.. _onemkl_blas_nrm2:

nrm2
====

Computes the Euclidean norm of a vector.

Description
***********

The ``nrm2`` routines compute Euclidean norm of a vector. The operation is defined as:

.. math::

      result = ||x||

where:

- ``x`` is a vector of ``n`` elements

``nrm2`` supports the following precisions:

.. list-table::
   :header-rows: 1

   * -  T
     -  T_res
   * -  ``float``
     -  ``float``
   * -  ``double``
     -  ``double``
   * -  ``std::complex<float>``
     -  ``float``
   * -  ``std::complex<double>``
     -  ``double``


nrm2 (Buffer Version)
*********************

Syntax
------

.. code-block:: cpp

   namespace oneapi::mkl::blas::column_major {
       void nrm2(sycl::queue &queue,
                 std::int64_t n,
                 sycl::buffer<T,1> &x,
                 std::int64_t incx,
                 sycl::buffer<T_res,1> &result)
   }

.. code-block:: cpp

   namespace oneapi::mkl::blas::row_major {
       void nrm2(sycl::queue &queue,
                 std::int64_t n,
                 sycl::buffer<T,1> &x,
                 std::int64_t incx,
                 sycl::buffer<T_res,1> &result)
   }

Input Parameters
----------------

queue
   The queue where the routine should be executed.

n
   Number of elements in vector ``x``.

x
   Buffer holding input vector ``x``. Size of the buffer must be at
   least (1 + (``n`` - 1)*abs(``incx``)). See :ref:`matrix-storage` for more details. 

incx
   Stride of vector ``x``.

Output Parameters
-----------------

result
   Buffer where the Euclidean norm of the vector ``x`` is
   stored.


nrm2 (USM Version)
*********************

Syntax
------

.. code-block:: cpp

   namespace oneapi::mkl::blas::column_major {
       sycl::event nrm2(sycl::queue &queue,
                        std::int64_t n,
                        const T *x,
                        std::int64_t incx,
                        T_res *result,
                        const std::vector<sycl::event> &dependencies = {})
   }

.. code-block:: cpp

   namespace oneapi::mkl::blas::row_major {
       sycl::event nrm2(sycl::queue &queue,
                        std::int64_t n,
                        const T *x,
                        std::int64_t incx,
                        T_res *result,
                        const std::vector<sycl::event> &dependencies = {})
   }

Input Parameters
----------------

queue
   The queue where the routine should be executed.

n
   Number of elements in vector ``x``.

x
   Pointer to input vector ``x``. Size of the array holding input vector
   ``x`` must be at least (1 + (``n`` - 1)*abs(``incx``)). See :ref:`matrix-storage` for more details.

incx
   Stride of vector ``x``.

dependencies
   List of events to wait for before starting computation, if any. If
   omitted, defaults to no dependencies.

Output Parameters
-----------------

result
   Pointer to where the Euclidean norm of the vector ``x`` is stored.

Return Values
-------------

Output event to wait on to ensure computation is complete.