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Add local commands for website chapter and fix error vector size

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Mickaël Véril 2020-10-27 11:48:58 +01:00
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Manuscript/QUEST_WIREs.tex
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@ -662,6 +662,11 @@ MAE & & 0.22 & 0.16 & 0.22 & 0.11 & 0.12 & 0.05 & 0.04 & 0.02 & 0.20 & 0.22
Here we describe the feature of the website that we have specifically designed to gather the entire data generated during these last few years.
Thanks to this website, one can easily test and compare the accuracy of a given method with respect to various variables such as the molecule size or its family, the nature of the excited states, the size of the basis set, etc.
%=======================
{
\newcommand{\meth}{\text{meth}}
\newcommand{\err}{\mathcal{E}}
\newcommand{\nEx}{X}
\newcommand{\nExnn}{\mathcal{X}}
\subsection{Introduction}
\label{sec:websiteIntro}
%=======================
@ -703,21 +708,21 @@ uncertainty.
\paragraph{Statistics calculations}
We want to calculate the accuracy of each couple method/basis compared to the reference (usually TBEs).
for each method we define a vector containing all the energies of the user selected vertical transitions.
With $\text{meth}$ a couple method/basis and $E^x_\text{meth}$ the energy of the vertical excitation $x$ for the method $\text{meth}$.
And $\mathcal{E}_\text{meth}$ the error vector of the method $\text{meth}$ compared to the reference $\text{ref}$
With $\meth$ a couple method/basis and $E^x_\meth$ the energy of the vertical excitation $\nEx$ for the method $\meth$.
And $\err_\meth$ the error vector of the method $\meth$ compared to the reference $\text{ref}$
\begin{equation}
\vec{E_\text{meth}} = \qty{E^1_\text{meth}, \ldots , E^X_\text{meth}}
\vec{E_\meth} = \qty{E^1_\meth, \ldots , E^\nEx_\meth}
\end{equation}
\begin{equation}
\mathcal{E}^x_\text{meth} = E^x_\text{ref} - E^x_\text{meth}
\err^x_\meth = E^x_\text{ref} - E^x_\meth
\end{equation}
When the vertical excitation $x$ is defined for the method $\text{meth}$ and the method $\text{ref}$.
So with $X$ the size of the vector $\vec{\mathcal{E}^x_\text{meth}}$
When the vertical excitation $x$ is defined for the method $\meth$ and the method $\text{ref}$.
So with $\nExnn$ the size of the vector $\vec{\err^x_\meth}$
\begin{gather}
MSE_\text{meth} = \overline{{\vec{\mathcal{E}_\text{meth}}}} \\
MAE_\text{meth} = \overline{\abs{\vec{\mathcal{E}_\text{meth}}}} \\
RMSE_\text{meth} = \sqrt{\overline{\vec{\mathcal{E}_\text{meth}}^2}} \\
SDE_\text{meth} = \sqrt{\frac{1}{X}\sum_{x=1}^X\mathcal{E}_x^2-MAE^2}
MSE_\meth = \overline{{\vec{\err_\meth}}} \\
MAE_\meth = \overline{\abs{\vec{\err_\meth}}} \\
RMSE_\meth = \sqrt{\overline{\vec{\err_\meth}^2}} \\
SDE_\meth = \sqrt{\frac{1}{\nExnn}\sum_{x=1}^\nExnn\err_x^2-MAE^2}
\end{gather}
These statistics allow user to determine the accuracy of each couple methods/basis.
On the website the statistics are forwarded in a tabular and in a box plot graph.
@ -743,7 +748,7 @@ And the value is considered as not safe when one or more value as not safe
\begin{equation}
\mathrm{unsafe}_\text{ADC(23)} = \mathrm{unsafe}_\text{ADC(2)} \lor \mathrm{unsafe}_\text{ADC(3)}
\end{equation}
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Concluding remarks}
\label{sec:ccl}