centroid

std.geometry.centroid · Level L0

Centroid (mean point) of a set of points.

c = (1/m)·Σᵢ xᵢ

Signature

centroid(X: f64[m, d]) → f64[d]

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.

Xf64[m, d]Meanccf64[d]
  • input
  • operation
  • constant
  • call
  • output

Verification

  • Signature proven by NOVA’s shape solver, for every size.
  • Equal to the reference X.mean(axis=0) in exact rational arithmetic, on all 40 test cases.
  • All 158 float64 results inside the running error bound; the closest uses 44% of it.
  • Interpreter and NumPy backend return bit-identical results.
Accuracy in detail
correctly rounded (the float64 nearest the exact value)
85%
bit-equal to the NumPy formula in float64
100%
largest error, in units in the last place
16

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
—
Called by
—
sha256:acbccc234e8da554a87f879073a942eb440b80b417887ad7fa2f28196abeeb61

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

Control handle

Symbol
Ω:std.geometry.centroid · Ω:centroid
Pins
sha256:fc3ec14ff5d8246baf087aab7b901971a0b777184e31e90af99fa3035789ae2bthis graph alone
Evidence
sha256:fb3fef44bdb583ac4db99e1b058cd1bb111f088fdaa9ef083ceaf58f2aff0c34the 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.