norm2

std.linalg.norm2 · Level L4

The spectral norm of A: its largest singular value, the most A can stretch a unit vector.

‖A‖₂ = σ₁

Signature

norm2(A: f64[n+k, 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[n+k, n]SVDValuessReduceMaxnormnormf64[]
  • input
  • operation
  • constant
  • call
  • output

Verification

  • Signature proven by NOVA’s shape solver, for every size.
  • Agrees with the reference np.linalg.norm(A, 2) to 80 digits (100-digit arithmetic), on all 40 test cases.
  • All 40 float64 results inside the running error bound; the closest uses 22% of it.
  • Interpreter and NumPy backend return bit-identical results.
Accuracy in detail
correctly rounded (the float64 nearest the exact value)
40%
bit-equal to the NumPy formula in float64
53%
largest error, in units in the last place
5.33

Identity

Calls
—
Called by
—
sha256:03e2506800b57e83e9d56d2d99374ae37dcd2c00fee52d46082eca1400f42944

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.norm2 · Ω:norm2
Pins
sha256:2b733b667184766c0afb84b3ce0dc4d328ccd2725fa6b7b9200e28c1af4e03a2this graph alone
Evidence
sha256:9a5a708eacb9ed1681b4333f4a1135504dee8fce3ee570839bee4b466413de2cthe 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.