frobenius_sq

std.linalg.frobenius_sq · Level L0

Squared Frobenius norm: the sum of every squared entry.

‖A‖²_F = Σᵢⱼ Aᵢⱼ²

Signature

frobenius_sq(A: f64[m, n]) → f64[]

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]MultiplyAAReduceSumssf64[]
  • input
  • operation
  • constant
  • call
  • output

Verification

  • Signature proven by NOVA’s shape solver, for every size.
  • Equal to the reference np.sum(A * A) in exact rational arithmetic, on all 40 test cases.
  • All 40 float64 results inside the running error bound; the closest uses 53% of it.
  • Interpreter and NumPy backend return bit-identical results.
Accuracy in detail
correctly rounded (the float64 nearest the exact value)
80%
bit-equal to the NumPy formula in float64
100%
largest error, in units in the last place
0.73

Identity

Calls
—
Called by
l2_penalty
sha256:8a8a21c21ffc312c69149ef65498f4e76e28700e2a20e005212b13fe5cefa0ef

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