center

std.geometry.center · Level L0

Shift a set of points so that its centroid is the origin.

xᵢ − c

Signature

center(X: f64[m, d]) → f64[m, 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]MeancSubtractXcXcf64[m, d]
  • input
  • operation
  • constant
  • call
  • output

Verification

  • Signature proven by NOVA’s shape solver, for every size.
  • Equal to the reference X - X.mean(axis=0) in exact rational arithmetic, on all 40 test cases.
  • All 685 float64 results inside the running error bound; the closest uses 59% of it.
  • Interpreter and NumPy backend return bit-identical results.
Accuracy in detail
correctly rounded (the float64 nearest the exact value)
79%
bit-equal to the NumPy formula in float64
100%
largest error, in units in the last place
38

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
cov_matrix
sha256:1ca910a7b0c98957b1b3f26f45aced14133414cc9128dc997b3b197ca9ea1b08

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.center · Ω:center
Pins
sha256:9e0b5f62d1e02e56fac46f5f04c94c4923dbee11cae521ffa70cc834d9b7bb93this graph alone
Evidence
sha256:f2f0a86dc3c11f44abf9c84897d2e24f203ed85a2ca726eba7dad9d8cc9cb27ethe 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.