circular_variance

std.stats.circular_variance · Level L5

The circular variance of angles (radians): 1 − R̄, with R̄ the length of the mean of their unit vectors; 0 when every angle is the same, near 1 when they spread evenly around the circle.

1 − √((mean sin θ)² + (mean cos θ)²)

Signature

circular_variance(theta: f64[n]) → f64[]

Structure

The function as NOVA stores it: one box per input, operation and output, and arrows that carry values. A double border marks another library function this one runs — called once, or by Scan once per element; select it to open that function.

input
operation
constant
call
output

Verification

Signature proven by NOVA’s shape solver, for every size.
Agrees with the reference 1 − np.hypot(np.sin(theta).mean(), np.cos(theta).mean()) to 80 digits (100-digit arithmetic), on all 40 test cases.
All 40 float64 results inside the running error bound; the closest uses 9% of it.
Interpreter and NumPy backend return bit-identical results.
At float32 too: the 40 test cases rounded to float32, and 40 of them inside the running error bound at u = 2⁻²⁴; the closest uses 9% of it.

Accuracy in detail

correctly rounded (the float64 nearest the exact value): 48%
bit-equal to the NumPy formula in float64: 100%
largest error, in units in the last place: 454

Large ulp counts appear where a result is tiny next to the numbers it is computed from (after cancellation, for example), so one unit in the last place is tiny too; the absolute error is still inside the bound. Results within their own error of zero are not counted.

Identity

Calls

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Called by

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sha256:0c3b4881558fd35eb94d0962e88024118bbbabd10deb347a48b181e5e40af419

The semantic hash of the graph. It changes when the program changes, and never when only its documentation does.

Control handle

Symbol: Ω:std.stats.circular_variance · Ω:circular_variance
Pins: sha256:03818c7b759762a69d58ea2c23b13f5e0eaae1bb4434526898766a0dcf6ad560this graph alone
Evidence: sha256:d728c4a61e02e22273cb396c7e633f30b7df802971cc68bb262487994db75b6ethe hash of its verification record
Needs: no capability: a pure function

Through NOVA’s control layer, the symbol launches this function only while the program still matches what it pins: a change to this graph, or to any graph it reaches, needs a migration first.