Programmable filter - eigenvalues/lambda2

[bastian]

@flotus1

My script looks like this:

import numpy as np
from vtk.numpy_interface import algorithms as algs

input=inputs[0]
Velocity_Vector = input.PointData['velocity']
STRAIN = strain(Velocity_Vector)
V_gradient = gradient(Velocity_Vector)
AAA=STRAIN**2+(V_gradient - STRAIN)**2
print(shape(AAA))
Lambda_2 = np.linalg.eigvals(AAA[:])
Lambda_2 = np.real(Lambda_2)
output.PointData.append(Lambda_2, 'Lambda_2')

I think that you have a few errors in your code:

1. STRAIN**2 is probably an elementwise square. What you actually want is the matrix product that matches the signature (n,k),(k,m)→(n,m), which matmul should provide
2. np.linalg.eigvals does not order the eigenvalues, but you want lambda_2 to correspond to the second largest eigenvalue.

I wrote a filter that should give you the proper result, but I haven’t validated it:

import numpy as np
from vtk.numpy_interface import algorithms as algs

# Compute the lambda_2 Vortex criterion, see pp.76-77 in
# J. Jeong and F. Hussain, “On the identification of a vortex,” 
#  Journal of Fluid Mechanics, vol. 285, pp. 69–94, 1995, doi: 10.1017/S0022112095000462.

vvector = inputs[0].PointData['velocity']

vstrain = strain(vvector)
vskew = gradient(vvector) - vstrain

aaa = matmul(vstrain, vstrain) + matmul(vskew, vskew)

# since aaa is symmetric, it only has real eigenvalues
lambdas = eigenvalue(aaa)
lambdas = real(lambdas)
lambda2 = sort(lambdas)[:,1]

output.PointData.append(lambda2, 'lambda2')