cholesky_solve

std.linalg.cholesky_solve · Level L3

Solve A·x = b for a symmetric positive-definite A the way it is done in practice: factor A = L·Lᵀ, then one forward and one back substitution.

L·z = b, Lᵀ·x = z

Signature

cholesky_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]CholeskyLTransposeLtTriangularSolvezTriangularSolvexxf64[k]
  • input
  • operation
  • constant
  • call
  • output

Verification

  • Signature proven by NOVA’s shape solver, for every size.
  • Agrees with the reference np.linalg.solve(A, b) to 80 digits (100-digit arithmetic), on all 40 test cases.
  • All 165 float64 results inside the running error bound; the closest uses 25% of it.
  • Interpreter and NumPy backend return bit-identical results.
Accuracy in detail
correctly rounded (the float64 nearest the exact value)
33%
bit-equal to the NumPy formula in float64
44%
largest error, in units in the last place
11

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
gp_posterior_mean
sha256:f7b44b09958467e766a6116f20b14d9664868eafafd973c26fb443269888d0dc

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.cholesky_solve · Ω:cholesky_solve
Pins
sha256:ea70956e71ad715a013c1a56ce77531437316cefe1fd89bbbd9aa49a86ff5bc3this graph alone
Evidence
sha256:cf93d6c49d17ef596717ac3b90bab5d073d1a97fe1634f99a9e5fb51d8498e88the 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.