cut_capacity

std.linalg.cut_capacity · Level L0

The capacity of the cut with source side S (a 0/1 vector): the total capacity of the edges from S to its complement. Edges back into S do not count. Every feasible flow's value is at most every cut's capacity.

cap(S) = Σ_{u∈S, v∉S} C(u, v)

Signature

cut_capacity(C: f64[n, n], S: f64[n]) → 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 sum of C[u, v] over u in S, v not in S in exact rational arithmetic, on all 40 test cases.
All 40 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

dot matvec

Called by

—

sha256:a43cb4c1e9c444a9893933440e344b215cf7e9a509585597793074603ca4556a

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.cut_capacity · Ω:cut_capacity
Pins: sha256:ac373fc2961c90a9811cc029da513486adc9608c0fb0621f49cae1fb5b22c735this graph and the 2 it reaches through calls
Evidence: sha256:66c9d26d057db95d3a6bb79ee7bb729bfbeb045d3a676950fd6434db042383b0the 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.