PyAnsys Math basic operations

This tutorial shows how you can use PyAnsys Math for basic operations on AnsMath vectors and matrices in the APDL memory workspace.

Perform required imports and start PyAnsys

Perform required imports.

import matplotlib.pyplot as plt
import numpy as np

import ansys.math.core.math as pymath

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

Create and manipulate vectors

Create two AnsMath vectors of size 5. The \(\vec{v}\) method is initialized with ones, and the \(\vec{w}\) is filled with random values.

v = mm.ones(2)
w = mm.rand(2)
print(v)
print(w)

SPFKEP :
 Size : 2
  1.000e+00   1.000e+00
JNYLAR :
 Size : 2
  4.170e-01   9.972e-01

Plot vectors

Plot the created vectors.

origin = np.array([[0, 0], [0, 0]])
plt.title("Vectors V and W")
plt.quiver(*origin, v, w, angles="xy", scale_units="xy", scale=1, color=["orange", "gray"])
plt.xlim(-1.5, 1.5)
plt.ylim(-1.5, 1.5)
plt.show()

Use operators on vectors

Like NumPy vectors, AnsMath vectors can use most of the standard operators, such as +, -, +=, -=, and *=.

Here this form is used: \(\vec{z}=\vec{v}+\vec{w}\)

Compute \(\|z\|_2\). (The default norm is nrm2. Note that you can use .norm('nrm1') or .norm('nrminf') for different normals. For more information, see help(z.norm).

z = v + w
z.norm()

2.448815734735383

Methods

Alternatively you can use methods, following the NumPy standards. Available methods are:

• mm.add()

• mm.subtract()

• mm.dot()

Equivalent operator for addition: z = v + w

z = mm.add(v, w)
z.norm()

2.448815734735383

Equivalent operator for subtraction: z = v - w

z = mm.subtract(v, w)
print(z)

ZXGAIX :
 Size : 2
  5.830e-01   2.815e-03

Equivalent dot operation for the product of two vectors:

vw = mm.dot(v, w)
print("Dot product :", str(vw))

Dot product : 1.4142068068031222

Perform in-place operations (without copying vectors)

Perform in-place addition.

v += v
print(v)

SPFKEP :
 Size : 2
  2.000e+00   2.000e+00

Perform in-place multiplication.

v *= 2
print(v)

SPFKEP :
 Size : 2
  4.000e+00   4.000e+00

Perform another in-place multiplication.

v /= 2.0
print(v)

SPFKEP :
 Size : 2
  2.000e+00   2.000e+00

Working with dense matrices

Allocate two dense matrices with random values.

m1 = mm.rand(4, 5)
m2 = mm.ones(4, 5)
m1, m2

(AnsMath dense matrix (4, 5, AnsMath dense matrix (4, 5)

Add these 2 dense matrices and then scale the result matrix.

m3 = m1 + m2
print(m3)

m3 *= 2
print(m3)

LKGFJC:
 [1,1]: 1.417e+00 [1,2]: 1.000e+00 [1,3]: 1.147e+00 [1,4]: 1.186e+00 [1,5]: 1.397e+00
 [2,1]: 1.997e+00 [2,2]: 1.128e+00 [2,3]: 1.236e+00 [2,4]: 1.388e+00 [2,5]: 1.936e+00
 [3,1]: 1.720e+00 [3,2]: 1.302e+00 [3,3]: 1.092e+00 [3,4]: 1.346e+00 [3,5]: 1.539e+00
 [4,1]: 1.933e+00 [4,2]: 1.999e+00 [4,3]: 1.397e+00 [4,4]: 1.670e+00 [4,5]: 1.846e+00
LKGFJC:
 [1,1]: 2.834e+00 [1,2]: 2.000e+00 [1,3]: 2.294e+00 [1,4]: 2.373e+00 [1,5]: 2.794e+00
 [2,1]: 3.994e+00 [2,2]: 2.256e+00 [2,3]: 2.472e+00 [2,4]: 2.776e+00 [2,5]: 3.871e+00
 [3,1]: 3.441e+00 [3,2]: 2.605e+00 [3,3]: 2.185e+00 [3,4]: 2.691e+00 [3,5]: 3.078e+00
 [4,1]: 3.865e+00 [4,2]: 3.998e+00 [4,3]: 2.793e+00 [4,4]: 3.339e+00 [4,5]: 3.693e+00

Transpose a matrix.

m4 = m3.T
print(m4)

UGYKWV:
 [1,1]: 2.834e+00 [1,2]: 3.994e+00 [1,3]: 3.441e+00 [1,4]: 3.865e+00
 [2,1]: 2.000e+00 [2,2]: 2.256e+00 [2,3]: 2.605e+00 [2,4]: 3.998e+00
 [3,1]: 2.294e+00 [3,2]: 2.472e+00 [3,3]: 2.185e+00 [3,4]: 2.793e+00
 [4,1]: 2.373e+00 [4,2]: 2.776e+00 [4,3]: 2.691e+00 [4,4]: 3.339e+00
 [5,1]: 2.794e+00 [5,2]: 3.871e+00 [5,3]: 3.078e+00 [5,4]: 3.693e+00

As for vectors, methods are available as an alternative to operators.

m3 = mm.add(m1, m2)
print(m3)

AQPSEI:
 [1,1]: 1.417e+00 [1,2]: 1.000e+00 [1,3]: 1.147e+00 [1,4]: 1.186e+00 [1,5]: 1.397e+00
 [2,1]: 1.997e+00 [2,2]: 1.128e+00 [2,3]: 1.236e+00 [2,4]: 1.388e+00 [2,5]: 1.936e+00
 [3,1]: 1.720e+00 [3,2]: 1.302e+00 [3,3]: 1.092e+00 [3,4]: 1.346e+00 [3,5]: 1.539e+00
 [4,1]: 1.933e+00 [4,2]: 1.999e+00 [4,3]: 1.397e+00 [4,4]: 1.670e+00 [4,5]: 1.846e+00

Compute a matrix vector multiplication.

mw = m3.dot(m4)
print(mw)

QLOFMT:
 [1,1]: 1.536e+01 [1,2]: 1.945e+01 [1,3]: 1.748e+01 [1,4]: 2.180e+01
 [2,1]: 1.945e+01 [2,2]: 2.492e+01 [2,3]: 2.220e+01 [2,4]: 2.746e+01
 [3,1]: 1.748e+01 [3,2]: 2.220e+01 [3,3]: 2.005e+01 [3,4]: 2.508e+01
 [4,1]: 2.180e+01 [4,2]: 2.746e+01 [4,3]: 2.508e+01 [4,4]: 3.176e+01

AnsMath matrices can be identified by printing, viewing their types, or using the __repr__ method by simply typing out the variable.

Here is an example with an AnsMath matrix.

type(m1)
print(m1)
m1

DSDZUU:
 [1,1]: 4.170e-01 [1,2]: 1.144e-04 [1,3]: 1.468e-01 [1,4]: 1.863e-01 [1,5]: 3.968e-01
 [2,1]: 9.972e-01 [2,2]: 1.281e-01 [2,3]: 2.361e-01 [2,4]: 3.879e-01 [2,5]: 9.355e-01
 [3,1]: 7.203e-01 [3,2]: 3.023e-01 [3,3]: 9.234e-02 [3,4]: 3.456e-01 [3,5]: 5.388e-01
 [4,1]: 9.326e-01 [4,2]: 9.990e-01 [4,3]: 3.966e-01 [4,4]: 6.697e-01 [4,5]: 8.463e-01

AnsMath dense matrix (4, 5

Here is an example with an AnsMath vector.

type(w)
print(w)
w

JNYLAR :
 Size : 2
  4.170e-01   9.972e-01

AnsMath vector size 2

Use NumPy methods on AnsMath objects

Regardless of the underlying AnsMath object type, you are generally able to perform most NumPy or SciPy operations on these arrays. You can do this in one of two ways.

You can convert a matrix to a NumPy array.

apdl_mat = mm.rand(5, 5)
np_mat = apdl_mat.asarray()
print(np_mat)

[[4.17021999e-01 1.28124448e-01 9.23385957e-02 6.69746040e-01
  4.19194519e-01]
 [9.97184808e-01 3.02332568e-01 3.96580726e-01 3.96767469e-01
  3.13273513e-01]
 [7.20324489e-01 9.99040516e-01 1.86260211e-01 9.35539073e-01
  6.85219501e-01]
 [9.32557361e-01 1.46755893e-01 3.87910740e-01 5.38816732e-01
  5.24548163e-01]
 [1.14381197e-04 2.36088976e-01 3.45560725e-01 8.46310918e-01
  2.04452249e-01]]

Alternatively, you can use NumPy to compute the maximum of the array.

This works because PyAnsys Math copies over the matrix to the local Python memory and then computes the maximum using NumPy.

print(np.max(apdl_mat))

0.9990405155112967

While this works for most NumPy operations, keep in mind that operations supported within PyAnsys Math (such as adding or multiplying arrays) compute much faster because the data is not copied.

apdl_arr = mm.rand(5, 5)
np_array = apdl_mat.asarray()
print(np.allclose(apdl_mat, np_array))

True

Stop PyAnsys Math

Stop PyAnsys Math.

mm._mapdl.exit()

/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(