RcdMathLib is an open-source library for numerical linear and non-linear
algebra designed to match the requirements of resource-limited or embedded
devices. RcdMathLib supports solving linear and non-linear equation systems.
Furthermore, it provides general-purpose implemented methods that facilitate
solving problems of regression smoothing and curve fitting. It also allows for
calculating as well as optimizing a position on a mobile device.
# Download and use the RcdMathLib
The simplest way to use the RcdMathLib for resource-limited devices is to
download the [Eclipse project for resource-limited devices](https://git.imp.fu-berlin.de/zkasmi/RcdMathLib/-/blob/master/eclipse_projects/RcdMathLib_resource_limited_devices.zip) zip file. Another [Eclipse project for full-fledged devices](https://git.imp.fu-berlin.de/zkasmi/RcdMathLib/-/blob/master/eclipse_projects/RcdMathLib_full_fledged_devices.zip) zip file enables also the use of the RcdMathLib for full-fledged platforms or single-board computers such as a [Raspberry Pi](https://www.elinux.org/RPi_Hub).
# The quickest start
You can run the RcdMathLib on most resource-limited devices such as the [STM32F4 Discovery board](https://www.st.com/en/evaluation-tools/stm32f4discovery.html) as well as on full-fledged computers like a PC, or single-board devices such as a [Raspberry Pi](https://www.elinux.org/RPi_Hub).
Try it right now in your terminal window:
~~~~~~~{.sh}
mkdir RcdMathLib_resource_limited_devices
cd RcdMathLib_resource_limited_devices
git clone git://github.com/RIOT-OS/RIOT.git # assumption: git is pre-installed (To update)
unzip RcdMathLib_resource_limited_devices.zip
cd RcdMathLib/examples/linear_algebra/basic_operation/
make all
~~~~~~~
The example above shows how to use the basic operations of the RcdMathLib such as the vector or
the matrix operations.
# Structure
This section walks you through the RcdMathLib's structure to easily find your way around in RcdMathLib's code base.
RcdMathLib's source code is composed into three groups:
- Linear algebra
- Non-linear algebra
- Localization
In addition RcdMathLib includes various [examples](https://git.imp.fu-berlin.de/zkasmi/RcdMathLib/-/tree/master/examples)
to familiarize the user with the software as well as an API to facilitate the use and the further development of the library.
The structural groups are projected onto the [directory structure](https://git.imp.fu-berlin.de/zkasmi/RcdMathLib) of
RcdMathLib, where each of these groups resides in one or two directories in the [main](https://git.imp.fu-berlin.de/zkasmi/RcdMathLib/) RcdMathLib directory.
The following list gives a more detailed description of each of RcdMathLib's
top-level directories:
## Linear Algebra
This directory contains functions that are specific to vector and matrix operations, and
other algebraic operations. It provides functions to perform basic matrix operations such
as matrix addition, multiplication, or transposition. It also provides algorithms for complex
operations like matrix decomposition algorithms, algorithms to calculate the pseudo-inverse
of a matrix, or methods to solve systems of linear equations. The linear algebra module is
divided in the following sub-modules:
- Basic operations sub-module.
- Matrix decompositions sub-module.
- Pseudo-Inverse sub-module.
- Solve linear equations sub-module.
- Utilities sub-module.
See the [linear algebra module](https://git.imp.fu-berlin.de/zkasmi/RcdMathLib/-/tree/master/linear_algebra) in the [main](https://git.imp.fu-berlin.de/zkasmi/RcdMathLib/) RcdMathLib directory as well as in the [documentation](https://git.imp.fu-berlin.de/zkasmi/RcdMathLib/-/tree/master/doc/doxygen) repository directory for further information and API documentations.
## Non-Linear Algebra
The non-linear algebra module contains functions to solve multi-variant nonlinear
equations as wells algorithms solving problems of regression smoothing and curve
fitting. This module also enables enables the optimization of an approximate solution
by using Non-linear Least Squares (NLS) methods such as modified Gauss--Newton (GN) or
the Levenberg--Marquardt (LVM) algorithms. The non-linear algebra module is
divided in the two following sub-modules:
- Solve non-linear equations sub-module.
- Optimization sub-module.
See the [non-linear algebra module](https://git.imp.fu-berlin.de/zkasmi/RcdMathLib/-/tree/master/non_linear_algebra) in the [main](https://git.imp.fu-berlin.de/zkasmi/RcdMathLib/) RcdMathLib directory as well as in the [documentation](https://git.imp.fu-berlin.de/zkasmi/RcdMathLib/-/tree/master/doc/doxygen) repository directory for further information.
## Localization
The localization module contains functions to compute a position of a mobile device
using distance measurements or DC-pulsed, magnetic signals. This module also includes
optimization algorithms such as the Levenberg--Marquardt approach to optimize the
calculated position. The localization module also involves a method to recognize and
mitigate the multipath errors on the mobile station.
In the `position_algos`[sub-directory](https://git.imp.fu-berlin.de/zkasmi/RcdMathLib/-/tree/master/localization/position_algos)
you can find the implementations of the distance-based localization system (see the
[distance-based module](https://git.imp.fu-berlin.de/zkasmi/RcdMathLib/-/tree/master/localization/position_algos/distance_based)) as well as the implementations of the DC-pulsed, magnetic position system (see the [magnetic-based module](https://git.imp.fu-berlin.de/zkasmi/RcdMathLib/-/tree/master/localization/position_algos/magnetic_based)). The `pos_algos_common` sub-directory contains common localization algorithms like the trilateration method (see the [common module of position algorithms](https://git.imp.fu-berlin.de/zkasmi/RcdMathLib/-/tree/master/localization/position_algos/pos_algos_common)). The optimization algorithms are located in the `position optimization`[sub-directory](https://git.imp.fu-berlin.de/zkasmi/RcdMathLib/-/tree/master/localization/position_optimization) providing the following optimization approaches:
- Gauss--Newton (GN) algorithm.
- Levenberg--Marquardt (LVM) algorithm.
- Multipath Distance Detection and Mitigation (MDDM) algorithm.
See the [localization module](https://git.imp.fu-berlin.de/zkasmi/RcdMathLib/-/tree/master/localization) for more detailed information.
## examples
Here you find a number of example applications that demonstrate certain
features of RcdMathLib. The examples found in this [directory](https://git.imp.fu-berlin.de/zkasmi/RcdMathLib/-/tree/master/examples) is a good starting point for anyone who is new to RcdMathLib.
For more information best browse that directory and have a look at the
`README.md` files that ship with each example.
To create your own application - here or anywhere else - see the page for
[creating an application](https://git.imp.fu-berlin.de/zkasmi/RcdMathLib/-/wikis/Creating-an-application).
## doc
The [doc directory](https://git.imp.fu-berlin.de/zkasmi/RcdMathLib/-/tree/master/doc/doxygen) contains the doxygen configuration and also contains the compiled doxygen output after running `make doc`.
