component_count

std.linalg.component_count · Level L2

The number of connected components of a finite undirected graph: the vertices that are their own label.

#{i : label(i) = i}

Signature

component_count(A: f64[n, 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 the number of distinct breadth-first-search roots 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

component_labels

Called by

is_tree

sha256:2305aedb73d3b60772d8ad63a60168037f027426e3d22f320388e8460fb9d94b

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.component_count · Ω:component_count
Pins: sha256:ec3088c7de08ff6c110bb6fcdb192280f3676bebbaa8c1a304fb1788efca4b89this graph and the 3 it reaches through calls
Evidence: sha256:d9ce11b59c378e34d2e1beb6c4955936a81f9af5d83d1140301616e3072c20eathe 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.