# PyAnsys Math documentation#

## Introduction#

PyAnsys Math aims to gather all mathematical calculation tools present in Ansys software.

This Python library allows you to access and manipulate large sparse matrices and solve a variety of eigenproblems. It is presented in a similar manner to the popular NumPy and SciPy libraries.

The command set for PyAnsys Math is based on tools for manipulating large mathematical matrices and vectors that provide access to standard linear algebra operations and the powerful sparse linear solvers of Ansys Mechanical APDL (MAPDL), providing the ability to solve eigenproblems.

Python and MATLAB eigensolvers are based on the publicly available LAPACK libraries and provide reasonable solve times for eigenproblems with relatively small degrees of freedom (DOF), perhaps 100,000. However, Ansys solvers are designed for the scale of hundreds of millions of DOF, providing a variety of situations where you can directly leverage Ansys high-performance solvers on a variety of eigenproblems. Fortunately, you can leverage this without relearning an entirely new language because PyAnsys Math is written in a similar manner as the NumPy and SciPy libraries. For example, here is a comparison between the NumPy and SciPy linear algebra solvers and the PyAnsys Math solver:

NumPy and SciPy |
PyAnsys Math |
---|---|

```
k_py = k + sparse.triu(k, 1).T
m_py = m + sparse.triu(m, 1).T
n = 10
ev = linalg.eigsh(k_py, k=neqv, M=m_py)
``` |
```
k = mm.matrix(k_py, triu=True)
m = mm.matrix(m_py, triu=True)
n = 10
ev = mm.eigs(n, k, m)
``` |

## Background#

PyAnsys Math uses the MAPDL solver in the background. It is based on the
`launch_mapdl()`

method from PyMAPDL’s ansys-mapdl-core
package.

Because PyMAPDL is gRPC-based, the MAPDL solver can function as a server, ready to respond to connecting clients. With gRPC establishing secure connections, a client app can directly call methods on a potentially remote MAPDL instance as if it were a local object. The use of HTTP/2 makes gRPC friendly to modern internet infrastructures. This, along with the use of binary transmission formats, favors higher performance.

## Quick code#

Here is a brief example of how you use PyAnsys Math:

```
import ansys.math.core.math as pymath
mm = pymath.AnsMath()
u = mm.ones(5)
v = mm.rand(5)
w = u + v
print(w)
```

```
UDWZKD :
Size : 5
1.417e+00 1.997e+00 1.720e+00 1.933e+00 1.000e+00 < 5
```

For comprehensive PyAnsys Math examples, see Examples.