lp_slacks

std.optim.lp_slacks · Level L0

The slacks s = b − A·x of the constraints A·x ≤ b at a point x: x satisfies them exactly when every slack is non-negative.

s = b − A·x

Signature

lp_slacks(A: f64[m, n], b: f64[m], x: f64[n]) → f64[m]

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 b - A @ x in exact rational arithmetic, on all 40 test cases.
All 140 float64 results inside the running error bound; the closest uses 80% 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 77% of it.

Accuracy in detail

correctly rounded (the float64 nearest the exact value): 73%
bit-equal to the NumPy formula in float64: 100%
largest error, in units in the last place: 214

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

matvec

Called by

—

sha256:c3239c5499084b25d489391fbae145af520ae6c9fbbb60094f9bfddb51e66e8d

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

Control handle

Symbol: Ω:std.optim.lp_slacks · Ω:lp_slacks
Pins: sha256:fd08efa2966daba9d5d2cdce6d1af7b0d6713a9783841705aa7b3c5419fbcf12this graph and the 1 it reaches through calls
Evidence: sha256:211620f6a04d7fb6041376f0dfa43445e9f0661cf5661dd8e71a9334a67ea430the 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.