# Tips About Numpy Arrays

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## Differences Between Numpy Arrays and Python Lists

There are some differences between Numpy Arrays and Python Lists. We will provide some examples of algebraic operators.

### ‘**+’ Operator**

import numpy as np alist = [1, 2, 3, 4, 5] # Define a python list. It looks like an np array narray = np.array([1, 2, 3, 4]) # Define a numpy array print(narray + narray) print(alist + alist)

[2 4 6 8] [1, 2, 3, 4, 5, 1, 2, 3, 4, 5]

Note that the **‘+’ **operator on NumPy arrays perform an element-wise addition, while the same operation on Python lists results in a list concatenation. Be careful while coding. Knowing this can save many headaches.

### ‘***’ Operator**

It is the same as with the product operator, `*`

. In the first case, we scale the vector, while in the second case, we concatenate three times the same list.

print(narray * 3) print(alist * 3)

[ 3 6 9 12] [1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5]

** Matrix or Array of Arrays **

In linear algebra, a matrix is a structure composed of n rows by m columns. That means each row must have the same number of columns. With NumPy, we have two ways to create a matrix:

- Creating an array of arrays using
`np.array`

(recommended). - Creating a matrix using
`np.matrix`

(still available but might be removed soon).

NumPy arrays or lists can be used to initialize a matrix, but the resulting matrix will be composed of NumPy arrays only.

npmatrix1 = np.array([narray, narray, narray]) # Matrix initialized with NumPy arrays npmatrix2 = np.array([alist, alist, alist]) # Matrix initialized with lists npmatrix3 = np.array([narray, [1, 1, 1, 1], narray]) # Matrix initialized with both types print(npmatrix1) print(npmatrix2) print(npmatrix3)

[[1 2 3 4] [1 2 3 4] [1 2 3 4]] [[1 2 3 4 5] [1 2 3 4 5] [1 2 3 4 5]] [[1 2 3 4] [1 1 1 1] [1 2 3 4]]

However, when defining a matrix, be sure that all the rows contain the same number of elements. Otherwise, the linear algebra operations could lead to unexpected results.

Analyze the following two examples:

# Example 1: okmatrix = np.array([[1, 2], [3, 4]]) # Define a 2x2 matrix print(okmatrix) # Print okmatrix print(okmatrix * 2) # Print a scaled version of okmatrix

[[1 2] [3 4]] [[2 4] [6 8]]

# Example 2: badmatrix = np.array([[1, 2], [3, 4], [5, 6, 7]]) # Define a matrix. Note the third row contains 3 elements print(badmatrix) # Print the malformed matrix print(badmatrix * 2) # It is supposed to scale the whole matrix

[list([1, 2]) list([3, 4]) list([5, 6, 7])] [list([1, 2, 1, 2]) list([3, 4, 3, 4]) list([5, 6, 7, 5, 6, 7])]

## Get the norm of an numpy array or matrix

Let’s recall that:

\(norm(\vec a) = ||\vec a|| = \sqrt {\sum_{i=1}^{n} a_i ^ 2}\)

nparray1 = np.array([1, 2, 3, 4]) # Define an array norm1 = np.linalg.norm(nparray1) nparray2 = np.array([[1, 2], [3, 4]]) # Define a 2 x 2 matrix. Note the 2 level of square brackets norm2 = np.linalg.norm(nparray2) print(norm1) print(norm2)

5.477225575051661 5.477225575051661

Note that without any other parameter, the norm function treats the matrix as being just an array of numbers. However, it is possible to get the norm by rows or by columns. The **axis** parameter controls the form of the operation:

**axis=0**means get the norm of each column**axis=1**means get the norm of each row.

nparray2 = np.array([[1, 1], [2, 2], [3, 3]]) # Define a 3 x 2 matrix. normByCols = np.linalg.norm(nparray2, axis=0) # Get the norm for each column. Returns 2 elements normByRows = np.linalg.norm(nparray2, axis=1) # get the norm for each row. Returns 3 elements print(normByCols) print(normByRows)

[3.74165739 3.74165739] [1.41421356 2.82842712 4.24264069]

## The dot product between numpy arrays: All the flavors

The dot product or scalar product or inner product between two vectors \(\vec a\) and \(\vec a\) of the same size is defined as:

\(\vec a \cdot \vec b = \sum_{i=1}^{n} a_i b_i\)

The dot product takes two vectors and returns a single number.

nparray1 = np.array([0, 1, 2, 3]) # Define an array nparray2 = np.array([4, 5, 6, 7]) # Define an array flavor1 = np.dot(nparray1, nparray2) # Recommended way print(flavor1) flavor2 = np.sum(nparray1 * nparray2) # Ok way print(flavor2) flavor3 = nparray1 @ nparray2 # Geeks way print(flavor3) # As you never should do: # Noobs way flavor4 = 0 for a, b in zip(nparray1, nparray2): flavor4 += a * b print(flavor4)

38 38 38 38

## Get the mean and sum by rows or columns of numpy arrays

Another general operation performed on matrices is the sum by rows or columns. Just as we did for the function norm, the **axis** parameter controls the form of the operation:

**axis=0**means to sum the elements of each column together.**axis=1**means to sum the elements of each row together.

nparray2 = np.array([[1, -1], [2, -2], [3, -3]]) # Define a 3 x 2 matrix. sumByCols = np.sum(nparray2, axis=0) # Get the sum for each column. Returns 2 elements sumByRows = np.sum(nparray2, axis=1) # get the sum for each row. Returns 3 elements print('Sum by columns: ') print(sumByCols) print('Sum by rows:') print(sumByRows)

Sum by columns: [ 6 -6] Sum by rows: [0 0 0]

nparray2 = np.array([[1, -1], [2, -2], [3, -3]]) # Define a 3 x 2 matrix. Chosen to be a matrix with 0 mean mean = np.mean(nparray2) # Get the mean for the whole matrix meanByCols = np.mean(nparray2, axis=0) # Get the mean for each column. Returns 2 elements meanByRows = np.mean(nparray2, axis=1) # get the mean for each row. Returns 3 elements print('Matrix mean: ') print(mean) print('Mean by columns: ') print(meanByCols) print('Mean by rows:') print(meanByRows)

Matrix mean: 0.0 Mean by columns: [ 2. -2.] Mean by rows: [0. 0. 0.]

## Some other useful commands

`numpy.squeeze`

: Remove single-dimensional entries from the shape of an array`numpy.expand_dims(a,axis)`

: Expand the shape of an array`numpy.broadcast_arrays(*args, subok=False)`

: Broadcast any number of arrays against each other`numpy.reshape(a, newshape, order='C)`

: Gives a new shape to an array without changing its data`numpy.ravel(a, order='C')`

: Return a contiguous flattened array.`ndarray.flatten(order='C')`

: Return a copy of the array collapsed into one dimension.`numpy.unique(a, return_counts=True)`

: Count the frequency of unique values in numpy array`a`

.

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