From 5b22c181be29268254d14a0b42c9c6dab386b558 Mon Sep 17 00:00:00 2001 From: Stefan Dresselhaus Date: Wed, 25 Oct 2017 20:40:51 +0200 Subject: [PATCH] savepoint --- arbeit/img/3d_grid_resolution.png | Bin 0 -> 397063 bytes arbeit/ma.md | 563 +++--- arbeit/ma.pdf | Bin 2790201 -> 3119393 bytes arbeit/ma.tex | 617 ++++--- arbeit/settings/commands.tex | 3 + arbeit/template.tex | 1 + .../20170926_3dFit_4x4x4_100times.csv | 200 +-- .../20170926_3dFit_4x4x4_100times.error | 101 ++ .../20170926_3dFit_4x4x4_100times.mms | 9 + .../20170926_3dFit_4x4x4_100times.spearman | 49 + .../20170926_3dFit_5x5x5_100times.csv | 200 +-- .../20170926_3dFit_5x5x5_100times.error | 101 ++ .../20170926_3dFit_5x5x5_100times.mms | 9 + .../20170926_3dFit_5x5x5_100times.spearman | 49 + .../20171005_3dFit_4x4x5_100times.csv | 200 +-- .../20171005_3dFit_4x4x5_100times.error | 101 ++ .../20171005_3dFit_4x4x5_100times.mms | 9 + .../20171005_3dFit_4x4x5_100times.spearman | 49 + .../20171005_3dFit_7x4x4_100times.csv | 200 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.../evolution3d/YxYxY.gnuplot.fit.log | 8 +- .../evolution3d/YxYxY.gnuplot.script | 8 +- dokumentation/evolution3d/YxYxY.mms | 9 + dokumentation/evolution3d/YxYxY.spearman | 49 + .../YxYxY_improvement-vs-evo-error.png | Bin 7928 -> 8220 bytes .../YxYxY_improvement-vs-steps.png | Bin 7394 -> 7804 bytes .../evolution3d/YxYxY_regularity-vs-steps.png | Bin 7884 -> 8352 bytes .../YxYxY_variability-vs-evo-error.png | Bin 5886 -> 6012 bytes dokumentation/evolution3d/all.csv | 911 ++++++++++ dokumentation/evolution3d/all.gnuplot.fit.log | 184 ++ dokumentation/evolution3d/all.gnuplot.log | 304 ++++ dokumentation/evolution3d/all.gnuplot.script | 26 + dokumentation/evolution3d/all.mms | 9 + dokumentation/evolution3d/all.spearman | 49 + .../all_improvement-vs-evo-error.png | Bin 0 -> 12064 bytes .../evolution3d/all_improvement-vs-steps.png | Bin 0 -> 11890 bytes .../evolution3d/all_regularity-vs-steps.png | Bin 0 -> 13783 bytes .../all_variability-vs-evo-error.png | Bin 0 -> 7316 bytes dokumentation/evolution3d/combine.sh | 24 +- dokumentation/evolution3d/combine7.sh | 71 + dokumentation/evolution3d/errors.csv | 111 ++ dokumentation/evolution3d/errors.mms | 9 + dokumentation/evolution3d/errors.spearman | 49 + dokumentation/evolution3d/images.sh | 8 + .../evolution3d/improvement_montage.png | Bin 0 -> 35240 bytes dokumentation/evolution3d/post_tmp.sh | 17 + .../evolution3d/regularity_montage.png | Bin 0 -> 38395 bytes dokumentation/evolution3d/variability.gnuplot | 21 + .../evolution3d/variability2.gnuplot | 24 + .../evolution3d/variability2_boxplot.png | Bin 0 -> 4752 bytes .../evolution3d/variability_boxplot.png | Bin 0 -> 5702 bytes 106 files changed, 9502 insertions(+), 2144 deletions(-) create mode 100644 arbeit/img/3d_grid_resolution.png create mode 100644 dokumentation/evolution3d/20170926_3dFit_4x4x4_100times.error create mode 100644 dokumentation/evolution3d/20170926_3dFit_4x4x4_100times.mms create mode 100644 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@@ -28,7 +28,7 @@ Unless otherwise noted the following holds: Many modern industrial design processes require advanced optimization methods due to the increased complexity resulting from more and more degrees of freedom as methods refine and/or other methods are used. Examples for this are physical -domains like aerodynamic (i.e. drag), fluid dynamics (i.e. throughput of liquid) +domains like aerodynamics (i.e. drag), fluid dynamics (i.e. throughput of liquid) --- where the complexity increases with the temporal and spatial resolution of the simulation --- or known hard algorithmic problems in informatics (i.e. layouting of circuit boards or stacking of 3D--objects). Moreover these are @@ -45,7 +45,7 @@ representation (the *genome*) can be challenging. This translation is often necessary as the target of the optimization may have too many degrees of freedom. In the example of an aerodynamic simulation of drag -onto an object, those objects--designs tend to have a high number of vertices to +onto an object, those object--designs tend to have a high number of vertices to adhere to various requirements (visual, practical, physical, etc.). A simpler representation of the same object in only a few parameters that manipulate the whole in a sensible matter are desirable, as this often decreases the @@ -425,7 +425,7 @@ the given direction. The definition for an *improvement potential* $P$ is\cite{anrichterEvol}: $$ -P(\vec{U}) := 1 - \|(\vec{1} - \vec{UU}^+)\vec(G)\|^2_F +P(\vec{U}) := 1 - \|(\vec{1} - \vec{UU}^+)\vec{G}\|^2_F $$ given some approximate $n \times d$ fitness--gradient $\vec{G}$, normalized to $\|\vec{G}\|_F = 1$, whereby $\|\cdot\|_F$ denotes the Frobenius--Norm. @@ -549,6 +549,7 @@ and use Cramers rule for inverting the small Jacobian and solving this system of linear equations. ## Deformation Grid +\label{sec:impl:grid} As mentioned in chapter \ref{sec:back:evo}, the way of choosing the representation to map the general problem (mesh--fitting/optimization in our @@ -565,19 +566,9 @@ control point without having a $1:1$--correlation, and a smooth deformation. While the advantages are great, the issues arise from the problem to decide where to place the control--points and how many. -One would normally think, that the more control--points you add, the better the -result will be, but this is not the case for our B--Splines. Given any point $p$ -only the $2 \cdot (d-1)$ control--points contribute to the parametrization of -that point^[Normally these are $d-1$ to each side, but at the boundaries the -number gets increased to the inside to meet the required smoothness]. -This means, that a high resolution can have many control-points that are not -contributing to any point on the surface and are thus completely irrelevant to -the solution. - -\begin{figure}[!ht] -\begin{center} +\begin{figure}[!tbh] +\centering \includegraphics{img/enoughCP.png} -\end{center} \caption[Example of a high resolution control--grid]{A high resolution ($10 \times 10$) of control--points over a circle. Yellow/green points contribute to the parametrization, red points don't.\newline @@ -586,6 +577,14 @@ control--points.} \label{fig:enoughCP} \end{figure} +One would normally think, that the more control--points you add, the better the +result will be, but this is not the case for our B--Splines. Given any point $p$ +only the $2 \cdot (d-1)$ control--points contribute to the parametrization of +that point^[Normally these are $d-1$ to each side, but at the boundaries the +number gets increased to the inside to meet the required smoothness]. +This means, that a high resolution can have many control-points that are not +contributing to any point on the surface and are thus completely irrelevant to +the solution. We illustrate this phenomenon in figure \ref{fig:enoughCP}, where the four red central points are not relevant for the parametrization of the circle. @@ -619,14 +618,14 @@ In this scenario we used the shape defined by Giannelli et al.\cite{giannelli201 which is also used by Richter et al.\cite{anrichterEvol} using the same discretization to $150 \times 150$ points for a total of $n = 22\,500$ vertices. The shape is given by the following definition -$$ +\begin{equation} t(x,y) = \begin{cases} 0.5 \cos(4\pi \cdot q^{0.5}) + 0.5 & q(x,y) < \frac{1}{16},\\ 2(y-x) & 0 < y-x < 0.5,\\ 1 & 0.5 < y - x \end{cases} -$$ +\end{equation} with $(x,y) \in [0,2] \times [0,1]$ and $q(x,y)=(x-1.5)^2 + (y-0.5)^2$, which we have visualized in figure \ref{fig:1dtarget}. @@ -645,9 +644,9 @@ correct. Regarding the *fitness--function* $f(\vec{p})$, we use the very simple approach of calculating the squared distances for each corresponding vertex -$$ +\begin{equation} \textrm{f(\vec{p})} = \sum_{i=1}^{n} \|(\vec{Up})_i - t_i\|_2^2 = \|\vec{Up} - \vec{t}\|^2 \rightarrow \min -$$ +\end{equation} where $t_i$ are the respective target--vertices to the parametrized source--vertices^[The parametrization is encoded in $\vec{U}$ and the initial position of the control points. See \ref{sec:ffd:adapt}] with the current @@ -659,6 +658,108 @@ This formula is also the least--squares approximation error for which we can compute the analytic solution $\vec{p^{*}} = \vec{U^+}\vec{t}$, yielding us the correct gradient in which the evolutionary optimizer should move. +## Test Scenario: 3D Function Approximation +\label{sec:test:3dfa} +Opposed to the 1--dimensional scenario before, the 3--dimensional scenario is +much more complex --- not only because we have more degrees of freedom on each +control point, but also because the *fitness--function* we will use has no known +analytic solution and multiple local minima. + +\begin{figure}[ht] +\begin{center} +\includegraphics[width=0.9\textwidth]{img/3dtarget.png} +\end{center} +\caption[3D source and target meshes]{\newline +Left: The sphere we start from with 10\,807 vertices\newline +Right: The face we want to deform the sphere into with 12\,024 vertices.} +\label{fig:3dtarget} +\end{figure} + +First of all we introduce the set up: We have given a triangulated model of a +sphere consisting of $10\,807$ vertices, that we want to deform into a +the target--model of a face with a total of $12\,024$ vertices. Both of +these Models can be seen in figure \ref{fig:3dtarget}. + +Opposed to the 1D--case we cannot map the source and target--vertices in a +one--to--one--correspondence, which we especially need for the approximation of +the fitting--error. Hence we state that the error of one vertex is the distance +to the closest vertex of the other model. + +We therefore define the *fitness--function* to be: + +\begin{equation} +f(\vec{P}) = \frac{1}{n} \underbrace{\sum_{i=1}^n \|\vec{c_T(s_i)} - +\vec{s_i}\|_2^2}_{\textrm{source-to-target--distance}} ++ \frac{1}{m} \underbrace{\sum_{i=1}^m \|\vec{c_S(t_i)} - +\vec{t_i}\|_2^2}_{\textrm{target-to-source--distance}} ++ \lambda \cdot \textrm{regularization}(\vec{P}) +\label{eq:fit3d} +\end{equation} + +where $\vec{c_T(s_i)}$ denotes the target--vertex that is corresponding to the +source--vertex $\vec{s_i}$ and $\vec{c_S(t_i)}$ denotes the source--vertex that +corresponds to the target--vertex $\vec{t_i}$. Note that the target--vertices +are given and fixed by the target--model of the face we want to deform into, +whereas the source--vertices vary depending on the chosen parameters $\vec{P}$, +as those get calculated by the previously introduces formula $\vec{S} = \vec{UP}$ +with $\vec{S}$ being the $n \times 3$--matrix of source--vertices, $\vec{U}$ the +$n \times m$--matrix of calculated coefficients for the \ac{FFD} --- analog to +the 1D case --- and finally $\vec{P}$ being the $m \times 3$--matrix of the +control--grid defining the whole deformation. + +As regularization-term we add a weighted Laplacian of the deformation that has +been used before by Aschenbach et al.\cite[Section 3.2]{aschenbach2015} on +similar models and was shown to lead to a more precise fit. The Laplacian +\begin{equation} +\textrm{regularization}(\vec{P}) = \frac{1}{\sum_i A_i} \sum_{i=1}^n A_i \cdot \left( \sum_{\vec{s_j} \in \mathcal{N}(\vec{s_i})} w_j \cdot \|\Delta \vec{s_j} - \Delta \vec{\overline{s}_j}\|^2 \right) +\label{eq:reg3d} +\end{equation} +is determined by the cotangent weighted displacement $w_j$ of the to $s_i$ +connected vertices $\mathcal{N}(s_i)$ and $A_i$ is the Voronoi--area of the corresponding vertex +$\vec{s_i}$. We leave out the $\vec{R}_i$--term from the original paper as our +deformation is merely linear. + +This regularization--weight gives us a measure of stiffness for the material +that we will influence via the $\lambda$--coefficient to start out with a stiff +material that will get more flexible per iteration. +\unsure[inline]{Andreas: hast du nen cite, wo gezeigt ist, dass das so sinnvoll ist?} + +# Evaluation of Scenarios +\label{sec:res} + +To compare our results to the ones given by Richter et al.\cite{anrichterEvol}, +we also use Spearman's rank correlation coefficient. Opposed to other popular +coefficients, like the Pearson correlation coefficient, which measures a linear +relationship between variables, the Spearmans's coefficient assesses \glqq how +well an arbitrary monotonic function can descripbe the relationship between two +variables, without making any assumptions about the frequency distribution of +the variables\grqq\cite{hauke2011comparison}. + +As we don't have any prior knowledge if any of the criteria is linear and we are +just interested in a monotonic relation between the criteria and their +predictive power, the Spearman's coefficient seems to fit out scenario best. + +For interpretation of these values we follow the same interpretation used in +\cite{anrichterEvol}, based on \cite{weir2015spearman}: The coefficient +intervals $r_S \in [0,0.2[$, $[0.2,0.4[$, $[0.4,0.6[$, $[0.6,0.8[$, and $[0.8,1]$ are +classified as *very weak*, *weak*, *moderate*, *strong* and *very strong*. We +interpret p--values smaller than $0.1$ as *significant* and cut off the +precision of p--values after four decimal digits (thus often having a p--value +of $0$ given for p--values $< 10^{-4}$). + + +As we are looking for anti--correlation (i.e. our criterion should be maximized +indicating a minimal result in --- for example --- the reconstruction--error) +instead of correlation we flip the sign of the correlation--coefficient for +readability and to have the correlation--coefficients be in the +classification--range given above. + +For the evolutionary optimization we employ the CMA--ES (covariance matrix +adaptation evolution strategy) of the shark3.1 library \cite{shark08}, as this +algorithm was used by \cite{anrichterEvol} as well. We leave the parameters at +their sensible defaults as further explained in +\cite[Appendix~A: Table~1]{hansen2016cma}. + ## Procedure: 1D Function Approximation \label{sec:proc:1d} @@ -702,144 +803,6 @@ appropriate.]. An Example of such a testcase can be seen for a $7 \times 4$--grid in figure \ref{fig:example1d_grid}. -## Test Scenario: 3D Function Approximation - -Opposed to the 1--dimensional scenario before, the 3--dimensional scenario is -much more complex --- not only because we have more degrees of freedom on each -control point, but also because the *fitness--function* we will use has no known -analytic solution and multiple local minima. - -\begin{figure}[ht] -\begin{center} -\includegraphics[width=0.7\textwidth]{img/3dtarget.png} -\end{center} -\caption[3D source and target meshes]{\newline -Left: The sphere we start from with 10\,807 vertices\newline -Right: The face we want to deform the sphere into with 12\,024 vertices.} -\label{fig:3dtarget} -\end{figure} - -First of all we introduce the set up: We have given a triangulated model of a -sphere consisting of 10\,807 vertices, that we want to deform into a -the target--model of a face with a total of 12\,024 vertices. Both of -these Models can be seen in figure \ref{fig:3dtarget}. - -Opposed to the 1D--case we cannot map the source and target--vertices in a -one--to--one--correspondence, which we especially need for the approximation of -the fitting--error. Hence we state that the error of one vertex is the distance -to the closest vertex of the other model. - -We therefore define the *fitness--function* to be: -$$ -f(\vec{P}) = \frac{1}{n} \underbrace{\sum_{i=1}^n \|\vec{c_T(s_i)} - -\vec{s_i}\|_2^2}_{\textrm{source-to-target--distance}} -+ \frac{1}{m} \underbrace{\sum_{i=1}^m \|\vec{c_S(t_i)} - -\vec{t_i}\|_2^2}_{\textrm{target-to-source--distance}} -+ \lambda \cdot \textrm{regularization}(\vec{P}) -$$ -where $\vec{c_T(s_i)}$ denotes the target--vertex that is corresponding to the -source--vertex $\vec{s_i}$ and $\vec{c_S(t_i)}$ denotes the source--vertex that -corresponds to the target--vertex $\vec{t_i}$. Note that the target--vertices -are given and fixed by the target--model of the face we want to deform into, -whereas the source--vertices vary depending on the chosen parameters $\vec{P}$, -as those get calculated by the previously introduces formula $\vec{S} = \vec{UP}$ -with $\vec{S}$ being the $n \times 3$--matrix of source--vertices, $\vec{U}$ the -$n \times m$--matrix of calculated coefficients for the \ac{FFD} --- analog to -the 1D case --- and finally $\vec{P}$ being the $m \times 3$--matrix of the -control--grid defining the whole deformation. - -As regularization-term we add a weighted Laplacian of the deformation that has -been used before by Aschenbach et al.\cite[Section 3.2]{aschenbach2015} on -similar models and was shown to lead to a more precise fit. The Laplacian -$$ -\textrm{regularization}(\vec{P}) = \frac{1}{\sum_i A_i} \sum_{i=1}^n A_i \cdot \left( \sum_{\vec{s_j} \in \mathcal{N}(\vec{s_i})} w_j \cdot \|\Delta \vec{s_j} - \Delta \vec{\overline{s}_j}\|^2 \right) -$$ -is determined by the cotangent weighted displacement $w_j$ of the to $s_i$ -connected vertices $\mathcal{N}(s_i)$ and $A_i$ is the Voronoi--area of the corresponding vertex -$\vec{s_i}$. We leave out the $\vec{R}_i$--term from the original paper as our -deformation is merely linear. - -This regularization--weight gives us a measure of stiffness for the material -that we will influence via the $\lambda$--coefficient to start out with a stiff -material that will get more flexible per iteration. -\unsure[inline]{Andreas: hast du nen cite, wo gezeigt ist, dass das so sinnvoll ist?} - -## Procedure: 3D Function Approximation - -Initially we set up the correspondences $\vec{c_T(\dots)}$ and $\vec{c_S(\dots)}$ to be -the respectively closest vertices of the other model. We then calculate the -analytical solution given these correspondences via $\vec{P^{*}} = \vec{U^+}\vec{T}$, -and also use the first solution as guessed gradient for the calculation of the -*improvement--potential*, as the optimal solution is not known. -We then let the evolutionary algorithm run up within $1.05$ times the error of -this solution and afterwards recalculate the correspondences $\vec{c_T(\dots)}$ -and $\vec{c_S(\dots)}$. -For the next step we then halve the regularization--impact $\lambda$ and -calculate the next incremental solution $\vec{P^{*}} = \vec{U^+}\vec{T}$ with -the updated correspondences to get our next target--error. -We repeat this process as long as the target--error keeps decreasing. - -\begin{figure}[ht] -\begin{center} -\includegraphics[width=\textwidth]{img/example3d_grid.png} -\end{center} -\caption[Example of a 3D--grid]{\newline Left: The 3D--setup with a $4\times -4\times 4$--grid.\newline Right: The same grid after added noise to the -control--points.} -\label{fig:setup3d} -\end{figure} - -The grid we use for our experiments is just very coarse due to computational -limitations. We are not interested in a good reconstruction, but an estimate if -the mentioned evolvability criteria are good. - -In figure \ref{fig:setup3d} we show an example setup of the scene with a -$4\times 4\times 4$--grid. Identical to the 1--dimensional scenario before, we create a -regular grid and move the control-points uniformly random between their -neighbours, but in three instead of two dimensions^[Again, we flip the signs for -the edges, if necessary to have the object still in the convex hull.]. - -As is clearly visible from figure \ref{fig:3dtarget}, the target--model has many -vertices in the facial area, at the ears and in the neck--region. Therefore we -chose to increase the grid-resolutions for our tests in two different dimensions -and see how well the criteria predict a suboptimal placement of these -control-points. - -# Evaluation of Scenarios -\label{sec:res} - -To compare our results to the ones given by Richter et al.\cite{anrichterEvol}, -we also use Spearman's rank correlation coefficient. Opposed to other popular -coefficients, like the Pearson correlation coefficient, which measures a linear -relationship between variables, the Spearmans's coefficient assesses \glqq how -well an arbitrary monotonic function can descripbe the relationship between two -variables, without making any assumptions about the frequency distribution of -the variables\grqq\cite{hauke2011comparison}. - -As we don't have any prior knowledge if any of the criteria is linear and we are -just interested in a monotonic relation between the criteria and their -predictive power, the Spearman's coefficient seems to fit out scenario best. - -For interpretation of these values we follow the same interpretation used in -\cite{anrichterEvol}, based on \cite{weir2015spearman}: The coefficient -intervals $r_S \in [0,0.2[$, $[0.2,0.4[$, $[0.4,0.6[$, $[0.6,0.8[$, and $[0.8,1]$ are -classified as *very weak*, *weak*, *moderate*, *strong* and *very strong*. We -interpret p--values smaller than $0.1$ as *significant* and cut off the -precision of p--values after four decimal digits (thus often having a p--value -of $0$ given for p--values $< 10^{-4}$). - -As we are looking for anti--correlation (i.e. our criterion should be maximized -indicating a minimal result in --- for example --- the reconstruction--error) -instead of correlation we flip the sign of the correlation--coefficient for -readability and to have the correlation--coefficients be in the -classification--range given above. - -For the evolutionary optimization we employ the CMA--ES (covariance matrix -adaptation evolution strategy) of the shark3.1 library \cite{shark08}, as this -algorithm was used by \cite{anrichterEvol} as well. We leave the parameters at -their sensible defaults as further explained in -\cite[Appendix~A: Table~1]{hansen2016cma}. - ## Results of 1D Function Approximation In the case of our 1D--Optimization--problem, we have the luxury of knowing the @@ -894,21 +857,6 @@ between the variability and the evolutionary error. ### Regularity -\begin{table}[bht] -\centering -\begin{tabular}{c|c|c|c|c} -$5 \times 5$ & $7 \times 4$ & $4 \times 7$ & $7 \times 7$ & $10 \times 10$\\ -\hline -$0.28$ ($0.0045$) & \textcolor{red}{$0.21$} ($0.0396$) & \textcolor{red}{$0.1$} ($0.3019$) & \textcolor{red}{$0.01$} ($0.9216$) & \textcolor{red}{$0.01$} ($0.9185$) -\end{tabular} -\caption[Correlation 1D Regularity/Steps]{Spearman's correlation (and p-values) -between regularity and convergence speed for the 1D function approximation -problem.\newline -Not significant entries are marked in red. -} -\label{tab:1dreg} -\end{table} - \begin{figure}[ht] \centering \includegraphics[width=\textwidth]{img/evolution1d/55_to_1010_steps.png} @@ -920,6 +868,21 @@ dataset.} \label{fig:1dreg} \end{figure} +\begin{table}[b] +\centering +\begin{tabular}{c|c|c|c|c} +$5 \times 5$ & $7 \times 4$ & $4 \times 7$ & $7 \times 7$ & $10 \times 10$\\ +\hline +$0.28$ ($0.0045$) & \textcolor{red}{$0.21$} ($0.0396$) & \textcolor{red}{$0.1$} ($0.3019$) & \textcolor{red}{$0.01$} ($0.9216$) & \textcolor{red}{$0.01$} ($0.9185$) +\end{tabular} +\caption[Correlation 1D Regularity/Steps]{Spearman's correlation (and p-values) +between regularity and convergence speed for the 1D function approximation +problem. +\newline Note: Not significant results are marked in \textcolor{red}{red}. +} +\label{tab:1dreg} +\end{table} + Regularity should correspond to the convergence speed (measured in iteration--steps of the evolutionary algorithm), and is computed as inverse condition number $\kappa(\vec{U})$ of the deformation--matrix. @@ -936,13 +899,11 @@ improvement-potential against the steps next to the regularity--plot. Our theory is that the *very strong* correlation ($-r_S = -0.82, p=0$) between improvement--potential and number of iterations hints that the employed algorithm simply takes longer to converge on a better solution (as seen in -figure \ref{fig:1dvar} and \ref{fig:1dimp}) offsetting any gain the regularity--measurement could -achieve. +figure \ref{fig:1dvar} and \ref{fig:1dimp}) offsetting any gain the +regularity--measurement could achieve. ### Improvement Potential -- Alle Spearman 1 und p-value 0. - \begin{figure}[ht] \centering \includegraphics[width=0.8\textwidth]{img/evolution1d/55_to_1010_improvement-vs-evo-error.png} @@ -952,36 +913,246 @@ grid--resolutions} \label{fig:1dimp} \end{figure} - - - - - +\improvement[inline]{write something about it..} + +- spearman 1 (p=0) +- gradient macht keinen unterschied +- $UU^+$ scheint sehr kleine EW zu haben, s. regularität +- trotzdem sehr gutes kriterium - auch ohne Richtung. + +## Procedure: 3D Function Approximation +\label{sec:proc:3dfa} + +As explained in section \ref{sec:test:3dfa} in detail, we do not know the +analytical solution to the global optimum. Additionally we have the problem of +finding the right correspondences between the original sphere--model and the +target--model, as they consist of $10\,807$ and $12\,024$ vertices respectively, +so we cannot make a one--to--one--correspondence between them as we did in the +one--dimensional case. + +Initially we set up the correspondences $\vec{c_T(\dots)}$ and $\vec{c_S(\dots)}$ to be +the respectively closest vertices of the other model. We then calculate the +analytical solution given these correspondences via $\vec{P^{*}} = \vec{U^+}\vec{T}$, +and also use the first solution as guessed gradient for the calculation of the +*improvement--potential*, as the optimal solution is not known. +We then let the evolutionary algorithm run up within $1.05$ times the error of +this solution and afterwards recalculate the correspondences $\vec{c_T(\dots)}$ +and $\vec{c_S(\dots)}$. + +\begin{figure}[ht] +\begin{center} +\includegraphics[width=\textwidth]{img/example3d_grid.png} +\end{center} +\caption[Example of a 3D--grid]{\newline Left: The 3D--setup with a $4\times +4\times 4$--grid.\newline Right: The same grid after added noise to the +control--points.} +\label{fig:setup3d} +\end{figure} + +For the next step we then halve the regularization--impact $\lambda$ (starting +at $1$) of our *fitness--function* (\ref{eq:fit3d}) and calculate the next +incremental solution $\vec{P^{*}} = \vec{U^+}\vec{T}$ with the updated +correspondences to get our next target--error. We repeat this process as long as +the target--error keeps decreasing and use the number of these iterations as +measure of the convergence speed. As the resulting evolutional error without +regularization is in the numeric range of $\approx 100$, whereas the +regularization is numerically $\approx 7000$ we need at least $10$ to $15$ iterations +until the regularization--effect wears off. + +The grid we use for our experiments is just very coarse due to computational +limitations. We are not interested in a good reconstruction, but an estimate if +the mentioned evolvability criteria are good. + +In figure \ref{fig:setup3d} we show an example setup of the scene with a +$4\times 4\times 4$--grid. Identical to the 1--dimensional scenario before, we create a +regular grid and move the control-points \todo{wie?} random between their +neighbours, but in three instead of two dimensions^[Again, we flip the signs for +the edges, if necessary to have the object still in the convex hull.]. + +\begin{figure}[!htb] +\includegraphics[width=\textwidth]{img/3d_grid_resolution.png} +\caption[Different resolution of 3D grids]{\newline +Left: A $7 \times 4 \times 4$ grid suited to better deform into facial +features.\newline +Right: A $4 \times 4 \times 7$ grid that we expect to perform worse.} +\label{fig:3dgridres} +\end{figure} + +As is clearly visible from figure \ref{fig:3dgridres}, the target--model has many +vertices in the facial area, at the ears and in the neck--region. Therefore we +chose to increase the grid-resolutions for our tests in two different dimensions +and see how well the criteria predict a suboptimal placement of these +control-points. ## Results of 3D Function Approximation +In the 3D--Approximation we tried to evaluate further on the impact of the +grid--layout to the overall criteria. As the target--model has many vertices in +concentrated in the facial area we start from a $4 \times 4 \times 4$ grid and +only increase the number of control points in one dimension, yielding a +resolution of $7 \times 4 \times 4$ and $4 \times 4 \times 7$ respectively. We +visualized those two grids in figure \ref{fig:3dgridres}. -\begin{figure}[!ht] -\includegraphics[width=\textwidth]{img/evolution3d/4x4xX_montage.png} -\caption{Results 3D for 4x4xX} +To evaluate the performance of the evolvability--criteria we also tested a more +neutral resolution of $4 \times 4 \times 4$, $5 \times 5 \times 5$, and $6 \times 6 \times 6$ --- +similar to the 1D--setup. + +\begin{figure}[ht] +\centering +\includegraphics[width=0.7\textwidth]{img/evolution3d/variability_boxplot.png} +\caption[3D Fitting Errors for various grids]{The fitting error for the various +grids we examined.\newline +Note that the number of control--points is a product of the resolution, so $X +\times 4 \times 4$ and $4 \times 4 \times X$ have the same number of +control--points.} +\label{fig:3dvar} \end{figure} -\begin{figure}[!ht] -\includegraphics[width=\textwidth]{img/evolution3d/Xx4x4_montage.png} -\caption{Results 3D for Xx4x4} +### Variability + +\begin{table}[tbh] +\centering +\begin{tabular}{c|c|c|c} +$4 \times 4 \times \mathrm{X}$ & $\mathrm{X} \times 4 \times 4$ & $\mathrm{Y} \times \mathrm{Y} \times \mathrm{Y}$ & all \\ +\hline +0.89 (0) & 0.9 (0) & 0.91 (0) & 0.94 (0) +\end{tabular} +\caption[Correlation between variability and fitting error for 3D]{Correlation +between variability and fitting error for the 3D fitting scenario.\newline +Displayed are the negated Spearman coefficients with the corresponding p-values +in brackets for three cases of increasing variability ($\mathrm{X} \in [4,5,7], +\mathrm{Y} \in [4,5,6]$). +\newline Note: Not significant results are marked in \textcolor{red}{red}.} +\label{tab:3dvar} +\end{table} + +Similar to the 1D case all our tested matrices had a constant rank (being +$m = x \cdot y \cdot z$ for a $x \times y \times z$ grid), so we again have merely plotted +the errors in the boxplot in figure \ref{fig:3dvar}. + +As expected the $\mathrm{X} \times 4 \times 4$ grids performed +slightly better than their $4 \times 4 \times \mathrm{X}$ counterparts with a +mean$\pm$sigma of $101.25 \pm 7.45$ to $102.89 \pm 6.74$ for $\mathrm{X} = 5$ and +$85.37 \pm 7.12$ to $89.22 \pm 6.49$ for $\mathrm{X} = 7$. + +Interestingly both variants end up closer in terms of fitting error than we +anticipated, which shows that the evolutionary algorithm we employed is capable +of correcting a purposefully created \glqq bad\grqq \ grid. Also this confirms, +that in our cases the number of control--points is more important for quality +than their placement, which is captured by the variability via the rank of the +deformation--matrix. + +\begin{figure}[hbt] +\centering +\includegraphics[width=0.8\textwidth]{img/evolution3d/variability2_boxplot.png} +\caption[Histogram of ranks of high--resolution deformation--matrices]{ +Histogram of ranks of various $10 \times 10 \times 10$ grids. +} +\label{fig:histrank3d} \end{figure} -\begin{figure}[!ht] -\includegraphics[width=\textwidth]{img/evolution3d/YxYxY_montage.png} -\caption{Results 3D for YxYxY for Y $\in [4,5,6]$} +Overall the correlation between variability and fitness--error were +*significantly* and showed a *very strong* correlation in all our tests. +The detailed correlation--coefficients are given in table \ref{tab:3dvar} +alongside their p--values. + +As introduces in section \ref{sec:impl:grid} and visualized in figure +\ref{fig:enoughCP}, we know, that not all control points have to necessarily +contribute to the parametrization of our 3D--model. Because we are starting from +a sphere, some control-points are too far away from the surface to contribute +to the deformation at all. + +One can already see in 2D in figure \ref{fig:enoughCP}, that this effect +starts with a regular $9 \times 9$ grid on a perfect circle. To make sure we +observe this, we evaluated the variability for 100 randomly moved $10 \times 10 \times 10$ +grids on the sphere we start out with. + +As the variability is defined by $\frac{\mathrm{rank}(\vec{U})}{n}$ we can +easily recover the rank of the deformation--matrix $\vec{U}$. The results are +shown in the histogram in figure \ref{fig:histrank3d}. Especially in the centre +of the sphere and in the corners of our grid we effectively loose +control--points for our parametrization. + +This of course yields a worse error as when those control--points would be put +to use and one should expect a loss in quality evident by a higher +reconstruction--error opposed to a grid where they are used. Sadly we could not +run a in--depth test on this due to computational limitations. + +Nevertheless this hints at the notion, that variability is a good measure for +the overall quality of a fit. + +### Regularity + +\begin{table}[tbh] +\centering +\begin{tabular}{c|c|c|c} + & $5 \times 4 \times 4$ & $7 \times 4 \times 4$ & $\mathrm{X} \times 4 \times 4$ \\ +\cline{2-4} + & \textcolor{red}{0.15} (0.147) & \textcolor{red}{0.09} (0.37) & 0.46 (0) \B \\ +\cline{2-4} +\multicolumn{4}{c}{} \\[-1.4em] +\hline +$4 \times 4 \times 4$ & $4 \times 4 \times 5$ & $4 \times 4 \times 7$ & $4 \times 4 \times \mathrm{X}$ \T \\ +\hline +0.38 (0) & \textcolor{red}{0.17} (0.09) & 0.40 (0) & 0.46 (0) \B \\ +\hline +\multicolumn{4}{c}{} \\[-1.4em] +\cline{2-4} + & $5 \times 5 \times 5$ & $6 \times 6 \times 6$ & $\mathrm{Y} \times \mathrm{Y} \times \mathrm{Y}$ \T \\ +\cline{2-4} + & \textcolor{red}{-0.18} (0.0775) & \textcolor{red}{-0.13} (0.1715) & -0.25 (0) \B \\ +\cline{2-4} +\multicolumn{4}{c}{} \\[-1.4em] +\cline{2-4} +\multicolumn{3}{c}{} & all: 0.15 (0) \T +\end{tabular} +\caption[Correlation between regularity and iterations for 3D]{Correlation +between regularity and number of iterations for the 3D fitting scenario. +Displayed are the negated Spearman coefficients with the corresponding p--values +in brackets for various given grids ($\mathrm{X} \in [4,5,7], \mathrm{Y} \in [4,5,6]$). +\newline Note: Not significant results are marked in \textcolor{red}{red}.} +\label{tab:3dvar} +\end{table} + + + +Opposed to the predictions of variability our test on regularity gave a mixed +result --- similar to the 1D--case. + +In half scenarios we have a *significant*, but *weak* to *moderate* correlation +between regularity and number of iterations. On the other hand in the scenarios +where we increased the number of control--points, namely $125$ for the +$5 \times 5 \times 5$ grid and $216$ for the $6 \times 6 \times 6$ grid we found +a *significant*, but *weak* anti--correlation, which seem to contradict the +findings/trends for the sets with $64$, $80$, and $112$ control--points (first +two rows of table \ref{tab:3dvar}). + +Taking all results together we only find a *very weak*, but *significant* link +between regularity and the number of iterations needed for the algorithm to +converge. + +\begin{figure}[!htb] +\centering +\includegraphics[width=\textwidth]{img/evolution3d/regularity_montage.png} +\caption[Regularity for different 3D--grids]{ +**BLINDTEXT** +} +\label{fig:resreg3d} +\end{figure} + +As can be seen from figure \ref{fig:resreg3d}, we can observe\todo{things}. + +### Improvement Potential + +\begin{figure}[!htb] +\centering +\includegraphics[width=\textwidth]{img/evolution3d/improvement_montage.png} +\caption[Improvement potential for different 3D--grids]{ +**BLINDTEXT** +} +\label{fig:resimp3d} \end{figure} - - - - - - # Schluss \label{sec:dis} diff --git a/arbeit/ma.pdf b/arbeit/ma.pdf index 9fa5a96b908f94bf685527ed0c2d2605be1ac523..085731ec3b70ca22ca69d28f2dae2b1856d99e93 100644 GIT binary patch delta 534444 zcmY(qQ*b6+u&^83m?RUM6XT6-+Y{S%-q^Nn+s?$cZQDBE-ltBT|G!vOeX%aP`swxb z>h_Wf(ENrT&^UG=8y_E>le43VfeoDdx=o^NY$hX0$juif-|zCfcX-^Flr3u#RV^3( z)ADnFNV9qo`(F}8k1KB0p<80naRIOo)7%e}e%q+R81x~m;#xRL*eW-(+$0&6uHU*k zJm#7xV{-*@0gNdH)J&Y~MH{#sf99q#h$(R90ty`?lT^rn(0|Z%(3JBU-h$Oulz8FP>=duf6#Z`xo4(q0u3v z_M@oq7p$RxD^Yh#Q(8nw$uy{zdVbodT%}P8IKqS#4h_QN+AXfmxm?43`UKANDBy9R z`4Vjv)Kt#aH>5h~(}u4?kpK*07}>Ct^gQ=ORyW^Pes6c%5QNn$ZFM~s(*zK_n((-v zHwub$2oImr5@k;obUGF&KkKdMo(H?q^k&rX#Ew3o&xN&FtAmhk;{E647SjQm7<%H!z+ zv7Yy}uzABgKN%UjNoO8`2g`r`f(C>UJzgu6x*0-!MnMBPJLXCkI3$LG24VwaArsnr z{BQ`kqL}KKP$nENKXGz$hdZLD8Qp%Rq$e8JJAPbe?dNA`p)IE?bzNrms~vbO>28JC 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regularity,variability,improvement,"Evolution error",steps +# 6.57581e-05,0.00592209,0.622392,113.016,2368 + +if [[ -f "$2" ]]; then + +R -q --slave --vanilla < " +fi + diff --git a/dokumentation/evolution3d/Xx4x4.csv b/dokumentation/evolution3d/Xx4x4.csv index 1ece114..92e9b0d 100644 --- a/dokumentation/evolution3d/Xx4x4.csv +++ b/dokumentation/evolution3d/Xx4x4.csv @@ -1,301 +1,301 @@ regularity,variability,improvement,"Evolution error",steps -6.57581e-05,0.00592209,0.622392,113.016.,2368 -5.16451e-05,0.00592209,0.610293,118.796.,2433 -6.45083e-05,0.00592209,0.592139,127.157.,1655 -7.14801e-05,0.00592209,0.624039,121.613.,1933 -5.62707e-05,0.00592209,0.611091,119.539.,2618 -5.55953e-05,0.00592209,0.625812,119.512.,2505 -5.96026e-05,0.00592209,0.622873,118.285.,1582 -6.63676e-05,0.00592209,0.602386,126.579.,2214 -5.93125e-05,0.00592209,0.608913,122.512.,2262 -6.05066e-05,0.00592209,0.621467,118.473.,2465 -6.42976e-05,0.00592209,0.602593,121.998.,2127 -5.32868e-05,0.00592209,0.616501,115.313.,2746 -5.47856e-05,0.00592209,0.615173,118.034.,2148 -6.47209e-05,0.00592209,0.603935,120.003.,2304 -7.07812e-05,0.00592209,0.620422,123.494.,1941 -6.49313e-05,0.00592209,0.616232,122.989.,2214 -6.64295e-05,0.00592209,0.605206,123.757.,1675 -5.88806e-05,0.00592209,0.628055,110.67.,2230 -7.56461e-05,0.00592209,0.625361,121.232.,2187 -4.932e-05,0.00592209,0.612261,120.979.,2280 -5.45998e-05,0.00592209,0.61935,115.394.,2380 -6.10654e-05,0.00592209,0.614029,116.928.,2327 -6.09488e-05,0.00592209,0.611892,125.294.,1609 -5.85691e-05,0.00592209,0.632686,111.635.,2831 -6.87292e-05,0.00592209,0.61519,114.681.,2565 -6.53377e-05,0.00592209,0.627408,111.935.,2596 -6.98345e-05,0.00592209,0.616158,111.392.,2417 -7.90547e-05,0.00592209,0.620575,115.346.,2031 -6.50231e-05,0.00592209,0.625725,119.055.,1842 -6.76541e-05,0.00592209,0.625399,117.452.,1452 -5.72222e-05,0.00592209,0.614171,123.379.,2186 -7.42483e-05,0.00592209,0.624683,115.053.,2236 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+86.4099 +87.3714 +77.0284 +74.9314 +87.7317 +91.005 +76.2978 +84.0268 +82.958 +80.859 +78.3619 +87.6379 +82.0693 +75.4678 +85.7208 +78.6163 +97.2452 +80.0625 +85.7072 +75.0646 +82.1324 +90.3791 +99.9413 +72.5502 +83.4268 +87.4954 +83.3203 +91.7128 diff --git a/dokumentation/evolution3d/Xx4x4.gnuplot.fit.log b/dokumentation/evolution3d/Xx4x4.gnuplot.fit.log index 9c7e917..bb17725 100644 --- a/dokumentation/evolution3d/Xx4x4.gnuplot.fit.log +++ b/dokumentation/evolution3d/Xx4x4.gnuplot.fit.log @@ -1,7 +1,7 @@ ******************************************************************************* -Mon Oct 16 12:15:22 2017 +Wed Oct 25 19:14:30 2017 FIT: data read from "Xx4x4.csv" every ::1 using 1:5 @@ -47,7 +47,7 @@ b -0.934 1.000 ******************************************************************************* -Mon Oct 16 12:15:22 2017 +Wed Oct 25 19:14:30 2017 FIT: data read from "Xx4x4.csv" every ::1 using 3:5 @@ -93,7 +93,7 @@ bb -0.999 1.000 ******************************************************************************* -Mon Oct 16 12:15:22 2017 +Wed Oct 25 19:14:30 2017 FIT: data read from "Xx4x4.csv" every ::1 using 3:4 @@ -139,7 +139,7 @@ bbb -0.999 1.000 ******************************************************************************* -Mon Oct 16 12:15:22 2017 +Wed Oct 25 19:14:30 2017 FIT: data read from "Xx4x4.csv" every ::1 using 2:4 diff --git a/dokumentation/evolution3d/Xx4x4.gnuplot.script b/dokumentation/evolution3d/Xx4x4.gnuplot.script index e4a19e8..3d5f05d 100644 --- a/dokumentation/evolution3d/Xx4x4.gnuplot.script +++ b/dokumentation/evolution3d/Xx4x4.gnuplot.script @@ -5,22 +5,22 @@ set terminal png set xlabel 'regularity' set ylabel 'steps' set output "Xx4x4_regularity-vs-steps.png" -plot "20170926_3dFit_4x4x4_100times.csv" every ::1 using 1:5 title "4x4x4", "20171013_3dFit_5x4x4_100times.csv" every ::1 using 1:5 title "5x4x4", "20171005_3dFit_7x4x4_100times.csv" every ::1 using 1:5 title "7x4x4", f(x) title "lin. fit" lc rgb "black" +plot "20170926_3dFit_4x4x4_100times.csv" every ::1 using 1:5 title "4x4x4" pt 2, "20171013_3dFit_5x4x4_100times.csv" every ::1 using 1:5 title "5x4x4" pt 2, "20171005_3dFit_7x4x4_100times.csv" every ::1 using 1:5 title "7x4x4" pt 2, f(x) title "lin. fit" lc rgb "black" g(x)=aa*x+bb fit g(x) "Xx4x4.csv" every ::1 using 3:5 via aa,bb set xlabel 'improvement potential' set ylabel 'steps' set output "Xx4x4_improvement-vs-steps.png" -plot "20170926_3dFit_4x4x4_100times.csv" every ::1 using 3:5 title "4x4x4", "20171013_3dFit_5x4x4_100times.csv" every ::1 using 3:5 title "5x4x4", "20171005_3dFit_7x4x4_100times.csv" every ::1 using 3:5 title "7x4x4", g(x) title "lin. fit" lc rgb "black" +plot "20170926_3dFit_4x4x4_100times.csv" every ::1 using 3:5 title "4x4x4" pt 2, "20171013_3dFit_5x4x4_100times.csv" every ::1 using 3:5 title "5x4x4" pt 2, "20171005_3dFit_7x4x4_100times.csv" every ::1 using 3:5 title "7x4x4" pt 2, g(x) title "lin. fit" lc rgb "black" h(x)=aaa*x+bbb fit h(x) "Xx4x4.csv" every ::1 using 3:4 via aaa,bbb set xlabel 'improvement potential' set ylabel 'evolution error' set output "Xx4x4_improvement-vs-evo-error.png" -plot "20170926_3dFit_4x4x4_100times.csv" every ::1 using 3:4 title "4x4x4", "20171013_3dFit_5x4x4_100times.csv" every ::1 using 3:4 title "5x4x4", "20171005_3dFit_7x4x4_100times.csv" every ::1 using 3:4 title "7x4x4", h(x) title "lin. fit" lc rgb "black" +plot "20170926_3dFit_4x4x4_100times.csv" every ::1 using 3:4 title "4x4x4" pt 2, "20171013_3dFit_5x4x4_100times.csv" every ::1 using 3:4 title "5x4x4" pt 2, "20171005_3dFit_7x4x4_100times.csv" every ::1 using 3:4 title "7x4x4" pt 2, h(x) title "lin. fit" lc rgb "black" i(x)=aaaa*x+bbbb fit i(x) "Xx4x4.csv" every ::1 using 2:4 via aaaa,bbbb set xlabel 'variability' set ylabel 'evolution error' set output "Xx4x4_variability-vs-evo-error.png" -plot "20170926_3dFit_4x4x4_100times.csv" every ::1 using 2:4 title "4x4x4", "20171013_3dFit_5x4x4_100times.csv" every ::1 using 2:4 title "5x4x4", "20171005_3dFit_7x4x4_100times.csv" every ::1 using 2:4 title "7x4x4", i(x) title "lin. fit" lc rgb "black" +plot "20170926_3dFit_4x4x4_100times.csv" every ::1 using 2:4 title "4x4x4" pt 2, "20171013_3dFit_5x4x4_100times.csv" every ::1 using 2:4 title "5x4x4" pt 2, "20171005_3dFit_7x4x4_100times.csv" every ::1 using 2:4 title "7x4x4" pt 2, i(x) title "lin. fit" lc rgb "black" diff --git a/dokumentation/evolution3d/Xx4x4.mms b/dokumentation/evolution3d/Xx4x4.mms new file mode 100644 index 0000000..e138d53 --- /dev/null +++ b/dokumentation/evolution3d/Xx4x4.mms @@ -0,0 +1,9 @@ +[1] "================ Analyzing Xx4x4.csv" +[1] "Mean:" +[1] 101.9338 +[1] "Median:" +[1] 101.4365 +[1] "Sigma:" +[1] 15.31929 +[1] "Range:" +[1] 72.2744 130.8540 diff --git a/dokumentation/evolution3d/Xx4x4.spearman b/dokumentation/evolution3d/Xx4x4.spearman new file mode 100644 index 0000000..6268991 --- /dev/null +++ b/dokumentation/evolution3d/Xx4x4.spearman @@ -0,0 +1,49 @@ +[1] 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b/dokumentation/evolution3d/all.gnuplot.fit.log @@ -0,0 +1,184 @@ + + +******************************************************************************* +Wed Oct 25 19:09:05 2017 + + +FIT: data read from "all.csv" every ::1 using 1:5 + format = x:z + #datapoints = 910 + residuals are weighted equally (unit weight) + +function used for fitting: f(x) +fitted parameters initialized with current variable values + + + + Iteration 0 + WSSR : 2.69952e+09 delta(WSSR)/WSSR : 0 + delta(WSSR) : 0 limit for stopping : 1e-05 + lambda : 0.707107 + +initial set of free parameter values + +a = 1 +b = 1 + +After 6 iterations the fit converged. +final sum of squares of residuals : 5.77426e+08 +rel. change during last iteration : -1.48436e-07 + +degrees of freedom (FIT_NDF) : 908 +rms of residuals (FIT_STDFIT) = sqrt(WSSR/ndf) : 797.454 +variance of residuals (reduced chisquare) = WSSR/ndf : 635932 + +Final set of parameters Asymptotic Standard Error +======================= ========================== + +a = -5.38736e+06 +/- 8.165e+05 (15.16%) +b = 1966.44 +/- 72.92 (3.708%) + + +correlation matrix of the fit parameters: + + a b +a 1.000 +b -0.932 1.000 + + +******************************************************************************* +Wed Oct 25 19:09:05 2017 + + +FIT: data read from "all.csv" every ::1 using 3:5 + format = x:z + #datapoints = 910 + residuals are weighted equally (unit weight) + +function used for fitting: g(x) +fitted parameters initialized with current variable values + + + + Iteration 0 + WSSR : 2.6977e+09 delta(WSSR)/WSSR : 0 + delta(WSSR) : 0 limit for stopping : 1e-05 + lambda : 0.857335 + +initial set of free parameter values + +aa = 1 +bb = 1 + +After 3 iterations the fit converged. +final sum of squares of residuals : 3.3878e+08 +rel. change during last iteration : -3.41053e-07 + +degrees of freedom (FIT_NDF) : 908 +rms of residuals (FIT_STDFIT) = sqrt(WSSR/ndf) : 610.824 +variance of residuals (reduced chisquare) = WSSR/ndf : 373106 + +Final set of parameters Asymptotic Standard Error +======================= ========================== + +aa = -8301.78 +/- 310.7 (3.743%) +bb = 7184 +/- 213 (2.965%) + + +correlation matrix of the fit parameters: + + aa bb +aa 1.000 +bb -0.995 1.000 + + +******************************************************************************* +Wed Oct 25 19:09:05 2017 + + +FIT: data read from "all.csv" every ::1 using 3:4 + format = x:z + #datapoints = 910 + residuals are weighted equally (unit weight) + +function used for fitting: h(x) +fitted parameters initialized with current variable values + + + + Iteration 0 + WSSR : 8.64029e+06 delta(WSSR)/WSSR : 0 + delta(WSSR) : 0 limit for stopping : 1e-05 + lambda : 0.857335 + +initial set of free parameter values + +aaa = 1 +bbb = 1 + +After 3 iterations the fit converged. +final sum of squares of residuals : 44319.2 +rel. change during last iteration : -3.6749e-06 + +degrees of freedom (FIT_NDF) : 908 +rms of residuals (FIT_STDFIT) = sqrt(WSSR/ndf) : 6.98639 +variance of residuals (reduced chisquare) = WSSR/ndf : 48.8097 + +Final set of parameters Asymptotic Standard Error +======================= ========================== + +aaa = -292.832 +/- 3.554 (1.214%) +bbb = 296.825 +/- 2.437 (0.8209%) + + +correlation matrix of the fit parameters: + + aaa bbb +aaa 1.000 +bbb -0.995 1.000 + + +******************************************************************************* +Wed Oct 25 19:09:05 2017 + + +FIT: data read from "all.csv" every ::1 using 2:4 + format = x:z + #datapoints = 910 + residuals are weighted equally (unit weight) + +function used for fitting: i(x) +fitted parameters initialized with current variable values + + + + Iteration 0 + WSSR : 8.75529e+06 delta(WSSR)/WSSR : 0 + delta(WSSR) : 0 limit for stopping : 1e-05 + lambda : 0.707146 + +initial set of free parameter values + +aaaa = 1 +bbbb = 1 + +After 4 iterations the fit converged. +final sum of squares of residuals : 84605.2 +rel. change during last iteration : -1.31864e-06 + +degrees of freedom (FIT_NDF) : 908 +rms of residuals (FIT_STDFIT) = sqrt(WSSR/ndf) : 9.65285 +variance of residuals (reduced chisquare) = WSSR/ndf : 93.1775 + +Final set of parameters Asymptotic Standard Error +======================= ========================== + +aaaa = -4091.03 +/- 73.19 (1.789%) +bbbb = 136.014 +/- 0.7684 (0.5649%) + + +correlation matrix of the fit parameters: + + aaaa bbbb +aaaa 1.000 +bbbb -0.909 1.000 diff --git a/dokumentation/evolution3d/all.gnuplot.log b/dokumentation/evolution3d/all.gnuplot.log new file mode 100644 index 0000000..651dd02 --- /dev/null +++ b/dokumentation/evolution3d/all.gnuplot.log @@ -0,0 +1,304 @@ + + + Iteration 0 + WSSR : 2.69952e+09 delta(WSSR)/WSSR : 0 + delta(WSSR) : 0 limit for stopping : 1e-05 + lambda : 0.707107 + +initial set of free parameter values + +a = 1 +b = 1 +/ + + Iteration 1 + WSSR : 6.0511e+08 delta(WSSR)/WSSR : -3.4612 + delta(WSSR) : -2.09441e+09 limit for stopping : 1e-05 + lambda : 0.0707107 + +resultant parameter values + +a = -9.15081 +b = 1517.25 +/ + + Iteration 2 + WSSR : 6.05099e+08 delta(WSSR)/WSSR : -1.84933e-05 + delta(WSSR) : -11190.3 limit for stopping : 1e-05 + lambda : 0.00707107 + +resultant parameter values + +a = -1036.65 +b = 1518.17 +/ + + Iteration 3 + WSSR : 6.04072e+08 delta(WSSR)/WSSR : -0.00169898 + delta(WSSR) : -1.02631e+06 limit for stopping : 1e-05 + lambda : 0.000707107 + +resultant parameter values + +a = -101864 +b = 1526.56 +/ + + Iteration 4 + WSSR : 5.80578e+08 delta(WSSR)/WSSR : -0.040467 + delta(WSSR) : -2.34943e+07 limit for stopping : 1e-05 + lambda : 7.07107e-05 + +resultant parameter values + +a = -3.56955e+06 +b = 1815.15 +/ + + Iteration 5 + WSSR : 5.77427e+08 delta(WSSR)/WSSR : -0.00545821 + delta(WSSR) : -3.15172e+06 limit for stopping : 1e-05 + lambda : 7.07107e-06 + +resultant parameter values + +a = -5.37788e+06 +b = 1965.65 +/ + + Iteration 6 + WSSR : 5.77426e+08 delta(WSSR)/WSSR : -1.48436e-07 + delta(WSSR) : -85.7109 limit for stopping : 1e-05 + lambda : 7.07107e-07 + +resultant parameter values + +a = -5.38736e+06 +b = 1966.44 + +After 6 iterations the fit converged. +final sum of squares of residuals : 5.77426e+08 +rel. change during last iteration : -1.48436e-07 + +degrees of freedom (FIT_NDF) : 908 +rms of residuals (FIT_STDFIT) = sqrt(WSSR/ndf) : 797.454 +variance of residuals (reduced chisquare) = WSSR/ndf : 635932 + +Final set of parameters Asymptotic Standard Error +======================= ========================== + +a = -5.38736e+06 +/- 8.165e+05 (15.16%) +b = 1966.44 +/- 72.92 (3.708%) + + +correlation matrix of the fit parameters: + + a b +a 1.000 +b -0.932 1.000 + + + Iteration 0 + WSSR : 2.6977e+09 delta(WSSR)/WSSR : 0 + delta(WSSR) : 0 limit for stopping : 1e-05 + lambda : 0.857335 + +initial set of free parameter values + +aa = 1 +bb = 1 +/ + + Iteration 1 + WSSR : 3.537e+08 delta(WSSR)/WSSR : -6.62708 + delta(WSSR) : -2.344e+09 limit for stopping : 1e-05 + lambda : 0.0857335 + +resultant parameter values + +aa = -6338.16 +bb = 5839.13 +/ + + Iteration 2 + WSSR : 3.3878e+08 delta(WSSR)/WSSR : -0.0440412 + delta(WSSR) : -1.49203e+07 limit for stopping : 1e-05 + lambda : 0.00857335 + +resultant parameter values + +aa = -8296.31 +bb = 7180.26 +/ + + Iteration 3 + WSSR : 3.3878e+08 delta(WSSR)/WSSR : -3.41053e-07 + delta(WSSR) : -115.542 limit for stopping : 1e-05 + lambda : 0.000857335 + +resultant parameter values + +aa = -8301.78 +bb = 7184 + +After 3 iterations the fit converged. +final sum of squares of residuals : 3.3878e+08 +rel. change during last iteration : -3.41053e-07 + +degrees of freedom (FIT_NDF) : 908 +rms of residuals (FIT_STDFIT) = sqrt(WSSR/ndf) : 610.824 +variance of residuals (reduced chisquare) = WSSR/ndf : 373106 + +Final set of parameters Asymptotic Standard Error +======================= ========================== + +aa = -8301.78 +/- 310.7 (3.743%) +bb = 7184 +/- 213 (2.965%) + + +correlation matrix of the fit parameters: + + aa bb +aa 1.000 +bb -0.995 1.000 + + + Iteration 0 + WSSR : 8.64029e+06 delta(WSSR)/WSSR : 0 + delta(WSSR) : 0 limit for stopping : 1e-05 + lambda : 0.857335 + +initial set of free parameter values + +aaa = 1 +bbb = 1 +/ + + Iteration 1 + WSSR : 65352.7 delta(WSSR)/WSSR : -131.21 + delta(WSSR) : -8.57494e+06 limit for stopping : 1e-05 + lambda : 0.0857335 + +resultant parameter values + +aaa = -219.119 +bbb = 246.318 +/ + + Iteration 2 + WSSR : 44319.4 delta(WSSR)/WSSR : -0.474585 + delta(WSSR) : -21033.3 limit for stopping : 1e-05 + lambda : 0.00857335 + +resultant parameter values + +aaa = -292.627 +bbb = 296.685 +/ + + Iteration 3 + WSSR : 44319.2 delta(WSSR)/WSSR : -3.6749e-06 + delta(WSSR) : -0.162868 limit for stopping : 1e-05 + lambda : 0.000857335 + +resultant parameter values + +aaa = -292.832 +bbb = 296.825 + +After 3 iterations the fit converged. +final sum of squares of residuals : 44319.2 +rel. change during last iteration : -3.6749e-06 + +degrees of freedom (FIT_NDF) : 908 +rms of residuals (FIT_STDFIT) = sqrt(WSSR/ndf) : 6.98639 +variance of residuals (reduced chisquare) = WSSR/ndf : 48.8097 + +Final set of parameters Asymptotic Standard Error +======================= ========================== + +aaa = -292.832 +/- 3.554 (1.214%) +bbb = 296.825 +/- 2.437 (0.8209%) + + +correlation matrix of the fit parameters: + + aaa bbb +aaa 1.000 +bbb -0.995 1.000 + + + Iteration 0 + WSSR : 8.75529e+06 delta(WSSR)/WSSR : 0 + delta(WSSR) : 0 limit for stopping : 1e-05 + lambda : 0.707146 + +initial set of free parameter values + +aaaa = 1 +bbbb = 1 +/ + + Iteration 1 + WSSR : 356710 delta(WSSR)/WSSR : -23.5445 + delta(WSSR) : -8.39858e+06 limit for stopping : 1e-05 + lambda : 0.0707146 + +resultant parameter values + +aaaa = -135.643 +bbbb = 98.21 +/ + + Iteration 2 + WSSR : 98176.3 delta(WSSR)/WSSR : -2.63337 + delta(WSSR) : -258534 limit for stopping : 1e-05 + lambda : 0.00707146 + +resultant parameter values + +aaaa = -3207.68 +bbbb = 127.583 +/ + + Iteration 3 + WSSR : 84605.3 delta(WSSR)/WSSR : -0.160403 + delta(WSSR) : -13570.9 limit for stopping : 1e-05 + lambda : 0.000707146 + +resultant parameter values + +aaaa = -4088.49 +bbbb = 135.99 +/ + + Iteration 4 + WSSR : 84605.2 delta(WSSR)/WSSR : -1.31864e-06 + delta(WSSR) : -0.111564 limit for stopping : 1e-05 + lambda : 7.07146e-05 + +resultant parameter values + +aaaa = -4091.03 +bbbb = 136.014 + +After 4 iterations the fit converged. +final sum of squares of residuals : 84605.2 +rel. change during last iteration : -1.31864e-06 + +degrees of freedom (FIT_NDF) : 908 +rms of residuals (FIT_STDFIT) = sqrt(WSSR/ndf) : 9.65285 +variance of residuals (reduced chisquare) = WSSR/ndf : 93.1775 + +Final set of parameters Asymptotic Standard Error +======================= ========================== + +aaaa = -4091.03 +/- 73.19 (1.789%) +bbbb = 136.014 +/- 0.7684 (0.5649%) + + +correlation matrix of the fit parameters: + + aaaa bbbb +aaaa 1.000 +bbbb -0.909 1.000 diff --git a/dokumentation/evolution3d/all.gnuplot.script b/dokumentation/evolution3d/all.gnuplot.script new file mode 100644 index 0000000..0175d8f --- /dev/null +++ b/dokumentation/evolution3d/all.gnuplot.script @@ -0,0 +1,26 @@ +set datafile separator "," +f(x)=a*x+b +fit f(x) "all.csv" every ::1 using 1:5 via a,b +set terminal png +set xlabel 'regularity' +set ylabel 'steps' +set output "all_regularity-vs-steps.png" +plot "20170926_3dFit_4x4x4_100times.csv" every ::1 using 1:5 title "4x4x4" pt 2, "20171013_3dFit_5x4x4_100times.csv" every ::1 using 1:5 title "5x4x4" pt 2, "20171005_3dFit_7x4x4_100times.csv" every ::1 using 1:5 title "7x4x4" pt 2, "20171005_3dFit_4x4x5_100times.csv" every ::1 using 1:5 title "4x4x5" pt 2, "20171013_3dFit_4x4x7_100times.csv" every ::1 using 1:5 title "4x4x7" pt 2, "20170926_3dFit_5x5x5_100times.csv" every ::1 using 1:5 title "5x5x5" pt 2, "20171021-evolution3D_6x6_100Times.csv" every ::1 using 1:5 title "6x6x6" pt 2, f(x) title "lin. fit" lc rgb "black" +g(x)=aa*x+bb +fit g(x) "all.csv" every ::1 using 3:5 via aa,bb +set xlabel 'improvement potential' +set ylabel 'steps' +set output "all_improvement-vs-steps.png" +plot "20170926_3dFit_4x4x4_100times.csv" every ::1 using 3:5 title "4x4x4" pt 2, "20171013_3dFit_5x4x4_100times.csv" every ::1 using 3:5 title "5x4x4" pt 2, "20171005_3dFit_7x4x4_100times.csv" every ::1 using 3:5 title "7x4x4" pt 2, "20171005_3dFit_4x4x5_100times.csv" every ::1 using 3:5 title "4x4x5" pt 2, "20171013_3dFit_4x4x7_100times.csv" every ::1 using 3:5 title "4x4x7" pt 2, "20170926_3dFit_5x5x5_100times.csv" every ::1 using 3:5 title "5x5x5" pt 2, "20171021-evolution3D_6x6_100Times.csv" every ::1 using 3:5 title "6x6x6" pt 2, g(x) title "lin. fit" lc rgb "black" +h(x)=aaa*x+bbb +fit h(x) "all.csv" every ::1 using 3:4 via aaa,bbb +set xlabel 'improvement potential' +set ylabel 'evolution error' +set output "all_improvement-vs-evo-error.png" +plot "20170926_3dFit_4x4x4_100times.csv" every ::1 using 3:4 title "4x4x4" pt 2, "20171013_3dFit_5x4x4_100times.csv" every ::1 using 3:4 title "5x4x4" pt 2, "20171005_3dFit_7x4x4_100times.csv" every ::1 using 3:4 title "7x4x4" pt 2, "20171005_3dFit_4x4x5_100times.csv" every ::1 using 3:4 title "4x4x5" pt 2, "20171013_3dFit_4x4x7_100times.csv" every ::1 using 3:4 title "4x4x7" pt 2, "20170926_3dFit_5x5x5_100times.csv" every ::1 using 3:4 title "5x5x5" pt 2, "20171021-evolution3D_6x6_100Times.csv" every ::1 using 3:4 title "6x6x6" pt 2, h(x) title "lin. fit" lc rgb "black" +i(x)=aaaa*x+bbbb +fit i(x) "all.csv" every ::1 using 2:4 via aaaa,bbbb +set xlabel 'variability' +set ylabel 'evolution error' +set output "all_variability-vs-evo-error.png" +plot "20170926_3dFit_4x4x4_100times.csv" every ::1 using 2:4 title "4x4x4" pt 2, "20171013_3dFit_5x4x4_100times.csv" every ::1 using 2:4 title "5x4x4" pt 2, "20171005_3dFit_7x4x4_100times.csv" every ::1 using 2:4 title "7x4x4" pt 2, "20171005_3dFit_4x4x5_100times.csv" every ::1 using 2:4 title "4x4x5" pt 2, "20171013_3dFit_4x4x7_100times.csv" every ::1 using 2:4 title "4x4x7" pt 2, "20170926_3dFit_5x5x5_100times.csv" every ::1 using 2:4 title "5x5x5" pt 2, "20171021-evolution3D_6x6_100Times.csv" every ::1 using 2:4 title "6x6x6" pt 2, i(x) title "lin. fit" lc rgb "black" diff --git a/dokumentation/evolution3d/all.mms b/dokumentation/evolution3d/all.mms new file mode 100644 index 0000000..864f65c --- /dev/null +++ b/dokumentation/evolution3d/all.mms @@ -0,0 +1,9 @@ +[1] "================ Analyzing all.csv" +[1] "Mean:" +[1] 96.96886 +[1] "Median:" +[1] 97.8825 +[1] "Sigma:" +[1] 20.3298 +[1] "Range:" +[1] 52.0186 130.8540 diff --git a/dokumentation/evolution3d/all.spearman b/dokumentation/evolution3d/all.spearman new file mode 100644 index 0000000..0c55cb2 --- /dev/null +++ b/dokumentation/evolution3d/all.spearman @@ -0,0 +1,49 @@ +[1] "================ Analyzing all.csv" +[1] "spearman for improvement-potential vs. evolution-error" + x y +x 1.00 -0.95 +y -0.95 1.00 + +n= 910 + + +P + x y +x 0 +y 0 +[1] "spearman for improvement-potential vs. steps" 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zcc&Fr@EC&5qdFUn#>-<4*Ys&Nhi@7G@JRQAdas>f=?AtKk~QKqY=(5nNy!2|aAq;= z%oXOtqKqXKL)P54u4BSL7|3V$9>YC73%0w!AH@g#Z_oMfXK`sApOkYESvW}M$cxPH zjpmS7BLV}_mV6L|$HmYqWak~1Pb-f)hQsa-St@Bv3_NFB#`tY)1VY1#GVAn=-f*4! zlPU1oMc#F&yg1!?B|!Y5(of&_G!*WH?NB}jk|%gf^Ku- zOX886y>S3%<*TQb75kPmT3&8<{i&uoU$%FsYF(LXRPcE^%jStK@>h06G^X+Dar%*H3@xO$JS2Y#oPD9qJK`00 y`U}|){6c|#MrYW5t%qF^%=tA1`(Kj*T+5QT0~Wc@dpe^3!j2xXH-BbIqWll7btXdq literal 0 HcmV?d00001 diff --git a/dokumentation/evolution3d/combine.sh b/dokumentation/evolution3d/combine.sh index e554650..ee08351 100755 --- a/dokumentation/evolution3d/combine.sh +++ b/dokumentation/evolution3d/combine.sh @@ -14,9 +14,9 @@ set xlabel 'regularity' set ylabel 'steps' set output "${png}_regularity-vs-steps.png" plot \ - "$2" every ::1 using 1:5 title "$3", \ - "$4" every ::1 using 1:5 title "$5", \ - "$6" every ::1 using 1:5 title "$7", \ + "$2" every ::1 using 1:5 title "$3" pt 2, \ + "$4" every ::1 using 1:5 title "$5" pt 2, \ + "$6" every ::1 using 1:5 title "$7" pt 2, \ f(x) title "lin. fit" lc rgb "black" g(x)=aa*x+bb fit g(x) "$data" every ::1 using 3:5 via aa,bb @@ -24,9 +24,9 @@ set xlabel 'improvement potential' set ylabel 'steps' set output "${png}_improvement-vs-steps.png" plot \ - "$2" every ::1 using 3:5 title "$3", \ - "$4" every ::1 using 3:5 title "$5", \ - "$6" every ::1 using 3:5 title "$7", \ + "$2" every ::1 using 3:5 title "$3" pt 2, \ + "$4" every ::1 using 3:5 title "$5" pt 2, \ + "$6" every ::1 using 3:5 title "$7" pt 2, \ g(x) title "lin. fit" lc rgb "black" h(x)=aaa*x+bbb fit h(x) "$data" every ::1 using 3:4 via aaa,bbb @@ -34,9 +34,9 @@ set xlabel 'improvement potential' set ylabel 'evolution error' set output "${png}_improvement-vs-evo-error.png" plot \ - "$2" every ::1 using 3:4 title "$3", \ - "$4" every ::1 using 3:4 title "$5", \ - "$6" every ::1 using 3:4 title "$7", \ + "$2" every ::1 using 3:4 title "$3" pt 2, \ + "$4" every ::1 using 3:4 title "$5" pt 2, \ + "$6" every ::1 using 3:4 title "$7" pt 2, \ h(x) title "lin. fit" lc rgb "black" i(x)=aaaa*x+bbbb fit i(x) "$data" every ::1 using 2:4 via aaaa,bbbb @@ -44,9 +44,9 @@ set xlabel 'variability' set ylabel 'evolution error' set output "${png}_variability-vs-evo-error.png" plot \ - "$2" every ::1 using 2:4 title "$3", \ - "$4" every ::1 using 2:4 title "$5", \ - "$6" every ::1 using 2:4 title "$7", \ + "$2" every ::1 using 2:4 title "$3" pt 2, \ + "$4" every ::1 using 2:4 title "$5" pt 2, \ + "$6" every ::1 using 2:4 title "$7" pt 2, \ i(x) title "lin. fit" lc rgb "black" EOD ) > "${png}.gnuplot.script" diff --git a/dokumentation/evolution3d/combine7.sh b/dokumentation/evolution3d/combine7.sh new file mode 100755 index 0000000..5d76548 --- /dev/null +++ b/dokumentation/evolution3d/combine7.sh @@ -0,0 +1,71 @@ +#!/bin/bash + +if [[ $# -eq 0 ]]; then + echo "usage: $0 " +else + data="$1"; + png="`echo $1 | sed -s "s/\.csv$//"`" # strip ending + (cat < "${png}.gnuplot.script" + gnuplot "${png}.gnuplot.script" 2> "${png}.gnuplot.log" + mv fit.log "${png}.gnuplot.fit.log" +fi diff --git a/dokumentation/evolution3d/errors.csv b/dokumentation/evolution3d/errors.csv new file mode 100644 index 0000000..ec47a0a --- /dev/null +++ b/dokumentation/evolution3d/errors.csv @@ -0,0 +1,111 @@ +"4x4x4","4x4x5","5x4x4","4x4x7","7x4x4","5x5x5","6x6x6" +113.016,104.911,91.4882,85.1149,105.032,73.9627,56.9424 +118.796,102.122,95.001,82.2095,91.0336,79.3303,65.8672 +127.157,100.463,97.72,93.8283,74.0894,72.8373,61.6979 +121.613,111.329,99.0429,99.4121,77.0829,60.0032,64.1851 +119.539,104.712,102.273,84.7928,84.9413,80.1321,55.1204 +119.512,100.048,98.0028,89.4784,103.909,66.1526,63.4494 +118.285,102.05,101.929,98.0445,88.0771,74.6032,56.8508 +126.579,98.3549,103.969,82.4413,93.4708,71.3161,68.7883 +122.512,93.4038,92.5069,95.9898,83.1573,71.9377,63.1337 +118.473,104.028,118.88,82.9514,80.9548,70.127,71.6163 +121.998,102.965,96.2138,95.6417,78.1902,61.7195,71.1037 +115.313,102.822,100.164,97.597,84.7296,86.6101,55.0916 +118.034,97.9662,95.9282,92.8455,94.4156,77.235,63.109 +120.003,100.341,96.3737,87.554,84.0696,70.3058,56.7978 +123.494,109.73,107.927,88.0962,83.4435,73.3268,64.0039 +122.989,99.6362,98.0377,92.764,88.5741,72.8603,63.2723 +123.757,113.29,94.9011,92.6177,77.5017,70.5867,57.7703 +110.67,112.572,102.223,91.9667,82.8934,79.8851,61.9955 +121.232,86.3175,126.177,82.2732,89.5173,89.169,55.9687 +120.979,91.637,101.879,94.741,92.6297,86.3505,78.0966 +115.394,107.27,90.0009,87.4631,88.5844,77.8282,65.5659 +116.928,110.797,101.026,99.0457,82.1173,70.418,65.5294 +125.294,99.0484,94.5618,83.0585,73.2,82.3889,52.8169 +111.635,94.2222,99.2481,87.7612,84.76,80.3257,59.6491 +114.681,104.417,94.1741,92.4952,73.4001,85.6612,54.1868 +111.935,96.4144,102.894,87.4672,92.3227,76.2377,64.4377 +111.392,108.23,103.993,85.5196,84.2123,76.8062,64.634 +115.346,98.5045,96.549,96.1244,84.2583,75.0253,61.125 +119.055,93.4554,90.1281,80.3879,78.5571,73.6296,59.6531 +117.452,110.564,104.444,88.557,89.2675,71.8145,61.0567 +123.379,104.082,104.542,80.9192,81.8836,82.1172,66.6297 +115.053,95.1024,107.051,88.0159,83.885,68.4228,70.4683 +123.994,100.132,102.128,92.5849,91.469,74.5628,63.4839 +118.576,102.451,105.315,95.6485,81.0534,82.4297,58.2558 +116.894,116.302,104.097,82.6378,90.3739,74.6568,66.0124 +120.129,98.5173,96.8133,86.2912,85.6114,76.5874,57.8232 +126.708,104.428,99.8496,87.6295,91.687,82.2821,63.7635 +114.595,104.909,103.385,93.7818,90.1008,71.321,58.0721 +120.056,106.289,108.874,81.2872,89.7677,80.1887,60.9659 +122.057,106.708,112.975,92.884,79.4512,60.0022,62.2392 +116.846,108.022,113.068,85.1577,86.5543,73.5674,75.0921 +124.35,97.8253,99.4226,82.4601,88.7329,68.7547,55.2029 +118.43,114.829,115.742,88.7562,91.8764,97.4154,82.5252 +116.574,115.054,94.4964,85.7044,85.9747,81.1639,60.4597 +128.474,106.6,103.45,90.0389,82.843,82.2747,58.192 +111.111,105.157,116.123,90.6256,83.5281,70.415,65.2124 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+118.787,106.656,95.6589,94.3315,82.7487,81.597,66.071 +112.061,102.299,98.2938,89.9138,84.791,74.8947,66.9982 +110.262,104.71,103.401,89.7127,93.4055,71.937,56.1226 +116.504,99.6516,110.527,88.7631,74.1192,82.8423,66.7656 +109.607,85.3402,96.7363,86.5084,83.2161,66.0827,65.502 +122.198,103.875,95.9747,93.2268,94.8049,79.8222,59.5304 +124.527,99.7871,93.9381,86.4354,72.2744,80.2208,59.7764 +120.886,99.823,101.823,91.7037,93.935,76.7288,62.1932 +119.176,110.554,115.05,89.9394,96.7835,75.2866,61.2462 +121.081,114.952,101.306,82.762,86.4099,75.6383,75.8608 +121.038,99.7046,102.493,81.379,87.3714,79.3073,69.8036 +112.392,96.1227,94.8579,80.2224,77.0284,69.5742,64.1075 +121.148,94.9822,108.05,79.8926,74.9314,76.4946,66.444 +117.053,109.207,101.873,95.5281,87.7317,92.7633,55.9495 +123.651,106.855,113.606,87.6941,91.005,83.3937,74.2188 +128.446,110.589,97.6295,101.649,76.2978,83.8943,61.8076 +115.527,96.4926,94.5646,85.3415,84.0268,73.5603,65.2168 +121.456,104.201,89.2764,86.2938,82.958,76.8801,57.2958 +127.418,95.364,97.445,101.265,80.859,70.703,52.0186 +113.541,95.9782,101.923,84.5136,78.3619,69.1493,66.3049 +116.805,109.152,103.308,90.5252,87.6379,79.6539,68.9979 +123.244,99.7984,92.9774,90.4494,82.0693,83.4016,64.4292 +123.095,106.249,95.1595,94.5348,75.4678,88.5801,57.3039 +115.9,91.3925,101.54,77.2599,85.7208,85.8292,60.8438 +124.024,102.095,106.698,89.5657,78.6163,72.5448,61.5872 +114.685,108.615,108.192,78.0427,97.2452,82.2857,58.9557 +113.428,100.235,101.598,91.3327,80.0625,83.8247,58.0811 +117.456,102.616,102.393,116.609,85.7072,78.3849,61.8499 +122.15,114.163,105.018,83.6798,75.0646,84.6062,58.8907 +124.576,107.106,94.0851,89.0655,82.1324,75.7662,60.5339 +113.63,94.8621,97.1255,82.225,90.3791,78.4256,66.9486 +126.608,91.0518,100.425,90.5327,99.9413,68.3999,57.7944 +129.916,112.361,100.988,78.9694,72.5502,72.1529,62.5237 +119.673,119.675,100.096,83.061,83.4268,78.0544,60.6411 +116.233,102.147,95.9289,97.7498,87.4954,89.1144,72.3431 +125.086,103.006,89.3173,87.9928,83.3203,86.8059,61.1932 +112.897,104.759,103.315,83.4737,91.7128,75.2054,59.7782 +,,,,,,58.5321 +,,,,,,60.3221 +,,,,,,62.104 +,,,,,,65.3453 +,,,,,,61.6116 +,,,,,,62.1421 +,,,,,,64.1642 +,,,,,,59.2356 +,,,,,,55.0987 +,,,,,,64.6963 diff --git a/dokumentation/evolution3d/errors.mms b/dokumentation/evolution3d/errors.mms new file mode 100644 index 0000000..ae4e2d0 --- /dev/null +++ b/dokumentation/evolution3d/errors.mms @@ -0,0 +1,9 @@ +[1] "================ Analyzing errors.csv" +[1] "Mean:" +[1] NA +[1] "Median:" +[1] NA +[1] "Sigma:" +[1] NA +[1] "Range:" +[1] NA NA diff --git a/dokumentation/evolution3d/errors.spearman b/dokumentation/evolution3d/errors.spearman new file mode 100644 index 0000000..fe9441f --- /dev/null +++ b/dokumentation/evolution3d/errors.spearman @@ -0,0 +1,49 @@ +[1] "================ Analyzing errors.csv" +[1] "spearman for improvement-potential vs. evolution-error" + x y +x 1.00 -0.09 +y -0.09 1.00 + +n= 100 + + +P + x y +x 0.3979 +y 0.3979 +[1] "spearman for improvement-potential vs. steps" + x y +x 1.00 0.11 +y 0.11 1.00 + +n= 100 + + +P + x y +x 0.258 +y 0.258 +[1] "spearman for regularity vs. steps" + x y +x 1.00 -0.09 +y -0.09 1.00 + +n= 100 + + +P + x y +x 0.3491 +y 0.3491 +[1] "spearman for variability vs. evolution-error" + x y +x 1.00 -0.01 +y -0.01 1.00 + +n= 100 + + +P + x y +x 0.9057 +y 0.9057 diff --git a/dokumentation/evolution3d/images.sh b/dokumentation/evolution3d/images.sh index 359de55..1b91ba7 100755 --- a/dokumentation/evolution3d/images.sh +++ b/dokumentation/evolution3d/images.sh @@ -26,6 +26,14 @@ set xlabel 'improvement potential' set ylabel 'evolution error' set output "${png}_improvement-vs-evo-error.png" plot "$data" every ::1 using 3:4 title "data", h(x) title "lin. fit" lc rgb "black" +i(x)=aaaa*x+bbbb +fit i(x) "$data" every ::1 using 2:4 via aaaa,bbbb +set xlabel 'variability' +set ylabel 'evolution error' +set output 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