reject

std.linalg.reject · Level L0

The part of x orthogonal to u: x minus its projection. Calls proj.

x − proj(x, u)

Signature

reject(x: f64[n], u: 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.

xf64[n]uf64[n]projpSubtractrrf64[n]
  • input
  • operation
  • constant
  • call
  • output

Verification

  • Signature proven by NOVA’s shape solver, for every size.
  • Equal to the reference x - (np.dot(x, u) / np.dot(u, u)) * u in exact rational arithmetic, on all 40 test cases.
  • All 164 float64 results inside the running error bound; the closest uses 77% 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
87%
largest error, in units in the last place
8.3e+3

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

Identity

Calls
proj
Called by
—
sha256:c890d2932c03753dfd33de0d6919c043fcf2829f9d4858013e7926617b163740

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