minor_step

std.linalg.minor_step · Level L4

One step of fraction-free elimination without row exchanges: the pivot M[k, k] is the k-th leading principal minor, and the later rows are eliminated exactly by it over the previous pivot. The body leading_minors scans.

Δ_k = M[k, k]; row_i ← (Δ_k·row_i − M[i, k]·row_k)/Δ_{k−1}

Signature

minor_step(M: f64[n, n], prev: f64[], minors: f64[n], k: f64[]) → f64[n, n], f64[], f64[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 the same step on Python integers in exact rational arithmetic, on all 40 test cases.
All 1,098 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: 99%
largest error, in units in the last place: 0

Identity

Calls

—

Called by

leading_minors

sha256:6962bc19f0b7b07d15a45516fd8b1f987bdfe54e0c41d886e1be5b490a926f99

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.minor_step · Ω:minor_step
Pins: sha256:b7cd03ab5aded679128bd8c352243b1afa7f9fdf3b6508ddf1306b8b8ecbeeecthis graph alone
Evidence: sha256:41632864f5bd9090ddb684f90d8ed89a7b79b62d1e547ce19d92b1a5c6fad770the 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.