kalman_level_step

std.stats.kalman_level_step · Level L0

One step of the Kalman filter for a local-level model, independently in each coordinate: predict the variance P + Q, weigh the observation z by the gain K = (P + Q)/(P + Q + R), and update the mean m and the variance. The body that kalman_level scans.

K = (P+Q)/(P+Q+R); m′ = m + K(z − m); P′ = K·R

Signature

kalman_level_step(m: f64[k], P: f64[k], z: f64[k], Q: f64[k], R: f64[k]) → f64[k], f64[k]

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 K = (P + Q) / (P + Q + R); m + K * (z - m), K * R in exact rational arithmetic, on all 40 test cases.
All 334 float64 results inside the running error bound; the closest uses 84% 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 78% of it.

Accuracy in detail

correctly rounded (the float64 nearest the exact value): 62%
bit-equal to the NumPy formula in float64: 100%
largest error, in units in the last place: 2.5e+3

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

kalman_level

sha256:b0d27f157b3170b6f1a08fb075799613d9301147ab71defbd7590995e3fa5140

The semantic hash of the graph. It changes when the program changes, and never when only its documentation does.

Control handle

Symbol: Ω:std.stats.kalman_level_step · Ω:kalman_level_step
Pins: sha256:25a1391c5e6a3f9ede791b8013cb17500f95a04a60693f28b8eceae9aefceac3this graph alone
Evidence: sha256:473aa7eb1bc0edd13bb5cab82b935f873611cb9cb5241025bb259bbba9b32559the 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.