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Closed 2 years ago .

Here are several free software that may suit your needs.

Example

Initialize a 2-D array and compute the sum of one of its rows and a 1-D array.

#include <iostream>
#include "xtensor/xarray.hpp"
#include "xtensor/xio.hpp"
xt::xarray<double> arr1
  {{1.0, 2.0, 3.0},
   {2.0, 5.0, 7.0},
   {2.0, 5.0, 7.0}};
xt::xarray<double> arr2
  {5.0, 6.0, 7.0};
xt::xarray<double> res = xt::view(arr1, 1) + arr2;
std::cout << res;
Outputs
{7, 11, 14}
Initialize a 1-D array and reshape it inplace.
#include <iostream>
#include "xtensor/xarray.hpp"
#include "xtensor/xio.hpp"
xt::xarray<int> arr
  {1, 2, 3, 4, 5, 6, 7, 8, 9};
arr.reshape({3, 3});
std::cout << arr;
Outputs
{{1, 2, 3},
 {4, 5, 6},
 {7, 8, 9}}
DyND is designed to be, among other things, a NumPy-like library for C++. Things like broadcasting, arithmetic operators, and slicing all work fine. On the other hand, it is still very experimental and many features haven't been implemented yet.
Here's a simple implementation of the de Casteljau algorithm in C++ using DyND arrays:
#include <iostream>
#include <dynd/array.hpp>
using namespace dynd;
nd::array decasteljau(nd::array a, double t){
    size_t e = a.get_dim_size();
    for(size_t i=0; i < e-1; i++){
        a = (1.-t) * a(irange()<(e-i-1)) + t * a(0<irange());
    return a;
int main(){
    nd::array a = {1., 2., 2., -1.};
    std::cout << decasteljau(a, .25) << std::endl;
I wrote a blog post a little while back with more examples and side-by-side comparisons of the syntax for Fortran 90, DyND in C++, and NumPy in Python.
Disclaimer: I'm one of the current DyND developers.
This is an old question. Still felt like answering. Thought might help many, Especially pydevs coding in C++.
If you have already worked with python numpy, then NumCpp is a great choice. It's minimalistic in syntax and has got similar functions or methods as py numpy.
The comparison part in the readme doc is also very very cool.
NumCpp
nc::NdArray<int> arr = {{4, 2}, {9, 4}, {5, 6}};
arr.reshape(5, 3);
arr.astype<double>();
                @Cypher Answer: a.index({Slice(None, 4), Slice(None, None, -1), Slice(), 19}) = b.index({None, Slice(-5, None), None}) Docs: pytorch.org/cppdocs/notes/tensor_indexing.html
– Martin Trenkmann
                Feb 20, 2022 at 23:19
                Thanks. I wish there was a better syntactic way to do this. Doesn't Operator Overloading in C++ allow to achieve something like what Numpy Arrays do?
– Cypher
                Feb 21, 2022 at 5:21
If you want to use multidimensional array(like numpy) for image processing or neural network, you can use OpenCV cv::Mat along with tons of image processing algorithms. In case you just want to use it for matrix operations ONLY, you just have to compile respective opencv modules to reduce the size and have tiny OpenCV library.
cv::Mat(Matrix) is an n-dimensional array that can be used to store various type of data, such as RGB, HSV or grayscale images, vectors with real or complex values, other matrices etc.
A Mat contains the following information: width, height, type, channels, data, flags, datastart, dataend and so on.
It has several methods for matrix manipulation. Bonus you can create then on CUDA cores as well as cv::cuda::GpuMat.
Consider I want to create a matrix with 10 rows, 20 columns, type CV_32FC3:
int R = 10, C = 20;
Mat m1; 
m1.create(R, C, CV_32FC3); //creates empty matrix
Mat m2(cv::Size(R, C), CV_32FC3); // creates a matrix with R rows, C columns with data type T where R and C are integers, 
Mat m3(R, C, CV_32FC3); // same as m2
BONUS:
Compile tiny and compact opencv library for just matrix operations. One of the ways is like as mentioned in this article.
compile opencv source code using following cmake command:
$ git clone https://github.com/opencv/opencv.git
$ cd opencv
$ git checkout <version you want to checkout>
$ mkdir build
$ cd build
$ cmake -D WITH_CUDA=OFF -D WITH_MATLAB=OFF -D BUILD_ANDROID_EXAMPLES=OFF -D BUILD_DOCS=OFF -D BUILD_PERF_TESTS=OFF -D BUILD_TESTS=OFF -DANDROID_STL=c++_shared -DBUILD_SHARED_LIBS=ON -D BUILD_opencv_objdetect=OFF -D BUILD_opencv_video=OFF -D BUILD_opencv_videoio=OFF -D BUILD_opencv_features2d=OFF -D BUILD_opencv_flann=OFF -D BUILD_opencv_highgui=OFF -D BUILD_opencv_ml=OFF -D BUILD_opencv_photo=OFF -D BUILD_opencv_python=OFF -D BUILD_opencv_shape=OFF -D BUILD_opencv_stitching=OFF -D BUILD_opencv_superres=OFF -D BUILD_opencv_ts=OFF -D BUILD_opencv_videostab=OFF -D BUILD_opencv_dnn=OFF -D BUILD_opencv_imgproc=OFF ..
$ make -j $nproc
$ sudo make install
Try this example:
 #include "opencv2/core.hpp"
 #include<iostream>
 int main()
     std::cout << "OpenCV Version " << CV_VERSION << std::endl;
     int R = 2, C = 4;
     cv::Mat m1;
     m1.create(R, C, CV_32FC1); //creates empty matrix
     std::cout << "My Mat : \n" << m1 << std::endl;
Compile the code with following command:
$ g++ -std=c++11 opencv_mat.cc -o opencv_mat `pkg-config --libs opencv` `pkg-config --cflags opencv`
Run the executable:
$ ./opencv_mat
OpenCV Version 3.4.2
My Mat :
[0, 0, 0, 0;
 0, 0, 0, 0]
Eigen is a good linear algebra library. 
http://eigen.tuxfamily.org/index.php?title=Main_Page
It is quite easy to install since it's a header-only library. It relies on template in order to to generate well optimized code. It vectorizes automatically the matrix operations.
It also fully support coefficient wise operations, such as the "per element multiplication" between two matrices for instance. It is what you need?
                The syntax of Eigen is pretty terrible though. There is none of that smooth slicing syntax you find in Numpy. And it's not a general n-dimensional array library, it's more for 1D vectors and 2D matrices only. The fact that they have VectorXd for 1D arrays and MatrixXd for 2D arrays repels me already.
– Alex
                May 30, 2017 at 23:50
xtensor is good, but I ended up writing a mini-library myself as a toy project with c++20, while trying to keep the interface as simple as possible. Here it is: https://github.com/gbalduzz/NDArray
Example code:
using namespace nd;
NDArray<int, 2> m(3, 3); // 3x3 matrix
m = 2; // assign 2 to all
m(-1, all) = 1; // assign 1 to the last row.
auto tile = m(range{1, end}, range{1, end}); // 2x2 tile
std::sort(tile.begin(), tile.end());
std::cout << m; // prints [[2, 2, 2], [2, 1, 1], [1, 2, 2]]
It does not provide fancy arithmetic operators collapsing multiple operations together, yet, but you can broadcast arbitrary lambdas to a set of tensors with the same shape, or use lazily evaluated arithmetic operators.
Let me know what do you think about the interface and how it compares with the other options, and if this has any hope, what sort of operations you would like to see implemented.
Free license and no dependency!
Addendum: I managed to properly compile and run xtensor, and the result is that my library is significantly faster when iterating over views (2 to 3X)
Blitz++ supports arrays with an arbitrary number of axes, whereas Armadillo only supports up to three (vectors, matrices, and cubes).  Eigen only supports vectors and matrices (not cubes).  The downside is that Blitz++ doesn't have linear algebra functions beyond the basic entrywise operations and tensor contractions.  Development seems to have slowed down quite some time ago, but perhaps that's just because the library does what it does and not many changes need to be made.
VIGRA contains a good N-dimensional array implementation:
http://ukoethe.github.io/vigra/doc/vigra/Tutorial.html
I use it extensively, and find it very simple and effective. It's also header only, so very easy to integrate into your development environment. It's the closest thing I've come across to using NumPy in terms of it's API.  
The main downside is that it isn't so widely used as the others, so you won't find much help online. That, and it's awkwardly named (try searching for it!)
While GLM is designed to mesh easily with OpenGL and GLSL, it is a fully functional header only math library for C++ with a very intuitive set of interfaces.
It declares vector & matrix types as well as various operations on them.
Multiplying two matrices is a simple as (M1 * M2). Subtracting two vectors (V1- V2).
Accessing values contained in vectors or matrices is equally simple. After declaring a vec3 vector for example, one can access its first element with vector.x.  Check it out.