svdvals

std.linalg.svdvals · Level L4

The singular values of A, largest first.

σ₁ ≥ … ≥ σₙ ≥ 0

Signature

svdvals(A: f64[n+k, n]) → f64[n]

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]SVDValuesssf64[n]
  • input
  • operation
  • constant
  • call
  • output

Verification

  • Signature proven by NOVA’s shape solver, for every size.
  • Agrees with the reference np.linalg.svd(A)[1] to 80 digits (100-digit arithmetic), on all 40 test cases.
  • All 162 float64 results inside the running error bound; the closest uses 26% of it.
  • Interpreter and NumPy backend return bit-identical results.
Accuracy in detail
correctly rounded (the float64 nearest the exact value)
15%
bit-equal to the NumPy formula in float64
100%
largest error, in units in the last place
11

Large ulp counts appear where a result is zero or tiny next to the numbers it is computed from (after cancellation, for example), so one unit in the last place is tiny too; the absolute error is still inside the bound.

Note

The reference goes through the eigenvalues of AᵀA; the exact check takes the singular values directly, so two different routes have to agree.

Identity

Calls
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Called by
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sha256:a5d40471ed240a98ff1f698faf32767a390e843b22bf2ff13fc9b716c81a581c

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