def test_fit_real_numpy(self):
log = logging.getLogger('TestFitZern.test_fit_real_numpy')
z = RZern(4)
F = FitZern(z, self.L, self.K)
theta_i = F.theta_i
rho_j = F.rho_j
c = normal(size=z.nk)
Phi = [z.eval_a(c, rh, th) for rh in rho_j for th in theta_i]
time1 = time()
ce = F._fit_slow(Phi)
time2 = time()
log.debug('elapsed FIT_LIST {:.6f}'.format(time2 - time1))
time1 = time()
ce2 = F.fit(np.array(Phi, order='F'))
time2 = time()
log.debug('elapsed FIT_NUMPY {:.6f}'.format(time2 - time1))
enorm = norm(ce2 - np.array(ce, order='F'))
log.debug('enorm {:e}'.format(enorm))
self.assertTrue(enorm < self.max_enorm)
def test_fit_real_numpy(self):
log = logging.getLogger('TestFitZern.test_fit_real_numpy')
z = RZern(4)
F = FitZern(z, self.L, self.K)
theta_i = F.theta_i
rho_j = F.rho_j
c = normal(size=z.nk)
Phi = [z.eval_a(c, rh, th) for rh in rho_j for th in theta_i]
time1 = time()
ce = F._fit_slow(Phi)
time2 = time()
log.debug('elapsed FIT_LIST {:.6f}'.format(time2 - time1))
time1 = time()
ce2 = F.fit(np.array(Phi, order='F'))
time2 = time()
log.debug('elapsed FIT_NUMPY {:.6f}'.format(time2 - time1))
enorm = norm(ce2 - np.array(ce, order='F'))
log.debug('enorm {:e}'.format(enorm))
self.assertTrue(enorm < self.max_enorm)
def do_test(cls, complex_a):
z = cls(4)
F = FitZern(z, self.L, self.K)
theta_i = F.theta_i
rho_j = F.rho_j
z.make_pol_grid(rho_j, theta_i)
if complex_a:
c = normal(size=z.nk) + 1j * normal(size=z.nk)
else:
c = normal(size=z.nk)
PhiN = np.array(
[z.eval_a(c, rh, th) for rh in rho_j for th in theta_i],
order='F')
ce1 = F.fit(PhiN)
# create tmp path
tmpfile = NamedTemporaryFile()
tmppath = tmpfile.name
tmpfile.close()
F.save(tmppath)
F2 = FitZern.load(tmppath)
PhiN1 = np.array(
[F.z.eval_a(c, rh, th) for rh in rho_j for th in theta_i],
order='F')
PhiN2 = np.array(
[F2.z.eval_a(c, rh, th) for rh in rho_j for th in theta_i],
order='F')
self.assertTrue(isinstance(F, FitZern))
self.assertTrue(isinstance(F2, FitZern))
if complex_a:
self.assertTrue(isinstance(F.z, CZern))
self.assertTrue(isinstance(F2.z, CZern))
else:
self.assertTrue(isinstance(F.z, RZern))
self.assertTrue(isinstance(F2.z, RZern))
self.assertTrue(norm(PhiN - PhiN1) == 0)
self.assertTrue(norm(PhiN - PhiN2) == 0)
self.assertTrue(norm(F.z.coefnorm - F2.z.coefnorm) == 0)
self.assertTrue(norm(F.z.ntab - F2.z.ntab) == 0)
self.assertTrue(norm(F.z.mtab - F2.z.mtab) == 0)
self.assertTrue(F.z.n == F2.z.n)
self.assertTrue(F.z.nk == F2.z.nk)
self.assertTrue(F.z.normalise == F2.z.normalise)
self.assertTrue(norm(F.z.rhoitab - F2.z.rhoitab) == 0)
self.assertTrue(norm(F.z.rhotab - F2.z.rhotab) == 0)
self.assertTrue(F.z.numpy_dtype == F2.z.numpy_dtype)
self.assertTrue(norm(F.z.ZZ - F2.z.ZZ) == 0)
self.assertTrue(norm(F.A - F2.A) == 0)
self.assertTrue(norm(F.I_cosm - F2.I_cosm) == 0)
self.assertTrue(norm(F.I_sinm - F2.I_sinm) == 0)
self.assertTrue(norm(F.I_Rnmrho - F2.I_Rnmrho) == 0)
self.assertTrue(F.K == F2.K)
self.assertTrue(F.L == F2.L)
self.assertTrue(norm(F.rho_a - F2.rho_a) == 0)
self.assertTrue(norm(F.rho_b - F2.rho_b) == 0)
self.assertTrue(norm(F.rho_j - F2.rho_j) == 0)
self.assertTrue(norm(F.theta_a - F2.theta_a) == 0)
self.assertTrue(norm(F.theta_b - F2.theta_b) == 0)
self.assertTrue(norm(F.theta_i - F2.theta_i) == 0)
ce2 = F2.fit(PhiN)
self.assertTrue(norm(ce2 - ce1) < self.max_enorm)
os.unlink(tmppath)
del z, F, F2, c, ce1, ce2, PhiN, PhiN1, PhiN2
# set the alpha coefficients randomly
if args.random:
alpha1 = normal(size=alpha.size-1)
alpha1 = (args.rms/norm(alpha1))*alpha1
alpha[1:] = alpha1
del alpha1
# evaluate the phase corresponding to alpha
Phi = phase_pol.eval_grid(alpha)
# evaluate the generalised pupil function P corresponding to alpha
P = np.exp(1j*Phi)
# estimate the beta coefficients from P
beta_hat = ip.fit(P)
# plot the results
phaseplot = PhasePlot(n=args.n_alpha) # to plot beta and the PSF
betaplot = BetaPlot(args) # to plot the phase
# plot alpha
p.figure(10)
p.subplot2grid((1, 3), (0, 0), colspan=2)
h1 = p.plot(range(1, phase_pol.nk + 1), alpha, marker='o')
p.legend(h1, [r'$\alpha$'])
p.ylabel('[rad]')
p.xlabel('$k$')
p.subplot2grid((1, 3), (0, 2))
phaseplot.plot_alpha(alpha)
p.title(r'$\alpha$')
# complex-valued Zernike polynomials up to the 4-th radial order
gpf_pol = CZern(4) # to approximate the GPF
# FitZern computes the approximate inner products, see Eq. (B4) in [A2015]
ip = FitZern(gpf_pol, L, K)
gpf_pol.make_pol_grid(ip.rho_j, ip.theta_i) # make a polar grid
# random vector of Zernike coefficients to be estimated
beta_true = normal(size=gpf_pol.nk) + 1j * normal(size=gpf_pol.nk)
# random generalised pupil function P
P = gpf_pol.eval_grid(beta_true)
# estimate the random vector from the GPF grid
beta_hat = ip.fit(P)
# plot the results
p.figure(2)
# real part of the Zernike coefficients of beta_true and beta_hat
ax = p.subplot(3, 1, 1)
h1 = ax.plot(range(1, gpf_pol.nk + 1), beta_true.real, marker='o')
h2 = ax.plot(range(1, gpf_pol.nk + 1), beta_hat.real, marker='x')
p.legend(h1 + h2, [r'$\mathcal{R}[\beta]$', r'$\mathcal{R}[\hat{\beta}]$'])
p.ylabel('[rad]')
p.xlabel('$k$')
# imaginary part of the Zernike coefficients of beta_true and beta_hat
ax = p.subplot(3, 1, 2)
h1 = ax.plot(range(1, gpf_pol.nk + 1), beta_true.imag, marker='o')
# real-valued Zernike polynomials up to the 6-th radial order
phase_pol = RZern(6)
# FitZern computes the approximate inner products, see Eq. (B2) in [A2015]
ip = FitZern(phase_pol, L, K)
phase_pol.make_pol_grid(ip.rho_j, ip.theta_i) # make a polar grid
# random vector of Zernike coefficients to be estimated
alpha_true = normal(size=phase_pol.nk)
# phase grid
Phi = phase_pol.eval_grid(alpha_true)
# estimate the random vector from the phase grid
alpha_hat = ip.fit(Phi)
# plot the results
p.figure(2)
# Zernike coefficients of alpha_true and alpha_hat
ax = p.subplot2grid((3, 3), (0, 0), colspan=3)
h1 = ax.plot(range(1, phase_pol.nk + 1), alpha_true, marker='o')
h2 = ax.plot(range(1, phase_pol.nk + 1), alpha_hat, marker='x')
p.legend(h1 + h2, [r'$\alpha$', r'$\hat{\alpha}$'])
p.ylabel('[rad]')
p.xlabel('$k$')
# Zernike coefficients error between alpha_true and alpha_hat
ax = p.subplot2grid((3, 3), (1, 0), colspan=3)
err = alpha_true - alpha_hat
def do_test(cls, complex_a):
z = cls(4)
F = FitZern(z, self.L, self.K)
theta_i = F.theta_i
rho_j = F.rho_j
z.make_pol_grid(rho_j, theta_i)
if complex_a:
c = normal(size=z.nk) + 1j*normal(size=z.nk)
else:
c = normal(size=z.nk)
PhiN = np.array(
[z.eval_a(c, rh, th) for rh in rho_j for th in theta_i],
order='F')
ce1 = F.fit(PhiN)
# create tmp path
tmpfile = NamedTemporaryFile()
tmppath = tmpfile.name
tmpfile.close()
F.save(tmppath)
F2 = FitZern.load(tmppath)
PhiN1 = np.array(
[F.z.eval_a(c, rh, th) for rh in rho_j for th in theta_i],
order='F')
PhiN2 = np.array(
[F2.z.eval_a(c, rh, th) for rh in rho_j for th in theta_i],
order='F')
self.assertTrue(isinstance(F, FitZern))
self.assertTrue(isinstance(F2, FitZern))
if complex_a:
self.assertTrue(isinstance(F.z, CZern))
self.assertTrue(isinstance(F2.z, CZern))
else:
self.assertTrue(isinstance(F.z, RZern))
self.assertTrue(isinstance(F2.z, RZern))
self.assertTrue(norm(PhiN - PhiN1) == 0)
self.assertTrue(norm(PhiN - PhiN2) == 0)
self.assertTrue(norm(F.z.coefnorm - F2.z.coefnorm) == 0)
self.assertTrue(norm(F.z.ntab - F2.z.ntab) == 0)
self.assertTrue(norm(F.z.mtab - F2.z.mtab) == 0)
self.assertTrue(F.z.n == F2.z.n)
self.assertTrue(F.z.nk == F2.z.nk)
self.assertTrue(F.z.normalise == F2.z.normalise)
self.assertTrue(norm(F.z.rhoitab - F2.z.rhoitab) == 0)
self.assertTrue(norm(F.z.rhotab - F2.z.rhotab) == 0)
self.assertTrue(F.z.numpy_dtype == F2.z.numpy_dtype)
self.assertTrue(norm(F.z.ZZ - F2.z.ZZ) == 0)
self.assertTrue(norm(F.A - F2.A) == 0)
self.assertTrue(norm(F.I_cosm - F2.I_cosm) == 0)
self.assertTrue(norm(F.I_sinm - F2.I_sinm) == 0)
self.assertTrue(norm(F.I_Rnmrho - F2.I_Rnmrho) == 0)
self.assertTrue(F.K == F2.K)
self.assertTrue(F.L == F2.L)
self.assertTrue(norm(F.rho_a - F2.rho_a) == 0)
self.assertTrue(norm(F.rho_b - F2.rho_b) == 0)
self.assertTrue(norm(F.rho_j - F2.rho_j) == 0)
self.assertTrue(norm(F.theta_a - F2.theta_a) == 0)
self.assertTrue(norm(F.theta_b - F2.theta_b) == 0)
self.assertTrue(norm(F.theta_i - F2.theta_i) == 0)
ce2 = F2.fit(PhiN)
self.assertTrue(norm(ce2 - ce1) < self.max_enorm)
os.unlink(tmppath)
del z, F, F2, c, ce1, ce2, PhiN, PhiN1, PhiN2
# real-valued Zernike polynomials up to the 6-th radial order
phase_pol = RZern(6)
# FitZern computes the approximate inner products, see Eq. (B2) in [A2015]
ip = FitZern(phase_pol, L, K)
phase_pol.make_pol_grid(ip.rho_j, ip.theta_i) # make a polar grid
# random vector of Zernike coefficients to be estimated
alpha_true = normal(size=phase_pol.nk)
# phase grid
Phi = phase_pol.eval_grid(alpha_true)
# estimate the random vector from the phase grid
alpha_hat = ip.fit(Phi)
# plot the results
p.figure(2)
# Zernike coefficients of alpha_true and alpha_hat
ax = p.subplot2grid((3, 3), (0, 0), colspan=3)
h1 = ax.plot(range(1, phase_pol.nk + 1), alpha_true, marker='o')
h2 = ax.plot(range(1, phase_pol.nk + 1), alpha_hat, marker='x')
p.legend(h1 + h2, [r'$\alpha$', r'$\hat{\alpha}$'])
p.ylabel('[rad]')
p.xlabel('$k$')
# Zernike coefficients error between alpha_true and alpha_hat
ax = p.subplot2grid((3, 3), (1, 0), colspan=3)
err = alpha_true - alpha_hat
