correlation

std.stats.correlation · Level L1

Pearson correlation of two paired samples. Calls covariance and std.

cov(x, y) / (σₓ·σᵧ)

Signature

correlation(x: f64[n], y: f64[n]) → f64[]

Requires: n ≥ 2

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]stdsxstdsycovariancecMultiplydenDividerrf64[]
  • input
  • operation
  • constant
  • call
  • output

Verification

  • Signature proven by NOVA’s shape solver, for every size with n ≥ 2.
  • Agrees with the reference np.corrcoef(x, y)[0, 1] to 80 digits (100-digit arithmetic), on all 40 test cases.
  • All 40 float64 results inside the running error bound; the closest uses 9% of it.
  • Interpreter and NumPy backend return bit-identical results.
Accuracy in detail
correctly rounded (the float64 nearest the exact value)
50%
bit-equal to the NumPy formula in float64
70%
largest error, in units in the last place
1.87

Identity

Calls
covariancestd
Called by
—
sha256:b9ee5479ce5ccc1616d0e2fa81effd419febbd58132c8480eb7949929ed74c4a

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.correlation · Ω:correlation
Pins
sha256:dd82c9c2ca5d03a114cbf858abf330d25c5bc99df69e8188c32901dd100f6768this graph and the 3 it reaches through calls
Evidence
sha256:8a6bc5b624c9e9dd7f9117571ff6f2b75a93a30a346537b48f4bedfff764b11ethe 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.