trace

std.linalg.trace · Level L2

The trace of a square matrix: the sum of its diagonal, which is also the sum of its eigenvalues.

tr A = Σᵢ Aᵢᵢ

Signature

trace(A: 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.

input
operation
constant
call
output

Verification

Signature proven by NOVA’s shape solver, for every size.
Equal to the reference np.trace(A) in exact rational arithmetic, on all 40 test cases.
All 40 float64 results inside the running error bound; the closest uses 26% 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 18% of it.

Accuracy in detail

correctly rounded (the float64 nearest the exact value): 90%
bit-equal to the NumPy formula in float64: 98%
largest error, in units in the last place: 2.62

Identity

Calls

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Called by

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sha256:e4a459604d2c82d4b47ec225164a19e9eb49fcb7bc78bf81640cd09476b00609

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.trace · Ω:trace
Pins: sha256:0d9eff92c241ce72b6fe676832d75f2f74625a89a3dafed535fe85b43fbabb44this graph alone
Evidence: sha256:cb2adaacf4c29a5652b1fbc3b1ade8400ecd0e46cf851b90d481753d54c3d818the 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.