cov_matrix

std.stats.cov_matrix · Level L1

Population covariance matrix of the columns of X. Calls center; the row count comes from Size.

C = X_cᵀ·X_c / m

Signature

cov_matrix(X: f64[m, d]) → f64[d, 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]centerXcSizemTransposeXctMatMulGDivideCCf64[d, d]
  • input
  • operation
  • constant
  • call
  • output

Verification

  • Signature proven by NOVA’s shape solver, for every size.
  • Equal to the reference np.cov(X, rowvar=False, ddof=0) in exact rational arithmetic, on all 40 test cases.
  • All 829 float64 results inside the running error bound; the closest uses 18% of it.
  • Interpreter and NumPy backend return bit-identical results.
Accuracy in detail
correctly rounded (the float64 nearest the exact value)
64%
bit-equal to the NumPy formula in float64
100%
largest error, in units in the last place
25

Large ulp counts appear only where cancellation drives a result toward zero; the absolute error is still inside the bound.

Identity

Calls
center
Called by
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