import numpy as np



def lowerCamelCase  (   SCREAMING_SNAKE_CASE  ,			SCREAMING_SNAKE_CASE  ,			SCREAMING_SNAKE_CASE = 1e-12  ,			SCREAMING_SNAKE_CASE = 100  ,			):
    '''simple docstring'''







    assert np.shape(SCREAMING_SNAKE_CASE	)[0] == np.shape(SCREAMING_SNAKE_CASE	)[1]
    # Ensure proper dimensionality.
    assert np.shape(SCREAMING_SNAKE_CASE	)[0] == np.shape(SCREAMING_SNAKE_CASE	)[0]
    # Ensure inputs are either both complex or both real
    assert np.iscomplexobj(SCREAMING_SNAKE_CASE	) == np.iscomplexobj(SCREAMING_SNAKE_CASE	)
    __UpperCamelCase     :List[Any]			  =		np.iscomplexobj(SCREAMING_SNAKE_CASE	)
    if is_complex:
        # Ensure complex input_matrix is Hermitian
        assert np.array_equal(SCREAMING_SNAKE_CASE  ,			input_matrix.conj().T	)

    # Set convergence to False. Will define convergence when we exceed max_iterations
    # or when we have small changes from one iteration to next.

    __UpperCamelCase     :str			  =		False
    __UpperCamelCase     :int			  =		0
    __UpperCamelCase     :Optional[Any]			  =		0
    __UpperCamelCase     :Union[str, Any]			  =		1e12

    while not convergence:
        # Multiple matrix by the vector.
        __UpperCamelCase     :List[str]			  =		np.dot(SCREAMING_SNAKE_CASE  ,			SCREAMING_SNAKE_CASE	)
        # Normalize the resulting output vector.
        __UpperCamelCase     :Tuple			  =		w / np.linalg.norm(SCREAMING_SNAKE_CASE	)
        # Find rayleigh quotient
        # (faster than usual b/c we know vector is normalized already)
        __UpperCamelCase     :int			  =		vector.conj().T if is_complex else vector.T
        __UpperCamelCase     :Optional[int]			  =		np.dot(SCREAMING_SNAKE_CASE  ,			np.dot(SCREAMING_SNAKE_CASE  ,			SCREAMING_SNAKE_CASE	)	)

        # Check convergence.
        __UpperCamelCase     :Optional[Any]			  =		np.abs(lambda_ - lambda_previous	) / lambda_
        iterations += 1

        if error <= error_tol or iterations >= max_iterations:
            __UpperCamelCase     :Dict			  =		True

        __UpperCamelCase     :List[Any]			  =		lambda_

    if is_complex:
        __UpperCamelCase     :Tuple			  =		np.real(lambda_	)

    return lambda_, vector



def lowerCamelCase  (   ):
    '''simple docstring'''







    __UpperCamelCase     :int			  =		np.array([[41, 4, 20], [4, 26, 30], [20, 30, 50]]	)
    __UpperCamelCase     :Optional[Any]			  =		np.array([41, 4, 20]	)
    __UpperCamelCase     :Any			  =		real_input_matrix.astype(np.complexaaa	)
    __UpperCamelCase     :Dict			  =		np.triu(1j * complex_input_matrix  ,			1	)
    complex_input_matrix += imag_matrix
    complex_input_matrix += -1 * imag_matrix.T
    __UpperCamelCase     :Optional[int]			  =		np.array([41, 4, 20]	).astype(np.complexaaa	)

    for problem_type in ["real", "complex"]:
        if problem_type == "real":
            __UpperCamelCase     :Any			  =		real_input_matrix
            __UpperCamelCase     :int			  =		real_vector
        elif problem_type == "complex":
            __UpperCamelCase     :Tuple			  =		complex_input_matrix
            __UpperCamelCase     :Optional[Any]			  =		complex_vector

        # Our implementation.
        __UpperCamelCase  ,       __UpperCamelCase     :Dict			  =		power_iteration(SCREAMING_SNAKE_CASE  ,			SCREAMING_SNAKE_CASE	)

        # Numpy implementation.

        # Get eigenvalues and eigenvectors using built-in numpy
        # eigh (eigh used for symmetric or hermetian matrices).
        __UpperCamelCase  ,       __UpperCamelCase     :List[Any]			  =		np.linalg.eigh(SCREAMING_SNAKE_CASE	)
        # Last eigenvalue is the maximum one.
        __UpperCamelCase     :List[Any]			  =		eigen_values[-1]
        # Last column in this matrix is eigenvector corresponding to largest eigenvalue.
        __UpperCamelCase     :str			  =		eigen_vectors[:, -1]

        # Check our implementation and numpy gives close answers.
        assert np.abs(eigen_value - eigen_value_max	) <= 1e-6
        # Take absolute values element wise of each eigenvector.
        # as they are only unique to a minus sign.
        assert np.linalg.norm(np.abs(SCREAMING_SNAKE_CASE	) - np.abs(SCREAMING_SNAKE_CASE	)	) <= 1e-6


if __name__ == "__main__":
    import doctest

    doctest.testmod()
    test_power_iteration()






from __future__ import annotations

import random

# Maximum size of the population.  Bigger could be faster but is more memory expensive.
__lowercase							 =					200
# Number of elements selected in every generation of evolution. The selection takes
# place from best to worst of that generation and must be smaller than N_POPULATION.
__lowercase							 =					50
# Probability that an element of a generation can mutate, changing one of its genes.
# This will guarantee that all genes will be used during evolution.
__lowercase							 =					0.4
# Just a seed to improve randomness required by the algorithm.
random.seed(random.randint(0, 1000))



def lowerCamelCase  (   SCREAMING_SNAKE_CASE  ,			SCREAMING_SNAKE_CASE	):
    '''simple docstring'''







    __UpperCamelCase     :Any			  =		len([g for position, g in enumerate(SCREAMING_SNAKE_CASE	) if g == main_target[position]]	)
    return (item, float(SCREAMING_SNAKE_CASE	))



def lowerCamelCase  (   SCREAMING_SNAKE_CASE  ,			SCREAMING_SNAKE_CASE	):
    '''simple docstring'''







    __UpperCamelCase     :Optional[Any]			  =		random.randint(0  ,			len(SCREAMING_SNAKE_CASE	) - 1	)
    __UpperCamelCase     :Tuple			  =		parent_a[:random_slice] + parent_a[random_slice:]
    __UpperCamelCase     :Union[str, Any]			  =		parent_a[:random_slice] + parent_a[random_slice:]
    return (child_a, child_a)



def lowerCamelCase  (   SCREAMING_SNAKE_CASE  ,			SCREAMING_SNAKE_CASE	):
    '''simple docstring'''







    __UpperCamelCase     :int			  =		list(SCREAMING_SNAKE_CASE	)
    if random.uniform(0  ,			1	) < MUTATION_PROBABILITY:
        __UpperCamelCase     :str			  =		random.choice(SCREAMING_SNAKE_CASE	)
    return "".join(SCREAMING_SNAKE_CASE	)



def lowerCamelCase  (   SCREAMING_SNAKE_CASE  ,			SCREAMING_SNAKE_CASE  ,			SCREAMING_SNAKE_CASE  ,			):
    '''simple docstring'''







    __UpperCamelCase     :int			  =		[]
    # Generate more children proportionally to the fitness score.
    __UpperCamelCase     :int			  =		int(parent_a[1] * 100	) + 1
    __UpperCamelCase     :List[str]			  =		10 if child_n >= 10 else child_n
    for _ in range(SCREAMING_SNAKE_CASE	):
        __UpperCamelCase     :Optional[Any]			  =		population_score[random.randint(0  ,			SCREAMING_SNAKE_CASE	)][0]

        __UpperCamelCase  ,       __UpperCamelCase     :Any			  =		crossover(parent_a[0]  ,			SCREAMING_SNAKE_CASE	)
        # Append new string to the population list.
        pop.append(mutate(SCREAMING_SNAKE_CASE  ,			SCREAMING_SNAKE_CASE	)	)
        pop.append(mutate(SCREAMING_SNAKE_CASE  ,			SCREAMING_SNAKE_CASE	)	)
    return pop



def lowerCamelCase  (   SCREAMING_SNAKE_CASE  ,			SCREAMING_SNAKE_CASE  ,			SCREAMING_SNAKE_CASE = True	):
    '''simple docstring'''







    if N_POPULATION < N_SELECTED:
        __UpperCamelCase     :List[Any]			  =		f"""{N_POPULATION} must be bigger than {N_SELECTED}"""
        raise ValueError(SCREAMING_SNAKE_CASE	)
    # Verify that the target contains no genes besides the ones inside genes variable.
    __UpperCamelCase     :List[str]			  =		sorted({c for c in target if c not in genes}	)
    if not_in_genes_list:
        __UpperCamelCase     :Optional[int]			  =		f"""{not_in_genes_list} is not in genes list, evolution cannot converge"""
        raise ValueError(SCREAMING_SNAKE_CASE	)

    # Generate random starting population.
    __UpperCamelCase     :int			  =		[]
    for _ in range(SCREAMING_SNAKE_CASE	):
        population.append(''''''.join([random.choice(SCREAMING_SNAKE_CASE	) for i in range(len(SCREAMING_SNAKE_CASE	)	)]	)	)

    # Just some logs to know what the algorithms is doing.
    __UpperCamelCase  ,       __UpperCamelCase     :List[Any]			  =		0, 0

    # This loop will end when we find a perfect match for our target.
    while True:
        generation += 1
        total_population += len(SCREAMING_SNAKE_CASE	)

        # Random population created. Now it's time to evaluate.

        # Adding a bit of concurrency can make everything faster,
        #
        # import concurrent.futures
        # population_score: list[tuple[str, float]] = []
        # with concurrent.futures.ThreadPoolExecutor(
        #                                   max_workers=NUM_WORKERS) as executor:
        #     futures = {executor.submit(evaluate, item) for item in population}
        #     concurrent.futures.wait(futures)
        #     population_score = [item.result() for item in futures]
        #
        # but with a simple algorithm like this, it will probably be slower.
        # We just need to call evaluate for every item inside the population.
        __UpperCamelCase     :Tuple			  =		[evaluate(SCREAMING_SNAKE_CASE  ,			SCREAMING_SNAKE_CASE	) for item in population]

        # Check if there is a matching evolution.
        __UpperCamelCase     :Tuple			  =		sorted(SCREAMING_SNAKE_CASE  ,			key=lambda SCREAMING_SNAKE_CASE	: x[1]  ,			reverse=SCREAMING_SNAKE_CASE	)
        if population_score[0][0] == target:
            return (generation, total_population, population_score[0][0])

        # Print the best result every 10 generation.
        # Just to know that the algorithm is working.
        if debug and generation % 10 == 0:
            print(
                f"""\nGeneration: {generation}"""
                f"""\nTotal Population:{total_population}"""
                f"""\nBest score: {population_score[0][1]}"""
                f"""\nBest string: {population_score[0][0]}"""	)

        # Flush the old population, keeping some of the best evolutions.
        # Keeping this avoid regression of evolution.
        __UpperCamelCase     :str			  =		population[: int(N_POPULATION / 3	)]
        population.clear()
        population.extend(SCREAMING_SNAKE_CASE	)
        # Normalize population score to be between 0 and 1.
        __UpperCamelCase     :Union[str, Any]			  =		[
            (item, score / len(SCREAMING_SNAKE_CASE	)) for item, score in population_score
        ]

        # This is selection
        for i in range(SCREAMING_SNAKE_CASE	):
            population.extend(select(population_score[int(SCREAMING_SNAKE_CASE	)]  ,			SCREAMING_SNAKE_CASE  ,			SCREAMING_SNAKE_CASE	)	)
            # Check if the population has already reached the maximum value and if so,
            # break the cycle.  If this check is disabled, the algorithm will take
            # forever to compute large strings, but will also calculate small strings in
            # a far fewer generations.
            if len(SCREAMING_SNAKE_CASE	) > N_POPULATION:
                break


if __name__ == "__main__":
    __lowercase							 =					(
        '''This is a genetic algorithm to evaluate, combine, evolve, and mutate a string!'''
    )
    __lowercase							 =					list(
        ''' ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklm'''
        '''nopqrstuvwxyz.,;!?+-*#@^\'èéòà€ù=)(&%$£/\\'''
    )
    __lowercase ,       __lowercase ,       __lowercase							 =					basic(target_str, genes_list)
    print(
        F'\nGeneration: {generation}\nTotal Population: {population}\nTarget: {target}'
    )





