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 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:bc6ce34c70f4d04ee2a2e3ef4302fdb7fa04f6acbb0a1db49b2317e721cc8009

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.inverse · Ω:inverse
Pins
sha256:ddbfe67377de0296caea36059d2baa5ed0fbebad6f07d038da6c7367de0dc542this graph alone
Evidence
sha256:de4e48a4994f2908e81a628333da8c7170093c6916b3de7ad6fc626845f91048the 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.