measure_check

std.stats.measure_check · Level L3

The axioms of a measure on a finite σ-algebra (its members one per row, with their measures μ): whether μ ≥ 0 and whether μ(∅) = 0, each as 1 or 0; and the additivity gap, the largest |μ(A ∪ B) − μ(A) − μ(B)| over disjoint members A, B, which is 0 for a measure. On a finite σ-algebra countable additivity reduces to additivity over pairs of disjoint sets.

μ ≥ 0, μ(∅) = 0, μ(A ∪ B) = μ(A) + μ(B) for A ∩ B = ∅

Signature

measure_check(F: f64[m, n], mu: f64[m]) → f64[], f64[], 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.
Equal to the reference every disjoint pair, the member equal to its union, in exact arithmetic in exact rational arithmetic, on all 40 test cases.
All 120 float64 results inside the running error bound; the closest uses 68% 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 18% of it.

Accuracy in detail

correctly rounded (the float64 nearest the exact value): 96%
bit-equal to the NumPy formula in float64: 98%
largest error, in units in the last place: 1.0e+9

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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sha256:4e1dcee8f469ab899a019a328ae62bdb98fdd63ff9843682843d50ffcbde4666

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.measure_check · Ω:measure_check
Pins: sha256:c5af89997e1a4c95394778f8f6f4d1773526f038351e05c50c19339442309de9this graph alone
Evidence: sha256:ba3404022a877595617f9b4725bfacd99de572b049ad19e17261df58aa037dfbthe 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.