.. Copyright (c) 2017, Wolf Vollprecht, Johan Mabille and Sylvain Corlay

   Distributed under the terms of the BSD 3-Clause License.

   The full license is in the file LICENSE, distributed with this software.


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Usage
=====

To use xtensor-blas functions, the ``xlinalg.hpp`` header has to be included.
In the ``xt::linalg`` namespace, many of NumPy's ``np.linalg`` functions are implemented. 
We make an effort to keep the interfaces very similar.

For example, calculating a determinant:

.. highlight cpp

.. code-block:: cpp

    #include "xtensor-blas/xlinalg.hpp"
    
    int main()
    {
        xt::xarray<double> a = {{3, 2, 1}, {0, 4, 2}, {1, 3, 5}};
        auto d = xt::linalg::det(a);
        std::cout << d << std::endl;  // 42.0
    }

We can also try to compute the same determinant using the ``slogdet`` function, which
is more robust against under- or overflows by summing up the logarithm. The slogdet
function in NumPy returns a tuple of (sign, val). In C++, we emulate the behaviour by
returning a ``std::tuple``, which can be unpacked using ``std::get<N>(tuple)``.

.. code-block:: cpp

    xt::xarray<double> a = {{3, 2, 1}, {0, 4, 2}, {1, 3, 5}};
    auto d = xt::linalg::slogdet(a);
    std::cout << std::get<0>(d) << ", " << std::get<1>(d) << std::endl;  // +1, 3.7376696

Returning tuples is used throughout the xlinalg package.

Using xblas and xlapack directly
--------------------------------

It is not necessarily recommended to use ``xblas`` or ``xlapack`` directly, but it's possible and can improve performance in certain cases. Some things have to be taken into consideration:
For one thing, the result container needs to be allocated and passed into the
function beforehand. And for the LAPACK functions, all arguments have to be in column_major order.
Furthermore it's required that the xexpressions are evaluated and are stored in contiguous memory.
All of this is taken care of when using ``xlinalg``.
