Magnitude |z|

Shipping

magnitude

Element-wise modulus |z| = √(re² + im²) of a complex (or real) array

Signature

Inputs

zArray|Complex|Scalarrequired— Complex or real input. A real input yields |re| (absolute value).

Outputs

magnitudeArray— Real array of moduli, keeping z's physical unit.

Description

Magnitude |z| returns the element-wise modulus of a complex array: $∣ z ∣ = ℜ (z)^{2} + ℑ (z)^{2}$ , computed per element with hypot for overflow-safe accuracy. The result is always a real array and keeps z's physical unit (the magnitude of a volt is a volt).

The node handles a real input gracefully by treating the imaginary part as zero, so on real data it simply returns the absolute value $∣ ℜ (z) ∣$ — making it a dual-purpose magnitude / abs helper. It is stateless.

Mathematics

∣ z_{k} ∣ = ℜ (z_{k})^{2} + ℑ (z_{k})^{2}

real input: ∣ z_{k} ∣ = ∣ℜ (z_{k}) ∣

Examples

Modulus of a phasor

Feeding $[3 + 4 i]$ gives $[5]$ (a 3-4-5 triangle). Feeding a real $[- 2, 5]$ gives $[2, 5]$ .

Magnitude spectrum

Wire a complex FFT output into z to obtain the amplitude spectrum $∣ X (f) ∣$ directly.

Applications

Computing the amplitude spectrum from a complex FFT result.
Taking the envelope magnitude of an analytic (I/Q) signal.
Using it as an absolute-value node on purely real data.

Neat

Uses f64::hypot per element rather than a naive √(r²+i²), so it stays accurate even when re or im is large enough to overflow the intermediate square.

The imaginary buffer is read directly from the structure-of-arrays layout — the node never routes through the real-only tensor wall that would reject complex values.