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|
.. Copyright (c) 2016, Johan Mabille, Sylvain Corlay and Wolf Vollprecht
Distributed under the terms of the BSD 3-Clause License.
The full license is in the file LICENSE, distributed with this software.
From NumPy to xtensor
=====================
.. image:: numpy.svg
:height: 100px
:align: right
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Containers
----------
Two container types are provided. :cpp:type:`xt::xarray` (dynamic number of dimensions)
and :cpp:type:`xt::xtensor` (static number of dimensions).
.. table::
:widths: 50 50
+------------------------------------------------------+------------------------------------------------------------------------+
| Python 3 - NumPy | C++ 14 - xtensor |
+======================================================+========================================================================+
| :any:`np.array([[3, 4], [5, 6]]) <numpy.array>` || :cpp:type:`xt::xarray\<double\>({{3, 4}, {5, 6}}) <xt::xarray>` |
| || :cpp:type:`xt::xtensor\<double, 2\>({{3, 4}, {5, 6}}) <xt::xtensor>` |
+------------------------------------------------------+------------------------------------------------------------------------+
| :any:`arr.reshape([3, 4]) <numpy.ndarray.reshape>` | :cpp:func:`arr.reshape({3, 4}) <xt::xstrided_container::reshape>` |
+------------------------------------------------------+------------------------------------------------------------------------+
| :any:`arr.astype(np.float64) <numpy.ndarray.astype>` | :cpp:func:`xt::cast\<double\>(arr) <xt::cast>` |
+------------------------------------------------------+------------------------------------------------------------------------+
Initializers
------------
Lazy helper functions return tensor expressions. Return types don't hold any value and are
evaluated upon access or assignment. They can be assigned to a container or directly used in
expressions.
.. table::
:widths: 50 50
+----------------------------------------------------------------+-------------------------------------------------------------------+
| Python 3 - NumPy | C++ 14 - xtensor |
+================================================================+===================================================================+
| :any:`np.linspace(1.0, 10.0, 100) <numpy.linspace>` | :cpp:func:`xt::linspace\<double\>(1.0, 10.0, 100) <xt::linspace>` |
+----------------------------------------------------------------+-------------------------------------------------------------------+
| :any:`np.logspace(2.0, 3.0, 4) <numpy.logspace>` | :cpp:func:`xt::logspace\<double\>(2.0, 3.0, 4) <xt::logspace>` |
+----------------------------------------------------------------+-------------------------------------------------------------------+
| :any:`np.arange(3, 7) <numpy.arange>` | :cpp:func:`xt::arange(3, 7) <xt::arange>` |
+----------------------------------------------------------------+-------------------------------------------------------------------+
| :any:`np.eye(4) <numpy.eye>` | :cpp:func:`xt::eye(4) <xt::eye>` |
+----------------------------------------------------------------+-------------------------------------------------------------------+
| :any:`np.zeros([3, 4]) <numpy.zeros>` | :cpp:func:`xt::zeros\<double\>({3, 4}) <xt::zeros>` |
+----------------------------------------------------------------+-------------------------------------------------------------------+
| :any:`np.ones([3, 4]) <numpy.ones>` | :cpp:func:`xt::ones\<double\>({3, 4}) <xt::ones>` |
+----------------------------------------------------------------+-------------------------------------------------------------------+
| :any:`np.empty([3, 4]) <numpy.empty>` | :cpp:func:`xt::empty\<double\>({3, 4}) <xt::empty>` |
+----------------------------------------------------------------+-------------------------------------------------------------------+
| :any:`np.meshgrid(x0, x1, x2, indexing='ij') <numpy.meshgrid>` | :cpp:func:`xt::meshgrid(x0, x1, x2) <xt::meshgrid>` |
+----------------------------------------------------------------+-------------------------------------------------------------------+
xtensor's :cpp:func:`meshgrid <xt::meshgrid>` implementation corresponds to numpy's ``'ij'`` indexing order.
Slicing and indexing
--------------------
See :any:`numpy indexing <numpy:arrays.indexing>` page.
.. table::
:widths: 50 50
+-----------------------------------------+---------------------------------------------------------------------------+
| Python 3 - NumPy | C++ 14 - xtensor |
+=========================================+===========================================================================+
| ``a[3, 2]`` | :cpp:func:`a(3, 2) <xt::xcontainer::operator()>` |
+-----------------------------------------+---------------------------------------------------------------------------+
| :any:`a.flat[4] <numpy.ndarray.flat>` | :cpp:func:`a.flat(4) <xt::xcontainer::flat>` |
+-----------------------------------------+---------------------------------------------------------------------------+
| ``a[3]`` || :cpp:func:`xt::view(a, 3, xt::all()) <xt::view>` |
| || :cpp:func:`xt::row(a, 3) <xt::row>` |
+-----------------------------------------+---------------------------------------------------------------------------+
| ``a[:, 2]`` || :cpp:func:`xt::view(a, xt::all(), 2) <xt::view>` |
| || :cpp:func:`xt::col(a, 2) <xt::col>` |
+-----------------------------------------+---------------------------------------------------------------------------+
| ``a[:5, 1:]`` | :cpp:func:`xt::view(a, xt::range(_, 5), xt::range(1, _)) <xt::range>` |
+-----------------------------------------+---------------------------------------------------------------------------+
| ``a[5:1:-1, :]`` | :cpp:func:`xt::view(a, xt::range(5, 1, -1), xt::all()) <xt::all>` |
+-----------------------------------------+---------------------------------------------------------------------------+
| ``a[..., 3]`` | :cpp:func:`xt::strided_view(a, {xt::ellipsis(), 3}) <xt::ellipsis>` |
+-----------------------------------------+---------------------------------------------------------------------------+
| :any:`a[:, np.newaxis] <numpy.newaxis>` | :cpp:func:`xt::view(a, xt::all(), xt::newaxis()) <xt::newaxis>` |
+-----------------------------------------+---------------------------------------------------------------------------+
Broadcasting
------------
xtensor offers lazy numpy-style broadcasting, and universal functions. Unlike numpy, no copy
or temporary variables are created.
.. table::
:widths: 50 50
+-----------------------------------------------------+------------------------------------------------------------------+
| Python 3 - NumPy | C++ 14 - xtensor |
+=====================================================+==================================================================+
| :any:`np.broadcast(a, [4, 5, 7]) <numpy.broadcast>` | :cpp:func:`xt::broadcast(a, {4, 5, 7}) <xt::broadcast>` |
+-----------------------------------------------------+------------------------------------------------------------------+
| :any:`np.vectorize(f) <numpy.vectorize>` | :cpp:func:`xt::vectorize(f) <xt::vectorize>` |
+-----------------------------------------------------+------------------------------------------------------------------+
| ``a[a > 5]`` | :cpp:func:`xt::filter(a, a > 5) <xt::filter>` |
+-----------------------------------------------------+------------------------------------------------------------------+
| ``a[[0, 1], [0, 0]]`` | :cpp:func:`xt::index_view(a, {{0, 0}, {1, 0}}) <xt::index_view>` |
+-----------------------------------------------------+------------------------------------------------------------------+
Random
------
The random module provides simple ways to create random tensor expressions, lazily.
See :any:`numpy.random` and :ref:`xtensor random <random>` page.
.. table::
:widths: 50 50
+-----------------------------------------------------------------------+-----------------------------------------------------------------------------------+
| Python 3 - NumPy | C++ 14 - xtensor |
+=======================================================================+===================================================================================+
| :any:`np.random.seed(0) <numpy.random.seed>` | :cpp:func:`xt::random::seed(0) <xt::random::seed>` |
+-----------------------------------------------------------------------+-----------------------------------------------------------------------------------+
| :any:`np.random.randn(10, 10) <numpy.random.randn>` | :cpp:func:`xt::random::randn\<double\>({10, 10}) <xt::random::randn>` |
+-----------------------------------------------------------------------+-----------------------------------------------------------------------------------+
| :any:`np.random.randint(10, 10) <numpy.random.randint>` | :cpp:func:`xt::random::randint\<int\>({10, 10}) <xt::random::randint>` |
+-----------------------------------------------------------------------+-----------------------------------------------------------------------------------+
| :any:`np.random.rand(3, 4) <numpy.random.rand>` | :cpp:func:`xt::random::rand\<double\>({3, 4}) <xt::random::rand>` |
+-----------------------------------------------------------------------+-----------------------------------------------------------------------------------+
| :any:`np.random.choice(arr, 5[, replace][, p]) <numpy.random.choice>` | :cpp:func:`xt::random::choice(arr, 5[, weights][, replace]) <xt::random::choice>` |
+-----------------------------------------------------------------------+-----------------------------------------------------------------------------------+
| :any:`np.random.shuffle(arr) <numpy.random.shuffle>` | :cpp:func:`xt::random::shuffle(arr) <xt::random::shuffle>` |
+-----------------------------------------------------------------------+-----------------------------------------------------------------------------------+
| :any:`np.random.permutation(30) <numpy.random.permutation>` | :cpp:func:`xt::random::permutation(30) <xt::random::permutation>` |
+-----------------------------------------------------------------------+-----------------------------------------------------------------------------------+
Concatenation, splitting, squeezing
-----------------------------------
Concatenating expressions does not allocate memory, it returns a tensor or view expression holding
closures on the specified arguments.
.. table::
:widths: 50 50
+-----------------------------------------------------------------------------+----------------------------------------------------------------------------+
| Python 3 - NumPy | C++ 14 - xtensor |
+=============================================================================+============================================================================+
| :any:`np.stack([a, b, c], axis=1) <numpy.stack>` | :cpp:func:`xt::stack(xtuple(a, b, c), 1) <xt::stack>` |
+-----------------------------------------------------------------------------+----------------------------------------------------------------------------+
| :any:`np.hstack([a, b, c]) <numpy.hstack>` | :cpp:func:`xt::hstack(xtuple(a, b, c)) <xt::hstack>` |
+-----------------------------------------------------------------------------+----------------------------------------------------------------------------+
| :any:`np.vstack([a, b, c]) <numpy.vstack>` | :cpp:func:`xt::vstack(xtuple(a, b, c)) <xt::vstack>` |
+-----------------------------------------------------------------------------+----------------------------------------------------------------------------+
| :any:`np.concatenate([a, b, c], axis=1) <numpy.concatenate>` | :cpp:func:`xt::concatenate(xtuple(a, b, c), 1) <xt::concatenate>` |
+-----------------------------------------------------------------------------+----------------------------------------------------------------------------+
| :any:`np.tile(a, reps) <numpy.tile>` | :cpp:func:`xt::tile(a, reps) <xt::tile>` |
+-----------------------------------------------------------------------------+----------------------------------------------------------------------------+
| :any:`np.squeeze(a) <numpy.squeeze>` | :cpp:func:`xt::squeeze(a) <xt::squeeze>` |
+-----------------------------------------------------------------------------+----------------------------------------------------------------------------+
| :any:`np.expand_dims(a, 1) <numpy.expand_dims>` | :cpp:func:`xt::expand_dims(a ,1) <xt::expand_dims>` |
+-----------------------------------------------------------------------------+----------------------------------------------------------------------------+
| :any:`np.atleast_3d(a) <numpy.atleast_3d>` | :cpp:func:`xt::atleast_3d(a) <xt::atleast_3d>` |
+-----------------------------------------------------------------------------+----------------------------------------------------------------------------+
| :any:`np.split(a, 4, axis=0) <numpy.split>` | :cpp:func:`xt::split(a, 4, 0) <xt::split>` |
+-----------------------------------------------------------------------------+----------------------------------------------------------------------------+
| :any:`np.hsplit(a, 4) <numpy.hsplit>` | :cpp:func:`xt::hsplit(a, 4) <xt::hsplit>` |
+-----------------------------------------------------------------------------+----------------------------------------------------------------------------+
| :any:`np.vsplit(a, 4) <numpy.vsplit>` | :cpp:func:`xt::vsplit(a, 4) <xt::vsplit>` |
+-----------------------------------------------------------------------------+----------------------------------------------------------------------------+
| :any:`np.trim_zeros(a, trim='fb') <numpy.trim_zeros>` | :cpp:func:`xt::trim_zeros(a, "fb") <xt::trim_zeros>` |
+-----------------------------------------------------------------------------+----------------------------------------------------------------------------+
| :any:`np.pad(a, pad_width, mode='constant', constant_values=0) <numpy.pad>` | :cpp:func:`xt::pad(a, pad_width[, xt::pad_mode::constant][, 0]) <xt::pad>` |
+-----------------------------------------------------------------------------+----------------------------------------------------------------------------+
Rearrange elements
------------------
In the same spirit as concatenation, the following operations do not allocate any memory and do
not modify the underlying xexpression.
.. list-table::
:widths: 50 50
:header-rows: 1
* - Python3 - NumPy
- C++14 - xtensor
* - :any:`np.nan_to_num(a) <numpy.nan_to_num>`
- :cpp:func:`xt::nan_to_num(a) <xt::nan_to_num>`
* - :any:`np.diag(a) <numpy.diag>`
- :cpp:func:`xt::diag(a) <xt::diag>`
* - :any:`np.diagonal(a) <numpy.diagonal>`
- :cpp:func:`xt::diagonal(a) <xt::diagonal>`
* - :any:`np.triu(a) <numpy.triu>`
- :cpp:func:`xt::triu(a) <xt::triu>`
* - :any:`np.tril(a, k=1) <numpy.tril>`
- :cpp:func:`xt::tril(a, 1) <xt::tril>`
* - :any:`np.flip(a, axis=3) <numpy.flip>`
- :cpp:func:`xt::flip(a, 3) <xt::flip>`
* - :any:`np.flipud(a) <numpy.flipud>`
- :cpp:func:`xt::flip(a, 0) <xt::flip>`
* - :any:`np.fliplr(a) <numpy.fliplr>`
- :cpp:func:`xt::flip(a, 1) <xt::flip>`
* - :any:`np.transpose(a, (1, 0, 2)) <numpy.transpose>`
- :cpp:func:`xt::transpose(a, {1, 0, 2}) <xt::transpose>`
* - :any:`np.swapaxes(a, 0, -1) <numpy.swapaxes>`
- :cpp:func:`xt::swapaxes(a, 0, -1) <xt::swapaxes>`
* - :any:`np.moveaxis(a, 0, -1) <numpy.moveaxis>`
- :cpp:func:`xt::moveaxis(a, 0, -1) <xt::moveaxis>`
* - :any:`np.ravel(a, order='F') <numpy.ravel>`
- :cpp:func:`xt::ravel\<xt::layout_type::column_major\>(a) <xt::ravel>`
* - :any:`np.rot90(a) <numpy.rot90>`
- :cpp:func:`xt::rot90(a) <xt::rot90>`
* - :any:`np.rot90(a, 2, (1, 2)) <numpy.rot90>`
- :cpp:func:`xt::rot90\<2\>(a, {1, 2}) <xt::rot90>`
* - :any:`np.roll(a, 2, axis=1) <numpy.roll>`
- :cpp:func:`xt::roll(a, 2, 1) <xt::roll>`
Iteration
---------
xtensor follows the idioms of the C++ STL providing iterator pairs to iterate on arrays in
different fashions.
.. table::
:widths: 50 50
+-----------------------------------------------------------+------------------------------------------------+
| Python 3 - NumPy | C++ 14 - xtensor |
+===========================================================+================================================+
| :any:`for x in np.nditer(a): <numpy.nditer>` | ``for(auto it=a.begin(); it!=a.end(); ++it)`` |
+-----------------------------------------------------------+------------------------------------------------+
| Iterating over ``a`` with a prescribed broadcasting shape | | ``a.begin({3, 4})`` |
| | | ``a.end({3, 4})`` |
+-----------------------------------------------------------+------------------------------------------------+
| Iterating over ``a`` in a row-major fashion | | ``a.begin<xt::layout_type::row_major>()`` |
| | | ``a.begin<xt::layout_type::row_major>()`` |
+-----------------------------------------------------------+------------------------------------------------+
| Iterating over ``a`` in a column-major fashion | | ``a.begin<xt::layout_type::column_major>()`` |
| | | ``a.end<xt::layout_type::column_major>()`` |
+-----------------------------------------------------------+------------------------------------------------+
Logical
-------
Logical universal functions are truly lazy.
:cpp:func:`xt::where(condition, a, b) <xt::where>` does not evaluate ``a`` where ``condition``
is falsy, and it does not evaluate ``b`` where ``condition`` is truthy.
.. table::
:widths: 50 50
+-------------------------------------------------+------------------------------------------------+
| Python 3 - NumPy | C++ 14 - xtensor |
+=================================================+================================================+
| :any:`np.where(a > 5, a, b) <numpy.where>` | :cpp:func:`xt::where(a > 5, a, b) <xt::where>` |
+-------------------------------------------------+------------------------------------------------+
| :any:`np.where(a > 5) <numpy.where>` | :cpp:func:`xt::where(a > 5) <xt::where>` |
+-------------------------------------------------+------------------------------------------------+
| :any:`np.argwhere(a > 5) <numpy.argwhere>` | :cpp:func:`xt::argwhere(a > 5) <xt::argwhere>` |
+-------------------------------------------------+------------------------------------------------+
| :any:`np.any(a) <numpy.any>` | :cpp:func:`xt::any(a) <xt::any>` |
+-------------------------------------------------+------------------------------------------------+
| :any:`np.all(a) <numpy.all>` | :cpp:func:`xt::all(a) <xt::all>` |
+-------------------------------------------------+------------------------------------------------+
| :any:`np.isin(a, b) <numpy.isin>` | :cpp:func:`xt::isin(a, b) <xt::isin>` |
+-------------------------------------------------+------------------------------------------------+
| :any:`np.in1d(a, b) <numpy.in1d>` | :cpp:func:`xt::in1d(a, b) <xt::in1d>` |
+-------------------------------------------------+------------------------------------------------+
| :any:`np.logical_and(a, b) <numpy.logical_and>` | ``a && b`` |
+-------------------------------------------------+------------------------------------------------+
| :any:`np.logical_or(a, b) <numpy.logical_or>` | ``a || b`` |
+-------------------------------------------------+------------------------------------------------+
| :any:`np.isclose(a, b) <numpy.isclose>` | :cpp:func:`xt::isclose(a, b) <xt::isclose>` |
+-------------------------------------------------+------------------------------------------------+
| :any:`np.allclose(a, b) <numpy.allclose>` | :cpp:func:`xt::allclose(a, b) <xt::allclose>` |
+-------------------------------------------------+------------------------------------------------+
| :any:`a = ~b <numpy.invert>` | ``a = !b`` |
+-------------------------------------------------+------------------------------------------------+
Indices
-------
.. table::
:widths: 50 50
+-------------------------------------------------------------------------+-----------------------------------------------------------------------+
| Python 3 - NumPy | C++ 14 - xtensor |
+=========================================================================+=======================================================================+
| :any:`np.ravel_multi_index(indices, a.shape) <numpy.ravel_multi_index>` | :cpp:func:`xt::ravel_indices(indices, a.shape()) <xt::ravel_indices>` |
+-------------------------------------------------------------------------+-----------------------------------------------------------------------+
Comparisons
-----------
.. table::
:widths: 50 50
+-----------------------------------------------------+----------------------------------------------------------+
| Python 3 - NumPy | C++ 14 - xtensor |
+=====================================================+==========================================================+
| :any:`np.equal(a, b) <numpy.equal>` | :cpp:func:`xt::equal(a, b) <xt::equal>` |
+-----------------------------------------------------+----------------------------------------------------------+
| :any:`np.not_equal(a, b) <numpy.not_equal>` | :cpp:func:`xt::not_equal(a, b) <xt::not_equal>` |
+-----------------------------------------------------+----------------------------------------------------------+
| :any:`np.less(a, b) <numpy.less>` || :cpp:func:`xt::less(a, b) <xt::less>` |
| || ``a < b`` |
+-----------------------------------------------------+----------------------------------------------------------+
| :any:`np.less_equal(a, b) <numpy.less_equal>` || :cpp:func:`xt::less_equal(a, b) <xt::less_equal>` |
| || ``a <= b`` |
+-----------------------------------------------------+----------------------------------------------------------+
| :any:`np.greater(a, b) <numpy.greater>` || :cpp:func:`xt::greater(a, b) <xt::greater>` |
| || ``a > b`` |
+-----------------------------------------------------+----------------------------------------------------------+
| :any:`np.greater_equal(a, b) <numpy.greater_equal>` || :cpp:func:`xt::greater_equal(a, b) <xt::greater_equal>` |
| || ``a >= b`` |
+-----------------------------------------------------+----------------------------------------------------------+
| :any:`np.nonzero(a) <numpy.nonzero>` | :cpp:func:`xt::nonzero(a) <xt::nonzero>` |
+-----------------------------------------------------+----------------------------------------------------------+
| :any:`np.flatnonzero(a) <numpy.flatnonzero>` | :cpp:func:`xt::flatnonzero(a) <xt::flatnonzero>` |
+-----------------------------------------------------+----------------------------------------------------------+
Minimum, Maximum, Sorting
-------------------------
.. list-table::
:widths: 50 50
:header-rows: 1
* - Python3 - NumPy
- C++14 - xtensor
* - :any:`np.amin(a) <numpy.amin>`
- :cpp:func:`xt::amin(a) <xt::amin>`
* - :any:`np.amax(a) <numpy.amax>`
- :cpp:func:`xt::amax(a) <xt::amax>`
* - :any:`np.argmin(a) <numpy.argmin>`
- :cpp:func:`xt::argmin(a) <xt::argmin>`
* - :any:`np.argmax(a, axis=1) <numpy.argmax>`
- :cpp:func:`xt::argmax(a, 1) <xt::argmax>`
* - :any:`np.sort(a, axis=1) <numpy.sort>`
- :cpp:func:`xt::sort(a, 1) <xt::sort>`
* - :any:`np.argsort(a, axis=1) <numpy.argsort>`
- :cpp:func:`xt::argsort(a, 1) <xt::argsort>`
* - :any:`np.unique(a) <numpy.unique>`
- :cpp:func:`xt::unique(a) <xt::unique>`
* - :any:`np.setdiff1d(ar1, ar2) <numpy.setdiff1d>`
- :cpp:func:`xt::setdiff1d(ar1, ar2) <xt::setdiff1d>`
* - :any:`np.partition(a, kth) <numpy.partition>`
- :cpp:func:`xt::partition(a, kth) <xt::partition>`
* - :any:`np.argpartition(a, kth) <numpy.argpartition>`
- :cpp:func:`xt::argpartition(a, kth) <xt::argpartition>`
* - :any:`np.quantile(a, [.1 .3], method="linear") <numpy.quantile>`
- :cpp:func:`xt::quantile(a, {.1, .3}, xt::quantile_method::linear) <xt::quantile>`
* - :any:`np.quantile(a, [.1, .3], axis=1 method="linear") <numpy.quantile>`
- :cpp:func:`xt::quantile(a, {.1, .3}, 1, xt::quantile_method::linear) <xt::quantile>`
* -
- :cpp:func:`xt::quantile(a, {.1, .3}, 1, 1.0, 1.0) <xt::quantile>`
* - :any:`np.median(a, axis=1) <numpy.median>`
- :cpp:func:`xt::median(a, 1) <xt::median>`
Complex numbers
---------------
Functions :cpp:func:`xt::real` and :cpp:func:`xt::imag` respectively return views on the real and imaginary part
of a complex expression.
The returned value is an expression holding a closure on the passed argument.
.. table::
:widths: 50 50
+--------------------------------+------------------------------------+
| Python 3 - NumPy | C++ 14 - xtensor |
+================================+====================================+
| :any:`np.real(a) <numpy.real>` | :cpp:func:`xt::real(a) <xt::real>` |
+--------------------------------+------------------------------------+
| :any:`np.imag(a) <numpy.imag>` | :cpp:func:`xt::imag(a) <xt::imag>` |
+--------------------------------+------------------------------------+
| :any:`np.conj(a) <numpy.conj>` | :cpp:func:`xt::conj(a) <xt::conj>` |
+--------------------------------+------------------------------------+
- The constness and value category (rvalue / lvalue) of :cpp:func:`xt::real(a) <xt::real>` is the same as that of ``a``.
Hence, if ``a`` is a non-const lvalue, :cpp:func:`real(a) <xt::real>` is an non-const lvalue reference, to which
one can assign a real expression.
- If ``a`` has complex values, the same holds for :cpp:func:`xt::imag(a) <xt::imag>`. The constness and value category of
:cpp:func:`xt::imag(a) <xt::imag>` is the same as that of ``a``.
- If ``a`` has real values, :cpp:func:`xt::imag(a) <xt::imag>` returns :cpp:func:`xt::zeros(a.shape()) <xt::zeros>`.
Reducers
--------
Reducers accumulate values of tensor expressions along specified axes. When no axis is specified,
values are accumulated along all axes. Reducers are lazy, meaning that returned expressions don't
hold any values and are computed upon access or assignment.
.. table::
:widths: 50 50
+---------------------------------------------------------------+--------------------------------------------------------------+
| Python 3 - NumPy | C++ 14 - xtensor |
+===============================================================+==============================================================+
| :any:`np.sum(a, axis=(0, 1)) <numpy.sum>` | :cpp:func:`xt::sum(a, {0, 1}) <xt::sum>` |
+---------------------------------------------------------------+--------------------------------------------------------------+
| :any:`np.sum(a, axis=1) <numpy.sum>` | :cpp:func:`xt::sum(a, 1) <xt::sum>` |
+---------------------------------------------------------------+--------------------------------------------------------------+
| :any:`np.sum(a) <numpy.sum>` | :cpp:func:`xt::sum(a) <xt::sum>` |
+---------------------------------------------------------------+--------------------------------------------------------------+
| :any:`np.prod(a, axis=(0, 1)) <numpy.prod>` | :cpp:func:`xt::prod(a, {0, 1}) <xt::prod>` |
+---------------------------------------------------------------+--------------------------------------------------------------+
| :any:`np.prod(a, axis=1) <numpy.prod>` | :cpp:func:`xt::prod(a, 1) <xt::prod>` |
+---------------------------------------------------------------+--------------------------------------------------------------+
| :any:`np.prod(a) <numpy.prod>` | :cpp:func:`xt::prod(a) <xt::prod>` |
+---------------------------------------------------------------+--------------------------------------------------------------+
| :any:`np.mean(a, axis=(0, 1)) <numpy.mean>` | :cpp:func:`xt::mean(a, {0, 1}) <xt::mean>` |
+---------------------------------------------------------------+--------------------------------------------------------------+
| :any:`np.mean(a, axis=1) <numpy.mean>` | :cpp:func:`xt::mean(a, 1) <xt::mean>` |
+---------------------------------------------------------------+--------------------------------------------------------------+
| :any:`np.mean(a) <numpy.mean>` | :cpp:func:`xt::mean(a) <xt::mean>` |
+---------------------------------------------------------------+--------------------------------------------------------------+
| :any:`np.std(a, [axis]) <numpy.std>` | :cpp:func:`xt::stddev(a, [axis]) <xt::stddev>` |
+---------------------------------------------------------------+--------------------------------------------------------------+
| :any:`np.var(a, [axis]) <numpy.var>` | :cpp:func:`xt::variance(a, [axis]) <xt::variance>` |
+---------------------------------------------------------------+--------------------------------------------------------------+
| :any:`np.diff(a[, n, axis]) <numpy.diff>` | :cpp:func:`xt::diff(a[, n, axis]) <xt::diff>` |
+---------------------------------------------------------------+--------------------------------------------------------------+
| :any:`np.trapz(a, dx=2.0, axis=-1) <numpy.trapz>` | :cpp:func:`xt::trapz(a, 2.0, -1) <xt::trapz>` |
+---------------------------------------------------------------+--------------------------------------------------------------+
| :any:`np.trapz(a, x=b, axis=-1) <numpy.trapz>` | :cpp:func:`xt::trapz(a, b, -1) <xt::trapz>` |
+---------------------------------------------------------------+--------------------------------------------------------------+
| :any:`np.count_nonzero(a, axis=(0, 1)) <numpy.count_nonzero>` | :cpp:func:`xt::count_nonzero(a, {0, 1}) <xt::count_nonzero>` |
+---------------------------------------------------------------+--------------------------------------------------------------+
| :any:`np.count_nonzero(a, axis=1) <numpy.count_nonzero>` | :cpp:func:`xt::count_nonzero(a, 1) <xt::count_nonzero>` |
+---------------------------------------------------------------+--------------------------------------------------------------+
| :any:`np.count_nonzero(a) <numpy.count_nonzero>` | :cpp:func:`xt::count_nonzero(a) <xt::count_nonzero>` |
+---------------------------------------------------------------+--------------------------------------------------------------+
More generally, one can use the :cpp:func:`xt::reduce(function, input, axes) <xt::reduce>` which allows the specification
of an arbitrary binary function for the reduction.
The binary function must be commutative and associative up to rounding errors.
NaN functions
-------------
NaN functions allow disregarding NaNs during computation, changing the effective number of elements
considered in reductions.
.. list-table::
:widths: 50 50
:header-rows: 1
* - Python3 - NumPy
- C++14 - xtensor
* - :any:`np.nan_to_num(a) <numpy.nan_to_num>`
- :cpp:func:`xt::nan_to_num(a) <xt::nan_to_num>`
* - :any:`np.nanmin(a) <numpy.nanmin>`
- :cpp:func:`xt::nanmin(a) <xt::nanmin>`
* - :any:`np.nanmin(a, axis=(0, 1)) <numpy.nanmin>`
- :cpp:func:`xt::nanmin(a, {0, 1}) <xt::nanmin>`
* - :any:`np.nanmax(a) <numpy.nanmax>`
- :cpp:func:`xt::nanmax(a) <xt::nanmax>`
* - :any:`np.nanmax(a, axis=(0, 1)) <numpy.nanmax>`
- :cpp:func:`xt::nanmax(a, {0, 1}) <xt::nanmax>`
* - :any:`np.nansum(a) <numpy.nansum>`
- :cpp:func:`xt::nansum(a) <xt::nansum>`
* - :any:`np.nansum(a, axis=0) <numpy.nansum>`
- :cpp:func:`xt::nansum(a, 0) <xt::nansum>`
* - :any:`np.nansum(a, axis=(0, 1)) <numpy.nansum>`
- :cpp:func:`xt::nansum(a, {0, 1}) <xt::nansum>`
* - :any:`np.nanprod(a) <numpy.nanprod>`
- :cpp:func:`xt::nanprod(a) <xt::nanprod>`
* - :any:`np.nanprod(a, axis=0) <numpy.nanprod>`
- :cpp:func:`xt::nanprod(a, 0) <xt::nanprod>`
* - :any:`np.nanprod(a, axis=(0, 1)) <numpy.nanprod>`
- :cpp:func:`xt::nanprod(a, {0, 1}) <xt::nanprod>`
* - :any:`np.nancumsum(a) <numpy.nancumsum>`
- :cpp:func:`xt::nancumsum(a) <xt::nancumsum>`
* - :any:`np.nancumsum(a, axis=0) <numpy.nancumsum>`
- :cpp:func:`xt::nancumsum(a, 0) <xt::nancumsum>`
* - :any:`np.nancumprod(a) <numpy.nancumsum>`
- :cpp:func:`xt::nancumsum(a) <xt::nancumsum>`
* - :any:`np.nancumprod(a, axis=0) <numpy.nancumsum>`
- :cpp:func:`xt::nancumsum(a, 0) <xt::nancumsum>`
* - :any:`np.nanmean(a) <numpy.nanmean>`
- :cpp:func:`xt::nanmean(a) <xt::nanmean>`
* - :any:`np.nanmean(a, axis=(0, 1)) <numpy.nanmean>`
- :cpp:func:`xt::nanmean(a, {0, 1}) <xt::nanmean>`
* - :any:`np.nanvar(a) <numpy.nanvar>`
- :cpp:func:`xt::nanvar(a) <xt::nanvar>`
* - :any:`np.nanvar(a, axis=(0, 1)) <numpy.nanvar>`
- :cpp:func:`xt::nanvar(a, {0, 1}) <xt::nanvar>`
* - :any:`np.nanstd(a) <numpy.nanstd>`
- :cpp:func:`xt::nanstd(a) <xt::nanstd>`
* - :any:`np.nanstd(a, axis=(0, 1)) <numpy.nanstd>`
- :cpp:func:`xt::nanstd(a, {0, 1}) <xt::nanstd>`
I/O
---
**Print options**
These options determine the way floating point numbers, tensors and other xtensor expressions are displayed.
.. table::
:widths: 50 50
+--------------------------------------------------------------------+----------------------------------------------------------------------------------------+
| Python 3 - NumPy | C++ 14 - xtensor |
+====================================================================+========================================================================================+
| :any:`np.set_printoptions(precision=4) <numpy.set_printoptions>` | :cpp:func:`xt::print_options::set_precision(4) <xt::print_options::set_precision>` |
+--------------------------------------------------------------------+----------------------------------------------------------------------------------------+
| :any:`np.set_printoptions(threshold=5) <numpy.set_printoptions>` | :cpp:func:`xt::print_options::set_threshold(5) <xt::print_options::set_threshold>` |
+--------------------------------------------------------------------+----------------------------------------------------------------------------------------+
| :any:`np.set_printoptions(edgeitems=3) <numpy.set_printoptions>` | :cpp:func:`xt::print_options::set_edgeitems(3) <xt::print_options::set_edgeitems>` |
+--------------------------------------------------------------------+----------------------------------------------------------------------------------------+
| :any:`np.set_printoptions(linewidth=100) <numpy.set_printoptions>` | :cpp:func:`xt::print_options::set_line_width(100) <xt::print_options::set_line_width>` |
+--------------------------------------------------------------------+----------------------------------------------------------------------------------------+
**Reading npy, csv file formats**
Functions :cpp:func:`xt::load_csv` and :cpp:func:`xt::dump_csv` respectively take input and output streams as arguments.
.. table::
:widths: 50 50
+------------------------------------------------------------+-------------------------------------------------------------+
| Python 3 - NumPy | C++ 14 - xtensor |
+============================================================+=============================================================+
| :any:`np.load(filename) <numpy.load>` | :cpp:func:`xt::load_npy\<double\>(filename) <xt::load_npy>` |
+------------------------------------------------------------+-------------------------------------------------------------+
| :any:`np.save(filename, arr) <numpy.save>` | :cpp:func:`xt::dump_npy(filename, arr) <xt::dump_npy>` |
+------------------------------------------------------------+-------------------------------------------------------------+
| :any:`np.loadtxt(filename, delimiter=',') <numpy.loadtxt>` | :cpp:func:`xt::load_csv\<double\>(stream) <xt::load_csv>` |
+------------------------------------------------------------+-------------------------------------------------------------+
Mathematical functions
----------------------
xtensor universal functions are provided for a large set number of mathematical functions.
**Basic functions:**
.. table::
:widths: 50 50
+------------------------------------------------------------+----------------------------------------------------------------+
| Python 3 - NumPy | C++ 14 - xtensor |
+============================================================+================================================================+
| :any:`np.absolute(a) <numpy.absolute>` | :cpp:func:`xt::abs(a) <xt::abs>` |
+------------------------------------------------------------+----------------------------------------------------------------+
| :any:`np.sign(a) <numpy.sign>` | :cpp:func:`xt::sign(a) <xt::sign>` |
+------------------------------------------------------------+----------------------------------------------------------------+
| :any:`np.remainder(a, b) <numpy.remainder>` | :cpp:func:`xt::remainder(a, b) <xt::remainder>` |
+------------------------------------------------------------+----------------------------------------------------------------+
| :any:`np.minimum(a, b) <numpy.minimum>` | :cpp:func:`xt::minimum(a, b) <xt::minimum>` |
+------------------------------------------------------------+----------------------------------------------------------------+
| :any:`np.maximum(a, b) <numpy.maximum>` | :cpp:func:`xt::maximum(a, b) <xt::maximum>` |
+------------------------------------------------------------+----------------------------------------------------------------+
| :any:`np.clip(a, min, max) <numpy.clip>` | :cpp:func:`xt::clip(a, min, max) <xt::clip>` |
+------------------------------------------------------------+----------------------------------------------------------------+
| | :cpp:func:`xt::fma(a, b, c) <xt::fma>` |
+------------------------------------------------------------+----------------------------------------------------------------+
| :any:`np.interp(x, xp, fp, [,left, right]) <numpy.interp>` | :cpp:func:`xt::interp(x, xp, fp, [,left, right]) <xt::interp>` |
+------------------------------------------------------------+----------------------------------------------------------------+
| :any:`np.rad2deg(a) <numpy.rad2deg>` | :cpp:func:`xt::rad2deg(a) <xt::rad2deg>` |
+------------------------------------------------------------+----------------------------------------------------------------+
| :any:`np.degrees(a) <numpy.degrees>` | :cpp:func:`xt::degrees(a) <xt::degrees>` |
+------------------------------------------------------------+----------------------------------------------------------------+
| :any:`np.deg2rad(a) <numpy.deg2rad>` | :cpp:func:`xt::deg2rad(a) <xt::deg2rad>` |
+------------------------------------------------------------+----------------------------------------------------------------+
| :any:`np.radians(a) <numpy.radians>` | :cpp:func:`xt::radians(a) <xt::radians>` |
+------------------------------------------------------------+----------------------------------------------------------------+
**Exponential functions:**
.. table::
:widths: 50 50
+----------------------------------+--------------------------------------+
| Python 3 - NumPy | C++ 14 - xtensor |
+==================================+======================================+
| :any:`np.exp(a) <numpy.exp>` | :cpp:func:`xt::exp(a) <xt::exp>` |
+----------------------------------+--------------------------------------+
| :any:`np.expm1(a) <numpy.expm1>` | :cpp:func:`xt::expm1(a) <xt::expm1>` |
+----------------------------------+--------------------------------------+
| :any:`np.log(a) <numpy.log>` | :cpp:func:`xt::log(a) <xt::log>` |
+----------------------------------+--------------------------------------+
| :any:`np.log1p(a) <numpy.log1p>` | :cpp:func:`xt::log1p(a) <xt::log1p>` |
+----------------------------------+--------------------------------------+
**Power functions:**
.. table::
:widths: 50 50
+-------------------------------------+----------------------------------------+
| Python 3 - NumPy | C++ 14 - xtensor |
+=====================================+========================================+
| :any:`np.power(a, p) <numpy.power>` | :cpp:func:`xt::pow(a, b) <xt::pow>` |
+-------------------------------------+----------------------------------------+
| :any:`np.sqrt(a) <numpy.sqrt>` | :cpp:func:`xt::sqrt(a) <xt::sqrt>` |
+-------------------------------------+----------------------------------------+
| :any:`np.square(a) <numpy.square>` | :cpp:func:`xt::square(a) <xt::square>` |
| | :cpp:func:`xt::cube(a) <xt::cube>` |
+-------------------------------------+----------------------------------------+
| :any:`np.cbrt(a) <numpy.cbrt>` | :cpp:func:`xt::cbrt(a) <xt::cbrt>` |
+-------------------------------------+----------------------------------------+
**Trigonometric functions:**
.. table::
:widths: 50 50
+------------------------------+----------------------------------+
| Python 3 - NumPy | C++ 14 - xtensor |
+==============================+==================================+
| :any:`np.sin(a) <numpy.sin>` | :cpp:func:`xt::sin(a) <xt::sin>` |
+------------------------------+----------------------------------+
| :any:`np.cos(a) <numpy.cos>` | :cpp:func:`xt::cos(a) <xt::cos>` |
+------------------------------+----------------------------------+
| :any:`np.tan(a) <numpy.tan>` | :cpp:func:`xt::tan(a) <xt::tan>` |
+------------------------------+----------------------------------+
**Hyperbolic functions:**
.. table::
:widths: 50 50
+--------------------------------+------------------------------------+
| Python 3 - NumPy | C++ 14 - xtensor |
+================================+====================================+
| :any:`np.sinh(a) <numpy.sinh>` | :cpp:func:`xt::sinh(a) <xt::sinh>` |
+--------------------------------+------------------------------------+
| :any:`np.cosh(a) <numpy.cosh>` | :cpp:func:`xt::cosh(a) <xt::cosh>` |
+--------------------------------+------------------------------------+
| :any:`np.tanh(a) <numpy.tanh>` | :cpp:func:`xt::tanh(a) <xt::tanh>` |
+--------------------------------+------------------------------------+
**Error and gamma functions:**
.. table::
:widths: 50 50
+---------------------------------------------------------+----------------------------------------+
| Python 3 - NumPy | C++ 14 - xtensor |
+=========================================================+========================================+
| :any:`scipy.special.erf(a) <scipy.special.erf>` | :cpp:func:`xt::erf(a) <xt::erf>` |
+---------------------------------------------------------+----------------------------------------+
| :any:`scipy.special.gamma(a) <scipy.special.gamma>` | :cpp:func:`xt::tgamma(a) <xt::tgamma>` |
+---------------------------------------------------------+----------------------------------------+
| :any:`scipy.special.gammaln(a) <scipy.special.gammaln>` | :cpp:func:`xt::lgamma(a) <xt::lgamma>` |
+---------------------------------------------------------+----------------------------------------+
**Classification functions:**
.. table::
:widths: 50 50
+-----------------------------------------------------------+----------------------------------------------------------------+
| Python 3 - NumPy | C++ 14 - xtensor |
+===========================================================+================================================================+
| :any:`np.isnan(a) <numpy.isnan>` | :cpp:func:`xt::isnan(a) <xt::isnan>` |
+-----------------------------------------------------------+----------------------------------------------------------------+
| :any:`np.isinf(a) <numpy.isinf>` | :cpp:func:`xt::isinf(a) <xt::isinf>` |
+-----------------------------------------------------------+----------------------------------------------------------------+
| :any:`np.isfinite(a) <numpy.isfinite>` | :cpp:func:`xt::isfinite(a) <xt::isfinite>` |
+-----------------------------------------------------------+----------------------------------------------------------------+
| :any:`np.searchsorted(a, v[, side]) <numpy.searchsorted>` | :cpp:func:`xt::searchsorted(a, v[, right]) <xt::searchsorted>` |
+-----------------------------------------------------------+----------------------------------------------------------------+
**Histogram:**
.. table::
:widths: 50 50
+--------------------------------------------------------------------------------------------------------------+------------------------------------------------------------------------------------------------------------------+
| Python 3 - NumPy | C++ 14 - xtensor |
+==============================================================================================================+==================================================================================================================+
| :any:`np.histogram(a, bins[, weights][, density]) <numpy.histogram>` | :cpp:func:`xt::histogram(a, bins[, weights][, density]) <xt::histogram>` |
+--------------------------------------------------------------------------------------------------------------+------------------------------------------------------------------------------------------------------------------+
| :any:`np.histogram_bin_edges(a, bins[, weights][, left, right][, bins][, mode]) <numpy.histogram_bin_edges>` | :cpp:func:`xt::histogram_bin_edges(a, bins[, weights][, left, right][, bins][, mode]) <xt::histogram_bin_edges>` |
+--------------------------------------------------------------------------------------------------------------+------------------------------------------------------------------------------------------------------------------+
| :any:`np.bincount(arr) <numpy.bincount>` | :cpp:func:`xt::bincount(arr) <xt::bincount>` |
+--------------------------------------------------------------------------------------------------------------+------------------------------------------------------------------------------------------------------------------+
| :any:`np.digitize(data, bin_edges[, right]) <numpy.digitize>` | :cpp:func:`xt::digitize(data, bin_edges[, right][, assume_sorted]) <xt::digitize>` |
+--------------------------------------------------------------------------------------------------------------+------------------------------------------------------------------------------------------------------------------+
See :ref:`histogram`.
**Numerical constants:**
.. table::
:widths: 50 50
+------------------+----------------------------------------------------------------------------+
| Python 3 - NumPy | C++ 14 - xtensor |
+==================+============================================================================+
| :any:`numpy.pi` | :cpp:var:`xt::numeric_constants\<double\>::PI <xt::numeric_constants::PI>` |
+------------------+----------------------------------------------------------------------------+
Linear algebra
--------------
Many functions found in the :any:`numpy.linalg` module are implemented in `xtensor-blas`_, a separate package offering BLAS and LAPACK bindings,
as well as a convenient interface replicating the ``linalg`` module.
Please note, however, that while we're trying to be as close to NumPy as possible, some features are not
implemented yet. Most prominently that is broadcasting for all functions except for :cpp:func:`xt::linalg::dot`.
**Matrix, vector and tensor products**
.. table::
:widths: 50 50
+-------------------------------------------------------------------+---------------------------------------------------------------------------------+
| Python 3 - NumPy | C++ 14 - xtensor |
+===================================================================+=================================================================================+
| :any:`np.dot(a, b) <numpy.dot>` | :cpp:func:`xt::linalg::dot(a, b) <xt::linalg::dot>` |
+-------------------------------------------------------------------+---------------------------------------------------------------------------------+
| :any:`np.vdot(a, b) <numpy.vdot>` | :cpp:func:`xt::linalg::vdot(a, b) <xt::linalg::vdot>` |
+-------------------------------------------------------------------+---------------------------------------------------------------------------------+
| :any:`np.outer(a, b) <numpy.outer>` | :cpp:func:`xt::linalg::outer(a, b) <xt::linalg::outer>` |
+-------------------------------------------------------------------+---------------------------------------------------------------------------------+
| :any:`np.linalg.matrix_power(a, 123) <numpy.linalg.matrix_power>` | :cpp:func:`xt::linalg::matrix_power(a, 123) <xt::linalg::matrix_power>` |
+-------------------------------------------------------------------+---------------------------------------------------------------------------------+
| :any:`np.kron(a, b) <numpy.kron>` | :cpp:func:`xt::linalg::kron(a, b) <xt::linalg::kron>` |
+-------------------------------------------------------------------+---------------------------------------------------------------------------------+
| :any:`np.tensordot(a, b, axes=3) <numpy.tensordot>` | :cpp:func:`xt::linalg::tensordot(a, b, 3) <xt::linalg::tensordot>` |
+-------------------------------------------------------------------+---------------------------------------------------------------------------------+
| :any:`np.tensordot(a, b, axes=((0,2),(1,3)) <numpy.tensordot>` | :cpp:func:`xt::linalg::tensordot(a, b, {0, 2}, {1, 3}) <xt::linalg::tensordot>` |
+-------------------------------------------------------------------+---------------------------------------------------------------------------------+
**Decompositions**
.. table::
:widths: 50 50
+------------------------------------------------------+------------------------------------------------------------+
| Python 3 - NumPy | C++ 14 - xtensor |
+======================================================+============================================================+
| :any:`np.linalg.cholesky(a) <numpy.linalg.cholesky>` | :cpp:func:`xt::linalg::cholesky(a) <xt::linalg::cholesky>` |
+------------------------------------------------------+------------------------------------------------------------+
| :any:`np.linalg.qr(a) <numpy.linalg.qr>` | :cpp:func:`xt::linalg::qr(a) <xt::linalg::qr>` |
+------------------------------------------------------+------------------------------------------------------------+
| :any:`np.linalg.svd(a) <numpy.linalg.svd>` | :cpp:func:`xt::linalg::svd(a) <xt::linalg::svd>` |
+------------------------------------------------------+------------------------------------------------------------+
**Matrix eigenvalues**
.. table::
:widths: 50 50
+------------------------------------------------------+------------------------------------------------------------+
| Python 3 - NumPy | C++ 14 - xtensor |
+======================================================+============================================================+
| :any:`np.linalg.eig(a) <numpy.linalg.eig>` | :cpp:func:`xt::linalg::eig(a) <xt::linalg::eig>` |
+------------------------------------------------------+------------------------------------------------------------+
| :any:`np.linalg.eigvals(a) <numpy.linalg.eigvals>` | :cpp:func:`xt::linalg::eigvals(a) <xt::linalg::eigvals>` |
+------------------------------------------------------+------------------------------------------------------------+
| :any:`np.linalg.eigh(a) <numpy.linalg.eigh>` | :cpp:func:`xt::linalg::eigh(a) <xt::linalg::eigh>` |
+------------------------------------------------------+------------------------------------------------------------+
| :any:`np.linalg.eigvalsh(a) <numpy.linalg.eigvalsh>` | :cpp:func:`xt::linalg::eigvalsh(a) <xt::linalg::eigvalsh>` |
+------------------------------------------------------+------------------------------------------------------------+
**Norms and other numbers**
.. table::
:widths: 50 50
+------------------------------------------------------------+------------------------------------------------------------------+
| Python 3 - NumPy | C++ 14 - xtensor |
+============================================================+==================================================================+
| :any:`np.linalg.norm(a, order=2) <numpy.linalg.norm>` | :cpp:func:`xt::linalg::norm(a, 2) <xt::linalg::norm>` |
+------------------------------------------------------------+------------------------------------------------------------------+
| :any:`np.linalg.cond(a) <numpy.linalg.cond>` | :cpp:func:`xt::linalg::cond(a) <xt::linalg::cond>` |
+------------------------------------------------------------+------------------------------------------------------------------+
| :any:`np.linalg.det(a) <numpy.linalg.det>` | :cpp:func:`xt::linalg::det(a) <xt::linalg::det>` |
+------------------------------------------------------------+------------------------------------------------------------------+
| :any:`np.linalg.matrix_rank(a) <numpy.linalg.matrix_rank>` | :cpp:func:`xt::linalg::matrix_rank(a) <xt::linalg::matrix_rank>` |
+------------------------------------------------------------+------------------------------------------------------------------+
| :any:`np.linalg.slogdet(a) <numpy.linalg.slogdet>` | :cpp:func:`xt::linalg::slogdet(a) <xt::linalg::slogdet>` |
+------------------------------------------------------------+------------------------------------------------------------------+
| :any:`np.trace(a) <numpy.trace>` | :cpp:func:`xt::linalg::trace(a) <xt::linalg::trace>` |
+------------------------------------------------------------+------------------------------------------------------------------+
**Solving equations and inverting matrices**
.. table::
:widths: 50 50
+---------------------------------------------------+---------------------------------------------------------+
| Python 3 - NumPy | C++ 14 - xtensor |
+===================================================+=========================================================+
| :any:`np.linalg.inv(a) <numpy.linalg.inv>` | :cpp:func:`xt::linalg::inv(a) <xt::linalg::inv>` |
+---------------------------------------------------+---------------------------------------------------------+
| :any:`np.linalg.pinv(a) <numpy.linalg.pinv>` | :cpp:func:`xt::linalg::pinv(a) <xt::linalg::pinv>` |
+---------------------------------------------------+---------------------------------------------------------+
| :any:`np.linalg.solve(A, b) <numpy.linalg.solve>` | :cpp:func:`xt::linalg::solve(A, b) <xt::linalg::solve>` |
+---------------------------------------------------+---------------------------------------------------------+
| :any:`np.linalg.lstsq(A, b) <numpy.linalg.lstsq>` | :cpp:func:`xt::linalg::lstsq(A, b) <xt::linalg::lstsq>` |
+---------------------------------------------------+---------------------------------------------------------+
.. _`xtensor-blas`: https://github.com/xtensor-stack/xtensor-blas
|
