matvec

std.linalg.matvec · Level L0

Matrix times vector.

(A·x)ᵢ = Σⱼ Aᵢⱼ·xⱼ

Signature

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

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.

Af64[m, n]xf64[n]ReshapexcMatMulycReshapeyyf64[m]
  • input
  • operation
  • constant
  • call
  • output

Verification

  • Signature proven by NOVA’s shape solver, for every size.
  • Equal to the reference A @ x in exact rational arithmetic, on all 40 test cases.
  • All 205 float64 results inside the running error bound; the closest uses 80% of it.
  • Interpreter and NumPy backend return bit-identical results.
Accuracy in detail
correctly rounded (the float64 nearest the exact value)
79%
bit-equal to the NumPy formula in float64
100%
largest error, in units in the last place
21

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
bilinear
sha256:a27b556b469fb391b53106a6d1cb46addbfc86ed13ab70f4134331cb8b591577

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.matvec · Ω:matvec
Pins
sha256:6da155e58ecffa4a5c3a8228bf5a4ea8348853ac284f1105206b609c3c9fa96athis graph alone
Evidence
sha256:776842ae63dfdd5815620a758c47200f7af48b65a5826f344bd8e6e57a7a9cf2the 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.