Giter Site home page Giter Site logo

tensor's Introduction

alpine_877

ch.alpine.tensor

Library for tensor computations in Java.

The tensor library was developed with the following objectives in mind

  • support for exact precision using integer fractions
  • support for calculation with physical units
  • suitable for use in safety-critical real-time systems
  • API and string expressions inspired by Mathematica

Diverse projects rely on the tensor library:

usecase_amodeus

Mobility-on-Demand

usecase_swisstrolley

SwissTrolley+

usecase_motionplan

Motion Planning

usecase_gokart

Autonomous Gokart

Features

  • multi-dimensional arrays: scalars, vectors, matrices, n-linear forms, Lie-algebra ad-tensor, ...
  • unstructured, nested tensors, for instance {{1+2*I[A], -3/4}, {{5.678}, 9[kg*s^-1], 2[m^3]}}
  • scalars are real-, or complex numbers, from finite fields, or quantities with physical units
  • values are encoded as exact integer fractions, in double precision, and as java.math.BigDecimal
  • probability distributions for random variate generation: Binomial-, Poisson-, Exponential-distribution, etc.
  • linear solvers GaussianElimination, CholeskyDecomposition, QRDecomposition, SingularValueDecomposition
  • matrix functions MatrixExp, MatrixLog, MatrixSqrt, ...
  • tensor functions TensorProduct, TensorWedge, Trace, HodgeDual, ...
  • Lie theory: BakerCampbellHausdorff
  • parametric functions LinearInterpolation, BSplineFunction
  • window functions: Gaussian, Hamming, Hann, Blackman, ...
  • spectral analysis: Fourier, SpectrogramArray
  • import from and export to Mathematica, CSV, and image files

Gallery

gammademo

Gamma function

inversetrigdemo2

Trigonometry

mandelbulbdemo

Nylander's formula

newtondemo

Newton's method

Examples

Exact Precision

Solving systems of linear equations

Tensor matrix = Tensors.matrixInt(new int[][] { { 2, -3, 2 }, { 4, 9, -3 }, { -1, 3, 2 } });
System.out.println(Pretty.of(Inverse.of(matrix)));

[
 [   9/37    4/37   -3/37 ]
 [ -5/111    2/37  14/111 ]
 [   7/37   -1/37   10/37 ]
]

Linear programming

Tensor x = LinearOptimization.maxLessEquals( //
    Tensors.vector(1, 1), // rewards
    Tensors.fromString("{{4, -1}, {2, 1}, {-5, 2}}"), // matrix
    Tensors.vector(8, 7, 2)); // rhs
System.out.println(x);

{4/3, 13/3}

Pseudoinverse, Moore-Penrose inverse

Tensor matrix = Tensors.fromString("{{-1 + I, 0}, {-I, 2}, {2 - I, 2 * I}}");
System.out.println(Pretty.of(PseudoInverse.of(matrix)));

[
 [   -1/3-I/3     1/6-I/6     1/6+I/6 ]
 [    1/6-I/3   5/12+I/12  -1/12-I/12 ]
]

Nullspace

Tensor matrix = Tensors.fromString("{{-1/3, 0, I}}");
System.out.println(Pretty.of(NullSpace.of(matrix)));

[
 [    1     0  -I/3 ]
 [    0     1     0 ]
]

Statistics

Distribution distribution = HypergeometricDistribution.of(10, 50, 100);
System.out.println(RandomVariate.of(distribution, 20));
PDF pdf = PDF.of(distribution);
System.out.println("P(X=3)=" + pdf.at(RealScalar.of(3)));

{6, 5, 1, 4, 3, 4, 7, 5, 7, 4, 6, 3, 5, 4, 5, 4, 6, 2, 6, 7}
P(X=3)=84000/742729

Physical Quantities

The tensor library implements Quantity, i.e. numbers with physical units. Several algorithms are verified to work with scalars of type Quantity.

Tensor matrix = Tensors.fromString( //
  "{{60[m^2], 30[m*rad], 20[kg*m]}, {30[m*rad], 20[rad^2], 15[kg*rad]}, {20[kg*m], 15[kg*rad], 12[kg^2]}}");
CholeskyDecomposition cd = CholeskyDecomposition.of(matrix);
System.out.println(cd.diagonal());
System.out.println(Pretty.of(cd.getL()));
System.out.println(cd.det().divide(Quantity.of(20, "m^2*rad")));

{60[m^2], 5[rad^2], 1/3[kg^2]}
[
 [             1              0              0 ]
 [ 1/2[m^-1*rad]              1              0 ]
 [  1/3[kg*m^-1]   1[kg*rad^-1]              1 ]
]
5[kg^2*rad]

The units of a quantity are chosen by the application layer. For instance, Quantity.of(3, "Apples") is valid syntax.

The tensor library contains the resource /unit/si.properties that encodes the SI unit system in the familiar strings such as m, kg, s, but the use of this convention is optional. The example below makes use of these provided definitions

Scalar mass = Quantity.of(300, "g"); // in gram
Scalar a = Quantity.of(981, "cm*s^-2"); // in centi-meters per seconds square
Scalar force = mass.multiply(a);
System.out.println(force);
Scalar force_N = UnitConvert.SI().to(Unit.of("N")).apply(force);
System.out.println(force_N);

294300[cm*g*s^-2]
2943/1000[N]

The scalar type Quantity was developed in collaboration with SwissTrolley+.

Date and Time

The tensor library implements DateTime for calendar arithmetic and data sets with calendar entries. The arithmetic and string expressions are identical to those of the java class LocalDateTime.

Scalar mean = DateTime.of(2022, Month.FEBRUARY, 28, 12, 00);
Scalar sigma = Quantity.of(30, "h");
Distribution distribution = NormalDistribution.of(mean, sigma);
Scalar guess = RandomVariate.of(distribution);
System.out.println(mean.add(sigma));
System.out.println(guess);

2022-03-01T18:00
2022-03-02T10:12:06.641540174

The scalar type DateTime was developed in collaboration with GRZ Technologies.

Miscellaneous

Tensors of rank 3

Tensor ad = LeviCivitaTensor.of(3).negate();
Tensor x = Tensors.vector(7, 2, -4);
Tensor y = Tensors.vector(-3, 5, 2);
System.out.println(ad);
System.out.println(ad.dot(x).dot(y)); // coincides with cross product of x and y

{{{0, 0, 0}, {0, 0, -1}, {0, 1, 0}}, {{0, 0, 1}, {0, 0, 0}, {-1, 0, 0}}, {{0, -1, 0}, {1, 0, 0}, {0, 0, 0}}}
{24, -2, 41}

Functions for complex numbers

System.out.println(Sqrt.of(RationalScalar.of(-9, 16)));

3/4*I

Several functions support evaluation to higher than machine precision for type DecimalScalar.

System.out.println(Exp.of(DecimalScalar.of(10)));
System.out.println(Sqrt.of(DecimalScalar.of(2)));

220255.6579480671651695790064528423`34
1.414213562373095048801688724209698`34

The number after the prime indicates the precision of the decimal. The string representation is compatible with Mathematica.

Indices for the set and get functions start from zero like in C/Java:

Tensor matrix = Array.zeros(3, 4);
matrix.set(Tensors.vector(9, 8, 4, 5), 2);
matrix.set(Tensors.vector(6, 7, 8), Tensor.ALL, 1);
System.out.println(Pretty.of(matrix));
System.out.println(matrix.get(Tensor.ALL, 3)); // extraction of the 4th column

[
 [ 0  6  0  0 ]
 [ 0  7  0  0 ]
 [ 9  8  4  5 ]
]
{0, 0, 5}

Optimization

Distance-based queries for point sets in Euclidean space

image

k-nearest neighbors

image

radius search

Visualization

Predefined color gradients

colordatagradients

Predefined color lists

colordatalists

Integration

From time to time, a version is deployed and made available for maven integration. Specify repository and dependency of the library tensor in the pom.xml file of your maven project:

<dependencies>
  <!-- other dependencies -->
  <dependency>
    <groupId>ch.alpine</groupId>
    <artifactId>tensor</artifactId>
    <version>1.0.6</version>
  </dependency>
</dependencies>

<repositories>
  <!-- other repositories -->
  <repository>
    <id>tensor-mvn-repo</id>
    <url>https://raw.github.com/datahaki/tensor/mvn-repo/</url>
    <snapshots>
      <enabled>true</enabled>
      <updatePolicy>always</updatePolicy>
    </snapshots>
  </repository>
</repositories>

For Java 17, for version use 1.0.6 .

For Java 11, for version use 1.1.1-jdk-11.

The source code is attached to every release.

The branch master always contains the latest features for Java 17, and does not correspond to the most recent deployed version generally.

tensor's People

Contributors

axkr avatar claudioglasses avatar datahaki avatar guedelmi avatar joelgaechter avatar

Stargazers

 avatar  avatar  avatar  avatar  avatar  avatar  avatar  avatar  avatar  avatar  avatar  avatar

Watchers

 avatar  avatar  avatar

Forkers

axkr grzhe

tensor's Issues

QuantityImpl::one does not have a unit

When calling Scalar::one on a Quantity the resulting value does not have a unit.
Its implementation seems to lack ofUnit, see QuantityImpl::zero for comparison.

Recommend Projects

  • React photo React

    A declarative, efficient, and flexible JavaScript library for building user interfaces.

  • Vue.js photo Vue.js

    ๐Ÿ–– Vue.js is a progressive, incrementally-adoptable JavaScript framework for building UI on the web.

  • Typescript photo Typescript

    TypeScript is a superset of JavaScript that compiles to clean JavaScript output.

  • TensorFlow photo TensorFlow

    An Open Source Machine Learning Framework for Everyone

  • Django photo Django

    The Web framework for perfectionists with deadlines.

  • D3 photo D3

    Bring data to life with SVG, Canvas and HTML. ๐Ÿ“Š๐Ÿ“ˆ๐ŸŽ‰

Recommend Topics

  • javascript

    JavaScript (JS) is a lightweight interpreted programming language with first-class functions.

  • web

    Some thing interesting about web. New door for the world.

  • server

    A server is a program made to process requests and deliver data to clients.

  • Machine learning

    Machine learning is a way of modeling and interpreting data that allows a piece of software to respond intelligently.

  • Game

    Some thing interesting about game, make everyone happy.

Recommend Org

  • Facebook photo Facebook

    We are working to build community through open source technology. NB: members must have two-factor auth.

  • Microsoft photo Microsoft

    Open source projects and samples from Microsoft.

  • Google photo Google

    Google โค๏ธ Open Source for everyone.

  • D3 photo D3

    Data-Driven Documents codes.