Logspace

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array_logspace

numpy logspace: base raised to a linspace of exponents (spans base^start … base^stop)

Signature

Outputs

arrayArray— A 1-D Vector spanning base^start … base^stop, log-spaced.

Parameters

Key	Type	Default	Notes
`start`	float	0.0	Exponent of the first value (result = base^start).
`stop`	float	2.0	Exponent of the last value (result = base^stop).
`num`	int	50	Number of samples.
`base`	float	10.0	The base raised to each exponent (10 = decades, 2 = octaves).
`endpoint`	boolean	true	When on, the last exponent is exactly Stop.
`unit`	text		Optional physical unit for the resulting 1-D Vector.

Description

Logspace is numpy.logspace: it raises Base to each value of a linspace over the exponents Start … Stop. The result therefore spans $base^{start}$ to $base^{stop}$ with points evenly spaced on a log scale.

Crucially the Start/Stop parameters are exponents, not the endpoints themselves — set them to $0$ and $2$ with base $10$ to get $1 \dots 100$ . Base $10$ gives decades, base $2$ gives octaves. Under the hood it is base ** linspace(start, stop, num, endpoint), so it inherits linspace's endpoint pinning. If you would rather specify the actual first/last values, use Geomspace.

Mathematics

y_{i} = base^{e_{i}}, e_{i} = linspace (start, stop, num, endpoint)

y_{0} = base^{start}, y_{num - 1} = base^{stop}

Examples

Three decades

Start exponent = 0, Stop exponent = 2, Count = 3, Base = 10 → $[1, 10, 100]$ .

Octave band centres

Base = 2, Start exponent = 0, Stop exponent = 10, Count = 11 → $[1, 2, 4, 8, \dots, 1024]$ (powers of two).

Applications

A log-spaced frequency axis for a Bode plot or filter sweep.
Decade/octave grids for spectral analysis and audio.
Sweeping a gain, time-constant, or hyperparameter across orders of magnitude.

Neat

It is a thin composition: logspace(start, stop, num, base, endpoint) = map(base.powf, linspace(start, stop, num, endpoint)) — so it inherits linspace's exact endpoint pinning on the exponent grid.

A common gotcha it makes explicit in the labels: Start/Stop are EXPONENTS. logspace(0, 2) is 1..100, not 0..2.

Known issues

Start/Stop are exponents, not the literal endpoints — a frequent source of confusion; use Geomspace to give the actual first/last values.

Count is capped at 100,000,000 samples.