projector

std.linalg.projector · Level L4

The orthogonal projection onto A's column space, Q·Qᵀ from the QR factorization.

P = Q·Qᵀ = A·(AᵀA)⁻¹·Aᵀ

Signature

projector(A: f64[n+k, n]) → f64[n+k, n+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.
Agrees with the reference A @ np.linalg.solve(A.T @ A, A.T) to 80 digits (100-digit arithmetic), on all 40 test cases.
All 3,083 float64 results inside the running error bound; the closest uses 2% of it.
Interpreter and NumPy backend return bit-identical results.

Accuracy in detail

correctly rounded (the float64 nearest the exact value): 17%
bit-equal to the NumPy formula in float64: 14%
largest error, in units in the last place: 7.2e+4

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

—

sha256:c92f29b2cd5883187213609e99ba1c55fd7852ae5566e24e6eddca8f986ff6c2

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.projector · Ω:projector
Pins: sha256:42a536689012c93988c6295afaa326bbf0d5b1c80e397a808f669999d5a75c10this graph alone
Evidence: sha256:da0d4681f3b1efa9343342e8a02931187d9d6553cd8fe6391ab895c441366ee7the 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.