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 another library function this one runs — called once, or by Scan once per element; 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 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
center
Called by
—
sha256:9bd2b24e709b09b8aac885caf85f24f1fd1c204fec81fb8efeb0ec7977ccb04e

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.cov_matrix · Ω:cov_matrix
Pins
sha256:7c2ad995bc9bcbcd5fea3a561a5c48606a6da1d3b93e44c3f18be47058c9fe00this graph and the 1 it reaches through calls
Evidence
sha256:3c28c801b14bbc14b43fa99bbda95bb286616b4e8d30f3d1a27d92a0206bc90cthe 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.