Eigen of c++ on nim

This is a high level wrap of Eigen lib. The fundamental package for scientific computing with Nim and ready for real world.

Why should you use nimeigen instead of native linear algebra like Arraymancer?

You want to use nim now. However Arraymancer has not finished and it is not ready for all real work.
You have some c/c++ legacy codes, and you do not want to rewrite them all.
You want a mature reliable and fast matrix library with full support for MKL.
You want seamless operability between nim and Python(numpy) using Pybind11.
You want to copy your python (numpy) code and run it on nim compiler with little change.

How to

A easy example

1. First of all, you need Eigen(3.3.7).

Try apt-get install libeigen3-dev, which will install Eigen at /usr/include/eigen3.

2. Of course You also need nimeigen.

git clone https://github.com/chimez/nimeigen.git

3. Create your first nimeigen source

hello.nim

echo "1. import, Complex32 and Complex64 of stdlib complex is realy bad"
import complex except Complex32, Complex64
from nimeigen import Complex32, Complex64
import nimeigen as np # I love numpy

echo "2. data types are float32, float64, complex[float32], complex[float64](default)"
let mat1 = np.matrix([[1,2],[3,4]],dtype=float64)
echo mat1

echo "3. operators are like matlab instead of numpy"
let mat2 = np.matrix([[1,2],[3,4]])
echo ".*"
echo mat2 .* 2
echo "*"
echo mat2 * mat2

echo "4. all functions are like numpy, and may be easier"
let
  mat3 = np.rand(4)
  mat3_vals = np.eigenvalues(mat3)
echo "eigenvalues:"
echo mat3_vals

4. Let's compile it!

nim cpp --path:/Path/to/nimeigen/src --passc:"-I/usr/include/eigen3" --run hello.nim

5. You will see

1. import, Complex32 and Complex64 of stdlib complex is realy bad
2. data types are float32, float64, complex[float32], complex[float64](default)
|	1.0	2.0	|
|	3.0	4.0	|
3. operators are like matlab instead of numpy
.*
|	(2.0, 0.0)	(4.0, 0.0)	|
|	(6.0, 0.0)	(8.0, 0.0)	|
*
|	(7.0, 0.0)	(10.0, 0.0)	|
|	(15.0, 0.0)	(22.0, 0.0)	|
4. all functions are like numpy, and may be easier
eigenvalues:
|	(0.1373818674426576, 0.5054111094536585)	|
|	(-0.7576949962329355, 1.215356386483473)	|
|	(1.522050871699843, -0.401625756423867)	|
|	(-0.6912320291028429, -1.625506269422067)	|

How to use MKL?

We don't neet to change any codes!

1. (recommend) use g++

generate cpp

 nim cpp --path:/Path/to/nimeigen/src --passc:"-I/usr/include/eigen3" --nimcache:cppsrc --header hello.nim

compile There will be lots of warnings. Don't worry. They are just warnings.

g++ -o hello cppsrc/*.cpp -I/Path/to/Nim/lib/ -I/usr/include/eigen3 -I/usr/include/mkl `pkg-config --libs mkl-sdl-lp64` -DEIGEN_USE_MKL_ALL

run it! ./hello

2. use nim compiler

There may be some bug(?) of nim compiler.

nim cpp --path:/Path/to/nimeigen/src --passc:"-I/usr/include/eigen3" --passc:"`pkg-config --libs mkl-sdl-lp64`" --passc:"-I/usr/include/mkl" --passc:"-DEIGEN_USE_MKL_ALL" --run a.nim

How to use Pybind11 and any c++ code

Let's write a package which can calculate eigenvalues of matrix. All files are in examples/pyeigs.

To install pybind11, you can apt-get install pybind11-dev

1. write nim code

we should add {.exportc.} to those we want to use in python.

eigs.nim:

import complex except Complex32, Complex64
from nimeigen import Complex32, Complex64
import nimeigen as np

proc eigs(x:MatrixXcd):MatrixXcd {.exportc.}=
  result=x.eigenvalues()

2. write c++ code

pybind11 is quite easy to use.

pyeigs.cpp:

#include <pybind11/complex.h>
#include <pybind11/eigen.h>
#include <pybind11/pybind11.h>
#include <pybind11/stl.h>

#include "eigs.h"

namespace py = pybind11;

PYBIND11_MODULE(pyeigs, m) {
  m.doc() = "nimeigen pybind11 example";
  m.def("eigs", &eigs, "matrix eigenvalues");
}

3. write CMakeLists.txt

cmake version should > 3.4
First, we should compile .nim to .cpp.
We also need set path NIMEIGEN and NIMLIB
finally, compile pybind11 by pybind11_add_module(pyeigs pyeigs.cpp ${cpp_src})

cmake_minimum_required(VERSION 3.13.4)
project(pyeigs)

# 1. set or find dirs
set(NIMEIGEN "/PATH/to/nimeigen/src")
set(NIMLIB "/PATH/to/Nim/lib")

set(nimsrc ${PROJECT_SOURCE_DIR}/eigs.nim)
set(nimcache ${PROJECT_SOURCE_DIR}/cpp)

find_package(Eigen3 REQUIRED)
find_package(pybind11 REQUIRED)

# 2. compile eigs.nim to *.cpp
add_custom_target(nim ALL
  DEPENDS ${nimsrc})

add_custom_command(TARGET nim
  PRE_BUILD
  COMMAND nim cpp --path:${NIMEIGEN} --passc:"-I${EIGEN3_INCLUDE_DIR}" --nimcache:${nimcache}  --noMain --noLinking --header ${nimsrc}
  COMMENT "compile nim")

# 3. include all header files
include_directories(${EIGEN3_INCLUDE_DIR})
include_directories(${PROJECT_SOURCE_DIR}/cpp)
include_directories(${NIMLIB})
include_directories(${NIMEIGEN})

# 4. compile cpp
file(GLOB cpp_src "${PROJECT_SOURCE_DIR}/cpp/*.cpp")
pybind11_add_module(pyeigs pyeigs.cpp ${cpp_src})

4. compile it!

we have to run cmake twice, first for nim compiler and second for g++ compiler

mkdir build
cd build
# first, nim -> cpp
cmake ..
make
# second, cpp -> so
cmake ..
make

5. run test.py

we should copy .so to same dir, maybe: cp build/pyeigs.cpython-37m-x86_64-linux-gnu.so .

test.py:

import numpy as np

import pyeigs

mat = np.array([[1, 2j], [3, 4]])
print("numpy:", np.linalg.eigvals(mat))
print("pyeigs:", pyeigs.eigs(mat).transpose())

And you will see:

numpy: [0.41937476-1.44187427j 4.58062524+1.44187427j]
pyeigs: [[0.41937476-1.44187427j 4.58062524+1.44187427j]]

As a scientific computing library

ODE solver (Explicit Runge-Kutta method of order 5(4))

This is an example from scipy's solve_ivp

import complex except Complex32, Complex64
import nimeigen
import nimeigen/sci/ode/solve_ivp

let y0 = matrix([[2,4,8]])
func exponential_decay(t:float64, y:MatrixXcd):MatrixXcd= -0.5*y
let (t,y) = solve_ivp(exponential_decay, (0.0,10.0), y0)

echo t 
echo y[len(y)-1]

Tips

all available functions are listed in quick_reference.org
tests/test_matrix.nim is a good example.

TODO

tensor or ndarray

Contributing

feel free to open an issue for any feature requests, not only wrap Eigen functions but also any numpy/scipy useful functions.
Any PR are Welcome.

License

MPL2, same as Eigen