed) fitting formula.

fdatfDataContainer

Instance of class fDataContainer. This is the (Fourier-transformed) data to fit.

guess_dictdict

Dict of form {sympy.Symbol:float}. This is the initial guess.

bounds_dictdict

Dict of form {sympy.Symbol:tuple}. tuple should be of form (lower_bound, upper_bound).

niterint

Number of basinhopping iterations (see scipy documentation)

methodstr, optional

Minimization method to use, defaults to ‘L-BFGS-B’. See scipy documentation for more information.

argstuple, optional

Additional arguments to give to the minimizer.

stepsizefloat, optional

Basinhopping stepsize, defaults to 0.5. See scipy documentation for more information.

basinhopping_kwargsdict, optional

Other options to pass to the basinhopping routine. See scipy documentation for more information.

chunk_cost_funcbool, optional

Whether to chunk the cost function generation into multiple parts. Default is False.

save_cost_func_filenamepath-like, optional

If provided, save the cost function (as a shared library) at this location.

load_cost_func_filenamepath-like, optional

If provided, load the cost function at this location.

Returns:

retscipy.optimize.OptimizeResult

Instance of class OptimizeResult. See scipy documentation for further description. Includes additional attribute ret.xdict which is a dict of {sympy.Symbol:float} indicating the final answer as a dictionary.

shgpy.fformfit.dual_annealing_fit_with_bounds(fform, fdat, guess_dict, bounds_dict, maxiter=1000, local_search_options={}, initial_temp=5230, restart_temp_ratio=2e-05, visit=2.62, accept=-5.0, maxfun=10000000.0, seed=None, no_local_search=True, callback=None, chunk_cost_func=False, save_cost_func_filename=None, load_cost_func_filename=None)

Simulated annealing fit of RA-SHG data with bounds.

Parameters:

fformfFormContainer

Instance of class fFormContainer. This is the (Fourier-transformed) fitting formula.

fdatfDataContainer

Instance of class fDataContainer. This is the (Fourier-transformed) data to fit.

guess_dictdict

Dict of form {sympy.Symbol:float}. This is the initial guess.

bounds_dictdict

Dict of form {sympy.Symbol:tuple}. tuple should be of form (lower_bound, upper_bound).

maxiterint

Maximum number of global search iterations.

local_search_optionsdict, optional

Extra keyword arguments to be passed to the local minimizer.

initial_tempfloat, optional

Initial temperature. Default is 5230.

restart_temp_ratiofloat, optional

When the temperature reaches initial_temp * restart_temp_ratio, the reannealing process is triggered. Default value is 2e-5. Range is (0,1).

visitfloat, optional

Parameter for visiting distribution. Default value is 2.62.

acceptfloat, optional

Parameter for acceptance distribution. Default is -5.0.

maxfunint, optional

Soft limit for the number of objective function calls. Default is 1e7.

seed{int, RandomState, Generator}, optional

The random seed to use.

no_local_searchbool, optional

If True, perform traditional generalized simulated annealing with no local search.

callbackcallable, optional

A callback function with signature callback(x, f, context) which will be called for all minima found.

x0ndarray, shape(n,), optional

Initial guess.

chunk_cost_funcbool, optional

Whether to chunk the cost function generation into multiple parts. Default is False.

save_cost_func_filenamepath-like, optional

If provided, save the cost function (as a shared library) at this location.

load_cost_func_filenamepath-like, optional

If provided, load the cost function at this location.

Returns:

retscipy.optimize.OptimizeResult

Instance of class OptimizeResult. See scipy documentation for further description. Includes additional attribute ret.xdict which is a dict of {sympy.Symbol:float} indicating the final answer as a dictionary.

Notes

See the scipy.optimize.dual_annealing documentation for more info.

shgpy.fformfit.gen_cost_func(fform, fdat, argument_list=None, chunk=False, save_filename=None, method='gcc')

Generate a cost function as an .so file and save it to disk.

Parameters:

fformfFormContainer

The Fourier formula to use

fdatfDataContainer

The fourier data to fit

argument_listarray_like of sympy.Symbol, optional

Specify an order for the arguments. Default is alphabetical by str(sympy.Symbol).

chunkbool, optional

Chunk the function generation into multiple steps (one for each Fourier component in fform and fdat). Default is False.

save_filenamepath_like, optional

Filename to save the result. Default is not to save.

methodstr, optional

Compiler to use. Tested with gcc and clang. Default is gcc.

Returns:

cost_funcfunction

Result after compiling generated C code. Signature is cost_func(xs), where xs is a numpy.ndarray of floats in the order of fform.get_free_symbols.

shgpy.fformfit.gen_model_func(fform, save_folder, method='gcc', max_terms_per_file=10)

Generate a model function (a folder of .so files) and save them to disk.

Parameters:

fformfFormContainer

The Fourier formula to use

save_folderpath_like

Folder to save the result.

methodstr, optional

Compiler to use. Tested with gcc and clang. Default is gcc.

max_terms_per_fileint, optional

If there are too many terms per file, sometimes the compiler fails. This constrains the number of terms per file. Default is 10.

Returns:

model_funcfunction

Result after compiling generated C code. Signature is model_func(xs, pc, m), where xs is a numpy.ndarray of floats in the order of fform.get_free_symbols, pc is the polarization combination, and m is the Fourier component.

shgpy.fformfit.least_squares_fit(fform, fdat, guess_dict, chunk_cost_func=False, save_cost_func_filename=None, load_cost_func_filename=None, least_sq_kwargs={})

No nonsense least-squares fit of RA-SHG data.

Parameters:

fformfFormContainer

Instance of class fFormContainer. This is the (Fourier-transformed) fitting formula.

fdatfDataContainer

Instance of class fDataContainer. This is the (Fourier-transformed) data to fit.

guess_dictdict

Dict of form {sympy.Symbol:float}. This is the initial guess.

chunk_cost_funcbool, optional

Whether to chunk the cost function generation into multiple parts. Default is False.

save_cost_func_filenamepath-like, optional

If provided, save the cost function (as a shared library) at this location.

load_cost_func_filenamepath-like, optional

If provided, load the cost function at this location.

least_sq_kwargsdict, optional

Dictionary of additional options to pass to scipy.optimize.least_squares. Default is {}.

Returns:

retscipy.optimize.OptimizeResult

Instance of class OptimizeResult. See scipy documentation for further description. Includes additional attribute ret.xdict which is a dict of {sympy.Symbol:float} indicating the final answer as a dictionary.

shgpy.fformfit.least_squares_fit_with_bounds(fform, fdat, guess_dict, bounds_dict, chunk_cost_func=False, save_cost_func_filename=None, load_cost_func_filename=None, least_sq_kwargs={})

No nonsense least-squares fit of RA-SHG data.

Parameters:

fformfFormContainer

Instance of class fFormContainer. This is the (Fourier-transformed) fitting formula.

fdatfDataContainer

Instance of class fDataContainer. This is the (Fourier-transformed) data to fit.

guess_dictdict

Dict of form {sympy.Symbol:float}. This is the initial guess.

bounds_dictdict

Dict of form {sympy.Symbol:tuple}. tuple should be of form (lower_bound, upper_bound).

chunk_cost_funcbool, optional

Whether to chunk the cost function generation into multiple parts. Default is False.

save_cost_func_filenamepath-like, optional

If provided, save the cost function (as a shared library) at this location.

load_cost_func_filenamepath-like, optional

If provided, load the cost function at this location.

least_sq_kwargsdict, optional

Dictionary of additional options to pass to scipy.optimize.least_squares. Default is {}.

Returns:

retscipy.optimize.OptimizeResult

Instance of class OptimizeResult. See scipy documentation for further description. Includes additional attribute ret.xdict which is a dict of {sympy.Symbol:float} indicating the final answer as a dictionary.

shgpy.fformfit.load_func(load_cost_func_filename, multiprocessing=False)

Load a cost function generated by gen_cost_func

shgpy.fformfit.load_model_func(fform, save_folder, multiprocessing=False)

Load a model function generated by gen_model_func

Returns:

model_funcfunction

Result after compiling generated C code. Signature is model_func(xs, pc, m), where xs is a numpy.ndarray of floats in the order of fform.get_free_symbols, pc is the polarization combination, and m is the Fourier component.