KO
|
EN
gitlite — search
Search
#python
#java
#python3
#arduino
#golang
#machine-learning
#rust
#html
#flask
#javascript
#seismology
#nodejs
tjungblut-math
★ 13
Open GitHub ↗
My personal math library
Download README (.md)
Explore Similar Repositories
SimpleSocketConnection
:
Simple socket connections in iOS
IRCBalloon
:
IRC / Justin.tv Chatroom / Twitch Chatroom popup notification.
connect-architect
:
build a connect server using architect plugins
node-sessions
:
NodeJS Session Management
HTMLFeedback
:
jQuery website feedback plugin (like Google) using the canvas element.
// repository documentation
Was this content helpful?
★ 0
(0 ratings)
Select Rating:
★
★
★
★
★
Submit Feedback
Recent Feedback
×
Download README
Do you want to download the
README.md
file for
tjungblut-math
?
Download (.md)
 ## tjungblut-math This is my own Math library. It features some daily math operations on sparse/dense vectors and matrices. Features -------- - Basic linear algebra primitives and operations - Sparse (Ordered, Unordered, Bit, Named, OneDimensional and Keyed) and Dense vector - Sparse and Dense matrix (row-wise sharding, column major ordering) - Tuples (two and three dimensional) - Functions on all primitives for lambdas in Java 8 Roadmap ------- - Byte code optimizer (read further below) - Tensors - More operations and implementations of the interfaces Trivia ------ Parts of this library are also featured in Apache Hama's ML module and power several algorithms there. Chain Calling ------------- My library was intentionally build to easily translate octave/matlab code from MOOC's to Java. For example the following octave code (simple gradient descent): > theta = theta - alpha * gradient; Is written in Java as: ```java double alpha = 0.1; DoubleVector theta = new DenseDoubleVector(new double[] {x, y}); DoubleVector gradient = new DenseDoubleVector(new double[] {1, 1}); theta = theta.subtract(gradient.multiply(alpha)); ``` You see that this is a bit more expressive and verbose, but since you can't overload operators this is the only way to solve it. ### Also note: Since this method chaining requires multiple iterations on the internal datastructure, this might be slower than hand-optimized code. Take the simple euclidian distance for example: > Math.sqrt(vec2.subtract(vec1).pow(2).sum()); This will need to iterate three times over your whole vector size of size N (subtract, pow and sum). So you have a quite high constant opposed to a single loop from 0 to N: ```java double sum = 0; for (int i = 0; i < vec1.getLength(); i++) { double diff = vec2[i] - vec1[i]; sum += (diff * diff); } ``` Currently I have an idea to write a bytecode optimizer that will unchain such calls to minimize the performance penalty. This optimizer would be hooked into a classloader and optimize the bytecode at load-time or at build time as part of maven. Benchmarks ------- You may want to see a Caliper benchmark result of comparing matrix multiplications of square matrices using GPU (JCUDA)/ JBLAS (lapack lite)/ Java implementations on windows: ``` n type us linear runtime 10 GPU 238,18 = 10 JBLAS 5,14 = 10 TJ_MATH 4,88 = 20 GPU 694,48 = 20 JBLAS 15,70 = 20 TJ_MATH 15,74 = 40 GPU 257,27 = 40 JBLAS 74,38 = 40 TJ_MATH 86,26 = 60 GPU 650,83 = 60 JBLAS 224,14 = 60 TJ_MATH 277,91 = 80 GPU 684,96 = 80 JBLAS 542,27 = 80 TJ_MATH 645,70 = 100 GPU 858,59 = 100 JBLAS 1019,58 = 100 TJ_MATH 1245,27 = 500 GPU 10996,48 = 500 JBLAS 116263,36 = 500 TJ_MATH 152830,94 = 1000 GPU 71822,50 = 1000 JBLAS 953681,51 == 1000 TJ_MATH 1358882,88 === 2000 GPU 395683,94 = 2000 JBLAS 9465452,45 ====================== 2000 TJ_MATH 12386527,91 ============================== Hardware: Intel i7 920, Nvidia GTX580, Java7 ``` Until ~50x50 there is no benefit in using JBLAS and even later on there is little benefit. This is largely due to the overhead of copying the matrix representations from heap to native memory and the slowness of lapack lite. The GPU gives great improvements when matrices get very large > 500x500 and copy costs (main to device memory) start to amortize itself. On Linux this looks a bit more in favor of JBLAS (take care, this is comparing different hardware): ``` n type us linear runtime 10 GPU 82,86 = 10 JBLAS 4,09 = 10 TJ_MATH 3,27 = 20 GPU 204,50 = 20 JBLAS 7,91 = 20 TJ_MATH 9,55 = 40 GPU 103,20 = 40 JBLAS 34,71 = 40 TJ_MATH 53,18 = 60 GPU 267,69 = 60 JBLAS 63,40 = 60 TJ_MATH 163,84 = 80 GPU 324,13 = 80 JBLAS 143,65 = 80 TJ_MATH 358,85 = 100 GPU 475,00 = 100 JBLAS 295,71 = 100 TJ_MATH 675,14 = 500 GPU 18507,11 = 500 JBLAS 24072,70 = 500 TJ_MATH 84433,83 = 1000 GPU 139407,39 = 1000 JBLAS 183385,59 = 1000 TJ_MATH 842254,72 === 2000 GPU 961625,41 === 2000 JBLAS 1320723,49 ===== 2000 TJ_MATH 7436553,82 ============================== Hardware: Intel i7-3740QM, Nvidia GeForce GT 650M (mobile) ``` ATLAS does in fact better from 10x10 matrices. The GPU outperforms the Java code earlier on 100x100 matrices, and outperforms ATLAS from 500x500. The difference isn't extreme between ATLAS and the GPU, because I benchmarked on a laptop and the memory interface width is much more narrow than on the desktop (128 bit vs. at least 384 bit). The benchmark code can be found [here.](https://gist.github.com/thomasjungblut/5652037 "here") License ------- Since I am Apache committer, I consider everything inside of this repository licensed by Apache 2.0 license, although I haven't put the usual header into the source files. If something is not licensed via Apache 2.0, there is a reference or an additional licence header included in the specific source file. Maven ----- If you use maven, you can get the latest release using the following dependency: ``` <dependency> <groupId>de.jungblut.math</groupId> <artifactId>tjungblut-math</artifactId> <version>1.3</version> </dependency> ``` Build ----- To build locally, you will need at least Java 8 to build this library. You can simply build with: > mvn clean package install The created jars contains debuggable code + sources + javadocs. If you want to skip testcases you can use: > mvn clean package install -DskipTests If you want to skip the signing process you can do: > mvn clean package install -Dgpg.skip=true
