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 another library function this one runs — called once, or by Scan once per element; 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
frobeniusl2_penalty
sha256:8a8a21c21ffc312c69149ef65498f4e76e28700e2a20e005212b13fe5cefa0ef

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

Control handle

Symbol
Ω:std.linalg.frobenius_sq · Ω:frobenius_sq
Pins
sha256:2c70815945adb7b86226c5a673af5ebe9dca1c1f13c7cf083769a9c3099293e5this graph alone
Evidence
sha256:9d0815810f36828673d1a02a55bdda9181be7c5eac29f13b56a1e284d8cb8605the hash of its verification record
Needs
no capability: a pure function

Through NOVA’s control layer, the symbol launches this function only while the program still matches what it pins: a change to this graph, or to any graph it reaches, needs a migration first.