# -*- 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')