├── Makefile
├── .gitignore
├── README.md
├── minted.sty
├── paper.bib
├── paper.tex
└── llncs.cls


/Makefile:
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 1 | paper.pdf: paper.bib paper.tex
 2 | 	pdflatex -shell-escape paper.tex
 3 | 	bibtex paper
 4 | 	pdflatex -shell-escape paper.tex
 5 | 	pdflatex -shell-escape paper.tex
 6 | 
 7 | partial: 
 8 | 	pdflatex -shell-escape paper.tex
 9 | 
10 | clean:
11 | 	rm -f *.log *.out *.aux *.bbl *.blg paper.pdf
12 | 


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/.gitignore:
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 1 | # Vim temporaries
 2 | .*.sw[op]
 3 | 
 4 | # LaTeX output
 5 | *.dvi
 6 | *.pdf
 7 | *.ps
 8 | 
 9 | # LaTeX cruft
10 | *.aux
11 | *.glo
12 | *.idx
13 | *.log
14 | *.toc
15 | *.ist
16 | *.acn
17 | *.acr
18 | *.alg
19 | *.bbl
20 | *.blg
21 | *.dvi
22 | *.glg
23 | *.gls
24 | *.ilg
25 | *.ind
26 | *.lof
27 | *.lot
28 | *.maf
29 | *.mtc
30 | *.mtc1
31 | *.out
32 | *.synctex.gz
33 | 


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/README.md:
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 1 | ECML/PKDD 2013 workshop paper
 2 | =============================
 3 | 
 4 | Paper by scikit-learn contributers for the ECML/PKDD 2013 Workshop "Languages
 5 | for Data Mining and Machine Learning".
 6 | 
 7 | Website: http://dtai.cs.kuleuven.be/lml/
 8 | <del>Submission deadline: Fri. 28 June</del>
 9 | Deadline for revisions: Thu. 15 August
10 | 
11 | Maximum number of pages: 15
12 | 


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/minted.sty:
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  1 | %%
  2 | %% This is file `minted.sty',
  3 | %% generated with the docstrip utility.
  4 | %%
  5 | %% The original source files were:
  6 | %%
  7 | %% minted.dtx  (with options: `package')
  8 | %% Copyright 2010--2011 Konrad Rudolph
  9 | %% 
 10 | %% This work may be distributed and/or modified under the
 11 | %% conditions of the LaTeX Project Public License, either version 1.3
 12 | %% of this license or (at your option) any later version.
 13 | %% The latest version of this license is in
 14 | %%   http://www.latex-project.org/lppl.txt
 15 | %% and version 1.3 or later is part of all distributions of LaTeX
 16 | %% version 2005/12/01 or later.
 17 | %% 
 18 | %% Additionally, the project may be distributed under the terms of the new BSD
 19 | %% license.
 20 | %% 
 21 | %% This work has the LPPL maintenance status `maintained'.
 22 | %% 
 23 | %% The Current Maintainer of this work is Konrad Rudolph.
 24 | %% 
 25 | %% This work consists of the files minted.dtx and minted.ins
 26 | %% and the derived file minted.sty.
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146 | \newcommand\minted@pygmentize[2][\jobname.pyg]{
147 |   \def\minted@cmd{pygmentize -l #2 -f latex -F tokenmerge
148 |     \minted@opt{gobble} \minted@opt{texcl} \minted@opt{mathescape}
149 |     \minted@opt{startinline} \minted@opt{funcnamehighlighting}
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190 |   \minted@pygmentize[#3]{#2}}
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192 |   \ifthenelse{\equal{#1}{}}
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195 |   \newenvironment{\minted@envname}
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199 |    {\VerbatimEnvironment\begin{minted}[#3,##1]{#2}}
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202 |   \ifthenelse{\equal{#1}{}}
203 |    {\def\minted@shortname{#2}}
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205 |   \expandafter\newcommand\csname\minted@shortname\endcsname[2][]{
206 |     \mint[#3,##1]{#2}##2}}
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208 |   \ifthenelse{\equal{#1}{}}
209 |    {\def\minted@shortname{#2file}}
210 |    {\def\minted@shortname{#1}}
211 |   \expandafter\newcommand\csname\minted@shortname\endcsname[2][]{
212 |     \inputminted[#3,##1]{#2}{##2}}}
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240 | 


--------------------------------------------------------------------------------
/paper.bib:
--------------------------------------------------------------------------------
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290 | booktitle = {Knowledge Discovery in Databases PKDD 2004},
291 | publisher = {Springer},
292 | series = {Lecture Notes in Computer Science},
293 | title = {Orange: From Experimental Machine Learning to Interactive Data Mining},
294 | year = {2004}
295 | }
296 | 
297 | @inproceedings{sculley2009large,
298 |   title={Large scale learning to rank},
299 |   author={Sculley, D},
300 |   booktitle={NIPS Workshop on Advances in Ranking},
301 |   pages={1--6},
302 |   year={2009}
303 | }
304 | 


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  1 | \documentclass{llncs}
  2 | 
  3 | \usepackage[utf8]{inputenc}
  4 | \usepackage{amsmath}
  5 | %\usepackage{hyperref}
  6 | \usepackage[authoryear,round]{natbib}
  7 | \usepackage{xcolor}
  8 | \usepackage{xspace}
  9 | \usepackage{minted}
 10 | 
 11 | \definecolor{rulecolor}{rgb}{0.80,0.80,0.80}
 12 | \newminted{python}{frame=single,rulecolor=\color{rulecolor}}
 13 | 
 14 | % tt font with bold support
 15 | %\renewcommand{\ttdefault}{pcr}
 16 | 
 17 | \pagestyle{headings}
 18 | 
 19 | \newcommand{\sklearn}{\textit{scikit-learn}\xspace}
 20 | 
 21 | \title{API design for machine learning software: experiences from the
 22 | scikit-learn project}
 23 | 
 24 | \author{Lars~Buitinck~\inst{1} \and
 25 |         Gilles~Louppe~\inst{2} \and
 26 |         Mathieu~Blondel~\inst{3} \and
 27 |         Fabian~Pedregosa~\inst{4} \and
 28 |         Andreas~C.~M\"uller~\inst{5} \and
 29 |         Olivier~Grisel~\inst{6} \and
 30 |         Vlad~Niculae~\inst{7} \and
 31 |         Peter~Prettenhofer~\inst{8} \and
 32 |         Alexandre~Gramfort~\inst{4,9} \and
 33 |         Jaques~Grobler~\inst{4} \and
 34 |         Robert~Layton~\inst{10} \and
 35 |         Jake~Vanderplas~\inst{11} \and
 36 |         Arnaud~Joly~\inst{2} \and
 37 |         Brian Holt~\inst{12} \and
 38 |         Gaël~Varoquaux~\inst{4}}
 39 | 
 40 | \institute{ILPS, Informatics Institute, University of Amsterdam \and
 41 |            University of Liège \and
 42 |            Kobe University \and
 43 |            Parietal, INRIA Saclay \and
 44 |            University of Bonn \and
 45 |            Independent consultant \and
 46 |            University of Bucharest \and
 47 |            Ciuvo GmbH \and
 48 |            Institut Mines-Telecom, Telecom ParisTech, CNRS LTCI \and
 49 |            University of Ballarat \and
 50 |            University of Washington \and
 51 |            Samsung Electronics Research Institute}
 52 | 
 53 | % Dutch name sorting hack as per http://tex.stackexchange.com/a/40750/2806
 54 | \DeclareRobustCommand{\VAN}[3]{#2}
 55 | 
 56 | \begin{document}
 57 | 
 58 | \maketitle
 59 | 
 60 | \begin{abstract}
 61 | \sklearn is an increasingly popular machine learning
 62 | library. Written in Python, it is designed to be simple and efficient, accessible to
 63 | non-experts, and reusable in various contexts. In this paper, we present and
 64 | discuss our design choices for the application programming interface (API) of
 65 | the project. In particular, we describe the simple and elegant interface shared
 66 | by all learning and processing units in the library and then discuss its
 67 | advantages in terms of composition and reusability. The paper also comments on
 68 | implementation details specific to the Python ecosystem and analyzes obstacles
 69 | faced by users and developers of the library.
 70 | \end{abstract}
 71 | 
 72 | \setcounter{footnote}{0}
 73 | 
 74 | \section{Introduction}
 75 | 
 76 | The \sklearn project\footnote{\url{http://scikit-learn.org}}
 77 | \citep{pedregosa2011} provides an open source machine learning
 78 | library for the Python programming language. The ambition of the project is to
 79 | provide efficient and well-established machine learning tools within a
 80 | programming environment that is accessible to non-machine learning experts and
 81 | reusable in various scientific areas. The project is not a novel domain-specific
 82 | language, but a library that provides machine learning idioms to a
 83 | general-purpose high-level language. Among other things, it includes classical learning
 84 | algorithms, model evaluation and selection tools, as well as
 85 | preprocessing procedures. The library is
 86 | distributed under the simplified BSD license, encouraging its use in both
 87 | academic and commercial settings.
 88 | 
 89 | \sklearn is a library, i.e.\ a collection of classes
 90 | and functions that users import into Python programs. Using \sklearn therefore
 91 | requires basic Python programming knowledge. No command-line interface, let
 92 | alone a graphical user interface, is offered for non-programmer users. Instead,
 93 | interactive use is made possible by the Python interactive interpreter, and its
 94 | enhanced replacement IPython \citep{perez2007ipython}, which offer a
 95 | \textsc{matlab}-like working environment specifically designed for scientific
 96 | use.
 97 | 
 98 | The library has been designed to tie in with the set of numeric
 99 | and scientific packages centered around the NumPy and SciPy libraries. NumPy
100 | \citep{vanderwalt2011} augments Python with a contiguous numeric array datatype
101 | and fast array computing primitives,
102 | while SciPy \citep{varoquaux2013scipy} extends it
103 | further with common numerical operations, either by implementing
104 | these in Python/NumPy or by wrapping existing C/C{}\verb!++!/Fortran
105 | implementations. Building upon this stack, a series of libraries called
106 | \textit{scikits} were created, to complement SciPy with
107 | domain-specific toolkits. Currently, the two most popular and feature-complete
108 | ones are by far \sklearn and
109 | \textit{scikit-image},\footnote{\url{http://scikit-image.org}}
110 | which does image processing.
111 | 
112 | Started in 2007, \sklearn is developed by an international team of over a dozen
113 | core developers, mostly researchers from various fields (e.g.,
114 | computer science, neuroscience, astrophysics). The project also benefits
115 | from many occasional contributors proposing small bugfixes or
116 | improvements. Development proceeds on GitHub\footnote{\url{https://github.com/scikit-learn}},
117 | a platform which greatly facilitates this kind of
118 | collaboration. Because of the large number of developers, emphasis is
119 | put on keeping the project maintainable. In particular, code must follow
120 | specific quality guidelines, such as style consistency and unit-test coverage.
121 | Documentation and examples are required for all features,
122 | and major changes must pass code review by at least two
123 | developers not involved in the implementation of the proposed change.
124 | 
125 | \sklearn's popularity can be gauged from various indicators such as the hundreds
126 | of citations in scientific publications, successes in various machine learning
127 | challenges (e.g., Kaggle), and statistics derived from our
128 | repositories and mailing list.  At the time of writing, the project is watched
129 | by 1365 people and forked 693 times on GitHub; the mailing list receives more
130 | than 300 mails per month; version control logs
131 | % ddaa494c116e3c16bf032003c5cccbed851733d2
132 | show 183 unique contributors to the codebase and the online documentation
133 | receives 37,000 unique visitors and 295,000 pageviews per month.
134 | 
135 | \citet{pedregosa2011} briefly presented \sklearn and
136 | benchmarked it against several competitors.
137 | In this paper, we instead present an
138 | in-depth analysis of design choices made when building the library,
139 | detailing how we organized and operationalized
140 | common machine learning concepts.
141 | We first present in section~\ref{sec:core-api} the central application
142 | programming interface (API) and then describe, in section~\ref{sec:advanced-api},
143 | advanced API mechanisms built on the core interface.
144 | Section~\ref{sec:implementation} briefly describes the implementation.
145 | Section~\ref{sec:comparison} then
146 | compares \sklearn to other major projects in terms of API\@.
147 | Section~\ref{sec:future_work} outlines some of the objectives for
148 | a \sklearn 1.0 release.
149 | We conclude by summarizing the major points of this paper in
150 | section~\ref{sec:conclusions}.
151 | 
152 | \section{Core API}
153 | 
154 | \label{sec:core-api}
155 | 
156 | All objects within \sklearn share a uniform common basic API consisting of three
157 | complementary interfaces: an \textit{estimator} interface for building and
158 | fitting models, a \textit{predictor} interface for making predictions and a
159 | \textit{transformer} interface for converting data. In this section, we describe
160 | these three interfaces, after reviewing our general principles and data
161 | representation choices.
162 | 
163 | \subsection{General principles}
164 | 
165 | As much as possible, our
166 | design choices have been guided so as to avoid the proliferation of framework
167 | code. We try to adopt simple conventions and to limit to a minimum the number of
168 | methods an object must implement. The API is designed to adhere to the following
169 | broad principles:
170 | 
171 | \begin{description}
172 |   \item[Consistency.]
173 |        All objects (basic or composite) share a consistent interface composed of
174 |        a limited set of methods. This interface is documented in a consistent
175 |        manner for all objects.
176 |   \item[Inspection.]
177 |        Constructor parameters and parameter values determined by learning
178 |        algorithms are stored and exposed as public attributes.
179 |   \item[Non-proliferation of classes.]
180 |        Learning algorithms are the only objects to be represented using custom classes.
181 |        Datasets are represented as NumPy arrays or SciPy sparse matrices.
182 |        Hyper-parameter names and values are represented as standard
183 |        Python strings or numbers whenever possible.
184 |        This keeps \sklearn easy to use and easy to combine with other libraries.
185 |   \item[Composition.]
186 |        Many machine learning tasks are expressible
187 |        as sequences or combinations of transformations to data.
188 |        Some learning algorithms are also naturally viewed
189 |        as meta-algorithms parametrized on other algorithms.
190 |        Whenever feasible, such algorithms are implemented and composed from
191 |        existing building blocks.
192 |   \item[Sensible defaults.]
193 |        Whenever an operation requires a user-defined parameter,
194 |        an appropriate default value is defined by the library.
195 |        The default value should cause the operation to be performed
196 |        in a sensible way (giving a baseline solution for the task at hand).
197 | \end{description}
198 | 
199 | \subsection{Data representation}
200 | \label{sec:arrays}
201 | 
202 | In most machine learning tasks, data is modeled as a set of variables.  For
203 | example, in a supervised learning task, the goal is to find a mapping
204 | from input variables $X_1, \ldots X_p$, called features, to
205 | some output variables $Y$. A sample is then defined as a pair of
206 | values $([x_1, \ldots, x_p]^\mathrm{T}, y)$ of these variables. A widely used
207 | representation of a dataset, a collection of
208 | such samples, is a pair of matrices with numerical values: one for the input
209 | values and one for the output values. Each row of these matrices
210 | corresponds to one sample of the dataset and each column to one variable of
211 | the problem.
212 | 
213 | In \sklearn, we chose a representation of data that is as close as
214 | possible to the matrix representation: datasets are encoded as NumPy
215 | multidimensional arrays for dense data and as SciPy sparse matrices for sparse
216 | data. While these may seem rather unsophisticated data representations when
217 | compared to more object-oriented constructs, such as the ones used by
218 | Weka \citep{hall2009weka}, they bring the prime advantage of allowing us to rely
219 | on efficient NumPy and SciPy vectorized operations while keeping
220 | the code short and readable.  This design choice has also been motivated by
221 | the fact that, given their pervasiveness in many other scientific Python
222 | packages, many scientific users of Python are already familiar with NumPy dense
223 | arrays and SciPy sparse matrices.
224 | From a practical point of view, these formats also provide a collection of
225 | data loading and conversion tools which make them very easy to use in many
226 | contexts. Moreover, for tasks where the inputs are text files or semi-structured
227 | objects, we provide \textit{vectorizer} objects that efficiently convert such
228 | data to the NumPy or SciPy formats.
229 | 
230 | For efficiency reasons, the public interface is oriented towards processing
231 | batches of samples rather than single samples per API call. While classification
232 | and regression algorithms can indeed make predictions for single samples,
233 | \sklearn objects are not optimized for this use case. (The few online learning
234 | algorithms implemented are intended to take mini-batches.) Batch processing makes
235 | optimal use of NumPy and SciPy by preventing the overhead inherent to Python
236 | function calls or due to per-element dynamic type checking. Although this might
237 | seem to be an artifact of the Python language, and therefore an implementation
238 | detail that leaks into the API, we argue that APIs should be designed so as not
239 | to tie a library to a suboptimal implementation strategy. As such, batch
240 | processing enables fast implementations in lower-level languages (where memory
241 | hierarchy effects and the possibility of internal parallelization come into
242 | play).
243 | 
244 | 
245 | \subsection{Estimators}
246 | \label{sec:estimators}
247 | 
248 | The \textit{estimator} interface is at the core of the
249 | library. It defines instantiation mechanisms of objects and exposes a
250 | \texttt{fit} method for learning a model from training data.  All supervised and
251 | unsupervised learning algorithms (e.g., for classification, regression or
252 | clustering) are offered as objects implementing this interface. Machine
253 | learning tasks like feature extraction, feature selection or dimensionality
254 | reduction are also provided as estimators.
255 | 
256 | Estimator initialization and actual learning are strictly separated,
257 | in a way that is similar to partial function application:
258 | an estimator is initialized from a set of named constant hyper-parameter values
259 | (e.g., the $C$ constant in SVMs)
260 | and can be considered as a function
261 | that maps these values to actual learning algorithms.
262 | The constructor of an estimator does not see any actual data, nor does it perform any actual learning.
263 | All it does is attach the given parameters to the object.
264 | For the sake of convenient model inspection, hyper-parameters are set as public attributes,
265 | which is especially important in model selection settings.
266 | For ease of use, default hyper-parameter values are also provided
267 | for all built-in estimators.
268 | These default values are set to be relevant in many common
269 | situations in order to make estimators as effective as possible
270 | \textit{out-of-box} for non-experts.
271 | 
272 | Actual learning is performed by the \texttt{fit} method. This method is called
273 | with training data (e.g., supplied as two arrays \texttt{X\_train} and
274 | \texttt{y\_train} in supervised learning estimators). Its task is to run a
275 | learning algorithm and to determine model-specific parameters from the training
276 | data and set these as attributes on the estimator object. As a convention, the
277 | parameters learned by an estimator are exposed as public attributes with names
278 | suffixed with a trailing underscore (e.g., \texttt{coef\_} for the
279 | learned coefficients of a linear model),
280 | again to facilitate model inspection.
281 | In the partial application view,
282 | \texttt{fit} is a function from data to a model of that data.
283 | It always returns the estimator object it was called on,
284 | which now serves as a model of its input and can be used to perform predictions or transformations of input data.
285 | 
286 | From the start, the choice to let a single object serve dual purpose as
287 | estimator and model has mostly been driven by usability and technical
288 | considerations. From the user point of view, having two coupled instances (i.e.,
289 | an estimator object, used as a factory, and a model object, produced by the
290 | estimator) indeed decreases the ease of use and is also more likely to
291 | unnecessarily confuse newcomers. From the developer point of view, decoupling
292 | estimators from models also creates parallel class hierarchies and increases the
293 | overall maintenance complexity of the project. For these practical reasons, we
294 | believe that decoupling estimators from models is not worth the effort. A good
295 | reason for decoupling however, would be that it makes it possible to ship a
296 | model in a new environment without having to deal with potentially complex
297 | software dependencies. Such a feature could however still be implemented in
298 | \sklearn by making estimators able to export a fitted model, using the
299 | information from its public attributes, to an agnostic model description such as
300 | PMML~\citep{guazzelli2009pmml}.
301 | 
302 | To illustrate the initialize-fit sequence,
303 | let us consider a supervised learning task using logistic regression.
304 | Given the API defined above, solving this problem is as simple as the following
305 | example.
306 | \begin{pythoncode}
307 | from sklearn.linear_model import LogisticRegression
308 | 
309 | clf = LogisticRegression(penalty="l1")
310 | clf.fit(X_train, y_train)
311 | \end{pythoncode}
312 | In this snippet, a \texttt{LogisticRegression} estimator is first initialized by
313 | setting the \texttt{penalty} hyper-parameter to \texttt{"l1"} for
314 | $\ell_1$ regularization. Other hyper-parameters (such as \texttt{C},
315 | the strength of the regularization) are not explicitly given and
316 | thus set to the default values. Upon calling \texttt{fit}, a model is
317 | learned from the training arrays \texttt{X\_train} and \texttt{y\_train},
318 | and stored within the object for later use.
319 | %% (In this example, \texttt{fit} is called solely for its side effects.)
320 | Since all estimators share the same interface, using a different learning algorithm is
321 | as simple as replacing the constructor (the class name);
322 | to build a random forest on
323 | the same data, one would simply replace
324 | \texttt{LogisticRegression(penalty="l1")} in the snippet above by
325 | \texttt{RandomForestClassifier()}.
326 | 
327 | In \sklearn, classical learning algorithms are not the only objects to be
328 | implemented as estimators. For example, preprocessing routines (e.g., scaling of
329 | features) or feature extraction techniques (e.g., vectorization of text
330 | documents) also implement the \textit{estimator} interface. Even stateless
331 | processing steps, that do not require the \texttt{fit} method to
332 | perform useful work, implement the estimator interface. As we will illustrate
333 | in the next sections, this design pattern is indeed of prime importance for
334 | consistency, composition and model selection reasons.
335 | 
336 | \subsection{Predictors}
337 | 
338 | The \textit{predictor} interface extends the notion of an estimator
339 | by adding a \texttt{predict}
340 | method that takes an array \texttt{X\_test} and produces
341 | predictions for \texttt{X\_test}, based on the learned parameters of the
342 | estimator (we call the input to \texttt{predict} ``\texttt{X\_test}'' in order
343 | to emphasize that \texttt{predict} generalizes to new data). In the case of
344 | supervised learning estimators, this method typically returns the predicted
345 | labels or values computed by the model.  Continuing with the previous example,
346 | predicted labels for \texttt{X\_test} can be obtained using the following
347 | snippet:
348 | \begin{pythoncode}
349 | y_pred = clf.predict(X_test)
350 | \end{pythoncode}
351 | 
352 | Some unsupervised learning estimators may also implement the \texttt{predict}
353 | interface. The code in the snippet below fits a $k$-means model with $k=10$ on
354 | training data \texttt{X\_train}, and then uses the  \texttt{predict} method to
355 | obtain cluster labels (integer indices) for unseen data \texttt{X\_test}.
356 | \begin{pythoncode}
357 | from sklearn.cluster import KMeans
358 | 
359 | km = KMeans(n_clusters=10)
360 | km.fit(X_train)
361 | clust_pred = km.predict(X_test)
362 | \end{pythoncode}
363 | 
364 | Apart from \texttt{predict}, predictors may also implement methods
365 | that quantify the confidence of predictions. In the case of
366 | linear models, the \texttt{decision\_function} method returns
367 | the distance of samples to the separating hyperplane. Some
368 | predictors also provide a \texttt{predict\_proba} method which returns
369 | class probabilities.
370 | 
371 | Finally, predictors must provide a \texttt{score} function to assess their
372 | performance on a batch of input data. In supervised estimators, this method
373 | takes as input arrays \texttt{X\_test} and \texttt{y\_test} and typically
374 | computes the coefficient of determination between \texttt{y\_test} and
375 | \texttt{predict(X\_test)} in regression, or the accuracy
376 | in classification.
377 | The only requirement is that the \texttt{score} method return a value
378 | that quantifies the quality of its predictions (the higher, the better).
379 | An unsupervised estimator may also expose a \texttt{score} function
380 | to compute, for instance, the likelihood of the given data under its model.
381 | 
382 | \subsection{Transformers}
383 | 
384 | Since it is common to modify or filter data before feeding it to a learning
385 | algorithm, some estimators in the library implement a \textit{transformer}
386 | interface which defines a \texttt{transform} method. It takes as input some new
387 | data \texttt{X\_test} and yields as output a transformed version of
388 | \texttt{X\_test}. Preprocessing, feature selection, feature extraction and dimensionality reduction
389 | algorithms are all provided as transformers within the library.  In our example,
390 | to standardize the input \texttt{X\_train} to zero mean and unit variance
391 | before fitting the logistic regression estimator,
392 | one would write:
393 | \begin{pythoncode}
394 | from sklearn.preprocessing import StandardScaler
395 | 
396 | scaler = StandardScaler()
397 | scaler.fit(X_train)
398 | X_train = scaler.transform(X_train)
399 | \end{pythoncode}
400 | Of course, in practice, it is important to apply the same preprocessing to the
401 | test data \texttt{X\_test}. Since a \texttt{StandardScaler} estimator stores the
402 | mean and standard deviation that it computed for the training set, transforming
403 | an unseen test set \texttt{X\_test} maps it into the appropriate region of
404 | feature space:
405 | \begin{pythoncode}
406 | X_test = scaler.transform(X_test)
407 | \end{pythoncode}
408 | Transformers also include a variety of learning algorithms, such as
409 | dimension reduction (PCA, manifold learning), kernel approximation,
410 | and other mappings from one feature space to another.
411 | 
412 | Additionally, by leveraging the fact that \texttt{fit} always returns the
413 | estimator it was called on, the \texttt{StandardScaler} example above can be
414 | rewritten in a single line using method chaining:
415 | \begin{pythoncode}
416 | X_train = StandardScaler().fit(X_train).transform(X_train)
417 | \end{pythoncode}
418 | 
419 | Furthermore, every transformer allows \texttt{fit(X\_train).transform(X\_train)}
420 | to be written as \texttt{fit\_transform(X\_train)}.
421 | The combined \texttt{fit\_transform} method prevents repeated computations.
422 | Depending on the transformer,
423 | it may skip only an input validation step,
424 | or in fact use a more efficient algorithm for the transformation.
425 | In the same spirit, clustering algorithms provide a
426 | \texttt{fit\_predict} method
427 | that is equivalent to \texttt{fit} followed by \texttt{predict},
428 | returning cluster labels assigned to the training samples.
429 | 
430 | 
431 | \section{Advanced API}
432 | 
433 | \label{sec:advanced-api}
434 | 
435 | Building on the core interface introduced in the previous section, we now
436 | present advanced API mechanisms for building meta-estimators,
437 | composing complex estimators and selecting models. We also discuss design
438 | choices allowing for easy usage and extension of \sklearn.
439 | 
440 | \subsection{Meta-estimators}
441 | 
442 | Some machine learning algorithms are expressed naturally
443 | as meta-algorithms parametrized on simpler algorithms.
444 | Examples include ensemble methods which
445 | build and combine several simpler models (e.g., decision trees), or multiclass
446 | and multilabel classification schemes which can be used to turn a binary
447 | classifier into a multiclass or multilabel classifier. In \sklearn, such algorithms are
448 | implemented as \textit{meta-estimators}. They take as input an existing base
449 | estimator and use it internally for learning and making predictions.
450 | All meta-estimators implement the regular estimator interface.
451 | 
452 | As an example, a logistic regression classifier
453 | uses by default a one-vs.-rest scheme
454 | for performing multiclass classification.
455 | A different scheme can be achieved
456 | by a meta-estimator wrapping a logistic regression estimator:
457 | \begin{pythoncode}
458 | from sklearn.multiclass import OneVsOneClassifier
459 | 
460 | ovo_lr = OneVsOneClassifier(LogisticRegression(penalty="l1"))
461 | \end{pythoncode}
462 | For learning, the \texttt{OneVsOneClassifier} object
463 | \textit{clones} the logistic regression estimator multiple times,
464 | resulting in a set of $\frac{K(K-1)}{2}$ estimator objects
465 | for $K$-way classification,
466 | all with the same settings.
467 | For predictions, all estimators perform a binary classification and then vote to make the final decision.
468 | The snippet exemplifies the importance
469 | of separating object instantiation and actual learning.
470 | 
471 | Since meta-estimators require users to construct nested objects,
472 | the decision to implement a meta-estimator
473 | rather than integrate the behavior it implements
474 | into existing estimators classes
475 | is always based on a trade-off between generality and ease of use.
476 | Relating to the example just given,
477 | all \sklearn classifiers are designed to do multiclass classification
478 | and the use of the \texttt{multiclass} module
479 | is only necessary in advanced use cases.
480 | 
481 | % TODO: show a grid search on this estimator
482 | 
483 | \subsection{Pipelines and feature unions}
484 | 
485 | A distinguishing feature of the \sklearn API is its ability to
486 | compose new estimators from several base estimators. Composition mechanisms can
487 | be used to combine typical machine learning workflows into a single object which
488 | is itself an estimator, and can be employed wherever usual estimators can be used.
489 | In particular, \sklearn's model selection routines
490 | can be applied to composite estimators, allowing global optimization
491 | of all parameters in a complex workflow.
492 | Composition of estimators can be done in two
493 | ways: either sequentially through \texttt{Pipeline} objects, or in a parallel
494 | fashion through \texttt{FeatureUnion} objects.
495 | 
496 | \texttt{Pipeline} objects chain multiple estimators into a single one. This is
497 | useful since a machine learning workflow typically involves a fixed sequence of
498 | processing steps (e.g., feature extraction, dimensionality reduction, learning
499 | and making predictions), many of which perform some kind of learning.
500 | A sequence of $N$ such steps can be combined into a
501 | \texttt{Pipeline} if the first $N-1$ steps are transformers; the last can be
502 | either a predictor, a transformer or both.
503 | 
504 | Conceptually, fitting a pipeline to
505 | a training set amounts to the following recursive procedure: i) when only one
506 | step remains, call its \texttt{fit} method; ii) otherwise, \texttt{fit} the
507 | first step, use it to \texttt{transform} the training set and \texttt{fit} the
508 | rest of the pipeline with the transformed data. The pipeline exposes all the
509 | methods the last estimator in the pipe exposes. That is, if the last estimator
510 | is a predictor, the pipeline can itself be used as a predictor. If the last
511 | estimator is a transformer, then the pipeline is itself a transformer.
512 | 
513 | \texttt{FeatureUnion} objects combine multiple transformers into a single one
514 | that concatenates their outputs. A union of two transformers that
515 | map input having $d$ features to $d'$ and $d''$ features respectively is
516 | a transformer that maps its $d$ input features to $d' + d''$ features.
517 | This generalizes in the obvious way to more than two transformers.
518 | In terms of API, a \texttt{FeatureUnion} takes as input a list of transformers.
519 | Calling \texttt{fit} on the union is the same as calling \texttt{fit}
520 | independently on each of the transformers and then joining their outputs.
521 | 
522 | \texttt{Pipeline} and \texttt{FeatureUnion} can be
523 | combined to create complex and nested workflows.
524 | The following snippet illustrates how to create a complex estimator
525 | that computes both linear PCA and kernel PCA features on \texttt{X\_train}
526 | (through a \texttt{FeatureUnion}),
527 | selects the 10 best features in the combination according to an ANOVA test
528 | and feeds those to an $\ell_2$-regularized logistic regression model.
529 | \begin{pythoncode}
530 | from sklearn.pipeline import FeatureUnion, Pipeline
531 | from sklearn.decomposition import PCA, KernelPCA
532 | from sklearn.feature_selection import SelectKBest
533 | 
534 | union = FeatureUnion([("pca", PCA()),
535 |                       ("kpca", KernelPCA(kernel="rbf"))])
536 | 
537 | Pipeline([("feat_union", union),
538 |           ("feat_sel", SelectKBest(k=10)),
539 |           ("log_reg", LogisticRegression(penalty="l2"))
540 |          ]).fit(X_train, y_train).predict(X_test)
541 | \end{pythoncode}
542 | 
543 | \subsection{Model selection}
544 | 
545 | As introduced in Section~\ref{sec:estimators}, hyper-parameters set in the
546 | constructor of an estimator
547 | determine the behavior of the learning algorithm
548 | and hence the performance of the resulting model on unseen data.
549 | The problem of \textit{model selection} is therefore to find, within
550 | some hyper-parameter space, the best combination of hyper-parameters, with
551 | respect to some user-specified criterion. For example, a decision
552 | tree with too small a value for the maximal tree depth
553 | parameter will tend to underfit, while too large a value will make it overfit.
554 | 
555 | In \sklearn, model selection is supported in two distinct meta-estimators,
556 | \texttt{GridSearchCV} and \texttt{RandomizedSearchCV}.  They take as input an
557 | estimator (basic or composite), whose hyper-parameters must be optimized, and a
558 | set of hyperparameter settings to search through.
559 | This set is represented as a mapping of parameter names
560 | to a set of discrete choices in the case of grid search,
561 | which exhaustively enumerates the ``grid'' (cartesian product)
562 | of complete parameter combinations.
563 | Randomized search is a smarter algorithm
564 | that avoids the combinatorial explosion in grid search
565 | by sampling a fixed number of times from its parameter distributions
566 | (see \citealp{bergstra2012}).
567 | 
568 | Optionally, the model selection algorithms
569 | also take a cross-validation scheme and a score function.  \sklearn provides
570 | various such cross-validation schemes, including $k$-fold (default),
571 | stratified $k$-fold and leave-one-out.
572 | The score function used by default is the estimator's \texttt{score} method,
573 | but the library provides a variety of
574 | alternatives that the user can choose from,
575 | including accuracy, AUC and $F_1$ score for classification,
576 | $R^2$ score and mean squared error for regression.
577 | 
578 | For each hyper-parameter combination and each train/validation split
579 | generated by the cross-validation scheme, \texttt{GridSearchCV}
580 | and \texttt{RandomizedSearchCV} fit their base estimator on the training set and
581 | evaluate its performance on the validation set.  In the end, the best performing
582 | model on average is retained and exposed as the public attribute
583 | \texttt{best\_estimator\_}.
584 | 
585 | The snippet below illustrates how to find
586 | hyper-parameter settings for an SVM classifier (SVC)
587 | that maximize $F_1$ score
588 | through 10-fold cross-validation on the training set.
589 | \begin{pythoncode}
590 | from sklearn.grid_search import GridSearchCV
591 | from sklearn.svm import SVC
592 | 
593 | param_grid = [
594 |   {"kernel": ["linear"], "C": [1, 10, 100, 1000]},
595 |   {"kernel": ["rbf"], "C": [1, 10, 100, 1000],
596 |    "gamma": [0.001, 0.0001]}
597 | ]
598 | 
599 | clf = GridSearchCV(SVC(), param_grid, scoring="f1", cv=10)
600 | clf.fit(X_train, y_train)
601 | y_pred = clf.predict(X_test)
602 | \end{pythoncode}
603 | In this example, two distinct hyper-parameter grids are
604 | considered for the linear and radial basis function (RBF) kernels;
605 | an SVM with a linear kernel accepts a $\gamma$ parameter, but ignores it,
606 | so using a single parameter grid would waste computing time
607 | trying out effectively equivalent settings.
608 | Additionally, we see that
609 | \texttt{GridSearchCV} has a \texttt{predict} method, just like any other classifier:
610 | it delegates the \texttt{predict}, \texttt{predict\_proba}, \texttt{transform} and
611 | \texttt{score} methods to the best estimator
612 | (optionally after re-fitting it on the whole training set).
613 | 
614 | \subsection{Extending scikit-learn}
615 | 
616 | To ease code reuse, simplify implementation and skip the introduction of
617 | superfluous classes, the Python principle of \textit{duck typing} is exploited
618 | throughout the codebase. This means that estimators are defined by interface,
619 | not by inheritance, where the interface is entirely implicit
620 | as far as the programming language is concerned.
621 | Duck typing allows both for extensibility and
622 | flexibility: as long as an estimator follows the API and conventions
623 | outlined in Section~\ref{sec:core-api}, then it can be used in lieu of a
624 | built-in estimator (e.g., it can be plugged into pipelines or grid search)
625 | and external developers are not forced to inherit from any \sklearn class.
626 | 
627 | In other places of the library, in particular in the vectorization code
628 | for unstructured input, the toolkit is also designed to be
629 | extensible. Here, estimators provide hooks for user-defined code: objects or
630 | functions that follow a specific API can be given as arguments at vectorizer
631 | construction time. The library then calls into this code, communicating with it by passing objects of standard Python/NumPy types.
632 | Again, such external user code can be kept agnostic of the \sklearn
633 | class hierarchy.
634 | 
635 | Our rule of thumb is that user code should not be tied to \sklearn---which is a
636 | \textit{library}, and not a \textit{framework}. This principle indeed avoids a
637 | well-known problem with object-oriented design, which is that users wanting a
638 | ``banana'' should not get ``a gorilla holding the banana and the entire jungle''
639 | (J.~Armstrong, cited by \citealp[p.~213]{seibel2009coders}).
640 | That is, programs using \sklearn should not be intimately tied to it,
641 | so that their code can be reused with other toolkits or in other contexts.
642 | 
643 | 
644 | \section{Implementation}
645 | \label{sec:implementation}
646 | 
647 | Our implementation guidelines emphasize writing efficient but readable code.
648 | In particular, we focus on making the codebase easily maintainable and
649 | understandable in order to favor external contributions. Whenever practicable,
650 | algorithms implemented in \sklearn are written in Python,
651 | using NumPy vector operations for numerical work.
652 | This allows for the code to remain concise, readable and
653 | efficient. For critical algorithms that cannot be easily and efficiently
654 | expressed as NumPy operations, we rely on Cython \citep{behnel2011cython}
655 | to achieve competitive performance and scalability. Cython is a
656 | compiled programming language that extends Python with static typing. It
657 | produces efficient C extension modules that are directly importable from the
658 | Python run-time system. Examples of algorithms written in Cython include
659 | stochastic gradient descent for linear models, some graph-based clustering
660 | algorithms and decision trees.
661 | 
662 | To facilitate the installation and thus adoption of \sklearn,
663 | the set of external dependencies is kept to a bare minimum:
664 | only Python, NumPy and SciPy are required for a functioning installation.
665 | Binary distributions of these are available for the major platforms.
666 | Visualization functionality depends on Matplotlib \citep{hunter2007matplotlib}
667 | and/or Graphviz \citep{gansner2000},
668 | but neither is required to perform machine learning or prediction.
669 | When feasible, external libraries are integrated into the codebase.
670 | In particular, \sklearn includes modified versions of \textsf{LIBSVM} and \textsf{LIBLINEAR}
671 | \citep{chang2011libsvm,fan2008}, both written in C{}\verb!++!
672 | and wrapped using Cython modules.
673 | 
674 | \section{Related software}
675 | \label{sec:comparison}
676 | 
677 | Recent years have witnessed a rising interest in machine learning and data
678 | mining with applications in many fields. With this rise comes a host of machine
679 | learning packages (both open source and proprietary) with which \sklearn
680 | competes. Some of those, including Weka~\citep{hall2009weka} or
681 | Orange~\citep{Demsar2004}, offer APIs but actually focus on the use of a graphical user interface (GUI)
682 | which allows novices to easily apply machine learning algorithms. By
683 | contrast, the target audience of \sklearn is capable of programming, and
684 | therefore we focus on developing a usable and consistent API, rather than expend
685 | effort into creating a GUI\@. In addition, while GUIs are useful tools, they
686 | sometimes make reproducibility difficult in the case of complex workflows
687 | (although those packages usually have developed a GUI for managing complex
688 | tasks).
689 | 
690 | Other existing machine learning packages
691 | such as SofiaML\footnote{\url{https://code.google.com/p/sofia-ml}}~\citep{sculley2009large}
692 | and Vowpal~Wabbit\footnote{\url{http://hunch.net/$\sim$vw}}
693 | are intended to be used as command-line tools
694 | (and sometimes do not offer any type of API).
695 | While these packages have the advantage
696 | that their users are not tied to a particular programming language,
697 | the users will find that they still need programming to process input/output,
698 | and will do so in a variety of languages.
699 | By contrast, \sklearn allows users to implement that entire workflow
700 | in a single program, written in a single language,
701 | and developed in a single working environment.
702 | This also makes it easier for researchers and developers
703 | to exchange and collaborate on software, as dependencies and setup are kept to a
704 | minimum.
705 | 
706 | Similar benefits hold in the case of specialized languages
707 | for numeric and statistical programming
708 | such as \textsc{matlab} and R \citep{r}.
709 | In comparison to these, though, Python has the distinct advantage
710 | that it is a \textit{general purpose} language,
711 | while NumPy and SciPy extend it with functionality
712 | similar to that offered by \textsc{matlab} and R.
713 | Python has strong language and standard library support for such tasks as
714 | string/text processing, interprocess communication, networking
715 | and many of the other auxiliary tasks that machine learning programs
716 | (whether academic or commercial) routinely need to perform.
717 | While support for many of these tasks is improving in languages such as
718 | \textsc{matlab} and R, they still lag behind Python in their general purpose
719 | applicability.
720 | In many applications of machine learning these tasks, such as data access,
721 | data preprocessing and reporting, can be a more significant task than applying
722 | the actual learning algorithm.
723 | 
724 | Within the realm of Python,
725 | a package that deserves mention is the Gensim topic modeling toolkit
726 | \citep{rehurek2010gensim},
727 | which exemplifies a different style of API design
728 | geared toward scalable processing of ``big data''.
729 | Gensim's method of dealing with large datasets is to use algorithms
730 | that have $O(1)$ space complexity and can be updated online.
731 | The API is designed around the Python concept of an \textit{iterable}
732 | (supported in the language by a restricted form of co-routines called
733 | \textit{generators}).
734 | While the text vectorizers part of \sklearn
735 | also use iterables to some extent,
736 | they still produce entire sparse matrices, intended to be used for batch or
737 | mini-batch learning. This is the case
738 | even in the stateless, O(1) memory vectorizers
739 | that implement the hashing trick of \citet{weinberger2009}.
740 | This way of processing, as argued earlier in Section~\ref{sec:arrays},
741 | reduces various forms of overhead
742 | and allows effective use of the vectorized operations provided by NumPy and
743 | SciPy.  We make no attempt to hide this batch-oriented processing from the user,
744 | allowing control over the amount of memory actually dedicated
745 | to \sklearn algorithms.
746 | 
747 | \section{Future directions}
748 | \label{sec:future_work}
749 | There are several directions that the \sklearn project
750 | aims to focus on in future development.
751 | At present, the library does not support some classical machine learning
752 | algorithms,
753 | including neural networks, ensemble meta-estimators for
754 | bagging or subsampling strategies and missing value completion algorithms.
755 | However, tasks like structured prediction or reinforcement learning are
756 | considered out of scope for the project,
757 | since they would require quite different data representations and APIs.
758 | 
759 | At a lower-level, parallel processing is a potential point of improvement.
760 | Some estimators in \sklearn are already able to leverage multicore processors,
761 | but only in a coarse-grained fashion.
762 | At present, parallel processing is difficult to accomplish in the Python environment;
763 | \sklearn targets the main implementation, CPython,
764 | which cannot execute Python code on multiple CPUs simultaneously.
765 | It follows that any parallel task decomposition must either be done
766 | inside Cython modules,
767 | or at a level high enough to warrant the overhead
768 | of creating multiple OS-level processes,
769 | and the ensuing inter-process communication.
770 | Parallel grid search is an example of the latter approach
771 | which has already been implemented.
772 | Recent versions of Cython include support for the OpenMP standard
773 | \citep{dagum1998openmp},
774 | which is a viable candidate technology
775 | for more fine-grained multicore support in \sklearn.
776 | 
777 | Finally, a long-term solution for model persistence is missing.
778 | Currently, Python's \texttt{pickle} module is recommended for serialization,
779 | but this only offers a file format,
780 | not a way of preserving compatibility between versions.
781 | Also, it has security problems because its deserializer
782 | may execute arbitrary Python code,
783 | so models from untrusted sources cannot be safely ``unpickled''.
784 | 
785 | These API issues will be addressed in the future in preparation for
786 | the 1.0 release of \sklearn.
787 | 
788 | 
789 | \section{Conclusion}
790 | \label{sec:conclusions}
791 | 
792 | We have discussed the \sklearn API
793 | and the way it maps machine learning concepts and tasks
794 | onto objects and operations in the Python programming language.
795 | We have shown how a consistent API across the package makes \sklearn
796 | very \textbf{usable} in practice: experimenting with different learning
797 | algorithm is as simple as substituting a new class definition.
798 | Through composition interfaces such as Pipelines, Feature Unions,
799 | and meta-estimators, these simple building blocks lead to an API which is
800 | \textbf{powerful}, and can accomplish a wide variety of learning tasks
801 | within a small amount of easy-to-read code.
802 | Through duck-typing, the consistent API leads to a library that is
803 | easily \textbf{extensible}, and allows user-defined estimators to be
804 | incorporated into the \sklearn workflow without any explicit object
805 | inheritance.
806 | 
807 | While part of the \sklearn API is necessarily Python-specific,
808 | core concepts may be applicable to
809 | machine learning applications and toolkits
810 | written in other (dynamic) programming languages.
811 | The power, and extensibility of the \sklearn API is evidenced
812 | by the large and growing user-base, its use to solve real
813 | problems across a wide array of fields,
814 | as well as the appearance of third-party packages
815 | that follow the \sklearn conventions. Examples of such packages include
816 | \textit{astroML}\footnote{\url{http://astroml.org}}
817 | \citep{vanderplas2012astroML}, a package providing
818 | machine learning tools for astronomers, and
819 | \textit{wiseRF}\footnote{\url{http://wise.io}}, a commercial random forest
820 | implementation. The source code of
821 | the recently-proposed sparse multiclass
822 | algorithm of \citet{mblondel-mlj2013}, released as
823 | part of the
824 | \textit{lightning}\footnote{\url{https://github.com/mblondel/lightning}}
825 | package, also follows the \sklearn conventions.
826 | To maximize ease of use, we encourage more researchers
827 | to follow these conventions when releasing their software.
828 | 
829 | \subsection*{Acknowledgments}
830 | 
831 | The authors and contributors acknowledge active support from INRIA\@. Past and
832 | present sponsors of the project also include Google for funding
833 | scholarships through its Summer of Code program,
834 | the Python Software Foundation and Tinyclues for funding coding sprints.
835 | 
836 | Gilles~Louppe and Arnaud~Joly are research fellows of the Belgian
837 | Fonds de la Recherche Scientifique (FNRS)
838 | and acknowledge its financial support.
839 | 
840 | {\small
841 | \bibliographystyle{abbrvnat}
842 | \DeclareRobustCommand{\VAN}[3]{#3}
843 | \bibliography{paper}
844 | }
845 | 
846 | \end{document}
847 | 


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 221 | \setlength\headsep   {16\p@}
 222 | 
 223 | \setlength\footnotesep{7.7\p@}
 224 | \setlength\textfloatsep{8mm\@plus 2\p@ \@minus 4\p@}
 225 | \setlength\intextsep   {8mm\@plus 2\p@ \@minus 2\p@}
 226 | 
 227 | \setcounter{secnumdepth}{2}
 228 | 
 229 | \newcounter {chapter}
 230 | \renewcommand\thechapter      {\@arabic\c@chapter}
 231 | 
 232 | \newif\if@mainmatter \@mainmattertrue
 233 | \newcommand\frontmatter{\cleardoublepage
 234 |             \@mainmatterfalse\pagenumbering{Roman}}
 235 | \newcommand\mainmatter{\cleardoublepage
 236 |        \@mainmattertrue\pagenumbering{arabic}}
 237 | \newcommand\backmatter{\if@openright\cleardoublepage\else\clearpage\fi
 238 |       \@mainmatterfalse}
 239 | 
 240 | \renewcommand\part{\cleardoublepage
 241 |                  \thispagestyle{empty}%
 242 |                  \if@twocolumn
 243 |                      \onecolumn
 244 |                      \@tempswatrue
 245 |                    \else
 246 |                      \@tempswafalse
 247 |                  \fi
 248 |                  \null\vfil
 249 |                  \secdef\@part\@spart}
 250 | 
 251 | \def\@part[#1]#2{%
 252 |     \ifnum \c@secnumdepth >-2\relax
 253 |       \refstepcounter{part}%
 254 |       \addcontentsline{toc}{part}{\thepart\hspace{1em}#1}%
 255 |     \else
 256 |       \addcontentsline{toc}{part}{#1}%
 257 |     \fi
 258 |     \markboth{}{}%
 259 |     {\centering
 260 |      \interlinepenalty \@M
 261 |      \normalfont
 262 |      \ifnum \c@secnumdepth >-2\relax
 263 |        \huge\bfseries \partname~\thepart
 264 |        \par
 265 |        \vskip 20\p@
 266 |      \fi
 267 |      \Huge \bfseries #2\par}%
 268 |     \@endpart}
 269 | \def\@spart#1{%
 270 |     {\centering
 271 |      \interlinepenalty \@M
 272 |      \normalfont
 273 |      \Huge \bfseries #1\par}%
 274 |     \@endpart}
 275 | \def\@endpart{\vfil\newpage
 276 |               \if@twoside
 277 |                 \null
 278 |                 \thispagestyle{empty}%
 279 |                 \newpage
 280 |               \fi
 281 |               \if@tempswa
 282 |                 \twocolumn
 283 |               \fi}
 284 | 
 285 | \newcommand\chapter{\clearpage
 286 |                     \thispagestyle{empty}%
 287 |                     \global\@topnum\z@
 288 |                     \@afterindentfalse
 289 |                     \secdef\@chapter\@schapter}
 290 | \def\@chapter[#1]#2{\ifnum \c@secnumdepth >\m@ne
 291 |                        \if@mainmatter
 292 |                          \refstepcounter{chapter}%
 293 |                          \typeout{\@chapapp\space\thechapter.}%
 294 |                          \addcontentsline{toc}{chapter}%
 295 |                                   {\protect\numberline{\thechapter}#1}%
 296 |                        \else
 297 |                          \addcontentsline{toc}{chapter}{#1}%
 298 |                        \fi
 299 |                     \else
 300 |                       \addcontentsline{toc}{chapter}{#1}%
 301 |                     \fi
 302 |                     \chaptermark{#1}%
 303 |                     \addtocontents{lof}{\protect\addvspace{10\p@}}%
 304 |                     \addtocontents{lot}{\protect\addvspace{10\p@}}%
 305 |                     \if@twocolumn
 306 |                       \@topnewpage[\@makechapterhead{#2}]%
 307 |                     \else
 308 |                       \@makechapterhead{#2}%
 309 |                       \@afterheading
 310 |                     \fi}
 311 | \def\@makechapterhead#1{%
 312 | % \vspace*{50\p@}%
 313 |   {\centering
 314 |     \ifnum \c@secnumdepth >\m@ne
 315 |       \if@mainmatter
 316 |         \large\bfseries \@chapapp{} \thechapter
 317 |         \par\nobreak
 318 |         \vskip 20\p@
 319 |       \fi
 320 |     \fi
 321 |     \interlinepenalty\@M
 322 |     \Large \bfseries #1\par\nobreak
 323 |     \vskip 40\p@
 324 |   }}
 325 | \def\@schapter#1{\if@twocolumn
 326 |                    \@topnewpage[\@makeschapterhead{#1}]%
 327 |                  \else
 328 |                    \@makeschapterhead{#1}%
 329 |                    \@afterheading
 330 |                  \fi}
 331 | \def\@makeschapterhead#1{%
 332 | % \vspace*{50\p@}%
 333 |   {\centering
 334 |     \normalfont
 335 |     \interlinepenalty\@M
 336 |     \Large \bfseries  #1\par\nobreak
 337 |     \vskip 40\p@
 338 |   }}
 339 | 
 340 | \renewcommand\section{\@startsection{section}{1}{\z@}%
 341 |                        {-18\p@ \@plus -4\p@ \@minus -4\p@}%
 342 |                        {12\p@ \@plus 4\p@ \@minus 4\p@}%
 343 |                        {\normalfont\large\bfseries\boldmath
 344 |                         \rightskip=\z@ \@plus 8em\pretolerance=10000 }}
 345 | \renewcommand\subsection{\@startsection{subsection}{2}{\z@}%
 346 |                        {-18\p@ \@plus -4\p@ \@minus -4\p@}%
 347 |                        {8\p@ \@plus 4\p@ \@minus 4\p@}%
 348 |                        {\normalfont\normalsize\bfseries\boldmath
 349 |                         \rightskip=\z@ \@plus 8em\pretolerance=10000 }}
 350 | \renewcommand\subsubsection{\@startsection{subsubsection}{3}{\z@}%
 351 |                        {-18\p@ \@plus -4\p@ \@minus -4\p@}%
 352 |                        {-0.5em \@plus -0.22em \@minus -0.1em}%
 353 |                        {\normalfont\normalsize\bfseries\boldmath}}
 354 | \renewcommand\paragraph{\@startsection{paragraph}{4}{\z@}%
 355 |                        {-12\p@ \@plus -4\p@ \@minus -4\p@}%
 356 |                        {-0.5em \@plus -0.22em \@minus -0.1em}%
 357 |                        {\normalfont\normalsize\itshape}}
 358 | \renewcommand\subparagraph[1]{\typeout{LLNCS warning: You should not use
 359 |                   \string\subparagraph\space with this class}\vskip0.5cm
 360 | You should not use \verb|\subparagraph| with this class.\vskip0.5cm}
 361 | 
 362 | \DeclareMathSymbol{\Gamma}{\mathalpha}{letters}{"00}
 363 | \DeclareMathSymbol{\Delta}{\mathalpha}{letters}{"01}
 364 | \DeclareMathSymbol{\Theta}{\mathalpha}{letters}{"02}
 365 | \DeclareMathSymbol{\Lambda}{\mathalpha}{letters}{"03}
 366 | \DeclareMathSymbol{\Xi}{\mathalpha}{letters}{"04}
 367 | \DeclareMathSymbol{\Pi}{\mathalpha}{letters}{"05}
 368 | \DeclareMathSymbol{\Sigma}{\mathalpha}{letters}{"06}
 369 | \DeclareMathSymbol{\Upsilon}{\mathalpha}{letters}{"07}
 370 | \DeclareMathSymbol{\Phi}{\mathalpha}{letters}{"08}
 371 | \DeclareMathSymbol{\Psi}{\mathalpha}{letters}{"09}
 372 | \DeclareMathSymbol{\Omega}{\mathalpha}{letters}{"0A}
 373 | 
 374 | \let\footnotesize\small
 375 | 
 376 | \if@custvec
 377 | \def\vec#1{\mathchoice{\mbox{\boldmath$\displaystyle#1$}}
 378 | {\mbox{\boldmath$\textstyle#1$}}
 379 | {\mbox{\boldmath$\scriptstyle#1$}}
 380 | {\mbox{\boldmath$\scriptscriptstyle#1$}}}
 381 | \fi
 382 | 
 383 | \def\squareforqed{\hbox{\rlap{$\sqcap$}$\sqcup$}}
 384 | \def\qed{\ifmmode\squareforqed\else{\unskip\nobreak\hfil
 385 | \penalty50\hskip1em\null\nobreak\hfil\squareforqed
 386 | \parfillskip=0pt\finalhyphendemerits=0\endgraf}\fi}
 387 | 
 388 | \def\getsto{\mathrel{\mathchoice {\vcenter{\offinterlineskip
 389 | \halign{\hfil
 390 | $\displaystyle##$\hfil\cr\gets\cr\to\cr}}}
 391 | {\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr\gets
 392 | \cr\to\cr}}}
 393 | {\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr\gets
 394 | \cr\to\cr}}}
 395 | {\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil\cr
 396 | \gets\cr\to\cr}}}}}
 397 | \def\lid{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil
 398 | $\displaystyle##$\hfil\cr<\cr\noalign{\vskip1.2pt}=\cr}}}
 399 | {\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr<\cr
 400 | \noalign{\vskip1.2pt}=\cr}}}
 401 | {\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr<\cr
 402 | \noalign{\vskip1pt}=\cr}}}
 403 | {\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil\cr
 404 | <\cr
 405 | \noalign{\vskip0.9pt}=\cr}}}}}
 406 | \def\gid{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil
 407 | $\displaystyle##$\hfil\cr>\cr\noalign{\vskip1.2pt}=\cr}}}
 408 | {\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr>\cr
 409 | \noalign{\vskip1.2pt}=\cr}}}
 410 | {\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr>\cr
 411 | \noalign{\vskip1pt}=\cr}}}
 412 | {\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil\cr
 413 | >\cr
 414 | \noalign{\vskip0.9pt}=\cr}}}}}
 415 | \def\grole{\mathrel{\mathchoice {\vcenter{\offinterlineskip
 416 | \halign{\hfil
 417 | $\displaystyle##$\hfil\cr>\cr\noalign{\vskip-1pt}<\cr}}}
 418 | {\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr
 419 | >\cr\noalign{\vskip-1pt}<\cr}}}
 420 | {\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr
 421 | >\cr\noalign{\vskip-0.8pt}<\cr}}}
 422 | {\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil\cr
 423 | >\cr\noalign{\vskip-0.3pt}<\cr}}}}}
 424 | \def\bbbr{{\rm I\!R}} %reelle Zahlen
 425 | \def\bbbm{{\rm I\!M}}
 426 | \def\bbbn{{\rm I\!N}} %natuerliche Zahlen
 427 | \def\bbbf{{\rm I\!F}}
 428 | \def\bbbh{{\rm I\!H}}
 429 | \def\bbbk{{\rm I\!K}}
 430 | \def\bbbp{{\rm I\!P}}
 431 | \def\bbbone{{\mathchoice {\rm 1\mskip-4mu l} {\rm 1\mskip-4mu l}
 432 | {\rm 1\mskip-4.5mu l} {\rm 1\mskip-5mu l}}}
 433 | \def\bbbc{{\mathchoice {\setbox0=\hbox{$\displaystyle\rm C$}\hbox{\hbox
 434 | to0pt{\kern0.4\wd0\vrule height0.9\ht0\hss}\box0}}
 435 | {\setbox0=\hbox{$\textstyle\rm C$}\hbox{\hbox
 436 | to0pt{\kern0.4\wd0\vrule height0.9\ht0\hss}\box0}}
 437 | {\setbox0=\hbox{$\scriptstyle\rm C$}\hbox{\hbox
 438 | to0pt{\kern0.4\wd0\vrule height0.9\ht0\hss}\box0}}
 439 | {\setbox0=\hbox{$\scriptscriptstyle\rm C$}\hbox{\hbox
 440 | to0pt{\kern0.4\wd0\vrule height0.9\ht0\hss}\box0}}}}
 441 | \def\bbbq{{\mathchoice {\setbox0=\hbox{$\displaystyle\rm
 442 | Q$}\hbox{\raise
 443 | 0.15\ht0\hbox to0pt{\kern0.4\wd0\vrule height0.8\ht0\hss}\box0}}
 444 | {\setbox0=\hbox{$\textstyle\rm Q$}\hbox{\raise
 445 | 0.15\ht0\hbox to0pt{\kern0.4\wd0\vrule height0.8\ht0\hss}\box0}}
 446 | {\setbox0=\hbox{$\scriptstyle\rm Q$}\hbox{\raise
 447 | 0.15\ht0\hbox to0pt{\kern0.4\wd0\vrule height0.7\ht0\hss}\box0}}
 448 | {\setbox0=\hbox{$\scriptscriptstyle\rm Q$}\hbox{\raise
 449 | 0.15\ht0\hbox to0pt{\kern0.4\wd0\vrule height0.7\ht0\hss}\box0}}}}
 450 | \def\bbbt{{\mathchoice {\setbox0=\hbox{$\displaystyle\rm
 451 | T$}\hbox{\hbox to0pt{\kern0.3\wd0\vrule height0.9\ht0\hss}\box0}}
 452 | {\setbox0=\hbox{$\textstyle\rm T$}\hbox{\hbox
 453 | to0pt{\kern0.3\wd0\vrule height0.9\ht0\hss}\box0}}
 454 | {\setbox0=\hbox{$\scriptstyle\rm T$}\hbox{\hbox
 455 | to0pt{\kern0.3\wd0\vrule height0.9\ht0\hss}\box0}}
 456 | {\setbox0=\hbox{$\scriptscriptstyle\rm T$}\hbox{\hbox
 457 | to0pt{\kern0.3\wd0\vrule height0.9\ht0\hss}\box0}}}}
 458 | \def\bbbs{{\mathchoice
 459 | {\setbox0=\hbox{$\displaystyle     \rm S$}\hbox{\raise0.5\ht0\hbox
 460 | to0pt{\kern0.35\wd0\vrule height0.45\ht0\hss}\hbox
 461 | to0pt{\kern0.55\wd0\vrule height0.5\ht0\hss}\box0}}
 462 | {\setbox0=\hbox{$\textstyle        \rm S$}\hbox{\raise0.5\ht0\hbox
 463 | to0pt{\kern0.35\wd0\vrule height0.45\ht0\hss}\hbox
 464 | to0pt{\kern0.55\wd0\vrule height0.5\ht0\hss}\box0}}
 465 | {\setbox0=\hbox{$\scriptstyle      \rm S$}\hbox{\raise0.5\ht0\hbox
 466 | to0pt{\kern0.35\wd0\vrule height0.45\ht0\hss}\raise0.05\ht0\hbox
 467 | to0pt{\kern0.5\wd0\vrule height0.45\ht0\hss}\box0}}
 468 | {\setbox0=\hbox{$\scriptscriptstyle\rm S$}\hbox{\raise0.5\ht0\hbox
 469 | to0pt{\kern0.4\wd0\vrule height0.45\ht0\hss}\raise0.05\ht0\hbox
 470 | to0pt{\kern0.55\wd0\vrule height0.45\ht0\hss}\box0}}}}
 471 | \def\bbbz{{\mathchoice {\hbox{$\mathsf\textstyle Z\kern-0.4em Z$}}
 472 | {\hbox{$\mathsf\textstyle Z\kern-0.4em Z$}}
 473 | {\hbox{$\mathsf\scriptstyle Z\kern-0.3em Z$}}
 474 | {\hbox{$\mathsf\scriptscriptstyle Z\kern-0.2em Z$}}}}
 475 | 
 476 | \let\ts\,
 477 | 
 478 | \setlength\leftmargini  {17\p@}
 479 | \setlength\leftmargin    {\leftmargini}
 480 | \setlength\leftmarginii  {\leftmargini}
 481 | \setlength\leftmarginiii {\leftmargini}
 482 | \setlength\leftmarginiv  {\leftmargini}
 483 | \setlength  \labelsep  {.5em}
 484 | \setlength  \labelwidth{\leftmargini}
 485 | \addtolength\labelwidth{-\labelsep}
 486 | 
 487 | \def\@listI{\leftmargin\leftmargini
 488 |             \parsep 0\p@ \@plus1\p@ \@minus\p@
 489 |             \topsep 8\p@ \@plus2\p@ \@minus4\p@
 490 |             \itemsep0\p@}
 491 | \let\@listi\@listI
 492 | \@listi
 493 | \def\@listii {\leftmargin\leftmarginii
 494 |               \labelwidth\leftmarginii
 495 |               \advance\labelwidth-\labelsep
 496 |               \topsep    0\p@ \@plus2\p@ \@minus\p@}
 497 | \def\@listiii{\leftmargin\leftmarginiii
 498 |               \labelwidth\leftmarginiii
 499 |               \advance\labelwidth-\labelsep
 500 |               \topsep    0\p@ \@plus\p@\@minus\p@
 501 |               \parsep    \z@
 502 |               \partopsep \p@ \@plus\z@ \@minus\p@}
 503 | 
 504 | \renewcommand\labelitemi{\normalfont\bfseries --}
 505 | \renewcommand\labelitemii{$\m@th\bullet$}
 506 | 
 507 | \setlength\arraycolsep{1.4\p@}
 508 | \setlength\tabcolsep{1.4\p@}
 509 | 
 510 | \def\tableofcontents{\chapter*{\contentsname\@mkboth{{\contentsname}}%
 511 |                                                     {{\contentsname}}}
 512 |  \def\authcount##1{\setcounter{auco}{##1}\setcounter{@auth}{1}}
 513 |  \def\lastand{\ifnum\value{auco}=2\relax
 514 |                  \unskip{} \andname\
 515 |               \else
 516 |                  \unskip \lastandname\
 517 |               \fi}%
 518 |  \def\and{\stepcounter{@auth}\relax
 519 |           \ifnum\value{@auth}=\value{auco}%
 520 |              \lastand
 521 |           \else
 522 |              \unskip,
 523 |           \fi}%
 524 |  \@starttoc{toc}\if@restonecol\twocolumn\fi}
 525 | 
 526 | \def\l@part#1#2{\addpenalty{\@secpenalty}%
 527 |    \addvspace{2em plus\p@}%  % space above part line
 528 |    \begingroup
 529 |      \parindent \z@
 530 |      \rightskip \z@ plus 5em
 531 |      \hrule\vskip5pt
 532 |      \large               % same size as for a contribution heading
 533 |      \bfseries\boldmath   % set line in boldface
 534 |      \leavevmode          % TeX command to enter horizontal mode.
 535 |      #1\par
 536 |      \vskip5pt
 537 |      \hrule
 538 |      \vskip1pt
 539 |      \nobreak             % Never break after part entry
 540 |    \endgroup}
 541 | 
 542 | \def\@dotsep{2}
 543 | 
 544 | \let\phantomsection=\relax
 545 | 
 546 | \def\hyperhrefextend{\ifx\hyper@anchor\@undefined\else
 547 | {}\fi}
 548 | 
 549 | \def\addnumcontentsmark#1#2#3{%
 550 | \addtocontents{#1}{\protect\contentsline{#2}{\protect\numberline
 551 |                      {\thechapter}#3}{\thepage}\hyperhrefextend}}%
 552 | \def\addcontentsmark#1#2#3{%
 553 | \addtocontents{#1}{\protect\contentsline{#2}{#3}{\thepage}\hyperhrefextend}}%
 554 | \def\addcontentsmarkwop#1#2#3{%
 555 | \addtocontents{#1}{\protect\contentsline{#2}{#3}{0}\hyperhrefextend}}%
 556 | 
 557 | \def\@adcmk[#1]{\ifcase #1 \or
 558 | \def\@gtempa{\addnumcontentsmark}%
 559 |   \or    \def\@gtempa{\addcontentsmark}%
 560 |   \or    \def\@gtempa{\addcontentsmarkwop}%
 561 |   \fi\@gtempa{toc}{chapter}%
 562 | }
 563 | \def\addtocmark{%
 564 | \phantomsection
 565 | \@ifnextchar[{\@adcmk}{\@adcmk[3]}%
 566 | }
 567 | 
 568 | \def\l@chapter#1#2{\addpenalty{-\@highpenalty}
 569 |  \vskip 1.0em plus 1pt \@tempdima 1.5em \begingroup
 570 |  \parindent \z@ \rightskip \@tocrmarg
 571 |  \advance\rightskip by 0pt plus 2cm
 572 |  \parfillskip -\rightskip \pretolerance=10000
 573 |  \leavevmode \advance\leftskip\@tempdima \hskip -\leftskip
 574 |  {\large\bfseries\boldmath#1}\ifx0#2\hfil\null
 575 |  \else
 576 |       \nobreak
 577 |       \leaders\hbox{$\m@th \mkern \@dotsep mu.\mkern
 578 |       \@dotsep mu$}\hfill
 579 |       \nobreak\hbox to\@pnumwidth{\hss #2}%
 580 |  \fi\par
 581 |  \penalty\@highpenalty \endgroup}
 582 | 
 583 | \def\l@title#1#2{\addpenalty{-\@highpenalty}
 584 |  \addvspace{8pt plus 1pt}
 585 |  \@tempdima \z@
 586 |  \begingroup
 587 |  \parindent \z@ \rightskip \@tocrmarg
 588 |  \advance\rightskip by 0pt plus 2cm
 589 |  \parfillskip -\rightskip \pretolerance=10000
 590 |  \leavevmode \advance\leftskip\@tempdima \hskip -\leftskip
 591 |  #1\nobreak
 592 |  \leaders\hbox{$\m@th \mkern \@dotsep mu.\mkern
 593 |  \@dotsep mu$}\hfill
 594 |  \nobreak\hbox to\@pnumwidth{\hss #2}\par
 595 |  \penalty\@highpenalty \endgroup}
 596 | 
 597 | \def\l@author#1#2{\addpenalty{\@highpenalty}
 598 |  \@tempdima=15\p@ %\z@
 599 |  \begingroup
 600 |  \parindent \z@ \rightskip \@tocrmarg
 601 |  \advance\rightskip by 0pt plus 2cm
 602 |  \pretolerance=10000
 603 |  \leavevmode \advance\leftskip\@tempdima %\hskip -\leftskip
 604 |  \textit{#1}\par
 605 |  \penalty\@highpenalty \endgroup}
 606 | 
 607 | \setcounter{tocdepth}{0}
 608 | \newdimen\tocchpnum
 609 | \newdimen\tocsecnum
 610 | \newdimen\tocsectotal
 611 | \newdimen\tocsubsecnum
 612 | \newdimen\tocsubsectotal
 613 | \newdimen\tocsubsubsecnum
 614 | \newdimen\tocsubsubsectotal
 615 | \newdimen\tocparanum
 616 | \newdimen\tocparatotal
 617 | \newdimen\tocsubparanum
 618 | \tocchpnum=\z@            % no chapter numbers
 619 | \tocsecnum=15\p@          % section 88. plus 2.222pt
 620 | \tocsubsecnum=23\p@       % subsection 88.8 plus 2.222pt
 621 | \tocsubsubsecnum=27\p@    % subsubsection 88.8.8 plus 1.444pt
 622 | \tocparanum=35\p@         % paragraph 88.8.8.8 plus 1.666pt
 623 | \tocsubparanum=43\p@      % subparagraph 88.8.8.8.8 plus 1.888pt
 624 | \def\calctocindent{%
 625 | \tocsectotal=\tocchpnum
 626 | \advance\tocsectotal by\tocsecnum
 627 | \tocsubsectotal=\tocsectotal
 628 | \advance\tocsubsectotal by\tocsubsecnum
 629 | \tocsubsubsectotal=\tocsubsectotal
 630 | \advance\tocsubsubsectotal by\tocsubsubsecnum
 631 | \tocparatotal=\tocsubsubsectotal
 632 | \advance\tocparatotal by\tocparanum}
 633 | \calctocindent
 634 | 
 635 | \def\l@section{\@dottedtocline{1}{\tocchpnum}{\tocsecnum}}
 636 | \def\l@subsection{\@dottedtocline{2}{\tocsectotal}{\tocsubsecnum}}
 637 | \def\l@subsubsection{\@dottedtocline{3}{\tocsubsectotal}{\tocsubsubsecnum}}
 638 | \def\l@paragraph{\@dottedtocline{4}{\tocsubsubsectotal}{\tocparanum}}
 639 | \def\l@subparagraph{\@dottedtocline{5}{\tocparatotal}{\tocsubparanum}}
 640 | 
 641 | \def\listoffigures{\@restonecolfalse\if@twocolumn\@restonecoltrue\onecolumn
 642 |  \fi\section*{\listfigurename\@mkboth{{\listfigurename}}{{\listfigurename}}}
 643 |  \@starttoc{lof}\if@restonecol\twocolumn\fi}
 644 | \def\l@figure{\@dottedtocline{1}{0em}{1.5em}}
 645 | 
 646 | \def\listoftables{\@restonecolfalse\if@twocolumn\@restonecoltrue\onecolumn
 647 |  \fi\section*{\listtablename\@mkboth{{\listtablename}}{{\listtablename}}}
 648 |  \@starttoc{lot}\if@restonecol\twocolumn\fi}
 649 | \let\l@table\l@figure
 650 | 
 651 | \renewcommand\listoffigures{%
 652 |     \section*{\listfigurename
 653 |       \@mkboth{\listfigurename}{\listfigurename}}%
 654 |     \@starttoc{lof}%
 655 |     }
 656 | 
 657 | \renewcommand\listoftables{%
 658 |     \section*{\listtablename
 659 |       \@mkboth{\listtablename}{\listtablename}}%
 660 |     \@starttoc{lot}%
 661 |     }
 662 | 
 663 | \ifx\oribibl\undefined
 664 | \ifx\citeauthoryear\undefined
 665 | \renewenvironment{thebibliography}[1]
 666 |      {\section*{\refname}
 667 |       \def\@biblabel##1{##1.}
 668 |       \small
 669 |       \list{\@biblabel{\@arabic\c@enumiv}}%
 670 |            {\settowidth\labelwidth{\@biblabel{#1}}%
 671 |             \leftmargin\labelwidth
 672 |             \advance\leftmargin\labelsep
 673 |             \if@openbib
 674 |               \advance\leftmargin\bibindent
 675 |               \itemindent -\bibindent
 676 |               \listparindent \itemindent
 677 |               \parsep \z@
 678 |             \fi
 679 |             \usecounter{enumiv}%
 680 |             \let\p@enumiv\@empty
 681 |             \renewcommand\theenumiv{\@arabic\c@enumiv}}%
 682 |       \if@openbib
 683 |         \renewcommand\newblock{\par}%
 684 |       \else
 685 |         \renewcommand\newblock{\hskip .11em \@plus.33em \@minus.07em}%
 686 |       \fi
 687 |       \sloppy\clubpenalty4000\widowpenalty4000%
 688 |       \sfcode`\.=\@m}
 689 |      {\def\@noitemerr
 690 |        {\@latex@warning{Empty `thebibliography' environment}}%
 691 |       \endlist}
 692 | \def\@lbibitem[#1]#2{\item[{[#1]}\hfill]\if@filesw
 693 |      {\let\protect\noexpand\immediate
 694 |      \write\@auxout{\string\bibcite{#2}{#1}}}\fi\ignorespaces}
 695 | \newcount\@tempcntc
 696 | \def\@citex[#1]#2{\if@filesw\immediate\write\@auxout{\string\citation{#2}}\fi
 697 |   \@tempcnta\z@\@tempcntb\m@ne\def\@citea{}\@cite{\@for\@citeb:=#2\do
 698 |     {\@ifundefined
 699 |        {b@\@citeb}{\@citeo\@tempcntb\m@ne\@citea\def\@citea{,}{\bfseries
 700 |         ?}\@warning
 701 |        {Citation `\@citeb' on page \thepage \space undefined}}%
 702 |     {\setbox\z@\hbox{\global\@tempcntc0\csname b@\@citeb\endcsname\relax}%
 703 |      \ifnum\@tempcntc=\z@ \@citeo\@tempcntb\m@ne
 704 |        \@citea\def\@citea{,}\hbox{\csname b@\@citeb\endcsname}%
 705 |      \else
 706 |       \advance\@tempcntb\@ne
 707 |       \ifnum\@tempcntb=\@tempcntc
 708 |       \else\advance\@tempcntb\m@ne\@citeo
 709 |       \@tempcnta\@tempcntc\@tempcntb\@tempcntc\fi\fi}}\@citeo}{#1}}
 710 | \def\@citeo{\ifnum\@tempcnta>\@tempcntb\else
 711 |                \@citea\def\@citea{,\,\hskip\z@skip}%
 712 |                \ifnum\@tempcnta=\@tempcntb\the\@tempcnta\else
 713 |                {\advance\@tempcnta\@ne\ifnum\@tempcnta=\@tempcntb \else
 714 |                 \def\@citea{--}\fi
 715 |       \advance\@tempcnta\m@ne\the\@tempcnta\@citea\the\@tempcntb}\fi\fi}
 716 | \else
 717 | \renewenvironment{thebibliography}[1]
 718 |      {\section*{\refname}
 719 |       \small
 720 |       \list{}%
 721 |            {\settowidth\labelwidth{}%
 722 |             \leftmargin\parindent
 723 |             \itemindent=-\parindent
 724 |             \labelsep=\z@
 725 |             \if@openbib
 726 |               \advance\leftmargin\bibindent
 727 |               \itemindent -\bibindent
 728 |               \listparindent \itemindent
 729 |               \parsep \z@
 730 |             \fi
 731 |             \usecounter{enumiv}%
 732 |             \let\p@enumiv\@empty
 733 |             \renewcommand\theenumiv{}}%
 734 |       \if@openbib
 735 |         \renewcommand\newblock{\par}%
 736 |       \else
 737 |         \renewcommand\newblock{\hskip .11em \@plus.33em \@minus.07em}%
 738 |       \fi
 739 |       \sloppy\clubpenalty4000\widowpenalty4000%
 740 |       \sfcode`\.=\@m}
 741 |      {\def\@noitemerr
 742 |        {\@latex@warning{Empty `thebibliography' environment}}%
 743 |       \endlist}
 744 |       \def\@cite#1{#1}%
 745 |       \def\@lbibitem[#1]#2{\item[]\if@filesw
 746 |         {\def\protect##1{\string ##1\space}\immediate
 747 |       \write\@auxout{\string\bibcite{#2}{#1}}}\fi\ignorespaces}
 748 |    \fi
 749 | \else
 750 | \@cons\@openbib@code{\noexpand\small}
 751 | \fi
 752 | 
 753 | \def\idxquad{\hskip 10\p@}% space that divides entry from number
 754 | 
 755 | \def\@idxitem{\par\hangindent 10\p@}
 756 | 
 757 | \def\subitem{\par\setbox0=\hbox{--\enspace}% second order
 758 |                 \noindent\hangindent\wd0\box0}% index entry
 759 | 
 760 | \def\subsubitem{\par\setbox0=\hbox{--\,--\enspace}% third
 761 |                 \noindent\hangindent\wd0\box0}% order index entry
 762 | 
 763 | \def\indexspace{\par \vskip 10\p@ plus5\p@ minus3\p@\relax}
 764 | 
 765 | \renewenvironment{theindex}
 766 |                {\@mkboth{\indexname}{\indexname}%
 767 |                 \thispagestyle{empty}\parindent\z@
 768 |                 \parskip\z@ \@plus .3\p@\relax
 769 |                 \let\item\par
 770 |                 \def\,{\relax\ifmmode\mskip\thinmuskip
 771 |                              \else\hskip0.2em\ignorespaces\fi}%
 772 |                 \normalfont\small
 773 |                 \begin{multicols}{2}[\@makeschapterhead{\indexname}]%
 774 |                 }
 775 |                 {\end{multicols}}
 776 | 
 777 | \renewcommand\footnoterule{%
 778 |   \kern-3\p@
 779 |   \hrule\@width 2truecm
 780 |   \kern2.6\p@}
 781 |   \newdimen\fnindent
 782 |   \fnindent1em
 783 | \long\def\@makefntext#1{%
 784 |     \parindent \fnindent%
 785 |     \leftskip \fnindent%
 786 |     \noindent
 787 |     \llap{\hb@xt@1em{\hss\@makefnmark\ }}\ignorespaces#1}
 788 | 
 789 | \long\def\@makecaption#1#2{%
 790 |   \small
 791 |   \vskip\abovecaptionskip
 792 |   \sbox\@tempboxa{{\bfseries #1.} #2}%
 793 |   \ifdim \wd\@tempboxa >\hsize
 794 |     {\bfseries #1.} #2\par
 795 |   \else
 796 |     \global \@minipagefalse
 797 |     \hb@xt@\hsize{\hfil\box\@tempboxa\hfil}%
 798 |   \fi
 799 |   \vskip\belowcaptionskip}
 800 | 
 801 | \def\fps@figure{htbp}
 802 | \def\fnum@figure{\figurename\thinspace\thefigure}
 803 | \def \@floatboxreset {%
 804 |         \reset@font
 805 |         \small
 806 |         \@setnobreak
 807 |         \@setminipage
 808 | }
 809 | \def\fps@table{htbp}
 810 | \def\fnum@table{\tablename~\thetable}
 811 | \renewenvironment{table}
 812 |                {\setlength\abovecaptionskip{0\p@}%
 813 |                 \setlength\belowcaptionskip{10\p@}%
 814 |                 \@float{table}}
 815 |                {\end@float}
 816 | \renewenvironment{table*}
 817 |                {\setlength\abovecaptionskip{0\p@}%
 818 |                 \setlength\belowcaptionskip{10\p@}%
 819 |                 \@dblfloat{table}}
 820 |                {\end@dblfloat}
 821 | 
 822 | \long\def\@caption#1[#2]#3{\par\addcontentsline{\csname
 823 |   ext@#1\endcsname}{#1}{\protect\numberline{\csname
 824 |   the#1\endcsname}{\ignorespaces #2}}\begingroup
 825 |     \@parboxrestore
 826 |     \@makecaption{\csname fnum@#1\endcsname}{\ignorespaces #3}\par
 827 |   \endgroup}
 828 | 
 829 | % LaTeX does not provide a command to enter the authors institute
 830 | % addresses. The \institute command is defined here.
 831 | 
 832 | \newcounter{@inst}
 833 | \newcounter{@auth}
 834 | \newcounter{auco}
 835 | \newdimen\instindent
 836 | \newbox\authrun
 837 | \newtoks\authorrunning
 838 | \newtoks\tocauthor
 839 | \newbox\titrun
 840 | \newtoks\titlerunning
 841 | \newtoks\toctitle
 842 | 
 843 | \def\clearheadinfo{\gdef\@author{No Author Given}%
 844 |                    \gdef\@title{No Title Given}%
 845 |                    \gdef\@subtitle{}%
 846 |                    \gdef\@institute{No Institute Given}%
 847 |                    \gdef\@thanks{}%
 848 |                    \global\titlerunning={}\global\authorrunning={}%
 849 |                    \global\toctitle={}\global\tocauthor={}}
 850 | 
 851 | \def\institute#1{\gdef\@institute{#1}}
 852 | 
 853 | \def\institutename{\par
 854 |  \begingroup
 855 |  \parskip=\z@
 856 |  \parindent=\z@
 857 |  \setcounter{@inst}{1}%
 858 |  \def\and{\par\stepcounter{@inst}%
 859 |  \noindent$^{\the@inst}$\enspace\ignorespaces}%
 860 |  \setbox0=\vbox{\def\thanks##1{}\@institute}%
 861 |  \ifnum\c@@inst=1\relax
 862 |    \gdef\fnnstart{0}%
 863 |  \else
 864 |    \xdef\fnnstart{\c@@inst}%
 865 |    \setcounter{@inst}{1}%
 866 |    \noindent$^{\the@inst}$\enspace
 867 |  \fi
 868 |  \ignorespaces
 869 |  \@institute\par
 870 |  \endgroup}
 871 | 
 872 | \def\@fnsymbol#1{\ensuremath{\ifcase#1\or\star\or{\star\star}\or
 873 |    {\star\star\star}\or \dagger\or \ddagger\or
 874 |    \mathchar "278\or \mathchar "27B\or \|\or **\or \dagger\dagger
 875 |    \or \ddagger\ddagger \else\@ctrerr\fi}}
 876 | 
 877 | \def\inst#1{\unskip$^{#1}$}
 878 | \def\fnmsep{\unskip$^,$}
 879 | \def\email#1{{\tt#1}}
 880 | \AtBeginDocument{\@ifundefined{url}{\def\url#1{#1}}{}%
 881 | \@ifpackageloaded{babel}{%
 882 | \@ifundefined{extrasenglish}{}{\addto\extrasenglish{\switcht@albion}}%
 883 | \@ifundefined{extrasfrenchb}{}{\addto\extrasfrenchb{\switcht@francais}}%
 884 | \@ifundefined{extrasgerman}{}{\addto\extrasgerman{\switcht@deutsch}}%
 885 | }{\switcht@@therlang}%
 886 | \providecommand{\keywords}[1]{\par\addvspace\baselineskip
 887 | \noindent\keywordname\enspace\ignorespaces#1}%
 888 | }
 889 | \def\homedir{\~{ }}
 890 | 
 891 | \def\subtitle#1{\gdef\@subtitle{#1}}
 892 | \clearheadinfo
 893 | %
 894 | %%% to avoid hyperref warnings
 895 | \providecommand*{\toclevel@author}{999}
 896 | %%% to make title-entry parent of section-entries
 897 | \providecommand*{\toclevel@title}{0}
 898 | %
 899 | \renewcommand\maketitle{\newpage
 900 | \phantomsection
 901 |   \refstepcounter{chapter}%
 902 |   \stepcounter{section}%
 903 |   \setcounter{section}{0}%
 904 |   \setcounter{subsection}{0}%
 905 |   \setcounter{figure}{0}
 906 |   \setcounter{table}{0}
 907 |   \setcounter{equation}{0}
 908 |   \setcounter{footnote}{0}%
 909 |   \begingroup
 910 |     \parindent=\z@
 911 |     \renewcommand\thefootnote{\@fnsymbol\c@footnote}%
 912 |     \if@twocolumn
 913 |       \ifnum \col@number=\@ne
 914 |         \@maketitle
 915 |       \else
 916 |         \twocolumn[\@maketitle]%
 917 |       \fi
 918 |     \else
 919 |       \newpage
 920 |       \global\@topnum\z@   % Prevents figures from going at top of page.
 921 |       \@maketitle
 922 |     \fi
 923 |     \thispagestyle{empty}\@thanks
 924 | %
 925 |     \def\\{\unskip\ \ignorespaces}\def\inst##1{\unskip{}}%
 926 |     \def\thanks##1{\unskip{}}\def\fnmsep{\unskip}%
 927 |     \instindent=\hsize
 928 |     \advance\instindent by-\headlineindent
 929 |     \if!\the\toctitle!\addcontentsline{toc}{title}{\@title}\else
 930 |        \addcontentsline{toc}{title}{\the\toctitle}\fi
 931 |     \if@runhead
 932 |        \if!\the\titlerunning!\else
 933 |          \edef\@title{\the\titlerunning}%
 934 |        \fi
 935 |        \global\setbox\titrun=\hbox{\small\rm\unboldmath\ignorespaces\@title}%
 936 |        \ifdim\wd\titrun>\instindent
 937 |           \typeout{Title too long for running head. Please supply}%
 938 |           \typeout{a shorter form with \string\titlerunning\space prior to
 939 |                    \string\maketitle}%
 940 |           \global\setbox\titrun=\hbox{\small\rm
 941 |           Title Suppressed Due to Excessive Length}%
 942 |        \fi
 943 |        \xdef\@title{\copy\titrun}%
 944 |     \fi
 945 | %
 946 |     \if!\the\tocauthor!\relax
 947 |       {\def\and{\noexpand\protect\noexpand\and}%
 948 |       \protected@xdef\toc@uthor{\@author}}%
 949 |     \else
 950 |       \def\\{\noexpand\protect\noexpand\newline}%
 951 |       \protected@xdef\scratch{\the\tocauthor}%
 952 |       \protected@xdef\toc@uthor{\scratch}%
 953 |     \fi
 954 |     \addtocontents{toc}{\noexpand\protect\noexpand\authcount{\the\c@auco}}%
 955 |     \addcontentsline{toc}{author}{\toc@uthor}%
 956 |     \if@runhead
 957 |        \if!\the\authorrunning!
 958 |          \value{@inst}=\value{@auth}%
 959 |          \setcounter{@auth}{1}%
 960 |        \else
 961 |          \edef\@author{\the\authorrunning}%
 962 |        \fi
 963 |        \global\setbox\authrun=\hbox{\small\unboldmath\@author\unskip}%
 964 |        \ifdim\wd\authrun>\instindent
 965 |           \typeout{Names of authors too long for running head. Please supply}%
 966 |           \typeout{a shorter form with \string\authorrunning\space prior to
 967 |                    \string\maketitle}%
 968 |           \global\setbox\authrun=\hbox{\small\rm
 969 |           Authors Suppressed Due to Excessive Length}%
 970 |        \fi
 971 |        \xdef\@author{\copy\authrun}%
 972 |        \markboth{\@author}{\@title}%
 973 |      \fi
 974 |   \endgroup
 975 |   \setcounter{footnote}{\fnnstart}%
 976 |   \clearheadinfo}
 977 | %
 978 | \def\@maketitle{\newpage
 979 |  \markboth{}{}%
 980 |  \def\lastand{\ifnum\value{@inst}=2\relax
 981 |                  \unskip{} \andname\
 982 |               \else
 983 |                  \unskip \lastandname\
 984 |               \fi}%
 985 |  \def\and{\stepcounter{@auth}\relax
 986 |           \ifnum\value{@auth}=\value{@inst}%
 987 |              \lastand
 988 |           \else
 989 |              \unskip,
 990 |           \fi}%
 991 |  \begin{center}%
 992 |  \let\newline\\
 993 |  {\Large \bfseries\boldmath
 994 |   \pretolerance=10000
 995 |   \@title \par}\vskip .8cm
 996 | \if!\@subtitle!\else {\large \bfseries\boldmath
 997 |   \vskip -.65cm
 998 |   \pretolerance=10000
 999 |   \@subtitle \par}\vskip .8cm\fi
1000 |  \setbox0=\vbox{\setcounter{@auth}{1}\def\and{\stepcounter{@auth}}%
1001 |  \def\thanks##1{}\@author}%
1002 |  \global\value{@inst}=\value{@auth}%
1003 |  \global\value{auco}=\value{@auth}%
1004 |  \setcounter{@auth}{1}%
1005 | {\lineskip .5em
1006 | \noindent\ignorespaces
1007 | \@author\vskip.35cm}
1008 |  {\small\institutename}
1009 |  \end{center}%
1010 |  }
1011 | 
1012 | % definition of the "\spnewtheorem" command.
1013 | %
1014 | % Usage:
1015 | %
1016 | %     \spnewtheorem{env_nam}{caption}[within]{cap_font}{body_font}
1017 | % or  \spnewtheorem{env_nam}[numbered_like]{caption}{cap_font}{body_font}
1018 | % or  \spnewtheorem*{env_nam}{caption}{cap_font}{body_font}
1019 | %
1020 | % New is "cap_font" and "body_font". It stands for
1021 | % fontdefinition of the caption and the text itself.
1022 | %
1023 | % "\spnewtheorem*" gives a theorem without number.
1024 | %
1025 | % A defined spnewthoerem environment is used as described
1026 | % by Lamport.
1027 | %
1028 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1029 | 
1030 | \def\@thmcountersep{}
1031 | \def\@thmcounterend{.}
1032 | 
1033 | \def\spnewtheorem{\@ifstar{\@sthm}{\@Sthm}}
1034 | 
1035 | % definition of \spnewtheorem with number
1036 | 
1037 | \def\@spnthm#1#2{%
1038 |   \@ifnextchar[{\@spxnthm{#1}{#2}}{\@spynthm{#1}{#2}}}
1039 | \def\@Sthm#1{\@ifnextchar[{\@spothm{#1}}{\@spnthm{#1}}}
1040 | 
1041 | \def\@spxnthm#1#2[#3]#4#5{\expandafter\@ifdefinable\csname #1\endcsname
1042 |    {\@definecounter{#1}\@addtoreset{#1}{#3}%
1043 |    \expandafter\xdef\csname the#1\endcsname{\expandafter\noexpand
1044 |      \csname the#3\endcsname \noexpand\@thmcountersep \@thmcounter{#1}}%
1045 |    \expandafter\xdef\csname #1name\endcsname{#2}%
1046 |    \global\@namedef{#1}{\@spthm{#1}{\csname #1name\endcsname}{#4}{#5}}%
1047 |                               \global\@namedef{end#1}{\@endtheorem}}}
1048 | 
1049 | \def\@spynthm#1#2#3#4{\expandafter\@ifdefinable\csname #1\endcsname
1050 |    {\@definecounter{#1}%
1051 |    \expandafter\xdef\csname the#1\endcsname{\@thmcounter{#1}}%
1052 |    \expandafter\xdef\csname #1name\endcsname{#2}%
1053 |    \global\@namedef{#1}{\@spthm{#1}{\csname #1name\endcsname}{#3}{#4}}%
1054 |                                \global\@namedef{end#1}{\@endtheorem}}}
1055 | 
1056 | \def\@spothm#1[#2]#3#4#5{%
1057 |   \@ifundefined{c@#2}{\@latexerr{No theorem environment `#2' defined}\@eha}%
1058 |   {\expandafter\@ifdefinable\csname #1\endcsname
1059 |   {\newaliascnt{#1}{#2}%
1060 |   \expandafter\xdef\csname #1name\endcsname{#3}%
1061 |   \global\@namedef{#1}{\@spthm{#1}{\csname #1name\endcsname}{#4}{#5}}%
1062 |   \global\@namedef{end#1}{\@endtheorem}}}}
1063 | 
1064 | \def\@spthm#1#2#3#4{\topsep 7\p@ \@plus2\p@ \@minus4\p@
1065 | \refstepcounter{#1}%
1066 | \@ifnextchar[{\@spythm{#1}{#2}{#3}{#4}}{\@spxthm{#1}{#2}{#3}{#4}}}
1067 | 
1068 | \def\@spxthm#1#2#3#4{\@spbegintheorem{#2}{\csname the#1\endcsname}{#3}{#4}%
1069 |                     \ignorespaces}
1070 | 
1071 | \def\@spythm#1#2#3#4[#5]{\@spopargbegintheorem{#2}{\csname
1072 |        the#1\endcsname}{#5}{#3}{#4}\ignorespaces}
1073 | 
1074 | \def\@spbegintheorem#1#2#3#4{\trivlist
1075 |                  \item[\hskip\labelsep{#3#1\ #2\@thmcounterend}]#4}
1076 | 
1077 | \def\@spopargbegintheorem#1#2#3#4#5{\trivlist
1078 |       \item[\hskip\labelsep{#4#1\ #2}]{#4(#3)\@thmcounterend\ }#5}
1079 | 
1080 | % definition of \spnewtheorem* without number
1081 | 
1082 | \def\@sthm#1#2{\@Ynthm{#1}{#2}}
1083 | 
1084 | \def\@Ynthm#1#2#3#4{\expandafter\@ifdefinable\csname #1\endcsname
1085 |    {\global\@namedef{#1}{\@Thm{\csname #1name\endcsname}{#3}{#4}}%
1086 |     \expandafter\xdef\csname #1name\endcsname{#2}%
1087 |     \global\@namedef{end#1}{\@endtheorem}}}
1088 | 
1089 | \def\@Thm#1#2#3{\topsep 7\p@ \@plus2\p@ \@minus4\p@
1090 | \@ifnextchar[{\@Ythm{#1}{#2}{#3}}{\@Xthm{#1}{#2}{#3}}}
1091 | 
1092 | \def\@Xthm#1#2#3{\@Begintheorem{#1}{#2}{#3}\ignorespaces}
1093 | 
1094 | \def\@Ythm#1#2#3[#4]{\@Opargbegintheorem{#1}
1095 |        {#4}{#2}{#3}\ignorespaces}
1096 | 
1097 | \def\@Begintheorem#1#2#3{#3\trivlist
1098 |                            \item[\hskip\labelsep{#2#1\@thmcounterend}]}
1099 | 
1100 | \def\@Opargbegintheorem#1#2#3#4{#4\trivlist
1101 |       \item[\hskip\labelsep{#3#1}]{#3(#2)\@thmcounterend\ }}
1102 | 
1103 | \if@envcntsect
1104 |    \def\@thmcountersep{.}
1105 |    \spnewtheorem{theorem}{Theorem}[section]{\bfseries}{\itshape}
1106 | \else
1107 |    \spnewtheorem{theorem}{Theorem}{\bfseries}{\itshape}
1108 |    \if@envcntreset
1109 |       \@addtoreset{theorem}{section}
1110 |    \else
1111 |       \@addtoreset{theorem}{chapter}
1112 |    \fi
1113 | \fi
1114 | 
1115 | %definition of divers theorem environments
1116 | \spnewtheorem*{claim}{Claim}{\itshape}{\rmfamily}
1117 | \spnewtheorem*{proof}{Proof}{\itshape}{\rmfamily}
1118 | \if@envcntsame % alle Umgebungen wie Theorem.
1119 |    \def\spn@wtheorem#1#2#3#4{\@spothm{#1}[theorem]{#2}{#3}{#4}}
1120 | \else % alle Umgebungen mit eigenem Zaehler
1121 |    \if@envcntsect % mit section numeriert
1122 |       \def\spn@wtheorem#1#2#3#4{\@spxnthm{#1}{#2}[section]{#3}{#4}}
1123 |    \else % nicht mit section numeriert
1124 |       \if@envcntreset
1125 |          \def\spn@wtheorem#1#2#3#4{\@spynthm{#1}{#2}{#3}{#4}
1126 |                                    \@addtoreset{#1}{section}}
1127 |       \else
1128 |          \def\spn@wtheorem#1#2#3#4{\@spynthm{#1}{#2}{#3}{#4}
1129 |                                    \@addtoreset{#1}{chapter}}%
1130 |       \fi
1131 |    \fi
1132 | \fi
1133 | \spn@wtheorem{case}{Case}{\itshape}{\rmfamily}
1134 | \spn@wtheorem{conjecture}{Conjecture}{\itshape}{\rmfamily}
1135 | \spn@wtheorem{corollary}{Corollary}{\bfseries}{\itshape}
1136 | \spn@wtheorem{definition}{Definition}{\bfseries}{\itshape}
1137 | \spn@wtheorem{example}{Example}{\itshape}{\rmfamily}
1138 | \spn@wtheorem{exercise}{Exercise}{\itshape}{\rmfamily}
1139 | \spn@wtheorem{lemma}{Lemma}{\bfseries}{\itshape}
1140 | \spn@wtheorem{note}{Note}{\itshape}{\rmfamily}
1141 | \spn@wtheorem{problem}{Problem}{\itshape}{\rmfamily}
1142 | \spn@wtheorem{property}{Property}{\itshape}{\rmfamily}
1143 | \spn@wtheorem{proposition}{Proposition}{\bfseries}{\itshape}
1144 | \spn@wtheorem{question}{Question}{\itshape}{\rmfamily}
1145 | \spn@wtheorem{solution}{Solution}{\itshape}{\rmfamily}
1146 | \spn@wtheorem{remark}{Remark}{\itshape}{\rmfamily}
1147 | 
1148 | \def\@takefromreset#1#2{%
1149 |     \def\@tempa{#1}%
1150 |     \let\@tempd\@elt
1151 |     \def\@elt##1{%
1152 |         \def\@tempb{##1}%
1153 |         \ifx\@tempa\@tempb\else
1154 |             \@addtoreset{##1}{#2}%
1155 |         \fi}%
1156 |     \expandafter\expandafter\let\expandafter\@tempc\csname cl@#2\endcsname
1157 |     \expandafter\def\csname cl@#2\endcsname{}%
1158 |     \@tempc
1159 |     \let\@elt\@tempd}
1160 | 
1161 | \def\theopargself{\def\@spopargbegintheorem##1##2##3##4##5{\trivlist
1162 |       \item[\hskip\labelsep{##4##1\ ##2}]{##4##3\@thmcounterend\ }##5}
1163 |                   \def\@Opargbegintheorem##1##2##3##4{##4\trivlist
1164 |       \item[\hskip\labelsep{##3##1}]{##3##2\@thmcounterend\ }}
1165 |       }
1166 | 
1167 | \renewenvironment{abstract}{%
1168 |       \list{}{\advance\topsep by0.35cm\relax\small
1169 |       \leftmargin=1cm
1170 |       \labelwidth=\z@
1171 |       \listparindent=\z@
1172 |       \itemindent\listparindent
1173 |       \rightmargin\leftmargin}\item[\hskip\labelsep
1174 |                                     \bfseries\abstractname]}
1175 |     {\endlist}
1176 | 
1177 | \newdimen\headlineindent             % dimension for space between
1178 | \headlineindent=1.166cm              % number and text of headings.
1179 | 
1180 | \def\ps@headings{\let\@mkboth\@gobbletwo
1181 |    \let\@oddfoot\@empty\let\@evenfoot\@empty
1182 |    \def\@evenhead{\normalfont\small\rlap{\thepage}\hspace{\headlineindent}%
1183 |                   \leftmark\hfil}
1184 |    \def\@oddhead{\normalfont\small\hfil\rightmark\hspace{\headlineindent}%
1185 |                  \llap{\thepage}}
1186 |    \def\chaptermark##1{}%
1187 |    \def\sectionmark##1{}%
1188 |    \def\subsectionmark##1{}}
1189 | 
1190 | \def\ps@titlepage{\let\@mkboth\@gobbletwo
1191 |    \let\@oddfoot\@empty\let\@evenfoot\@empty
1192 |    \def\@evenhead{\normalfont\small\rlap{\thepage}\hspace{\headlineindent}%
1193 |                   \hfil}
1194 |    \def\@oddhead{\normalfont\small\hfil\hspace{\headlineindent}%
1195 |                  \llap{\thepage}}
1196 |    \def\chaptermark##1{}%
1197 |    \def\sectionmark##1{}%
1198 |    \def\subsectionmark##1{}}
1199 | 
1200 | \if@runhead\ps@headings\else
1201 | \ps@empty\fi
1202 | 
1203 | \setlength\arraycolsep{1.4\p@}
1204 | \setlength\tabcolsep{1.4\p@}
1205 | 
1206 | \endinput
1207 | %end of file llncs.cls
1208 | 


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