import matplotlib
matplotlib.use('Agg')

from collections import namedtuple
import matplotlib.pylab as plt
import numpy as np
import os.path

from pySDC.implementations.datatype_classes.mesh import mesh
from pySDC.implementations.problem_classes.HeatEquation_1D_FD import heat1d

# setup id for gathering the results (will sort by nvars)
ID = namedtuple('ID', 'nvars')


def main():
    """
    A simple test program to check order of accuracy in space for a simple test problem
    """

    # initialize problem parameters
    problem_params = dict()
    problem_params['nu'] = 0.1  # diffusion coefficient
    problem_params['freq'] = 4  # frequency for the test value

    # create list of nvars to do the accuracy test with
    nvars_list = [2 ** p - 1 for p in range(4, 15)]

    # run accuracy test for all nvars
    results = run_accuracy_check(nvars_list=nvars_list, problem_params=problem_params)

    # compute order of accuracy
    order = get_accuracy_order(results)

    f = open('step_1_B_out.txt', 'w')
    for l in range(len(order)):
        out = 'Expected order: %2i -- Computed order %4.3f' % (2, order[l])
        f.write(out + '\n')
        print(out)
    f.close()

    # visualize results
    plot_accuracy(results)

    assert os.path.isfile('step_1_accuracy_test_space.png'), 'ERROR: plotting did not create file'

    assert (all(np.isclose(order, 2, rtol=0.06))), "ERROR: spatial order of accuracy is not as expected, got %s" % order


def run_accuracy_check(nvars_list, problem_params):
    """
    Routine to check the error of the Laplacian vs. its FD discretization

    Args:
        nvars_list: list of nvars to do the testing with
        problem_params: dictionary containing the problem-dependent parameters

    Returns:
        a dictionary containing the errors and a header (with nvars_list)
    """

    results = {}
    # loop over all nvars
    for nvars in nvars_list:
        # setup problem
        problem_params['nvars'] = nvars
        prob = heat1d(problem_params=problem_params, dtype_u=mesh, dtype_f=mesh)

        # create x values, use only inner points
        xvalues = np.array([(i + 1) * prob.dx for i in range(prob.params.nvars)])

        # create a mesh instance and fill it with a sine wave
        u = prob.u_exact(t=0)

        # create a mesh instance and fill it with the Laplacian of the sine wave
        u_lap = prob.dtype_u(init=prob.init)
        u_lap.values = -(np.pi * prob.params.freq) ** 2 * prob.params.nu * np.sin(np.pi * prob.params.freq * xvalues)

        # compare analytic and computed solution using the eval_f routine of the problem class
        err = abs(prob.eval_f(u, 0) - u_lap)

        # get id for this nvars and put error into dictionary
        id = ID(nvars=nvars)
        results[id] = err

    # add nvars_list to dictionary for easier access later on
    results['nvars_list'] = nvars_list

    return results


def get_accuracy_order(results):
    """
    Routine to compute the order of accuracy in space

    Args:
        results: the dictionary containing the errors

    Returns:
        the list of orders
    """

    # retrieve the list of nvars from results
    assert 'nvars_list' in results, 'ERROR: expecting the list of nvars in the results dictionary'
    nvars_list = sorted(results['nvars_list'])

    order = []
    # loop over two consecutive errors/nvars pairs
    for i in range(1, len(nvars_list)):
        # get ids
        id = ID(nvars=nvars_list[i])
        id_prev = ID(nvars=nvars_list[i - 1])

        # compute order as log(prev_error/this_error)/log(this_nvars/old_nvars) <-- depends on the sorting of the list!
        tmp = np.log(results[id_prev] / results[id]) / np.log(nvars_list[i] / nvars_list[i - 1])
        order.append(tmp)

    return order


def plot_accuracy(results):
    """
    Routine to visualize the errors as well as the expected errors

    Args:
        results: the dictionary containing the errors
    """

    # retrieve the list of nvars from results
    assert 'nvars_list' in results, 'ERROR: expecting the list of nvars in the results dictionary'
    nvars_list = sorted(results['nvars_list'])

    # Set up plotting parameters
    params = {'legend.fontsize': 20,
              'figure.figsize': (12, 8),
              'axes.labelsize': 20,
              'axes.titlesize': 20,
              'xtick.labelsize': 16,
              'ytick.labelsize': 16,
              'lines.linewidth': 3
              }
    plt.rcParams.update(params)

    # create new figure
    plt.figure()
    # take x-axis limits from nvars_list + some spacning left and right
    plt.xlim([min(nvars_list) / 2, max(nvars_list) * 2])
    plt.xlabel('nvars')
    plt.ylabel('abs. error')
    plt.grid()

    # get guide for the order of accuracy, i.e. the errors to expect
    # get error for first entry in nvars_list
    id = ID(nvars=nvars_list[0])
    base_error = results[id]
    # assemble optimal errors for 2nd order method and plot
    order_guide_space = [base_error / (2 ** (2 * i)) for i in range(0, len(nvars_list))]
    plt.loglog(nvars_list, order_guide_space, color='k', ls='--', label='2nd order')

    min_err = 1E99
    max_err = 0E00
    err_list = []
    # loop over nvars, get errors and find min/max error for y-axis limits
    for nvars in nvars_list:
        id = ID(nvars=nvars)
        err = results[id]
        min_err = min(err, min_err)
        max_err = max(err, max_err)
        err_list.append(err)
    plt.loglog(nvars_list, err_list, ls=' ', marker='o', markersize=10, label='experiment')

    # adjust y-axis limits, add legend
    plt.ylim([min_err / 10, max_err * 10])
    plt.legend(loc=1, ncol=1, numpoints=1)

    # save plot as PDF, beautify
    fname = 'step_1_accuracy_test_space.png'
    plt.savefig(fname, rasterized=True, bbox_inches='tight')

    return None


if __name__ == "__main__":
    main()
