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 a call to another library function; 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 only where cancellation drives a result toward zero; the absolute error is still inside the bound.

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.