vecmat

std.linalg.vecmat · Level L0

Row vector times matrix.

(xᵀ·A)ⱼ = Σᵢ xᵢ·Aᵢⱼ

Signature

vecmat(x: f64[m], A: f64[m, 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.

xf64[m]Af64[m, n]ReshapexrMatMulyrReshapeyyf64[n]
  • input
  • operation
  • constant
  • call
  • output

Verification

  • Signature proven by NOVA’s shape solver, for every size.
  • Equal to the reference x @ A in exact rational arithmetic, on all 40 test cases.
  • All 136 float64 results inside the running error bound; the closest uses 75% 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
11

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
—
sha256:019ef059173c7e93c3e0f9fa3928571535cd733b7028ece30083ef7d241d1c50

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.vecmat · Ω:vecmat
Pins
sha256:eb70e19fe2b9c04f4ae0d1a83f12da9754c8fb8b6ec898bf90f22fdf454a9715this graph alone
Evidence
sha256:426d53ecaf11a43442c98741b83b96808379108de3e3556e14cc1cdbb9dee566the 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.