initial checkin

git-svn-id: https://phat.googlecode.com/svn/trunk@2 8e3bb3c2-eed4-f18f-5264-0b6c94e6926d

38 files changed, 5178 insertions, 0 deletions

diff --git a/CMakeLists.txt b/CMakeLists.txt
new file mode 100644
index 0000000..e670d81
--- /dev/null
+++ b/CMakeLists.txt
@@ -0,0 +1,17 @@
+cmake_minimum_required(VERSION 2.8)
+
+include_directories (include)
+
+FIND_PACKAGE(OpenMP)
+
+if(OPENMP_FOUND)
+set(CMAKE_C_FLAGS "${CMAKE_C_FLAGS} ${OpenMP_C_FLAGS}")
+set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} ${OpenMP_CXX_FLAGS}")
+set(CMAKE_EXE_LINKER_FLAGS "${CMAKE_EXE_LINKER_FLAGS} ${OpenMP_EXE_LINKER_FLAGS}")
+else()
+message("OpenMP not supported by the compiler! \nTo get optimal performance for the \"chunk\" algorithm, use a C++ compiler with OpenMP support (e.g., GCC).\nTo use a different compiler, pass it to cmake in the variable CMAKE_CXX_COMPILER: \n  cmake . -DCMAKE_CXX_COMPILER=g++")
+endif()
+
+add_executable (simple_example src/simple_example.cpp)
+add_executable (self_test src/self_test.cpp)
+add_executable (phat src/phat.cpp)
diff --git a/COPYING b/COPYING
new file mode 100644
index 0000000..94a9ed0
--- /dev/null
+++ b/COPYING
@@ -0,0 +1,674 @@
+                    GNU GENERAL PUBLIC LICENSE
+                       Version 3, 29 June 2007
+
+ Copyright (C) 2007 Free Software Foundation, Inc. <http://fsf.org/>
+ Everyone is permitted to copy and distribute verbatim copies
+ of this license document, but changing it is not allowed.
+
+                            Preamble
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+if any, to sign a "copyright disclaimer" for the program, if necessary.
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+<http://www.gnu.org/licenses/>.
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+may consider it more useful to permit linking proprietary applications with
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diff --git a/COPYING.LESSER b/COPYING.LESSER
new file mode 100644
index 0000000..65c5ca8
--- /dev/null
+++ b/COPYING.LESSER
@@ -0,0 +1,165 @@
+                   GNU LESSER GENERAL PUBLIC LICENSE
+                       Version 3, 29 June 2007
+
+ Copyright (C) 2007 Free Software Foundation, Inc. <http://fsf.org/>
+ Everyone is permitted to copy and distribute verbatim copies
+ of this license document, but changing it is not allowed.
+
+
+  This version of the GNU Lesser General Public License incorporates
+the terms and conditions of version 3 of the GNU General Public
+License, supplemented by the additional permissions listed below.
+
+  0. Additional Definitions.
+
+  As used herein, "this License" refers to version 3 of the GNU Lesser
+General Public License, and the "GNU GPL" refers to version 3 of the GNU
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+Library.
diff --git a/README b/README
new file mode 100644
index 0000000..a165026
--- /dev/null
+++ b/README
@@ -0,0 +1,121 @@
+PHAT (Persistent Homology Algorithm Toolbox) - Version 1.0
+Copyright 2013 IST Austria
+
+Authors:
+
+Ulrich Bauer (ulrich.bauer@ist.ac.at)
+Michael Kerber (mkerber@mpi-inf.mpg.de)
+Jan Reininghaus (jan.reininghaus@ist.ac.at)
+
+Description:
+
+This software library contains methods for computing the persistence pairs of a 
+filtered cell complex represented by an ordered boundary matrix with Z_2 coefficients. 
+For an introduction to persistent homology, see the textbook [1]. This software package
+contains code for several algorithmic variants:
+
+- The standard algorithm (see [1], p.153)
+- The "row algorithm" from [2] (called pHrow in there)
+- The "twist algorithm", as described in [3] (default algorithm)
+- The "chunk algorithm" presented in [4]
+
+The last two algorithms exploit the special structure of the boundary matrix
+to take shortcuts in the computation. The chunk algorithm makes use of multiple 
+CPU cores if it is compiled with OpenMP support.
+
+All algorithms are implemented as classes with a common interface: 
+they provide a member function "reduce" which takes a Boundary_matrix object
+as input (to be defined below) and manipulate it to reduced form. 
+From this reduced form one can then easily extract the persistence pairs. 
+Alternatively, the algorithms can compute the associated "Persistence_pairs"
+directly using the "get_pairs" method.
+
+The algorithm classes, as well as the Boundary_matrix class, are templates
+that take a "Representation" class as parameter. This representation defines
+how columns of the matrix are represented and how low-level operations 
+(e.g., column additions) are performed. The right choice of the representation
+class can be as important for the performance of the program as choosing the
+algorithm. We provide the following choices of representation classes:
+
+- "vector_vector": Each column is represented as a sorted std::vector of integers,
+  containing the indices of the non-zero entries of the column. The matrix
+  itself is a std::vector of such columns.
+- "vector_set": Each column is a std::set of integers, with the same meaning
+  as before. The matrix is stored as a std::vector of such columns.
+- "sparse_pivot_column" (default representation): The matrix is stored as in the 
+  vector_vector representation. However, when a column is manipulated, it is first
+  converted into a std::set, using an extra data field called the "pivot column".
+  When another column is manipulated later, the pivot column is converted back to
+  the std::vector representation. This can lead to speed improvements when many columns
+  are added to a given pivot column consecutively. In a multicore setup, there is one 
+  pivot column per core.
+- "full_pivot_column": The same idea as in the sparse version. However,
+  instead of a std::set, the pivot column is expanded into a bit vector of size n 
+  (the dimension of the matrix). To avoid costly initializations,
+  the class remembers which entries have been manipulated for a pivot column
+  and updates only those entries when another column becomes the pivot.
+  
+There are two ways to interface with the library:
+
+A) using files: 
+	1) write the boundary matrix / filtration into a file "input" (see below for the file format). 
+	2) compile src/phat.cpp and run it:
+		phat input output (if you use the binary encoding, see below)
+		phat --ascii input output (if you use ascii encoding, see below)
+	3) read the resulting persistence pairs into your program 
+
+B) using the C++ library interface:
+	0) include all headers found in src/phat.cpp
+	1) define a boundary matrix object, e.g. 
+		phat::boundary_matrix< full_pivot_column > boundary_matrix;
+	2) set the number of columns:
+		boundary_matrix.set_num_cols(...);
+	3) initialize each column using 
+		boundary_matrix.set_col(...) and boundary_matrix.set_dim(...)
+	4) define an object to hold the result:
+		phat::persistence_pairs pairs;
+	5) run an algorithm like this:
+		phat::compute_persistence_pairs< phat::chunk_reduction >( pairs, boundary_matrix );
+	6) use pairs.get_num_pairs() and pairs.get_pair(...) to examine the result
+	
+	A simple example that demonstrates this functionality can be found in src/simple_example.cpp
+
+File Formats:
+
+The library supports input and output in ascii and binary format
+through the methods "[load|save]_[ascii|binary]" in the classes boundary_matrix 
+and persistence_pairs. The file formats are defined as follows:
+
+boundary_matrix - ascii:
+	The file represents the filtration of the cell complex, containing one cell 
+	per line (empty lines and lines starting with "#" are ignored). A cell is given by 
+	a sequence of integers, separated by spaces, where the first integer denotes the
+	dimension of the cell, and all following integers give the indices
+	of the cells that form its boundary (the index of a cell is its position 
+	in the filtration, starting with 0). 
+	A sample file "single_triangle.dat" can be found in the examples folder.
+
+boundary_matrix - binary:
+	I binary format, the file is simply interpreted as a sequence of 64 bit signed integer 
+	numbers. The first number is interpreted as the number of cells of the complex. The 	
+	descriptions of the cells is expected to follow, with the first number representing the 
+	dimension of the cell, the next number, say N, representing the size of the boundary, 
+	followed by N numbers denoting the indices of the boundary cells. 
+	A sample file "single_triangle.bin"	can be found in the examples folder.
+
+persistence_pairs - ascii: 
+	The file contains the persistence pairs, sorted by birth index. The first integer in the
+	file is equal to the number of pairs. It is followed by pairs of integers encode the 
+	respective birth and death indices. 
+	A sample file "single_triangle_persistence_pairs.dat" can be found in the examples folder.
+
+persistence_pairs - binary: 
+	Same as ascii format, see above. Only now the integers are encoded as 64bit signed integers.
+	A sample file "single_triangle_persistence_pairs.bin" can be found in the examples folder.
+
+References:
+
+[1] H.Edelsbrunner, J.Harer: Computational Topology, An Introduction. American Mathematical Society, 2010, ISBN 0-8218-4925-5
+[2] V.de Silva, D.Morozov, M.Vejdemo-Johansson: Dualities in persistent (co)homology. Inverse Problems 27, 2011
+[3] C.Chen, M.Kerber: Persistent Homology Computation With a Twist. 27th European Workshop on Computational Geometry, 2011.
+[4] U.Bauer, M.Kerber, J.Reininghaus: Clear and Compress: Computing Persistent Homology in Chunks. arxiv: ????.????
diff --git a/build/Visual Studio/VisualStudio2008.sln b/build/Visual Studio/VisualStudio2008.sln
new file mode 100644
index 0000000..b325a17
--- /dev/null
+++ b/build/Visual Studio/VisualStudio2008.sln
@@ -0,0 +1,44 @@
+

+Microsoft Visual Studio Solution File, Format Version 10.00

+# Visual Studio 2008

+Project("{8BC9CEB8-8B4A-11D0-8D11-00A0C91BC942}") = "phat", "phat\phat.vcproj", "{B070D449-386F-4B1D-B405-168D9B960591}"

+EndProject

+Project("{8BC9CEB8-8B4A-11D0-8D11-00A0C91BC942}") = "self_test", "self_test\self_test.vcproj", "{A2E06E7F-73D2-4735-9306-010BA873D72A}"

+EndProject

+Project("{8BC9CEB8-8B4A-11D0-8D11-00A0C91BC942}") = "simple_example", "simple_example\simple_example.vcproj", "{EF3AAC07-A647-49F8-B6E0-DA9525C93569}"

+EndProject

+Global

+	GlobalSection(SolutionConfigurationPlatforms) = preSolution

+		Debug|Win32 = Debug|Win32

+		Debug|x64 = Debug|x64

+		Release|Win32 = Release|Win32

+		Release|x64 = Release|x64

+	EndGlobalSection

+	GlobalSection(ProjectConfigurationPlatforms) = postSolution

+		{B070D449-386F-4B1D-B405-168D9B960591}.Debug|Win32.ActiveCfg = Debug|Win32

+		{B070D449-386F-4B1D-B405-168D9B960591}.Debug|Win32.Build.0 = Debug|Win32

+		{B070D449-386F-4B1D-B405-168D9B960591}.Debug|x64.ActiveCfg = Debug|x64

+		{B070D449-386F-4B1D-B405-168D9B960591}.Debug|x64.Build.0 = Debug|x64

+		{B070D449-386F-4B1D-B405-168D9B960591}.Release|Win32.ActiveCfg = Release|Win32

+		{B070D449-386F-4B1D-B405-168D9B960591}.Release|Win32.Build.0 = Release|Win32

+		{B070D449-386F-4B1D-B405-168D9B960591}.Release|x64.ActiveCfg = Release|x64

+		{B070D449-386F-4B1D-B405-168D9B960591}.Release|x64.Build.0 = Release|x64

+		{A2E06E7F-73D2-4735-9306-010BA873D72A}.Debug|Win32.ActiveCfg = Debug|Win32

+		{A2E06E7F-73D2-4735-9306-010BA873D72A}.Debug|Win32.Build.0 = Debug|Win32

+		{A2E06E7F-73D2-4735-9306-010BA873D72A}.Debug|x64.ActiveCfg = Debug|x64

+		{A2E06E7F-73D2-4735-9306-010BA873D72A}.Release|Win32.ActiveCfg = Release|Win32

+		{A2E06E7F-73D2-4735-9306-010BA873D72A}.Release|Win32.Build.0 = Release|Win32

+		{A2E06E7F-73D2-4735-9306-010BA873D72A}.Release|x64.ActiveCfg = Release|x64

+		{A2E06E7F-73D2-4735-9306-010BA873D72A}.Release|x64.Build.0 = Release|x64

+		{EF3AAC07-A647-49F8-B6E0-DA9525C93569}.Debug|Win32.ActiveCfg = Debug|Win32

+		{EF3AAC07-A647-49F8-B6E0-DA9525C93569}.Debug|Win32.Build.0 = Debug|Win32

+		{EF3AAC07-A647-49F8-B6E0-DA9525C93569}.Debug|x64.ActiveCfg = Debug|Win32

+		{EF3AAC07-A647-49F8-B6E0-DA9525C93569}.Release|Win32.ActiveCfg = Release|Win32

+		{EF3AAC07-A647-49F8-B6E0-DA9525C93569}.Release|Win32.Build.0 = Release|Win32

+		{EF3AAC07-A647-49F8-B6E0-DA9525C93569}.Release|x64.ActiveCfg = Release|x64

+		{EF3AAC07-A647-49F8-B6E0-DA9525C93569}.Release|x64.Build.0 = Release|x64

+	EndGlobalSection

+	GlobalSection(SolutionProperties) = preSolution

+		HideSolutionNode = FALSE

+	EndGlobalSection

+EndGlobal

diff --git a/build/Visual Studio/VisualStudio2012.sln b/build/Visual Studio/VisualStudio2012.sln
new file mode 100644
index 0000000..2282a26
--- /dev/null
+++ b/build/Visual Studio/VisualStudio2012.sln
@@ -0,0 +1,46 @@
+

+Microsoft Visual Studio Solution File, Format Version 12.00

+# Visual Studio Express 2012 for Windows Desktop

+Project("{8BC9CEB8-8B4A-11D0-8D11-00A0C91BC942}") = "phat", "phat\phat.vcxproj", "{B070D449-386F-4B1D-B405-168D9B960591}"

+EndProject

+Project("{8BC9CEB8-8B4A-11D0-8D11-00A0C91BC942}") = "self_test", "self_test\self_test.vcxproj", "{A2E06E7F-73D2-4735-9306-010BA873D72A}"

+EndProject

+Project("{8BC9CEB8-8B4A-11D0-8D11-00A0C91BC942}") = "simple_example", "simple_example\simple_example.vcxproj", "{EF3AAC07-A647-49F8-B6E0-DA9525C93569}"

+EndProject

+Global

+	GlobalSection(SolutionConfigurationPlatforms) = preSolution

+		Debug|Win32 = Debug|Win32

+		Debug|x64 = Debug|x64

+		Release|Win32 = Release|Win32

+		Release|x64 = Release|x64

+	EndGlobalSection

+	GlobalSection(ProjectConfigurationPlatforms) = postSolution

+		{B070D449-386F-4B1D-B405-168D9B960591}.Debug|Win32.ActiveCfg = Debug|Win32

+		{B070D449-386F-4B1D-B405-168D9B960591}.Debug|Win32.Build.0 = Debug|Win32

+		{B070D449-386F-4B1D-B405-168D9B960591}.Debug|x64.ActiveCfg = Debug|x64

+		{B070D449-386F-4B1D-B405-168D9B960591}.Debug|x64.Build.0 = Debug|x64

+		{B070D449-386F-4B1D-B405-168D9B960591}.Release|Win32.ActiveCfg = Release|Win32

+		{B070D449-386F-4B1D-B405-168D9B960591}.Release|Win32.Build.0 = Release|Win32

+		{B070D449-386F-4B1D-B405-168D9B960591}.Release|x64.ActiveCfg = Release|x64

+		{B070D449-386F-4B1D-B405-168D9B960591}.Release|x64.Build.0 = Release|x64

+		{A2E06E7F-73D2-4735-9306-010BA873D72A}.Debug|Win32.ActiveCfg = Debug|Win32

+		{A2E06E7F-73D2-4735-9306-010BA873D72A}.Debug|Win32.Build.0 = Debug|Win32

+		{A2E06E7F-73D2-4735-9306-010BA873D72A}.Debug|x64.ActiveCfg = Debug|x64

+		{A2E06E7F-73D2-4735-9306-010BA873D72A}.Debug|x64.Build.0 = Debug|x64

+		{A2E06E7F-73D2-4735-9306-010BA873D72A}.Release|Win32.ActiveCfg = Release|Win32

+		{A2E06E7F-73D2-4735-9306-010BA873D72A}.Release|Win32.Build.0 = Release|Win32

+		{A2E06E7F-73D2-4735-9306-010BA873D72A}.Release|x64.ActiveCfg = Release|x64

+		{A2E06E7F-73D2-4735-9306-010BA873D72A}.Release|x64.Build.0 = Release|x64

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new file mode 100644
index 0000000..d0c1cbb
--- /dev/null
+++ b/build/Visual Studio/phat/phat.vcproj
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+				Name="VCCLCompilerTool"

+				Optimization="0"

+				AdditionalIncludeDirectories="$(SolutionDir)\..\..\include"

+				PreprocessorDefinitions="WIN32;_DEBUG;_CONSOLE"

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+			/>

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+			OutputDirectory="$(SolutionDir)$(PlatformName)\$(ConfigurationName)"

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+				Name="VCXMLDataGeneratorTool"

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+				Name="VCMIDLTool"

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+			/>

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+				Name="VCResourceCompilerTool"

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+				Name="VCPreLinkEventTool"

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+				Name="VCLinkerTool"

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+				Name="VCALinkTool"

+			/>

+			<Tool

+				Name="VCManifestTool"

+			/>

+			<Tool

+				Name="VCXDCMakeTool"

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+				Name="VCBscMakeTool"

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+				Name="VCFxCopTool"

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+			<Tool

+				Name="VCAppVerifierTool"

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+			<Tool

+				Name="VCPostBuildEventTool"

+			/>

+		</Configuration>

+		<Configuration

+			Name="Release|Win32"

+			OutputDirectory="$(SolutionDir)$(PlatformName)\$(ConfigurationName)"

+			IntermediateDirectory="$(PlatformName)\$(ConfigurationName)"

+			ConfigurationType="1"

+			CharacterSet="1"

+			WholeProgramOptimization="1"

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+			<Tool

+				Name="VCPreBuildEventTool"

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+				Name="VCCLCompilerTool"

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+			/>

+			<Tool

+				Name="VCPostBuildEventTool"

+			/>

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+	</Configurations>

+	<References>

+	</References>

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+			Name="Source Files"

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+			>

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+			Filter="h;hpp;hxx;hm;inl;inc;xsd"

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+			<Filter

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+			<Filter

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+					>

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+				<File

+					RelativePath="..\..\..\include\phat\representations\full_pivot_column.h"

+					>

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+					RelativePath="..\..\..\include\phat\representations\sparse_pivot_column.h"

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+					RelativePath="..\..\..\include\phat\representations\vector_set.h"

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+					RelativePath="..\..\..\include\phat\representations\vector_vector.h"

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+			</Filter>

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+		<Filter

+			Name="Resource Files"

+			Filter="rc;ico;cur;bmp;dlg;rc2;rct;bin;rgs;gif;jpg;jpeg;jpe;resx;tiff;tif;png;wav"

+			UniqueIdentifier="{67DA6AB6-F800-4c08-8B7A-83BB121AAD01}"

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+	<Globals>

+	</Globals>

+</VisualStudioProject>

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new file mode 100644
index 0000000..9729f72
--- /dev/null
+++ b/build/Visual Studio/phat/phat.vcxproj
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new file mode 100644
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new file mode 100644
index 0000000..3ad6d7e
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new file mode 100644
index 0000000..144f1cd
--- /dev/null
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new file mode 100644
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new file mode 100644
index 0000000..f073257
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+			<Tool

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+					>

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+					RelativePath="..\..\..\include\phat\representations\sparse_pivot_column.h"

+					>

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+					RelativePath="..\..\..\include\phat\representations\vector_set.h"

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+					RelativePath="..\..\..\include\phat\representations\vector_vector.h"

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+			Name="Resource Files"

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+			UniqueIdentifier="{67DA6AB6-F800-4c08-8B7A-83BB121AAD01}"

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+</VisualStudioProject>

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new file mode 100644
index 0000000..098a027
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+++ b/build/Visual Studio/simple_example/simple_example.vcxproj
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new file mode 100644
index 0000000..d033114
--- /dev/null
+++ b/build/Visual Studio/simple_example/simple_example.vcxproj.filters
@@ -0,0 +1,78 @@
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diff --git a/examples/single_triangle.bin b/examples/single_triangle.bin
new file mode 100644
index 0000000..8d5c8fb
--- /dev/null
+++ b/examples/single_triangle.bin
diff --git a/examples/single_triangle.dat b/examples/single_triangle.dat
new file mode 100644
index 0000000..928ee9b
--- /dev/null
+++ b/examples/single_triangle.dat
@@ -0,0 +1,12 @@
+# A simple matrix
+0
+0
+0
+1 0 1
+1 0 2
+1 1 2
+# Here is the triangle
+2 3 4 5
+
+
+
diff --git a/examples/single_triangle_persistence_pairs.bin b/examples/single_triangle_persistence_pairs.bin
new file mode 100644
index 0000000..fe864ac
--- /dev/null
+++ b/examples/single_triangle_persistence_pairs.bin
diff --git a/examples/single_triangle_persistence_pairs.dat b/examples/single_triangle_persistence_pairs.dat
new file mode 100644
index 0000000..daaeef5
--- /dev/null
+++ b/examples/single_triangle_persistence_pairs.dat
@@ -0,0 +1,4 @@
+3

+1 3

+2 4

+5 6

diff --git a/examples/torus.bin b/examples/torus.bin
new file mode 100644
index 0000000..47373db
--- /dev/null
+++ b/examples/torus.bin
diff --git a/include/phat/algorithms/chunk_reduction.h b/include/phat/algorithms/chunk_reduction.h
new file mode 100644
index 0000000..ebba266
--- /dev/null
+++ b/include/phat/algorithms/chunk_reduction.h
@@ -0,0 +1,235 @@
+/*  Copyright 2013 IST Austria

+    Contributed by: Ulrich Bauer, Michael Kerber, Jan Reininghaus

+

+    This file is part of PHAT.

+

+    PHAT is free software: you can redistribute it and/or modify

+    it under the terms of the GNU Lesser General Public License as published by

+    the Free Software Foundation, either version 3 of the License, or

+    (at your option) any later version.

+

+    PHAT is distributed in the hope that it will be useful,

+    but WITHOUT ANY WARRANTY; without even the implied warranty of

+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the

+    GNU Lesser General Public License for more details.

+

+    You should have received a copy of the GNU Lesser General Public License

+    along with PHAT.  If not, see <http://www.gnu.org/licenses/>. */

+

+#pragma once

+

+#include <phat/helpers/misc.h>

+#include <phat/boundary_matrix.h>

+

+namespace phat {

+    class chunk_reduction {

+    public:

+        enum column_type { GLOBAL

+                         , LOCAL_POSITIVE

+                         , LOCAL_NEGATIVE };

+

+    public:

+        template< typename Representation >

+        void operator() ( boundary_matrix< Representation >& boundary_matrix ) {

+

+            const index nr_columns = boundary_matrix.get_num_cols();

+            const dimension max_dim = boundary_matrix.get_max_dim();

+

+            std::vector< index > lowest_one_lookup( nr_columns, -1 );

+            std::vector < column_type > column_type( nr_columns, GLOBAL );

+            std::vector< char > is_active( nr_columns, false );

+

+            std::vector<index> chunk_boundaries;

+            _get_chunks( boundary_matrix, chunk_boundaries );

+

+            // Phase 1: Reduce chunks locally -- 1st pass

+            #pragma omp parallel for schedule( guided, 1 )

+            for( index chunk_id = 0; chunk_id < (index) chunk_boundaries.size() - 2; chunk_id += 2 ) 

+                _local_chunk_reduction( boundary_matrix, lowest_one_lookup, column_type, max_dim,

+                                        chunk_boundaries[chunk_id], chunk_boundaries[chunk_id+2] - 1 );

+            boundary_matrix.sync();

+

+            // Phase 1: Reduce chunks locally -- 2nd pass

+            #pragma omp parallel for schedule( guided, 1 )

+            for( index chunk_id = 1; chunk_id < (index) chunk_boundaries.size() - 2; chunk_id += 2 )

+                _local_chunk_reduction( boundary_matrix, lowest_one_lookup, column_type, max_dim,

+                                        chunk_boundaries[chunk_id], chunk_boundaries[chunk_id+2] - 1 );

+            boundary_matrix.sync();

+

+            // get global columns

+            std::vector< index > global_columns;

+            for( index cur_col_idx = 0; cur_col_idx < nr_columns; cur_col_idx++ )

+                if( column_type[ cur_col_idx ] == GLOBAL )

+                    global_columns.push_back( cur_col_idx );

+

+            // get active columns

+            #pragma omp parallel for

+            for( index idx = 0; idx < (index)global_columns.size(); idx++ )

+                is_active[ global_columns[ idx ] ] = true;

+            _get_active_columns( boundary_matrix, lowest_one_lookup, column_type, global_columns, is_active );

+

+            // Phase 2+3: Simplify columns and reduce them

+            for( dimension cur_dim = max_dim; cur_dim >= 1; cur_dim-- ) {

+                // Phase 2: Simplify columns 

+                std::vector< index > temp_col;

+                #pragma omp parallel for schedule( guided, 1 ), private( temp_col )

+                for( index idx = 0; idx < (index)global_columns.size(); idx++ )

+                    if( boundary_matrix.get_dim( global_columns[ idx ] ) == cur_dim )

+                        _global_column_simplification( global_columns[ idx ], boundary_matrix, lowest_one_lookup, column_type, is_active, temp_col );

+                boundary_matrix.sync();

+

+                // Phase 3: Reduce columns

+                for( index idx = 0; idx < (index)global_columns.size(); idx++ ) {

+                    index cur_col = global_columns[ idx ];

+                    if( boundary_matrix.get_dim( cur_col ) == cur_dim && column_type[ cur_col ] == GLOBAL ) {

+                        index lowest_one = boundary_matrix.get_max_index( cur_col );

+                        while( lowest_one != -1 && lowest_one_lookup[ lowest_one ] != -1 ) {

+                            boundary_matrix.add_to( lowest_one_lookup[ lowest_one ], cur_col );

+                            lowest_one = boundary_matrix.get_max_index( cur_col );

+                        }

+                        if( lowest_one != -1 ) {

+                            lowest_one_lookup[ lowest_one ] = cur_col;

+                            boundary_matrix.clear( lowest_one );

+                        }

+                    }

+                }

+            }

+

+            boundary_matrix.sync();

+        }

+    

+    protected:

+        template< typename Representation >

+        void _get_chunks( const boundary_matrix< Representation >& boundary_matrix

+                        , std::vector< index >& chunk_boundaries) 

+        {

+            chunk_boundaries.clear();

+            std::vector<index> temp_chunk_boundaries;

+            const index nr_columns = boundary_matrix.get_num_cols();

+            

+            const index chunk_size = (index) sqrt( (float)nr_columns );

+            for ( index cur_col = 0; cur_col < nr_columns; cur_col++ )

+                if( cur_col % chunk_size == 0 )

+                    temp_chunk_boundaries.push_back( cur_col );

+            temp_chunk_boundaries.push_back( nr_columns );

+            

+            // subdivide chunks for interleaved 2 pass appraoch

+            for( index chunk_id = 0; chunk_id < (index) temp_chunk_boundaries.size(); chunk_id ++ ) {

+                chunk_boundaries.push_back( temp_chunk_boundaries[ chunk_id ] );

+                if( chunk_id < (index) temp_chunk_boundaries.size() - 1 ) {

+                    index midPoint = ( temp_chunk_boundaries[ chunk_id ] + temp_chunk_boundaries[ chunk_id + 1 ] ) / 2;

+                    chunk_boundaries.push_back( midPoint );

+                }

+            }

+        }

+    

+        template< typename Representation >

+        void _local_chunk_reduction( boundary_matrix< Representation >& boundary_matrix

+                                   , std::vector<index>& lowest_one_lookup

+                                   , std::vector< column_type >& column_type

+                                   , const dimension max_dim

+                                   , const index chunk_begin

+                                   , const index chunk_end ) {

+            for( dimension cur_dim = max_dim; cur_dim >= 1; cur_dim-- ) {

+                for( index cur_col = chunk_begin; cur_col <= chunk_end; cur_col++ ) {

+                    if( column_type[ cur_col ] == GLOBAL && boundary_matrix.get_dim( cur_col ) == cur_dim ) {

+                        index lowest_one = boundary_matrix.get_max_index( cur_col );

+                        while( lowest_one != -1 && lowest_one >= chunk_begin && lowest_one_lookup[ lowest_one ] != -1  ) {

+                            boundary_matrix.add_to( lowest_one_lookup[ lowest_one ], cur_col );

+                            lowest_one = boundary_matrix.get_max_index( cur_col );

+                        }

+                        if( lowest_one >= chunk_begin ) {

+                            lowest_one_lookup[ lowest_one ] = cur_col;

+                            column_type[ cur_col ] = LOCAL_NEGATIVE;

+                            column_type[ lowest_one ] = LOCAL_POSITIVE;

+                            boundary_matrix.clear( lowest_one );

+                        }

+                    }

+                }

+            }

+        }

+

+        template< typename Representation >

+        void _get_active_columns( const boundary_matrix< Representation >& boundary_matrix

+                                , const std::vector< index >& lowest_one_lookup

+                                , const std::vector< column_type >& column_type

+                                , const std::vector< index >& global_columns

+                                , std::vector< char >& is_active ) {

+            

+            const index nr_columns = boundary_matrix.get_num_cols();

+            std::vector< char > finished( nr_columns, false );

+

+            std::vector< std::pair < index, index > > stack;

+            std::vector< index > cur_col_values;

+            #pragma omp parallel for schedule( guided, 1 ), private( stack, cur_col_values )

+            for( index idx = 0; idx < (index)global_columns.size(); idx++ ) {

+                bool pop_next = false;

+                index start_col = global_columns[ idx ];

+                stack.push_back( std::pair< index, index >( start_col, -1 ) );

+                while( !stack.empty() ) {

+                    index cur_col = stack.back().first;

+                    index prev_col = stack.back().second;

+                    if( pop_next ) {

+                        stack.pop_back();

+                        pop_next = false;

+                        if( prev_col != -1 ) {

+                            if( is_active[ cur_col ] ) {

+                                is_active[ prev_col ] = true;

+                            }

+                            if( prev_col == stack.back().first ) {

+                                finished[ prev_col ] = true;

+                                pop_next = true;

+                            }

+                        }

+                    } else {

+                        pop_next = true;

+                        boundary_matrix.get_col( cur_col, cur_col_values );

+                        for( index idx = 0; idx < (index) cur_col_values.size(); idx++ ) {

+                            index cur_row = cur_col_values[ idx ];

+                            if( ( column_type[ cur_row ] == GLOBAL ) ) {

+                                is_active[ cur_col ] = true;

+                            } else if( column_type[ cur_row ] == LOCAL_POSITIVE ) {

+                                index next_col = lowest_one_lookup[ cur_row ];

+                                if( next_col != cur_col && !finished[ cur_col ] ) {

+                                    stack.push_back( std::make_pair( next_col, cur_col ) );

+                                    pop_next = false;

+                                }

+                            }

+                        }

+                    }

+                }

+            }

+        }

+        

+        template< typename Representation >

+        void _global_column_simplification( const index col_idx

+                                          , boundary_matrix< Representation >& boundary_matrix

+                                          , const std::vector< index >& lowest_one_lookup

+                                          , const std::vector< column_type >& column_type

+                                          , const std::vector< char >& is_active

+                                          , std::vector< index >& temp_col ) 

+        {

+            temp_col.clear();

+            while( !boundary_matrix.is_empty( col_idx ) ) {

+                index cur_row = boundary_matrix.get_max_index( col_idx );

+                switch( column_type[ cur_row ] ) {

+                case GLOBAL:

+                    temp_col.push_back( cur_row );

+                    boundary_matrix.remove_max( col_idx );

+                    break;

+                case LOCAL_NEGATIVE:

+                    boundary_matrix.remove_max( col_idx );

+                    break;

+                case LOCAL_POSITIVE:

+                    if( is_active[ lowest_one_lookup[ cur_row ] ] )

+                        boundary_matrix.add_to( lowest_one_lookup[ cur_row ], col_idx );

+                    else

+                        boundary_matrix.remove_max( col_idx );

+                    break;

+                }

+            }

+            std::reverse( temp_col.begin(), temp_col.end() );

+            boundary_matrix.set_col( col_idx, temp_col );

+        }

+    };

+}

diff --git a/include/phat/algorithms/row_reduction.h b/include/phat/algorithms/row_reduction.h
new file mode 100644
index 0000000..62528e1
--- /dev/null
+++ b/include/phat/algorithms/row_reduction.h
@@ -0,0 +1,55 @@
+/*  Copyright 2013 IST Austria

+    Contributed by: Ulrich Bauer, Michael Kerber, Jan Reininghaus

+

+    This file is part of PHAT.

+

+    PHAT is free software: you can redistribute it and/or modify

+    it under the terms of the GNU Lesser General Public License as published by

+    the Free Software Foundation, either version 3 of the License, or

+    (at your option) any later version.

+

+    PHAT is distributed in the hope that it will be useful,

+    but WITHOUT ANY WARRANTY; without even the implied warranty of

+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the

+    GNU Lesser General Public License for more details.

+

+    You should have received a copy of the GNU Lesser General Public License

+    along with PHAT.  If not, see <http://www.gnu.org/licenses/>. */

+

+#pragma once

+

+#include <phat/helpers/misc.h>

+#include <phat/boundary_matrix.h>

+

+namespace phat {

+    class row_reduction {

+    public:

+        template< typename Representation >

+        void operator() ( boundary_matrix< Representation >& boundary_matrix ) {

+            

+            const index nr_columns = boundary_matrix.get_num_cols();

+            std::vector< std::vector< index > > lowest_one_lookup( nr_columns );

+            

+            for( index cur_col = nr_columns - 1; cur_col >= 0; cur_col-- ) {

+                if( !boundary_matrix.is_empty( cur_col ) )

+                    lowest_one_lookup[ boundary_matrix.get_max_index( cur_col ) ].push_back( cur_col );

+                

+                if( !lowest_one_lookup[ cur_col ].empty() ) {

+                    boundary_matrix.clear( cur_col );

+                    std::vector< index >& cols_with_cur_lowest = lowest_one_lookup[ cur_col ];

+                    index source = *min_element( cols_with_cur_lowest.begin(), cols_with_cur_lowest.end() );

+                    for( index idx = 0; idx < (index)cols_with_cur_lowest.size(); idx++ ) {

+                        index target = cols_with_cur_lowest[ idx ];

+                        if( target != source && !boundary_matrix.is_empty( target ) ) {

+                            boundary_matrix.add_to( source, target );     

+                            if( !boundary_matrix.is_empty( target ) ) {

+                                index lowest_one_of_target = boundary_matrix.get_max_index( target );

+                                lowest_one_lookup[ lowest_one_of_target ].push_back( target );

+                            }

+                        } 

+                    }

+                }

+            }

+        }

+    };

+}
\ No newline at end of file
diff --git a/include/phat/algorithms/standard_reduction.h b/include/phat/algorithms/standard_reduction.h
new file mode 100644
index 0000000..9b3a286
--- /dev/null
+++ b/include/phat/algorithms/standard_reduction.h
@@ -0,0 +1,45 @@
+/*  Copyright 2013 IST Austria

+    Contributed by: Ulrich Bauer, Michael Kerber, Jan Reininghaus

+

+    This file is part of PHAT.

+

+    PHAT is free software: you can redistribute it and/or modify

+    it under the terms of the GNU Lesser General Public License as published by

+    the Free Software Foundation, either version 3 of the License, or

+    (at your option) any later version.

+

+    PHAT is distributed in the hope that it will be useful,

+    but WITHOUT ANY WARRANTY; without even the implied warranty of

+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the

+    GNU Lesser General Public License for more details.

+

+    You should have received a copy of the GNU Lesser General Public License

+    along with PHAT.  If not, see <http://www.gnu.org/licenses/>. */

+

+#pragma once

+

+#include <phat/helpers/misc.h>

+#include <phat/boundary_matrix.h>

+

+namespace phat {

+    class standard_reduction {

+    public:

+        template< typename Representation >

+        void operator() ( boundary_matrix< Representation >& boundary_matrix ) {

+

+            const index nr_columns = boundary_matrix.get_num_cols();

+            std::vector< index > lowest_one_lookup( nr_columns, -1 );

+            

+            for( index cur_col = 0; cur_col < nr_columns; cur_col++ ) {

+                index lowest_one = boundary_matrix.get_max_index( cur_col );

+                while( lowest_one != -1 && lowest_one_lookup[ lowest_one ] != -1 ) {

+                    boundary_matrix.add_to( lowest_one_lookup[ lowest_one ], cur_col );

+                    lowest_one = boundary_matrix.get_max_index( cur_col );

+                }

+                if( lowest_one != -1 ) {

+                    lowest_one_lookup[ lowest_one ] = cur_col;

+                }

+            }

+        }

+    };

+}

diff --git a/include/phat/algorithms/twist_reduction.h b/include/phat/algorithms/twist_reduction.h
new file mode 100644
index 0000000..b9aae08
--- /dev/null
+++ b/include/phat/algorithms/twist_reduction.h
@@ -0,0 +1,50 @@
+/*  Copyright 2013 IST Austria

+    Contributed by: Ulrich Bauer, Michael Kerber, Jan Reininghaus

+

+    This file is part of PHAT.

+

+    PHAT is free software: you can redistribute it and/or modify

+    it under the terms of the GNU Lesser General Public License as published by

+    the Free Software Foundation, either version 3 of the License, or

+    (at your option) any later version.

+

+    PHAT is distributed in the hope that it will be useful,

+    but WITHOUT ANY WARRANTY; without even the implied warranty of

+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the

+    GNU Lesser General Public License for more details.

+

+    You should have received a copy of the GNU Lesser General Public License

+    along with PHAT.  If not, see <http://www.gnu.org/licenses/>. */

+

+#pragma once

+

+#include <phat/helpers/misc.h>

+#include <phat/boundary_matrix.h>

+

+namespace phat {

+    class twist_reduction {

+    public:

+        template< typename Representation >

+        void operator () ( boundary_matrix< Representation >& boundary_matrix ) {

+

+            const index nr_columns = boundary_matrix.get_num_cols();

+            std::vector< index > lowest_one_lookup( nr_columns, -1 );

+            

+            for( index cur_dim = boundary_matrix.get_max_dim(); cur_dim >= 1 ; cur_dim-- ) {

+                for( index cur_col = 0; cur_col < nr_columns; cur_col++ ) {

+                    if( boundary_matrix.get_dim( cur_col ) == cur_dim ) {

+                        index lowest_one = boundary_matrix.get_max_index( cur_col );

+                        while( lowest_one != -1 && lowest_one_lookup[ lowest_one ] != -1 ) {

+                            boundary_matrix.add_to( lowest_one_lookup[ lowest_one ], cur_col );

+                            lowest_one = boundary_matrix.get_max_index( cur_col );

+                        }

+                        if( lowest_one != -1 ) {

+                            lowest_one_lookup[ lowest_one ] = cur_col;

+                            boundary_matrix.clear( lowest_one );

+                        }

+                    }

+                }

+            }

+        }

+    };

+}

diff --git a/include/phat/boundary_matrix.h b/include/phat/boundary_matrix.h
new file mode 100644
index 0000000..63c0dc4
--- /dev/null
+++ b/include/phat/boundary_matrix.h
@@ -0,0 +1,283 @@
+/*  Copyright 2013 IST Austria

+    Contributed by: Ulrich Bauer, Michael Kerber, Jan Reininghaus

+

+    This file is part of PHAT.

+

+    PHAT is free software: you can redistribute it and/or modify

+    it under the terms of the GNU Lesser General Public License as published by

+    the Free Software Foundation, either version 3 of the License, or

+    (at your option) any later version.

+

+    PHAT is distributed in the hope that it will be useful,

+    but WITHOUT ANY WARRANTY; without even the implied warranty of

+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the

+    GNU Lesser General Public License for more details.

+

+    You should have received a copy of the GNU Lesser General Public License

+    along with PHAT.  If not, see <http://www.gnu.org/licenses/>. */

+

+#pragma once

+

+#include <phat/helpers/misc.h>

+

+// interface class for the main data structure -- implementations of the interface can be found in ./representations

+namespace phat {

+    template< class Representation = default_representation >

+    class boundary_matrix

+    {

+        

+    protected:

+        Representation rep;

+

+    // interface functions -- actual implementation and complexity depends on chosen @Representation template

+    public:

+        // get overall number of columns in boundary_matrix

+        index get_num_cols() const { return rep._get_num_cols(); }

+

+        // set overall number of columns in boundary_matrix

+        void set_num_cols( index nr_of_columns ) { rep._set_num_cols( nr_of_columns ); }

+

+        // get dimension of given index

+        dimension get_dim( index idx ) const { return rep._get_dim( idx ); }

+

+        // set dimension of given index

+        void set_dim( index idx, dimension dim ) { rep._set_dim( idx, dim ); }

+

+        // replaces content of @col with boundary of given index

+        void get_col( index idx, column& col  ) const { rep._get_col( idx, col ); }

+

+        // set column @idx to the values contained in @col

+        void set_col( index idx, const column& col  ) { rep._set_col( idx, col ); }

+

+        // true iff boundary of given column is empty

+        bool is_empty( index idx ) const { return rep._is_empty( idx ); }

+

+        // largest index of given column (new name for lowestOne())

+        index get_max_index( index idx ) const { return rep._get_max_index( idx ); }

+

+        // removes maximal index from given column 

+        void remove_max( index idx ) { rep._remove_max( idx ); }

+

+        // adds column @source to column @target'

+        void add_to( index source, index target ) { rep._add_to( source, target ); }

+

+        // clears given column

+        void clear( index idx ) { rep._clear( idx ); }

+

+        // syncronizes all internal data structures -- has to be called before and after any multithreaded access!

+        void sync() { rep._sync(); }

+

+    // helper functions / operators -- independent of chosen 'Representation'

+    public:

+        // returns maximal dimension

+        dimension get_max_dim() const {

+            dimension cur_max_dim = 0;

+            for( index idx = 0; idx < get_num_cols(); idx++ )

+                cur_max_dim = get_dim( idx ) > cur_max_dim ? get_dim( idx ) : cur_max_dim;

+            return cur_max_dim;

+        }

+

+        // number of nonzero rows for given column @idx

+        index get_num_rows( index idx ) const {

+            column cur_col;

+            get_col( idx, cur_col );

+            return cur_col.size();

+        }

+

+        // overall number of entries in the matrix

+        index get_num_entries() const {

+            index number_of_nonzero_entries = 0;

+            const index nr_of_columns = get_num_cols();

+            for( index idx = 0; idx < nr_of_columns; idx++ ) {

+                number_of_nonzero_entries += get_num_rows( idx );

+            }

+            return number_of_nonzero_entries;

+        }

+    

+    // operators / constructors

+    public:

+        boundary_matrix() {};

+

+        template< class OtherRepresentation >

+        boundary_matrix( const boundary_matrix< OtherRepresentation >& other ) {

+            *this = other;

+        }

+

+        template< typename OtherRepresentation >

+        bool operator==( const boundary_matrix< OtherRepresentation >& other_boundary_matrix ) const {

+            const index number_of_columns = this->get_num_cols();

+

+            if( number_of_columns != other_boundary_matrix.get_num_cols() )

+                return false;

+

+            column temp_col;

+            column other_temp_col;

+            for( index idx = 0; idx < number_of_columns; idx++ ) {

+                this->get_col( idx, temp_col );

+                other_boundary_matrix.get_col( idx, other_temp_col );

+                if( temp_col != other_temp_col )

+                    return false;

+            }

+            return true;

+        }

+

+        template< typename OtherRepresentation >

+        bool operator!=( const boundary_matrix< OtherRepresentation >& other_boundary_matrix ) const {

+            return !( *this == other_boundary_matrix );

+        }

+

+        template< typename OtherRepresentation >

+        boundary_matrix< Representation >& operator=( const boundary_matrix< OtherRepresentation >& other )

+        {

+            const index nr_of_columns = other.get_num_cols();

+            this->set_num_cols( nr_of_columns );

+            column temp_col;

+            for( index cur_col = 0; cur_col <  nr_of_columns; cur_col++ ) {

+                this->set_dim( cur_col, other.get_dim( cur_col ) );

+                other.get_col( cur_col, temp_col );

+                this->set_col( cur_col, temp_col );

+            }

+

+            // by convention, always return *this

+            return *this;

+        }

+

+    // I/O -- independent of chosen 'Representation'

+    public:

+

+        // initializes boundary_matrix from (vector<vector>, vector) pair -- untested

+        void init( const std::vector< std::vector< index > >& input_matrix, const std::vector< dimension >& input_dims ) { 

+            const index nr_of_columns = (index)input_matrix.size();

+            this->set_num_cols( nr_of_columns );

+            for( index cur_col = 0; cur_col <  nr_of_columns; cur_col++ ) {

+                this->set_dim( cur_col, input_dims[ cur_col ] );

+                this->set_col( cur_col, input_matrix[ cur_col ] );

+            }

+        }

+

+        // Loads the boundary_matrix from given file in ascii format 

+        // Format: each line represents a column, first number is dimension, other numbers are the content of the column.

+        // Ignores empty lines and lines starting with a '#'.

+        bool load_ascii( std::string filename ) { 

+            // first count number of columns:

+            std::string cur_line;

+            std::ifstream dummy( filename .c_str() );

+            if( dummy.fail() )

+                return false;

+

+            index number_of_columns = 0;

+            while( getline( dummy, cur_line ) )

+                if( cur_line != "" && cur_line[ 0 ] != '#' )

+                    number_of_columns++;

+            this->set_num_cols( number_of_columns );

+            dummy.close();

+

+            std::ifstream input_stream( filename.c_str() );

+            if( input_stream.fail() )

+                return false;

+            

+            column temp_col;

+            index cur_col = -1;

+            while( getline( input_stream, cur_line ) ) {

+                if( cur_line != "" && cur_line[ 0 ] != '#' ) {

+                    cur_col++;

+                    std::stringstream ss( cur_line );

+                    

+                    int64_t temp_dim;

+                    ss >> temp_dim;

+                    this->set_dim( cur_col, (dimension) temp_dim );

+

+                    int64_t temp_index;

+                    temp_col.clear();

+                    while( ss.good() ) {

+                        ss >> temp_index;

+                        temp_col.push_back( (index)temp_index );

+                    }

+                    std::sort( temp_col.begin(), temp_col.end() );

+                    this->set_col( cur_col, temp_col );

+                }

+            }

+

+            input_stream.close();

+            return true;

+        }

+

+        // Saves the boundary_matrix to given file in ascii format

+        // Format: each line represents a column, first number is dimension, other numbers are the content of the column

+        bool save_ascii( std::string filename ) {

+            std::ofstream output_stream( filename.c_str() );

+            if( output_stream.fail() )

+                return false;

+

+            const index nr_columns = this->get_num_cols();

+            column tempCol;

+            for( index cur_col = 0; cur_col < nr_columns; cur_col++ ) {

+                output_stream << (int64_t)this->get_dim( cur_col );

+                this->get_col( cur_col, tempCol );

+                for( index cur_row_idx = 0; cur_row_idx < (index)tempCol.size(); cur_row_idx++ )

+                    output_stream << " " << tempCol[ cur_row_idx ];

+                output_stream << std::endl;

+            }

+

+            output_stream.close();

+            return true;

+        }

+

+        // Loads boundary_matrix from given file 

+        // Format: nr_columns % dim1 % N1 % row1 row2 % ...% rowN1 % dim2 % N2 % ...

+        bool load_binary( std::string filename ) { 

+            std::ifstream input_stream( filename.c_str(), std::ios_base::binary | std::ios_base::in );

+            if( input_stream.fail() )

+                return false;

+

+            int64_t nr_columns;

+            input_stream.read( (char*)&nr_columns, sizeof( int64_t ) );

+            this->set_num_cols( (index)nr_columns );

+

+            column temp_col;

+            for( index cur_col = 0; cur_col < nr_columns; cur_col++ ) {

+                int64_t cur_dim;

+                input_stream.read( (char*)&cur_dim, sizeof( int64_t ) );

+                this->set_dim( cur_col, (dimension) cur_dim );

+                int64_t nr_rows;

+                input_stream.read( (char*)&nr_rows, sizeof( int64_t ) );

+                temp_col.resize( (std::size_t)nr_rows );

+                for( index idx = 0; idx < nr_rows; idx++ ) {

+                    int64_t cur_row;

+                    input_stream.read( (char*)&cur_row, sizeof( int64_t ) );

+                    temp_col[ idx ] = (index)cur_row;

+                }

+                this->set_col( cur_col, temp_col );

+            }

+

+            input_stream.close();

+            return true;

+        }

+

+        // Saves the boundary_matrix to given file in binary format 

+        // Format: nr_columns % dim1 % N1 % row1 row2 % ...% rowN1 % dim2 % N2 % ...

+        bool save_binary( std::string filename ) {

+            std::ofstream output_stream( filename.c_str(), std::ios_base::binary | std::ios_base::out );

+            if( output_stream.fail() )

+                return false;

+

+            const int64_t nr_columns = this->get_num_cols();

+            output_stream.write( (char*)&nr_columns, sizeof( int64_t ) );

+            column tempCol;

+            for( index cur_col = 0; cur_col < nr_columns; cur_col++ ) {

+                int64_t cur_dim = this->get_dim( cur_col );

+                output_stream.write( (char*)&cur_dim, sizeof( int64_t ) );

+                this->get_col( cur_col, tempCol );

+                int64_t cur_nr_rows = tempCol.size();

+                output_stream.write( (char*)&cur_nr_rows, sizeof( int64_t ) );

+                for( index cur_row_idx = 0; cur_row_idx < (index)tempCol.size(); cur_row_idx++ ) {

+                    int64_t cur_row = tempCol[ cur_row_idx ];

+                    output_stream.write( (char*)&cur_row, sizeof( int64_t ) );

+                }

+            }

+

+            output_stream.close();

+            return true;

+        }

+    };

+}

diff --git a/include/phat/compute_persistence_pairs.h b/include/phat/compute_persistence_pairs.h
new file mode 100644
index 0000000..e782bd7
--- /dev/null
+++ b/include/phat/compute_persistence_pairs.h
@@ -0,0 +1,69 @@
+/*  Copyright 2013 IST Austria
+    Contributed by: Ulrich Bauer, Michael Kerber, Jan Reininghaus
+
+    This file is part of PHAT.
+
+    PHAT is free software: you can redistribute it and/or modify
+    it under the terms of the GNU Lesser General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    PHAT is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU Lesser General Public License for more details.
+
+    You should have received a copy of the GNU Lesser General Public License
+    along with PHAT.  If not, see <http://www.gnu.org/licenses/>. */
+
+#pragma once
+
+#include <phat/persistence_pairs.h>
+#include <phat/boundary_matrix.h>
+#include <phat/helpers/dualize.h>
+#include <phat/algorithms/twist_reduction.h>
+
+namespace phat {
+
+    template< typename ReductionAlgorithm, typename Representation >
+    void compute_persistence_pairs( persistence_pairs& pairs, boundary_matrix< Representation >& boundary_matrix ) {
+        ReductionAlgorithm reduce;
+        reduce( boundary_matrix );
+        pairs.clear();
+        for( index idx = 0; idx < boundary_matrix.get_num_cols(); idx++ ) {
+            if( !boundary_matrix.is_empty( idx ) ) {
+                index birth = boundary_matrix.get_max_index( idx );
+                index death = idx;
+                pairs.append_pair( birth, death );
+            }
+        }
+    }
+    
+    template< typename ReductionAlgorithm, typename Representation >
+    void compute_persistence_pairs_dualized( persistence_pairs& pairs, boundary_matrix< Representation >& boundary_matrix ) {
+        ReductionAlgorithm reduce;
+        const index nr_columns = boundary_matrix.get_num_cols();
+        dualize( boundary_matrix );
+        reduce( boundary_matrix );
+        pairs.clear();
+        for( index idx = 0; idx < nr_columns; idx++ ) {
+            if( !boundary_matrix.is_empty( idx ) ) {
+                index death = nr_columns - 1 - boundary_matrix.get_max_index( idx );
+                index birth = nr_columns - 1 - idx;
+                pairs.append_pair( birth, death );
+            }
+        }
+    }
+    
+    template< typename Representation >
+    void compute_persistence_pairs( persistence_pairs& pairs, boundary_matrix< Representation >& boundary_matrix ) {
+        phat::compute_persistence_pairs< twist_reduction >( pairs, boundary_matrix );
+    }
+    
+    
+    template< typename Representation >
+    void compute_persistence_pairs_dualized( persistence_pairs& pairs, boundary_matrix< Representation >& boundary_matrix ) {
+        compute_persistence_pairs_dualized< twist_reduction >( pairs, boundary_matrix );
+    }
+
+}
\ No newline at end of file
diff --git a/include/phat/helpers/dualize.h b/include/phat/helpers/dualize.h
new file mode 100644
index 0000000..15f7c57
--- /dev/null
+++ b/include/phat/helpers/dualize.h
@@ -0,0 +1,51 @@
+/*  Copyright 2013 IST Austria

+    Contributed by: Ulrich Bauer, Michael Kerber, Jan Reininghaus

+

+    This file is part of PHAT.

+

+    PHAT is free software: you can redistribute it and/or modify

+    it under the terms of the GNU Lesser General Public License as published by

+    the Free Software Foundation, either version 3 of the License, or

+    (at your option) any later version.

+

+    PHAT is distributed in the hope that it will be useful,

+    but WITHOUT ANY WARRANTY; without even the implied warranty of

+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the

+    GNU Lesser General Public License for more details.

+

+    You should have received a copy of the GNU Lesser General Public License

+    along with PHAT.  If not, see <http://www.gnu.org/licenses/>. */

+

+#pragma once

+

+#include <phat/helpers/misc.h>

+#include <phat/boundary_matrix.h>

+

+namespace phat {

+    template< typename Representation >

+    void dualize( boundary_matrix< Representation >& boundary_matrix ) {

+

+        std::vector< dimension > dual_dims;

+        std::vector< std::vector< index > > dual_matrix;

+

+        index nr_of_columns = boundary_matrix.get_num_cols();

+        dual_matrix.resize( nr_of_columns );

+        dual_dims.resize( nr_of_columns );

+    

+        column temp_col;

+        for( index cur_col = 0; cur_col < nr_of_columns; cur_col++ ) {

+            boundary_matrix.get_col( cur_col, temp_col );

+            for( index idx = 0; idx < (index)temp_col.size(); idx++)

+                dual_matrix[ nr_of_columns - 1 - temp_col[ idx ]  ].push_back( nr_of_columns - 1 - cur_col );

+        }

+

+        const dimension max_dim = boundary_matrix.get_max_dim();

+        for( index cur_col = 0; cur_col < nr_of_columns; cur_col++ )

+            dual_dims[ nr_of_columns - 1 - cur_col ] = max_dim - boundary_matrix.get_dim( cur_col );

+

+        for( index cur_col = 0; cur_col < nr_of_columns; cur_col++ )

+            std::reverse( dual_matrix[ cur_col ].begin(), dual_matrix[ cur_col ].end() );

+

+        boundary_matrix.init( dual_matrix, dual_dims );

+    }

+}

diff --git a/include/phat/helpers/misc.h b/include/phat/helpers/misc.h
new file mode 100644
index 0000000..93af132
--- /dev/null
+++ b/include/phat/helpers/misc.h
@@ -0,0 +1,75 @@
+/*  Copyright 2013 IST Austria

+    Contributed by: Ulrich Bauer, Michael Kerber, Jan Reininghaus

+

+    This file is part of PHAT.

+

+    PHAT is free software: you can redistribute it and/or modify

+    it under the terms of the GNU Lesser General Public License as published by

+    the Free Software Foundation, either version 3 of the License, or

+    (at your option) any later version.

+

+    PHAT is distributed in the hope that it will be useful,

+    but WITHOUT ANY WARRANTY; without even the implied warranty of

+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the

+    GNU Lesser General Public License for more details.

+

+    You should have received a copy of the GNU Lesser General Public License

+    along with PHAT.  If not, see <http://www.gnu.org/licenses/>. */

+

+#pragma once

+

+// STL includes

+#include <iostream>

+#include <fstream>

+#include <string>

+#include <vector>

+#include <set>

+#include <map>

+#include <algorithm>

+#include <queue>

+#include <cassert>

+#include <sstream>

+#include <algorithm>

+#include <iomanip>

+#include <cmath>

+#include <cstdlib>

+     

+// VS2008 and below unfortunately do not support stdint.h

+#if defined(_MSC_VER)&& _MSC_VER < 1600

+    typedef __int8 int8_t;

+    typedef unsigned __int8 uint8_t;

+    typedef __int16 int16_t;

+    typedef unsigned __int16 uint16_t;

+    typedef __int32 int32_t;

+    typedef unsigned __int32 uint32_t;

+    typedef __int64 int64_t;

+    typedef unsigned __int64 uint64_t;

+#else

+    #include <stdint.h>

+#endif

+

+// basic types. index can be changed to int32_t to save memory on small instances

+namespace phat {

+    typedef int64_t index;

+    typedef int8_t dimension;

+    typedef std::vector< index > column;

+}

+

+// OpenMP (proxy) functions

+#if defined _OPENMP

+    #include <omp.h>

+#else

+    #define omp_get_thread_num() 0

+    #define omp_get_max_threads() 1

+    #define omp_get_num_threads() 1

+    #include <time.h>

+    #define omp_get_wtime() (float)clock() / (float)CLOCKS_PER_SEC

+#endif

+

+#include <phat/helpers/thread_local_storage.h>

+

+#include <phat/representations/sparse_pivot_column.h>

+

+namespace phat { 

+    typedef phat::sparse_pivot_column default_representation;

+}

diff --git a/include/phat/helpers/thread_local_storage.h b/include/phat/helpers/thread_local_storage.h
new file mode 100644
index 0000000..ce3c1ed
--- /dev/null
+++ b/include/phat/helpers/thread_local_storage.h
@@ -0,0 +1,52 @@
+/*  Copyright 2013 IST Austria

+    Contributed by: Ulrich Bauer, Michael Kerber, Jan Reininghaus

+

+    This file is part of PHAT.

+

+    PHAT is free software: you can redistribute it and/or modify

+    it under the terms of the GNU Lesser General Public License as published by

+    the Free Software Foundation, either version 3 of the License, or

+    (at your option) any later version.

+

+    PHAT is distributed in the hope that it will be useful,

+    but WITHOUT ANY WARRANTY; without even the implied warranty of

+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the

+    GNU Lesser General Public License for more details.

+

+    You should have received a copy of the GNU Lesser General Public License

+    along with PHAT.  If not, see <http://www.gnu.org/licenses/>. */

+

+#pragma once

+

+#include <phat/helpers/misc.h>

+

+// should ideally be equal to the cache line size of the CPU

+#define PHAT_TLS_SPACING_FACTOR 64

+

+// ThreadLocalStorage with some spacing to avoid "false sharing" (see wikipedia)

+template< typename T > 

+class thread_local_storage

+{

+public:

+

+    thread_local_storage() : per_thread_storage( omp_get_max_threads() * PHAT_TLS_SPACING_FACTOR ) {};

+

+	T& operator()() {

+		return per_thread_storage[ omp_get_thread_num() * PHAT_TLS_SPACING_FACTOR ];

+	}

+

+    const T& operator()() const {

+		return per_thread_storage[ omp_get_thread_num() * PHAT_TLS_SPACING_FACTOR ];

+	}

+

+	T& operator[]( int tid ) {

+		return per_thread_storage[ tid * PHAT_TLS_SPACING_FACTOR ];

+	}

+

+    const T& operator[]( int tid ) const {

+		return per_thread_storage[ tid * PHAT_TLS_SPACING_FACTOR ];

+	}

+

+protected:

+    std::vector< T > per_thread_storage; 

+};

diff --git a/include/phat/persistence_pairs.h b/include/phat/persistence_pairs.h
new file mode 100644
index 0000000..b808a28
--- /dev/null
+++ b/include/phat/persistence_pairs.h
@@ -0,0 +1,151 @@
+/*  Copyright 2013 IST Austria

+    Contributed by: Ulrich Bauer, Michael Kerber, Jan Reininghaus

+

+    This file is part of PHAT.

+

+    PHAT is free software: you can redistribute it and/or modify

+    it under the terms of the GNU Lesser General Public License as published by

+    the Free Software Foundation, either version 3 of the License, or

+    (at your option) any later version.

+

+    PHAT is distributed in the hope that it will be useful,

+    but WITHOUT ANY WARRANTY; without even the implied warranty of

+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the

+    GNU Lesser General Public License for more details.

+

+    You should have received a copy of the GNU Lesser General Public License

+    along with PHAT.  If not, see <http://www.gnu.org/licenses/>. */

+

+#pragma once

+

+#include <phat/helpers/misc.h>

+

+namespace phat {

+    class persistence_pairs {

+

+    protected:

+        std::vector< std::pair< index, index > > pairs;

+

+    public:

+        index get_num_pairs() const { 

+            return (index)pairs.size();

+        }

+

+        void append_pair( index birth, index death ) {

+            pairs.push_back( std::make_pair( birth, death ) );

+        }

+

+        std::pair< index, index > get_pair( index idx ) const {

+            return pairs[ idx ];

+        }

+

+        void clear() {

+            pairs.clear();

+        }

+

+        void sort() {

+            std::sort( pairs.begin(), pairs.end() );

+        }

+

+        // Loads the persistence pairs from given file in asci format 

+        // Format: nr_pairs % newline % birth1 % death1 % newline % birth2 % death2 % newline ...

+        bool load_ascii( std::string filename ) {

+            std::ifstream input_stream( filename.c_str() );

+            if( input_stream.fail() )

+                return false;

+

+            int64_t nr_pairs;

+            input_stream >> nr_pairs;

+            pairs.clear();

+            for( index idx = 0; idx < nr_pairs; idx++ ) {

+                int64_t birth;

+                input_stream >> birth;

+                int64_t death;

+                input_stream >> death;

+                append_pair(  (index)birth,  (index)death );

+            }

+

+            input_stream.close();

+            return true;

+        }

+

+        // Saves the persistence pairs to given file in binary format 

+        // Format: nr_pairs % newline % birth1 % death1 % newline % birth2 % death2 % newline ...

+        bool save_ascii( std::string filename ) {

+            std::ofstream output_stream( filename.c_str() );

+            if( output_stream.fail() )

+                return false;

+

+            this->sort();

+            output_stream << get_num_pairs() << std::endl;

+            for( std::size_t idx = 0; idx < pairs.size(); idx++ ) {

+                output_stream << pairs[idx].first << " " << pairs[idx].second << std::endl;

+            }

+

+            output_stream.close();

+            return true;

+        }

+

+        // Loads the persistence pairs from given file in binary format 

+        // Format: nr_pairs % birth1 % death1 % birth2 % death2 ...

+        bool load_binary( std::string filename ) {

+            std::ifstream input_stream( filename.c_str(), std::ios_base::binary | std::ios_base::in );

+            if( input_stream.fail() )

+                return false;

+

+            int64_t nr_pairs;

+            input_stream.read( (char*)&nr_pairs, sizeof( int64_t ) );

+            for( index idx = 0; idx < nr_pairs; idx++ ) {

+                int64_t birth;

+                input_stream.read( (char*)&birth, sizeof( int64_t ) );

+                int64_t death;

+                input_stream.read( (char*)&death, sizeof( int64_t ) );

+                append_pair(  (index)birth,  (index)death );

+            }

+

+            input_stream.close();

+            return true;

+        }

+

+        // Saves the persistence pairs to given file in binary format 

+        // Format: nr_pairs % birth1 % death1 % birth2 % death2 ...

+        bool save_binary( std::string filename ) {

+            std::ofstream output_stream( filename.c_str(), std::ios_base::binary | std::ios_base::out );

+            if( output_stream.fail() )

+                return false;

+

+            this->sort();

+            int64_t nr_pairs = get_num_pairs();

+            output_stream.write( (char*)&nr_pairs, sizeof( int64_t ) );

+            for( std::size_t idx = 0; idx < pairs.size(); idx++ ) {

+                int64_t birth = pairs[ idx ].first;

+                output_stream.write( (char*)&birth, sizeof( int64_t ) );

+                int64_t death = pairs[ idx ].second;

+                output_stream.write( (char*)&death, sizeof( int64_t ) );

+            }

+

+            output_stream.close();

+            return true;

+        }

+

+        bool operator==( persistence_pairs& other_pairs ) {

+            this->sort();

+            other_pairs.sort();

+            if( pairs.size() != (std::size_t)other_pairs.get_num_pairs() )

+                return false;

+

+            for( index idx = 0; idx < (index)pairs.size(); idx++ )

+                if( get_pair( idx ) != other_pairs.get_pair( idx ) )

+                    return false;

+

+            return true;

+        }

+

+        bool operator!=( persistence_pairs& other_pairs ) {

+            return !( *this == other_pairs );

+        }

+    };

+    

+

+    

+}

diff --git a/include/phat/representations/abstract_pivot_column.h b/include/phat/representations/abstract_pivot_column.h
new file mode 100644
index 0000000..a84e013
--- /dev/null
+++ b/include/phat/representations/abstract_pivot_column.h
@@ -0,0 +1,158 @@
+/*  Copyright 2013 IST Austria

+    Contributed by: Ulrich Bauer, Michael Kerber, Jan Reininghaus

+

+    This file is part of PHAT.

+

+    PHAT is free software: you can redistribute it and/or modify

+    it under the terms of the GNU Lesser General Public License as published by

+    the Free Software Foundation, either version 3 of the License, or

+    (at your option) any later version.

+

+    PHAT is distributed in the hope that it will be useful,

+    but WITHOUT ANY WARRANTY; without even the implied warranty of

+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the

+    GNU Lesser General Public License for more details.

+

+    You should have received a copy of the GNU Lesser General Public License

+    along with PHAT.  If not, see <http://www.gnu.org/licenses/>. */

+

+#pragma once

+

+#include <phat/helpers/misc.h>

+#include <phat/representations/vector_vector.h>

+

+namespace phat {

+

+    // Note: We could even make the rep generic in the underlying Const representation

+    //       But I cannot imagine that anything else than vector<vector<index>> would

+    //       make sense

+    template< typename PivotColumn >

+    class abstract_pivot_column : public vector_vector {

+    public:

+        

+    protected:

+        typedef vector_vector Base;

+        typedef PivotColumn pivot_column;

+

+        // For parallization purposes, it could be more than one full column

+        mutable thread_local_storage< pivot_column > _pivot_columns;

+        mutable thread_local_storage< index > pos_of_pivot_columns;

+

+        pivot_column& get_pivot_column() const {

+            return _pivot_columns();

+        }

+

+        bool is_represented_by_pivot_column( index idx ) const {

+            return pos_of_pivot_columns() == idx;

+        }

+      

+        void unset_pos_of_pivot_column() {

+            index idx = pos_of_pivot_columns();

+            if( idx != -1 ) {

+                _pivot_columns().get_column_and_clear( this->matrix[ idx ] );

+            }

+            pos_of_pivot_columns() = -1;

+        }

+        

+        void represent_by_pivot_column( index idx ) {

+            pos_of_pivot_columns() = idx;

+            get_pivot_column().add_column( matrix[ idx ] );

+        }

+

+    public:  

+

+        void _set_num_cols( index nr_of_columns ) {

+            #pragma omp parallel for

+            for( int tid = 0; tid < omp_get_num_threads(); tid++ ) {

+                _pivot_columns[ tid ].init( nr_of_columns );

+                pos_of_pivot_columns[ tid ] = -1;

+            }

+            Base::_set_num_cols( nr_of_columns );

+        }

+        // replaces(!) content of 'col' with boundary of given index

+        void _get_col( index idx, column& col  ) const {

+            col.clear();

+            if( is_represented_by_pivot_column( idx ) ) {

+                pivot_column& pivot_column = get_pivot_column();

+                pivot_column.get_column_and_clear( col );

+                pivot_column.add_column( col );

+            } else {

+                Base::_get_col( idx, col );

+            }

+        }

+        

+        // true iff boundary of given idx is empty

+        bool _is_empty( index idx ) const {

+            return is_represented_by_pivot_column( idx ) ? get_pivot_column().empty() : Base::_is_empty( idx );

+        }

+

+        // largest row index of given column idx (new name for lowestOne())

+        index _get_max_index( index idx ) const {

+            if( is_represented_by_pivot_column( idx ) ) {

+                pivot_column& pivot_column = get_pivot_column();

+                if( pivot_column.empty() ) {

+                    return -1;

+                } else {

+                    return pivot_column.max_index();

+                }

+            } else {

+                return Base::_get_max_index( idx );

+            }

+        }

+

+        // adds column 'source' to column 'target'

+        void _add_to( index source, index target ) {

+            if( !is_represented_by_pivot_column( target ) ) {

+                unset_pos_of_pivot_column();

+                represent_by_pivot_column( target );

+            } 

+            get_pivot_column().add_column( matrix[source] );

+        }

+

+        // clears given column

+        void _clear( index idx ) {

+            if( is_represented_by_pivot_column( idx ) ) {

+                column dummy;

+                get_pivot_column().get_column_and_clear(dummy);

+            } else {

+                Base::_clear( idx );

+            }

+        }

+

+        void _set_col( index idx, const column& col  ) {

+            if( is_represented_by_pivot_column( idx ) ) {

+                column dummy;

+                pivot_column& pivot_column = get_pivot_column();

+                pivot_column.get_column_and_clear( dummy );

+                pivot_column.add_column( col );

+            } else {

+                Base::_set_col( idx, col );

+            }

+        }

+

+        // removes the maximal index of a column

+        void _remove_max( index idx ) {

+            _toggle( idx, _get_max_index( idx ) );

+        }

+

+        //// toggles given index pair

+        void _toggle( index col_idx, index row_idx ) {

+            if( !is_represented_by_pivot_column( col_idx ) ) {

+                unset_pos_of_pivot_column();

+                represent_by_pivot_column( col_idx );

+            } 

+            get_pivot_column().add_index( row_idx );

+        }

+

+        // syncronizes all data structures (essential for openmp stuff)

+        // has to be called before and after any multithreaded access!

+        void _sync() { 

+            #pragma omp parallel for

+            for( int tid = 0; tid < omp_get_num_threads(); tid++ )

+                unset_pos_of_pivot_column();

+        } 

+

+    };

+}

+

+

diff --git a/include/phat/representations/full_pivot_column.h b/include/phat/representations/full_pivot_column.h
new file mode 100644
index 0000000..9e0c348
--- /dev/null
+++ b/include/phat/representations/full_pivot_column.h
@@ -0,0 +1,81 @@
+/*  Copyright 2013 IST Austria

+    Contributed by: Ulrich Bauer, Michael Kerber, Jan Reininghaus

+

+    This file is part of PHAT.

+

+    PHAT is free software: you can redistribute it and/or modify

+    it under the terms of the GNU Lesser General Public License as published by

+    the Free Software Foundation, either version 3 of the License, or

+    (at your option) any later version.

+

+    PHAT is distributed in the hope that it will be useful,

+    but WITHOUT ANY WARRANTY; without even the implied warranty of

+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the

+    GNU Lesser General Public License for more details.

+

+    You should have received a copy of the GNU Lesser General Public License

+    along with PHAT.  If not, see <http://www.gnu.org/licenses/>. */

+

+#pragma once

+

+#include <phat/helpers/misc.h>

+#include <phat/representations/abstract_pivot_column.h>

+

+namespace phat {

+    class full_column {

+

+    protected:

+        std::priority_queue< index > m_history;

+        std::vector< char > m_isInHistory;

+        std::vector< char > m_data;

+

+    public:

+        void init( const index total_size ) {

+            m_data.resize( total_size, false );

+            m_isInHistory.resize( total_size, false );

+        }

+

+        void add_column( const column& col ) {

+            for( index idx = 0; idx < (index) col.size(); idx++ ) {

+                add_index( col[ idx ] );

+            }

+        }

+        void add_index( const index idx ) {

+            if( !m_isInHistory[ idx ] ) {

+                m_history.push( idx );

+                m_isInHistory[ idx ] = true; 

+            }

+

+            m_data[ idx ] = !m_data[ idx ];

+        }

+

+        index max_index() {

+            while( m_history.size() > 0 ) {

+                index topIndex = m_history.top();

+                if( m_data[ topIndex ] ) {

+                    return topIndex;

+                } else {

+                    m_history.pop();

+                    m_isInHistory[ topIndex ] = false;

+                }

+            }

+    

+            return -1;

+        }

+

+        void get_column_and_clear( column& col ) {

+            col.clear();

+            while( !empty() ) {

+                col.push_back( max_index() );

+                add_index( max_index() );

+            }

+            std::reverse( col.begin(), col.end() );

+        }

+

+        bool empty() {

+            return (max_index() == -1);   

+        }

+    };

+

+    typedef abstract_pivot_column< full_column > full_pivot_column;

+}

diff --git a/include/phat/representations/sparse_pivot_column.h b/include/phat/representations/sparse_pivot_column.h
new file mode 100644
index 0000000..c851a2b
--- /dev/null
+++ b/include/phat/representations/sparse_pivot_column.h
@@ -0,0 +1,62 @@
+/*  Copyright 2013 IST Austria

+    Contributed by: Ulrich Bauer, Michael Kerber, Jan Reininghaus

+

+    This file is part of PHAT.

+

+    PHAT is free software: you can redistribute it and/or modify

+    it under the terms of the GNU Lesser General Public License as published by

+    the Free Software Foundation, either version 3 of the License, or

+    (at your option) any later version.

+

+    PHAT is distributed in the hope that it will be useful,

+    but WITHOUT ANY WARRANTY; without even the implied warranty of

+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the

+    GNU Lesser General Public License for more details.

+

+    You should have received a copy of the GNU Lesser General Public License

+    along with PHAT.  If not, see <http://www.gnu.org/licenses/>. */

+

+#pragma once

+

+#include <phat/helpers/misc.h>

+#include <phat/representations/abstract_pivot_column.h>

+

+namespace phat {

+    class sparse_column {

+

+    protected:

+        std::set< index > m_data;

+

+    public:

+        void init( const index total_size ) {

+            m_data.clear(); 

+        }

+

+        void add_column( const column& col ) {

+            for( index idx = 0; idx < (index) col.size(); idx++ )

+                add_index( col[ idx ] );

+        }

+

+        void add_index( const index idx ) {

+            std::pair< std::set< index >::iterator, bool > result = m_data.insert( idx );

+            if( result.second == false )

+                m_data.erase( result.first );

+        }

+

+        index max_index() {

+            return m_data.empty() ? -1 : *m_data.rbegin();

+        }

+

+        void get_column_and_clear( column& col ) {

+            col.clear();

+            col.assign( m_data.begin(), m_data.end() );

+            m_data.clear();

+        }

+

+        bool empty() {

+            return m_data.empty();

+        }

+    };

+

+    typedef abstract_pivot_column< sparse_column > sparse_pivot_column;

+}

diff --git a/include/phat/representations/vector_set.h b/include/phat/representations/vector_set.h
new file mode 100644
index 0000000..2ce0c56
--- /dev/null
+++ b/include/phat/representations/vector_set.h
@@ -0,0 +1,104 @@
+/*  Copyright 2013 IST Austria
+    Contributed by: Ulrich Bauer, Michael Kerber, Jan Reininghaus
+
+    This file is part of PHAT.
+
+    PHAT is free software: you can redistribute it and/or modify
+    it under the terms of the GNU Lesser General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    PHAT is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU Lesser General Public License for more details.
+
+    You should have received a copy of the GNU Lesser General Public License
+    along with PHAT.  If not, see <http://www.gnu.org/licenses/>. */
+
+#pragma once
+
+#include <phat/helpers/misc.h>
+
+namespace phat {
+    class vector_set {
+
+    protected:
+        typedef std::set< index > internal_column; 
+        std::vector< dimension > dims;
+        std::vector< internal_column > matrix;
+
+    public:
+        // overall number of cells in boundary_matrix
+        index _get_num_cols() const {
+            return (index)matrix.size(); 
+        }
+        void _set_num_cols( index nr_of_columns ) {
+            dims.resize( nr_of_columns );
+            matrix.resize( nr_of_columns );
+        }
+
+         // dimension of given index
+        dimension _get_dim( index idx ) const { 
+            return dims[ idx ]; 
+        }
+        void _set_dim( index idx, dimension dim ) { 
+            dims[ idx ] = dim; 
+        }
+
+        // replaces(!) content of 'col' with boundary of given index
+        void _get_col( index idx, column& col  ) const {
+            col.clear();
+            col.reserve( matrix[idx].size() );
+            std::copy (matrix[idx].begin(), matrix[idx].end(), std::back_inserter(col) );
+            std::sort( col.begin(), col.end() );
+        }
+        void _set_col( index idx, const column& col  ) {
+            matrix[ idx ].clear();
+            matrix[ idx ].insert( col.begin(), col.end() );
+        }
+
+        // true iff boundary of given idx is empty
+        bool _is_empty( index idx ) const {
+            return matrix[ idx ].empty();    
+        }
+
+        // largest row index of given column idx (new name for lowestOne())
+        index _get_max_index( index idx ) const {
+            return matrix[ idx ].empty() ? -1 : *matrix[ idx ].rbegin();
+        }
+
+        // removes the maximal index of a column
+        void _remove_max( index idx ) {
+            internal_column::iterator it = matrix[ idx ].end();
+            it--;
+            matrix[ idx ].erase( it );
+        }
+        
+        // clears given column
+        void _clear( index idx ) {
+            matrix[ idx ].clear();    
+        }
+
+        // syncronizes all data structures (essential for openmp stuff)
+        void _sync() {}
+
+        // adds column 'source' to column 'target'
+        void _add_to( index source, index target ) {
+            internal_column& source_col = matrix[ source ];
+            for( internal_column::const_iterator source_it = source_col.begin(); 
+                 source_it != source_col.end(); source_it++ ) {
+                _toggle(target, *source_it);
+            }
+        }
+
+        //// toggles given index pair
+        void _toggle( index col_idx, index row_idx ) {
+            internal_column& col = matrix[ col_idx ];
+            std::pair< internal_column::iterator, bool > result = col.insert( row_idx );
+            if( !result.second ) {
+                col.erase( result.first );
+            }
+        }
+    };
+}
diff --git a/include/phat/representations/vector_vector.h b/include/phat/representations/vector_vector.h
new file mode 100644
index 0000000..c313c20
--- /dev/null
+++ b/include/phat/representations/vector_vector.h
@@ -0,0 +1,90 @@
+/*  Copyright 2013 IST Austria

+    Contributed by: Ulrich Bauer, Michael Kerber, Jan Reininghaus

+

+    This file is part of PHAT.

+

+    PHAT is free software: you can redistribute it and/or modify

+    it under the terms of the GNU Lesser General Public License as published by

+    the Free Software Foundation, either version 3 of the License, or

+    (at your option) any later version.

+

+    PHAT is distributed in the hope that it will be useful,

+    but WITHOUT ANY WARRANTY; without even the implied warranty of

+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the

+    GNU Lesser General Public License for more details.

+

+    You should have received a copy of the GNU Lesser General Public License

+    along with PHAT.  If not, see <http://www.gnu.org/licenses/>. */

+

+#pragma once

+

+#include <phat/helpers/misc.h>

+

+namespace phat {

+    class vector_vector {

+

+    protected:

+        std::vector< dimension > dims;

+        std::vector< column > matrix;

+

+    public:

+        // overall number of cells in boundary_matrix

+        index _get_num_cols() const {

+            return (index)matrix.size(); 

+        }

+        void _set_num_cols( index nr_of_columns ) {

+            dims.resize( nr_of_columns );

+            matrix.resize( nr_of_columns );

+        }

+

+        // dimension of given index

+        dimension _get_dim( index idx ) const { 

+            return dims[ idx ]; 

+        }

+        void _set_dim( index idx, dimension dim ) { 

+            dims[ idx ] = dim; 

+        }

+

+        // replaces(!) content of 'col' with boundary of given index

+        void _get_col( index idx, column& col  ) const { 

+            col = matrix[ idx ]; 

+        }

+        void _set_col( index idx, const column& col  ) { 

+            matrix[ idx ] = col; 

+        }

+

+        // true iff boundary of given idx is empty

+        bool _is_empty( index idx ) const { 

+            return matrix[ idx ].empty(); 

+        }

+

+        // largest row index of given column idx (new name for lowestOne())

+        index _get_max_index( index idx ) const { 

+            return matrix[ idx ].empty() ? -1 : matrix[ idx ].back(); 

+        }

+

+        // removes the maximal index of a column

+        void _remove_max( index idx ) {

+            matrix[ idx ].pop_back();

+        }

+

+        // clears given column

+        void _clear( index idx ) { 

+            matrix[ idx ].clear(); 

+        }

+

+        // syncronizes all data structures (essential for openmp stuff)

+        void _sync() {}

+

+        // adds column 'source' to column 'target'

+        void _add_to( index source, index target ) {

+            column& source_col = matrix[ source ];

+            column& target_col = matrix[ target ];

+            column temp_col = target_col;

+            target_col.clear();

+            std::set_symmetric_difference( temp_col.begin(), temp_col.end(),

+                                           source_col.begin(), source_col.end(),

+                                           std::back_inserter( target_col ) );

+        }

+    };

+}

diff --git a/src/phat.cpp b/src/phat.cpp
new file mode 100644
index 0000000..895d52d
--- /dev/null
+++ b/src/phat.cpp
@@ -0,0 +1,173 @@
+/*  Copyright 2013 IST Austria

+    Contributed by: Ulrich Bauer, Michael Kerber, Jan Reininghaus

+

+    This file is part of PHAT.

+

+    PHAT is free software: you can redistribute it and/or modify

+    it under the terms of the GNU Lesser General Public License as published by

+    the Free Software Foundation, either version 3 of the License, or

+    (at your option) any later version.

+

+    PHAT is distributed in the hope that it will be useful,

+    but WITHOUT ANY WARRANTY; without even the implied warranty of

+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the

+    GNU Lesser General Public License for more details.

+

+    You should have received a copy of the GNU Lesser General Public License

+    along with PHAT.  If not, see <http://www.gnu.org/licenses/>. */

+

+#include <phat/compute_persistence_pairs.h>

+

+#include <phat/representations/vector_vector.h>

+#include <phat/representations/vector_set.h>

+#include <phat/representations/sparse_pivot_column.h>

+#include <phat/representations/full_pivot_column.h> 

+

+#include <phat/algorithms/twist_reduction.h>

+#include <phat/algorithms/standard_reduction.h> 

+#include <phat/algorithms/row_reduction.h>

+#include <phat/algorithms/chunk_reduction.h>

+

+

+enum Representation_type  {VEC_VEC, VEC_SET, SPARSE_PIVOT, FULL_PIVOT};

+enum Algorithm_type  {STANDARD, TWIST, ROW, CHUNK };

+

+void print_help() {

+    std::cerr << "Usage: " << "phat " << "[options] input_filename output_filename" << std::endl;

+    std::cerr << std::endl;

+    std::cerr << "Options:" << std::endl;

+    std::cerr << std::endl;

+    std::cerr << "--ascii   --  use ascii file format" << std::endl;

+    std::cerr << "--binary  --  use binary file format (default)" << std::endl;

+    std::cerr << "--help    --  prints this screen" << std::endl;

+    std::cerr << "--verbose --  verbose output" << std::endl;

+    std::cerr << "--dualize   --  use dualization approach" << std::endl;

+    std::cerr << "--vec-vec, --vec-set, --full-pivot, --sparse-pivot  --  selects a representation data structure for boundary matrices (default is '--sparse-pivot')" << std::endl;

+    std::cerr << "--standard, --twist, --chunk, --row  --  selects a reduction algorithm (default is '--twist')" << std::endl;

+}

+

+void print_help_and_exit() {

+    print_help();

+    exit( EXIT_FAILURE );

+}   

+

+void parse_command_line( int argc, char** argv, bool& use_binary, Representation_type& rep_type, Algorithm_type& reduction,

+                         std::string& input_filename, std::string& output_filename, bool& verbose, bool& dualize ) {

+    

+    if( argc < 3 ) print_help_and_exit();

+

+    input_filename = argv[ argc - 2 ];

+    output_filename = argv[ argc - 1 ];

+    

+    for( int idx = 1; idx < argc - 2; idx++ ) {

+        const std::string option = argv[ idx ];

+

+        if( option == "--ascii" ) use_binary = false;

+        else if( option == "--binary" ) use_binary = true;

+        else if( option == "--dualize" ) dualize = true;

+        else if( option == "--vec-vec" ) rep_type = VEC_VEC;

+        else if( option == "--vec-set" ) rep_type = VEC_SET;

+        else if( option == "--full-pivot" )  rep_type = FULL_PIVOT;

+        else if( option == "--sparse-pivot" ) rep_type = SPARSE_PIVOT;

+        else if( option == "--standard" ) reduction = STANDARD;

+        else if( option == "--twist" ) reduction = TWIST;

+        else if( option == "--row" ) reduction = ROW;

+        else if( option == "--chunk" ) reduction = CHUNK;

+        else if( option == "--verbose" ) verbose = true;

+        else if( option == "--help" ) print_help_and_exit();

+        else print_help_and_exit();

+    }

+}

+

+#define LOG(msg) if( verbose ) std::cout << msg << std::endl; 

+

+template<typename Representation, typename Algorithm>

+void generic_compute_pairing( std::string input_filename,

+                              std::string output_filename,

+	                          bool use_binary,

+	                          bool verbose,

+                              bool dualize ) {

+

+    phat::boundary_matrix< Representation > matrix;

+    bool read_successful;

+

+    double read_timer = omp_get_wtime();

+    if( use_binary ) {

+	    LOG( "Reading input file " << input_filename << " in binary mode" )

+        read_successful = matrix.load_binary( input_filename );

+    } else {

+        LOG( "Reading input file " << input_filename << " in ascii mode" )

+        read_successful = matrix.load_ascii( input_filename );

+    }

+    LOG( "Reading input file took " << omp_get_wtime() - read_timer <<"s" )

+

+    if( !read_successful ) {

+        std::cerr << "Error opening file " << input_filename << std::endl;

+        print_help_and_exit();

+    }

+

+    double pairs_timer = omp_get_wtime();

+    phat::persistence_pairs pairs;

+    LOG( "Computing persistence pairs ..." )

+    if( dualize )

+        phat::compute_persistence_pairs_dualized< Algorithm > ( pairs, matrix );

+    else 

+        phat::compute_persistence_pairs < Algorithm > ( pairs, matrix );

+    LOG( "Computing persistence pairs took " << omp_get_wtime() - pairs_timer <<"s" )

+

+    double write_timer = omp_get_wtime();

+    if( use_binary ) {

+        LOG( "Writing output file " << output_filename << " in binary mode ..." )

+        pairs.save_binary( output_filename );

+    } else {

+        LOG( "Writing output file " << output_filename << " in ascii mode ..." )

+        pairs.save_ascii( output_filename );

+    }

+    LOG( "Writing output file took " << omp_get_wtime() - write_timer <<"s" )

+    

+}

+

+#define CALL_GENERIC_CODE(rep,alg) generic_compute_pairing < rep, alg >( input_filename, output_filename, use_binary, verbose, dualize );

+

+int main( int argc, char** argv ) 

+{

+    bool use_binary = true; // interpret input as binary or ascii file

+    Representation_type rep_type = SPARSE_PIVOT; // representation class

+    Algorithm_type reduction = TWIST; // reduction algorithm

+    std::string input_filename; // name of file that contains the boundary matrix

+    std::string output_filename; // name of file that will contain the persistence pairs

+    bool verbose = false; // print timings / info

+    bool dualize = false; // toggle for dualization approach

+

+    parse_command_line( argc, argv, use_binary, rep_type, reduction, input_filename, output_filename, verbose, dualize );

+

+    switch( rep_type ) {

+    case VEC_VEC:       switch( reduction ) {

+                        case STANDARD: CALL_GENERIC_CODE(phat::vector_vector, phat::standard_reduction) break;

+                        case TWIST: CALL_GENERIC_CODE(phat::vector_vector, phat::twist_reduction) break;

+                        case ROW: CALL_GENERIC_CODE(phat::vector_vector, phat::row_reduction) break;

+                        case CHUNK: CALL_GENERIC_CODE(phat::vector_vector, phat::chunk_reduction) break;

+                        } break;

+

+    case VEC_SET:       switch( reduction ) {

+                        case STANDARD: CALL_GENERIC_CODE(phat::vector_set, phat::standard_reduction) break;

+                        case TWIST: CALL_GENERIC_CODE(phat::vector_set, phat::twist_reduction) break;

+                        case ROW: CALL_GENERIC_CODE(phat::vector_set, phat::row_reduction) break;

+                        case CHUNK: CALL_GENERIC_CODE(phat::vector_set, phat::chunk_reduction) break;

+                        } break;

+

+    case FULL_PIVOT:    switch( reduction ) {

+                        case STANDARD: CALL_GENERIC_CODE(phat::full_pivot_column, phat::standard_reduction) break;

+                        case TWIST: CALL_GENERIC_CODE(phat::full_pivot_column, phat::twist_reduction) break;

+                        case ROW: CALL_GENERIC_CODE(phat::full_pivot_column, phat::row_reduction) break;

+                        case CHUNK: CALL_GENERIC_CODE(phat::full_pivot_column, phat::chunk_reduction) break;

+                        } break;

+

+    case SPARSE_PIVOT:  switch( reduction ) {

+                        case STANDARD: CALL_GENERIC_CODE(phat::sparse_pivot_column, phat::standard_reduction) break;

+                        case TWIST: CALL_GENERIC_CODE(phat::sparse_pivot_column, phat::twist_reduction) break;

+                        case ROW: CALL_GENERIC_CODE(phat::sparse_pivot_column, phat::row_reduction) break;

+                        case CHUNK: CALL_GENERIC_CODE(phat::sparse_pivot_column, phat::chunk_reduction) break;

+                        } break;

+    }

+}

diff --git a/src/self_test.cpp b/src/self_test.cpp
new file mode 100644
index 0000000..4cda0ae
--- /dev/null
+++ b/src/self_test.cpp
@@ -0,0 +1,154 @@
+/*  Copyright 2013 IST Austria
+    Contributed by: Ulrich Bauer, Michael Kerber, Jan Reininghaus
+
+    This file is part of PHAT.
+
+    PHAT is free software: you can redistribute it and/or modify
+    it under the terms of the GNU Lesser General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    PHAT is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU Lesser General Public License for more details.
+
+    You should have received a copy of the GNU Lesser General Public License
+    along with PHAT.  If not, see <http://www.gnu.org/licenses/>. */
+
+#include <phat/compute_persistence_pairs.h>
+
+#include <phat/representations/vector_vector.h>
+#include <phat/representations/vector_set.h>
+#include <phat/representations/sparse_pivot_column.h>
+#include <phat/representations/full_pivot_column.h>
+
+#include <phat/algorithms/twist_reduction.h>
+#include <phat/algorithms/standard_reduction.h>
+#include <phat/algorithms/row_reduction.h>
+#include <phat/algorithms/chunk_reduction.h>
+
+int main( int argc, char** argv )
+{
+    std::string test_data = argc > 1 ? argv[ 1 ] : "torus.bin";
+    
+    typedef phat::sparse_pivot_column Sparse;
+    typedef phat::full_pivot_column Full;
+    typedef phat::vector_vector Vec_vec;
+    typedef phat::vector_set Vec_set;
+    
+    std::cout << "Reading test data " << test_data << " in binary format ..." << std::endl;
+    phat::boundary_matrix< Full > boundary_matrix;
+    if( !boundary_matrix.load_binary( test_data ) ) {
+        std::cerr << "Error: test data " << test_data << " not found!" << std::endl;
+        return EXIT_FAILURE;
+    }
+    
+    bool error = false;
+    std::cout << "Comparing representations using Chunk algorithm ..." << std::endl;
+    {
+        std::cout << "Running Chunk - Sparse ..." << std::endl;
+        phat::persistence_pairs sparse_pairs;
+        phat::boundary_matrix< Sparse > sparse_boundary_matrix = boundary_matrix;
+        phat::compute_persistence_pairs< phat::chunk_reduction >( sparse_pairs, sparse_boundary_matrix );
+        
+        std::cout << "Running Chunk - Full ..." << std::endl;
+        phat::persistence_pairs full_pairs;
+        phat::boundary_matrix< Full > full_boundary_matrix = boundary_matrix;
+        phat::compute_persistence_pairs< phat::chunk_reduction >( full_pairs, full_boundary_matrix );
+        
+        std::cout << "Running Chunk - Vec_vec ..." << std::endl;
+        phat::persistence_pairs vec_vec_pairs;
+        phat::boundary_matrix< Vec_vec > vec_vec_boundary_matrix = boundary_matrix;
+        phat::compute_persistence_pairs< phat::chunk_reduction >( vec_vec_pairs, vec_vec_boundary_matrix );
+        
+        std::cout << "Running Chunk - Vec_set ..." << std::endl;
+        phat::persistence_pairs vec_set_pairs;
+        phat::boundary_matrix< Vec_set > vec_set_boundary_matrix = boundary_matrix;
+        phat::compute_persistence_pairs< phat::chunk_reduction >( vec_set_pairs, vec_set_boundary_matrix );
+        
+        if( sparse_pairs != full_pairs ) {
+            std::cerr << "Error: sparse and full differ!" << std::endl;
+            error = true;
+        }
+        if( full_pairs != vec_vec_pairs ) {
+            std::cerr << "Error: full and vec_vec differ!" << std::endl;
+            error = true;
+        }
+        if( vec_vec_pairs != vec_set_pairs ) {
+            std::cerr << "Error: vec_vec and vec_set differ!" << std::endl;
+            error = true;
+        }
+        if( vec_set_pairs != sparse_pairs ) {
+            std::cerr << "Error: vec_set and sparse differ!" << std::endl;
+            error = true;
+        }
+        
+        if( error ) return EXIT_FAILURE;
+        else std::cout << "All results are identical (as they should be)" << std::endl;
+    }
+    
+    std::cout << "Comparing algorithms using full_pivot_column representation ..." << std::endl;
+    {
+        std::cout << "Running Twist - Full ..." << std::endl;
+        phat::persistence_pairs twist_pairs;
+        phat::boundary_matrix< Full > twist_boundary_matrix = boundary_matrix;
+        phat::compute_persistence_pairs< phat::twist_reduction >( twist_pairs, twist_boundary_matrix );
+        
+        std::cout << "Running Standard - Full ..." << std::endl;
+        phat::persistence_pairs std_pairs;
+        phat::boundary_matrix< Full > std_boundary_matrix = boundary_matrix;
+        phat::compute_persistence_pairs< phat::standard_reduction >( std_pairs, std_boundary_matrix );
+        
+        std::cout << "Running Chunk - Full ..." << std::endl;
+        phat::persistence_pairs chunk_pairs;
+        phat::boundary_matrix< Full > chunk_boundary_matrix = boundary_matrix;
+        phat::compute_persistence_pairs< phat::chunk_reduction >( chunk_pairs, chunk_boundary_matrix );
+        
+        std::cout << "Running Row - Full ..." << std::endl;
+        phat::persistence_pairs row_pairs;
+        phat::boundary_matrix< Full > row_boundary_matrix = boundary_matrix;
+        phat::compute_persistence_pairs< phat::row_reduction >( row_pairs, row_boundary_matrix );
+        
+        if( twist_pairs != std_pairs ) {
+            std::cerr << "Error: twist and standard differ!" << std::endl;
+            error = true;
+        }
+        if( std_pairs != chunk_pairs ) {
+            std::cerr << "Error: standard and chunk differ!" << std::endl;
+            error = true;
+        }
+        if( chunk_pairs != row_pairs ) {
+            std::cerr << "Error: chunk and row differ!" << std::endl;
+            error = true;
+        }
+        if( row_pairs != twist_pairs ) {
+            std::cerr << "Error: row and twist differ!" << std::endl;
+            error = true;
+        }
+        
+        if( error ) return EXIT_FAILURE;
+        else std::cout << "All results are identical (as they should be)" << std::endl;
+    }
+    
+    std::cout << "Comparing primal and dual approach using Chunk - Full ..." << std::endl;
+    {
+        phat::persistence_pairs primal_pairs;
+        phat::boundary_matrix< Full > primal_boundary_matrix = boundary_matrix;
+        phat::compute_persistence_pairs< phat::chunk_reduction >( primal_pairs, primal_boundary_matrix );
+        
+        phat::persistence_pairs dual_pairs;
+        phat::boundary_matrix< Full > dual_boundary_matrix = boundary_matrix;
+        phat::compute_persistence_pairs_dualized< phat::chunk_reduction >( dual_pairs, dual_boundary_matrix );
+        
+        if( primal_pairs != dual_pairs ) {
+            std::cerr << "Error: primal and dual differ!" << std::endl;
+            error = true;
+        }
+        
+        if( error ) return EXIT_FAILURE;
+        else std::cout << "All results are identical (as they should be)" << std::endl;
+    }
+    
+    return EXIT_SUCCESS;
+}
diff --git a/src/simple_example.cpp b/src/simple_example.cpp
new file mode 100644
index 0000000..aff3ff9
--- /dev/null
+++ b/src/simple_example.cpp
@@ -0,0 +1,127 @@
+/*  Copyright 2013 IST Austria
+    Contributed by: Ulrich Bauer, Michael Kerber, Jan Reininghaus
+
+    This file is part of PHAT.
+
+    PHAT is free software: you can redistribute it and/or modify
+    it under the terms of the GNU Lesser General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    PHAT is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU Lesser General Public License for more details.
+
+    You should have received a copy of the GNU Lesser General Public License
+    along with PHAT.  If not, see <http://www.gnu.org/licenses/>. */
+
+// This file contains a simple example that demonstrates the usage of the library interface
+
+// wrapper algorithm that computes the persistence pairs of a given boundary matrix using a specified algorithm
+#include <phat/compute_persistence_pairs.h>
+
+// main data structure (choice affects performance)
+#include <phat/representations/vector_vector.h>
+
+// algorithm (choice affects performance)
+#include <phat/algorithms/standard_reduction.h>
+#include <phat/algorithms/chunk_reduction.h>
+#include <phat/algorithms/row_reduction.h>
+#include <phat/algorithms/twist_reduction.h>
+
+int main( int argc, char** argv ) 
+{
+    std::cout << "We will build an ordered boundary matrix of this simplicial complex consisting of a single triangle: " << std::endl;
+    std::cout << std::endl;
+    std::cout << " 3" << std::endl;
+    std::cout << " |\\" << std::endl;
+    std::cout << " | \\" << std::endl;
+    std::cout << " |  \\" << std::endl;
+    std::cout << " |   \\ 4" << std::endl;
+    std::cout << "5|    \\" << std::endl;
+    std::cout << " |     \\" << std::endl;
+    std::cout << " |  6   \\" << std::endl;
+    std::cout << " |       \\" << std::endl;
+    std::cout << " |________\\" << std::endl;
+    std::cout << " 0    2    1" << std::endl;
+
+
+    // first define a boundary matrix with the chosen internal representation
+    phat::boundary_matrix< phat::vector_vector > boundary_matrix;
+
+    // set the number of columns (has to be 7 since we have 7 simplices)
+    boundary_matrix.set_num_cols( 7 );
+    
+    // set the dimension of the cell that a column represents:
+    boundary_matrix.set_dim( 0, 0 );
+    boundary_matrix.set_dim( 1, 0 );
+    boundary_matrix.set_dim( 2, 1 );
+    boundary_matrix.set_dim( 3, 0 );
+    boundary_matrix.set_dim( 4, 1 );
+    boundary_matrix.set_dim( 5, 1 );
+    boundary_matrix.set_dim( 6, 2 );
+
+    // set the respective columns -- the columns entries have to be sorted
+    std::vector< phat::index > temp_col;
+
+    boundary_matrix.set_col( 0, temp_col );
+
+    boundary_matrix.set_col( 1, temp_col );
+
+    temp_col.push_back( 0 );
+    temp_col.push_back( 1 );
+    boundary_matrix.set_col( 2, temp_col );
+    temp_col.clear();
+
+    boundary_matrix.set_col( 3, temp_col );
+
+    temp_col.push_back( 1 );
+    temp_col.push_back( 3 );
+    boundary_matrix.set_col( 4, temp_col );
+    temp_col.clear();
+
+    temp_col.push_back( 0 );
+    temp_col.push_back( 3 );
+    boundary_matrix.set_col( 5, temp_col );
+    temp_col.clear();
+
+    temp_col.push_back( 2 );
+    temp_col.push_back( 4 );
+    temp_col.push_back( 5 );
+    boundary_matrix.set_col( 6, temp_col );
+    temp_col.clear();
+
+    // print some information of the boundary matrix:
+    std::cout << std::endl;
+    std::cout << "The boundary matrix has " << boundary_matrix.get_num_cols() << " columns: " << std::endl;
+    for( phat::index col_idx = 0; col_idx < boundary_matrix.get_num_cols(); col_idx++ ) {
+        std::cout << "Colum " << col_idx << " represents a cell of dimension " << (int)boundary_matrix.get_dim( col_idx ) << ". ";
+        if( !boundary_matrix.is_empty( col_idx ) ) {
+            std::vector< phat::index > temp_col;
+            boundary_matrix.get_col( col_idx, temp_col ); 
+            std::cout << "Its boundary consists of the cells";
+            for( phat::index idx = 0; idx < (phat::index)temp_col.size(); idx++ )
+                std::cout << " " << temp_col[ idx ];
+        }
+        std::cout << std::endl;
+    }
+    std::cout << "Overall, the boundary matrix has " << boundary_matrix.get_num_entries() << " entries." << std::endl;  
+    
+
+    // define the object to hold the resulting persistence pairs
+    phat::persistence_pairs pairs;
+
+    // choose an algorithm (choice affects performance) and compute the persistence pair
+    // (modifies boundary_matrix)
+    phat::compute_persistence_pairs< phat::twist_reduction >( pairs, boundary_matrix );
+    
+    // sort the persistence pairs by birth index 
+    pairs.sort();
+
+    // print the pairs:
+    std::cout << std::endl;
+    std::cout << "There are " << pairs.get_num_pairs() << " persistence pairs: " << std::endl;
+    for( phat::index idx = 0; idx < pairs.get_num_pairs(); idx++ )
+        std::cout << "Birth: " << pairs.get_pair( idx ).first << ", Death: " << pairs.get_pair( idx ).second << std::endl;
+}