.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "examples/gallery_examples/01-apdlmath-examples/solve_sparse_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_gallery_examples_01-apdlmath-examples_solve_sparse_matrix.py>`
to download the full example code
.. rst-class:: sphx-glr-example-title
.. _sphx_glr_examples_gallery_examples_01-apdlmath-examples_solve_sparse_matrix.py:
Performing Sparse Factorization and Solve Operations
----------------------------------------------------
Using APDLMath, you can solve linear systems of equations based on
sparse or dense matrices.
.. GENERATED FROM PYTHON SOURCE LINES 9-17
.. code-block:: default
from ansys.mapdl.core import launch_mapdl
from ansys.mapdl.core.examples import vmfiles
# Start MAPDL as a service and create an APDLMath object.
mapdl = launch_mapdl()
mm = mapdl.math
.. GENERATED FROM PYTHON SOURCE LINES 18-26
Factorize and Solve Sparse Linear Systems
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
First, run a MAPDL solve to create a .full file
We use a model from the official verification manual.
After a solve command, the full contains the assemblied stiffness
matrix, mass matrix, and the load vector.
.. GENERATED FROM PYTHON SOURCE LINES 26-28
.. code-block:: default
out = mapdl.input(vmfiles["vm153"])
.. GENERATED FROM PYTHON SOURCE LINES 29-31
List the files in current directory
.. GENERATED FROM PYTHON SOURCE LINES 31-33
.. code-block:: default
mapdl.list_files()
.. rst-class:: sphx-glr-script-out
.. code-block:: none
['11_blades_mode_1_ND_0.csv', 'BeforeMapping.db', 'ExampleMapping.db', 'HexBeam.cdb', 'Mapping.db', 'PRSMEMB.DSP', 'PRSMEMB.emat', 'PRSMEMB.esav', 'PRSMEMB.full', 'PRSMEMB.mntr', 'PRSMEMB.mode', 'PRSMEMB.rst', 'PRSMEMB000.jpg', 'PRSMEMB001.jpg', 'PRSMEMB002.jpg', 'PRSMEMB003.jpg', 'PRSMEMB004.jpg', 'PRSMEMB005.jpg', 'PRSMEMB006.jpg', 'PRSMEMB007.jpg', 'PRSMEMB008.jpg', 'PRSMEMB009.jpg', 'PRSMEMB010.jpg', 'PRSMEMB011.jpg', 'SCRATCH', 'SOLVIT.MAC', 'TABLE_1', 'TABLE_2', '__tmp_sys_out_xztubsvxaf__', '_tmp.iges', 'anaconda-post.log', 'anstmp', 'ansys_inc', 'baseModel.cdb', 'baseModel.iges', 'bin', 'bracket.iges', 'dev', 'etc', 'file.DSP', 'file.ans_log', 'file.emat', 'file.err', 'file.esav', 'file.full', 'file.ldhi', 'file.log', 'file.mlv', 'file.mntr', 'file.mode', 'file.page', 'file.r001', 'file.rdb', 'file.rsx', 'file.rth', 'file.stat', 'file000.jpg', 'file000.png', 'file001.png', 'file002.png', 'file003.png', 'file004.png', 'file005.png', 'file006.png', 'file007.png', 'file008.png', 'home', 'lib', 'lib64', 'mappedHI.dat', 'media', 'mnt', 'opt', 'proc', 'root', 'run', 'sbin', 'sector.cdb', 'srv', 'sys', 'tmp', 'tmp.cdb', 'usr', 'var', 'vm1.vrt', 'vm153.vrt', 'vm5.vrt']
.. GENERATED FROM PYTHON SOURCE LINES 34-41
Extract the Stiffness matrix from the ``FULL`` file, in a sparse
matrix format.
You can get help on the stiff function with ``help(mm.stiff)``
Printout the dimensions of this Sparse Matrix
.. GENERATED FROM PYTHON SOURCE LINES 41-44
.. code-block:: default
k = mm.stiff(fname="PRSMEMB.full")
k
.. rst-class:: sphx-glr-script-out
.. code-block:: none
Sparse APDLMath Matrix (126, 126)
.. GENERATED FROM PYTHON SOURCE LINES 45-47
Get a copy of the K Sparse Matrix as a Numpy Array
.. GENERATED FROM PYTHON SOURCE LINES 47-50
.. code-block:: default
ky = k.asarray()
ky
.. rst-class:: sphx-glr-script-out
.. code-block:: none
<126x126 sparse matrix of type '<class 'numpy.float64'>'
with 738 stored elements in Compressed Sparse Row format>
.. GENERATED FROM PYTHON SOURCE LINES 51-55
Extract the load vector from the ``FULL`` file.
Printout the norm of this vector.
.. GENERATED FROM PYTHON SOURCE LINES 55-58
.. code-block:: default
b = mm.rhs(fname="PRSMEMB.full")
b.norm()
.. rst-class:: sphx-glr-script-out
.. code-block:: none
3.472960080375275e-05
.. GENERATED FROM PYTHON SOURCE LINES 59-61
Get a copy of the load vector as a numpy array
.. GENERATED FROM PYTHON SOURCE LINES 61-63
.. code-block:: default
by = b.asarray()
.. GENERATED FROM PYTHON SOURCE LINES 64-66
Factorize the Stifness Matrix using the MAPDL DSPARSE solver
.. GENERATED FROM PYTHON SOURCE LINES 66-68
.. code-block:: default
s = mm.factorize(k)
.. GENERATED FROM PYTHON SOURCE LINES 69-71
Solve the linear system
.. GENERATED FROM PYTHON SOURCE LINES 71-73
.. code-block:: default
x = s.solve(b)
.. GENERATED FROM PYTHON SOURCE LINES 74-76
Print the **norm** of the solution vector
.. GENERATED FROM PYTHON SOURCE LINES 76-78
.. code-block:: default
x.norm()
.. rst-class:: sphx-glr-script-out
.. code-block:: none
5.815928297030328e-08
.. GENERATED FROM PYTHON SOURCE LINES 79-83
We check the accuracy of the solution, by verifying that
:math:`KX - B = 0`
.. GENERATED FROM PYTHON SOURCE LINES 83-87
.. code-block:: default
kx = k.dot(x)
kx -= b
print("Residual error:", kx.norm() / b.norm())
.. rst-class:: sphx-glr-script-out
.. code-block:: none
Residual error: 1.7052976316939208e-15
.. GENERATED FROM PYTHON SOURCE LINES 88-90
Summary of all allocated APDLMath Objects
.. GENERATED FROM PYTHON SOURCE LINES 90-92
.. code-block:: default
mm.status()
.. rst-class:: sphx-glr-script-out
.. code-block:: none
APDLMATH PARAMETER STATUS- ( 5 PARAMETERS DEFINED)
Name Type Mem. (MB) Dims Workspace
NBZSPJ SMAT 0.011 [126:126] 1
RMTGCR VEC 0.001 126 1
TTFCYO VEC 0.001 126 1
TZJMNX VEC 0.001 126 1
RIATWL LSENGINE -- -- 1
.. GENERATED FROM PYTHON SOURCE LINES 93-95
Delete all APDLMath Objects
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.. code-block:: default
mm.free()
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Stop mapdl
~~~~~~~~~~
.. GENERATED FROM PYTHON SOURCE LINES 102-103
.. code-block:: default
mapdl.exit()
.. rst-class:: sphx-glr-timing
**Total running time of the script:** ( 0 minutes 0.858 seconds)
.. _sphx_glr_download_examples_gallery_examples_01-apdlmath-examples_solve_sparse_matrix.py:
.. only:: html
.. container:: sphx-glr-footer sphx-glr-footer-example
.. container:: sphx-glr-download sphx-glr-download-python
:download:`Download Python source code: solve_sparse_matrix.py <solve_sparse_matrix.py>`
.. container:: sphx-glr-download sphx-glr-download-jupyter
:download:`Download Jupyter notebook: solve_sparse_matrix.ipynb <solve_sparse_matrix.ipynb>`
.. only:: html
.. rst-class:: sphx-glr-signature
`Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_