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pacopy's Issues

Complex-Ginsburg-Landau

I'm getting this broadcasting error for the shapes and having trouble sourcing the error.... any idea? Thanks!

ValueError: operands could not be broadcast together with remapped shapes [original->remapped]: (3,19602,3)->(3,19602,3) (3,19602,2)->(3,19602,2)"

This is the error that is returned when code is run:

  # test_f_i_psi()
   # test_df_dlmbda()
--->      test_ginzburg_landau(max_steps=100, n=100)
   # plot_data()'''

<ipython-input-1-cd6944349cb4> in test_ginzburg_landau(max_steps, n)'''
   302         #     newton_tol=1.0e-10,
   303         # )
--> 304         pacopy.euler_newton(
   305             problem,
   306             u0,

~/opt/anaconda3/envs/fenicsproject/lib/python3.8/site-packages/pacopy/euler_newton.py in euler_newton(problem, u0, lmbda0, callback, max_steps, verbose, newton_tol, max_newton_steps, predictor_variant, corrector_variant, stepsize0, stepsize_max, stepsize_aggressiveness, cos_alpha_min, theta0, adaptive_theta, converge_onto_zero_eigenvalue)'''
   140     k = 0
   141     try:
--> 142         u, _ = newton(
   143             lambda u: problem.f(u, lmbda),
   144             lambda u, rhs: problem.jacobian_solver(u, lmbda, rhs),

~/opt/anaconda3/envs/fenicsproject/lib/python3.8/site-packages/pacopy/newton.py in newton(f, jacobian_solver, norm2, u0, tol, max_iter, verbose)'''
     9     u = u0
    10 
---> 11     fu = f(u)
    12     nrm = math.sqrt(norm2(fu))
    13     if verbose:

~/opt/anaconda3/envs/fenicsproject/lib/python3.8/site-packages/pacopy/euler_newton.py in <lambda>(u)'''
   141     try:
   142         u, _ = newton(
--> 143             lambda u: problem.f(u, lmbda),
   144             lambda u, rhs: problem.jacobian_solver(u, lmbda, rhs),
   145             problem.norm2_r,

<ipython-input-1-cd6944349cb4> in f(self, psi, mu)'''
    99     def f(self, psi, mu):
--> 100         keo = pyfvm.get_fvm_matrix(self.mesh, edge_kernels=[Energy(mu)])
   101         cv = self.mesh.control_volumes
   102         out = (keo * psi) / cv + (self.V + self.g * numpy.abs(psi) ** 2) * psi

~/opt/anaconda3/envs/fenicsproject/lib/python3.8/site-packages/pyfvm/fvm_matrix.py in get_fvm_matrix(mesh, edge_kernels, vertex_kernels, face_kernels, dirichlets)'''
    11     dirichlets = [] if dirichlets is None else dirichlets
    12 
---> 13     V, I, J = _get_VIJ(mesh, edge_kernels, vertex_kernels, face_kernels)
    14 
    15     # One unknown per vertex

~/opt/anaconda3/envs/fenicsproject/lib/python3.8/site-packages/pyfvm/fvm_matrix.py in _get_VIJ(mesh, edge_kernels, vertex_kernels, face_kernels)'''
    44             cell_mask = mesh.get_cell_mask(subdomain)
    45 
---> 46             v_matrix = edge_kernel.eval(mesh, cell_mask)
    47 
    48             V.append(v_matrix[0, 0].flatten())

<ipython-input-1-cd6944349cb4> in eval(self, mesh, cell_mask)'''
    35         # The dot product <magnetic_potential, edge>, executed for many
    36         # points at once; cf. <http://stackoverflow.com/a/26168677/353337>.
---> 37         beta = numpy.einsum("...k,...k->...", magnetic_potential, edge)
    38 
    39         return numpy.array( <__array_function__ internals> in einsum(*args, **kwargs)

~/opt/anaconda3/envs/fenicsproject/lib/python3.8/site-packages/numpy/core/einsumfunc.py in einsum(out, optimize, *operands, **kwargs)'''
  1348         if specified_out:
  1349             kwargs['out'] = out
-> 1350         return c_einsum(*operands, **kwargs)
  1351 
  1352     # Check the kwargs to avoid a more cryptic error later, without having to

ValueError: operands could not be broadcast together with remapped shapes [original->remapped]: (3,19602,3)->(3,19602,3) (3,19602,2)->(3,19602,2) 

version bump for pacopy.natural.milestones

pacopy.natural.milestones #5 is working nicely but I just realized that it's not yet available with pip install pacopy which is still at v. 0.1.0.

I'd submit a PR but I'm not sure whether it would mean 0.1.1 or 0.2.0.

default maximum parameter stepsize

The default maximum parameter stepsize is finite

https://github.com/nschloe/pacopy/blob/b5ae74c2c17349a04165291e2e74fbc865da660b/pacopy/natural.py#L12

and small, depending on the system. A couple of times I have forgotten this and removed the explicit setting, hoping for a faster run through the milestones #6 (Δλ ~ 10², in the example given there, kinnala/scikit-fem#145), only to have it tiptoe at Δλ = 1.

What about defaulting to no limit as for

https://github.com/nschloe/pacopy/blob/b5ae74c2c17349a04165291e2e74fbc865da660b/pacopy/natural.py#L16

?

(Otherwise, pacopy.natural is proving very useful for stationary Navier–Stokes work.)

readme dump

This thread is for storing videos to be used in the readme.

milestones

Would it be useful to add an optional argument to natural and euler_newton to force solution at certain values of λ ?

It's easy enough now to reproduce, as in test/test_bratu1d.py, most of the left plot in figure 1.1 of ‘Deflation techniques…’ (Farrell, Birkisson, & Funke), but not the blue or red cross at λ = 2 or the right plot with the corresponding solutions u (x; λ = 2).

scipy.integrate.solve_ivp has a couple of related features:

  • t_eval: ‘Times at which to store the computed solution’
  • events: ‘defined by a continuous function of time and state that becomes zero value in case of an event’

I envisage something like replacing

https://github.com/nschloe/pacopy/blob/1973500e422132f035fd9a419340c5100d6bb904/pacopy/natural.py#L79

with

milestone = next(milestones)
...
while ...:
    lmbda_next = lmbda + lmbda_stepsize
    if milestone < lmbda_next:
        lmbda = milestone
        milestone = next(milestones)
    else:
        lmbda = lmbda_next

plus handing:

  • lmbda_stepsize might be negative
  • milestones might be empty

The motivation is a steady Navier–Stokes solver for which the solutions are desired at certain Reynolds numbers.

Add very simple examples for beginners

Hi,

thank you for this great module! I think the included examples are fairly complicated, wouldn't it be nice to have some very simple examples? In my opinion a simple sin(u)-lmbda would be enough to show the "curve following process" of the given equilibrium equation(s).

My suggestion would be something like:

#from autograd import numpy
#import autograd
import numpy
import scipy
import matplotlib.pyplot as plt

import pacopy

class SimpleProblem1D:
    def __init__(self):
        self.n = 1

    def inner(self, a, b):
        """The inner product of the problem. Can be numpy.dot(a, b), but factoring in
        the mesh width stays true to the PDE.
        """
        return numpy.dot(a, b)

    def norm2_r(self, a):
        """The norm in the range space; used to determine if a solution has been found."""
        return numpy.dot(a, a)

    def f(self, u, lmbda):
        """The evaluation of the function to be solved"""
        out = numpy.sin(u) - lmbda
        return out

    def df_dlmbda(self, u, lmbda):
        """The function's derivative with respect to the parameter. Used in Euler-Newton
        continuation.
        """
        out = -numpy.ones_like(u)
        return out

    def jacobian_solver(self, u, lmbda, rhs):
        """A solver for the Jacobian problem."""
        #df_du = autograd.jacobian(self.f)(u, lmbda)
        df_du = numpy.array([numpy.cos(u)])
        return numpy.linalg.solve(df_du, rhs)
    
problem = SimpleProblem1D()
# Initial guess
u0 = numpy.zeros(problem.n)
# Initial parameter value
lmbda0 = 0.0

# Init lists
lmbda_list = []
values_list = []

def callback(k, lmbda, sol):
    # Use the callback for plotting, writing data to files etc.
    lmbda_list.append(lmbda)
    values_list.append(sol)

pacopy.euler_newton(problem, u0, lmbda0, callback, max_steps=20, newton_tol=1.0e-10)

# plot solution
fig = plt.figure()
data = numpy.hstack((numpy.array(values_list),
                     numpy.array(lmbda_list).reshape(-1,1))).T
plt.plot(*data,'.-')
plt.xlabel('$u_1$')
plt.ylabel('$\lambda$')

Best regards,
Andreas

no code in main branch

Hi,
I'm wondering why there is no code in the main branch?
If I'd like to use pacopy shall I consider using branch-switching instead

Best

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