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 another library function this one runs — called once, or by Scan once per element; 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 83% 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
—
sha256:ea8108bf98962f3e10ed22e144fc11a2e07e72647e0c81c111ebc419618a9335

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 · Ω:frobenius
Pins
sha256:8d37612924e40d419ca2731655221e4d4e7175029cc233efa5d9f0cc4926f33fthis graph and the 1 it reaches through calls
Evidence
sha256:9595d3bf3e112eb44b3fb0b888b305818df2737b57cf5207fb4d57d3ce923139the 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.