pytutorial/numpy/numerical_ranges​/README.md

Making a matrix from numerical ranges

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The goal

Making a matrix from numerical ranges...

Questions to David Rotermund

numpy.arange

numpy.arange([start, ]stop, [step, ]dtype=None, *, like=None)

Return evenly spaced values within a given interval.

arange can be called with a varying number of positional arguments:

arange(stop) : Values are generated within the half-open interval [0, stop) (in other words, the interval including start but excluding stop).

arange(start, stop) : Values are generated within the half-open interval [start, stop).

arange(start, stop, step) Values are generated within the half-open interval [start, stop), with spacing between values given by step.

For integer arguments the function is roughly equivalent to the Python built-in range, but returns an ndarray rather than a range instance.

When using a non-integer step, such as 0.1, it is often better to use numpy.linspace.

Examples:

import numpy as np

print(np.arange(5)) # -> [0 1 2 3 4]
print(np.arange(0, 5)) # -> [0 1 2 3 4]
print(np.arange(2, 5)) # -> [2 3 4]
print(np.arange(0, 5, 2)) # -> [0 2 4]

It can be nicely combined with reshape():

import numpy as np
print(np.arange(0, 9).reshape(3, 3))

Output:

[[0 1 2]
 [3 4 5]
 [6 7 8]]

Do not use it with non-integer values for step!!! This can happen and you don't want this to happen:

import numpy as np

print(np.arange(-3, 0, 0.5, dtype=int)) # -> [-3 -2 -1  0  1  2]

numpy.linspace

numpy.linspace(start, stop, num=50, endpoint=True, retstep=False, dtype=None, axis=0)

Return evenly spaced numbers over a specified interval.

Returns num evenly spaced samples, calculated over the interval [start, stop].

The endpoint of the interval can optionally be excluded.

start : array_like

The starting value of the sequence.

stop : array_like

The end value of the sequence, unless endpoint is set to False. In that case, the sequence consists of all but the last of num + 1 evenly spaced samples, so that stop is excluded. Note that the step size changes when endpoint is False.

num : int, optional

Number of samples to generate. Default is 50. Must be non-negative.

endpoint : bool, optional

If True, stop is the last sample. Otherwise, it is not included. Default is True.

An example:

import numpy as np

print(np.linspace(0, 1, num=10, endpoint=False))  # -> [0.  0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9]
print(np.arange(0, 10) / 10)  # -> [0.  0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9]

Be mindful concerning the endpoint setting (Notice the ... 8 10]):

import numpy as np

print(np.linspace(0, 10, num=10, endpoint=False, dtype=int))  # -> [0 1 2 3 4 5 6 7 8 9]
print(np.linspace(0, 10, num=10, endpoint=True, dtype=int))  # -> [ 0  1  2  3  4  5  6  7  8 10]

numpy.logspace

numpy.logspace(start, stop, num=50, endpoint=True, base=10.0, dtype=None, axis=0)

Return numbers spaced evenly on a log scale.

In linear space, the sequence starts at base ** start (base to the power of start) and ends with base ** stop (see endpoint below).