matrix_power

std.linalg.matrix_power · Level L2

The matrix power Aᵖ, p the length of k (only its length is read), by p − 1 multiplications after the first: a Scan of matpow_step from the identity. NumPy's np.linalg.matrix_power(A, p).

Aᵖ = A·A·…·A

Signature

matrix_power(A: f64[n, n], k: f64[p]) → 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 np.linalg.matrix_power(A, p) in exact rational arithmetic, on all 40 test cases.
All 894 float64 results inside the running error bound; the closest uses 25% 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 27% of it.

Accuracy in detail

correctly rounded (the float64 nearest the exact value): 67%
bit-equal to the NumPy formula in float64: 100%
largest error, in units in the last place: 532

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

matpow_step

Called by

—

sha256:88875536bbdd04a2a3bdfa579cbce6ef04947e25f924e0e41877cc5e1d0f968e

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.matrix_power · Ω:matrix_power
Pins: sha256:c825a76eff1a02682f552f009d81d3834d8537f1c91e069adc16277ce9539586this graph and the 1 it reaches through calls
Evidence: sha256:7331fce5c48cd4ebfc9a2108646bef1f44ac3400c700174a9f419ba717e96767the 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.