markov_step

std.stats.markov_step · Level L0

One step of a finite Markov chain: the distribution π over the states becomes π·P, for the transition matrix P with Pᵢⱼ = P(Xₙ₊₁ = j | Xₙ = i). The body markov_distribution scans; it does not read its sequence element.

πₙ₊₁ = πₙ·P

Signature

markov_step(pi: f64[k], t: f64[], Pm: f64[k, 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 pi @ P in exact rational arithmetic, on all 40 test cases.
All 123 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

vecmat

Called by

markov_distribution

sha256:472189695bc008506600b4ba80b4ef3f3224b8c58e130627bc510f2caec0a314

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.markov_step · Ω:markov_step
Pins: sha256:4ea0cb418ee81efe3bad2265ef8b7bd0d45f9a21a81fe044dbe3fcc29cee06c0this graph and the 1 it reaches through calls
Evidence: sha256:fd73ae3d59f07ccdce22bfe03051af86363055711c527390d6d14d5fcffaec17the 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.