pythonnumpy

Nola

Ben Gorman

Ben Gorman

Life's a garden. Dig it.

Make the following 4x7 array called nola that starts with 1 and steps by 2. However, note that the first element in each row is always 4 more than the last element in the previous row.

nola
[[ 1  3  5  7  9 11 13]
 [17 19 21 23 25 27 29]
 [33 35 37 39 41 43 45]
 [49 51 53 55 57 59 61]]

Solution

import numpy as np
 
nola = np.arange(start=1, stop=65, step=2).reshape(4,-1)
nola = nola[:, :-1]
 
print(nola)
# [[ 1  3  5  7  9 11 13]
#  [17 19 21 23 25 27 29]
#  [33 35 37 39 41 43 45]
#  [49 51 53 55 57 59 61]]

Explanation

The trick here is to think of nola as the first 7 columns in this 4x8 array.

[[ 1  3  5  7  9 11 13 15]
 [17 19 21 23 25 27 29 31]
 [33 35 37 39 41 43 45 47]
 [49 51 53 55 57 59 61 63]]
 ------ include ------

This array is simply the sequence 1, 3, 5, ... 61, 63 (without any weird gaps) arranged into a 4x8 shape. So, if we can build this array, we can easily chop off the last column to make nola.

  1. Build the sequence array: 1, 3, 5, ... 61, 63.

    import numpy as np
 
np.arange(start=1, stop=65, step=2)
# array([ 1,  3,  5, ..., 59, 61, 63])

    Here we use np.arange(), passing in start=1, stop=65, and step=2. Note that stop is exclusive, so the sequence goes from 1 up to but not including 65.

  2. Reshape the 1-D array into a 2-D array.

    Specifically, we convert the array from shape (32,) to shape (4,8). There are a few ways we can do this..

    nola = np.reshape(np.arange(start=1, stop=65, step=2), (4,8))
 
print(nola)
# [[ 1,  3,  5,  7,  9, 11, 13, 15],
#  [17, 19, 21, 23, 25, 27, 29, 31],
#  [33, 35, 37, 39, 41, 43, 45, 47],
#  [49, 51, 53, 55, 57, 59, 61, 63]]

    See numpy.reshape().

    nola = np.arange(start=1, stop=65, step=2).reshape(4,8)
 
print(nola)
# [[ 1,  3,  5,  7,  9, 11, 13, 15],
#  [17, 19, 21, 23, 25, 27, 29, 31],
#  [33, 35, 37, 39, 41, 43, 45, 47],
#  [49, 51, 53, 55, 57, 59, 61, 63]]

    See ndarray.reshape().

    Pro Tip

    In either of these methods, we can replace exactly one of the dimensions with -1 and NumPy will figure it out for us. For example,

    nola = np.arange(start=1, stop=65, step=2).reshape(4, -1)
 
print(nola)
# [[ 1,  3,  5,  7,  9, 11, 13, 15],
#  [17, 19, 21, 23, 25, 27, 29, 31],
#  [33, 35, 37, 39, 41, 43, 45, 47],
#  [49, 51, 53, 55, 57, 59, 61, 63]]

    Here we're basically telling NumPy, "reshape the array into an array with 4 rows". Since the original array had 32 elements, NumPy knows the resulting array must have 8 columns.

  3. Select all columns but the last.

    nola = nola[:, :-1]
 
print(nola)
# [[ 1  3  5  7  9 11 13]
#  [17 19 21 23 25 27 29]
#  [33 35 37 39 41 43 45]
#  [49 51 53 55 57 59 61]]

    nola[:, :-1] can be interpreted as "Select every row, and select all columns from the start, up to but excluding the last column". (-1 means "last" index. See negative indexing.)