cholesky

std.linalg.cholesky · Level L3

The Cholesky factor of a symmetric positive-definite A: the lower-triangular L with L·Lᵀ = A.

L·Lᵀ = A

Signature

cholesky(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]CholeskyLLf64[k, k]
  • input
  • operation
  • constant
  • call
  • output

Verification

  • Signature proven by NOVA’s shape solver, for every size.
  • Agrees with the reference np.linalg.cholesky(A) to 80 digits (100-digit arithmetic), on all 40 test cases.
  • All 877 float64 results inside the running error bound; the closest uses 22% of it.
  • Interpreter and NumPy backend return bit-identical results.
Accuracy in detail
correctly rounded (the float64 nearest the exact value)
80%
bit-equal to the NumPy formula in float64
100%
largest error, in units in the last place
87

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:c73a2a34c0a7b81711765ee76e41700dee4ff1654d428a8b7393a1c751057f6e

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 · Ω:cholesky
Pins
sha256:f90607e17441bf6886a7da8777d5e21de80337dda7d1b0e83be0fcfde9291503this graph alone
Evidence
sha256:cffab67ab4f46fe3805066dbd90c77d40af6741d92256f654ddb5d1975c3ce9bthe 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.