Multi-dimensional arrays with broadcasting and lazy computing.



In [1]:

    
#include <iostream>

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



In [2]:

    
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









    Out[2]:




  7.
 11.
 14.



In [3]:

    
arr1









    Out[3]:




 1.  2.  3.
 2.  5.  7.
 2.  5.  7.

Initialize a 1-D array and reshape it inplace



In [4]:

    
#include <iostream>
#include "xtensor/xarray.hpp"
#include "xtensor/xio.hpp"



In [5]:

    
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 [6]:

    
#include <iostream>
#include "xtensor/xarray.hpp"
#include "xtensor/xmath.hpp"
#include "xtensor/xio.hpp"



In [7]:

    
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)









    Out[7]:




    1.    16.    81.
    1.    32.   243.
    1.    64.   729.
    1.   128.  2187.

Random arrays with the random module



In [8]:

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



In [9]:

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









    Out[9]:




 0.13453 -0.146382  0.46065 
-1.871384  0.163712 -0.214253
 0.298595 -0.827944  0.010215
 1.055466 -0.546841  1.174568



In [10]:

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









    Out[10]:




 true false  true ⋯ false false false
false false false ⋯  true  true false
 true false false ⋯ false false false
⋮ ⋮ ⋮ ⋱ ⋮ ⋮ ⋮
 true false  true ⋯  true  true false
 true false  true ⋯  true false  true
 true false  true ⋯ false  true false
false false  true ⋯  true  true  true
 true false false ⋯ false false false
false  true false ⋯ false false  true
⋮ ⋮ ⋮ ⋱ ⋮ ⋮ ⋮
false  true  true ⋯  true false false
 true false  true ⋯  true  true  true
false  true false ⋯  true  true  true
 true false  true ⋯ false  true false
false false false ⋯  true  true false
 true false false ⋯  true false false
⋮ ⋮ ⋮ ⋱ ⋮ ⋮ ⋮
 true false  true ⋯ false false false
 true false false ⋯  true false  true
false false false ⋯ false false  true
false  true false ⋯ false false false
false false false ⋯ false false  true
 true  true false ⋯ false  true false
⋮ ⋮ ⋮ ⋱ ⋮ ⋮ ⋮
false  true false ⋯ false false  true
false  true  true ⋯ false  true false
false false false ⋯ false false  true
false false false ⋯  true false false
false  true  true ⋯ false  true  true
false  true  true ⋯  true false false
⋮ ⋮ ⋮ ⋱ ⋮ ⋮ ⋮
false false false ⋯  true false  true
false  true false ⋯  true false  true
false false false ⋯ false false  true
false false false ⋯ false  true false
 true false false ⋯ false false  true
false false false ⋯  true false false
⋮ ⋮ ⋮ ⋱ ⋮ ⋮ ⋮
false false  true ⋯ false false false
 true false false ⋯ false false false
 true false  true ⋯ false false false
 true false  true ⋯ false false false
false  true false ⋯  true false  true
 true false  true ⋯ false false false
⋮ ⋮ ⋮ ⋱ ⋮ ⋮ ⋮
false false  true ⋯  true false false
 true false  true ⋯  true false false
false  true false ⋯  true false false
 true false  true ⋯ false false  true
false  true false ⋯  true  true  true
false false false ⋯  true false  true
⋮ ⋮ ⋮ ⋱ ⋮ ⋮ ⋮
 true false  true ⋯  true  true false
false  true false ⋯ false false false
 true  true  true ⋯  true false false
false  true false ⋯ false  true false
false  true false ⋯  true false  true
 true false false ⋯ false false  true
⋮ ⋮ ⋮ ⋱ ⋮ ⋮ ⋮
false false  true ⋯ false false false
 true  true false ⋯ false  true false
false false  true ⋯  true false  true
 true false false ⋯ false false false
 true false false ⋯ false false false
 true false  true ⋯ false false false
⋮ ⋮ ⋮ ⋱ ⋮ ⋮ ⋮
false false false ⋯  true false false
 true false false ⋯ false  true false
false false  true ⋯ false false  true
 true  true  true ⋯ false  true  true
 true  true false ⋯ false  true  true
false false false ⋯ false false false
⋮ ⋮ ⋮ ⋱ ⋮ ⋮ ⋮
false  true  true ⋯  true false  true
false false  true ⋯  true false false
false  true false ⋯ false false false
false  true  true ⋯  true false false
false false  true ⋯  true  true false
 true false false ⋯ false false  true
⋮ ⋮ ⋮ ⋱ ⋮ ⋮ ⋮
 true  true false ⋯  true false  true
false  true  true ⋯ false  true false
 true  true false ⋯ false  true false
false false  true ⋯  true  true false
false false false ⋯ false  true  true
false false false ⋯ false false  true
⋮ ⋮ ⋮ ⋱ ⋮ ⋮ ⋮
false false false ⋯ false false false
false false false ⋯  true false false
 true false  true ⋯  true  true false
false  true  true ⋯ false  true  true
false false false ⋯  true  true false
false false false ⋯ false  true false
⋮ ⋮ ⋮ ⋱ ⋮ ⋮ ⋮
false  true false ⋯ false false  true
 true  true  true ⋯ false false false
 true false false ⋯ false false false
false false false ⋯ false false false
false  true  true ⋯  true  true  true
false false false ⋯  true false  true
⋮ ⋮ ⋮ ⋱ ⋮ ⋮ ⋮
false false false ⋯ false  true false
false false false ⋯  true false  true
false false false ⋯  true false false

Using `linspace`, `arange`, `ones`, `zeros`



In [11]:

    
#include "xtensor/xbuilder.hpp"



In [12]:

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









    Out[12]:




  0.        0.909091   1.818182
  2.727273   3.636364   4.545455
  5.454545   6.363636   7.272727
  8.181818   9.090909  10.



In [13]:

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









    Out[13]:




 1.  1.
 1.  1.



In [14]:

    
xt::arange<int>(1569325055)

Using `xt::broadcast`



In [15]:

    
#include <vector>
#include "xtensor/xbroadcast.hpp"



In [16]:

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









    Out[16]:




 0.       0.       0.       0.      
 3.333333  3.333333  3.333333  3.333333
 6.666667  6.666667  6.666667  6.666667

Using standard algorithms with xexpressions



In [17]:

    
#include <algorithm>



In [18]:

    
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









    



-2.01197





    Out[18]:




-2.339393  0.747579
-0.307341 -0.112812

Iterating over a prescribed broadcasted shape



In [19]:

    
// 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.



In [20]:

    
#include "xtensor-blas/xlinalg.hpp"



In [21]:

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



In [22]:

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









    



Matrix rank: 
2



In [23]:

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









    



Matrix inverse: 
{{ 0.869565, -0.434783},
 {-0.608696,  1.304348}}



In [24]:

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









    



Eigen values: 
{ 1.892262+0.i,  0.607738+0.i}



In [25]:

    
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;









    



{{{  15.,   18.,   21.},
  {  42.,   45.,   48.}},
 {{  42.,   54.,   66.},
  { 150.,  162.,  174.}},
 {{  69.,   90.,  111.},
  { 258.,  279.,  300.}}}



In [ ]:

0.13453	-0.146382	0.46065
-1.871384	0.163712	-0.214253
0.298595	-0.827944	0.010215
1.055466	-0.546841	1.174568

0.	0.909091	1.818182
2.727273	3.636364	4.545455
5.454545	6.363636	7.272727
8.181818	9.090909	10.

0.	0.	0.	0.
3.333333	3.333333	3.333333	3.333333
6.666667	6.666667	6.666667	6.666667

Initialize a 1-D array and reshape it inplace

Broadcasting the xt::pow universal functions

Random arrays with the random module

Using linspace, arange, ones, zeros

Using xt::broadcast

Using standard algorithms with xexpressions

Iterating over a prescribed broadcasted shape

Broadcasting the `xt::pow` universal functions

Using `linspace`, `arange`, `ones`, `zeros`

Using `xt::broadcast`