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https://github.com/kikuomax/singular
Singular value decomposition library
https://github.com/kikuomax/singular
Last synced: about 2 months ago
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Singular value decomposition library
- Host: GitHub
- URL: https://github.com/kikuomax/singular
- Owner: kikuomax
- License: mit
- Created: 2015-11-23T04:33:05.000Z (about 9 years ago)
- Default Branch: master
- Last Pushed: 2015-12-07T02:22:06.000Z (about 9 years ago)
- Last Synced: 2024-10-17T07:37:12.884Z (3 months ago)
- Language: C++
- Size: 125 KB
- Stars: 3
- Watchers: 3
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
Awesome Lists containing this project
README
*singular* is a C++ library which provides functions and classes to perform [singular value decomposition (SVD)](https://en.wikipedia.org/wiki/Singular_value_decomposition).
[](https://travis-ci.org/kikuomax/singular)
The goals of this reinvention are
- Learning Francis's algorithm
- Learning modern C++
Prerequisites
=============
You need the following software installed,
- [CMake](https://cmake.org) 2.8.4 or higher
- C++ compiler
Getting started
===============
*singular* consists of only header files.
The [CMake script](/CMakeLists.txt) does everything you need to install *singular*.
Please take the following steps,
1. Clone the repository anywhere you like and move down to it.
```shell
git clone https://github.com/kikuomax/singular.git
cd singular
```
2. Create a `build` directory and move down to it.
```shell
mkdir build
cd build
```
3. Configure the project.
Suppose you want to install *singular* into the directory `install-path`.
```shell
cmake -DCMAKE_INSTALL_PREFIX=install-path ..
```
4. Install headers.
```shell
cmake --build . --target install
```
5. You will find the headers in the following directory,
- `install-path/include/singular`
Creation of the `build` directory (step 2) is not necessary, but it prevents this directory being messy.
An [example program](/test/test.cpp) shows how to use *singular*.
Testing singular
================
If you have [googletest](https://code.google.com/p/googletest/) installed, unittests for *singular* are built by the CMake script as well.
You can run unittests by the following command after running the build step of *singular*,
```shell
ctest -V
```
pthread related errors
----------------------
With the following configuration, I got linker errors related to pthread.
- Ubuntu 14.04.3
- gcc 4.8.4
- googletest 1.7.0
One solution is to add a `-pthread` compiler flag followed by other objects and libraries.
[This conversation](https://github.com/google/googletest/issues/391) may help you.
You can specify the `-pthread` flag at the configuration step like,
```shell
cmake -DCMAKE_CXX_FLAGS=-pthread ..
```
Another solution is to compile googletest without pthread.
This can be done by turning on the `gtest_disable_pthreads` option at the configuration of **googletest**.
```shell
cmake -Dgtest_disable_pthreads=on .
```
Benchmarking
============
[`test/benchmark.cpp`](/test/benchmark.cpp) is a simple benchmarking program.
This program measures time needed to perform SVD over randomly generated matrices.
It also evaluates the following qualities,
- Reversibility (`A = USV*`)
- Orthonormality of left-singular vectors (`UU* = I`)
- Orthonormality of right-singular vectors (`VV* = I`)
If you do not want to compile the benchmark, turn off the `ENABLE_BENCHMARK` option.
[Eigen](http://eigen.tuxfamily.org/index.php?title=Main_Page) and [Armadillo](http://arma.sourceforge.net) can optionally be evaluated.
This feature is initially disabled.
To enable the benchmark on Eigen, please set the `EIGEN_INCLUDE` option to the directory where header files of Eigen are installed.
To enable the benchmark on Armadillo, please set the `ARMADILLO_ROOT` option to the directory where Armadillo is installed.
Armadillo needs [LAPACK](http://www.netlib.org/lapack/) and [BLAS](http://www.netlib.org/blas/) installed.
On Mac OS X, you can link LAPACK and BLAS by adding a compiler flag `-framework Accelerate`.
The following are the results on my PC (MacBook Pro, 2.4GHz Intel Core i5).
```
# of rows: 60
# of columns: 50
# of iterations: 100
rounded error: 1e-12
min value: -10
max value: 10
singular version: 0.1.3
Eigen version: 3.2.7
Armadillo version: 6.200.5 (Midnight Blue Deluxe)
verifying results ...
singular
# of reconstruction errors: 0 mean error: 1.96851e-14
# of orthonormal U errors: 0 mean error: 2.04803e-16
# of orthonormal V errors: 0 mean error: 2.42038e-16
# of singular value discrepancies: 0 mean error: 0
Eigen
# of reconstruction errors: 0 mean error: 1.13796e-13
# of orthonormal U errors: 0 mean error: 8.86169e-16
# of orthonormal V errors: 0 mean error: 4.77086e-16
# of singular value discrepancies: 0 mean error: 4.03472e-13
Armadillo
# of reconstruction errors: 0 mean error: 1.08298e-14
# of orthonormal U errors: 0 mean error: 1.60648e-16
# of orthonormal V errors: 0 mean error: 1.97627e-16
# of singular value discrepancies: 0 mean error: 5.28169e-14
measuring processing time ...
round 1
round 2
round 3
round 4
round 5
round 6
singular:
lap time[0]: 3.09783 seconds
lap time[1]: 3.08843 seconds
lap time[2]: 3.08597 seconds
lap time[3]: 3.07436 seconds
lap time[4]: 3.07892 seconds
lap time[5]: 3.08201 seconds
mean lap time: 3.08459 seconds
Eigen:
lap time[0]: 6.63677 seconds
lap time[1]: 6.61933 seconds
lap time[2]: 6.64333 seconds
lap time[3]: 6.66512 seconds
lap time[4]: 6.64167 seconds
lap time[5]: 6.62753 seconds
mean lap time: 6.63896 seconds
Armadillo:
lap time[0]: 0.0938214 seconds
lap time[1]: 0.0937346 seconds
lap time[2]: 0.0936364 seconds
lap time[3]: 0.0936577 seconds
lap time[4]: 0.100055 seconds
lap time[5]: 0.10046 seconds
mean lap time: 0.0958942 seconds
```
Yes! Armadillo could be the best choice if you can use LAPACK and BLAS on your application.
Generating documentation
========================
If you have [Doxygen](http://www.doxygen.org) installed, documentation of *singular* is generated by the CMake script as well.
You will find the `api` directory created by CMake.
License
=======
[MIT License](https://opensource.org/licenses/MIT)
References
==========
Most of the code was derived from the following great book.
- Watkins, David S. *Fundamentals of Matrix Computations*. 3rd ed. Hoboken: John Wiley & Sons, 2010
Test results of SVD were generated at the following site.
- http://www.bluebit.gr/matrix-calculator/