(c) 2016 Justin Bois. This work is licensed under a Creative Commons Attribution License CC-BY 4.0. All code contained herein is licensed under an MIT license.
This tutorial was generated from a Jupyter notebook. You can download the notebook here.
# NumPy, the engine of scientific computing
import numpy as np
Numpy arrays can take a while to get the hang of. Therefore, it's important to practice practice practice!
The functions np.arange() and np.linspace() are really useful.
np.arange?, or by reading the respective webpages (np.arange, np.linspace)).np.arange() to make an array of numbers 0 through 10.np.linspace().float.# Integers (as floats) 0 through 10
np.arange(11, dtype=float)
# Integers 0 through 10 with np.linspace()
np.linspace(0, 10, 11)
In the last lesson, we looked at a data set from Harvey and Orbidans on the cross-sectional area of C. elegans eggs. Recall, we loaded the data like this:
# Load in data
xa_high = np.loadtxt('data/xa_high_food.csv', comments='#')
xa_low = np.loadtxt('data/xa_low_food.csv', comments='#')
Now we would like to compute the diameter of the egg from the cross-sectional area. Write a function that takes in an array of cross-sectional areas and returns an array of diameters. Recall that the diameter $d$ and cross-sectional area $A$ are related by $A = \pi d^2/4$. There should be no for loops in your function!
Below, is a skeleton for your function for you to fill in.
def xa_to_diameter(xa):
"""
Convert an array of cross-sectional areas
to diameters with commensurate units.
"""
# Compute diameter from area
diameter = ____
return diameter
Use your function to compute the diameters of the eggs.
def xa_to_diameter(xa):
"""
Convert an array of cross-sectional areas
to diameters with commensurate units.
"""
# Compute diameter from area
diameter = 2 * np.sqrt(xa / np.pi)
return diameter
print('Diameters of eggs from well fed mothers:\n', xa_to_diameter(xa_high))
print('\nDiameters of eggs from poorly fed mothers:\n', xa_to_diameter(xa_low))
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 the code below into your script or IPython shell.
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])
First, let's practice slicing.
A.A.A that is greater than 2.A. using the np.diag() function.# 1.
print(A[1,:])
# 2.
print(A[:,[1,3]])
# 3.
print(A[A>2])
# 4.
print(np.diag(A))
The np.linalg module has some powerful linear algebra tools.
np.linalg.solve(). Store your answer in the Numpy array x.np.dot(A, x) to verify that $\mathsf{A}\cdot \mathbf{x} = \mathbf{b}$.np.transpose() to compute the transpose of A.np.linalg.inv() to compute the inverse of A.# 1.
x = np.linalg.solve(A, b)
# 2.
print('A . x:\n', np.dot(A, x))
print('\nb:\n', b)
# 3.
print('\ntranspose of A:\n', np.transpose(A))
# 4.
print('\ninverse of A:\n', np.linalg.inv(A))
Sometimes you want to convert a two-dimensional array to a one-dimensional array. This can be done with np.ravel().
B = np.ravel(A).np.reshape(). Then, reshape B to make it look like A again.# 1.
B = np.ravel(A)
print(B)
# 2.
np.reshape(B, A.shape)