<commit_before># coding=utf-8
from __future__ import division
from abc import ABCMeta, abstractmethod
import numpy as np
from scipy.integrate import ode

from pyinduct import get_initial_functions
from core import (Function, integrate_function, calculate_function_matrix,
                  project_on_initial_functions)
from placeholder import Scalars, TestFunction, Input, FieldVariable, EquationTerm, get_scalar_target
from utils import evaluate_approximation

__author__ = '<NAME>'


class SimulationInput(object):
    """
    base class for all objects that want to act as an input for the timestep simulation
    """
    __metaclass__ = ABCMeta

    def __init__(self):
        pass

    @abstractmethod
    def __call__(self, time, weights, **kwargs):
        """
        handle that will be used to retrieve input
        """
        pass


class Mixer(SimulationInput):
    """
    helper that represents a signal mixer
    """
    def __init__(self, inputs):
        SimulationInput.__init__(self)
        self._inputs = inputs

    def __call__(self, time, weights, **kwargs):
        outs = np.array([handle(time, weights) for handle in self._inputs])
        return np.sum(outs)


class WeakFormulation(object):
    """
    this class represents the weak formulation of a spatial problem.
    It can be initialized with several terms (see children of :py:class:`EquationTerm`).
    The equation is interpreted as term_0 + term_1 + ... + term_N = 0

    :param terms: (list of) of object(s) of type EquationTerm
    """
    def __init__(self, terms, name=None):
        if isinstance(terms, EquationTerm):
            terms = [terms]
        if not isinstance(terms, list):
            raise TypeError("only (list of) {0} allowed".format(EquationTerm))

        for term in terms:
            if not isinstance(term, EquationTerm):
                raise TypeError("Only EquationTerm(s) are accepted.")

        self.terms = terms
        self.name = name


class StateSpace(object):
    """
    wrapper class that represents the state space form of a dynamic system where
    :math:`\\boldsymbol{\\dot{x}}(t) = \\boldsymbol{A}\\boldsymbol{x}(t) + \\boldsymbol{B}u(t)` and
    :math:`\\boldsymbol{y}(t) = \\boldsymbol{C}\\boldsymbol{x}(t) + \\boldsymbol{D}u(t)`

    :param a_matrix: :math:`\\boldsymbol{A}`
    :param a_matrix: :math:`\\boldsymbol{B}`
    :param c_matrix: :math:`\\boldsymbol{C}`
    :param d_matrix: :math:`\\boldsymbol{D}`
    """
    def __init__(self, a_matrix, b_matrix, c_matrix=None, d_matrix=None):
        # TODO dimension checks
        self.A = a_matrix
        self.B = b_matrix
        self.C = c_matrix
        self.D = d_matrix


def simulate_systems(weak_forms, initial_states, time_interval, time_step, spatial_interval, spatial_step):
    """
    convenience wrapper for simulate system, see :ref:py:func:simulate_system for parameters
    :param weak_forms:
    :return:
    """
    return [simulate_system(sys, initial_states, time_interval, time_step, spatial_interval, spatial_step) for sys in
            weak_forms]


def simulate_system(weak_form, initial_states, time_interval, time_step, spatial_interval, spatial_step):
    """
    convenience wrapper that encapsulates the whole simulation process

    :param weak_form:
    :param initial_states: np.array of core.Functions for :math:`x(t=0, z), \\dot{x}(t=0, z), \\dotsc, x^{(n)}(t=0, z)`
    :param time_interval: tuple of (t_start and t_end)
    :return: tuple of integration time-steps and np.array of
    """
    print("simulating system: {0}".format(weak_form.name))
    if not isinstance(weak_form, WeakFormulation):
        raise TypeError("only WeakFormulation accepted.")

    initial_states = np.atleast_1d(initial_states)
    if not isinstance(initial_states[0], Function):
        raise TypeError("only core.Function accepted as initial state")

    if not isinstance(time_interval, tuple):
        raise TypeError("time_interval must be tuple")

    # parse input and create state space system
    print(">>> parsing formulation")
    canonical_form = parse_weak_formulation(weak_form)
    print(">>> creating state space system")
    state_space_form = canonical_form.convert_to_state_space()

    # calculate initial state
    print(">>> deriving initial conditions")
    dim = canonical_form.initial_functions.size
    q0 = np.array([project_on_initial_functions(initial_state, canonical_form.initial_functions) for initial_state in
                   initial_states]).flatten()

    # include boundary conditions
    # TODO

    # simulate
    print(">>> performing time step integration")
    t, q = simulate_state_space(state_space_form, canonical_form.input_function, q0, time_interval, time_step=time_step)

    # create handles and evaluate at given points
    print(">>> performing postprocessing")
    data = []
    for der_idx in range(initial_states.size):
        data.append(evaluate_approximation(q[:, der_idx*dim:(der_idx+1)*dim], canonical_form.initial_functions,
                                           t, spatial_interval, spatial_step))
        data[-1].name = "{0}{1}".format(canonical_form.name,
                                        "_" + "".join(["d" for x in range(der_idx)] + ["t"]) if der_idx > 0 else "")

    # return results
    print("finished simulation.")
    return data


class CanonicalForm(object):
    """
    represents the canonical form of n ordinary differential equation system of order n
    """
    def __init__(self, name=None):
        self.name = name
        self._max_idx = dict(E=0, f=0, g=0)
        self._initial_functions = None
        self._input_function = None

    @staticmethod
    def _build_name(term):
        return "_"+term[0]+str(term[1])

    @property
    def input_function(self):
        return self._input_function

    @input_function.setter
    def input_function(self, func):
        if self._input_function is None:
            self._input_function = func
        if self._input_function != func:
            raise ValueError("already defined input is overridden!")

    @property
    def initial_functions(self):
        return self._initial_functions

    @initial_functions.setter
    def initial_functions(self, funcs):
        if self._initial_functions is None:
            self._initial_functions = funcs
        if (self._initial_functions != funcs).any():
            raise ValueError("already defined initial functions are overridden!")

    def add_to(self, term, val):
        """
        adds the value val to term term
        :param term: tuple of name and index matrix(or vector) to add onto
        :param val: value to add
        :return:
        """
        if not isinstance(term, tuple):
            raise TypeError("term must be tuple.")
        if not isinstance(term[0], str) or term[0] not in "Efg":
            raise TypeError("term[0] must be string")
        if isinstance(term[1], int):
            name = self._build_name(term)
        else:
            raise TypeError("term index must be int")

        if not isinstance(val, np.ndarray):<commit_msg>hack bug in simulation.py<commit_after># coding=utf-8
from __future__ import division
from abc import ABCMeta, abstractmethod
import numpy as np
from scipy.integrate import ode

from pyinduct import get_initial_functions
from core import (Function, integrate_function, calculate_function_matrix,
                  project_on_initial_functions)
from placeholder import Scalars, TestFunction, Input, FieldVariable, EquationTerm, get_scalar_target
from utils import evaluate_approximation

__author__ = '<NAME>'


class SimulationInput(object):
    """
    base class for all objects that want to act as an input for the timestep simulation
    """
    __metaclass__ = ABCMeta

    def __init__(self):
        pass

    @abstractmethod
    def __call__(self, time, weights, **kwargs):
        """
        handle that will be used to retrieve input
        """
        pass


class Mixer(SimulationInput):
    """
    helper that represents a signal mixer
    """
    def __init__(self, inputs):
        SimulationInput.__init__(self)
        self._inputs = inputs

    def __call__(self, time, weights, **kwargs):
        outs = np.array([handle(time, weights) for handle in self._inputs])
        return np.sum(outs)


class WeakFormulation(object):
    """
    this class represents the weak formulation of a spatial problem.
    It can be initialized with several terms (see children of :py:class:`EquationTerm`).
    The equation is interpreted as term_0 + term_1 + ... + term_N = 0

    :param terms: (list of) of object(s) of type EquationTerm
    """
    def __init__(self, terms, name=None):
        if isinstance(terms, EquationTerm):
            terms = [terms]
        if not isinstance(terms, list):
            raise TypeError("only (list of) {0} allowed".format(EquationTerm))

        for term in terms:
            if not isinstance(term, EquationTerm):
                raise TypeError("Only EquationTerm(s) are accepted.")

        self.terms = terms
        self.name = name


class StateSpace(object):
    """
    wrapper class that represents the state space form of a dynamic system where
    :math:`\\boldsymbol{\\dot{x}}(t) = \\boldsymbol{A}\\boldsymbol{x}(t) + \\boldsymbol{B}u(t)` and
    :math:`\\boldsymbol{y}(t) = \\boldsymbol{C}\\boldsymbol{x}(t) + \\boldsymbol{D}u(t)`

    :param a_matrix: :math:`\\boldsymbol{A}`
    :param a_matrix: :math:`\\boldsymbol{B}`
    :param c_matrix: :math:`\\boldsymbol{C}`
    :param d_matrix: :math:`\\boldsymbol{D}`
    """
    def __init__(self, a_matrix, b_matrix, c_matrix=None, d_matrix=None):
        # TODO dimension checks
        self.A = a_matrix
        self.B = b_matrix
        self.C = c_matrix
        self.D = d_matrix


def simulate_systems(weak_forms, initial_states, time_interval, time_step, spatial_interval, spatial_step):
    """
    convenience wrapper for simulate system, see :ref:py:func:simulate_system for parameters
    :param weak_forms:
    :return:
    """
    return [simulate_system(sys, initial_states, time_interval, time_step, spatial_interval, spatial_step) for sys in
            weak_forms]


def simulate_system(weak_form, initial_states, time_interval, time_step, spatial_interval, spatial_step):
    """
    convenience wrapper that encapsulates the whole simulation process

    :param weak_form:
    :param initial_states: np.array of core.Functions for :math:`x(t=0, z), \\dot{x}(t=0, z), \\dotsc, x^{(n)}(t=0, z)`
    :param time_interval: tuple of (t_start and t_end)
    :return: tuple of integration time-steps and np.array of
    """
    print("simulating system: {0}".format(weak_form.name))
    if not isinstance(weak_form, WeakFormulation):
        raise TypeError("only WeakFormulation accepted.")

    initial_states = np.atleast_1d(initial_states)
    if not isinstance(initial_states[0], Function):
        raise TypeError("only core.Function accepted as initial state")

    if not isinstance(time_interval, tuple):
        raise TypeError("time_interval must be tuple")

    # parse input and create state space system
    print(">>> parsing formulation")
    canonical_form = parse_weak_formulation(weak_form)
    print(">>> creating state space system")
    state_space_form = canonical_form.convert_to_state_space()

    # calculate initial state
    print(">>> deriving initial conditions")
    dim = canonical_form.initial_functions.size
    q0 = np.array([project_on_initial_functions(initial_state, canonical_form.initial_functions) for initial_state in
                   initial_states]).flatten()

    # include boundary conditions
    # TODO

    # simulate
    print(">>> performing time step integration")
    t, q = simulate_state_space(state_space_form, canonical_form.input_function, q0, time_interval, time_step=time_step)

    # create handles and evaluate at given points
    print(">>> performing postprocessing")
    data = []
    for der_idx in range(initial_states.size):
        data.append(evaluate_approximation(q[:, der_idx*dim:(der_idx+1)*dim], canonical_form.initial_functions,
                                           t, spatial_interval, spatial_step))
        data[-1].name = "{0}{1}".format(canonical_form.name,
                                        "_" + "".join(["d" for x in range(der_idx)] + ["t"]) if der_idx > 0 else "")

    # return results
    print("finished simulation.")
    return data


class CanonicalForm(object):
    """
    represents the canonical form of n ordinary differential equation system of order n
    """
    def __init__(self, name=None):
        self.name = name
        self._max_idx = dict(E=0, f=0, g=0)
        self._initial_functions = None
        self._input_function = None

    @staticmethod
    def _build_name(term):
        return "_"+term[0]+str(term[1])

    @property
    def input_function(self):
        return self._input_function

    @input_function.setter
    def input_function(self, func):
        if self._input_function is None:
            self._input_function = func
        if self._input_function != func:
            raise ValueError("already defined input is overridden!")

    @property
    def initial_functions(self):
        return self._initial_functions

    @initial_functions.setter
    def initial_functions(self, funcs):
        if self._initial_functions is None:
            self._initial_functions = funcs
        if self._initial_functions != funcs:
            raise ValueError("already defined initial functions are overridden!")

    def add_to(self, term, val):
        """
        adds the value val to term term
        :param term: tuple of name and index matrix(or vector) to add onto
        :param val: value to add
        :return:
        """
        if not isinstance(term, tuple):
            raise TypeError("term must be tuple.")
        if not isinstance(term[0], str) or term[0] not in "Efg":
            raise TypeError("term[0] must be string")
        if isinstance(term[1], int):
            name = self._build_name(term)
        else:
            raise TypeError("term index must be int")

        if not isinstance(val, np.ndarray):
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