Use APDLMath to Solve a Dense Matrix Linear System

Use the APDLMath module to solve a Dense Matrix Linear System.

import time

import numpy.linalg as np

from ansys.mapdl.core import launch_mapdl

# Start MAPDL as a service and create an APDLMath object.
mapdl = launch_mapdl()
mm = mapdl.math

Allocate a Dense Matrix in the APDLMath workspace

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

Copy the matrices as numpy arrays before they are modified by factorization call

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

Solve using APDLMath

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

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

Solving a (1000 x 1000) dense linear system using MAPDL...
Elapsed time to solve the linear system using Mapdl: 0.017757177352905273 seconds

Norm of the MAPDL Solution

mm.norm(x)

1.0000000000000016

Solve the solution using numpy

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

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

Solving a (1000 x 1000) dense linear system using numpy...
Elapsed time to solve the linear system using numpy: 0.07700085639953613 seconds

Norm of the numpy Solution

np.linalg.norm(x_py)

0.9999999999999987

Stop mapdl

mapdl.exit()