inverse

std.linalg.inverse · Level L3

The inverse of A: Solve against the identity, which is built from two Iotas.

A⁻¹ = solve(A, I)

Signature

inverse(A: f64[k, k]) → f64[k, 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]Iotaeye_rIotaeye_cEqualeyeSolveAinvAinvf64[k, k]
  • input
  • operation
  • constant
  • call
  • output

Verification

  • Signature proven by NOVA’s shape solver, for every size.
  • Equal to the reference np.linalg.inv(A) in exact rational arithmetic, on all 40 test cases.
  • All 716 float64 results inside the running error bound; the closest uses 1% of it.
  • Interpreter and NumPy backend return bit-identical results.
Accuracy in detail
correctly rounded (the float64 nearest the exact value)
37%
bit-equal to the NumPy formula in float64
100%
largest error, in units in the last place
2.1e+4

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.

Identity

Calls
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Called by
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sha256:bc6ce34c70f4d04ee2a2e3ef4302fdb7fa04f6acbb0a1db49b2317e721cc8009

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