None intro_basics2
In [1]:
# problem 1
import random
# warning: don't execute in here, use ipython
def random_walk(max_iters: float=1e12) -> list[int]:
    walk: list[int] = []
    directions = [1, -1]
    i: int = 0
    try:
        while True:
            walk += [random.choice(directions)]
            i+=1
            if float(i) > max_iters:
                break
    except KeyboardInterrupt as e:
        print("Process interrupted at iteration ", e)
    else:
        print("Process completed")
    return walk

random_walk(10)

Process completed
Out[1]:
[-1, 1, -1, 1, -1, 1, -1, 1, 1, -1, 1]
In [ ]:
# problem 2
# warning: don't execute here, use ipython if the file does not exist
class ContentFilter:
    def __init__(self, given_file_name):
        self.file_name = ""
        self.contents = ""
        try:
            with open(given_file_name, "r") as f:
                self.file_name = given_file_name
                self.contents = f.read()
        except IOError:
            print("File not found. Try another name.")
            while (True):
                input_file_name = input()
                try:
                    with open(input_file_name, "r") as f:
                        self.file_name = input_file_name
                        self.contents = f.read()
                        break
                except IOError:
                    print("File not found. Try another name.")

content_filter = ContentFilter("foo.txt")
print("Name: {}, Contents: {}".format(content_filter.file_name, content_filter.contents))

File not found. Try another name.
In [1]:
# problem 3
import numpy

def multiply_matrices():
    A = numpy.array([[3, -1, 4], [1, 5, -9]])
    B = numpy.array([[2, 6, -5, 3], [5, -8, 9, 7], [9, -3, -2, -3]])
    return A @ B

multiply_matrices()
Out[1]:
array([[ 37,  14, -32, -10],
       [-54,  -7,  58,  65]])
In [4]:
# problem 4
def mult_matrix_with_self():
    A = numpy.array([[3, 1, 4], [1, 5, 9], [-5, 3, 1]])
    return -numpy.linalg.matrix_power(A, 3) + 9*numpy.linalg.matrix_power(A, 2) - 15*A

mult_matrix_with_self()
Out[4]:
array([[0, 0, 0],
       [0, 0, 0],
       [0, 0, 0]])
In [5]:
# problem 5
def array_creation():
    A = numpy.triu(numpy.ones((7, 7)))
    print(A)
    B1 = -numpy.ones((7, 7))
    B2 = numpy.triu(numpy.full((7, 7), 6))
    B3 = numpy.eye(7) * -6
    B = B1 + B2 + B3
    return A @ B @ A

array_creation()

[[1. 1. 1. 1. 1. 1. 1.]
 [0. 1. 1. 1. 1. 1. 1.]
 [0. 0. 1. 1. 1. 1. 1.]
 [0. 0. 0. 1. 1. 1. 1.]
 [0. 0. 0. 0. 1. 1. 1.]
 [0. 0. 0. 0. 0. 1. 1.]
 [0. 0. 0. 0. 0. 0. 1.]]
Out[5]:
array([[ -7.,  -8.,  -3.,   8.,  25.,  48.,  77.],
       [ -6., -12., -12.,  -6.,   6.,  24.,  48.],
       [ -5., -10., -15., -14.,  -7.,   6.,  25.],
       [ -4.,  -8., -12., -16., -14.,  -6.,   8.],
       [ -3.,  -6.,  -9., -12., -15., -12.,  -3.],
       [ -2.,  -4.,  -6.,  -8., -10., -12.,  -8.],
       [ -1.,  -2.,  -3.,  -4.,  -5.,  -6.,  -7.]])
In [6]:
# problem 6
def fancyZeroes(A):
    B = A.copy()
    B[B < 0] = 0
    return B

fancyZeroes(numpy.array([[-10, 5], [-30, 20]]))
Out[6]:
array([[ 0,  5],
       [ 0, 20]])
In [7]:
# problem 7
def stacking():
    A = numpy.array([[0, 2, 4], [1, 3, 5]])
    B = numpy.array([[3, 0, 0], [3, 3, 0], [3, 3, 3]])
    C = numpy.array([[-2, 0, 0], [0, -2, 0], [0, 0, -2]])
    col1 = numpy.vstack((numpy.zeros((2, 3)), A, B))
    col2 = numpy.vstack((A.T, numpy.zeros((2, 2)), numpy.zeros((2, 2))))
    col3 = numpy.vstack((numpy.eye(3), numpy.zeros((1, 3)), C))
    return numpy.hstack((col1, col2, col3))

stacking()
Out[7]:
array([[ 0.,  0.,  0.,  0.,  1.,  1.,  0.,  0.],
       [ 0.,  0.,  0.,  2.,  3.,  0.,  1.,  0.],
       [ 0.,  2.,  4.,  4.,  5.,  0.,  0.,  1.],
       [ 1.,  3.,  5.,  0.,  0.,  0.,  0.,  0.],
       [ 3.,  0.,  0.,  0.,  0., -2.,  0.,  0.],
       [ 3.,  3.,  0.,  0.,  0.,  0., -2.,  0.],
       [ 3.,  3.,  3.,  0.,  0.,  0.,  0., -2.]])
In [8]:
# problem 8
def stochasticMat(A):
    # it is a row vector when it should be column
    # Equivalent: return A/A.sum(axis=1).reshape(3,1)
    return A/A.sum(axis=1)[:, None]

stochasticMat(numpy.array([[2, 3],[3, 2]]))
Out[8]:
array([[0.4, 0.6],
       [0.6, 0.4]])