more graphs for evo1d

arbeit/bibma.bib

@@ -50,3 +50,28 @@
  publisher = {Springer-Verlag},
  address = {Berlin, Heidelberg},
 } 
+@book{golub2012matrix,
+  title={Matrix computations},
+  author={Golub, Gene H and Van Loan, Charles F},
+  volume={3},
+  year={2012},
+  publisher={JHU Press}
+}
+@article{weise2012evolutionary,
+  title={Evolutionary Optimization: Pitfalls and Booby Traps},
+  author={Weise, Thomas and Chiong, Raymond and Tang, Ke},
+  journal={J. Comput. Sci. \& Technol},
+  volume={27},
+  number={5},
+  year={2012},
+  url={http://jcst.ict.ac.cn:8080/jcst/EN/article/downloadArticleFile.do?attachType=PDF\&id=9543}
+}
+@inproceedings{thorhauer2014locality,
+  title={On the locality of standard search operators in grammatical evolution},
+  author={Thorhauer, Ann and Rothlauf, Franz},
+  booktitle={International Conference on Parallel Problem Solving from Nature},
+  pages={465--475},
+  year={2014},
+  organization={Springer},
+  url={https://www.lri.fr/~hansen/proceedings/2014/PPSN/papers/8672/86720465.pdf}
+}

arbeit/files/erklaerung.aux

@@ -22,7 +22,7 @@
 \setcounter{ContinuedFloat}{0}
 \setcounter{float@type}{16}
 \setcounter{lstnumber}{1}
-\setcounter{NAT@ctr}{5}
+\setcounter{NAT@ctr}{8}
 \setcounter{AM@survey}{0}
 \setcounter{r@tfl@t}{0}
 \setcounter{subfigure}{0}

arbeit/ma.md

@@ -4,14 +4,16 @@ fontsize: 11pt
 
 \chapter*{How to read this Thesis}
 
-As a guide through the nomenclature used in the formulas we prepend this chapter.
+As a guide through the nomenclature used in the formulas we prepend this
+chapter.
 
 Unless otherwise noted the following holds:
 
 - lowercase letters $x,y,z$  
   refer to real variables and represent a point in 3D-Space.
 - lowercase letters $u,v,w$  
-  refer to real variables between $0$ and $1$ used as coefficients in a 3D B-Spline grid.
+  refer to real variables between $0$ and $1$ used as coefficients in a 3D
+  B-Spline grid.
 - other lowercase letters  
   refer to other scalar (real) variables.
 - lowercase **bold** letters (e.g. $\vec{x},\vec{y}$)  
@@ -21,12 +23,13 @@ Unless otherwise noted the following holds:
 
 # Introduction
 
-In this Master Thesis we try to extend a previously proposed concept of predicting
-the evolvability of \acf{FFD} given a Deformation-Matrix\cite{anrichterEvol}.
-In the original publication the author used random sampled points weighted with
-\acf{RBF} to deform the mesh and defined three different criteria that can be
-calculated prior to using an evolutional optimisation algorithm to asses the
-quality and potential of such optimisation.
+In this Master Thesis we try to extend a previously proposed concept of
+predicting the evolvability of \acf{FFD} given a
+Deformation-Matrix\cite{anrichterEvol}. In the original publication the author
+used random sampled points weighted with \acf{RBF} to deform the mesh and
+defined three different criteria that can be calculated prior to using an
+evolutional optimization algorithm to asses the quality and potential of such
+optimization.
 
 We will replicate the same setup on the same meshes but use \acf{FFD} instead of
 \acf{RBF} to create a deformation and evaluate if the evolution-criteria still
@@ -35,12 +38,14 @@ work as a predictor given the different deformation scheme.
 ## What is \acf{FFD}?
 
 First of all we have to establish how a \ac{FFD} works and why this is a good
-tool for deforming meshes in the first place. For simplicity we only summarize the
-1D-case from \cite{spitzmuller1996bezier} here and go into the extension to the 3D case in chapter \ref{3dffd}.
+tool for deforming meshes in the first place. For simplicity we only summarize
+the 1D-case from \cite{spitzmuller1996bezier} here and go into the extension to
+the 3D case in chapter \ref{3dffd}.
 
 Given an arbitrary number of points $p_i$ alongside a line, we map a scalar
 value $\tau_i \in [0,1[$ to each point with $\tau_i < \tau_{i+1} \forall i$.
-Given a degree of the target polynomial $d$ we define the curve $N_{i,d,\tau_i}(u)$ as follows:
+Given a degree of the target polynomial $d$ we define the curve
+$N_{i,d,\tau_i}(u)$ as follows:
 
 \begin{equation} \label{eqn:ffd1d1}
 N_{i,0,\tau}(u) = \begin{cases} 1, & u \in [\tau_i, \tau_{i+1}[ \\ 0, & \mbox{otherwise} \end{cases}
@@ -52,12 +57,17 @@ and
 N_{i,d,\tau}(u) = \frac{u-\tau_i}{\tau_{i+d}} N_{i,d-1,\tau}(u) + \frac{\tau_{i+d+1} - u}{\tau_{i+d+1}-\tau_{i+1}} N_{i+1,d-1,\tau}(u)
 \end{equation}
 
-If we now multiply every $p_i$ with the corresponding $N_{i,d,\tau_i}(u)$ we get the contribution of each
-point $p_i$ to the final curve-point parameterized only by $u \in [0,1[$.
-As can be seen from \eqref{eqn:ffd1d2} we only access points $[i..i+d]$ for any given $i$^[one more for each recursive step.], which
-gives us, in combination with choosing $p_i$ and $\tau_i$ in order, only a local interference of $d+1$ points.
+If we now multiply every $p_i$ with the corresponding $N_{i,d,\tau_i}(u)$ we get
+the contribution of each point $p_i$ to the final curve-point parameterized only
+by $u \in [0,1[$.  As can be seen from \eqref{eqn:ffd1d2} we only access points
+$[i..i+d]$ for any given $i$^[one more for each recursive step.], which gives
+us, in combination with choosing $p_i$ and $\tau_i$ in order, only a local
+interference of $d+1$ points.
 
-We can even derive this equation straightforward for an arbitrary $N$^[*Warning:* in the case of $d=1$ the recursion-formula yields a $0$ denominator, but $N$ is also $0$. The right solution for this case is a derivative of $0$]:
+We can even derive this equation straightforward for an arbitrary
+$N$^[*Warning:* in the case of $d=1$ the recursion-formula yields a $0$
+denominator, but $N$ is also $0$. The right solution for this case is a
+derivative of $0$]:
 
 $$\frac{\partial}{\partial u} N_{i,d,r}(u) = \frac{d}{\tau_{i+d} - \tau_i} N_{i,d-1,\tau}(u) - \frac{d}{\tau_{i+d+1} - \tau_{i+1}} N_{i+1,d-1,\tau}(u)$$
 
@@ -65,30 +75,42 @@ For a B-Spline
 $$s(u) = \sum_{i} N_{i,d,\tau_i}(u) p_i$$
 these derivations yield $\frac{\partial^d}{\partial u} s(u) = 0$.
 
-Another interesting property of these recursive polynomials is that they are continuous (given $d \ge 1$) as every $p_i$ gets
-blended in linearly between $\tau_i$ and $\tau_{i+d}$ and out linearly between $\tau_{i+1}$ and $\tau_{i+d+1}$
-as can bee seen from the two coefficients in every step of the recursion.
+Another interesting property of these recursive polynomials is that they are
+continuous (given $d \ge 1$) as every $p_i$ gets blended in linearly between
+$\tau_i$ and $\tau_{i+d}$ and out linearly between $\tau_{i+1}$ and
+$\tau_{i+d+1}$ as can bee seen from the two coefficients in every step of the
+recursion.
 
 ### Why is \ac{FFD} a good deformation function?
 
-The usage of \ac{FFD} as a tool for manipulating follows directly from the properties of the polynomials and the correspondence to
-the control points.
-Having only a few control points gives the user a nicer high-level-interface, as she only needs to move these points and the
-model follows in an intuitive manner. The deformation is smooth as the underlying polygon is smooth as well and affects as many
-vertices of the model as needed. Moreover the changes are always local so one risks not any change that a user cannot immediately see.
+The usage of \ac{FFD} as a tool for manipulating follows directly from the
+properties of the polynomials and the correspondence to the control points.
+Having only a few control points gives the user a nicer high-level-interface, as
+she only needs to move these points and the model follows in an intuitive
+manner. The deformation is smooth as the underlying polygon is smooth as well
+and affects as many vertices of the model as needed. Moreover the changes are
+always local so one risks not any change that a user cannot immediately see.
 
-But there are also disadvantages of this approach. The user loses the ability to directly influence vertices and even seemingly simple tasks as
-creating a plateau can be difficult to achieve\cite[chapter~3.2]{hsu1991dmffd}\cite{hsu1992direct}.
+But there are also disadvantages of this approach. The user loses the ability to
+directly influence vertices and even seemingly simple tasks as creating a
+plateau can be difficult to
+achieve\cite[chapter~3.2]{hsu1991dmffd}\cite{hsu1992direct}.
 
-This disadvantages led to the formulation of \acf{DM-FFD}\cite[chapter~3.3]{hsu1991dmffd} in which the user directly interacts with the surface-mesh.
-All interactions will be applied proportionally to the control-points that make up the parametrization of the interaction-point
-itself yielding a smooth deformation of the surface *at* the surface without seemingly arbitrary scattered control-points.
-Moreover this increases the efficiency of an evolutionary optimization\cite{Menzel2006}, which we will use later on.
+This disadvantages led to the formulation of
+\acf{DM-FFD}\cite[chapter~3.3]{hsu1991dmffd} in which the user directly
+interacts with the surface-mesh.  All interactions will be applied
+proportionally to the control-points that make up the parametrization of the
+interaction-point itself yielding a smooth deformation of the surface *at* the
+surface without seemingly arbitrary scattered control-points.  Moreover this
+increases the efficiency of an evolutionary optimization\cite{Menzel2006}, which
+we will use later on.
 
-But this approach also has downsides as can be seen in \cite[figure~7]{hsu1991dmffd}\todo{figure hier einfügen?}, as the tessellation of
-the invisible grid has a major impact on the deformation itself.
+But this approach also has downsides as can be seen in
+\cite[figure~7]{hsu1991dmffd}\todo{figure hier einfügen?}, as the tessellation
+of the invisible grid has a major impact on the deformation itself.
 
-All in all \ac{FFD} and \ac{DM-FFD} are still good ways to deform a high-polygon mesh albeit the downsides.
+All in all \ac{FFD} and \ac{DM-FFD} are still good ways to deform a high-polygon
+mesh albeit the downsides.
 
 ## What is evolutional optimization?
 
@@ -96,26 +118,83 @@ All in all \ac{FFD} and \ac{DM-FFD} are still good ways to deform a high-polygon
 
 ## Wieso ist evo-Opt so cool?
 
-The main advantage of evolutional algorithms is the ability to find optima of general functions just with the help of a given
-error-function (or fitness-function in this domain). This avoids the general pitfalls of gradient-based procedures, which often
-target the same error-function as an evolutional algorithm, but can get stuck in local optima.
+The main advantage of evolutional algorithms is the ability to find optima of
+general functions just with the help of a given error-function (or
+fitness-function in this domain). This avoids the general pitfalls of
+gradient-based procedures, which often target the same error-function as an
+evolutional algorithm, but can get stuck in local optima.
 
-This is mostly due to the fact that a gradient-based procedure has only one point of observation from where it evaluates the next
-steps, whereas an evolutional strategy starts with a population of guessed solutions. Because an evolutional strategy modifies
-the solution randomly, keeps the best solutions and purges the worst, it can also target multiple different hypothesis at the same time
-where the local optima die out in the face of other, better candidates.
+This is mostly due to the fact that a gradient-based procedure has only one
+point of observation from where it evaluates the next steps, whereas an
+evolutional strategy starts with a population of guessed solutions. Because an
+evolutional strategy modifies the solution randomly, keeps the best solutions
+and purges the worst, it can also target multiple different hypothesis at the
+same time where the local optima die out in the face of other, better
+candidates.
 
-If an analytic best solution exists (i.e. because the error-function is convex) an evolutional algorithm is not the right choice. Although
-both converge to the same solution, the analytic one is usually faster. But in reality many problems have no analytic solution, because
-the problem is not convex. Here evolutional optimization has one more advantage as you get bad solutions fast, which refine over time.
+If an analytic best solution exists (i.e. because the error-function is convex)
+an evolutional algorithm is not the right choice. Although both converge to the
+same solution, the analytic one is usually faster. But in reality many problems
+have no analytic solution, because the problem is not convex. Here evolutional
+optimization has one more advantage as you get bad solutions fast, which refine
+over time.
 
+## Criteria for the evolvability of linear deformations
 
+### Variability
 
-## Evolvierbarkeitskriterien
+In \cite{anrichterEvol} variability is defined as
+$$V(\vec{U}) := \frac{\textrm{rank}(\vec{U})}{n},$$
+whereby $\vec{U}$ is the $m \times n$ deformation-Matrix used to map the $m$
+control points onto the $n$ vertices.
 
-- Konditionszahl etc.
+Given $n = m$, an identical number of control-points and vertices, this
+quotient will be $=1$ if all control points are independent of each other and
+the solution is to trivially move every control-point onto a target-point.
 
-# Hauptteil
+In praxis the value of $V(\vec{U})$ is typically $\ll 1$, because as
+there are only few control-points for many vertices, so $m \ll n$.
+
+Additionally in our setup we connect neighbouring control-points in a grid so
+each control point is not independent, but typically depends on $4^d$
+control-points for an $d$-dimensional control mesh.
+
+### Regularity
+
+Regularity is defined\cite{anrichterEvol} as
+$$R(\vec{U}) := \frac{1}{\kappa(\vec{U})} = \frac{\sigma_{min}}{\sigma_{max}}$$
+where $\sigma_{min}$ and $\sigma_{max}$ are the smallest and greatest right singular
+value of the deformation-matrix $\vec{U}$.
+
+As we deform the given Object only based on the parameters as $\vec{p} \mapsto
+f(\vec{x} + \vec{U}\vec{p})$ this makes sure that $\|\vec{Up}\| \propto
+\|\vec{p}\|$ when $\kappa(\vec{U}) \approx 1$. The inversion of $\kappa(\vec{U})$
+is only performed to map the criterion-range to $[0..1]$, whereas $1$ is the
+optimal value and $0$ is the worst value.
+
+This criterion should be characteristic for numeric stability on the on
+hand\cite[chapter 2.7]{golub2012matrix} and for convergence speed of evolutional
+algorithms on the other hand\cite{anrichterEvol} as it is tied to the notion of
+locality\cite{weise2012evolutionary,thorhauer2014locality}.
+
+### Improvement Potential
+
+In contrast to the general nature of variability and regularity, which are
+agnostic of the fitness-function at hand the third criterion should reflect a
+notion of potential.
+
+As during optimization some kind of gradient $g$ is available to suggest a
+direction worth pursuing we use this to guess how much change can be achieved in
+the given direction.
+
+The definition for an improvement potential $P$ is\cite{anrichterEvol}:
+$$
+P(\vec{U}) := 1 - \|(\vec{1} - \vec{UU}^+)\vec(G)\|^2_F
+$$
+given some approximate $n \times d$ fitness-gradient $\vec{G}$, normalized to
+$\|\vec{G}\|_F = 1$, whereby $\|\cdot\|_F$ denotes the Frobenius-Norm.
+
+# Implementation of \acf{FFD}
 
 ## Was ist FFD?
 \label{3dffd}
@@ -124,41 +203,43 @@ the problem is not convex. Here evolutional optimization has one more advantage
 - Wieso Newton-Optimierung?
   - Was folgt daraus?
 
-## Szenarien vorstellen
+## Test Scenario: 1D Function Approximation
 
-### 1D
-
-#### Optimierungszenario
+### Optimierungszenario
 
 - Ebene -> Template-Fit
 
-#### Matching in 1D
+### Matching in 1D
 
 - Trivial
 
-#### Besonderheiten der Auswertung
+### Besonderheiten der Auswertung
 
 - Analytische Lösung einzig beste
   - Ergebnis auch bei Rauschen konstant?
   - normierter 1-Vektor auf den Gradienten addieren
     - Kegel entsteht
 
-### 3D
+## Test Scenario: 3D Function Approximation
 
-#### Optimierungsszenario
+### Optimierungsszenario
 
 - Ball zu Mario
 
-#### Matching in 3D
+### Matching in 3D
 
 - alternierende Optimierung
 
-#### Besonderheiten der Optimierung
+### Besonderheiten der Optimierung
 
 - Analytische Lösung nur bis zur Optimierung der ersten Punkte gültig
 - Kriterien trotzdem gut
 
-# Evaluation
+# Evaluation of Scenarios
+
+## Results of 1D Function Approximation
+
+
 
 ## Spearman/Pearson-Metriken
 
@@ -166,7 +247,7 @@ the problem is not convex. Here evolutional optimization has one more advantage
 - Wieso sollte uns das interessieren?
 - Wieso reicht Monotonie?
 - Haben wir das gezeigt?
-- Stastik, Bilder, blah!
+- Statistik, Bilder, blah!
 
 # Schluss
 

arbeit/ma.tex

@@ -151,8 +151,8 @@ predicting the evolvability of \acf{FFD} given a
 Deformation-Matrix\cite{anrichterEvol}. In the original publication the
 author used random sampled points weighted with \acf{RBF} to deform the
 mesh and defined three different criteria that can be calculated prior
-to using an evolutional optimisation algorithm to asses the quality and
-potential of such optimisation.
+to using an evolutional optimization algorithm to asses the quality and
+potential of such optimization.
 
 We will replicate the same setup on the same meshes but use \acf{FFD}
 instead of \acf{RBF} to create a deformation and evaluate if the
@@ -265,13 +265,64 @@ in reality many problems have no analytic solution, because the problem
 is not convex. Here evolutional optimization has one more advantage as
 you get bad solutions fast, which refine over time.
 
-\section{Evolvierbarkeitskriterien}\label{evolvierbarkeitskriterien}
+\section{Criteria for the evolvability of linear
+deformations}\label{criteria-for-the-evolvability-of-linear-deformations}
 
-\begin{itemize}
-\tightlist
-\item
-  Konditionszahl etc.
-\end{itemize}
+\subsection{Variability}\label{variability}
+
+In \cite{anrichterEvol} variability is defined as
+\[V(\vec{U}) := \frac{\textrm{rank}(\vec{U})}{n},\] whereby \(\vec{U}\)
+is the \(m \times n\) deformation-Matrix used to map the \(m\) control
+points onto the \(n\) vertices.
+
+Given \(n = m\), an identical number of control-points and vertices,
+this quotient will be \(=1\) if all control points are independent of
+each other and the solution is to trivially move every control-point
+onto a target-point.
+
+In praxis the value of \(V(\vec{U})\) is typically \(\ll 1\), because as
+there are only few control-points for many vertices, so \(m \ll n\).
+
+Additionally in our setup we connect neighbouring control-points in a
+grid so each control point is not independent, but typically depends on
+\(4^d\) control-points for an \(d\)-dimensional control mesh.
+
+\subsection{Regularity}\label{regularity}
+
+Regularity is defined\cite{anrichterEvol} as
+\[R(\vec{U}) := \frac{1}{\kappa(\vec{U})} = \frac{\sigma_{min}}{\sigma_{max}}\]
+where \(\sigma_{min}\) and \(\sigma_{max}\) are the smallest and
+greatest right singular value of the deformation-matrix \(\vec{U}\).
+
+As we deform the given Object only based on the parameters as
+\(\vec{p} \mapsto f(\vec{x} + \vec{U}\vec{p})\) this makes sure that
+\(\|\vec{Up}\| \propto \|\vec{p}\|\) when \(\kappa(\vec{U}) \approx 1\).
+The inversion of \(\kappa(\vec{U})\) is only performed to map the
+criterion-range to \([0..1]\), whereas \(1\) is the optimal value and
+\(0\) is the worst value.
+
+This criterion should be characteristic for numeric stability on the on
+hand\cite[chapter 2.7]{golub2012matrix} and for convergence speed of
+evolutional algorithms on the other hand\cite{anrichterEvol} as it is
+tied to the notion of
+locality\cite{weise2012evolutionary,thorhauer2014locality}.
+
+\subsection{Improvement Potential}\label{improvement-potential}
+
+In contrast to the general nature of variability and regularity, which
+are agnostic of the fitness-function at hand the third criterion should
+reflect a notion of potential.
+
+As during optimization some kind of gradient \(g\) is available to
+suggest a direction worth pursuing we use this to guess how much change
+can be achieved in the given direction.
+
+The definition for an improvement potential \(P\)
+is\cite{anrichterEvol}: \[
+P(\vec{U}) := 1 - \|(\vec{1} - \vec{UU}^+)\vec(G)\|^2_F
+\] given some approximate \(n \times d\) fitness-gradient \(\vec{G}\),
+normalized to \(\|\vec{G}\|_F = 1\), whereby \(\|\cdot\|_F\) denotes the
+Frobenius-Norm.
 
 \chapter{Hauptteil}\label{hauptteil}
 
@@ -372,7 +423,7 @@ Optimierung}\label{besonderheiten-der-optimierung}
 \item
   Haben wir das gezeigt?
 \item
-  Stastik, Bilder, blah!
+  Statistik, Bilder, blah!
 \end{itemize}
 
 \chapter{Schluss}\label{schluss}

arbeit/settings/commands.tex

@@ -87,13 +87,13 @@
 \renewcommand\lq{\text{\textgravedbl}\!\!}\renewcommand\rq{\!\!\text{\textacutedbl}}
 
 % ##### tables #####
-\newcommand\rl[1]{\multicolumn{1}{r|}{#1}}			% item|
-\renewcommand\ll[1]{\multicolumn{1}{|r}{#1}}		% |item
-% \newcommand\cc[1]{\multicolumn{1}{|c|}{#1}} 		% |item|
-\newcommand\lc[2]{\multicolumn{#1}{|c|}{#2}}		%
-\newcommand\cc[1]{\multicolumn{1}{c}{#1}}
-% \renewcommand{\arraystretch}{1.2} % Tabellenzeilen ein bischen h?her machen.
-\newcommand\m[2]{\multirow{#1}{*}{$#2$}}
+% \newcommand\rl[1]{\multicolumn{1}{r|}{#1}}			% item|
+% \renewcommand\ll[1]{\multicolumn{1}{|r}{#1}}		% |item
+% % \newcommand\cc[1]{\multicolumn{1}{|c|}{#1}} 		% |item|
+% \newcommand\lc[2]{\multicolumn{#1}{|c|}{#2}}		%
+% \newcommand\cc[1]{\multicolumn{1}{c}{#1}}
+% % \renewcommand{\arraystretch}{1.2} % Tabellenzeilen ein bischen h?her machen.
+% \newcommand\m[2]{\multirow{#1}{*}{$#2$}}
 
 % ##### Text symbole #####
 % \newcommand\subdot[1]{\lower0.5em\hbox{$\stackrel{\displaystyle #1}{.}$}}

dokumentation/evolution1d/20170830-evolution1D_5x5_100Times-added_one.gnuplot.fit.log

@@ -1,7 +1,7 @@
 
 
 *******************************************************************************
-Wed Aug 30 22:31:49 2017
+Sun Oct  1 19:59:33 2017
 
 
 FIT:    data read from "20170830-evolution1D_5x5_100Times-added_one.csv" every ::1 using 2:5
@@ -47,7 +47,7 @@ b              -0.996  1.000
 
 
 *******************************************************************************
-Wed Aug 30 22:31:49 2017
+Sun Oct  1 19:59:33 2017
 
 
 FIT:    data read from "20170830-evolution1D_5x5_100Times-added_one.csv" every ::1 using 4:5
@@ -93,7 +93,7 @@ bb             -1.000  1.000
 
 
 *******************************************************************************
-Wed Aug 30 22:31:49 2017
+Sun Oct  1 19:59:33 2017
 
 
 FIT:    data read from "20170830-evolution1D_5x5_100Times-added_one.csv" every ::1 using 4:6

dokumentation/evolution1d/20170830-evolution1D_5x5_100Times-added_one.gnuplot.script

@@ -2,13 +2,19 @@ set datafile separator ","
 f(x)=a*x+b
 fit f(x) "20170830-evolution1D_5x5_100Times-added_one.csv" every ::1 using 2:5 via a,b
 set terminal png
+set xlabel 'regularity'
+set ylabel 'steps'
 set output "20170830-evolution1D_5x5_100Times-added_one_regularity-vs-steps.png"
-plot "20170830-evolution1D_5x5_100Times-added_one.csv" every ::1 using 2:5 title "regularity vs. steps", f(x) lc rgb "black"
+plot "20170830-evolution1D_5x5_100Times-added_one.csv" every ::1 using 2:5 title "data", f(x) title "lin. fit" lc rgb "black"
 g(x)=aa*x+bb
 fit g(x) "20170830-evolution1D_5x5_100Times-added_one.csv" every ::1 using 4:5 via aa,bb
+set xlabel 'improvement potential'
+set ylabel 'steps'
 set output "20170830-evolution1D_5x5_100Times-added_one_improvement-vs-steps.png"
-plot "20170830-evolution1D_5x5_100Times-added_one.csv" every ::1 using 4:5 title "improvement potential vs. steps", g(x) lc rgb "black"
+plot "20170830-evolution1D_5x5_100Times-added_one.csv" every ::1 using 4:5 title "data", g(x) title "lin. fit" lc rgb "black"
 h(x)=aaa*x+bbb
 fit h(x) "20170830-evolution1D_5x5_100Times-added_one.csv" every ::1 using 4:6 via aaa,bbb
+set xlabel 'improvement potential'
+set ylabel 'evolution error'
 set output "20170830-evolution1D_5x5_100Times-added_one_improvement-vs-evo-error.png"
-plot "20170830-evolution1D_5x5_100Times-added_one.csv" every ::1 using 4:6 title "improvement potential vs. evolution error", h(x) lc rgb "black"
+plot "20170830-evolution1D_5x5_100Times-added_one.csv" every ::1 using 4:6 title "data", h(x) title "lin. fit" lc rgb "black"

dokumentation/evolution1d/20170830-evolution1D_5x5_100Times-all.csv

@@ -0,0 +1,201 @@
+"Least squares",regularity,variability,improvement,steps,"Evolution error",sigma
+183.763,0.0179571,0.00111111,0.938632,228,192.44,0.032644
+229.099,0.0189281,0.00111111,0.923492,96,240.171,0.0562716
+238.479,0.0215758,0.00111111,0.920359,195,249.883,0.0272032
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+191.586,0.0207835,0.00111111,0.936019,156,201.143,0.0235659
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dokumentation/evolution1d/20170830-evolution1D_5x5_100Times-all.gnuplot.fit.log

@@ -0,0 +1,138 @@
+
+
+*******************************************************************************
+Sun Oct  1 20:05:21 2017
+
+
+FIT:    data read from "20170830-evolution1D_5x5_100Times-all.csv" every ::1 using 2:5
+        format = x:z
+        #datapoints = 200
+        residuals are weighted equally (unit weight)
+
+function used for fitting: f(x)
+fitted parameters initialized with current variable values
+
+
+
+ Iteration 0
+ WSSR        : 8.65799e+06       delta(WSSR)/WSSR   : 0
+ delta(WSSR) : 0                 limit for stopping : 1e-05
+ lambda	  : 0.707234
+
+initial set of free parameter values
+
+a               = 1
+b               = 1
+
+After 5 iterations the fit converged.
+final sum of squares of residuals : 387750
+rel. change during last iteration : -1.80465e-10
+
+degrees of freedom    (FIT_NDF)                        : 198
+rms of residuals      (FIT_STDFIT) = sqrt(WSSR/ndf)    : 44.2531
+variance of residuals (reduced chisquare) = WSSR/ndf   : 1958.33
+
+Final set of parameters            Asymptotic Standard Error
+=======================            ==========================
+
+a               = -7207.93         +/- 1699         (23.57%)
+b               = 339.971          +/- 32.22        (9.477%)
+
+
+correlation matrix of the fit parameters:
+
+               a      b      
+a               1.000 
+b              -0.995  1.000 
+
+
+*******************************************************************************
+Sun Oct  1 20:05:21 2017
+
+
+FIT:    data read from "20170830-evolution1D_5x5_100Times-all.csv" every ::1 using 4:5
+        format = x:z
+        #datapoints = 200
+        residuals are weighted equally (unit weight)
+
+function used for fitting: g(x)
+fitted parameters initialized with current variable values
+
+
+
+ Iteration 0
+ WSSR        : 8.58412e+06       delta(WSSR)/WSSR   : 0
+ delta(WSSR) : 0                 limit for stopping : 1e-05
+ lambda	  : 0.965888
+
+initial set of free parameter values
+
+aa              = 1
+bb              = 1
+
+After 5 iterations the fit converged.
+final sum of squares of residuals : 374307
+rel. change during last iteration : -1.28123e-12
+
+degrees of freedom    (FIT_NDF)                        : 198
+rms of residuals      (FIT_STDFIT) = sqrt(WSSR/ndf)    : 43.4792
+variance of residuals (reduced chisquare) = WSSR/ndf   : 1890.44
+
+Final set of parameters            Asymptotic Standard Error
+=======================            ==========================
+
+aa              = 2485.68          +/- 489.8        (19.71%)
+bb              = -2109            +/- 455.8        (21.61%)
+
+
+correlation matrix of the fit parameters:
+
+               aa     bb     
+aa              1.000 
+bb             -1.000  1.000 
+
+
+*******************************************************************************
+Sun Oct  1 20:05:21 2017
+
+
+FIT:    data read from "20170830-evolution1D_5x5_100Times-all.csv" every ::1 using 4:6
+        format = x:z
+        #datapoints = 200
+        residuals are weighted equally (unit weight)
+
+function used for fitting: h(x)
+fitted parameters initialized with current variable values
+
+
+
+ Iteration 0
+ WSSR        : 9.43971e+06       delta(WSSR)/WSSR   : 0
+ delta(WSSR) : 0                 limit for stopping : 1e-05
+ lambda	  : 0.965888
+
+initial set of free parameter values
+
+aaa             = 1
+bbb             = 1
+
+After 5 iterations the fit converged.
+final sum of squares of residuals : 11.3578
+rel. change during last iteration : -7.81502e-08
+
+degrees of freedom    (FIT_NDF)                        : 198
+rms of residuals      (FIT_STDFIT) = sqrt(WSSR/ndf)    : 0.239505
+variance of residuals (reduced chisquare) = WSSR/ndf   : 0.0573625
+
+Final set of parameters            Asymptotic Standard Error
+=======================            ==========================
+
+aaa             = -3135.44         +/- 2.698        (0.08605%)
+bbb             = 3135.83          +/- 2.511        (0.08006%)
+
+
+correlation matrix of the fit parameters:
+
+               aaa    bbb    
+aaa             1.000 
+bbb            -1.000  1.000 

dokumentation/evolution1d/20170830-evolution1D_5x5_100Times-all.gnuplot.log

@@ -0,0 +1,261 @@
+
+
+ Iteration 0
+ WSSR        : 8.65799e+06       delta(WSSR)/WSSR   : 0
+ delta(WSSR) : 0                 limit for stopping : 1e-05
+ lambda	  : 0.707234
+
+initial set of free parameter values
+
+a               = 1
+b               = 1
+/
+
+ Iteration 1
+ WSSR        : 422995            delta(WSSR)/WSSR   : -19.4683
+ delta(WSSR) : -8.235e+06        limit for stopping : 1e-05
+ lambda	  : 0.0707234
+
+resultant parameter values
+
+a               = -4.94625
+b               = 203.522
+/
+
+ Iteration 2
+ WSSR        : 415042            delta(WSSR)/WSSR   : -0.0191613
+ delta(WSSR) : -7952.76          limit for stopping : 1e-05
+ lambda	  : 0.00707234
+
+resultant parameter values
+
+a               = -864.859
+b               = 220.257
+/
+
+ Iteration 3
+ WSSR        : 387879            delta(WSSR)/WSSR   : -0.0700308
+ delta(WSSR) : -27163.5          limit for stopping : 1e-05
+ lambda	  : 0.000707234
+
+resultant parameter values
+
+a               = -6772.19
+b               = 331.747
+/
+
+ Iteration 4
+ WSSR        : 387750            delta(WSSR)/WSSR   : -0.000332164
+ delta(WSSR) : -128.797          limit for stopping : 1e-05
+ lambda	  : 7.07234e-05
+
+resultant parameter values
+
+a               = -7207.61
+b               = 339.965
+/
+
+ Iteration 5
+ WSSR        : 387750            delta(WSSR)/WSSR   : -1.80465e-10
+ delta(WSSR) : -6.99755e-05      limit for stopping : 1e-05
+ lambda	  : 7.07234e-06
+
+resultant parameter values
+
+a               = -7207.93
+b               = 339.971
+
+After 5 iterations the fit converged.
+final sum of squares of residuals : 387750
+rel. change during last iteration : -1.80465e-10
+
+degrees of freedom    (FIT_NDF)                        : 198
+rms of residuals      (FIT_STDFIT) = sqrt(WSSR/ndf)    : 44.2531
+variance of residuals (reduced chisquare) = WSSR/ndf   : 1958.33
+
+Final set of parameters            Asymptotic Standard Error
+=======================            ==========================
+
+a               = -7207.93         +/- 1699         (23.57%)
+b               = 339.971          +/- 32.22        (9.477%)
+
+
+correlation matrix of the fit parameters:
+
+               a      b      
+a               1.000 
+b              -0.995  1.000 
+
+
+ Iteration 0
+ WSSR        : 8.58412e+06       delta(WSSR)/WSSR   : 0
+ delta(WSSR) : 0                 limit for stopping : 1e-05
+ lambda	  : 0.965888
+
+initial set of free parameter values
+
+aa              = 1
+bb              = 1
+/
+
+ Iteration 1
+ WSSR        : 418736            delta(WSSR)/WSSR   : -19.5001
+ delta(WSSR) : -8.16538e+06      limit for stopping : 1e-05
+ lambda	  : 0.0965888
+
+resultant parameter values
+
+aa              = 112.257
+bb              = 99.0225
+/
+
+ Iteration 2
+ WSSR        : 395337            delta(WSSR)/WSSR   : -0.0591881
+ delta(WSSR) : -23399.2          limit for stopping : 1e-05
+ lambda	  : 0.00965888
+
+resultant parameter values
+
+aa              = 852.014
+bb              = -588.836
+/
+
+ Iteration 3
+ WSSR        : 374316            delta(WSSR)/WSSR   : -0.0561565
+ delta(WSSR) : -21020.3          limit for stopping : 1e-05
+ lambda	  : 0.000965888
+
+resultant parameter values
+
+aa              = 2450.37
+bb              = -2076.15
+/
+
+ Iteration 4
+ WSSR        : 374307            delta(WSSR)/WSSR   : -2.6247e-05
+ delta(WSSR) : -9.82442          limit for stopping : 1e-05
+ lambda	  : 9.65888e-05
+
+resultant parameter values
+
+aa              = 2485.68
+bb              = -2109
+/
+
+ Iteration 5
+ WSSR        : 374307            delta(WSSR)/WSSR   : -1.28123e-12
+ delta(WSSR) : -4.79573e-07      limit for stopping : 1e-05
+ lambda	  : 9.65888e-06
+
+resultant parameter values
+
+aa              = 2485.68
+bb              = -2109
+
+After 5 iterations the fit converged.
+final sum of squares of residuals : 374307
+rel. change during last iteration : -1.28123e-12
+
+degrees of freedom    (FIT_NDF)                        : 198
+rms of residuals      (FIT_STDFIT) = sqrt(WSSR/ndf)    : 43.4792
+variance of residuals (reduced chisquare) = WSSR/ndf   : 1890.44
+
+Final set of parameters            Asymptotic Standard Error
+=======================            ==========================
+
+aa              = 2485.68          +/- 489.8        (19.71%)
+bb              = -2109            +/- 455.8        (21.61%)
+
+
+correlation matrix of the fit parameters:
+
+               aa     bb     
+aa              1.000 
+bb             -1.000  1.000 
+
+
+ Iteration 0
+ WSSR        : 9.43971e+06       delta(WSSR)/WSSR   : 0
+ delta(WSSR) : 0                 limit for stopping : 1e-05
+ lambda	  : 0.965888
+
+initial set of free parameter values
+
+aaa             = 1
+bbb             = 1
+/
+
+ Iteration 1
+ WSSR        : 82262.8           delta(WSSR)/WSSR   : -113.751
+ delta(WSSR) : -9.35745e+06      limit for stopping : 1e-05
+ lambda	  : 0.0965888
+
+resultant parameter values
+
+aaa             = 93.9799
+bbb             = 130.237
+/
+
+ Iteration 2
+ WSSR        : 38961.1           delta(WSSR)/WSSR   : -1.11141
+ delta(WSSR) : -43301.7          limit for stopping : 1e-05
+ lambda	  : 0.00965888
+
+resultant parameter values
+
+aaa             = -912.157
+bbb             = 1067.01
+/
+
+ Iteration 3
+ WSSR        : 29.5535           delta(WSSR)/WSSR   : -1317.32
+ delta(WSSR) : -38931.6          limit for stopping : 1e-05
+ lambda	  : 0.000965888
+
+resultant parameter values
+
+aaa             = -3087.39
+bbb             = 3091.12
+/
+
+ Iteration 4
+ WSSR        : 11.3578           delta(WSSR)/WSSR   : -1.60205
+ delta(WSSR) : -18.1958          limit for stopping : 1e-05
+ lambda	  : 9.65888e-05
+
+resultant parameter values
+
+aaa             = -3135.43
+bbb             = 3135.82
+/
+
+ Iteration 5
+ WSSR        : 11.3578           delta(WSSR)/WSSR   : -7.81502e-08
+ delta(WSSR) : -8.87612e-07      limit for stopping : 1e-05
+ lambda	  : 9.65888e-06
+
+resultant parameter values
+
+aaa             = -3135.44
+bbb             = 3135.83
+
+After 5 iterations the fit converged.
+final sum of squares of residuals : 11.3578
+rel. change during last iteration : -7.81502e-08
+
+degrees of freedom    (FIT_NDF)                        : 198
+rms of residuals      (FIT_STDFIT) = sqrt(WSSR/ndf)    : 0.239505
+variance of residuals (reduced chisquare) = WSSR/ndf   : 0.0573625
+
+Final set of parameters            Asymptotic Standard Error
+=======================            ==========================
+
+aaa             = -3135.44         +/- 2.698        (0.08605%)
+bbb             = 3135.83          +/- 2.511        (0.08006%)
+
+
+correlation matrix of the fit parameters:
+
+               aaa    bbb    
+aaa             1.000 
+bbb            -1.000  1.000 

dokumentation/evolution1d/20170830-evolution1D_5x5_100Times-all.gnuplot.script

@@ -0,0 +1,20 @@
+set datafile separator ","
+f(x)=a*x+b
+fit f(x) "20170830-evolution1D_5x5_100Times-all.csv" every ::1 using 2:5 via a,b
+set terminal png
+set xlabel 'regularity'
+set ylabel 'steps'
+set output "20170830-evolution1D_5x5_100Times-all_regularity-vs-steps.png"
+plot "20170830-evolution1D_5x5_100Times.csv" every ::1 using 2:5 title "20170830-evolution1D_5x5_100Times.csv", "20170830-evolution1D_5x5_100Times-added_one.csv" every ::1 using 2:5 title "20170830-evolution1D_5x5_100Times-added_one.csv", f(x) title "lin. fit" lc rgb "black"
+g(x)=aa*x+bb
+fit g(x) "20170830-evolution1D_5x5_100Times-all.csv" every ::1 using 4:5 via aa,bb
+set xlabel 'improvement potential'
+set ylabel 'steps'
+set output "20170830-evolution1D_5x5_100Times-all_improvement-vs-steps.png"
+plot "20170830-evolution1D_5x5_100Times.csv" every ::1 using 4:5 title "20170830-evolution1D_5x5_100Times.csv", "20170830-evolution1D_5x5_100Times-added_one.csv" every ::1 using 4:5 title "20170830-evolution1D_5x5_100Times-added_one.csv", g(x) title "lin. fit" lc rgb "black"
+h(x)=aaa*x+bbb
+fit h(x) "20170830-evolution1D_5x5_100Times-all.csv" every ::1 using 4:6 via aaa,bbb
+set xlabel 'improvement potential'
+set ylabel 'evolution error'
+set output "20170830-evolution1D_5x5_100Times-all_improvement-vs-evo-error.png"
+plot "20170830-evolution1D_5x5_100Times.csv" every ::1 using 4:6 title "20170830-evolution1D_5x5_100Times.csv", "20170830-evolution1D_5x5_100Times-added_one.csv" every ::1 using 4:6 title "20170830-evolution1D_5x5_100Times-added_one.csv", h(x) title "lin. fit" lc rgb "black"

dokumentation/evolution1d/20170830-evolution1D_5x5_100Times.gnuplot.fit.log

@@ -1,7 +1,7 @@
 
 
 *******************************************************************************
-Wed Aug 30 21:11:12 2017
+Sun Oct  1 19:58:40 2017
 
 
 FIT:    data read from "20170830-evolution1D_5x5_100Times.csv" every ::1 using 2:5
@@ -47,7 +47,7 @@ b              -0.995  1.000
 
 
 *******************************************************************************
-Wed Aug 30 21:11:12 2017
+Sun Oct  1 19:58:40 2017
 
 
 FIT:    data read from "20170830-evolution1D_5x5_100Times.csv" every ::1 using 4:5
@@ -93,7 +93,7 @@ bb             -1.000  1.000
 
 
 *******************************************************************************
-Wed Aug 30 21:11:12 2017
+Sun Oct  1 19:58:40 2017
 
 
 FIT:    data read from "20170830-evolution1D_5x5_100Times.csv" every ::1 using 4:6

dokumentation/evolution1d/20170830-evolution1D_5x5_100Times.gnuplot.script

@@ -2,13 +2,19 @@ set datafile separator ","
 f(x)=a*x+b
 fit f(x) "20170830-evolution1D_5x5_100Times.csv" every ::1 using 2:5 via a,b
 set terminal png
+set xlabel 'regularity'
+set ylabel 'steps'
 set output "20170830-evolution1D_5x5_100Times_regularity-vs-steps.png"
-plot "20170830-evolution1D_5x5_100Times.csv" every ::1 using 2:5 title "regularity vs. steps", f(x) lc rgb "black"
+plot "20170830-evolution1D_5x5_100Times.csv" every ::1 using 2:5 title "data", f(x) title "lin. fit" lc rgb "black"
 g(x)=aa*x+bb
 fit g(x) "20170830-evolution1D_5x5_100Times.csv" every ::1 using 4:5 via aa,bb
+set xlabel 'improvement potential'
+set ylabel 'steps'
 set output "20170830-evolution1D_5x5_100Times_improvement-vs-steps.png"
-plot "20170830-evolution1D_5x5_100Times.csv" every ::1 using 4:5 title "improvement potential vs. steps", g(x) lc rgb "black"
+plot "20170830-evolution1D_5x5_100Times.csv" every ::1 using 4:5 title "data", g(x) title "lin. fit" lc rgb "black"
 h(x)=aaa*x+bbb
 fit h(x) "20170830-evolution1D_5x5_100Times.csv" every ::1 using 4:6 via aaa,bbb
+set xlabel 'improvement potential'
+set ylabel 'evolution error'
 set output "20170830-evolution1D_5x5_100Times_improvement-vs-evo-error.png"
-plot "20170830-evolution1D_5x5_100Times.csv" every ::1 using 4:6 title "improvement potential vs. evolution error", h(x) lc rgb "black"
+plot "20170830-evolution1D_5x5_100Times.csv" every ::1 using 4:6 title "data", h(x) title "lin. fit" lc rgb "black"

dokumentation/evolution1d/combine.sh

@@ -0,0 +1,33 @@
+#!/bin/bash
+
+if [[ $# -eq 0 ]]; then
+    echo "usage: $0 <DATA.csv>"
+else
+    data="$1";
+    png="`echo $1 | sed -s "s/\.csv$//"`" # strip ending
+    (cat <<EOD
+set datafile separator ","
+f(x)=a*x+b
+fit f(x) "$data" every ::1 using 2:5 via a,b
+set terminal png
+set xlabel 'regularity'
+set ylabel 'steps'
+set output "${png}_regularity-vs-steps.png"
+plot "$2" every ::1 using 2:5 title "$2", "$3" every ::1 using 2:5 title "$3", f(x) title "lin. fit" lc rgb "black"
+g(x)=aa*x+bb
+fit g(x) "$data" every ::1 using 4:5 via aa,bb
+set xlabel 'improvement potential'
+set ylabel 'steps'
+set output "${png}_improvement-vs-steps.png"
+plot "$2" every ::1 using 4:5 title "$2", "$3" every ::1 using 4:5 title "$3", g(x) title "lin. fit" lc rgb "black"
+h(x)=aaa*x+bbb
+fit h(x) "$data" every ::1 using 4:6 via aaa,bbb
+set xlabel 'improvement potential'
+set ylabel 'evolution error'
+set output "${png}_improvement-vs-evo-error.png"
+plot "$2" every ::1 using 4:6 title "$2", "$3" every ::1 using 4:6 title "$3", h(x) title "lin. fit" lc rgb "black"
+EOD
+) > "${png}.gnuplot.script" 
+    gnuplot "${png}.gnuplot.script" 2> "${png}.gnuplot.log"
+    mv fit.log "${png}.gnuplot.fit.log"
+fi

dokumentation/evolution1d/images.sh

@@ -10,16 +10,22 @@ set datafile separator ","
 f(x)=a*x+b
 fit f(x) "$data" every ::1 using 2:5 via a,b
 set terminal png
+set xlabel 'regularity'
+set ylabel 'steps'
 set output "${png}_regularity-vs-steps.png"
-plot "$data" every ::1 using 2:5 title "regularity vs. steps", f(x) lc rgb "black"
+plot "$data" every ::1 using 2:5 title "data", f(x) title "lin. fit" lc rgb "black"
 g(x)=aa*x+bb
 fit g(x) "$data" every ::1 using 4:5 via aa,bb
+set xlabel 'improvement potential'
+set ylabel 'steps'
 set output "${png}_improvement-vs-steps.png"
-plot "$data" every ::1 using 4:5 title "improvement potential vs. steps", g(x) lc rgb "black"
+plot "$data" every ::1 using 4:5 title "data", g(x) title "lin. fit" lc rgb "black"
 h(x)=aaa*x+bbb
 fit h(x) "$data" every ::1 using 4:6 via aaa,bbb
+set xlabel 'improvement potential'
+set ylabel 'evolution error'
 set output "${png}_improvement-vs-evo-error.png"
-plot "$data" every ::1 using 4:6 title "improvement potential vs. evolution error", h(x) lc rgb "black"
+plot "$data" every ::1 using 4:6 title "data", h(x) title "lin. fit" lc rgb "black"
 EOD
 ) > "${png}.gnuplot.script" 
     gnuplot "${png}.gnuplot.script" 2> "${png}.gnuplot.log"