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updated docstrings
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quattro committed Mar 26, 2024
1 parent 76ba869 commit 36c6f79
Showing 1 changed file with 3 additions and 3 deletions.
6 changes: 3 additions & 3 deletions src/traceax/_estimators.py
Original file line number Diff line number Diff line change
Expand Up @@ -50,7 +50,7 @@ def __call__(self, key: PRNGKeyArray, operator: AbstractLinearOperator, k: int)
class HutchinsonEstimator(AbstractTraceEstimator):
r"""Girard-Hutchinson Trace Estimator:
$\mathbb{E}[\omega^T \mathbf{A} \omega] = \\text{trace}(\mathbf{A})$,
$\mathbb{E}[\omega^T \mathbf{A} \omega] = \text{trace}(\mathbf{A})$,
where $\mathbb{E}[\omega] = 0$ and $\mathbb{E}[\omega \omega^T] = \mathbf{I}$.
!!! info
Expand Down Expand Up @@ -88,8 +88,8 @@ class HutchPlusPlusEstimator(AbstractTraceEstimator):
$\Omega = [\omega_1, \dotsc, \omega_k]$.
Hutch++ improves upon Girard-Hutchinson estimator by including the trace of the residuals. Namely,
Hutch++ estimates $\\text{trace}(\mathbf{A})$ as
$\\text{trace}(\hat{\mathbf{A}}) - \\text{trace}(\mathbf{A} - \hat{\mathbf{A}})$.
Hutch++ estimates $\text{trace}(\mathbf{A})$ as
$\text{trace}(\hat{\mathbf{A}}) - \text{trace}(\mathbf{A} - \hat{\mathbf{A}})$.
As with the Girard-Hutchinson estimator, it requires
$\mathbb{E}[\omega] = 0$ and $\mathbb{E}[\omega \omega^T] = \mathbf{I}$.
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