2. Creating Numpy Arrays

By Bernd Klein. Last modified: 24 Mar 2022.

We have alreday seen in the previous chapter of our Numpy tutorial that we can create Numpy arrays from lists and tuples. We want to introduce now further functions for creating basic arrays.

There are functions provided by Numpy to create arrays with evenly spaced values within a given interval. One 'arange' uses a given distance and the other one 'linspace' needs the number of elements and creates the distance automatically.

Creation of Arrays with Evenly Spaced Values

arange

The syntax of arange:

arange([start,] stop[, step], [, dtype=None])

arange returns evenly spaced values within a given interval. The values are generated within the half-open interval '[start, stop)' If the function is used with integers, it is nearly equivalent to the Python built-in function range, but arange returns an ndarray rather than a list iterator as range does. If the 'start' parameter is not given, it will be set to 0. The end of the interval is determined by the parameter 'stop'. Usually, the interval will not include this value, except in some cases where 'step' is not an integer and floating point round-off affects the length of output ndarray. The spacing between two adjacent values of the output array is set with the optional parameter 'step'. The default value for 'step' is 1. If the parameter 'step' is given, the 'start' parameter cannot be optional, i.e. it has to be given as well. The type of the output array can be specified with the parameter 'dtype'. If it is not given, the type will be automatically inferred from the other input arguments.

import numpy as np

a = np.arange(1, 10)
print(a)

x = range(1, 10)
print(x)    # x is an iterator
print(list(x))

# further arange examples:
x = np.arange(10.4)
print(x)
x = np.arange(0.5, 10.4, 0.8)
print(x)

[1 2 3 4 5 6 7 8 9]
range(1, 10)
[1, 2, 3, 4, 5, 6, 7, 8, 9]
[ 0.  1.  2.  3.  4.  5.  6.  7.  8.  9. 10.]
[ 0.5  1.3  2.1  2.9  3.7  4.5  5.3  6.1  6.9  7.7  8.5  9.3 10.1]

Be careful, if you use a float value for the step parameter, as you can see in the following example:

np.arange(12.04, 12.84, 0.08)

array([12.04, 12.12, 12.2 , 12.28, 12.36, 12.44, 12.52, 12.6 , 12.68,
       12.76, 12.84])

The help of arange has to say the following for the stop parameter: "End of interval. The interval does not include this value, except in some cases where step is not an integer and floating point round-off affects the length of out. This is what happened in our example.

The following usages of arange is a bit offbeat. Why should we use float values, if we want integers as result. Anyway, the result might be confusing. Before arange starts, it will round the start value, end value and the stepsize:

x = np.arange(0.5, 10.4, 0.8, int)
print(x)

[ 0  1  2  3  4  5  6  7  8  9 10 11 12]

This result defies all logical explanations. A look at help also helps here: "When using a non-integer step, such as 0.1, the results will often not be consistent. It is better to use numpy.linspace for these cases. Using linspace is not an easy workaround in some situations, because the number of values has to be known.

linspace

The syntax of linspace:

linspace(start, stop, num=50, endpoint=True, retstep=False)

linspace returns an ndarray, consisting of 'num' equally spaced samples in the closed interval [start, stop] or the half-open interval [start, stop). If a closed or a half-open interval will be returned, depends on whether 'endpoint' is True or False. The parameter 'start' defines the start value of the sequence which will be created. 'stop' will the end value of the sequence, unless 'endpoint' is set to False. In the latter case, the resulting sequence will consist of all but the last of 'num + 1' evenly spaced samples. This means that 'stop' is excluded. Note that the step size changes when 'endpoint' is False. The number of samples to be generated can be set with 'num', which defaults to 50. If the optional parameter 'endpoint' is set to True (the default), 'stop' will be the last sample of the sequence. Otherwise, it is not included.

import numpy as np

# 50 values between 1 and 10:
print