enable automatic DFT decimation by default

[oskooi]

Closes #1731.

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Attention: Patch coverage is 77.27273% with 5 lines in your changes missing coverage. Please review.

Project coverage is 73.46%. Comparing base (a523a87) to head (898d438).
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Files with missing lines	Patch %	Lines
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@@            Coverage Diff             @@
##           master    #1732      +/-   ##
==========================================
+ Coverage   73.39%   73.46%   +0.07%     
==========================================
  Files          13       13              
  Lines        4540     4557      +17     
==========================================
+ Hits         3332     3348      +16     
- Misses       1208     1209       +1     

Files with missing lines	Coverage Δ
python/adjoint/objective.py	75.15% <100.00%> (ø)
python/adjoint/optimization_problem.py	69.69% <ø> (ø)
python/adjoint/utils.py	93.44% <ø> (ø)
python/geom.py	93.98% <ø> (ø)
python/simulation.py	76.45% <75.00%> (+0.13%)	⬆️

[smartalecH]

Seems a bit odd that so many of the existing tests don't support decimation. Aren't all the tests involving DFTs using band-limited sources?

[oskooi]

Almost all the existing unit tests in which automatic decimation had to be disabled in this PR involved comparing results based on DFT fields to hard-coded values which were generated without decimation. I suppose we could update all unit tests which involve DFT fields (a large fraction of the overall total) to use decimation to possibly speed things up but that would be a bit of work.

[oskooi]

This is working now. I verified that the fwidth returned by gaussian_src_time::get_fwidth(double tol) for three different values of tol (1e-1, 1e-2, 1e-3) matches nearly exactly the bandwidth computed directly from the DTFT spectrum using this 1d test:

import meep as mp
import numpy as np
import matplotlib.pyplot as plt

sz = 10.0
dpml = 2.0

fcen = 1.0
df = 0.2
src = [mp.Source(mp.GaussianSource(fcen,fwidth=df),
                 mp.Ex,
                 mp.Vector3(z=-0.5*sz+dpml))]

sim = mp.Simulation(cell_size=mp.Vector3(z=sz),
                    dimensions=1,
                    sources=src,
                    resolution=50,
                    boundary_layers=[mp.PML(dpml)])

nfreq = 200
dft_mon = sim.add_dft_fields([mp.Ex], fcen, 2*df, nfreq, center=mp.Vector3(z=0.5*sz-dpml), size=mp.Vector3())
sim.run(until_after_sources=200)

ex_dft = [ np.absolute(sim.get_dft_array(dft_mon, mp.Ex, i)) for i in range(nfreq) ]
freqs = mp.get_flux_freqs(dft_mon)

tols = [ 1e-1, 1e-2, 1e-3 ]
for tol in tols:
    max_val = np.amax(ex_dft)
    idx = np.where(ex_dft > tol*max_val)[0]
    fwidth = freqs[idx[-1]] - freqs[idx[0]]
    print('fwidth({:.2E}) = {:.5f}'.format(tol,fwidth))

plt.figure()
plt.plot(freqs,ex_dft,'bo-')
plt.xlabel('frequency')
plt.ylabel('DTFT of Ex')
plt.savefig('ex_dft.png',dpi=150,bbox_inches='tight')

fwidth computed using gaussian_src_time::get_fwidth(double tol)

get_fwidth(1e-1) = 0.13662
get_fwidth(1e-2) = 0.19320
get_fwidth(1e-3) = 0.23663

fwidth computed from DTFT spectrum

fwidth(1.00E-01) = 0.13266
fwidth(1.00E-02) = 0.19296
fwidth(1.00E-03) = 0.23317