is_matching

std.linalg.is_matching · Level L1

Whether a symmetric 0/1 selection of edges M is a matching of the graph A, as 1 or 0: every selected edge is an edge of A, and no vertex meets two of them. Also its size. A maximal matching, to which no edge can be added, need not be maximum.

M ⊆ E, deg_M(v) ≤ 1

Signature

is_matching(A: f64[n, n], M: f64[n, 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 M within A, every degree at most 1; size = sum(M)/2 in exact rational arithmetic, on all 40 test cases.
All 80 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

—

Called by

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sha256:c69a2ce6837d89ae6f1b0b4e4f26efcd9f154fe8f5430e429fbc5b1ef5be9a54

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.is_matching · Ω:is_matching
Pins: sha256:50ea22824743171e6e74f628640efc8ba39541a7f542c344a9513f69821befacthis graph alone
Evidence: sha256:5c515096648a363cfc62b3c5abab1edc098101bfca467285e26f08271fc167d4the 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.