From 36c6f79a8156e9cfbd6420ab03e93578e3323975 Mon Sep 17 00:00:00 2001 From: quattro Date: Tue, 26 Mar 2024 12:45:12 -0700 Subject: [PATCH] updated docstrings --- src/traceax/_estimators.py | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/src/traceax/_estimators.py b/src/traceax/_estimators.py index 38d72a3..0aeed7b 100644 --- a/src/traceax/_estimators.py +++ b/src/traceax/_estimators.py @@ -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 @@ -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 $\mathbb{E}[\omega \omega^T] = \mathbf{I}$.