kmath/README.md

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# KMath

Could be pronounced as `key-math`. The Kotlin MATHematics library was initially intended as a Kotlin-based analog to 
Python's NumPy library. Later we found that kotlin is much more flexible language and allows superior architecture 
designs. In contrast to `numpy` and `scipy` it is modular and has a lightweight core. The `numpy`-like experience could 
be achieved with [kmath-for-real](/kmath-for-real) extension module.

## Publications and talks

* [A conceptual article about context-oriented design](https://proandroiddev.com/an-introduction-context-oriented-programming-in-kotlin-2e79d316b0a2)
* [Another article about context-oriented design](https://proandroiddev.com/diving-deeper-into-context-oriented-programming-in-kotlin-3ecb4ec38814)
* [ACAT 2019 conference paper](https://aip.scitation.org/doi/abs/10.1063/1.5130103)

# Goal

* Provide a flexible and powerful API to work with mathematics abstractions in Kotlin-multiplatform (JVM, JS and Native). 
* Provide basic multiplatform implementations for those abstractions (without significant performance optimization).
* Provide bindings and wrappers with those abstractions for popular optimized platform libraries.

## Non-goals

* Be like NumPy. It was the idea at the beginning, but we decided that we can do better in terms of API.
* Provide the best performance out of the box. We have specialized libraries for that. Need only API wrappers for them.
* Cover all cases as immediately and in one bundle. We will modularize everything and add new features gradually.
* Provide specialized behavior in the core. API is made generic on purpose, so one needs to specialize for types, like 
for `Double` in the core. For that we will have specialization modules like `for-real`, which will give better 
experience for those, who want to work with specific types.

## Features

Current feature list is [here](/docs/features.md)

* **Algebra**
    * Algebraic structures like rings, spaces and fields (**TODO** add example to wiki)
    * Basic linear algebra operations (sums, products, etc.), backed by the `Space` API.
    * Complex numbers backed by the `Field` API (meaning they will be usable in any structure like vectors and 
    N-dimensional arrays).
    * Advanced linear algebra operations like matrix inversion and LU decomposition.

* **Array-like structures** Full support of many-dimensional array-like structures 
including mixed arithmetic operations and function operations over arrays and numbers (with the added benefit of static type checking).

* **Expressions** By writing a single mathematical expression once, users will be able to apply different types of 
objects to the expression by providing a context. Expressions can be used for a wide variety of purposes from high 
performance calculations to code generation.

* **Histograms** Fast multi-dimensional histograms.

* **Streaming** Streaming operations on mathematical objects and objects buffers.

* **Type-safe dimensions** Type-safe dimensions for matrix operations.

* **Commons-math wrapper** It is planned to gradually wrap most parts of 
[Apache commons-math](http://commons.apache.org/proper/commons-math/) library in Kotlin code and maybe rewrite some 
parts to better suit the Kotlin programming paradigm, however there is no established roadmap for that. Feel free to 
submit a feature request if you want something to be implemented first.
                           
## Planned features

* **Messaging** A mathematical notation to support multi-language and multi-node communication for mathematical tasks.

* **Array statistics** 

* **Integration** Univariate and multivariate integration framework.

* **Probability and distributions**

* **Fitting** Non-linear curve fitting facilities

## Modules

<hr/>

* ### [examples](examples)
> 
>
> **Maturity**: EXPERIMENTAL
<hr/>

* ### [kmath-ast](kmath-ast)
> 
>
> **Maturity**: PROTOTYPE
>
> **Features:**
> - [expression-language](kmath-ast/src/jvmMain/kotlin/kscience/kmath/ast/parser.kt) : Expression language and its parser
> - [mst](kmath-ast/src/commonMain/kotlin/kscience/kmath/ast/MST.kt) : MST (Mathematical Syntax Tree) as expression language's syntax intermediate representation
> - [mst-building](kmath-ast/src/commonMain/kotlin/kscience/kmath/ast/MstAlgebra.kt) : MST building algebraic structure
> - [mst-interpreter](kmath-ast/src/commonMain/kotlin/kscience/kmath/ast/MST.kt) : MST interpreter
> - [mst-jvm-codegen](kmath-ast/src/jvmMain/kotlin/kscience/kmath/asm/asm.kt) : Dynamic MST to JVM bytecode compiler
> - [mst-js-codegen](kmath-ast/src/jsMain/kotlin/kscience/kmath/estree/estree.kt) : Dynamic MST to JS compiler

<hr/>

* ### [kmath-commons](kmath-commons)
> 
>
> **Maturity**: EXPERIMENTAL
<hr/>

* ### [kmath-complex](kmath-complex)
> Complex numbers and quaternions.
>
> **Maturity**: DEVELOPMENT
>
> **Features:**
> - [complex](kmath-complex/src/commonMain/kotlin/kscience/kmath/complex/Complex.kt) : Complex Numbers
> - [quaternion](kmath-complex/src/commonMain/kotlin/kscience/kmath/complex/Quaternion.kt) : Quaternions

<hr/>

* ### [kmath-core](kmath-core)
> Core classes, algebra definitions, basic linear algebra
>
> **Maturity**: DEVELOPMENT
>
> **Features:**
> - [algebras](kmath-core/src/commonMain/kotlin/kscience/kmath/operations/Algebra.kt) : Algebraic structures: contexts and elements
> - [nd](kmath-core/src/commonMain/kotlin/kscience/kmath/structures/NDStructure.kt) : Many-dimensional structures
> - [buffers](kmath-core/src/commonMain/kotlin/kscience/kmath/structures/Buffers.kt) : One-dimensional structure
> - [expressions](kmath-core/src/commonMain/kotlin/kscience/kmath/expressions) : Functional Expressions
> - [domains](kmath-core/src/commonMain/kotlin/kscience/kmath/domains) : Domains
> - [autodif](kmath-core/src/commonMain/kotlin/kscience/kmath/expressions/SimpleAutoDiff.kt) : Automatic differentiation

<hr/>

* ### [kmath-coroutines](kmath-coroutines)
> 
>
> **Maturity**: EXPERIMENTAL
<hr/>

* ### [kmath-dimensions](kmath-dimensions)
> 
>
> **Maturity**: PROTOTYPE
<hr/>

* ### [kmath-ejml](kmath-ejml)
> 
>
> **Maturity**: EXPERIMENTAL
<hr/>

* ### [kmath-for-real](kmath-for-real)
> Extension module that should be used to achieve numpy-like behavior. 
All operations are specialized to work with `Double` numbers without declaring algebraic contexts.
One can still use generic algebras though.
>
> **Maturity**: EXPERIMENTAL
>
> **Features:**
> - [RealVector](kmath-for-real/src/commonMain/kotlin/kscience/kmath/real/RealVector.kt) : Numpy-like operations for Buffers/Points
> - [RealMatrix](kmath-for-real/src/commonMain/kotlin/kscience/kmath/real/RealMatrix.kt) : Numpy-like operations for 2d real structures
> - [grids](kmath-for-real/src/commonMain/kotlin/kscience/kmath/structures/grids.kt) : Uniform grid generators

<hr/>

* ### [kmath-functions](kmath-functions)
> 
>
> **Maturity**: EXPERIMENTAL
<hr/>

* ### [kmath-geometry](kmath-geometry)
> 
>
> **Maturity**: EXPERIMENTAL
<hr/>

* ### [kmath-histograms](kmath-histograms)
> 
>
> **Maturity**: EXPERIMENTAL
<hr/>

* ### [kmath-kotlingrad](kmath-kotlingrad)
> 
>
> **Maturity**: EXPERIMENTAL
<hr/>

* ### [kmath-memory](kmath-memory)
> 
>
> **Maturity**: EXPERIMENTAL
<hr/>

* ### [kmath-nd4j](kmath-nd4j)
> ND4J NDStructure implementation and according NDAlgebra classes
>
> **Maturity**: EXPERIMENTAL
>
> **Features:**
> - [nd4jarraystructure](kmath-nd4j/src/commonMain/kotlin/kscience/kmath/operations/Algebra.kt) : NDStructure wrapper for INDArray
> - [nd4jarrayrings](kmath-nd4j/src/commonMain/kotlin/kscience/kmath/structures/NDStructure.kt) : Rings over Nd4jArrayStructure of Int and Long
> - [nd4jarrayfields](kmath-nd4j/src/commonMain/kotlin/kscience/kmath/structures/Buffers.kt) : Fields over Nd4jArrayStructure of Float and Double

<hr/>

* ### [kmath-stat](kmath-stat)
> 
>
> **Maturity**: EXPERIMENTAL
<hr/>

* ### [kmath-viktor](kmath-viktor)
> 
>
> **Maturity**: EXPERIMENTAL
<hr/>


## Multi-platform support

KMath is developed as a multi-platform library, which means that most of the interfaces are declared in the 
[common source sets](/kmath-core/src/commonMain) and implemented there wherever it is possible. In some cases, features 
are delegated to platform-specific implementations even if they could be provided in the common module for performance 
reasons. Currently, the Kotlin/JVM is the primary platform, however Kotlin/Native and Kotlin/JS contributions and 
feedback are also welcome.

## Performance

Calculation performance is one of major goals of KMath in the future, but in some cases it is impossible to achieve 
both performance and flexibility. 

We expect to focus on creating convenient universal API first and then work on increasing performance for specific 
cases. We expect the worst KMath benchmarks will perform better than native Python, but worse than optimized 
native/SciPy (mostly due to boxing operations on primitive numbers). The best performance of optimized parts could be 
better than SciPy.

### Repositories

Release artifacts are accessible from bintray with following configuration (see documentation of 
[Kotlin Multiplatform](https://kotlinlang.org/docs/reference/multiplatform.html) for more details):

```kotlin
repositories {
    maven("https://dl.bintray.com/mipt-npm/kscience")
}

dependencies {
    api("kscience.kmath:kmath-core:0.2.0-dev-4")
    // api("kscience.kmath:kmath-core-jvm:0.2.0-dev-4") for jvm-specific version
}
```

Gradle `6.0+` is required for multiplatform artifacts.

#### Development

Development builds are uploaded to the separate repository:

```kotlin
repositories {
    maven("https://dl.bintray.com/mipt-npm/dev")
}
```

## Contributing

The project requires a lot of additional work. The most important thing we need is a feedback about what features are 
required the most. Feel free to create feature requests. We are also welcome to code contributions, 
especially in issues marked with 
[waiting for a hero](https://github.com/mipt-npm/kmath/labels/waiting%20for%20a%20hero) label.