lp_norms

std.linalg.lp_norms · Level L1

The ℓ₁ and ℓ∞ norms of a vector: Σ|vᵢ| and max |vᵢ|. Each is a norm on Rⁿ: zero only at 0, absolutely homogeneous, and subadditive (the triangle inequality).

‖v‖₁ = Σ|vᵢ|, ‖v‖∞ = max|vᵢ|

Signature

lp_norms(v: f64[n]) → f64[], 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.

input
operation
constant
call
output

Verification

Signature proven by NOVA’s shape solver, for every size.
Equal to the reference the sum and the maximum of the magnitudes in exact rational arithmetic, on all 40 test cases.
All 80 float64 results inside the running error bound; the closest uses 47% of it.
Interpreter and NumPy backend return bit-identical results.
At float32 too: the 40 test cases rounded to float32, and 40 of them inside the running error bound at u = 2⁻²⁴; the closest uses 56% of it.

Accuracy in detail

correctly rounded (the float64 nearest the exact value): 94%
bit-equal to the NumPy formula in float64: 98%
largest error, in units in the last place: 1.00

Identity

Calls

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Called by

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sha256:746db1136edf817e7e8cdeb26d8ceeb1a47a1cee8cda65fc8108e285e75aa92a

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

Control handle

Symbol: Ω:std.linalg.lp_norms · Ω:lp_norms
Pins: sha256:cbd83ae25310fa7d38276f7a179d9a4421d74c7d883646921d5692267f2c3d1cthis graph alone
Evidence: sha256:9edc48de1718fe6403e336ccb48e44f436ad7cfd9e852c5d6f5cb9ff775dcebcthe 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.