frobenius

std.linalg.frobenius · Level L1

Frobenius norm of a matrix. Calls frobenius_sq.

‖A‖_F = √(Σᵢⱼ Aᵢⱼ²)

Signature

frobenius(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]frobenius_sqsqSqrtssf64[]
  • input
  • operation
  • constant
  • call
  • output

Verification

  • Signature proven by NOVA’s shape solver, for every size.
  • Agrees with the reference np.linalg.norm(A, 'fro') to 80 digits (100-digit arithmetic), on all 40 test cases.
  • All 40 float64 results inside the running error bound; the closest uses 36% of it.
  • Interpreter and NumPy backend return bit-identical results.
Accuracy in detail
correctly rounded (the float64 nearest the exact value)
93%
bit-equal to the NumPy formula in float64
100%
largest error, in units in the last place
0.76

Identity

Calls
frobenius_sq
Called by
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sha256:ea8108bf98962f3e10ed22e144fc11a2e07e72647e0c81c111ebc419618a9335

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