axpby

std.linalg.axpby · Level L0

Linear combination of two vectors with scalar weights.

a·x + b·y

Signature

axpby(a: f64[], x: f64[n], b: f64[], y: f64[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 a call to another library function; select it to open that function.

af64[]xf64[n]bf64[]yf64[n]MultiplyaxMultiplybyAddzzf64[n]
  • input
  • operation
  • constant
  • call
  • output

Verification

  • Signature proven by NOVA’s shape solver, for every size.
  • Equal to the reference a * x + b * y in exact rational arithmetic, on all 40 test cases.
  • All 174 float64 results inside the running error bound; the closest uses 66% of it.
  • Interpreter and NumPy backend return bit-identical results.
Accuracy in detail
correctly rounded (the float64 nearest the exact value)
78%
bit-equal to the NumPy formula in float64
100%
largest error, in units in the last place
39

Large ulp counts appear only where cancellation drives a result toward zero; the absolute error is still inside the bound.

Identity

Calls
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Called by
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sha256:2968a70a35c9ff19496b61e43129a5e1f4e5ee31cbf3c05d3406bf0cdf241617

The semantic hash of the graph. It changes when the program changes, and never when only its documentation does.