Geomspace

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array_geomspace

numpy geomspace: num samples geometrically (log-) spaced between actual start and stop

Signature

Outputs

arrayArray— A 1-D Vector of num values in a geometric progression from start to stop.

Parameters

Key	Type	Default	Notes
`start`	float	1.0	First value (non-zero).
`stop`	float	1000.0	Last value (non-zero, same sign as Start).
`num`	int	50	Number of samples, spaced evenly on a log scale.
`endpoint`	boolean	true	When on, the last sample is exactly Stop.
`unit`	text		Optional physical unit for the resulting 1-D Vector.

Description

Geomspace is numpy.geomspace: Count samples forming a geometric progression (a constant ratio between neighbours) from Start to Stop. Unlike Logspace, you give the actual endpoints — not exponents.

Internally it exponentiates a linspace of $ln ∣ \cdot ∣$ : sign · exp(linspace(ln|start|, ln|stop|, num)), then pins both endpoints exactly. Because a geometric series cannot cross zero, Start and Stop must both be non-zero and share the same sign — a violation is a clean error. The result is a Vector that may carry a Unit.

Mathematics

x_{i} = sign \cdot exp (e_{i}), e_{i} = linspace (ln ∣ start ∣, ln ∣ stop ∣, num)

\frac{x _{i + 1}}{x _{i}} = (\frac{stop}{start})^{1/ (num - 1)} (constant ratio)

Examples

Four points, decade-ish ratio

Start = 1, Stop = 1000, Count = 4 → $[1, 10, 100, 1000]$ (ratio $10$ between neighbours).

Same-sign requirement

Start = 1, Stop = -1000 errors: a geometric series can't change sign or pass through zero.

Applications

A log-spaced frequency or wavelength axis given by its true endpoints.
Geometrically increasing time constants, step sizes, or annealing schedules.
Resistor/component E-series-style value grids with a fixed ratio.

Neat

Endpoints are pinned to the exact Start and Stop after the exp() round-trip, so ln→exp float error never nudges the first/last value off the requested bound.

Negative ranges are supported by factoring out the sign and working on |start|, |stop| in log space — as long as both share that sign.

Known issues

Start and Stop must be non-zero and same-sign (the series cannot cross zero) — otherwise it errors.

Count is capped at 100,000,000 samples.