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Editing: _differentialevolution.cpython-311.pyc
� d�c � � � d Z ddlZddlZddlmZmZ ddlmZ ddl m Z m Z m Z ddl mZmZmZmZ ddlmZ dgZ ej ej � � j Z dddd�d�Z G d� d� � Z G d� d� � ZdS ) zn differential_evolution: The differential evolution global optimization algorithm Added by Andrew Nelson 2014 � N)�OptimizeResult�minimize)�_status_message)�check_random_state� MapWrapper�_FunctionWrapper)�Bounds�new_bounds_to_old�NonlinearConstraint�LinearConstraint)�issparse�differential_evolution� �best1bin�� � �{�G�z�?�� �?� �ffffff�?FT�latinhypercube� immediater �� integrality� vectorizedc �� � t | |fi d|�d|�d|�d|�d|�d|�d|�d| �d | �d | �d | �d | �d |�d|�d|�d|�d|�d|�d|��5 }|� � � }ddd� � n # 1 swxY w Y |S )aD Finds the global minimum of a multivariate function. The differential evolution method [1]_ is stochastic in nature. It does not use gradient methods to find the minimum, and can search large areas of candidate space, but often requires larger numbers of function evaluations than conventional gradient-based techniques. The algorithm is due to Storn and Price [2]_. Parameters ---------- func : callable The objective function to be minimized. Must be in the form ``f(x, *args)``, where ``x`` is the argument in the form of a 1-D array and ``args`` is a tuple of any additional fixed parameters needed to completely specify the function. The number of parameters, N, is equal to ``len(x)``. bounds : sequence or `Bounds` Bounds for variables. There are two ways to specify the bounds: 1. Instance of `Bounds` class. 2. ``(min, max)`` pairs for each element in ``x``, defining the finite lower and upper bounds for the optimizing argument of `func`. The total number of bounds is used to determine the number of parameters, N. args : tuple, optional Any additional fixed parameters needed to completely specify the objective function. strategy : str, optional The differential evolution strategy to use. Should be one of: - 'best1bin' - 'best1exp' - 'rand1exp' - 'randtobest1exp' - 'currenttobest1exp' - 'best2exp' - 'rand2exp' - 'randtobest1bin' - 'currenttobest1bin' - 'best2bin' - 'rand2bin' - 'rand1bin' The default is 'best1bin'. maxiter : int, optional The maximum number of generations over which the entire population is evolved. The maximum number of function evaluations (with no polishing) is: ``(maxiter + 1) * popsize * N`` popsize : int, optional A multiplier for setting the total population size. The population has ``popsize * N`` individuals. This keyword is overridden if an initial population is supplied via the `init` keyword. When using ``init='sobol'`` the population size is calculated as the next power of 2 after ``popsize * N``. tol : float, optional Relative tolerance for convergence, the solving stops when ``np.std(pop) <= atol + tol * np.abs(np.mean(population_energies))``, where and `atol` and `tol` are the absolute and relative tolerance respectively. mutation : float or tuple(float, float), optional The mutation constant. In the literature this is also known as differential weight, being denoted by F. If specified as a float it should be in the range [0, 2]. If specified as a tuple ``(min, max)`` dithering is employed. Dithering randomly changes the mutation constant on a generation by generation basis. The mutation constant for that generation is taken from ``U[min, max)``. Dithering can help speed convergence significantly. Increasing the mutation constant increases the search radius, but will slow down convergence. recombination : float, optional The recombination constant, should be in the range [0, 1]. In the literature this is also known as the crossover probability, being denoted by CR. Increasing this value allows a larger number of mutants to progress into the next generation, but at the risk of population stability. seed : {None, int, `numpy.random.Generator`, `numpy.random.RandomState`}, optional If `seed` is None (or `np.random`), the `numpy.random.RandomState` singleton is used. If `seed` is an int, a new ``RandomState`` instance is used, seeded with `seed`. If `seed` is already a ``Generator`` or ``RandomState`` instance then that instance is used. Specify `seed` for repeatable minimizations. disp : bool, optional Prints the evaluated `func` at every iteration. callback : callable, `callback(xk, convergence=val)`, optional A function to follow the progress of the minimization. ``xk`` is the best solution found so far. ``val`` represents the fractional value of the population convergence. When ``val`` is greater than one the function halts. If callback returns `True`, then the minimization is halted (any polishing is still carried out). polish : bool, optional If True (default), then `scipy.optimize.minimize` with the `L-BFGS-B` method is used to polish the best population member at the end, which can improve the minimization slightly. If a constrained problem is being studied then the `trust-constr` method is used instead. For large problems with many constraints, polishing can take a long time due to the Jacobian computations. init : str or array-like, optional Specify which type of population initialization is performed. Should be one of: - 'latinhypercube' - 'sobol' - 'halton' - 'random' - array specifying the initial population. The array should have shape ``(S, N)``, where S is the total population size and N is the number of parameters. `init` is clipped to `bounds` before use. The default is 'latinhypercube'. Latin Hypercube sampling tries to maximize coverage of the available parameter space. 'sobol' and 'halton' are superior alternatives and maximize even more the parameter space. 'sobol' will enforce an initial population size which is calculated as the next power of 2 after ``popsize * N``. 'halton' has no requirements but is a bit less efficient. See `scipy.stats.qmc` for more details. 'random' initializes the population randomly - this has the drawback that clustering can occur, preventing the whole of parameter space being covered. Use of an array to specify a population could be used, for example, to create a tight bunch of initial guesses in an location where the solution is known to exist, thereby reducing time for convergence. atol : float, optional Absolute tolerance for convergence, the solving stops when ``np.std(pop) <= atol + tol * np.abs(np.mean(population_energies))``, where and `atol` and `tol` are the absolute and relative tolerance respectively. updating : {'immediate', 'deferred'}, optional If ``'immediate'``, the best solution vector is continuously updated within a single generation [4]_. This can lead to faster convergence as trial vectors can take advantage of continuous improvements in the best solution. With ``'deferred'``, the best solution vector is updated once per generation. Only ``'deferred'`` is compatible with parallelization or vectorization, and the `workers` and `vectorized` keywords can over-ride this option. .. versionadded:: 1.2.0 workers : int or map-like callable, optional If `workers` is an int the population is subdivided into `workers` sections and evaluated in parallel (uses `multiprocessing.Pool <multiprocessing>`). Supply -1 to use all available CPU cores. Alternatively supply a map-like callable, such as `multiprocessing.Pool.map` for evaluating the population in parallel. This evaluation is carried out as ``workers(func, iterable)``. This option will override the `updating` keyword to ``updating='deferred'`` if ``workers != 1``. This option overrides the `vectorized` keyword if ``workers != 1``. Requires that `func` be pickleable. .. versionadded:: 1.2.0 constraints : {NonLinearConstraint, LinearConstraint, Bounds} Constraints on the solver, over and above those applied by the `bounds` kwd. Uses the approach by Lampinen [5]_. .. versionadded:: 1.4.0 x0 : None or array-like, optional Provides an initial guess to the minimization. Once the population has been initialized this vector replaces the first (best) member. This replacement is done even if `init` is given an initial population. ``x0.shape == (N,)``. .. versionadded:: 1.7.0 integrality : 1-D array, optional For each decision variable, a boolean value indicating whether the decision variable is constrained to integer values. The array is broadcast to ``(N,)``. If any decision variables are constrained to be integral, they will not be changed during polishing. Only integer values lying between the lower and upper bounds are used. If there are no integer values lying between the bounds then a `ValueError` is raised. .. versionadded:: 1.9.0 vectorized : bool, optional If ``vectorized is True``, `func` is sent an `x` array with ``x.shape == (N, S)``, and is expected to return an array of shape ``(S,)``, where `S` is the number of solution vectors to be calculated. If constraints are applied, each of the functions used to construct a `Constraint` object should accept an `x` array with ``x.shape == (N, S)``, and return an array of shape ``(M, S)``, where `M` is the number of constraint components. This option is an alternative to the parallelization offered by `workers`, and may help in optimization speed by reducing interpreter overhead from multiple function calls. This keyword is ignored if ``workers != 1``. This option will override the `updating` keyword to ``updating='deferred'``. See the notes section for further discussion on when to use ``'vectorized'``, and when to use ``'workers'``. .. versionadded:: 1.9.0 Returns ------- res : OptimizeResult The optimization result represented as a `OptimizeResult` object. Important attributes are: ``x`` the solution array, ``success`` a Boolean flag indicating if the optimizer exited successfully and ``message`` which describes the cause of the termination. See `OptimizeResult` for a description of other attributes. If `polish` was employed, and a lower minimum was obtained by the polishing, then OptimizeResult also contains the ``jac`` attribute. If the eventual solution does not satisfy the applied constraints ``success`` will be `False`. Notes ----- Differential evolution is a stochastic population based method that is useful for global optimization problems. At each pass through the population the algorithm mutates each candidate solution by mixing with other candidate solutions to create a trial candidate. There are several strategies [3]_ for creating trial candidates, which suit some problems more than others. The 'best1bin' strategy is a good starting point for many systems. In this strategy two members of the population are randomly chosen. Their difference is used to mutate the best member (the 'best' in 'best1bin'), :math:`b_0`, so far: .. math:: b' = b_0 + mutation * (population[rand0] - population[rand1]) A trial vector is then constructed. Starting with a randomly chosen ith parameter the trial is sequentially filled (in modulo) with parameters from ``b'`` or the original candidate. The choice of whether to use ``b'`` or the original candidate is made with a binomial distribution (the 'bin' in 'best1bin') - a random number in [0, 1) is generated. If this number is less than the `recombination` constant then the parameter is loaded from ``b'``, otherwise it is loaded from the original candidate. The final parameter is always loaded from ``b'``. Once the trial candidate is built its fitness is assessed. If the trial is better than the original candidate then it takes its place. If it is also better than the best overall candidate it also replaces that. To improve your chances of finding a global minimum use higher `popsize` values, with higher `mutation` and (dithering), but lower `recombination` values. This has the effect of widening the search radius, but slowing convergence. By default the best solution vector is updated continuously within a single iteration (``updating='immediate'``). This is a modification [4]_ of the original differential evolution algorithm which can lead to faster convergence as trial vectors can immediately benefit from improved solutions. To use the original Storn and Price behaviour, updating the best solution once per iteration, set ``updating='deferred'``. The ``'deferred'`` approach is compatible with both parallelization and vectorization (``'workers'`` and ``'vectorized'`` keywords). These may improve minimization speed by using computer resources more efficiently. The ``'workers'`` distribute calculations over multiple processors. By default the Python `multiprocessing` module is used, but other approaches are also possible, such as the Message Passing Interface (MPI) used on clusters [6]_ [7]_. The overhead from these approaches (creating new Processes, etc) may be significant, meaning that computational speed doesn't necessarily scale with the number of processors used. Parallelization is best suited to computationally expensive objective functions. If the objective function is less expensive, then ``'vectorized'`` may aid by only calling the objective function once per iteration, rather than multiple times for all the population members; the interpreter overhead is reduced. .. versionadded:: 0.15.0 References ---------- .. [1] Differential evolution, Wikipedia, http://en.wikipedia.org/wiki/Differential_evolution .. [2] Storn, R and Price, K, Differential Evolution - a Simple and Efficient Heuristic for Global Optimization over Continuous Spaces, Journal of Global Optimization, 1997, 11, 341 - 359. .. [3] http://www1.icsi.berkeley.edu/~storn/code.html .. [4] Wormington, M., Panaccione, C., Matney, K. M., Bowen, D. K., - Characterization of structures from X-ray scattering data using genetic algorithms, Phil. Trans. R. Soc. Lond. A, 1999, 357, 2827-2848 .. [5] Lampinen, J., A constraint handling approach for the differential evolution algorithm. Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No. 02TH8600). Vol. 2. IEEE, 2002. .. [6] https://mpi4py.readthedocs.io/en/stable/ .. [7] https://schwimmbad.readthedocs.io/en/latest/ Examples -------- Let us consider the problem of minimizing the Rosenbrock function. This function is implemented in `rosen` in `scipy.optimize`. >>> import numpy as np >>> from scipy.optimize import rosen, differential_evolution >>> bounds = [(0,2), (0, 2), (0, 2), (0, 2), (0, 2)] >>> result = differential_evolution(rosen, bounds) >>> result.x, result.fun (array([1., 1., 1., 1., 1.]), 1.9216496320061384e-19) Now repeat, but with parallelization. >>> result = differential_evolution(rosen, bounds, updating='deferred', ... workers=2) >>> result.x, result.fun (array([1., 1., 1., 1., 1.]), 1.9216496320061384e-19) Let's do a constrained minimization. >>> from scipy.optimize import LinearConstraint, Bounds We add the constraint that the sum of ``x[0]`` and ``x[1]`` must be less than or equal to 1.9. This is a linear constraint, which may be written ``A @ x <= 1.9``, where ``A = array([[1, 1]])``. This can be encoded as a `LinearConstraint` instance: >>> lc = LinearConstraint([[1, 1]], -np.inf, 1.9) Specify limits using a `Bounds` object. >>> bounds = Bounds([0., 0.], [2., 2.]) >>> result = differential_evolution(rosen, bounds, constraints=lc, ... seed=1) >>> result.x, result.fun (array([0.96632622, 0.93367155]), 0.0011352416852625719) Next find the minimum of the Ackley function (https://en.wikipedia.org/wiki/Test_functions_for_optimization). >>> def ackley(x): ... arg1 = -0.2 * np.sqrt(0.5 * (x[0] ** 2 + x[1] ** 2)) ... arg2 = 0.5 * (np.cos(2. * np.pi * x[0]) + np.cos(2. * np.pi * x[1])) ... return -20. * np.exp(arg1) - np.exp(arg2) + 20. + np.e >>> bounds = [(-5, 5), (-5, 5)] >>> result = differential_evolution(ackley, bounds, seed=1) >>> result.x, result.fun (array([0., 0.]), 4.440892098500626e-16) The Ackley function is written in a vectorized manner, so the ``'vectorized'`` keyword can be employed. Note the reduced number of function evaluations. >>> result = differential_evolution( ... ackley, bounds, vectorized=True, updating='deferred', seed=1 ... ) >>> result.x, result.fun (array([0., 0.]), 4.440892098500626e-16) �args�strategy�maxiter�popsize�tol�mutation� recombination�seed�polish�callback�disp�init�atol�updating�workers� constraints�x0r r N)�DifferentialEvolutionSolver�solve)�func�boundsr r r r! r" r# r$ r% r' r( r& r) r* r+ r, r- r. r r �solver�rets �G/usr/lib/python3/dist-packages/scipy/optimize/_differentialevolution.pyr r si � �P %�T�6� <� <� <��� <�.6�h� <�-4�W� <� .5�W� <� ;>�#� <� /7�h� <� 4A�=� <� +/�$� <� 8>�v� <� /7�h� <� +/�$� <� 6:�T� <� AE�� <� /7�h� <� .5�W� <� 2=�� <� )+�� <� 2=�� <� 1;� � <� � @F��l�l�n�n�� � � � � � � � � � � ���� � � � �" �Js �A'�'A+�.A+c �@ � e Zd ZdZddddddd�Zddddddd �Zd Zd d d dddddej dddddddd dfddd�d�Z d� Z d � Z d � Z d � Z ed � � � Zed � � � Zd!� Zd"� Zd#� Zd$� Zd%� Zd&� Zd'� Zd(� Zd)� Zd*� Zd+� Zd,� Z d-� Z d.� Z d/� Z d0� Z d1� Z!d2� Z"d3� Z#d4� Z$d5� Z%d6� Z&dS )7r/ a% This class implements the differential evolution solver Parameters ---------- func : callable The objective function to be minimized. Must be in the form ``f(x, *args)``, where ``x`` is the argument in the form of a 1-D array and ``args`` is a tuple of any additional fixed parameters needed to completely specify the function. The number of parameters, N, is equal to ``len(x)``. bounds : sequence or `Bounds` Bounds for variables. There are two ways to specify the bounds: 1. Instance of `Bounds` class. 2. ``(min, max)`` pairs for each element in ``x``, defining the finite lower and upper bounds for the optimizing argument of `func`. The total number of bounds is used to determine the number of parameters, N. args : tuple, optional Any additional fixed parameters needed to completely specify the objective function. strategy : str, optional The differential evolution strategy to use. Should be one of: - 'best1bin' - 'best1exp' - 'rand1exp' - 'randtobest1exp' - 'currenttobest1exp' - 'best2exp' - 'rand2exp' - 'randtobest1bin' - 'currenttobest1bin' - 'best2bin' - 'rand2bin' - 'rand1bin' The default is 'best1bin' maxiter : int, optional The maximum number of generations over which the entire population is evolved. The maximum number of function evaluations (with no polishing) is: ``(maxiter + 1) * popsize * N`` popsize : int, optional A multiplier for setting the total population size. The population has ``popsize * N`` individuals. This keyword is overridden if an initial population is supplied via the `init` keyword. When using ``init='sobol'`` the population size is calculated as the next power of 2 after ``popsize * N``. tol : float, optional Relative tolerance for convergence, the solving stops when ``np.std(pop) <= atol + tol * np.abs(np.mean(population_energies))``, where and `atol` and `tol` are the absolute and relative tolerance respectively. mutation : float or tuple(float, float), optional The mutation constant. In the literature this is also known as differential weight, being denoted by F. If specified as a float it should be in the range [0, 2]. If specified as a tuple ``(min, max)`` dithering is employed. Dithering randomly changes the mutation constant on a generation by generation basis. The mutation constant for that generation is taken from U[min, max). Dithering can help speed convergence significantly. Increasing the mutation constant increases the search radius, but will slow down convergence. recombination : float, optional The recombination constant, should be in the range [0, 1]. In the literature this is also known as the crossover probability, being denoted by CR. Increasing this value allows a larger number of mutants to progress into the next generation, but at the risk of population stability. seed : {None, int, `numpy.random.Generator`, `numpy.random.RandomState`}, optional If `seed` is None (or `np.random`), the `numpy.random.RandomState` singleton is used. If `seed` is an int, a new ``RandomState`` instance is used, seeded with `seed`. If `seed` is already a ``Generator`` or ``RandomState`` instance then that instance is used. Specify `seed` for repeatable minimizations. disp : bool, optional Prints the evaluated `func` at every iteration. callback : callable, `callback(xk, convergence=val)`, optional A function to follow the progress of the minimization. ``xk`` is the current value of ``x0``. ``val`` represents the fractional value of the population convergence. When ``val`` is greater than one the function halts. If callback returns `True`, then the minimization is halted (any polishing is still carried out). polish : bool, optional If True (default), then `scipy.optimize.minimize` with the `L-BFGS-B` method is used to polish the best population member at the end, which can improve the minimization slightly. If a constrained problem is being studied then the `trust-constr` method is used instead. For large problems with many constraints, polishing can take a long time due to the Jacobian computations. maxfun : int, optional Set the maximum number of function evaluations. However, it probably makes more sense to set `maxiter` instead. init : str or array-like, optional Specify which type of population initialization is performed. Should be one of: - 'latinhypercube' - 'sobol' - 'halton' - 'random' - array specifying the initial population. The array should have shape ``(S, N)``, where S is the total population size and N is the number of parameters. `init` is clipped to `bounds` before use. The default is 'latinhypercube'. Latin Hypercube sampling tries to maximize coverage of the available parameter space. 'sobol' and 'halton' are superior alternatives and maximize even more the parameter space. 'sobol' will enforce an initial population size which is calculated as the next power of 2 after ``popsize * N``. 'halton' has no requirements but is a bit less efficient. See `scipy.stats.qmc` for more details. 'random' initializes the population randomly - this has the drawback that clustering can occur, preventing the whole of parameter space being covered. Use of an array to specify a population could be used, for example, to create a tight bunch of initial guesses in an location where the solution is known to exist, thereby reducing time for convergence. atol : float, optional Absolute tolerance for convergence, the solving stops when ``np.std(pop) <= atol + tol * np.abs(np.mean(population_energies))``, where and `atol` and `tol` are the absolute and relative tolerance respectively. updating : {'immediate', 'deferred'}, optional If ``'immediate'``, the best solution vector is continuously updated within a single generation [4]_. This can lead to faster convergence as trial vectors can take advantage of continuous improvements in the best solution. With ``'deferred'``, the best solution vector is updated once per generation. Only ``'deferred'`` is compatible with parallelization or vectorization, and the `workers` and `vectorized` keywords can over-ride this option. workers : int or map-like callable, optional If `workers` is an int the population is subdivided into `workers` sections and evaluated in parallel (uses `multiprocessing.Pool <multiprocessing>`). Supply `-1` to use all cores available to the Process. Alternatively supply a map-like callable, such as `multiprocessing.Pool.map` for evaluating the population in parallel. This evaluation is carried out as ``workers(func, iterable)``. This option will override the `updating` keyword to `updating='deferred'` if `workers != 1`. Requires that `func` be pickleable. constraints : {NonLinearConstraint, LinearConstraint, Bounds} Constraints on the solver, over and above those applied by the `bounds` kwd. Uses the approach by Lampinen. x0 : None or array-like, optional Provides an initial guess to the minimization. Once the population has been initialized this vector replaces the first (best) member. This replacement is done even if `init` is given an initial population. ``x0.shape == (N,)``. integrality : 1-D array, optional For each decision variable, a boolean value indicating whether the decision variable is constrained to integer values. The array is broadcast to ``(N,)``. If any decision variables are constrained to be integral, they will not be changed during polishing. Only integer values lying between the lower and upper bounds are used. If there are no integer values lying between the bounds then a `ValueError` is raised. vectorized : bool, optional If ``vectorized is True``, `func` is sent an `x` array with ``x.shape == (N, S)``, and is expected to return an array of shape ``(S,)``, where `S` is the number of solution vectors to be calculated. If constraints are applied, each of the functions used to construct a `Constraint` object should accept an `x` array with ``x.shape == (N, S)``, and return an array of shape ``(M, S)``, where `M` is the number of constraint components. This option is an alternative to the parallelization offered by `workers`, and may help in optimization speed. This keyword is ignored if ``workers != 1``. This option will override the `updating` keyword to ``updating='deferred'``. �_best1� _randtobest1�_currenttobest1�_best2�_rand2�_rand1)r �randtobest1bin�currenttobest1bin�best2bin�rand2bin�rand1bin)�best1exp�rand1exp�randtobest1exp�currenttobest1exp�best2exp�rand2expz�The population initialization method must be one of 'latinhypercube' or 'random', or an array of shape (S, N) where N is the number of parameters and S>5r r r r r r r NFTr r r r r c � � || j v r!t | | j | � � | _ n9|| j v r!t | | j | � � | _ nt d� � �|| _ | | _ || _ |dv r|| _ || _ |dk r)|dk r#t j dt d�� � d| _ |r%|dk r t j d d�� � d x| _ }|r)|dk r#t j d t d�� � d| _ |rd � }|}t |� � | _ ||c| _ | _ || _ t% j t% j |� � � � rTt% j t% j |� � dk � � s*t% j t% j |� � d k � � rt d� � �d | _ t1 |d� � rAt3 |� � dk r.|d |d g| _ | j � � � | | _ t9 ||� � | _ || _ t? |t@ � � rQt% j tC |j" |j# t3 |j" � � � � tH �� � j% | _& n t% j |d�� � j% | _& t% j' | j& d � � dk s+t% j t% j | j& � � � � st d� � �|�d}|| _( | � t$ j) } | | _* d| j& d | j& d z z | _+ t% j, | j& d | j& d z � � | _- t% j' | j& d� � | _. t_ | � � | _0 t% j |� � �r&t% j1 || j. � � }t% j2 |tf � � }t% j4 | j& � � \ }}t% j5 |� � }t% j6 |� � }|| || k � � � st d� � �t% j7 || dz t$ j) � � }t% j7 || dz t$ j) � � }|| _8 || j& d | j8 f< || j& d| j8 f< nd | _8 ts d|| j. z � � | _: | j: | j. f| _; d | _< t? |tz � � r�|dk r| �> � � n�|dk rlt dt% j5 t% j@ | j: � � � � z � � } | | _: | j: | j. f| _; | �A d�� � na|dk r| �A d�� � nD|dk r| �B � � n)t | jC � � �| �D |� � |�_| �E t% j2 |� � � � } | d k | d k z � � � rt d � � �| | jF d < || _G g | _H t1 |d � � r3|D ]/} | jH �I t� | | jK � � � � �0nt� || jK � � g| _H t% jL d � | jH D � � � � | _M t% jN | j: df� � | _O t% jP | j: tf � � | _Q | | _R d S )!Nz'Please select a valid mutation strategy)r �deferredr r zhdifferential_evolution: the 'workers' keyword has overridden updating='immediate' to updating='deferred'� )� stacklevelrI zPdifferential_evolution: the 'workers' keyword overrides the 'vectorized' keywordFzkdifferential_evolution: the 'vectorized' keyword has overridden updating='immediate' to updating='deferred'c �F � t j | |j � � � � S �N)�np� atleast_1d�T)r1 �xs r5 �maplike_for_vectorized_funczIDifferentialEvolutionSolver.__init__.<locals>.maplike_for_vectorized_func� s � � �}�T�T�!�#�Y�Y�/�/�/� r z�The mutation constant must be a float in U[0, 2), or specified as a tuple(min, max) where min < max and min, max are in U[0, 2).�__iter__��dtype�floatzWbounds should be a sequence containing real valued (min, max) pairs for each value in xr r zlOne of the integrality constraints does not have any possible integer values between the lower/upper bounds.� r �sobol)� qmc_engine�halton�random� �?� z3Some entries in x0 lay outside the specified bounds�__len__c � � g | ] }|j �� S r )� num_constr)�.0�cs r5 � <listcomp>z8DifferentialEvolutionSolver.__init__.<locals>.<listcomp> s � � =� =� =�a�Q�\� =� =� =rS )S� _binomial�getattr� mutation_func� _exponential� ValueErrorr r' r& � _updatingr �warnings�warn� UserWarningr � _mapwrapperr" r* �scalerN �all�isfinite�any�array�dither�hasattr�len�sort�cross_over_probabilityr r1 r � isinstancer r �lb�ubrW rP �limits�sizer �inf�maxfun�(_DifferentialEvolutionSolver__scale_arg1�fabs�(_DifferentialEvolutionSolver__scale_arg2�parameter_countr �random_number_generator� broadcast_to�asarray�bool�copy�ceil�floor� nextafterr �max�num_population_members�population_shape�_nfev�str�init_population_lhs�int�log2�init_population_qmc�init_population_random�,_DifferentialEvolutionSolver__init_error_msg�init_population_array�_unscale_parameters� populationr- �_wrapped_constraints�append�_ConstraintWrapperrQ �sum�total_constraints�zeros�constraint_violation�ones�feasibler( ) �selfr1 r2 r r r r! r" r# r$ r% r r' r( r& r) r* r+ r, r- r. r r rR rz r{ �nlb�nub�n_s� x0_scaledrc s r5 �__init__z$DifferentialEvolutionSolver.__init__Z s� � � �t�~� %� %�!(��t�~�h�/G�!H�!H�D� � � ��*� *� *�!(��t�/@��/J�!K�!K�D� � � � F�G�G� G� �� � �� � �� � �0� 0� 0� %�D�N�$��� �a�<�<�H� � 3� 3� �M� 1�2=�!� M� M� M� M� (�D�N� � 1�'�Q�,�,� �M� @�LM� O� O� O� O�+0� 0�D�O�j� � (�(�k�1�1� �M� (�)4�� D� D� D� D� (�D�N� � 2� 0� 0� 0� 2�G�%�g�.�.��� "�4����$�)� �� ���r�{�8�,�,�-�-� N���r�x��)�)�Q�.�/�/� N���r�x��)�)�A�-�.�.� N� � M� N� N� N� �� � �8�Z� (� (� �S��]�]�Q�->�->�#�A�;��� �4�D�K� �K� � � � � �&3��#� %�T�4�0�0�� ��� � �f�f� %� %� <� �(�#4�V�Y�5;�Y�58���^�^�$E� $E� */�0� 0� 0� 12� �K�K� �(�6��9�9�9�;�D�K� �G�D�K�� #� #�q� (� (���r�{�4�;�/�/�0�0� )� � %� &� &� &� �?��G� �� � �>��V�F� �� � �4�;�q�>�D�K��N�#B� C��� �G�D�K��N�T�[��^�$C� D� D��� !�w�t�{�A� 6� 6�� �'9�$�'?�'?��$� �6�+� � � %� �/���$�� �K� �*�[�$�7�7�K� �W�T�[�)�)�F�B�������B���"� � �B��{�O�r�+��6�;�;�=�=� =� !� "<� =� =� =� �,�r�+��� 4�b�f�=�=�C��,�r�+��� 4�r�v�g�>�>�C� *�D� �/2�D�K��4�+�+� ,�/2�D�K��4�+�+� ,� ,� $�D� � '*�!�W�t�7K�-K�&L�&L��#�!%�!<�!%�!5�!7�� � �� � �d�C� � � -��'�'�'��(�(�*�*�*�*��� � ��!�r�w�r�w�t�/J�'K�'K� L� L�L�M�M��.1��+�)-�)D�)-�)=�)?��%��(�(�G�(�<�<�<�<���!�!��(�(�H�(�=�=�=�=���!�!��+�+�-�-�-�-� ��!6�7�7�7� � &� &�t� ,� ,� ,� �>� �0�0���B� � �@�@�I��S� �Y��_�5�:�:�<�<� � �I�� � � "+�D�O�A� � '���$&��!� �;� � *� *� � !� � ���)�0�0�&�q�$�&�1�1�� � � � � #�;���7�7�)�D� %� "$�� =� =�4�#<� =� =� =�" � " �� � %'�H�d�.I�1�-M�$N�$N��!���� ;�T�B�B�� ��� � � rS c � � | j }d| j z }||� | j �� � z t j dd| j d�� � dd�t j f z }t j |� � | _ t | j � � D ]?}|� t | j � � � � }|||f | j dd�|f< �@t j | j t j � � | _ d| _ dS )z� Initializes the population with Latin Hypercube Sampling. Latin Hypercube Sampling ensures that each parameter is uniformly sampled over its range. r] �r} r^ F)�endpointNr )r� r� �uniformr� rN �linspace�newaxis� zeros_liker� �ranger� � permutation�fullr~ �population_energiesr� )r� �rng�segsize�samples�j�orders r5 r� z/DifferentialEvolutionSolver.init_population_lhs' s � � �*�� ��3�3�� �S�[�[�d�.C�[� D� D�D� �[��R��)D�*/�1� 1� 1�12���B�J� �@�@�� �-��0�0��� �t�+�,�,� 6� 6�A��O�O�E�$�*E�$F�$F�G�G�E�$+�E�1�H�$5�D�O�A�A�A�q�D� !� !� $&�7�4�+F�+-�6�$3� $3�� � �� � � rS c � � ddl m} | j }|dk r |� | j |�� � }nZ|dk r |� | j |�� � }n7|dk r |� | j |�� � }nt | j � � �|� | j �� � | _ t j | j t j � � | _ d| _ dS ) aR Initializes the population with a QMC method. QMC methods ensures that each parameter is uniformly sampled over its range. Parameters ---------- qmc_engine : str The QMC method to use for initialization. Can be one of ``latinhypercube``, ``sobol`` or ``halton``. r )�qmcr )�dr% rY r[ )�nN)� scipy.statsr� r� �LatinHypercuber� �Sobol�Haltonri r� r\ r� r� rN r� r~ r� r� )r� rZ r� r� �samplers r5 r� z/DifferentialEvolutionSolver.init_population_qmcM s� � � $�#�#�#�#�#��*�� �)� )� )��(�(�4�+?�c�(�J�J�G�G� �7� "� "��i�i�$�"6�S�i�A�A�G�G� �8� #� #��j�j�4�#7�c�j�B�B�G�G� �T� 2�3�3� 3�!�.�.�4�+F�.�G�G��� $&�7�4�+F�+-�6�$3� $3�� � �� � � rS c � � | j }|� | j �� � | _ t j | j t j � � | _ d| _ dS )z� Initializes the population at random. This type of initialization can possess clustering, Latin Hypercube sampling is generally better. r� r N) r� r� r� r� rN r� r� r~ r� r� )r� r� s r5 r� z2DifferentialEvolutionSolver.init_population_randomq sQ � � �*�� �+�+�4�+@�+�A�A��� $&�7�4�+F�+-�6�$3� $3�� � �� � � rS c � � t j |� � }t j |d� � dk s.|j d | j k st |j � � dk rt d� � �t j | � |� � dd� � | _ t j | j d� � | _ | j | j f| _ t j | j t j � � | _ d| _ dS )ah Initializes the population with a user specified population. Parameters ---------- init : np.ndarray Array specifying subset of the initial population. The array should have shape (S, N), where N is the number of parameters. The population is clipped to the lower and upper bounds. r rX r rJ zEThe population supplied needs to have shape (S, len(x)), where S > 4.N)rN �asfarrayr} �shaper� rv ri �clipr� r� r� r� r� r~ r� r� )r� r) �popns r5 r� z1DifferentialEvolutionSolver.init_population_array� s� � � �{�4� � �� �G�D�!� � �q� � �� �1� ��!5�5�5��D�J���1�$�$� � :� ;� ;� ;� �'�$�":�":�4�"@�"@�!�Q�G�G���&(�g�d�o�q�&A�&A��#�!%�!<�!%�!5�!7�� � $&�7�4�+F�+-�6�$3� $3�� � �� � � rS c �B � | � | j d � � S )z3 The best solution from the solver r )�_scale_parametersr� �r� s r5 rQ z DifferentialEvolutionSolver.x� s � � �%�%�d�o�a�&8�9�9�9rS c � � t j t j | j � � � � r t j S t j | j � � t j t j | j � � t z � � z S )zb The standard deviation of the population energies divided by their mean. ) rN rr �isinfr� r~ �std�abs�mean�_MACHEPSr� s r5 � convergencez'DifferentialEvolutionSolver.convergence� se � � �6�"�(�4�3�4�4� 5� 5� ��6�M���t�/�0�0���r�w�t� 7�8�8�8�C�D�D�E� FrS c � � t j t j | j � � � � rdS t j | j � � | j | j t j t j | j � � � � z z k S )z: Return True if the solver has converged. F) rN rr r� r� r� r* r" r� r� r� s r5 � convergedz%DifferentialEvolutionSolver.converged� sp � � �6�"�(�4�3�4�4� 5� 5� ��5���t�/�0�0�� ���2�6�"�'�$�*B�"C�"C�D�D�D�E�E� FrS c � � � d\ }}t d }t j t j | j � � � � rm| � | j � � \ | _ | _ | � | j | j � � | j | j < | � � � t d| j dz � � D ]�} t | � � nC# t $ r6 d}| j | j k rt d }n| j | j k rd}Y n�w xY w| j r t% d|| j d fz � � | j rD| j | j t, z z }t/ | � | j |� � � � � }|rd }|s| � � � r n��t d }d}t5 | j | j d | j |||du� � � � | j �r�t j | j � � �s�t j | j � � r2| j | j }}� j | |d|f< � j | |d|f< d }| j rNd}| � � j � � }t j |dk � � rtC j" dtF � � | j rt% d|� d�� � tI | j% t j& � j � � || j j' | j( �� � } | xj | j) z c_ | j � _) | j* � j* k r�| j+ r�t j | j | j d k � � r}t j | j d | j k � � rU| j* � _* | j � _ | j, � _, | j* | j d< | �- | j � � | j d< | j ru� fd�| j D � � � _. t j/ t j0 � j. � � � � � _1 � j1 � _2 � j2 dk rd� _+ d� j2 � �� _3 � S )a� Runs the DifferentialEvolutionSolver. Returns ------- res : OptimizeResult The optimization result represented as a ``OptimizeResult`` object. Important attributes are: ``x`` the solution array, ``success`` a Boolean flag indicating if the optimizer exited successfully and ``message`` which describes the cause of the termination. See `OptimizeResult` for a description of other attributes. If `polish` was employed, and a lower minimum was obtained by the polishing, then OptimizeResult also contains the ``jac`` attribute. )r F�successr T�maxfevz8Maximum number of function evaluations has been reached.z(differential_evolution step %d: f(x)= %gr )r� z8callback function requested stop early by returning Truer )rQ �fun�nfev�nit�messager� zL-BFGS-Bz trust-constrr^ z�differential evolution didn't find a solution satisfying the constraints, attempting to polish from the least infeasible solutionzPolishing solution with '�')�methodr2 r- c �D �� g | ] }|� �j � � �� S r )� violationrQ )rb rc � DE_results �r5 rd z5DifferentialEvolutionSolver.solve.<locals>.<listcomp>: s= �� � @� @� @� !� !"� � �I�K� 8� 8� @� @� @rS Fz7The solution does not satisfy the constraints, MAXCV = )4r rN rp r� r� �#_calculate_population_feasibilitiesr� r� r� � _calculate_population_energies�_promote_lowest_energyr� r �next� StopIterationr� r r( �printr' r" r� r� r� rQ r� r r& r rr r| r� �_constraint_violation_fnrk rl rm r r1 r� rP r- r� r� r� �jacr� �constrr� � concatenate�constr_violation�maxcvr� ) r� r� � warning_flag�status_messagerc r| r � polish_methodr� �resultr� s @r5 r0 z!DifferentialEvolutionSolver.solve� s� �� � %���\�(��3�� �6�"�(�4�3�4�4� 5� 5� *��8�8�� �I�I� 5�D�M�4�4� �3�3��O�D�M�2�4� 4� � $�T�]� 3� � '� '� )� )� )� ��D�L�1� ,�-�-� � �C� ��T� � � � �� � � � � #� ��:�� �+�+�%4�X�%>�N�N��Z�4�;�.�.�';�N���� ���� �y� 7��@� � �1�!�4�6�6� 7� 7� 7� �}� <��H�� 0�8� ;�<�� #�D�M�M�$�&�a�M�$H�$H� I� I� � � <�';�N� � �t�~�~� /� /� ��� � -�Y� 7�N� �L�"��f��(��+����"�!��-� 0� 0� 0� � �;� + H�r�v�d�&6� 7� 7� + H��v�d�&�'�'� B� '+�k�4�3C� ��)2��[�)A��q�+�~�&�)2��[�)A��q�+�~�&� &�M��(� G� .� �#'�#@�#@���#M�#M� ��6�*�R�/�0�0� G� �M� #9� ;F�G� G� G� �y� D��B�-�B�B�B�C�C�C� �d�i� �g�i�k� 2� 2�%2�%)�[�]�*.�*:� <� <� <�F� �J�J�&�+� %�J�J� !�Z�I�N� � �Y�]�*�*��N� +��F�6�8�t�{�1�~�5�6�6� +� �F�4�;�q�>�V�X�5�6�6� +� !'� � � � $�h� � � &� � � �.4�j��(��+�%)�%=�%=�f�h�%G�%G����"� � $� P� @� @� @� @�%)�%>� @� @� @�I� �)+����y� /�0�0�*2� *2�I� &� '� 8�I�O����"�"�$)� �!�&O�=F�_�&O� &O� �!� �s �C�<D�Dc �n � t j |d� � }t || j | j z � � }t j |t j � � }| � |� � } t | � | j |d|� � � � � }t j |� � }n)# t t f$ r}t d� � |�d}~ww xY w|j |k r%| j rt d� � �t d� � �||d|�< | j r| xj dz c_ n| xj |z c_ |S )aw Calculate the energies of a population. Parameters ---------- population : ndarray An array of parameter vectors normalised to [0, 1] using lower and upper limits. Has shape ``(np.size(population, 0), N)``. Returns ------- energies : ndarray An array of energies corresponding to each population member. If maxfun will be exceeded during this call, then the number of function evaluations will be reduced and energies will be right-padded with np.inf. Has shape ``(np.size(population, 0),)`` r zzThe map-like callable must be of the form f(func, iterable), returning a sequence of numbers the same length as 'iterable'NzcThe vectorized function must return an array of shape (S,) when given an array of shape (len(x), S)z)func(x, *args) must return a scalar valuer )rN r} �minr r� r� r~ r� �listrn r1 �squeeze� TypeErrorri � RuntimeErrorr )r� r� � num_members�S�energies�parameters_pop� calc_energies�es r5 r� z:DifferentialEvolutionSolver._calculate_population_energiesG s[ � �$ �g�j�!�,�,� � � �T�[�4�:� 5� 6� 6���7�;���/�/�� �/�/� �;�;�� � �� � ���N�1�Q�3�,?�@�@� � �M� �J�}� 5� 5�M�M���:�&� � � � �P�� � � ����� ���� � �� "� "��� <�"� $;� <� <� <� � J�K�K� K�%���1�� � �?� � �J�J�!�O�J�J�J� �J�J�!�O�J�J��s �(AB- �-C�>C�Cc �� � t j | j � � }|| j }|j r(t j | j | � � }|| }n-t j t j | j d�� � � � }| j |dg | j d|g< | j |dgd d �f | j d|gd d �f< | j |dg | j d|g< | j |dgd d �f | j d|gd d �f< d S )Nr ��axisr ) rN �aranger� r� r} �argminr� r� r� r� )r� �idx�feasible_solutions�idx_t�ls r5 r� z2DifferentialEvolutionSolver._promote_lowest_energy~ s � � �i��3�4�4�� �� � /�� � "� E��I�d� 6�7I� J�K�K�E�"�5�)�A�A� � �"�&��!:��C�C�C�D�D�A�+/�+C�Q��F�+K�� �!�Q��(�%)�_�a��V�Q�Q�Q�Y�%?����A����� �"� $� �q�!�f� 5�� �q�!�f� � �!�1�a�&�!�!�!�)�,� �!�1�a�&�!�!�!�)�,�,�,rS c � � t j |� � | j z }t j || j f� � }d}| j D ]�}|� |j � � j }|j d |j k s|dk r |j d |k rt d� � �t j |||j f� � }||dd�|||j z �f< ||j z }��|S )a\ Calculates total constraint violation for all the constraints, for a set of solutions. Parameters ---------- x : ndarray Solution vector(s). Has shape (S, N), or (N,), where S is the number of solutions to investigate and N is the number of parameters. Returns ------- cv : ndarray Total violation of constraints. Has shape ``(S, M)``, where M is the total number of constraint components (which is not necessarily equal to len(self._wrapped_constraints)). r ���r �M An array returned from a Constraint has the wrong shape. If `vectorized is False` the Constraint should return an array of shape (M,). If `vectorized is True` then the Constraint must return an array of shape (M, S), where S is the number of solution vectors and M is the number of constraint components in a given Constraint object.N) rN r} r� r� r� r� r� rP r� ra r� �reshape)r� rQ r� �_out�offset�conrc s r5 r� z4DifferentialEvolutionSolver._constraint_violation_fn� s� � �* �G�A�J�J�$�.� .���x��D� 2�3�4�4�����,� %� %�C� � � �a�c�"�"�$�A� �w�r�{�c�n�,�,��Q���1�7�1�:��?�?�"� $9� :� :� :� � �1�q�#�.� 1�2�2�A�67�D����F�6�C�N�2�2�2� 3� �c�n� $�F�F�� rS c � � � t j |d� � }� j s0t j |t � � t j |df� � fS � � |� � }� j r(t j � � |� � � � }n,t j � fd�|D � � � � }|dd�df }t j |d�� � dk }||fS )a� Calculate the feasibilities of a population. Parameters ---------- population : ndarray An array of parameter vectors normalised to [0, 1] using lower and upper limits. Has shape ``(np.size(population, 0), N)``. Returns ------- feasible, constraint_violation : ndarray, ndarray Boolean array of feasibility for each population member, and an array of the constraint violation for each population member. constraint_violation has shape ``(np.size(population, 0), M)``, where M is the number of constraints. r r c �: �� g | ]}�� |� � ��S r )r� )rb rQ r� s �r5 rd zSDifferentialEvolutionSolver._calculate_population_feasibilities.<locals>.<listcomp>� s= �� � -F� -F� -F�12� .2�-J�-J�1�-M�-M� -F� -F� -FrS Nr� ) rN r} r� r� r� r� r� r rs r� r� )r� r� r� r� r� r� s ` r5 r� z?DifferentialEvolutionSolver._calculate_population_feasibilities� s �� �$ �g�j�!�,�,� ��(� J��7�;��-�-�r�x��a�8H�/I�/I�I� I� �/�/� �;�;�� �?� >�#%�8��-�-�n�=�=�$� $� � � $&�8� -F� -F� -F� -F�6D�-F� -F� -F� $G� $G� � $8����1��#=� ��V� 0�q�9�9�9�A�=�>���-�-�-rS c � � | S rM r r� s r5 rT z$DifferentialEvolutionSolver.__iter__� � � �� rS c � � | S rM r r� s r5 � __enter__z%DifferentialEvolutionSolver.__enter__� r rS c � � | j j |� S rM )rn �__exit__)r� r s r5 r z$DifferentialEvolutionSolver.__exit__ s � �(�t� �(�$�/�/rS c �^ � |r|r||k S |r|sdS |s||k � � � rdS dS )a Trial is accepted if: * it satisfies all constraints and provides a lower or equal objective function value, while both the compared solutions are feasible - or - * it is feasible while the original solution is infeasible, - or - * it is infeasible, but provides a lower or equal constraint violation for all constraint functions. This test corresponds to section III of Lampinen [1]_. Parameters ---------- energy_trial : float Energy of the trial solution feasible_trial : float Feasibility of trial solution cv_trial : array-like Excess constraint violation for the trial solution energy_orig : float Energy of the original solution feasible_orig : float Feasibility of original solution cv_orig : array-like Excess constraint violation for the original solution Returns ------- accepted : bool TF)rp )r� � energy_trial�feasible_trial�cv_trial� energy_orig� feasible_orig�cv_origs r5 � _accept_trialz)DifferentialEvolutionSolver._accept_trial s_ � �D � �^� � �;�.� .� � �M� ��4� � �X��%8�$=�$=�$?�$?� � �4��urS c �* � � t j t j � j � � � � rm� � � j � � \ � _ � _ � � � j � j � � � j � j < � � � � � j �6� j � � j d � j d � � � _ � j dk �r�t � j � � D �]�}� j � j k rt& �� � |� � }� � |� � � � |� � }� j rc� � |� � }d}t j }t j |� � dk s'd}� � |� � }� xj dz c_ n<d}t j dg� � }� � |� � }� xj dz c_ � � |||� j | � j | � j | � � r�|� j |< t j |� � � j |< |� j |< |� j |< � � |||� j d � j d � j d � � r� � � � ��ŐnÉ j dk �r�� j � j k rt& �t j � fd �t � j � � D � � � � }� � |� � � � |� � \ }}t j � j t j � � }� � || � � ||< � fd �tC |||� j � j � j � � D � � } t j | � � } t j" | dd�t j# f |� j � � � _ t j" | |� j � � � _ t j" | |� j � � � _ t j" | dd�t j# f |� j � � � _ � � � � � j$ � j d fS ) z� Evolve the population by a single generation Returns ------- x : ndarray The best solution from the solver. fun : float Value of objective function obtained from the best solution. Nr r r FTr^ rI c �: �� g | ]}�� |� � ��S r )�_mutate)rb �ir� s �r5 rd z8DifferentialEvolutionSolver.__next__.<locals>.<listcomp>� s# �� �M�M�M�Q�� � �a� � �M�M�MrS c �$ �� g | ] } �j |� �� S r )r )rb �valr� s �r5 rd z8DifferentialEvolutionSolver.__next__.<locals>.<listcomp>� s6 �� � B� B� B��%�4�%�s�+� B� B� BrS )%rN rp r� r� r� r� r� r� r� r� rt r� r� ro rj r� r� r� r r� r �_ensure_constraintr� r� r� r~ r� r1 � atleast_2dr r� rs r� �zip�wherer� rQ ) r� � candidate�trial� parameters�cvr� �energy� trial_pop�trial_energies�locs ` r5 �__next__z$DifferentialEvolutionSolver.__next__0 s� �� � �6�"�(�4�3�4�4� 5� 5� *��8�8�� �I�I� 5�D�M�4�4� �3�3��O�D�M�2�4� 4� � $�T�]� 3� � '� '� )� )� )� �;� "� �5�=�=�d�k�!�n�>B�k�!�n�N� N�D�J� �>�[� (� (� "�4�#>� ?� ?� - 6� - 6� ��:�� �+�+�'�'� � � �Y�/�/�� �'�'��.�.�.� "� 3� 3�E� :� :� � �,� $� �6�6�z�B�B�B� $�H� �V�F� �6�"�:�:��>�>�#'��!%���:�!6�!6�� � � �a�� � �� #�H�� ��t�,�,�B� !�Y�Y�z� 2� 2�F��J�J�!�O�J�J� �%�%�f�h��&*�&>�y�&I�&*�m�I�&>�&*�&?� �&J�L� L� 6� 27�D�O�I�.�:<�*�V�:L�:L�D�,�Y�7�/7�D�M�)�,�;=�D�-�i�8� �)�)�&�(�B�*.�*B�1�*E�*.�-��*:�*.�*C�A�*F�H� H� 6� �3�3�5�5�5��[- 6�^ �^�z� )� )��z�T�[�(�(�#�#� ��M�M�M�M�%��0K�*L�*L�M�M�M�O� O�I� � #� #�I� .� .� .� �C�C�I�N�N�L�H�b� �W�T�%@�"�&� I� I�N� (,�'J�'J��(�#�(%� (%�N�8� $�B� B� B� B��~�x��T�5M��}�d�&?�A� A�B� B� B�C� �(�3�-�-�C� �h�s�1�1�1�b�j�=�'9�'0�'+�� 8� 8�D�O� (*�x��0>�04�0H�(J� (J�D� $� �H�S�%-�%)�]� 4� 4�D�M� )+���Q�Q�Q�� �]�1C�13�15�1J�)L� )L�D� %� � '� '� )� )� )��v�t�/��2�2�2rS c �� � | j |dz | j z z }t j | j � � r<t j | j |j � � }t j || � � ||< |S )z2Scale from a number between 0 and 1 to parameters.r )r� r� rN rr r r� r� �round)r� r' �scaledr s r5 r� z-DifferentialEvolutionSolver._scale_parameters� sd � � �"�e�c�k�T�5F�%F�F�� �6�$�"� #� #� ,���� 0�&�,�?�?�A������+�+�F�1�I�� rS c �, � || j z | j z dz S )z2Scale from parameters to a number between 0 and 1.r )r� r� )r� r( s r5 r� z/DifferentialEvolutionSolver._unscale_parameters� s � ��T� .�.�$�2C�C�c�I�IrS c � � t j |dk |dk z � � }| j � |d j �� � ||< dS )z0Make sure the parameters lie between the limits.r r r� N)rN r% r� r� r� )r� r' �masks r5 r" z.DifferentialEvolutionSolver._ensure_constraint� sE � ��x����u�q�y�1�2�2���2�:�:��Q�� �:�N�N��d� � � rS c �� � t j | j | � � }| j }|� | j � � }| j dv r+| � || � |d� � � � }n)| � | � |d� � � � }| j | j v rC|� | j �� � }|| j k }d||< t j |||� � }|S | j | j v rrd}|� | j �� � }|| j k }d|d< || j k r8|| r0|| ||< |dz | j z }|dz }|| j k r|| �0|S dS )z3Create a trial vector based on a mutation strategy.)rE r> rX r� Tr r N)rN r� r� r� �choicer� r rg �_select_samplesre r� rx r% rh )r� r& r' r� � fill_point�bprime� crossoversr s r5 r z#DifferentialEvolutionSolver._mutate� s� � ����� �2�3�3���*���Z�Z�� 4�5�5� � �=� F� F� F��'�'� �(,�(<�(<�Y��(J�(J�L� L�F�F� �'�'��(<�(<�Y��(J�(J�K�K�F� �=�D�N� *� *� ���$�*>��?�?�J�#�d�&A�A�J� &*�J�z� "��H�Z���7�7�E��L� �]�d� /� /� /��A� ���$�*>��?�?�J�#�d�&A�A�J� �J�q�M��t�+�+�+� �1� �+�$*�:�$6��j�!� (�1�n��0D� D� ��Q��� �t�+�+�+� �1� �+� �L� 0� /rS c �~ � |dd� \ }}| j d | j | j | | j | z z z S )zbest1bin, best1expNrJ r �r� ro )r� r� �r0�r1s r5 r7 z"DifferentialEvolutionSolver._best1� sF � ���!�����B����"�T�Z�� ��$�t��r�':�:�&<� <� =rS c � � |dd� \ }}}| j | | j | j | | j | z z z S )zrand1bin, rand1expN� r< )r� r� r= r> �r2s r5 r< z"DifferentialEvolutionSolver._rand1� sH � � �R�a�R�[� ��B�����#�d�j�� ��$�t��r�':�:�'<� <� =rS c �� � |dd� \ }}}t j | j | � � }|| j | j d |z z z }|| j | j | | j | z z z }|S )z randtobest1bin, randtobest1expNr@ r )rN r� r� ro )r� r� r= r> rA r9 s r5 r8 z(DifferentialEvolutionSolver._randtobest1� sx � � �R�a�R�[� ��B����� ��,�-�-���$�*���� 2�V� ;�<�<���$�*���� 3� $��� 3�!4� 5� 5��� rS c � � |dd� \ }}| j | | j | j d | j | z | j | z | j | z z z }|S )z$currenttobest1bin, currenttobest1expNrJ r r< )r� r& r� r= r> r9 s r5 r9 z+DifferentialEvolutionSolver._currenttobest1� sh � ���!�����B��/�)�,�t�z��?�1�%��� �(B�B��?�2�&�'�)-� ��)<�=�0>� >�� � rS c � � |dd� \ }}}}| j d | j | j | | j | z | j | z | j | z z z }|S )zbest2bin, best2expN� r r< )r� r� r= r> rA �r3r9 s r5 r: z"DifferentialEvolutionSolver._best2 sl � � ��!�����B��B��/�!�$�t�z��?�2�&�� ��)<�<��?�2�&�'�)-� ��)<�=�(>� >�� � rS c � � |\ }}}}}| j | | j | j | | j | z | j | z | j | z z z }|S )zrand2bin, rand2expr< )r� r� r= r> rA rF �r4r9 s r5 r; z"DifferentialEvolutionSolver._rand2 sg � � $���B��B���/�"�%�� ��?�2�&�� ��)<�<��?�2�&�'�)-� ��)<�=�)>� >�� � rS c � � t t | j � � � � }|� |� � | j � |� � |d|� }|S )z� obtain random integers from range(self.num_population_members), without replacement. You can't have the original candidate either. N)r� r� r� �remover� �shuffle)r� r& �number_samples�idxss r5 r7 z+DifferentialEvolutionSolver._select_samples sX � � �E�$�5�6�6�7�7�� � � �I� � � � �$�,�,�T�2�2�2��O�^�O�$��� rS )'�__name__� __module__� __qualname__�__doc__re rh r� rN r~ r� r� r� r� r� �propertyrQ r� r� r0 r� r� r� r� rT r r r r. r� r� r" r r7 r< r8 r9 r: r; r7 r rS r5 r/ r/ � s� � � � � � �r� r�j &�#1�&7� %� %� %� '� '�I� !)� (�&4�):� (� (� *� *�L�M�� +-�$�d�B��H�C�d����E�$�&�Q����t� K� EI� !� K� K� K� K� K�Z$� $� $�L"� "� "�H � � � !� !� !�F �:� :� �X�:� �F� F� �X�F� F� F� F�E� E� E�N5� 5� 5�n.� .� .�(9� 9� 9�v+.� +.� +.�Z� � �� � �0� 0� 0�+� +� +�Zz3� z3� z3�x� � �J� J� J�O� O� O� #� #� #�J=� =� =� =� =� =� � � �� � �� � �� � � � � � � rS r/ c �$ � e Zd ZdZd� Zd� Zd� ZdS )r� a; Object to wrap/evaluate user defined constraints. Very similar in practice to `PreparedConstraint`, except that no evaluation of jac/hess is performed (explicit or implicit). If created successfully, it will contain the attributes listed below. Parameters ---------- constraint : {`NonlinearConstraint`, `LinearConstraint`, `Bounds`} Constraint to check and prepare. x0 : array_like Initial vector of independent variables, shape (N,) Attributes ---------- fun : callable Function defining the constraint wrapped by one of the convenience classes. bounds : 2-tuple Contains lower and upper bounds for the constraints --- lb and ub. These are converted to ndarray and have a size equal to the number of the constraints. c �d �� �| _ t �t � � r�fd�}nCt �t � � r�fd�}n(t �t � � rd� }nt d� � �|| _ t j �j t �� � }t j �j t �� � }t j |� � } ||� � }|j x| _ }|j | _ |j dk rt j ||� � }|j dk rt j ||� � }||f| _ d S )Nc �z �� t j | � � } t j �� | � � � � S rM )rN r� rO r� )rQ � constraints �r5 r� z(_ConstraintWrapper.__init__.<locals>.fun< s, �� ��J�q�M�M���}�Z�^�^�A�%6�%6�7�7�7rS c � �� t �j � � r�j }nt j �j � � }|� | � � S rM )r �ArN r# �dot)rQ rX rV s �r5 r� z(_ConstraintWrapper.__init__.<locals>.fun@ s> �� ��J�L�)�)� 4�"� �A�A�� �j�l�3�3�A��u�u�Q�x�x�rS c �* � t j | � � S rM )rN r� )rQ s r5 r� z(_ConstraintWrapper.__init__.<locals>.funG s � ��z�!�}�}�$rS z*`constraint` of an unknown type is passed.rU r )rV ry r r r ri r� rN r� rz rW r{ r} ra r� �ndim�resizer2 )r� rV r. r� rz r{ �f0�ms ` r5 r� z_ConstraintWrapper.__init__8 sX �� �$��� �j�"5� 6� 6� K� 8� 8� 8� 8� 8� 8� � �$4� 5� 5� K� � � � � � � � �F� +� +� K� %� %� %� %� � I�J�J� J���� �Z� � �U� 3� 3� 3�� �Z� � �U� 3� 3� 3�� �Z��^�^�� �S��W�W�� �g�%���!� !�w�� � �7�a�<�<���2�q�!�!�B� �7�a�<�<���2�q�!�!�B��2�h�� � � rS c �P � t j | � |� � � � S rM )rN rO r� )r� rQ s r5 �__call__z_ConstraintWrapper.__call___ s � ��}�T�X�X�a�[�[�)�)�)rS c �P � | � t j |� � � � } t j | j d |j z d� � }t j |j | j d z d� � }n"# t $ r}t d� � |�d}~ww xY w||z j }|S )a How much the constraint is exceeded by. Parameters ---------- x : array-like Vector of independent variables, (N, S), where N is number of parameters and S is the number of solutions to be investigated. Returns ------- excess : array-like How much the constraint is exceeded by, for each of the constraints specified by `_ConstraintWrapper.fun`. Has shape (M, S) where M is the number of constraint components. r r r N)r� rN r� �maximumr2 rP ri r� )r� rQ �ev� excess_lb� excess_ubr� �vs r5 r� z _ConstraintWrapper.violationb s� � �" �X�X�b�j��m�m� $� $�� =�� �4�;�q�>�B�D�#8�!�<�<�I�� �2�4�$�+�a�.�#8�!�<�<�I�I��� =� =� =� � 5� 6� 6� <=� =����� =���� �� "� %���s �AA: �: B�B�BN)rN rO rP rQ r� r` r� r rS r5 r� r� sL � � � � � �� �0% � % � % �N*� *� *�"� "� "� "� "rS r� )r r r r r r r NNFTr r r r r N) rQ rk �numpyrN �scipy.optimizer r �scipy.optimize._optimizer �scipy._lib._utilr r r �scipy.optimize._constraintsr r r r � scipy.sparser �__all__�finfo�float64�epsr� r r/ r� r rS r5 �<module>rq s� ��� � ���� � � � � 3� 3� 3� 3� 3� 3� 3� 3� 4� 4� 4� 4� 4� 4� M� M� M� M� M� M� M� M� M� M�P� P� P� P� P� P� P� P� P� P� P� P� !� !� !� !� !� !� #� $�� �2�8�B�J� � � #�� <F�9=�FJ�=A�CN�9=� y� (,�� y� y� y� y� y�x J� J� J� J� J� J� J� J�Z$e� e� e� e� e� e� e� e� e� erS
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