matpow_step

std.linalg.matpow_step · Level L0

One more factor of A: M ← M·A. The body that matrix_power scans; it does not read its sequence element, only counts the steps.

M′ = M·A

Signature

matpow_step(Mt: f64[n, n], t: f64[], A: f64[n, n]) → f64[n, n]

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 Mt @ A in exact rational arithmetic, on all 40 test cases.
All 847 float64 results inside the running error bound; the closest uses 63% of it.
Interpreter and NumPy backend return bit-identical results.
At float32 too: the 40 test cases rounded to float32, and 40 of them inside the running error bound at u = 2⁻²⁴; the closest uses 49% of it.

Accuracy in detail

correctly rounded (the float64 nearest the exact value): 82%
bit-equal to the NumPy formula in float64: 100%
largest error, in units in the last place: 41

Large ulp counts appear where a result is tiny next to the numbers it is computed from (after cancellation, for example), so one unit in the last place is tiny too; the absolute error is still inside the bound. Results within their own error of zero are not counted.

Identity

Calls

—

Called by

is_bipartite matrix_power

sha256:75e35ad286cf57fb6dd339d4f9957a94c0d999e84ff2d3f85da325cf17ea7c18

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.matpow_step · Ω:matpow_step
Pins: sha256:fc320d2f91f401b8da8151925a6756b42266d8992f01485dbbf788f7a7ea2bfdthis graph alone
Evidence: sha256:71b44875007f437e14ceb659a3ffa02b5fe9cfadf6f73b08d40a2bcae97434bcthe 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.