bilinear

std.linalg.bilinear · Level L0

Bilinear form xᵀ·A·y. Calls matvec, then dot.

xᵀ·A·y

Signature

bilinear(x: f64[m], A: f64[m, n], y: f64[n]) → f64[]

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.

xf64[m]Af64[m, n]yf64[n]matvecAydotssf64[]
  • input
  • operation
  • constant
  • call
  • output

Verification

  • Signature proven by NOVA’s shape solver, for every size.
  • Equal to the reference x @ A @ y in exact rational arithmetic, on all 40 test cases.
  • All 40 float64 results inside the running error bound; the closest uses 28% 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
58%
largest error, in units in the last place
8.72

Identity

Calls
dotmatvec
Called by
—
sha256:b8dc731c90bd55a4621afee1ce18e3409f0b84a50ff5a918226a9539bf0135bd

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.bilinear · Ω:bilinear
Pins
sha256:45f7128afd8b65fc0d21da6c0f82a0e0ba8afcfabb3774d27a4184c4063784dathis graph and the 2 it reaches through calls
Evidence
sha256:c8154c58f01fa36bf02567d621c18462b5c925d462e1ba3404c278c50d9bc099the 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.