In this tutorial, we will look at the syntax and usage of the numpy logspace function with the help of some examples.

## What is numpy logspace() used for?

The numpy `logspace()`

function is used to create an array of equally spaced values between two numbers on the logarithmic scale. The following is the syntax:

import numpy as np # np.logspace with all the default parameters arr = np.logspace(start, stop, num=50, endpoint=True, base=10.0, dtype=None, axis=0) # mostly you'll be only using these paramters arr = np.linspace(start, stop, num, base)

It returns a numpy array of equally spaced values on the log scale between `start`

and `stop`

(both included). This function is similar to the numpy linspace() function which creates an array of equally spaced values on the linear scale.

Like the `linspace()`

function, you can also customize the usage of the `logspace()`

function such as –

- You can exclude the
`stop`

value from the resulting array by passing`False`

to the`endpoint`

parameter which is`True`

by default. - You can also specify the number of values you want to generate by passing it to the
`num`

parameter which is 50 by default. - The dtype of the output array is inferred from the start and stop values. Note that, the inferred type will never be an integer, float is chosen even if the arguments would produce an array of integers. You can, however, specify the dtype if you don’t want it to be inferred.
- Additionally, you can specify the base of the log space you want to use with the
`base`

parameter which is 10 by default.

## Numpy logspace() Examples

Let’s look at the usage of the logspace() function with the help of some examples.

### 1. Equally spaced numbers on the log scale

Let’s create an array of equally spaced numbers on the log scale between 1 and 2.

import numpy as np # equally spaced values on log scale between 1 and 2 arr = np.logspace(1, 2) # display the resulting array print(arr)

Output:

[ 10. 10.48113134 10.98541142 11.51395399 12.06792641 12.64855217 13.25711366 13.89495494 14.56348478 15.26417967 15.9985872 16.76832937 17.57510625 18.42069969 19.30697729 20.23589648 21.20950888 22.22996483 23.29951811 24.42053095 25.59547923 26.82695795 28.11768698 29.47051703 30.88843596 32.37457543 33.93221772 35.56480306 37.2759372 39.06939937 40.94915062 42.9193426 44.98432669 47.14866363 49.41713361 51.79474679 54.28675439 56.89866029 59.63623317 62.50551925 65.51285569 68.6648845 71.9685673 75.43120063 79.06043211 82.86427729 86.85113738 91.0298178 95.40954763 100. ]

You can see that we get 50 values in the returned array. In linear space, the sequence starts at `base ** start`

(*base* to the power of *start*) and ends with `base ** stop`

. These values are equally spaced on the log scale.

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### 2. Specifying the number of samples

In the previous example, we specified the start and stop values and used all the default parameters. Let’s now specify the number of equally spaced values we want. For example, let’s generate 5 equally values on the log scale between 1 and 2.

# five equally spaced values on log scale between 1 and 2 arr = np.logspace(1, 2, num=5) # display the resulting array print(arr)

Output:

[ 10. 17.7827941 31.6227766 56.23413252 100. ]

We get five values between 10 (base to the power 1, the start value) and 100 (base to the power 2, the stop value). If you don’t want the stop endpoint to be included, pass `False`

to the endpoint parameter.

# exclude the stop endpoint arr = np.logspace(1, 2, num=5, endpoint=False) # display the resulting array print(arr)

Output:

[10. 15.84893192 25.11886432 39.81071706 63.09573445]

### 3. Using a different base for the log scale

The np.logspace() function uses 10 as the default base for the log scale. We can change that with the `base`

parameter. For example, let’s generate 5 equally spaced values on the log scale between 1 and 2 but using 2 as the base for the log scale this time.

# using 2 as base for the log scale arr = np.logspace(1, 2, num=5, base=2) # display the resulting array print(arr)

Output:

[2. 2.37841423 2.82842712 3.36358566 4. ]

We can see that now the resulting values are between 2 (base to the power 1) and 4 (base to the power 2).

### 4. Visualizing the results from numpy logspace()

How do you confirm that the numbers generated are actually equally spaced on the log scale?

One of the ways to do it is to visualize the values on a plot. For example, let’s plot the values returned from the np.logspace() function.

import matplotlib.pyplot as plt x1 = np.logspace(1, 2, num=5) y1 = np.zeros(5) # plot the values plt.plot(x1, y1, 'o')

Output:

You can see that the values grow wider apart as we move along the x-axis. This is because these values are equally spaced on the log scale and not the linear scale which we are viewing above. Let’s transform these values with a log transformation and then plot them.

# transform x1 to the log scale x2 = np.log10(x1) y2 = np.zeros(5) # plot the values plt.plot(x2, y2, 'o')

Output:

Now the values appear to be equally spaced since they have been transformed to the log scale.

For more on the numpy logspace() function, refer to its documentation.

With this, we come to the end of this tutorial. The code examples and results presented in this tutorial have been implemented in a Jupyter Notebook with a python (version 3.8.3) kernel having numpy version 1.18.5

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