Multi-dimensional arrays with broadcasting and lazy computing.

## Introduction¶

xtensor is a C++ library meant for numerical analysis with multi-dimensional array expressions.

xtensor provides

• an extensible expression system enabling lazy broadcasting.
• an API following the idioms of the C++ standard library.
• tools to manipulate array expressions and build upon xtensor.

The implementation of the containers of xtensor is inspired by NumPy, the Python array programming library. Adaptors for existing data structures to be plugged into our expression system can easily be written. In fact, xtensor can be used to process numpy data structures inplace using Python's buffer protocol.

xtensor requires a modern C++ compiler supporting C++14. The following C+ compilers are supported:

• On Windows platforms, Visual C++ 2015 Update 2, or more recent
• On Unix platforms, gcc 4.9 or a recent version of Clang

## Usage¶

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

In [ ]:
#include <iostream>

#include "xtensor/xarray.hpp"
#include "xtensor/xio.hpp"
#include "xtensor/xview.hpp"

In [ ]:
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::view(arr1, 1) + arr2

In [ ]:
arr1


### Initialize a 1-D array and reshape it inplace¶

In [ ]:
#include <iostream>
#include "xtensor/xarray.hpp"
#include "xtensor/xio.hpp"

In [ ]:
xt::xarray<int> arr
{1, 2, 3, 4, 5, 6, 7, 8, 9};

arr.reshape({3, 3});

arr


### Broadcasting the xt::pow universal functions¶

In [ ]:
#include <iostream>
#include "xtensor/xarray.hpp"
#include "xtensor/xmath.hpp"
#include "xtensor/xio.hpp"

In [ ]:
xt::xarray<double> arr3
{1.0, 2.0, 3.0};

xt::xarray<unsigned int> arr4
{4, 5, 6, 7};

arr4.reshape({4, 1});

xt::pow(arr3, arr4)


### Random arrays with the random module¶

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#include <iostream>
#include "xtensor/xrandom.hpp"

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xt::xarray<double> arr5 = xt::random::randn<double>({4, 3});
arr5

In [ ]:
xt::random::randn<double>({5, 3, 8, 10}) > 0.2


### Using linspace, arange, ones, zeros¶

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#include "xtensor/xbuilder.hpp"

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xt::xarray<double> ar = xt::linspace<double>(0.0, 10.0, 12);
ar.reshape({4, 3});
ar

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xt::xarray<double> fones = xt::ones<float>({2, 2});
fones

In [ ]:
xt::arange<int>(1569325055)


### Using xt::broadcast¶

In [ ]:
#include <vector>

In [ ]:
xt::broadcast(xt::linspace<double>(0.0, 10.0, 4),
std::vector<std::size_t>({3, 4}))


### Using standard algorithms with xexpressions¶

In [ ]:
#include <algorithm>

In [ ]:
xt::xarray<double> frand = xt::random::randn<double>({2, 2});

// begin() and end() provide and iterator pair iterating over the xexpression in a row-major fashion
std::cout << std::accumulate(frand.begin(), frand.end(), 0.0);

frand


### Iterating over a prescribed broadcasted shape¶

In [ ]:
// begin(shape) and end(shape) provide and iterator pair iterating
// over the xexpression broadcasted to the prescrived shape in a row-major fashion
std::vector<std::size_t> shape = {3, 2, 2};
std::cout << std::accumulate(frand.begin(shape), frand.end(shape), 0.0);

Blas bindings for xtensor.

xtensor-blas is an extension to the xtensor library, offering bindings to BLAS and LAPACK libraries through cxxblas and cxxlapack from the FLENS project.

xtensor-blas currently provides non-broadcasting dot, norm (1- and 2-norm for vectors), inverse, solve, eig, cross, det, slogdet, matrix_rank, inv, cholesky, qr, svd in the xt::linalg namespace (check the corresponding xlinalg.hpp header for the function signatures). The functions, and signatures, are trying to be 1-to-1 equivalent to NumPy. Low-level functions to interface with BLAS or LAPACK with xtensor containers are also offered in the blas and lapack namespace.

xtensor and xtensor-blas require a modern C++ compiler supporting C++14. The following C++ compilers are supported:

• On Windows platforms, Visual C++ 2015 Update 2, or more recent
• On Unix platforms, gcc 4.9 or a recent version of Clang
In [ ]:
#include "xtensor-blas/xlinalg.hpp"

In [ ]:
xt::xtensor<double, 2> m = {{1.5, 0.5}, {0.7, 1.0}};

In [ ]:
std::cout << "Matrix rank: " << std::endl << xt::linalg::matrix_rank(m);

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std::cout << "Matrix inverse: " << std::endl << xt::linalg::inv(m);

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std::cout << "Eigen values: " << std::endl << xt::linalg::eigvals(m);

In [ ]:
xt::xarray<double> arg1 = xt::arange<double>(9);
xt::xarray<double> arg2 = xt::arange<double>(18);
arg1.reshape({3, 3});
arg2.reshape({2, 3, 3});
std::cout << xt::linalg::dot(arg1, arg2) << std::endl;