Dear Andrew, I'm afraid that I don't know the most efficient way to do this sort of many small eigensolves, but you could get your solution in `np.ndarray` using `q_soln.dat.data` (`q_soln.dat` returns `PyOP2.Dat` object: https://op2.github.io/PyOP2/user.html#pyop2.Dat). You could also get the mesh data calling `mesh.coordinates.dat.data` . For instance:
from firedrake import * mesh = UnitSquareMesh(2,2) V = VectorFunctionSpace(mesh, "CG", 1) f = Function(V) f.dat.data array([[0., 0.], [0., 0.], [0., 0.], [0., 0.], [0., 0.], [0., 0.], [0., 0.], [0., 0.], [0., 0.]]) mesh.coordinates.dat.data array([[0. , 0. ], [0. , 0.5], [0.5, 0. ], [0.5, 0.5], [1. , 0. ], [0. , 1. ], [1. , 0.5], [0.5, 1. ], [1. , 1. ]])
I think you can use these data in your context. Taking a glance at the documentation, `numpy.linalg.eig` seems to take multiple matrices, so I think you can solve the node-wise eigen problems all at once. Thank you, Koki ________________________________ From: firedrake-bounces@imperial.ac.uk <firedrake-bounces@imperial.ac.uk> on behalf of Andrew Hicks <ahick17@lsu.edu> Sent: Friday, March 20, 2020 4:23 AM To: firedrake <firedrake@imperial.ac.uk> Subject: [firedrake] Returning eigenvectors of a solution to a PDE at each node Hello, I am currently using firedrake to solve a PDE. The solution to this PDE is vector-valued, and I have no problem finding the solution. However, I’d like to go a step further. I have named the solution “q_soln” and this is a 2-dimesional vector. I have used this vector to construct a 2x2 matrix at the node [0.5,0.5]. I then extracted an eigenvector from this matrix, and then I printed it: import numpy as np from numpy import linalg as la E1 = (1 / np.sqrt(2)) * np.array([[1,0],[0,-1]]) E2 = (1 / np.sqrt(2)) * np.array([[0,1],[1,0]]) # as an example, we evaluate the solution at the point [0.5,0.5], and pick the first eigenvector q_soln_atpoint = q_soln.at([0.5,0.5]) Q_soln = q_soln_atpoint[0] * E1 + q_soln_atpoint[1] * E2 evals, evecs = la.eig(Q_soln) # evec is a 2x2 array with the columns being the e-vectors q_soln_evec = np.zeros((1,2)) q_soln_evec += evecs[0,:] print(q_soln_evec) My question is this: how can I get firedrake to do this automatically for every node in my mesh, and then store it in as a Function “q_soln_evec”? The only reason I used numpy to get this one point is because I’m unfamiliar with firedrake. I bet firedrake has some built-in way of doing what I need here. Thanks, Andrew Hicks