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.

# 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()

Allocate dense matrix

Allocate a dense matrix in the MAPDL workspace.

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

Copy matrices as NumPy arrays

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

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

Solve using PyAnsys Math

Solve the dense matrix linear system using PyAnsys Math.

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")

Solving a (1000 x 1000) dense linear system using PyAnsys Math...
Elapsed time to solve the linear system using PyAnsys Math: 0.04627346992492676 seconds

Get norm of solution

Get the norm of the PyAnsys Math solution.

mm.norm(x)

1.000000000000001

Solve using NumPy

Solve the dense matrix linear system using NumPy.

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")

Solving a (1000 x 1000) dense linear system using NumPy...
Elapsed time to solve the linear system using NumPy: 0.18213391304016113 seconds

Plot elapsed times

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

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()

Get norm of solution

Get the norm of the NumPy solution.

npl.norm(x_py)

0.9999999999999996

Stop PyAnsys Math

Stop PyAnsys Math.

mm._mapdl.exit()

/opt/hostedtoolcache/Python/3.10.14/x64/lib/python3.10/site-packages/ansys/mapdl/core/launcher.py:811: UserWarning: The environment variable 'PYMAPDL_START_INSTANCE' is set, hence the argument 'start_instance' is overwritten.
  warnings.warn(