def test_normalisations_complex(self):
log = logging.getLogger('TestZern.test_normalisations_complex')
n_beta = 6
L, K = 400, 393
# polar grid
pol = CZern(n_beta)
fitBeta = FitZern(pol, L, K)
t1 = time()
pol.make_pol_grid(fitBeta.rho_j, fitBeta.theta_i)
t2 = time()
log.debug('make pol grid {:.6f}'.format(t2 - t1))
# cartesian grid
cart = CZern(n_beta)
dd = np.linspace(-1.0, 1.0, max(L, K))
xx, yy = np.meshgrid(dd, dd)
t1 = time()
cart.make_cart_grid(xx, yy)
t2 = time()
log.debug('make cart grid {:.6f}'.format(t2 - t1))
smap = np.isfinite(cart.eval_grid(np.zeros(cart.nk)))
scale = (1.0 / np.sum(smap))
log.debug('')
log.debug('{} modes, {} x {} grid'.format(n_beta, L, K))
for i in range(pol.nk):
a = np.zeros(pol.nk)
a[i] = 1.0
Phi_a = cart.eval_grid(a)
for j in range(pol.nk):
b = np.zeros(pol.nk)
b[j] = 1.0
Phi_b = cart.eval_grid(b)
ip = scale * np.sum(Phi_a[smap] * (Phi_b[smap].conj()))
if i == j:
eip = 1.0
else:
eip = 0.0
iperr = abs(ip - eip)
log.debug('<{:02},{:02}> = {:+e} {:+e}'.format(
i + 1, j + 1, ip, iperr))
self.assertTrue(iperr < self.max_ip_err)
def test_normalisations_complex(self):
log = logging.getLogger('TestZern.test_normalisations_complex')
n_beta = 6
L, K = 400, 393
# polar grid
pol = CZern(n_beta)
fitBeta = FitZern(pol, L, K)
t1 = time()
pol.make_pol_grid(fitBeta.rho_j, fitBeta.theta_i)
t2 = time()
log.debug('make pol grid {:.6f}'.format(t2 - t1))
# cartesian grid
cart = CZern(n_beta)
dd = np.linspace(-1.0, 1.0, max(L, K))
xx, yy = np.meshgrid(dd, dd)
t1 = time()
cart.make_cart_grid(xx, yy)
t2 = time()
log.debug('make cart grid {:.6f}'.format(t2 - t1))
smap = np.isfinite(cart.eval_grid(np.zeros(cart.nk)))
scale = (1.0/np.sum(smap))
log.debug('')
log.debug('{} modes, {} x {} grid'.format(n_beta, L, K))
for i in range(pol.nk):
a = np.zeros(pol.nk)
a[i] = 1.0
Phi_a = cart.eval_grid(a)
for j in range(pol.nk):
b = np.zeros(pol.nk)
b[j] = 1.0
Phi_b = cart.eval_grid(b)
ip = scale*np.sum(Phi_a[smap]*(Phi_b[smap].conj()))
if i == j:
eip = 1.0
else:
eip = 0.0
iperr = abs(ip - eip)
log.debug('<{:02},{:02}> = {:+e} {:+e}'.format(
i + 1, j + 1, ip, iperr))
self.assertTrue(iperr < self.max_ip_err)
# grid sizes
L, K = 95, 105
# 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('$k$')
# grid sizes
L, K = 95, 105
# 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('$k$')
