def reconstruct(c1, L, K, n=8):
from zernike import RZern
cart = RZern(n)
ddx = np.linspace(-1.0, 1.0, K)
ddy = np.linspace(-1.0, 1.0, L)
xv, yv = np.meshgrid(ddx, ddy)
cart.make_cart_grid(xv, yv)
return cart.eval_grid(c1[0:cart.nk], matrix=True)
def coeff(img, n=8):
from zernike import RZern
cart = RZern(n)
L, K = img.shape
ddx = np.linspace(-1.0, 1.0, K)
ddy = np.linspace(-1.0, 1.0, L)
xv, yv = np.meshgrid(ddx, ddy)
cart.make_cart_grid(xv, yv)
c1 = cart.fit_cart_grid(img)[0]
return c1, L, K
def phase_Zernike(self, Plot=True, Save=False):
SLMRes = np.min([self.SLMResX, self.SLMResY])
apertureD = int(round(self.aperture_radius / self.pixelpitch * 2))
Zmatrix_size = np.min([SLMRes, apertureD])
r0 = self.pixelpitch * Zmatrix_size / 2
r0mm = r0 * 1e3
cart = RZern(6)
ddx = np.linspace(-1.0, 1.0, Zmatrix_size)
ddy = np.linspace(-1.0, 1.0, Zmatrix_size)
xv, yv = np.meshgrid(ddx, ddy)
cart.make_cart_grid(xv, yv)
c = np.zeros(cart.nk)
c[[self.ind_Zernike]] = 1
Phi = cart.eval_grid(c, matrix=True)
# change all nan values in Phi matrix to be zero
where_are_NaNs = np.isnan(Phi)
Phi[where_are_NaNs] = 0
Phi_norm = Phi
n = cart.ntab[self.ind_Zernike]
m = cart.mtab[self.ind_Zernike]
zernike_str = f"Radial: {n}, Angular: {m}"
print(zernike_str)
# Launch the Zernike phase pattern to SLM screen
SLM_screen_aberr = np.zeros((int(self.SLMResY), int(self.SLMResX)))
col_Phi_norm = np.size(Phi_norm, axis=1)
row_Phi_norm = np.size(Phi_norm, axis=0)
startRow_screen = self.SLMResY / 2 - round(row_Phi_norm / 2)
endRow_screen = self.SLMResY / 2 + round(row_Phi_norm / 2)
startCol_screen = self.SLMResX / 2 - round(col_Phi_norm / 2)
endCol_screen = self.SLMResX / 2 + round(col_Phi_norm / 2)
SLM_screen_aberr[int(startRow_screen):int(endRow_screen), :][:, int(startCol_screen):int(endCol_screen)] = \
Phi_norm*self.percent
if Plot:
im = plt.imshow(Phi_norm,
origin='lower',
extent=(-r0mm, r0mm, -r0mm, r0mm))
plt.title(zernike_str)
plt.colorbar(im)
plt.show()
if Save:
np.savetxt(f"SLM_Zernike_{n}{m}_{percent}.csv",
SLM_screen_aberr,
delimiter=",")
return SLM_screen_aberr, m, n
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(self):
log = logging.getLogger('TestFitZern.test_fit_real')
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)
time1 = time()
Phi = [z.eval_a(c, rh, th) for rh in rho_j for th in theta_i]
time2 = time()
log.debug('eval Phi {:.4f}'.format(time2 - time1))
time1 = time()
ce = F._fit_slow(Phi)
time2 = time()
log.debug('elapsed time {:.4f}'.format(time2 - time1))
err1 = norm(np.array(c) - np.array(ce))
max1 = max([abs(c[i] - ce[i]) for i in range(z.nk)])
log.debug('err1 {:e} max1 {:e}'.format(err1, max1))
self.assertTrue(err1 < self.max_fit_norm)
def make_names(n):
r = RZern(n)
ntab = r.ntab
mtab = r.mtab
nolls = []
names = []
nms = []
for i in range(r.nk):
j = i + 1
n = ntab[i]
m = mtab[i]
names.append(default_name(j, ntab[i], mtab[i]))
nolls.append(j)
nms.append([int(n), int(m)])
return names, nolls, nms
def load_h5py(cls, f, prepend=None, lazy_cart_grid=False):
"""Load object contents from an opened HDF5 file object."""
z = cls()
prefix = cls.__name__ + '/'
if prepend is not None:
prefix = prepend + prefix
z.cart = RZern.load_h5py(f, prefix + 'cart/')
z.fringe = FringeAnalysis.load_h5py(f, prefix + 'fringe/')
z.zfA1 = None
z.zfA2 = None
z.zfm = f[prefix + 'zfm'][()]
z.shape = f[prefix + 'shape'][()]
z.H = f[prefix + 'H'][()]
z.mvaf = f[prefix + 'mvaf'][()]
z.phi0 = f[prefix + 'phi0'][()]
z.z0 = f[prefix + 'z0'][()]
z.uflat = f[prefix + 'uflat'][()]
z.C = f[prefix + 'C'][()]
z.alpha = f[prefix + 'alpha'][()][0]
z.lambda1 = f[prefix + 'lambda1'][()][0]
z.wavelength = f[prefix + 'wavelength'][()]
z.dm_serial = h5_read_str(f, prefix + 'dm_serial')
z.dm_transform = h5_read_str(f, prefix + 'dm_transform')
z.cam_pixel_size = f[prefix + 'cam_pixel_size'][()]
z.cam_serial = h5_read_str(f, prefix + 'cam_serial')
z.dname = h5_read_str(f, prefix + 'dname')
z.hash1 = h5_read_str(f, prefix + 'hash1')
if not lazy_cart_grid:
xx, yy, _ = z.fringe.get_unit_aperture()
z.cart.make_cart_grid(xx, yy)
z.zfA1TzfA1 = None
z.chzfA1TzfA1 = None
try:
z.dmplot = DMPlot.load_h5py(f, prefix + 'dmplot/')
except ValueError:
z.dmplot = None
return z
def setUp(self):
self.pupil = RZern(4)
self.max_enorm = 1e-9
self.max_ip_err = 5e-2
def calibrate(self,
U,
images,
fringe,
wavelength,
cam_pixel_size,
cam_serial='',
dname='',
dm_serial='',
dmplot_txs=(0, 0, 0),
dm_transform=SquareRoot.name,
hash1='',
n_radial=25,
alpha=.75,
lambda1=5e-3,
status_cb=False):
if status_cb:
status_cb('Computing Zernike polynomials ...')
t1 = time()
nu, ns = U.shape
xx, yy, shape = fringe.get_unit_aperture()
assert (xx.shape == shape)
assert (yy.shape == shape)
cart = RZern(n_radial)
cart.make_cart_grid(xx, yy)
LOG.info(
f'calibrate(): Computing Zernike polynomials {time() - t1:.1f}')
if status_cb:
status_cb('Computing masks ...')
t1 = time()
zfm = cart.matrix(np.isfinite(cart.ZZ[:, 0]))
self.cart = cart
self.zfm = zfm
zfA1, zfA2, mask = self._make_zfAs()
LOG.info(f'calibrate(): Computing masks {time() - t1:.1f}')
# TODO remove me
mask1 = np.sqrt(xx**2 + yy**2) >= 1.
assert (np.allclose(mask, mask1))
assert (np.allclose(fringe.mask, mask1))
if status_cb:
status_cb('Computing phases 00.00% ...')
t1 = time()
def make_progress():
prevts = [time()]
def f(pc):
t = time()
dt = t - prevts[0]
prevts[0] = t
if dt > 1.5 or pc > 99:
status_cb(f'Computing phases {pc:05.2f}% ...')
return f
with Pool() as p:
if status_cb:
chunksize = ns // (4 * cpu_count())
if chunksize < 4:
chunksize = 4
phases = []
progress_fun = make_progress()
for i, phi in enumerate(
p.imap(PhaseExtract(fringe),
[images[i, ...] for i in range(ns)], chunksize),
1):
phases.append(phi)
progress_fun(100 * i / ns)
else:
phases = p.map(PhaseExtract(fringe),
[images[i, ...] for i in range(ns)])
phases = np.array(phases)
inds0 = fix_principal_val(U, phases)
inds1 = np.setdiff1d(np.arange(ns), inds0)
assert (np.allclose(np.arange(ns), np.sort(np.hstack((inds0, inds1)))))
phi0 = phases[inds0, :].mean(axis=0)
z0 = lstsq(np.dot(zfA1.T, zfA1), np.dot(zfA1.T, phi0), rcond=None)[0]
phases -= phi0.reshape(1, -1)
LOG.info(f'calibrate(): Computing phases {time() - t1:.1f}')
if status_cb:
status_cb('Computing least-squares matrices ...')
t1 = time()
nphi = phases.shape[1]
uiuiT = np.zeros((nu, nu))
phiiuiT = np.zeros((nphi, nu))
for i in inds1:
uiuiT += np.dot(U[:, [i]], U[:, [i]].T)
phiiuiT += np.dot(phases[[i], :].T, U[:, [i]].T)
LOG.info(
f'calibrate(): Computing least-squares matrices {time() - t1:.1f}')
if status_cb:
status_cb('Solving least-squares ...')
t1 = time()
A = np.dot(zfA1.T, zfA1)
C = np.dot(zfA1.T, phiiuiT)
B = uiuiT
U1 = cholesky(A, lower=False, overwrite_a=True)
Y = solve_triangular(U1, C, trans='T', lower=False)
D = solve_triangular(U1, Y, trans='N', lower=False)
U2 = cholesky(B, lower=False, overwrite_a=True)
YT = solve_triangular(U2, D.T, trans='T', lower=False)
XT = solve_triangular(U2, YT, trans='N', lower=False)
H = XT.T
def vaf(y, ye):
return 100 * (1 - np.var(y - ye, axis=1) / np.var(y, axis=1))
mvaf = vaf(phases.T, zfA1 @ H @ U)
LOG.info(f'calibrate(): Solving least-squares {time() - t1:.1f}')
if status_cb:
status_cb('Applying regularisation ...')
t1 = time()
if alpha > 0.:
# weighted least squares
rr = np.sqrt(xx**2 + yy**2)
win = .5 * (1 + np.cos(np.pi * ((2 * rr /
(alpha) - 2 / alpha + 1))))
win[rr < 1 - alpha / 2] = 1
win[rr >= 1] = 0
stds = np.zeros(nu)
for i in range(nu):
ind = np.where(U[i, :] == U.max())[0][0]
stds[i] = np.std(phases[ind] * win[zfm])
stds -= stds.min()
stds /= stds.max()
assert (stds.min() == 0.)
assert (stds.max() == 1.)
C = np.dot(pinv(lambda1 * np.diag(1 - stds) + np.dot(H.T, H)), H.T)
else:
C = np.linalg.pinv(H)
uflat = -np.dot(C, z0)
self.fringe = fringe
self.shape = shape
self.H = H
self.mvaf = mvaf
self.phi0 = phi0
self.z0 = z0
self.uflat = uflat
self.C = C
self.alpha = alpha
self.lambda1 = lambda1
self.wavelength = wavelength
self.dm_serial = dm_serial
self.dm_transform = dm_transform
self.cam_pixel_size = cam_pixel_size
self.cam_serial = cam_serial
self.dmplot_txs = dmplot_txs
self.dname = dname
self.hash1 = hash1
LOG.info(f'calibrate(): Applying regularisation {time() - t1:.1f}')
import matplotlib.pyplot as plt
import time
import os
from zernike import RZern
from scipy.signal import convolve
from scipy.optimize import minimize_scalar
from scipy import stats
import pkg_resources
#Theoretical FWHM: 275nm
#Axial 0.89*lambda/(n-sqrt(n**2-NA**2))
#Axial 721 nm
rz = RZern(8)
FILE_SIGMAS = pkg_resources.resource_filename('psfsim', 'data/r1_50pts.npy')
def distance_map(image, xc=0, yc=0):
u, v = image.shape
#Meshgrid usses cartesian indexing, invert of normal matrix indexing
y = np.linspace(-u / 2, u / 2, u) - yc
x = np.linspace(-v / 2, v / 2, v) - xc
xx, yy = np.meshgrid(x, y)
return np.sqrt(xx**2 + yy**2)
class Simulator():
def __init__(self,
def __init__(self,
wavelength,
n_radial,
z0=None,
callback=None,
pars={},
parent=None):
super().__init__(parent=parent)
self.log = logging.getLogger(self.__class__.__name__)
self.pars = {**deepcopy(self.def_pars), **deepcopy(pars)}
self.units = 'rad'
self.status = None
self.mul = 1.0
self.figphi = None
self.ax = None
self.im = None
self.cb = None
self.shape = (128, 128)
self.P = 1
self.rzern = RZern(n_radial)
dd = np.linspace(-1, 1, self.shape[0])
xv, yv = np.meshgrid(dd, dd)
self.rzern.make_cart_grid(xv, yv)
self.rad_to_nm = wavelength / (2 * np.pi)
self.callback = callback
self.zernike_rows = []
if z0 is None:
self.z = np.zeros(self.rzern.nk)
else:
self.z = z0.copy()
assert (self.rzern.nk == self.z.size)
group_phase = QGroupBox('phase')
lay_phase = QGridLayout()
group_phase.setLayout(lay_phase)
self.figphi = FigureCanvas(Figure(figsize=(2, 2)))
self.ax = self.figphi.figure.add_subplot(1, 1, 1)
phi = self.rzern.matrix(self.rzern.eval_grid(np.dot(self.P, self.z)))
self.im = self.ax.imshow(phi, origin='lower')
self.cb = self.figphi.figure.colorbar(self.im)
self.cb.locator = ticker.MaxNLocator(nbins=5)
self.cb.update_ticks()
self.ax.axis('off')
self.status = QLabel('')
lay_phase.addWidget(self.figphi, 0, 0)
lay_phase.addWidget(self.status, 1, 0)
def nmodes():
return min(self.pars['shown_modes'], self.rzern.nk)
bot = QGroupBox('Zernike')
lay_zern = QGridLayout()
bot.setLayout(lay_zern)
labzm = QLabel('shown modes')
lezm = QLineEdit(str(nmodes()))
lezm.setMaximumWidth(50)
lezmval = MyQIntValidator(1, self.rzern.nk)
lezmval.setFixup(nmodes())
lezm.setValidator(lezmval)
brad = QCheckBox('rad')
brad.setChecked(True)
breset = QPushButton('reset')
lay_zern.addWidget(labzm, 0, 0)
lay_zern.addWidget(lezm, 0, 1)
lay_zern.addWidget(brad, 0, 2)
lay_zern.addWidget(breset, 0, 3)
scroll = QScrollArea()
lay_zern.addWidget(scroll, 1, 0, 1, 5)
scroll.setWidget(QWidget())
scrollLayout = QGridLayout(scroll.widget())
scroll.setWidgetResizable(True)
def make_hand_slider(ind):
def f(r):
self.z[ind] = r
self.update_phi_plot()
return f
def make_hand_lab(le, i):
def f():
self.pars['zernike_labels'][str(i)] = le.text()
return f
def default_zernike_name(i, n, m):
if i == 1:
return 'piston'
elif i == 2:
return 'tip'
elif i == 3:
return 'tilt'
elif i == 4:
return 'defocus'
elif m == 0:
return 'spherical'
elif abs(m) == 1:
return 'coma'
elif abs(m) == 2:
return 'astigmatism'
elif abs(m) == 3:
return 'trefoil'
elif abs(m) == 4:
return 'quadrafoil'
elif abs(m) == 5:
return 'pentafoil'
else:
return ''
def make_update_zernike_rows():
def f(mynk=None):
if mynk is None:
mynk = len(self.zernike_rows)
ntab = self.rzern.ntab
mtab = self.rzern.mtab
if len(self.zernike_rows) < mynk:
for i in range(len(self.zernike_rows), mynk):
lab = QLabel(
f'Z<sub>{i + 1}</sub> ' +
f'Z<sub>{ntab[i]}</sub><sup>{mtab[i]}</sup>')
slider = RelSlider(self.z[i], make_hand_slider(i))
if str(i) in self.pars['zernike_labels'].keys():
zname = self.pars['zernike_labels'][str(i)]
else:
zname = default_zernike_name(
i + 1, ntab[i], mtab[i])
self.pars['zernike_labels'][str(i)] = zname
lbn = QLineEdit(zname)
lbn.setMaximumWidth(120)
hand_lab = make_hand_lab(lbn, i)
lbn.editingFinished.connect(hand_lab)
scrollLayout.addWidget(lab, i, 0)
scrollLayout.addWidget(lbn, i, 1)
slider.add_to_layout(scrollLayout, i, 2)
self.zernike_rows.append((lab, slider, lbn, hand_lab))
assert (len(self.zernike_rows) == mynk)
elif len(self.zernike_rows) > mynk:
for i in range(len(self.zernike_rows) - 1, mynk - 1, -1):
lab, slider, lbn, hand_lab = self.zernike_rows.pop()
scrollLayout.removeWidget(lab)
slider.remove_from_layout(scrollLayout)
scrollLayout.removeWidget(lbn)
lbn.editingFinished.disconnect(hand_lab)
lab.setParent(None)
lbn.setParent(None)
assert (len(self.zernike_rows) == mynk)
return f
self.update_zernike_rows = make_update_zernike_rows()
def reset_fun():
self.z *= 0.
self.update_gui_controls()
self.update_phi_plot()
def change_nmodes():
try:
ival = int(lezm.text())
assert (ival > 0)
assert (ival <= self.rzern.nk)
except Exception:
lezm.setText(str(len(self.zernike_rows)))
return
if ival != len(self.zernike_rows):
self.update_zernike_rows(ival)
self.update_phi_plot()
lezm.setText(str(len(self.zernike_rows)))
def f2():
def f(b):
if b:
self.units = 'rad'
self.mul = 1.0
else:
self.units = 'nm'
self.mul = self.rad_to_nm
self.update_phi_plot()
return f
self.update_zernike_rows(nmodes())
brad.stateChanged.connect(f2())
breset.clicked.connect(reset_fun)
lezm.editingFinished.connect(change_nmodes)
splitv = QSplitter(Qt.Vertical)
top = QSplitter(Qt.Horizontal)
top.addWidget(group_phase)
splitv.addWidget(top)
splitv.addWidget(bot)
self.top = top
self.bot = bot
l1 = QGridLayout()
l1.addWidget(splitv)
self.setLayout(l1)
self.lezm = lezm
#!/usr/bin/env python3
# -*- coding: utf-8 -*-
import matplotlib.pyplot as plt
import numpy as np
from zernike import RZern
if __name__ == '__main__':
plt.close('all')
fs = 7
fs1 = 6
cart = RZern(6)
L, K = 300, 300
ddx = np.linspace(-1.0, 1.0, K)
ddy = np.linspace(-1.0, 1.0, L)
xv, yv = np.meshgrid(ddx, ddy)
cart.make_cart_grid(xv, yv)
c = np.zeros(cart.nk)
ns = np.unique(cart.ntab)
fig = plt.figure(1)
nradial = 6
span = 0.05
leftoff = .03
while nradial >= 0:
nk = (nradial + 1) * (nradial + 2) // 2
nrows = nradial + 1
ncols = np.where(cart.ntab == nradial)[0].size
def main_Calib(filename, output, mode, alg, basis, order, figure, verbose, offset, qt, pre, split):
'''
# main program
# input: radius: %+.3f, 'str' (in makefile, str is default)
# path: file storage path, 'str'
# fout: file output name as .h5, 'str' (.h5 not included')
# cut_max: cut off of Legendre
# output: the gathered result EventID, ChannelID, x, y, z
'''
if pre != 'r':
print('begin reading file', flush=True)
EventID, ChannelID, Q, PETime, photonTime, PulseTime, dETime, x, y, z = pub.ReadFile(filename)
VertexTruth = (np.vstack((x, y, z))/1e3).T
if(offset):
off = pub.LoadBase(offset)
else:
off = np.zeros_like(PMTPos[:,0])
print('total event: %d' % np.size(np.unique(EventID)), flush=True)
print('begin processing legendre coeff', flush=True)
# this part for the same vertex
tmp = time.time()
EventNo = np.size(np.unique(EventID))
PMTNo = np.size(PMTPos[:,0])
if mode == 'PE':
PMTPosRep = np.tile(PMTPos, (EventNo,1))
vertex = np.repeat(VertexTruth, PMTNo, axis=0)
elif mode == 'time':
counts = np.bincount(EventID)
counts = counts[counts!=0]
PMTPosRep = PMTPos[ChannelID]
vertex = np.repeat(VertexTruth, counts, axis=0)
elif mode == 'combined':
PMTPosRep = np.tile(PMTPos, (EventNo,1))
vertex = np.repeat(VertexTruth, PMTNo, axis=0)
if basis == 'Legendre':
X, cos_theta = pub.LegendreCoeff(PMTPosRep, vertex, order, Legendre=True)
elif basis == 'Zernike':
from zernike import RZern
cos_theta = pub.LegendreCoeff(PMTPosRep, vertex, order, Legendre=False)
cart = RZern(order)
nk = cart.nk
m = cart.mtab
n = cart.ntab
rho = np.linalg.norm(vertex, axis=1)/0.65
theta = np.arccos(cos_theta)
X = np.zeros((rho.shape[0], nk))
for i in np.arange(nk):
if not i % 5:
print(f'process {i}-th event')
X[:,i] = cart.Zk(i, rho, theta)
X = X[:,m>=0]
print(f'rank: {np.linalg.matrix_rank(X)}')
print(f'use {time.time() - tmp} s')
# which info should be used
if mode == 'PE':
y = Q
elif mode == 'time':
y = PulseTime
elif mode == 'combined':
# PulseTime = PulseTime - np.min(PulseTime)
# PulseTime = (PulseTime - np.max(PulseTime)/2)/np.max(PulseTime)*2
# print(np.min(PulseTime), np.max(PulseTime))
PulseTime = (PulseTime - np.max(PulseTime)/2)/np.max(PulseTime)*2
bins = np.arange(-1, 0.05, 0.1)
N = 10
# Legendre coeff
x = pub.legval(bins, np.eye(N).reshape(N, N, 1))
# 1st basis
Y = np.tile(x, len(np.unique(EventID))*len(np.unique(ChannelID))).T
# 2nd basis
X = np.repeat(X, bins.shape[0], axis=0)
# output
y = np.zeros((len(np.unique(EventID)), len(np.unique(ChannelID)), len(bins)))
'''
basis = np.zeros((X.shape[0], X.shape[1]*Y.shape[1]))
for i_index, i in enumerate(np.arange(X.shape[1])):
for j_index, j in enumerate(np.arange(Y.shape[1])):
total_index = i_index*Y.shape[1] + j_index
if not total_index % 10:
print(total_index)
basis[:, total_index] = X[:,i_index]*Y[:,j_index]
X = basis
'''
split_index = np.unique(EventID).shape[0]
for k_index, k in enumerate(np.unique(EventID)): # event begin with 1
if k_index > split_index * split:
break
if not k % 100:
print(k)
index = EventID == k
CID = ChannelID[index]
Pulse_t = PulseTime[index]
for i in np.unique(CID): # PMT begin with 0
y[k_index, i, 1:], _ = np.histogram(Pulse_t[CID==i], bins=bins)
y = np.reshape(y,(-1))
if verbose:
print(f'the basis shape is {X.shape}, and the dependent variable shape is {y.shape}')
if pre =='w':
if split != 1:
split_index = np.int(split*y.shape[0])
X = X[:split_index]
Y = Y[:split_index]
y = y[:split_index]
import pandas as pd
import pyarrow as pa
import pyarrow.parquet as pq
y = np.atleast_2d(y).T
#data = np.hstack((X, y, np.ones_like(y)))
df_X = pd.DataFrame(X)
X_names = []
for i in df_X.columns:
X_names.append('X' + str(i))
df_X.columns = X_names
df_Y = pd.DataFrame(Y)
Y_names = []
for i in df_Y.columns:
Y_names.append('Y' + str(i))
df_Y.columns = Y_names
df_y = pd.DataFrame(y)
df_y.columns = ['output']
df = pd.concat([df_X, df_Y, df_y], axis=1)
table = pa.Table.from_pandas(df)
pq.write_table(table, 'test1.parquet')
return
if not pre:
# Regression methods:
if alg == 'sms':
import statsmodels.api as sm
if mode == 'PE':
model = sm.GLM(y, X, family=sm.families.Poisson(), fit_intercept=False)
result = model.fit()
if verbose:
print(result.summary())
AIC = result.aic
coef_ = result.params
std = result.bse
elif mode == 'time':
import pandas as pd
data = pd.DataFrame(data = np.hstack((X, np.atleast_2d(y).T)))
strs = 'y ~ '
start = data.keys().start
stop = data.keys().stop
step = data.keys().step
cname = []
cname.append('X0')
for i in np.arange(start+1, stop, step):
if i == start + 1:
strs += 'X%d ' % i
elif i == stop - step:
pass
else:
strs += ' + X%d ' % i
if i == stop - step:
cname.append('y')
else:
cname.append('X%d' % i)
data.columns = cname
mod = sm.formula.quantreg(strs, data[cname])
result = mod.fit(q=qt,)
coef_ = result.params
AIC = np.zeros_like(coef_)
std = np.zeros_like(coef_)
print('Waring! No AIC and std value')
elif mode == 'combined':
# data = pd.DataFrame(data = np.hstack((basis, np.atleast_2d(y).T)))
with h5py.File(output,'w') as out:
out.create_dataset('X', data = X)
out.create_dataset('Y', data = y)
print('begin...')
model = sm.GLM(y, X, family=sm.families.Poisson())
result = model.fit()
if verbose:
print(result.summary())
coef_ = result.params
std = result.bse
AIC = result.aic
if verbose:
print(result.summary())
elif (alg == 'custom'):
from scipy.optimize import minimize
x0 = np.zeros_like(X[0]) # initial value (be careful of Zernike order)
if mode == 'PE':
x0[0] = 0.8 + np.log(2) # intercept is much more important
result = minimize(pub.CalibPE, x0=x0, method='SLSQP', args = (y, PMTPos, X))
elif mode == 'time':
x0[0] = np.mean(y)
qt = 0.1
ts = 2.6
result = minimize(pub.CalibTime, x0=x0, method='SLSQP', args = (np.hstack((EventID, EventID)), y, X, qt, ts))
elif mode == 'combined':
x0 = np.zeros_like(X[0])
x0[0] = 0.8 + np.log(2) # intercept is much more important
result = minimize(pub.CalibPE, x0=x0, method='SLSQP', args = (y, PMTPos, X))
coef_ = np.array(result.x, dtype=float)
if verbose:
print(result.message)
AIC = np.zeros_like(coef_)
std = np.zeros_like(coef_)
H = pub.MyHessian(result.x, pub.CalibPE, *(y, PMTPos, X))
# H = pub.MyHessian(result.x, *(Q, PMTPos, X, pub.CalibTime))
# std = 1/np.sqrt(-np.diag(np.linalg.pinv(H1)))
print(coef_)
# print(std)
print('Waring! No AIC and std value, std is testing')
elif alg == 'sk':
from sklearn.linear_model import TweedieRegressor
alpha = 0.001
reg = TweedieRegressor(power=1, alpha=alpha, link='log', max_iter=1000, tol=1e-6, fit_intercept=False)
reg.fit(X, y)
# just for point data
# pred = reg.predict(X[0:30,0:cut+1])
print('coeff:\n', reg.coef_,'\n')
coef_ = reg.coef_
AIC = np.zeros_like(coef_)
std = np.zeros_like(coef_)
print('Waring! No AIC and std value')
elif alg == 'h2o':
import h2o
from h2o.estimators.gbm import H2OGradientBoostingEstimator
from h2o.estimators.glm import H2OGeneralizedLinearEstimator
if mode != 'combined':
y = np.atleast_2d(y).T
data = np.hstack((X, y, np.ones_like(y)))
h2o.init()
hf = h2o.H2OFrame(data)
predictors = hf.columns[0:-2]
response_col = hf.columns[-2]
if mode == 'PE':
#offset_col = hf.columns[-1]
glm_model = H2OGeneralizedLinearEstimator(family= "poisson",
#offset_column = offset_col,
lambda_ = 0,
compute_p_values = True)
glm_model.train(predictors, response_col, training_frame=hf)
coef_table = glm_model._model_json['output']['coefficients_table']
coef_ = glm_model.coef()
elif mode == 'time':
gbm = H2OGradientBoostingEstimator(distribution="quantile", seed = 1234,
stopping_metric = "mse", stopping_tolerance = 1e-4)
gbm.train(x = predictors, y = response_col, training_frame = hf)
breakpoint()
print(gbm)
exit()
elif mode == 'combined':
y = np.atleast_2d(y).T
data = np.hstack((X, Y, y, np.ones_like(y)))
h2o.init()
hf = h2o.H2OFrame(data)
predictors = hf.columns[0:-2]
response_col = hf.columns[-2]
if verbose:
print(coef_)
if basis == 'Zernike':
print(f'Regession coef shape is f{np.array(coef_).shape}, Zernike shape is {nk}')
coef_ = coef_table['coefficients']
std = coef_table['std_error']
AIC = glm_model.aic()
h2o.cluster().shutdown()
elif pre == 'r':
import h2o
from h2o.estimators.gbm import H2OGradientBoostingEstimator
from h2o.estimators.glm import H2OGeneralizedLinearEstimator
h2o.init()
hf = h2o.import_file("electron-1.parquet")
pairs = []
for i in hf.columns:
for j in hf.columns:
if (i.startswith('Z') and j.startswith('L')):
if ((i!='X0') and (j != 'Y0')):
pairs.append((i,j))
predictors = hf.columns[2:]
response_col = hf.columns[0]
print(predictors)
print(response_col)
print(pairs)
if mode == 'PE':
#offset_col = hf.columns[-1]
glm_model = H2OGeneralizedLinearEstimator(family= "poisson",
#offset_column = offset_col,
lambda_ = 0,
compute_p_values = True)
glm_model.train(predictors, response_col, training_frame=hf)
elif mode == 'combined':
#offset_col = hf.columns[-1]
glm_model = H2OGeneralizedLinearEstimator(family= "poisson",
#offset_column = offset_col,
interaction_pairs=pairs,
lambda_ = 0,
#remove_collinear_columns = True,
compute_p_values = True)
glm_model.train(predictors, response_col, training_frame=hf)
breakpoint()
coef_table = glm_model._model_json['output']['coefficients_table']
coef_ = coef_table['coefficients']
std = coef_table['std_error']
AIC = glm_model.aic()
print(f'Regession coef is f{np.array(coef_)}')
if (figure=='ON'):
import matplotlib.pyplot as plt
L, K = 500, 500
ddx = np.linspace(-1.0, 1.0, K)
ddy = np.linspace(-1.0, 1.0, L)
xv, yv = np.meshgrid(ddx, ddy)
cart.make_cart_grid(xv, yv)
# normal scale
# im = plt.imshow(np.exp(cart.eval_grid(np.array(coef_), matrix=True)), origin='lower', extent=(-1, 1, -1, 1))
# log scale
im = plt.imshow(cart.eval_grid(np.array(coef_), matrix=True), origin='lower', extent=(-1, 1, -1, 1))
plt.colorbar()
plt.savefig('test.png')
else:
print('error regression algorithm')
with h5py.File(output,'w') as out:
out.create_dataset('coeff' + str(order), data = coef_)
out.create_dataset('std' + str(order), data = std)
out.create_dataset('AIC' + str(order), data = AIC)
"id": range(0, len(ent)),
"TriggerNo": ent["TriggerNo"],
"ChannelID": ent["ChannelID"],
}
)
ent["Pedestal"] = pedestal
ent = ent.groupby(by=["TriggerNo"])
Thres = 0.1
fipt = "{}.h5".format(basename)
ipt = h5.File(fipt, "r")
nt = 80
nr = 120
cart = RZern(20)
amn = np.zeros((nt, nr // 2 + 1))
zo = np.concatenate(([0], range(1, nr, 2))) # zernike orders
for i in range(nt):
for j in zo:
if i == 0 and j == 0:
a00 = coef["Intercept"]
elif j == 0:
amn[i, j] = coef["L{}".format(i)]
elif i == 0:
amn[i, (j + 1) // 2] = coef["Z{}".format(j)]
else:
amn[i, (j + 1) // 2] = coef["Z{}_L{}".format(j, i)]
zrho = cart.rhotab[zo, :]
class TestZern(unittest.TestCase):
def setUp(self):
self.pupil = RZern(4)
self.max_enorm = 1e-9
self.max_ip_err = 5e-2
def test_ntab(self):
self.assertTrue(self.pupil.ntab.size == 15)
expect = np.array([0, 1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4])
self.assertTrue(norm(self.pupil.ntab - expect) < self.max_enorm)
def test_mtab(self):
self.assertTrue(self.pupil.mtab.size == 15)
expect = np.array([0, 1, -1, 0, -2, 2, -1, 1, -3, 3, 0, 2, -2, 4, -4])
self.assertTrue(norm(self.pupil.mtab - expect) < self.max_enorm)
def test_rhotab(self):
expect = [
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 13.416407864999,
12.649110640674, 12.649110640674, 3.1622776601684,
3.1622776601684, 0, 0, 0, 0, 0, 0, 8.4852813742386,
8.4852813742386, 2.8284271247462, 2.8284271247462,
0, 0, 0, 0, 0, 0, 0, 0, 3.4641016151378,
2.4494897427832, 2.4494897427832, 0, 0, 0, 0,
-13.416407864999, -9.4868329805051, -9.4868329805051,
0, 0, 0, 2, 2, 0, 0, 0, -5.6568542494924,
-5.6568542494924, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0,
-1.7320508075689, 0, 0, 0, 0, 0, 0, 2.2360679774998,
0, 0, 0, 0
]
for c, v in enumerate(expect):
i, j = c % 15, c // 15
err = abs(self.pupil.coefnorm[i]*self.pupil.rhotab[i, j] - v)
self.assertTrue(err < self.max_enorm)
def test_Rnm(self):
inrho = [
0.19343375193909, 0.75442458148825, 0.34626071666477,
0.41862541430271, 0.15571983035489, 0.81900058392684,
0.62492352784628, 0.73856042161065, 0.80511242070695,
0.067222657563179, 0.95079031650557, 0.49757701102216,
0.75514590470052, 0.74240507067694, 0.83112957571011,
0.1565018467502, 0.45730872055141, 0.61810049609438,
0.93218335504705, 0.83508823555935, 0.89542351634235,
0.58251852466803, 0.58274680636179, 0.85492593896995,
0.034865700047931, 0.8854200954848, 0.40773081135598,
0.036382030447832, 0.74614794273772, 0.15482877075111
]
out3 = [
-1.6024358463019, 0.2395649672106, -1.3167172040235,
-1.1249765690963, -1.6480509660176, 0.59153676922049,
-0.37921722803669, 0.157517884017, 0.5134006785331,
-1.716396928352, 1.3995047634699, -0.87439854650643,
0.24333698669463, 0.177241760149, 0.66086873705921,
-1.6472051624093, -1.0075988516153, -0.40859694027142,
1.2781350494377, 0.68371791511127, 1.0454079255648,
-0.55658471812649, -0.55566323680867, 0.79985538570113,
-1.7278397866178, 0.98369658989472, -1.1561632626913,
-1.7274655420545, 0.19654187580572, -1.6490095429101
]
out4 = [
0.091651618055082, 1.3941428842409, 0.29368520752156,
0.42926631070763, 0.0593968575795, 1.6430245322286,
0.95659779790408, 1.3361268353382, 1.5877739726481,
0.011068964146113, 2.214344179944, 0.60645172969723,
1.3968101047969, 1.3500737219024, 1.6920496368403,
0.059994931046482, 0.51226489069861, 0.93582320415359,
2.1285228321212, 1.7082064455855, 1.9639599046646,
0.83118004289954, 0.83183162858811, 1.7903280385894,
0.0029776414702216, 1.9203234007362, 0.4072139881838,
0.0032422723387354, 1.3637209645609, 0.058719041358534
]
out10 = [
1.7528544047959, -1.0538684824995, 0.82035094947331,
0.29691883664534, 1.9186268081509, -0.72681628778909,
-0.95725432162119, -1.0902934593531, -0.82334230297547,
2.1757147314369, 1.0717625678433, -0.2632155912034,
-1.0518319661711, -1.082911351763, -0.62973545308711,
1.915510691432, 0.017056106891689, -0.93137658244662,
0.7084189870086, -0.59538643046011, 0.10384045987001,
-0.7716820983231, -0.77282798892389, -0.40275090649042,
2.2197785892442, -0.036158358505776, 0.37645712628727,
2.2183328268091, -1.0748457792076, 1.9221603389389
]
out13 = [
0.0044271987866637, 1.0243852641201, 0.0454582689999,
0.09711858840943, 0.0018594122493614, 1.4227770316249,
0.48228916269284, 0.9409014176698, 1.3286974659506,
6.4574746661877e-05, 2.5842766270514, 0.19383902995264,
1.0283086425533, 0.96064675024684, 1.5089503417078,
0.0018970460208737, 0.13830501642735, 0.4615687191036,
2.3878408401262, 1.5379048343826, 2.0328904888789,
0.36411532970706, 0.3646864342091, 1.6893279835042,
4.6729760834851e-06, 1.9435579666012, 0.08739651710603,
5.540484342947e-06, 0.98016633844227, 0.0018172164647309
]
outi = [3, 4, 10, 13]
outl = [out3, out4, out10, out13]
for c, i in enumerate(outi):
for j in range(len(inrho)):
a = self.pupil.coefnorm[i]*self.pupil.Rnm(i, inrho[j])
b = outl[c][j]
err = abs(a - b)
self.assertTrue(err < self.max_enorm)
def test_Zj(self):
rho = [
0, 0.11111111111111, 0.22222222222222,
0.33333333333333, 0.44444444444444,
0.55555555555556, 0.66666666666667,
0.77777777777778, 0.88888888888889, 1
]
theta = [
0, 0.69813170079773, 1.3962634015955,
2.0943951023932, 2.7925268031909,
3.4906585039887, 4.1887902047864,
4.8869219055841, 5.5850536063819,
6.2831853071796
]
c = [
0.54031374569774, 0.99075098653197, 0.98937811670199,
-0.68884118291816, -0.85683760660055, 0.048390017659746,
-0.66485340286758, 1.4527419609898, 1.3798457521444,
0.095136418969694, -0.42712706398395, 0.51080780984162,
-0.65627362438046, -0.12501677594865, -0.53046670030726
]
z = [
0.77833652275983, 0.085651919598506, -0.53679726827283,
-0.98349975448282, -1.1477173085559, -0.92148475591224,
-0.19560997786786, 1.1403260883655, 3.1979694496802,
6.090193057073, 0.77833652275983, 0.74923429103286,
0.92966992705808, 1.3229751043261, 1.8849792604988,
2.524009597409, 3.1008910810612, 3.4289464416307,
3.2739961734642, 2.3543585350795, 0.77833652275983,
1.3880071769557, 2.1381716926469, 2.8957139599519,
3.4767967033161, 3.6468614815119, 3.1206286876391,
1.5620975491243, -1.4154538722785, -6.2494686804882,
0.77833652275983, 1.6882064144334, 2.5555787288029,
3.2751193339259, 3.7304210304525, 3.7940035516249,
3.3273135632778, 2.1807246638382, 0.19353738432559,
-2.8060208116485, 0.77833652275983, 1.5982868830036,
2.2744826664559, 2.7560978140881, 3.0147604484415,
3.0445528736273, 2.8620115753266, 2.5061272207906,
2.0383446588402, 1.5425629198664, 0.77833652275983,
1.2214350933728, 1.5980879771486, 1.7569084557018,
1.5178403949563, 0.67215824514518, -1.0175329591891,
-3.8172975991948, -8.0218694717109, -13.954651789267,
0.77833652275983, 0.68350110425162, 0.77861386147368,
0.97581235178894, 1.1341939908368, 1.0598160525329,
0.50569566906943, -0.82819016908496, -3.2949046131853,
-7.3005509562103, 0.77833652275983, 0.12208636455387,
-0.30877246905582, -0.48094227889849, -0.39896357657152,
-0.10521508444048, 0.32008626436092, 0.75888532593079,
1.0552887455991, 1.0155649579277, 0.77833652275983,
-0.16765298701795, -1.0634255875761, -1.8055846686938,
-2.2742293038136, -2.3329542500415, -1.8288499481469,
-0.59250252256298, 1.5620062186141, 4.8370987836243,
0.77833652275983, 0.085651919598506, -0.53679726827283,
-0.98349975448283, -1.1477173085559, -0.92148475591224,
-0.19560997786786, 1.1403260883655, 3.1979694496802,
6.090193057073
]
count = 0
for th in theta:
for rh in rho:
zv = 0.0
for j, ci in enumerate(c):
zv += ci*self.pupil.Zk(j, rh, th)
err = abs(zv - z[count])
self.assertTrue(err <= self.max_enorm)
count += 1
def test_eval_a(self):
rho = [
0, 0.11111111111111, 0.22222222222222,
0.33333333333333, 0.44444444444444,
0.55555555555556, 0.66666666666667,
0.77777777777778, 0.88888888888889, 1
]
theta = [
0, 0.69813170079773, 1.3962634015955,
2.0943951023932, 2.7925268031909,
3.4906585039887, 4.1887902047864,
4.8869219055841, 5.5850536063819,
6.2831853071796
]
c = [
0.54031374569774, 0.99075098653197, 0.98937811670199,
-0.68884118291816, -0.85683760660055, 0.048390017659746,
-0.66485340286758, 1.4527419609898, 1.3798457521444,
0.095136418969694, -0.42712706398395, 0.51080780984162,
-0.65627362438046, -0.12501677594865, -0.53046670030726
]
phi = [
0.77833652275983, 0.085651919598506, -0.53679726827283,
-0.98349975448282, -1.1477173085559, -0.92148475591224,
-0.19560997786786, 1.1403260883655, 3.1979694496802,
6.090193057073, 0.77833652275983, 0.74923429103286,
0.92966992705808, 1.3229751043261, 1.8849792604988,
2.524009597409, 3.1008910810612, 3.4289464416307,
3.2739961734642, 2.3543585350795, 0.77833652275983,
1.3880071769557, 2.1381716926469, 2.8957139599519,
3.4767967033161, 3.6468614815119, 3.1206286876391,
1.5620975491243, -1.4154538722785, -6.2494686804882,
0.77833652275983, 1.6882064144334, 2.5555787288029,
3.2751193339259, 3.7304210304525, 3.7940035516249,
3.3273135632778, 2.1807246638382, 0.19353738432559,
-2.8060208116485, 0.77833652275983, 1.5982868830036,
2.2744826664559, 2.7560978140881, 3.0147604484415,
3.0445528736273, 2.8620115753266, 2.5061272207906,
2.0383446588402, 1.5425629198664, 0.77833652275983,
1.2214350933728, 1.5980879771486, 1.7569084557018,
1.5178403949563, 0.67215824514518, -1.0175329591891,
-3.8172975991948, -8.0218694717109, -13.954651789267,
0.77833652275983, 0.68350110425162, 0.77861386147368,
0.97581235178894, 1.1341939908368, 1.0598160525329,
0.50569566906943, -0.82819016908496, -3.2949046131853,
-7.3005509562103, 0.77833652275983, 0.12208636455387,
-0.30877246905582, -0.48094227889849, -0.39896357657152,
-0.10521508444048, 0.32008626436092, 0.75888532593079,
1.0552887455991, 1.0155649579277, 0.77833652275983,
-0.16765298701795, -1.0634255875761, -1.8055846686938,
-2.2742293038136, -2.3329542500415, -1.8288499481469,
-0.59250252256298, 1.5620062186141, 4.8370987836243,
0.77833652275983, 0.085651919598506, -0.53679726827283,
-0.98349975448283, -1.1477173085559, -0.92148475591224,
-0.19560997786786, 1.1403260883655, 3.1979694496802,
6.090193057073
]
count = 0
for th in theta:
for rh in rho:
phi2 = self.pupil.eval_a(c, rh, th)
err = abs(phi2 - phi[count])
self.assertTrue(err <= self.max_enorm)
count += 1
def test_rhoitab(self):
z = self.pupil
for k in range(z.nk):
for i in range(z.n + 1):
a = (z.rhoitab[k, i])*(z.n + 2 - i)
b = z.rhotab[k, i]
self.assertTrue(abs(a - b) < self.max_enorm)
def test_eval_grid(self):
log = logging.getLogger('TestZern.test_eval_grid')
z = self.pupil
rho_j = np.array([
0, 0.11111111111111, 0.22222222222222,
0.33333333333333, 0.44444444444444,
0.55555555555556, 0.66666666666667,
0.77777777777778, 0.88888888888889, 1])
theta_i = np.array([
0, 0.69813170079773, 1.3962634015955,
2.0943951023932, 2.7925268031909,
3.4906585039887, 4.1887902047864,
4.8869219055841, 5.5850536063819,
6.2831853071796])
a = normal(size=z.nk)
t1 = time()
Phi1 = [z.eval_a(a, rh, th) for rh in rho_j for th in theta_i]
t2 = time()
log.debug('list eval {:.6f}'.format(t2 - t1))
z.make_pol_grid(rho_j, theta_i)
t1 = time()
Phi2 = z.eval_grid(np.array(a))
t2 = time()
log.debug('numpy eval {:.6f}'.format(t2 - t1))
Phi1 = np.array(Phi1).ravel(order='F')
Phi2 = np.array(Phi2).ravel(order='F')
log.debug('norm(Phi1 - Phi2) {}'.format(norm(Phi1 - Phi2)))
self.assertTrue(norm(Phi1 - Phi2) < self.max_enorm)
def test_save_load(self):
rho_j = np.array([
0, 0.11111111111111, 0.22222222222222,
0.33333333333333, 0.44444444444444,
0.55555555555556, 0.66666666666667,
0.77777777777778, 0.88888888888889, 1])
theta_i = np.array([
0, 0.69813170079773, 1.3962634015955,
2.0943951023932, 2.7925268031909,
3.4906585039887, 4.1887902047864,
4.8869219055841, 5.5850536063819,
6.2831853071796])
def do_test(cls, complex_a):
rz1 = cls(4)
if complex_a:
a = normal(size=rz1.nk) + 1j*normal(size=rz1.nk)
else:
a = normal(size=rz1.nk)
rz1.make_pol_grid(rho_j, theta_i)
PhiA = rz1.eval_grid(a)
# create tmp path
tmpfile = NamedTemporaryFile()
tmppath = tmpfile.name
tmpfile.close()
rz1.save(tmppath)
rz2 = cls.load(tmppath)
PhiB = rz2.eval_grid(a)
self.assertTrue(norm(PhiA - PhiB) < self.max_enorm)
self.assertTrue(type(rz1) == type(rz2))
self.assertTrue(norm(rz1.coefnorm - rz2.coefnorm) == 0)
self.assertTrue(norm(rz1.ntab - rz2.ntab) == 0)
self.assertTrue(norm(rz1.mtab - rz2.mtab) == 0)
self.assertTrue(rz1.n == rz2.n)
self.assertTrue(rz1.nk == rz2.nk)
self.assertTrue(rz1.normalise == rz2.normalise)
self.assertTrue(norm(rz1.rhoitab - rz2.rhoitab) == 0)
self.assertTrue(norm(rz1.rhotab - rz2.rhotab) == 0)
self.assertTrue(rz1.numpy_dtype == rz2.numpy_dtype)
self.assertTrue(norm(rz1.ZZ - rz2.ZZ) == 0)
os.unlink(tmppath)
del rz1, rz2, a, PhiA, PhiB
do_test(RZern, False)
do_test(CZern, True)
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_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_nm2noll(self):
noll_indices = ((0, 0), (1, 1), (1, -1), (2, 0), (2, -2), (2, 2),
(3, -1), (3, 1), (3, -3), (3, 3), (4, 0), (4, 2),
(4, -2), (4, 4), (4, -4))
for k, (n, m) in enumerate(noll_indices):
self.assertEqual(RZern.nm2noll(n, m), k + 1)
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)