covariance

std.stats.covariance · Level L0

Population covariance of two paired samples.

(1/n)·Σᵢ (xᵢ − x̄)(yᵢ − ȳ)

Signature

covariance(x: f64[n], y: 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.

xf64[n]yf64[n]MeanmxMeanmySubtractdxSubtractdyMultiplypMeanccf64[]
  • input
  • operation
  • constant
  • call
  • output

Verification

  • Signature proven by NOVA’s shape solver, for every size.
  • Equal to the reference np.cov(x, y, ddof=0)[0, 1] in exact rational arithmetic, on all 40 test cases.
  • All 40 float64 results inside the running error bound; the closest uses 11% of it.
  • Interpreter and NumPy backend return bit-identical results.
Accuracy in detail
correctly rounded (the float64 nearest the exact value)
73%
bit-equal to the NumPy formula in float64
70%
largest error, in units in the last place
2.88

Identity

Calls
—
Called by
correlation
sha256:ec40212f08cb13562bae49fb135ccf07294933d168b22e0b0392874ac72a5692

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.covariance · Ω:covariance
Pins
sha256:66a15ca0465b13df4eb5d16e8780554f0caa7ecd56d9434545b1ada61e16399dthis graph alone
Evidence
sha256:0766a47a739ec8aadd143a7a478d5c4f0ce3b2e88528e89b5e538dee3ce7553dthe 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.