Exercise 4.3: Working with two-dimensional arrays
[1]:
import numpy as np
Numpy enables you do to matrix calculations on two-dimensional arrays. In exercise, you will practice doing matrix calculations on arrays. We’ll start by making a matrix and a vector to practice with. You can copy and paste the code below.
[2]:
A = np.array(
[
[6.7, 1.3, 0.6, 0.7],
[0.1, 5.5, 0.4, 2.4],
[1.1, 0.8, 4.5, 1.7],
[0.0, 1.5, 3.4, 7.5],
]
)
b = np.array([1.1, 2.3, 3.3, 3.9])
a) First, let’s practice slicing.
Print row 1 (remember, indexing starts at zero) of
A
.Print columns 1 and 3 of
A
.Print the values of every entry in
A
that is greater than 2.Print the diagonal of
A
. using thenp.diag()
function.
b) The np.linalg
module has some powerful linear algebra tools.
First, we’ll solve the linear system \(\mathsf{A}\cdot \mathbf{x} = \mathbf{b}\). Try it out: use
np.linalg.solve()
. Store your answer in the Numpy arrayx
.Now do
np.dot(A, x)
to verify that \(\mathsf{A}\cdot \mathbf{x} = \mathbf{b}\).Use
np.transpose()
to compute the transpose ofA
.Use
np.linalg.inv()
to compute the inverse ofA
.
c) Sometimes you want to convert a two-dimensional array to a one-dimensional array. This can be done with np.ravel()
.
See what happens when you do
B = np.ravel(A)
.Look of the documentation for
np.reshape()
. Then, reshapeB
to make it look likeA
again.