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Plotting.py

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    Plotting.py 10.86 KiB
    # -*- coding: utf-8 -*-
    """
    @author: Laura C. Kühle
    
    TODO: Give option to select plotting color
    TODO: Add documentation to plot_boxplot() -> Done
    TODO: Adjust documentation for plot_classification_accuracy() -> Done
    
    """
    from typing import Tuple
    
    import numpy as np
    import matplotlib
    from matplotlib import pyplot as plt
    import seaborn as sns
    from numpy import ndarray
    from sympy import Symbol
    
    from Quadrature import Quadrature
    from Initial_Condition import InitialCondition
    
    
    matplotlib.use('Agg')
    x = Symbol('x')
    z = Symbol('z')
    sns.set()
    
    
    def plot_solution_and_approx(grid: ndarray, exact: ndarray, approx: ndarray,
                                 color_exact: str, color_approx: str) -> None:
        """Plots approximate and exact solution against each other.
    
        Parameters
        ----------
        grid : ndarray
            List of mesh evaluation points.
        exact : ndarray
            Array containing exact evaluation of a function.
        approx : ndarray
            Array containing approximate evaluation of a function.
        color_exact : str
            String describing color to plot exact solution.
        color_approx : str
            String describing color to plot approximate solution.
    
        """
        print(color_exact, color_approx)
        plt.figure('exact_and_approx')
        plt.plot(grid[0], exact[0], color_exact)
        plt.plot(grid[0], approx[0], color_approx)
        plt.xlabel('x')
        plt.ylabel('u(x,t)')
        plt.title('Solution and Approximation')
    
    
    def plot_semilog_error(grid: ndarray, pointwise_error: ndarray) -> None:
        """Plots semi-logarithmic error between approximate and exact solution.
    
        Parameters
        ----------
        grid : ndarray
            List of mesh evaluation points.
        pointwise_error : ndarray
            Array containing pointwise difference between exact and approximate solution.
    
        """
        plt.figure('semilog_error')
        plt.semilogy(grid[0], pointwise_error[0])
        plt.xlabel('x')
        plt.ylabel('|u(x,t)-uh(x,t)|')
        plt.title('Semilog Error plotted at Evaluation points')
    
    
    def plot_error(grid: ndarray, exact: ndarray, approx: ndarray) -> None:
        """Plots error between approximate and exact solution.
    
        Parameters
        ----------
        grid : ndarray
            List of mesh evaluation points.
        exact : ndarray
            Array containing exact evaluation of a function.
        approx : ndarray
            Array containing approximate evaluation of a function.
    
        """
        plt.figure('error')
        plt.plot(grid[0], exact[0]-approx[0])
        plt.xlabel('X')
        plt.ylabel('u(x,t)-uh(x,t)')
        plt.title('Errors')
    
    
    def plot_shock_tube(num_grid_cells: int, troubled_cell_history: list, time_history: list) -> None:
        """Plots shock tube.
    
        Plots detected troubled cells over time to depict the evolution of shocks as shock tubes.
    
        Parameters
        ----------
        num_grid_cells : int
            Number of cells in the mesh. Usually exponential of 2.
        troubled_cell_history : list
            List of detected troubled cells for each time step.
        time_history : list
            List of value of each time step.
    
        """
        plt.figure('shock_tube')
        for pos in range(len(time_history)):
            current_cells = troubled_cell_history[pos]
            for cell in current_cells:
                plt.plot(cell, time_history[pos], 'k.')
        plt.xlim((0, num_grid_cells // 2))
        plt.xlabel('Cell')
        plt.ylabel('Time')
        plt.title('Shock Tubes')
    
    
    def plot_details(fine_projection: ndarray, fine_mesh: ndarray, coarse_projection: ndarray,
                     basis: ndarray, wavelet: ndarray, multiwavelet_coeffs: ndarray,
                     num_coarse_grid_cells: int, polynomial_degree: int) -> None:
        """Plots details of projection to coarser mesh.
    
        Parameters
        ----------
        fine_projection, coarse_projection : ndarray
            Matrix of projection for each polynomial degree.
        fine_mesh : ndarray
            List of evaluation points for fine mesh.
        basis : ndarray
            Basis vector for calculation.
        wavelet : ndarray
            Wavelet vector for calculation.
        multiwavelet_coeffs : ndarray
            Matrix of multiwavelet coefficients.
        num_coarse_grid_cells : int
            Number of cells in the coarse mesh (half the cells of the fine mesh).
            Usually exponential of 2.
        polynomial_degree : int
            Polynomial degree.
    
        """
        averaged_projection = [[coarse_projection[degree][cell] * basis[degree].subs(x, value)
                                for cell in range(num_coarse_grid_cells)
                                for value in [-0.5, 0.5]]
                               for degree in range(polynomial_degree + 1)]
    
        wavelet_projection = [[multiwavelet_coeffs[degree][cell] * wavelet[degree].subs(z, 0.5) * value
                               for cell in range(num_coarse_grid_cells)
                               for value in [(-1) ** (polynomial_degree + degree + 1), 1]]
                              for degree in range(polynomial_degree + 1)]
    
        projected_coarse = np.sum(averaged_projection, axis=0)
        projected_fine = np.sum([fine_projection[degree] * basis[degree].subs(x, 0)
                                 for degree in range(polynomial_degree + 1)], axis=0)
        projected_wavelet_coeffs = np.sum(wavelet_projection, axis=0)
    
        plt.figure('coeff_details')
        plt.plot(fine_mesh, projected_fine - projected_coarse, 'm-.')
        plt.plot(fine_mesh, projected_wavelet_coeffs, 'y')
        plt.legend(['Fine-Coarse', 'Wavelet Coeff'])
        plt.xlabel('X')
        plt.ylabel('Detail Coefficients')
        plt.title('Wavelet Coefficients')
    
    
    def calculate_approximate_solution(projection: ndarray, points: ndarray, polynomial_degree: int,
                                       basis: ndarray) -> ndarray:
        """Calculates approximate solution.
    
        Parameters
        ----------
        projection : ndarray
            Matrix of projection for each polynomial degree.
        points : ndarray
            List of evaluation points for mesh.
        polynomial_degree : int
            Polynomial degree.
        basis : ndarray
            Basis vector for calculation.
    
        Returns
        -------
        ndarray
            Array containing approximate evaluation of a function.
    
        """
        num_points = len(points)
    
        basis_matrix = [[basis[degree].subs(x, points[point]) for point in range(num_points)]
                        for degree in range(polynomial_degree+1)]
    
        approx = [[sum(projection[degree][cell] * basis_matrix[degree][point]
                       for degree in range(polynomial_degree+1))
                   for point in range(num_points)]
                  for cell in range(len(projection[0]))]
    
        return np.reshape(np.array(approx), (1, len(approx) * num_points))
    
    
    def calculate_exact_solution(mesh: ndarray, cell_len: float, wave_speed: float, final_time: float,
                                 interval_len: float, quadrature: Quadrature,
                                 init_cond: InitialCondition) -> Tuple[ndarray, ndarray]:
        """Calculates exact solution.
    
        Parameters
        ----------
        mesh : ndarray
            List of mesh valuation points.
        cell_len : float
            Length of a cell in mesh.
        wave_speed : float
            Speed of wave in rightward direction.
        final_time : float
            Final time for which approximation is calculated.
        interval_len : float
            Length of the interval between left and right boundary.
        quadrature : Quadrature object
            Quadrature for evaluation.
        init_cond : InitialCondition object
            Initial condition for evaluation.
    
        Returns
        -------
        grid : ndarray
            Array containing evaluation grid for a function.
        exact : ndarray
            Array containing exact evaluation of a function.
    
        """
        grid = []
        exact = []
        num_periods = np.floor(wave_speed * final_time / interval_len)
    
        for cell in range(len(mesh)):
            eval_points = mesh[cell]+cell_len / 2 * quadrature.get_eval_points()
    
            eval_values = []
            for point in range(len(eval_points)):
                new_entry = init_cond.calculate(eval_points[point] - wave_speed * final_time
                                                + num_periods * interval_len)
                eval_values.append(new_entry)
    
            grid.append(eval_points)
            exact.append(eval_values)
    
        exact = np.reshape(np.array(exact), (1, len(exact) * len(exact[0])))
        grid = np.reshape(np.array(grid), (1, len(grid) * len(grid[0])))
    
        return grid, exact
    
    
    def plot_classification_accuracy(evaluation_dict: dict, colors: dict) -> None:
        """Plots classification accuracy.
    
        Plots given evaluation measures in a bar plot for each model.
    
        Parameters
        ----------
        evaluation_dict : dict
            Dictionary containing classification evaluation data.
        colors : dict
            Dictionary containing plotting colors.
    
        """
        model_names = evaluation_dict[list(colors.keys())[0]].keys()
        font_size = 16 - (len(max(model_names, key=len))//3)
        pos = np.arange(len(model_names))
        width = 1/(3*len(model_names))
        fig = plt.figure('classification_accuracy')
        ax = fig.add_axes([0.15, 0.3, 0.75, 0.6])
        step_len = 1
        adjustment = -(len(model_names)//2)*step_len
        for measure in evaluation_dict:
            model_eval = [evaluation_dict[measure][model] for model in evaluation_dict[measure]]
            ax.bar(pos + adjustment*width, model_eval, width, label=measure, color=colors[measure])
            adjustment += step_len
        ax.set_xticks(pos)
        ax.set_xticklabels(model_names, rotation=50, ha='right', fontsize=font_size)
        ax.set_ylabel('Classification (%)')
        ax.set_ylim(bottom=-0.02)
        ax.set_ylim(top=1.02)
        ax.set_title('Classification Evaluation (Barplot)')
        ax.legend(loc='upper right')
    
    
    def plot_boxplot(evaluation_dict: dict, colors: dict) -> None:
        """Plots classification accuracy.
    
        Plots given evaluation measures in a boxplot for each model.
    
        Parameters
        ----------
        evaluation_dict : dict
            Dictionary containing classification evaluation data.
        colors : dict
            Dictionary containing plotting colors.
    
        """
        model_names = evaluation_dict[list(colors.keys())[0]].keys()
        font_size = 16 - (len(max(model_names, key=len))//3)
        fig = plt.figure('boxplot_accuracy')
        ax = fig.add_axes([0.15, 0.3, 0.75, 0.6])
        step_len = 1.5
        boxplots = []
        adjustment = -(len(model_names)//2)*step_len
        pos = np.arange(len(model_names))
        width = 1/(5*len(model_names))
        for measure in evaluation_dict:
            model_eval = [evaluation_dict[measure][model] for model in evaluation_dict[measure]]
            boxplot = ax.boxplot(model_eval, positions=pos + adjustment*width, widths=width,
                                 meanline=True, showmeans=True, patch_artist=True)
            for patch in boxplot['boxes']:
                patch.set(facecolor=colors[measure])
            boxplots.append(boxplot)
            adjustment += step_len
    
        ax.set_xticks(pos)
        ax.set_xticklabels(model_names, rotation=50, ha='right', fontsize=font_size)
        ax.set_ylim(bottom=-0.02)
        ax.set_ylim(top=1.02)
        ax.set_ylabel('Classification (%)')
        ax.set_title('Classification Evaluation (Boxplot)')
        ax.legend([bp["boxes"][0] for bp in boxplots], evaluation_dict.keys(), loc='upper right')