reject

std.linalg.reject · Level L0

The part of x orthogonal to u: x minus its projection. Calls proj.

x − proj(x, u)

Signature

reject(x: f64[n], u: f64[n]) → 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 x - (np.dot(x, u) / np.dot(u, u)) * u in exact rational arithmetic, on all 40 test cases.
All 164 float64 results inside the running error bound; the closest uses 77% of it.
Interpreter and NumPy backend return bit-identical results.

Accuracy in detail

correctly rounded (the float64 nearest the exact value): 70%
bit-equal to the NumPy formula in float64: 87%
largest error, in units in the last place: 8.3e+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

proj

Called by

—

sha256:c890d2932c03753dfd33de0d6919c043fcf2829f9d4858013e7926617b163740

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.reject · Ω:reject
Pins: sha256:2ff87a8664b6207c7f0fc2f06da8b490cfa60e4a753447f66a1edb430d803690this graph and the 2 it reaches through calls
Evidence: sha256:1e617dd5a695974cf0fb2f3476f2d132e15df6e1cf9295a62a43bd31d0dc41d0the 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.