Solution A+ Work

#!/usr/bin/env python """ Python code submission file. IMPORTANT: - Do not include any additional python packages. - Do not change the existing interface and return values of the task functions. - Prior to your submission, check that the pdf showing your plots is generated. """ import numpy as np import matplotlib.pyplot as plt from matplotlib.backends.backend_pdf import PdfPages from scipy.optimize import approx_fprime, linprog from typing import Callable # Modify the following global variables to be used in your functions """ Start of your code """ alpha = None beta = None d = None b = None D = None A = None """ End of your code """ def task1(): """ Characterization of Functions Requirements for the plots: - ax[0, 0] Contour plot for a) - ax[0, 1] Contour plot for b) - ax[1, 0] Contour plot for c) - ax[1, 1] Contour plot for d) """ fig, ax = plt.subplots(2, 2, figsize=(12,12)) fig.suptitle('Task 1 - Contour plots of functions', fontsize=16) ax[0, 0].set_title('a)') ax[0, 0].set_xlabel('$x_1$') ax[0, 0].set_ylabel('$x_2$') ax[0, 1].set_title('b)') ax[0, 1].set_xlabel('$x_1$') ax[0, 1].set_ylabel('$x_2$') ax[1, 0].set_title('c)') ax[1, 0].set_xlabel('$x_1$') ax[1, 0].set_ylabel('$x_2$') ax[1, 1].set_title('d)') ax[1, 1].set_xlabel('$x_1$') ax[1, 1].set_ylabel('$x_2$') """ Start of your code """ x1, x2 = np.meshgrid(np.linspace(-5, 5), np.linspace(-5, 5)) ax[0, 0].contour(x1, x2, x1**2 + 0.5*x2**2, 50) """ End of your code """ return fig # Modify the function bodies below to be used for function value and gradient computation def approx_grad_task1(func: Callable[[np.ndarray], float], x: np.ndarray) -> np.ndarray: """ Numerical Gradient Computation @param x Vector of size (2,) This function shall compute the gradient approximation for a given point 'x' and a function 'func' using the given central differences formulation for 2D functions. (Task1 functions) @return The gradient approximation """ assert(len(x) == 2) pass def approx_grad_task2(func: Callable[[np.ndarray], float], x: np.ndarray) -> np.ndarray: """ Numerical Gradient Computation @param x Vector of size (n,) This function shall compute the gradient approximation for a given point 'x' and a function 'func' using scipy.optimize.approx_fprime(). (Task2 functions) @return The gradient approximation """ pass def func_1a(x: np.ndarray) -> float: """ Computes and returns the function value for function 1a) at a given point x @param x Vector of size (2,) """ pass def grad_1a(x: np.ndarray) -> np.ndarray: """ Computes and returns the analytical gradient result for function 1a) at a given point x @param x Vector of size (2,) """ pass def func_1b(x: np.ndarray) -> float: """ Computes and returns the function value for function 1b) at a given point x @param x Vector of size (2,) """ pass def grad_1b(x: np.ndarray) -> np.ndarray: """ Computes and returns the analytical gradient result for function 1b) at a given point x @param x Vector of size (2,) """ pass def func_1c(x: np.ndarray) -> float: """ Computes and returns the function value for function 1c) at a given point x @param x Vector of size (2,) """ pass def grad_1c(x: np.ndarray) -> np.ndarray: """ Computes and returns the analytical gradient result for function 1c) at a given point x @param x Vector of size (2,) """ pass def func_1d(x: np.ndarray) -> float: """ Computes and returns the function value for function 1d) at a given point x @param x Vector of size (2,) """ pass def grad_1d(x: np.ndarray) -> np.ndarray: """ Computes and returns the analytical gradient result for function 1d) at a given point x @param x Vector of size (2,) """ pass def func_2a(x: np.ndarray) -> float: """ Computes and returns the function value for function 2a) at a given point x @param x Vector of size (n,) """ pass def grad_2a(x: np.ndarray) -> np.ndarray: """ Computes and returns the analytical gradient result for function 2a) at a given point x @param x Vector of size (n,) """ pass def func_2b(x: np.ndarray) -> float: """ Computes and returns the function value for function 2b) at a given point x @param x Vector of size (n,) """ pass def grad_2b(x: np.ndarray) -> np.ndarray: """ Computes and returns the analytical gradient result for function 2b) at a given point x @param x Vector of size (n,) """ pass def func_2c(x: np.ndarray) -> float: """ Computes and returns the function value for function 2c) at a given point x @param x Vector of size (n,) """ pass def grad_2c(x: np.ndarray) -> np.ndarray: """ Computes and returns the analytical gradient result for function 2c) at a given point x @param x Vector of size (n,) """ pass def task3(): """ Numerical Gradient Verification ax[0] to ax[3] Bar plot comparison, analytical vs numerical gradient for Task 1 ax[4] to ax[6] Bar plot comparison, analytical vs numerical gradient for Task 2 """ n = 5 fig = plt.figure(figsize=(15,10), constrained_layout=True) fig.suptitle('Task 3 - Barplots numerical vs analytical', fontsize=16) ax = [None, None, None, None, None, None, None] keys = ['a)', 'b)', 'c)', 'd)'] gs = fig.add_gridspec(7, 12) n = 2 for i in range(4): ax[i] = fig.add_subplot(gs[1:4, 3*i:(3*i+3)]) ax[i].set_title('1 '+keys[i]) ax[i].set_xticks(np.arange(n)) ax[i].set_xticklabels((r'$\frac{\partial}{\partial x_1}$', r'$\frac{\partial}{\partial x_2}$'), fontsize=16) n = 5 for k, i in enumerate(range(4, 7)): ax[i] = fig.add_subplot(gs[4:, 4*k:(4*k+4)]) ax[i].set_title('2 '+ keys[k]) ax[i].set_xticks(np.arange(n)) ax[i].set_xticklabels((r'$\frac{\partial}{\partial x_1}$', r'$\frac{\partial}{\partial x_2}$', r'$\frac{\partial}{\partial x_3}$', r'$\frac{\partial}{\partial x_4}$', r'$\frac{\partial}{\partial x_5}$'), fontsize=16) """ Start of your code """ # Example for plot usage bw = 0.3 ax[0].bar([0-bw/2,1-bw/2], [1.5, 1.1], bw) ax[0].bar([0+bw/2,1+bw/2], [1.5, 1.1], bw) """ End of your code """ return fig def task4(): """ Scheduling Optimization Problem @return The scheduling plan M """ """ Start of your code """ M = None """ End of your code """ return M if __name__ == '__main__': tasks = [task1, task3] pdf = PdfPages('figures.pdf') for task in tasks: retval = task() pdf.savefig(retval) pdf.close() task4()