mahalanobis

std.stats.mahalanobis · Level L3

The Mahalanobis distance of x from μ under covariance S: the length of x − μ after whitening by S's Cholesky factor.

√((x − μ)ᵀS⁻¹(x − μ))

Signature

mahalanobis(x: f64[k], mu: f64[k], S: f64[k, k]) → 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[k]muf64[k]Sf64[k, k]SubtractdCholeskyLTriangularSolvezMultiplyzzReduceSumqSqrtdistdistf64[]
  • input
  • operation
  • constant
  • call
  • output

Verification

  • Signature proven by NOVA’s shape solver, for every size.
  • Agrees with the reference np.sqrt((x - mu) @ np.linalg.solve(S, x - mu)) to 80 digits (100-digit arithmetic), on all 40 test cases.
  • All 40 float64 results inside the running error bound; the closest uses 22% of it.
  • Interpreter and NumPy backend return bit-identical results.
Accuracy in detail
correctly rounded (the float64 nearest the exact value)
68%
bit-equal to the NumPy formula in float64
78%
largest error, in units in the last place
0.93

Identity

Calls
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Called by
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sha256:27ad8fa6c6254ddaf43e213871d35e4eb9637b9c95c92dc0ca60d29ac8b7bd2b

The semantic hash of the graph. It changes when the program changes, and never when only its documentation does.