convex_set_membership

std.geometry.convex_set_membership · Level L1

Membership of points (the rows of X) in two convex sets: the closed box lo ≤ x ≤ hi, and the closed half-space w·x ≤ β, each as 1 or 0 per point. Both sets are convex for every choice of their data, which is the algebraic certificate; sampling convex combinations would not prove convexity, but one combination of members that falls outside refutes a set's convexity.

lo ≤ x ≤ hi; w·x ≤ β

Signature

convex_set_membership(X: f64[m, n], lo: f64[n], hi: f64[n], w: f64[n], beta: f64[]) → f64[m], 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 coordinatewise bounds, and the dot product against β in exact rational arithmetic, on all 40 test cases.
All 320 float64 results are exact: the error is zero.
Interpreter and NumPy backend return bit-identical results.
At float32 too: the 40 test cases rounded to float32, and 40 of them exact, with zero error.

Accuracy in detail

correctly rounded (the float64 nearest the exact value): 100%
bit-equal to the NumPy formula in float64: 100%
largest error, in units in the last place: 0

Identity

Calls

matvec

Called by

—

sha256:d96704ee29c527df36330733f5d713d64576b8e8047b61d124bfde43421099f0

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

Control handle

Symbol: Ω:std.geometry.convex_set_membership · Ω:convex_set_membership
Pins: sha256:7fedaea741e621578c3c65d95b87950326277fcd22075c3852cd86479273a4f5this graph and the 1 it reaches through calls
Evidence: sha256:0af5fa7baebae4b8f981af6ae70400c76213c339218c572ab63853e655966ed0the 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.