def test_15(self):
x = np.linspace(-1, 1, 21)
sprm, sfvl, fvmx, sidx = util.grid_search(fnv, (x, ))
assert np.abs(sprm[0][0] - 0.1) < 1e-14
assert np.abs(sprm[0][1] - 0.5) < 1e-14
assert sidx[0][0] == 11
assert sidx[0][1] == 15
def test_15(self):
x = np.linspace(-1, 1, 21)
sprm, sfvl, fvmx, sidx = util.grid_search(fnv, (x,))
assert np.abs(sprm[0][0] - 0.1) < 1e-14
assert np.abs(sprm[0][1] - 0.5) < 1e-14
assert sidx[0][0] == 11
assert sidx[0][1] == 15
"""
Select regularization parameter $\lambda$ by evaluating the error in recovering the sparse representation over a logarithmicaly spaced grid. (The reference representation is assumed to be known, which is not realistic in a real application.) A function is defined that evalues the BPDN recovery error for a specified $\lambda$, and this function is evaluated in parallel by :func:`sporco.util.grid_search`.
"""
# Function computing reconstruction error at lmbda
def evalerr(prm):
lmbda = prm[0]
b = bpdn.BPDN(D, s, lmbda, opt)
x = b.solve()
return np.sum(np.abs(x-x0))
# Parallel evalution of error function on lmbda grid
lrng = np.logspace(1, 2, 20)
sprm, sfvl, fvmx, sidx = util.grid_search(evalerr, (lrng,))
lmbda = sprm[0]
print('Minimum ℓ1 error: %5.2f at 𝜆 = %.2e' % (sfvl, lmbda))
"""
Once the best $\lambda$ has been determined, run BPDN with verbose display of ADMM iteration statistics.
"""
# Initialise and run BPDN object for best lmbda
opt['Verbose'] = True
b = bpdn.BPDN(D, s, lmbda, opt)
x = b.solve()
print("BPDN solve time: %.2fs" % b.timer.elapsed('solve'))
def test_08(self):
x = np.linspace(-1, 1, 21)
sprm, sfvl, fvmx, sidx = util.grid_search(fn, (x, ))
assert (np.abs(sprm[0] - 0.1) < 1e-14)
assert (sidx[0] == 11)
'AutoRho' : {'RsdlTarget' : 1.0}})
# Function computing reconstruction error for (lmbda, mu) pair
def evalerr(prm):
lmbda = prm[0]
mu = prm[1]
b = bpdn.BPDNJoint(D, s, lmbda, mu, opt)
x = b.solve()
return np.sum(np.abs(x-x0))
# Parallel evalution of error function on lmbda,mu grid
lrng = np.logspace(-4, 0.5, 10)
mrng = np.logspace(0.5, 1.6, 10)
sprm, sfvl, fvmx, sidx = util.grid_search(evalerr, (lrng, mrng))
lmbda = sprm[0]
mu = sprm[1]
print('Minimum ℓ1 error: %5.2f at (𝜆,μ) = (%.2e, %.2e)' % (sfvl, lmbda, mu))
# Initialise and run BPDNJoint object for best lmbda and mu
opt['Verbose'] = True
b = bpdn.BPDNJoint(D, s, lmbda, mu, opt)
b.solve()
print("BPDNJoint solve time: %.2fs" % b.runtime)
# Display recovery results
fig1 = plot.figure(1, figsize=(6,8))
plot.subplot(1,2,1)
# Select Lanczos kernel order depending on PSF shape
if shape == 'complex' or shape == 'narrow':
K = 5
else:
K = 10
# Load reference PSF
psffile = os.path.join(psfpath, '%s.npz' % shape)
npz = np.load(psffile, allow_pickle=True)
psfref = npz['refpsf'].item()[M]
# Evaluate performance over selected parameter ranges
perf = partial(psf_est_performance, K=K, img=img, psfref=psfref)
sprm, sfvl, fvmx, sidx = grid_search(
perf, (paramranges['sigma0'], paramranges['lmbdaX'],
paramranges['lmbdaG'], paramranges['rhoX'], paramranges['LG']),
fmin=False,
nproc=nproc)
# Add results for this image to results dict
results[basename] = {
'shape': shape,
'pps': pps,
'noise': noise,
'K': K,
'sprm': sprm,
'sfvl': sfvl,
'fvmx': fvmx,
'sidx': sidx
}
# Skip input images for different noise levels
if noise != slct_noise:
continue
basename = '%s_d%03d_n%7.1e.npz' % (shape, pps, noise)
print('Computing parameters for %s' % starfile)
stars = np.load(starfile)
pos = np.load(posfile)
# Load reference PSF
psffile = os.path.join(psfpath, '%s.npz' % shape)
npz = np.load(psffile, allow_pickle=True)
psfref = npz['refpsf'].item()[M]
# Evaluate performance over selected parameter ranges
perf = partial(psf_est_performance, stars=stars, pos=pos, psfref=psfref)
sprm, sfvl, fvmx, sidx = grid_search(
perf, (paramranges['n_comp'], paramranges['ksig'],
paramranges['n_scales'], paramranges['ksig_init'],
paramranges['psf_size'], paramranges['n_eigenvects']),
fmin=False, nproc=nproc)
# Add results for this image to results dict
results[basename] = {'shape': shape, 'pps': pps, 'noise': noise,
'sprm': sprm, 'sfvl': sfvl, 'fvmx': fvmx,
'sidx': sidx}
# Save data to NPZ file
np.savez(rsltfile, paramranges=paramranges, results=results)
