augment
std.linalg.augment · Level L3One Edmonds–Karp augmentation of a net flow F, skew-symmetric: breadth-first search in the residual network C − F, then push the bottleneck along the shortest path found, adding it forward and subtracting it backward. The body max_flow loops on.
Signature
augment(F: f64[n, n], C: f64[n, n]) → f64[n, n]
Requires: n ≥ 2
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 with n ≥ 2.
- Equal to the reference
BFS in C − F, walk back from the sink, push the bottleneckin exact rational arithmetic, on all 40 test cases. - All 1,146 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.
- 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
sha256:f4856fe12f9fc575ba3b79c0b4159ca4dd820863bf336a6c9dc7196dc0481b26The semantic hash of the graph. It changes when the program changes, and never when only its documentation does.
Control handle
- Symbol
- Ω:std.linalg.augment · Ω:augment
- Pins
sha256:462ec453a13ccab973ee93be991b19cf1d95457ea928626238d4cf0ed715bb73this graph and the 3 it reaches through calls- Evidence
sha256:88158f7160bed5192fd689cb6a39f0ffdd7a141ea86a4d41842ecc4117ee6935the 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.