ANN: xtensor and xtensor-python

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ANN: xtensor and xtensor-python

Sylvain Corlay

Hi all,

We are pleased to announce the release of the xtensor library and its python bindings xtensor-python, by Johan Mabille (@JohanMabille) and Sylvain Corlay (@SylvainCorlay).

1. xtensor

xtensor is a C++ template library for manipulating multi-dimensional array expressions.

It provides

  • an API following the idioms of the C++ standard library.
  • an extensible expression system enabling lazy broadcasting and universal functions.
  • python bindings for operating inplace on numpy arrays in your C++ thanks to Python's buffer protocol and pybind.

More details on lazy computing with xtensor are available below.

2. xtensor-cookiecutter

Besides, xtensor and xtensor-python, we provide a cookiecutter template project to help extension authors get started. The xtensor-cookiecutter generates a simple project for a Python C++ extension with

  • a working setup.py compiling the extension module
  • a few example of functions making use of xtensor exposed to python, and the example of a vectorized function exposed to python.
  • all the boilerplate for the setup of the unit testing and generation of the HTML documentation for these examples.

3. You can try it now!

You can try the xtensor live on the project website. The Try it Now button is powered by

  • The Cling C++ interpreter.
  • The Jupyter notebook.
  • The Binder project.


Getting started

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

Installation

xtensor and xtensor-python are header-only libraries. We provide packages for the conda package manager.

conda install -c conda-forge xtensor         # installs xtensor
conda install -c conda-forge xtensor-python  # installs xtensor and xtensor-python

Usage

Basic Usage

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::make_xview(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}}

Lazy Broadcasting with xtensor

We can operate on arrays of different shapes of dimensions in an elementwise fashion. Broadcasting rules of xtensor are similar to those of numpy and libdynd.

Broadcasting rules

In an operation involving two arrays of different dimensions, the array with the lesser dimensions is broadcast across the leading dimensions of the other.

For example, if A has shape (2, 3), and B has shape (4, 2, 3), the result of a broadcasted operation with A and has shape (4, 2, 3).

   (2, 3) # A
(4, 2, 3) # B
---------
(4, 2, 3) # Result

The same rule holds for scalars, which are handled as 0-D expressions. If matched up dimensions of two input arrays are different, and one of them has size 1, it is broadcast to match the size of the other. Let's say B has the shape (4, 2, 1) in the previous example, so the broadcasting happens as follows:

   (2, 3) # A
(4, 2, 1) # B
---------
(4, 2, 3) # Result

Universal functions, Laziness and Vectorization

With xtensor, if xy and z are arrays of broadcastable shapes, the return type of an expression such as x + y * sin(z) is not an array. It is an xexpression object offering the same interface as an N-dimensional array, which does not hold the result. Values are only computed upon access or when the expression is assigned to an xarray object. This allows to operate symbolically on very large arrays and only compute the result for the indices of interest.

We provide utilities to vectorize any scalar function (taking multiple scalar arguments) into a function that will perform on xexpressions, applying the lazy broadcasting rules which we just described. These functions are called xfunctions. They are xtensor's counterpart to numpy's universal functions.

In xtensor, arithmetic operations (+-*/) and all special functions are xfunctions.

Iterating over xexpressions and Broadcasting Iterators

All xexpressions offer two sets of functions to retrieve iterator pairs (and their const counterpart).

  • begin() and end() provide instances of xiterators which can be used to iterate over all the elements of the expression. The order in which elements are listed is row-major in that the index of last dimension is incremented first.
  • xbegin(shape) and xend(shape) are similar but take a broadcasting shape as an argument. Elements are iterated upon in a row-major way, but certain dimensions are repeated to match the provided shape as per the rules described above. For an expression ee.xbegin(e.shape()) and e.begin() are equivalent.

Fixed-dimension and Dynamic dimension

Two container classes implementing multi-dimensional arrays are provided: xarray and xtensor.

  • xarray can be reshaped dynamically to any number of dimensions. It is the container that is the most similar to numpy arrays.
  • xtensor has a dimension set at compilation time, which enables many optimizations. For example, shapes and strides of xtensor instances are allocated on the stack instead of the heap.

xarray and xtensor container are both xexpressions and can be involved and mixed in universal functions, assigned to each other etc...

Besides, two access operators are provided:

  • The variadic template operator() which can take multiple integral arguments or none.
  • And the operator[] which takes a single multi-index argument, which can be of size determined at runtime. operator[] also supports access with braced initializers.

Python bindings

The python bindings are built upon the pybind11 library, a lightweight header-only for creating bindings between the Python and C++ programming languages.

Example 1: Use an algorithm of the C++ library on a numpy array inplace.

C++ code

#include <numeric>                    // std::accumulate
#include "pybind11/pybind11.h"        // pybind11
#include "xtensor/xmath.hpp"          // C++ universal functions
#include "xtensor-python/pyarray.hpp" // numpy bindings

double sum_of_sines(xt::pyarray<double> &m)
{
    auto sines = xt::sin(m); // sines does not hold any value
    return std::accumulate(sines.begin(), sines.end(), 0.0);
}

PYBIND11_PLUGIN(xtensor_python_test)
{
    pybind11::module m("xtensor_python_test",
                       "Test module for xtensor python bindings");

    m.def("sum_of_sines",
          sum_of_sines,
          "Return the sum of the sines");

    return m.ptr();
}

Python Code

import numpy as np
import xtensor_python_test as xt

a = np.arange(15).reshape(3, 5)
s = xt.sum_of_sines(v)
s

Outputs

1.2853996391883833

Example 2: Create a universal function from a C++ scalar function

C++ code

#include "pybind11/pybind11.h"
#include "xtensor-python/pyvectorize.hpp"
#include <numeric>
#include <cmath>

namespace py = pybind11;

double scalar_func(double i, double j)
{
    return std::sin(i) - std::cos(j);
}

PYBIND11_PLUGIN(xtensor_python_test)
{
    py::module m("xtensor_python_test",
                 "Test module for xtensor python bindings");

    m.def("vectorized_func", xt::pyvectorize(scalar_func), "");

    return m.ptr();
}

Python Code

import numpy as np
import xtensor_python_test as xt

x = np.arange(15).reshape(3, 5)
y = [1, 2, 3]
z = xt.vectorized_func(x, y)
z

Outputs

[[-1.     ,  0.30116,  1.32544,  1.13111, -0.10315],
 [-1.95892, -0.81971,  1.07313,  1.97935,  1.06576],
 [-1.54402, -1.54029, -0.12042,  1.41016,  1.64425]]

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