# Practical 0 - Model Solutions

## Problem 1

>>> import datetime
>>> import numpy as np
>>> today = datetime.date.today()
>>> date = np.array([today.day, today.month, today.year % 100])

You can also use the datetime package from the python standard library

>>> import datetime
>>> datetime.date.today()

## Problem 2

>>> ints = np.arange(1, 101)
>>> ints.min()
>>> ints.max()
>>> ints.mean()
>>> ints.std()

## Problem 3

>>> pows_of_2 = np.logspace(0, 9, num=10, base=2)
>>> pows_of_2.sum()
>>> pows_of_2.mean()

## Problem 4

>>> pows_of_2[3] *= 10
>>> pows_of_2 = np.delete(pows_of_2, np.arange(4, 8))
>>> pows_of_2.mean()

## Problem 5

>>> A = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
>>> np.linalg.norm(A, ord=2)

## Problem 6

>>> A = np.arange(1, 1001).reshape(10, 100)
>>> np.linalg.norm(A, ord=2)

## Problem 7

>>> A = np.arange(1, 10).reshape(3, 3)
>>> x = np.linalg.solve(A + np.eye(3), np.array([1, 2, 3]))
>>> x[1]

## Problem 8

>>> A[0] = A[0][::-1]
>>> x = np.linalg.solve(A + np.eye(3), np.array([1, 2, 3]))
>>> x[1]

## Problem 9

>>> import string
>>> letters = np.random.choice(list(string.ascii_lowercase), (26,))
>>> len(np.unique(letters))

## Problem 10

>>> import matplotlib.pyplot as plt
>>> help(plt.plot)
>>> x = linspace(0, 10, 1000)
>>> plt.plot(x, np.sin(x), 'r-', label="sin(x)")
>>> plt.plot(x, np.sin(x**2), 'b--', label="sin(x^2)")
>>> plt.plot(x, np.sin(x) + np.sin(x**2), 'g-.', label="sin(x) + sin(x^2)")
>>> plt.legend()
>>> plt.title("sin(x) vs. sin(x^2) vs. sin(x) + sin(x^2)")
>>> plt.grid()
>>> plt.show()

## Problem 11

>>> x = np.linspace(0, 5, 1000)
>>> plt.semilogy(x, np.exp(-x**2))
>>> plt.show()

## Problem 12

>>> A = np.random.rand(10, 10)
>>> eigenvalues, eigenvectors = np.linalg.eig(A)
>>> plt.subplot(1, 2, 1)
>>> plt.scatter(np.real(eigenvalues), np.imag(eigenvalues), color='blue', marker='o')
>>> plt.title("Eigenvalues")
>>> plt.subplot(1, 2, 2)
>>> plt.scatter(np.real(eigenvectors.reshape(-1)), np.imag(eigenvectors.reshape(-1)), color='red', marker='*')
>>> plt.title("Eigenvectors")
>>> plt.show()