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 a call to another library function; 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 only where cancellation drives a result toward zero; the absolute error is still inside the bound.

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.