arange should return empty array if bounds are inconsistent

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NumPy's `arange` and Empty Arrays: A Comprehensive Tutorial

NumPy's `arange` function is a fundamental tool for creating sequences of numbers within a specified range. However, a key behavior of `arange` is that it returns an empty array when the specified range is inconsistent, leading to a zero-length sequence. This tutorial will delve into why and how `arange` generates empty arrays in such scenarios, providing detailed explanations, code examples, and best practices.

*1. Understanding `numpy.arange`*

The `numpy.arange` function creates a sequence of numbers within a given interval. It's analogous to Python's built-in `range` function but returns a NumPy array instead of a `range` object.

*Syntax:*



*Parameters:*

*`start`* (optional): The starting value of the sequence. Defaults to 0 if not specified.
*`stop`**: The end value of the sequence. *The sequence stops before this value. This is a crucial point. `stop` is not included in the generated array.
*`step`* (optional): The spacing between values. Defaults to 1 if not specified. If `step` is specified as a floating-point number, the result may not be perfectly consistent across platforms due to floating-point arithmetic.
*`dtype`* (optional): The data type of the resulting array. If not specified, it is inferred from the input arguments.
*`like`* (optional): Allows overriding the data type.

*Return Value:*

A NumPy array containing the sequence of numbers. Crucially, if the conditions for generating the sequence are inconsistent, it returns an empty array.

*2. Inconsistent Ranges Leading to Empty Arrays*

The core principle to understand is that `arange` tries to create a sequence that adheres to the specified `start`, `stop`, and `step`. If it's impossible to create such a sequence that meets all criteria, it returns an empty array. This prevents `arange` from generating unintended or unpredictable results.

**2.1. `start = stop` with a Po ...

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