Johnson's Math ToolBox: Linear Algebra Library
JMT Linear Algebra Library is a light weighted fast library for scientific computing with C++. Though the author does not claim the library can outperform the celebrated LAPCK library, it is nonetheless very easy to use and performs pretty well with matrices sized less than 100.
This library supports common operations for real and complex matrices including:
- Singular Value Decomposition
Single-sided Jacobi's rotation is used. This operation is similar to a compact SVD for thin matrices.
- QR/LQ Decomposition
Householder's Reflection is used for numerical robustness.
- Cholesky Decomposition
This directly leads to the ability for matrix inversion.
First, clone this repo using git:
git clone https://github.com/zjiayao/jmt-matrix
Then cd to the repo and build and run the example:
cd jmt-matrix && make example && ./example
For Windows users, a CMakeList is prepared, and thus
one may build using cmake:
cd jmt-matrix
cmake -H. -Bbuild
cmake --build build
./build/example
To use JMT Linear Algebra Library for operating on real numbers,
include dmatrix.hpp in the header; analogously, include cmatrix.hpp
for complex support.
A sample program for calling common APIs is given in the
examples folder.
- Zero Dependency, Platform Dependent
The whole library is self-contained, shipped with a dedicated complex library used for comlex manipulations.
- Template Programming
This library is written in template classes, that is, there is no need to compile or link before use. Directly include the desired headers (see previous section) and compile, voila!
This also makes the library very easy to extend to other data types, for examples, 16bit floats, etc.
- Intuitive API
Doing a SVD and print the result is as simple
as if in MatLAB or Python:
// a normal 5 * 3 real random matrix
jmt::dmat mat = jmt::dmat::getNRand(5, 3), u, s, v;
mat.SVD(u, s, v);
u.print();
- Portability
This library provides a handful of formats for
printing, hence it is easy to feed the results
to, for example, Python.
// print to file
jmt::cmat cmat = jmt::cmat::getNRand(6, 3), q, r;
cmat.QR(q, r);
q.print(fout); // fout is a FILE pointer
r.print(stdout, jmt::NUMPY);
this gives:
[[ 0.671 - 0.741i ,0.000 ,0.000 ],
[ 0.000 ,0.975 + 0.223i ,0.000 ],
[ 0.000 ,0.000 ,-0.625 - 0.781i ],
[ 0.000 ,0.000 ,0.000 ],
[ 0.000 ,0.000 ,0.000 ],
[ 0.000 ,0.000 ,0.000 ]]
Of course, directly std::cout and std::cin (yes!) are supported.
It is recommended NOT to use this library in production environment, rather, use well-crafted libraries such as LAPACK in lieu.