markov_distribution

std.stats.markov_distribution · Level L2

The distributions of a finite Markov chain after 1 … s steps from π₀, s the length of steps (only its length is read): row n is π₀·Pⁿ⁺¹. A Scan of markov_step.

πₙ = π₀·Pⁿ

Signature

markov_distribution(pi0: f64[k], Pm: f64[k, k], steps: f64[s]) → f64[s, 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 pi0 @ P^(n + 1) for each step n in exact rational arithmetic, on all 40 test cases.
All 852 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 inside the running error bound at u = 2⁻²⁴; the closest uses 9% of it.

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

markov_step

Called by

—

sha256:cae897565b45f33e76550bbe1e3dc76d5641d2b73736a798aa4cbb055cdc4de6

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_distribution · Ω:markov_distribution
Pins: sha256:bf8024547a4b7a3fa5499cb747fe401af3e96b1559be403560faeb795ecc4c18this graph and the 2 it reaches through calls
Evidence: sha256:eb69b3b07364101110d7beb9f8bd3022ff4a03f6aac9ff9bdb5744e5d60b2a3cthe 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.