NumPy exercises

Some of these come from / are inspired from https://github.com/rougier/numpy-100 and http://www.scipy-lectures.org/intro/numpy/exercises.html

You might want to look over these lists as well.



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import numpy as np

Q1

We can use np.random.random_sample() to create an array with random values. By default, these will be in the range [0.0, 1.0). You can multiple the output and add a scalar to it to get it to be in a different range.

Create a 10 x 10 array initialized with random numbers that lie between 0 and 10.

Then compute the average of the array (there is a numpy function for this, np.mean()).



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Q2

Create the array:

[[1,  6, 11],
 [2,  7, 12],
 [3,  8, 13],
 [4,  9, 14],
 [5, 10, 15]]

with out explicitly typing it in.

Now create a new array containing only its 2nd and 4th rows.



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Q3

Create a 2d array with 1 on the border and 0 on the inside, e.g., like:

Do this using array slice notation to let it work for an arbitrary-sized array



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Q4

Create an array with angles in degrees 0, 15, 30, ... 90 (i.e., every 15 degrees up to 90).
Now create 3 new arrays with the sine, cosine, and tangent of the elements of the first array
Finally, calculate the inverse sine, inverse cosine, and inverse tangent the arrays above and compare to the original angles



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Q5

Given the array:

x = np.array([1, -1, 2, 5, 8, 4, 10, 12, 3])

calculate the difference of each element with its neighbor.



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Q6

Here we will read in columns of numbers from a file and create a histogram, using NumPy routines. Make sure you have the data file "sample.txt" in the same directory as this notebook (you can download it from https://raw.githubusercontent.com/sbu-python-summer/python-tutorial/master/day-3/sample.txt

Use np.loadtxt() to read this file in.
Next, use np.histogram() to create a histogram array. The output returns both the count and an array of edges.
Finally, loop over the bins and print out the bin center (averaging the left and right edges of the bin) and the count for that bin.



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Q7

NumPy has a standard deviation function, np.std(), but here we'll write our own that works on a 1-d array (vector). The standard deviation is a measure of the "width" of the distribution of numbers in the vector.

Given an array, $a$, and an average $\bar{a}$, the standard deviation is: $$ \sigma = \left [ \frac{1}{N} \sum_{i=1}^N (a_i - \bar{a})^2 \right ]^{1/2} $$

Write a function to calculate the standard deviation for an input array, a:

First compute the average of the elements in a to define $\bar{a}$
Next compute the sum over the squares of $a - \bar{a}$
Then divide the sum by the number of elements in the array
Finally take the square root (you can use np.sqrt())

Test your function on a random array, and compare to the built-in np.std()



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