# Source code for deap.benchmarks.tools

    """Module containing tools that are useful when benchmarking algorithms
    """
    from math import hypot, sqrt
    from functools import wraps
    from itertools import repeat
    try:
        import numpy
        numpy_imported = True
    except ImportError:
        numpy_imported = False

    try:
        import scipy.spatial
        scipy_imported = True
    except ImportError:
        scipy_imported = False

    try:
        # try importing the C version
        from ..tools._hypervolume import hv
    except ImportError:
        # fallback on python version
        from ..tools._hypervolume import pyhv as hv

    class translate(object):
        """Decorator for evaluation functions, it translates the objective
        function by *vector* which should be the same length as the individual
        size. When called the decorated function should take as first argument the
        individual to be evaluated. The inverse translation vector is actually
        applied to the individual and the resulting list is given to the
        evaluation function. Thus, the evaluation function shall not be expecting
        an individual as it will receive a plain list.

        This decorator adds a :func:`translate` method to the decorated function.
        """
        def __init__(self, vector):
            self.vector = vector

        def __call__(self, func):
            # wraps is used to combine stacked decorators that would add functions
            @wraps(func)
            def wrapper(individual, *args, **kargs):
                # A subtraction is applied since the translation is applied to the
                # individual and not the function
                return func([v - t for v, t in zip(individual, self.vector)],
                            *args, **kargs)
            wrapper.translate = self.translate
            return wrapper

        def translate(self, vector):
            """Set the current translation to *vector*. After decorating the
            evaluation function, this function will be available directly from
            the function object. ::

                @translate([0.25, 0.5, ..., 0.1])
                def evaluate(individual):
                    return sum(individual),

                # This will cancel the translation
                evaluate.translate([0.0, 0.0, ..., 0.0])
            """
            self.vector = vector

    class rotate(object):
        """Decorator for evaluation functions, it rotates the objective function
        by *matrix* which should be a valid orthogonal NxN rotation matrix, with N
        the length of an individual. When called the decorated function should
        take as first argument the individual to be evaluated. The inverse
        rotation matrix is actually applied to the individual and the resulting
        list is given to the evaluation function. Thus, the evaluation function
        shall not be expecting an individual as it will receive a plain list
        (numpy.array). The multiplication is done using numpy.

        This decorator adds a :func:`rotate` method to the decorated function.

        .. note::

           A random orthogonal matrix Q can be created via QR decomposition. ::

               A = numpy.random.random((n,n))
               Q, _ = numpy.linalg.qr(A)
        """
        def __init__(self, matrix):
            if not numpy_imported:
                raise RuntimeError("Numpy is required for using the rotation "
                                   "decorator")
            # The inverse is taken since the rotation is applied to the individual
            # and not the function which is the inverse
            self.matrix = numpy.linalg.inv(matrix)

        def __call__(self, func):
            # wraps is used to combine stacked decorators that would add functions
            @wraps(func)
            def wrapper(individual, *args, **kargs):
                return func(numpy.dot(self.matrix, individual), *args, **kargs)
            wrapper.rotate = self.rotate
            return wrapper

        def rotate(self, matrix):
            """Set the current rotation to *matrix*. After decorating the
            evaluation function, this function will be available directly from
            the function object. ::

                # Create a random orthogonal matrix
                A = numpy.random.random((n,n))
                Q, _ = numpy.linalg.qr(A)

                @rotate(Q)
                def evaluate(individual):
                    return sum(individual),

                # This will reset rotation to identity
                evaluate.rotate(numpy.identity(n))
            """
            self.matrix = numpy.linalg.inv(matrix)

    class noise(object):
        """Decorator for evaluation functions, it evaluates the objective function
        and adds noise by calling the function(s) provided in the *noise*
        argument. The noise functions are called without any argument, consider
        using the :class:`~deap.base.Toolbox` or Python's
        :func:`functools.partial` to provide any required argument. If a single
        function is provided it is applied to all objectives of the evaluation
        function. If a list of noise functions is provided, it must be of length
        equal to the number of objectives. The noise argument also accept
        :obj:`None`, which will leave the objective without noise.

        This decorator adds a :func:`noise` method to the decorated
        function.
        """
        def __init__(self, noise):
            try:
                self.rand_funcs = tuple(noise)
            except TypeError:
                self.rand_funcs = repeat(noise)

        def __call__(self, func):
            # wraps is used to combine stacked decorators that would add functions
            @wraps(func)
            def wrapper(individual, *args, **kargs):
                result = func(individual, *args, **kargs)
                noisy = list()
                for r, f in zip(result, self.rand_funcs):
                    if f is None:
                        noisy.append(r)
                    else:
                        noisy.append(r + f())
                return tuple(noisy)
            wrapper.noise = self.noise
            return wrapper

        def noise(self, noise):
            """Set the current noise to *noise*. After decorating the
            evaluation function, this function will be available directly from
            the function object. ::

                prand = functools.partial(random.gauss, mu=0.0, sigma=1.0)

                @noise(prand)
                def evaluate(individual):
                    return sum(individual),

                # This will remove noise from the evaluation function
                evaluate.noise(None)
            """
            try:
                self.rand_funcs = tuple(noise)
            except TypeError:
                self.rand_funcs = repeat(noise)

    class scale(object):
        """Decorator for evaluation functions, it scales the objective function by
        *factor* which should be the same length as the individual size. When
        called the decorated function should take as first argument the individual
        to be evaluated. The inverse factor vector is actually applied to the
        individual and the resulting list is given to the evaluation function.
        Thus, the evaluation function shall not be expecting an individual as it
        will receive a plain list.

        This decorator adds a :func:`scale` method to the decorated function.
        """
        def __init__(self, factor):
            # Factor is inverted since it is applied to the individual and not the
            # objective function
            self.factor = tuple(1.0/f for f in factor)

        def __call__(self, func):
            # wraps is used to combine stacked decorators that would add functions
            @wraps(func)
            def wrapper(individual, *args, **kargs):
                return func([v * f for v, f in zip(individual, self.factor)],
                            *args, **kargs)
            wrapper.scale = self.scale
            return wrapper

        def scale(self, factor):
            """Set the current scale to *factor*. After decorating the
            evaluation function, this function will be available directly from
            the function object. ::

                @scale([0.25, 2.0, ..., 0.1])
                def evaluate(individual):
                    return sum(individual),

                # This will cancel the scaling
                evaluate.scale([1.0, 1.0, ..., 1.0])
            """
            # Factor is inverted since it is applied to the individual and not the
            # objective function
            self.factor = tuple(1.0/f for f in factor)

    class bound(object):
        """Decorator for crossover and mutation functions, it changes the
        individuals after the modification is done to bring it back in the allowed
        *bounds*. The *bounds* are functions taking individual and returning
        whether of not the variable is allowed. You can provide one or multiple such
        functions. In the former case, the function is used on all dimensions and
        in the latter case, the number of functions must be greater or equal to
        the number of dimension of the individuals.

        The *type* determines how the attributes are brought back into the valid
        range

        This decorator adds a :func:`bound` method to the decorated function.
        """
        def _clip(self, individual):
            return individual

        def _wrap(self, individual):
            return individual

        def _mirror(self, individual):
            return individual

        def __call__(self, func):
            @wraps(func)
            def wrapper(*args, **kargs):
                individuals = func(*args, **kargs)
                return self.bound(individuals)
            wrapper.bound = self.bound
            return wrapper

        def __init__(self, bounds, type):
            try:
                self.bounds = tuple(bounds)
            except TypeError:
                self.bounds = repeat(bounds)

            if type == "mirror":
                self.bound = self._mirror
            elif type == "wrap":
                self.bound = self._wrap
            elif type == "clip":
                self.bound = self._clip

    def diversity(first_front, first, last):
        """Given a Pareto front `first_front` and the two extreme points of the
        optimal Pareto front, this function returns a metric of the diversity
        of the front as explained in the original NSGA-II article by K. Deb.
        The smaller the value is, the better the front is.
        """
        df = hypot(first_front[0].fitness.values[0] - first[0],
                   first_front[0].fitness.values[1] - first[1])
        dl = hypot(first_front[-1].fitness.values[0] - last[0],
                   first_front[-1].fitness.values[1] - last[1])
        dt = [hypot(first.fitness.values[0] - second.fitness.values[0],
                    first.fitness.values[1] - second.fitness.values[1])
              for first, second in zip(first_front[:-1], first_front[1:])]

        if len(first_front) == 1:
            return df + dl

        dm = sum(dt)/len(dt)
        di = sum(abs(d_i - dm) for d_i in dt)
        delta = (df + dl + di)/(df + dl + len(dt) * dm)
        return delta

    def convergence(first_front, optimal_front):
        """Given a Pareto front `first_front` and the optimal Pareto front,
        this function returns a metric of convergence
        of the front as explained in the original NSGA-II article by K. Deb.
        The smaller the value is, the closer the front is to the optimal one.
        """
        distances = []

        for ind in first_front:
            distances.append(float("inf"))
            for opt_ind in optimal_front:
                dist = 0.
                for i in range(len(opt_ind)):
                    dist += (ind.fitness.values[i] - opt_ind[i])**2
                if dist < distances[-1]:
                    distances[-1] = dist
            distances[-1] = sqrt(distances[-1])

        return sum(distances) / len(distances)

    def hypervolume(front, ref=None):
        """Return the hypervolume of a *front*. If the *ref* point is not
        given, the worst value for each objective +1 is used.

        :param front: The population (usually a list of undominated individuals)
                      on which to compute the hypervolume.
        :param ref: A point of the same dimensionality as the individuals in *front*.
        """
        # Must use wvalues * -1 since hypervolume use implicit minimization
        wobj = numpy.array([ind.fitness.wvalues for ind in front]) * -1
        if ref is None:
            ref = numpy.max(wobj, axis=0) + 1
        return hv.hypervolume(wobj, ref)

    def igd(A, Z):
        """Inverse generational distance.
        """
        if not scipy_imported:
            raise ImportError("idg requires scipy module")
        distances = scipy.spatial.distance.cdist(A, Z)
        return numpy.average(numpy.min(distances, axis=0))