def __init__(self, n=6, L=200, K=250):
# real-valued Zernike polynomials up to the n-th radial order
rzern = RZern(n)
# make a cartesian grid (unit disk pupil coordinates)
ddx = np.linspace(-1.0, 1.0, K)
ddy = np.linspace(-1.0, 1.0, L)
xv, yv = np.meshgrid(ddx, ddy)
rzern.make_cart_grid(xv, yv)
self.rzern = rzern
self.grid_size = (L, K)
def __init__(self, n=6, L=200, K=250):
# real-valued Zernike polynomials up to the n-th radial order
rzern = RZern(n)
# make a cartesian grid (unit disk pupil coordinates)
ddx = np.linspace(-1.0, 1.0, K)
ddy = np.linspace(-1.0, 1.0, L)
xv, yv = np.meshgrid(ddx, ddy)
rzern.make_cart_grid(xv, yv)
self.rzern = rzern
self.grid_size = (L, K)
def test_normalisations_real(self):
log = logging.getLogger('TestZern.test_normalisations_real')
n_alpha = 6
L, K = 400, 357
# polar grid
pol = RZern(n_alpha)
fitAlpha = FitZern(pol, L, K)
t1 = time()
pol.make_pol_grid(fitAlpha.rho_j, fitAlpha.theta_i)
t2 = time()
log.debug('make pol grid {:.6f}'.format(t2 - t1))
# cartesian grid
cart = RZern(n_alpha)
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_alpha, 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])
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_real(self):
log = logging.getLogger('TestZern.test_normalisations_real')
n_alpha = 6
L, K = 400, 357
# polar grid
pol = RZern(n_alpha)
fitAlpha = FitZern(pol, L, K)
t1 = time()
pol.make_pol_grid(fitAlpha.rho_j, fitAlpha.theta_i)
t2 = time()
log.debug('make pol grid {:.6f}'.format(t2 - t1))
# cartesian grid
cart = RZern(n_alpha)
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_alpha, 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])
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)
