nuclear_norm

std.linalg.nuclear_norm · Level L4

The nuclear norm of A: the sum of its singular values, the convex stand-in for rank in low-rank recovery.

‖A‖_* = Σᵢ σᵢ

Signature

nuclear_norm(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]SVDValuessReduceSumnormnormf64[]
  • input
  • operation
  • constant
  • call
  • output

Verification

  • Signature proven by NOVA’s shape solver, for every size.
  • Agrees with the reference np.linalg.norm(A, 'nuc') to 80 digits (100-digit arithmetic), on all 40 test cases.
  • All 40 float64 results inside the running error bound; the closest uses 16% of it.
  • Interpreter and NumPy backend return bit-identical results.
Accuracy in detail
correctly rounded (the float64 nearest the exact value)
35%
bit-equal to the NumPy formula in float64
60%
largest error, in units in the last place
3.46

Identity

Calls
—
Called by
—
sha256:bc3df277f914b9b7f4e98a8b500aac888c27def276ea4700af51eefe4bdb6837

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.nuclear_norm · Ω:nuclear_norm
Pins
sha256:1c780df5329198771496b80daa79f5d34fdb754e1ae05856802101df43191d77this graph alone
Evidence
sha256:60fdcde79963d85ef8e46fe56c56222f8608bb48f6e5aac963f1a960ef723822the 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.