Arange

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array_arange

numpy arange: a half-open [start, stop) sequence spaced by step

Signature

Outputs

arrayArray— A 1-D Vector of evenly stepped values over the half-open interval [start, stop).

Parameters

Key	Type	Default	Notes
`start`	float	0.0	First value (inclusive).
`stop`	float	10.0	End value (EXCLUSIVE, like numpy.arange).
`step`	float	1.0	Spacing between values; must be non-zero (may be negative to count down).
`unit`	text		Optional physical unit for the resulting 1-D Vector.

Description

Arange is numpy.arange: a 1-D sequence over the half-open interval $[start, stop)$ spaced by Step. The stop value is excluded; the length is $⌈(stop - start) / step ⌉$ (clamped at $0$ ). A negative Step counts down.

Because it is index-driven ( $x_{i} = start + i \cdot step$ ) rather than division-based, Arange is exact for integer steps but can accumulate float drift near the endpoint for fractional steps — prefer Linspace when you need a precise, count-controlled endpoint. Step $= 0$ or a non-finite argument is an error. The output is always a Vector and may carry a Unit.

Mathematics

x_{i} = start + i \cdot step, i = 0, 1, \dots, N - 1

N = ⌈ \frac{stop - start}{step} ⌉, clamped to N \geq 0

Examples

Integer index vector

Start = 0, Stop = 5, Step = 1 → the Vector $[0, 1, 2, 3, 4]$ (note 5 is excluded).

Counting down

Start = 10, Stop = 0, Step = -2 → $[10, 8, 6, 4, 2]$ .

Applications

Generating integer index or sample-number axes.
Building a time or frequency axis with a known fixed spacing.
Driving a loop-like parameter sweep with a fixed increment.

Neat

Length is computed with a ceil, so a non-integer span like arange(0, 1, 0.3) yields ⌈1/0.3⌉ = 4 samples ([0, 0.3, 0.6, 0.9]) — exactly numpy's rule.

Values are generated as start + i·step (multiply, not repeated add), which keeps rounding error bounded per element instead of accumulating.

Known issues

The exclusive endpoint plus fractional steps can make the last element land just short of / past an expected value due to float rounding — use Linspace for a guaranteed endpoint.

Step = 0 or non-finite start/stop/step is an error, not an empty array.