eigvalsh

std.linalg.eigvalsh · Level L3

The eigenvalues of a symmetric matrix, ascending.

λ₁ ≤ … ≤ λₖ

Signature

eigvalsh(A: f64[k, k]) → f64[k]

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[k, k]EighValueswwf64[k]
  • input
  • operation
  • constant
  • call
  • output

Verification

  • Signature proven by NOVA’s shape solver, for every size.
  • Agrees with the reference np.linalg.eigvalsh(A) to 80 digits (100-digit arithmetic), on all 40 test cases.
  • All 153 float64 results inside the running error bound; the closest uses 19% of it.
  • Interpreter and NumPy backend return bit-identical results.
Accuracy in detail
correctly rounded (the float64 nearest the exact value)
31%
bit-equal to the NumPy formula in float64
34%
largest error, in units in the last place
5.6e+9

Large ulp counts appear where a result is 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. Results within their own error of zero are not counted.

Identity

Calls
—
Called by
—
sha256:634887e8291bc0b7206eb95183983fdaea3d233fdac37ac2c7ce02b9d19943d2

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.eigvalsh · Ω:eigvalsh
Pins
sha256:e201b17ac594331b9d63ff2da24764e2f893148f47929c7a8961bd38ef25e632this graph alone
Evidence
sha256:5f11fbf7ae8cfa800e67880651c014b642b5c7cb636b84d6bd1b5a1a3a0f5bdfthe 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.