.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "examples/solve_dense_matrix.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_examples_solve_dense_matrix.py>`
        to download the full example code.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_examples_solve_dense_matrix.py:


Use PyAnsys Math to solve a dense matrix linear system
------------------------------------------------------
This example shows how to use PyAnsys Math to solve a dense matrix linear system.

.. GENERATED FROM PYTHON SOURCE LINES 29-43

.. code-block:: Python

    # Perform required imports and start PyAnsys
    # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    # Perform required imports.

    import time

    import matplotlib.pyplot as plt
    import numpy.linalg as npl

    import ansys.math.core.math as pymath

    # Start PyAnsys Math as a server.
    mm = pymath.AnsMath()








.. GENERATED FROM PYTHON SOURCE LINES 44-47

Allocate dense matrix
~~~~~~~~~~~~~~~~~~~~~
Allocate a dense matrix in the MAPDL workspace.

.. GENERATED FROM PYTHON SOURCE LINES 47-54

.. code-block:: Python


    mm._mapdl.clear()
    dim = 1000
    a = mm.rand(dim, dim)
    b = mm.rand(dim)
    x = mm.zeros(dim)








.. GENERATED FROM PYTHON SOURCE LINES 55-60

Copy matrices as NumPy arrays
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Copy the matrices as NumPy arrays before they are modified by
a factorization call.


.. GENERATED FROM PYTHON SOURCE LINES 60-63

.. code-block:: Python

    a_py = a.asarray()
    b_py = b.asarray()








.. GENERATED FROM PYTHON SOURCE LINES 64-68

Solve using PyAnsys Math
~~~~~~~~~~~~~~~~~~~~~~~~
Solve the dense matrix linear system using PyAnsys Math.


.. GENERATED FROM PYTHON SOURCE LINES 68-77

.. code-block:: Python

    print(f"Solving a ({dim} x {dim}) dense linear system using PyAnsys Math...")

    t1 = time.time()
    s = mm.factorize(a)
    x = s.solve(b, x)
    t2 = time.time()
    pymath_time = t2 - t1
    print(f"Elapsed time to solve the linear system using PyAnsys Math: {pymath_time} seconds")





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    Solving a (1000 x 1000) dense linear system using PyAnsys Math...
    Elapsed time to solve the linear system using PyAnsys Math: 0.042484283447265625 seconds




.. GENERATED FROM PYTHON SOURCE LINES 78-81

Get norm of solution
~~~~~~~~~~~~~~~~~~~~
Get the norm of the PyAnsys Math solution.

.. GENERATED FROM PYTHON SOURCE LINES 81-84

.. code-block:: Python

    mm.norm(x)






.. rst-class:: sphx-glr-script-out

 .. code-block:: none


    1.000000000000001



.. GENERATED FROM PYTHON SOURCE LINES 85-89

Solve using NumPy
~~~~~~~~~~~~~~~~~
Solve the dense matrix linear system using NumPy.


.. GENERATED FROM PYTHON SOURCE LINES 89-97

.. code-block:: Python

    print(f"Solving a ({dim} x {dim}) dense linear system using NumPy...")

    t1 = time.time()
    x_py = npl.solve(a_py, b_py)
    t2 = time.time()
    numpy_time = t2 - t1
    print(f"Elapsed time to solve the linear system using NumPy: {numpy_time} seconds")





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    Solving a (1000 x 1000) dense linear system using NumPy...
    Elapsed time to solve the linear system using NumPy: 0.024129390716552734 seconds




.. GENERATED FROM PYTHON SOURCE LINES 98-103

Plot elapsed times
~~~~~~~~~~~~~~~~~~~
Plot the elapsed times for PyAnsys Math and Numpy to solve the dense
matrix linear system.


.. GENERATED FROM PYTHON SOURCE LINES 103-114

.. code-block:: Python

    max_time = max(pymath_time, numpy_time)
    fig = plt.figure(figsize=(12, 10))
    ax = plt.axes()
    x = ["PyAnsys Math", "NumPy"]
    y = [pymath_time, numpy_time]
    plt.title("Elapsed time to solve the linear system")
    plt.ylim([0, max_time + 0.2 * max_time])
    plt.ylabel("Elapsed time (s)")
    ax.bar(x, y, color="orange")
    plt.show()




.. image-sg:: /examples/images/sphx_glr_solve_dense_matrix_001.png
   :alt: Elapsed time to solve the linear system
   :srcset: /examples/images/sphx_glr_solve_dense_matrix_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 115-118

Get norm of solution
~~~~~~~~~~~~~~~~~~~~
Get the norm of the NumPy solution.

.. GENERATED FROM PYTHON SOURCE LINES 118-121

.. code-block:: Python


    npl.norm(x_py)





.. rst-class:: sphx-glr-script-out

 .. code-block:: none


    np.float64(0.9999999999999996)



.. GENERATED FROM PYTHON SOURCE LINES 122-125

Stop PyAnsys Math
~~~~~~~~~~~~~~~~~
Stop PyAnsys Math.

.. GENERATED FROM PYTHON SOURCE LINES 125-127

.. code-block:: Python


    mm._mapdl.exit()




.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    /home/runner/work/pyansys-math/pyansys-math/.venv/lib/python3.10/site-packages/ansys/mapdl/core/launcher.py:818: UserWarning: The environment variable 'PYMAPDL_START_INSTANCE' is set, hence the argument 'start_instance' is overwritten.
      warnings.warn(





.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 0.365 seconds)


.. _sphx_glr_download_examples_solve_dense_matrix.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: solve_dense_matrix.ipynb <solve_dense_matrix.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: solve_dense_matrix.py <solve_dense_matrix.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: solve_dense_matrix.zip <solve_dense_matrix.zip>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_