solve

std.linalg.solve · Level L3

The solution of A·x = b, by Gaussian elimination with partial pivoting (the Solve primitive).

x = A⁻¹·b

Signature

solve(A: f64[k, k], b: f64[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]bf64[k]Solvexxf64[k]
  • input
  • operation
  • constant
  • call
  • output

Verification

  • Signature proven by NOVA’s shape solver, for every size.
  • Equal to the reference np.linalg.solve(A, b) in exact rational arithmetic, on all 40 test cases.
  • All 163 float64 results inside the running error bound; the closest uses 0% of it.
  • Interpreter and NumPy backend return bit-identical results.
Accuracy in detail
correctly rounded (the float64 nearest the exact value)
42%
bit-equal to the NumPy formula in float64
100%
largest error, in units in the last place
174

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:f9c52e1783642256af1669fdb42b4dc8a32f3bcdd2e3dbbf4a3c7733bd49b504

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.solve · Ω:solve
Pins
sha256:caf0248547cc79ca7ef823ba566078e9a16887210840855cd10466316012a2a2this graph alone
Evidence
sha256:686fdab93cd25f4f6f3a04b07e0bd3d7e960519e8c69063af14e8b27d9e7267bthe 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.