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
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Called by
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sha256:bc3df277f914b9b7f4e98a8b500aac888c27def276ea4700af51eefe4bdb6837

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