pairwise_dist

std.geometry.pairwise_dist · Level L1

Distances between every point of X and every point of Y. Calls pairwise_sqdist, and clamps at zero before the square root.

Dᵢⱼ = √max(0, ‖xᵢ‖² + ‖yⱼ‖² − 2·xᵢ·yⱼ)

Signature

pairwise_dist(X: f64[m, d], Y: f64[k, d]) → f64[m, k]

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]Yf64[k, d]0.0pairwise_sqdistD2MaximumsafeSqrtDDf64[m, k]
  • input
  • operation
  • constant
  • call
  • output

Verification

  • Signature proven by NOVA’s shape solver, for every size.
  • Agrees with the reference np.sqrt(((X[:, None, :] - Y[None, :, :]) ** 2).sum(-1)) to 80 digits (100-digit arithmetic), on all 40 test cases.
  • All 662 float64 results inside the running error bound; the closest uses 44% of it.
  • Interpreter and NumPy backend return bit-identical results.
Accuracy in detail
correctly rounded (the float64 nearest the exact value)
82%
bit-equal to the NumPy formula in float64
81%
largest error, in units in the last place
9.2e+3

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

Note

The expanded squared distance can come out slightly negative when two points nearly coincide; Maximum clamps it so the square root never sees a negative number.

Identity

Calls
pairwise_sqdist
Called by
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