def test_orbit_bump(self):
v0 = ap.getOrbit()
bpm = ap.getElements("BPM")
hcor = ap.getElements("HCOR")
hcor1 = ap.getElements("cx*")
vcor = ap.getElements("VCOR")
vcor1 = ap.getElements("cy*")
# for e in hcor:
# print e.name, e.pv(field='x')
self.assertGreater(len(v0), 0)
self.assertGreaterEqual(len(bpm), 180)
self.assertEqual(len(hcor1), 180)
self.assertGreaterEqual(len(hcor), 180)
self.assertEqual(len(vcor1), 180)
self.assertGreaterEqual(len(vcor), 180)
# maximum deviation
mx, my = max(abs(v0[:, 0])), max(abs(v0[:, 1]))
ih = np.random.randint(0, len(hcor), 3)
iv = np.random.randint(0, len(vcor), 4)
for i in ih:
hcor[i].x = hcor[i].x + np.random.rand() * 1e-6
for i in iv:
vcor[i].y = vcor[i].y + np.random.rand() * 1e-6
ap.hlalib.waitStableOrbit(v0, minwait=5)
v1 = ap.getOrbit()
self.assertNotEqual(np.std(v1[:, 0]), np.std(v0[:, 0]))
self.logger.info("resetting trims")
ap.hlalib._reset_trims()
time.sleep(10)
def test_orbit_bump(self):
v0 = ap.getOrbit()
bpm = ap.getElements('BPM')
hcor = ap.getElements('HCOR')
hcor1 = ap.getElements('cx*')
vcor = ap.getElements('VCOR')
vcor1 = ap.getElements('cy*')
#for e in hcor:
# print e.name, e.pv(field='x')
self.assertGreater(len(v0), 0)
self.assertGreaterEqual(len(bpm), 180)
self.assertEqual(len(hcor1), 180)
self.assertGreaterEqual(len(hcor), 180)
self.assertEqual(len(vcor1), 180)
self.assertGreaterEqual(len(vcor), 180)
# maximum deviation
mx, my = max(abs(v0[:,0])), max(abs(v0[:,1]))
ih = np.random.randint(0, len(hcor), 3)
iv = np.random.randint(0, len(vcor), 4)
for i in ih: hcor[i].x = hcor[i].x+np.random.rand()*1e-6
for i in iv: vcor[i].y = vcor[i].y+np.random.rand()*1e-6
ap.hlalib.waitStableOrbit(v0, minwait=5)
v1 = ap.getOrbit()
self.assertNotEqual(np.std(v1[:,0]), np.std(v0[:,0]))
self.logger.info("resetting trims")
ap.hlalib._reset_trims()
time.sleep(10)
def test_linearity_l2(self):
bpms = self.ormdata.getBpmNames()
trims = self.ormdata.getTrimNames()
corrname = trims[4]
corr = ap.getExactElement(corrname)
x0 = corr.x
obt0 = ap.getOrbit(spos=True)
dxlst = np.linspace(-1e-4, 1e-4, 5) + x0
obt = []
for i,dx in enumerate(dxlst):
corr.x = dx
time.sleep(3)
obt.append(ap.getOrbit(spos=True))
jbpm = 36
bpm = ap.getExactElement(bpms[jbpm])
mij = self.ormdata.get(bpm.name, 'x', corr.name, 'x')
dxobt = [obt[i][jbpm,0] for i in range(len(dxlst))]
plt.clf()
plt.plot(dxlst, dxobt, 'r--o')
plt.plot(dxlst, mij*dxlst + obt0[jbpm,0])
plt.savefig(figname("test_ormdata_linearity.png"))
corr.x = x0
#print orm
#for i,b in enumerate(orm.bpm):
# print i, b[0], b[2]
#orm.checkLinearity(plot=True)
pass
def test_measure_orm_sub1_l2(self):
#trimlst = ['ch1g6c15b', 'cl2g6c14b', 'cm1g4c26a']
trimlst = ['cl2g6c14b']
#trimx = ['CXH1G6C15B']
bpmlst = [e.name for e in ap.getElements('BPM')]
trims = ap.getElements(trimlst)
for t in trims:
t.x = 0
t.y = 0
fname = time.strftime("orm_sub1_%Y%m%d_%H%M.hdf5")
orm1 = ap.measOrbitRm(bpmlst, trimlst, fname, verbose=2)
ormdat = ap.apdata.OrmData(fname)
corr = trims[0]
x0 = corr.x
obt0 = ap.getOrbit(spos=True)
dxlst = np.linspace(-1e-4, 1e-4, 5) + x0
obt = []
for i,dx in enumerate(dxlst):
corr.x = dx
time.sleep(3)
obt.append(ap.getOrbit(spos=True))
jbpm = 36
bpm = ap.getExactElement(bpmlst[jbpm])
mij = ormdat.get(bpm.name, 'x', corr.name, 'x')
dxobt = [obt[i][jbpm,0] for i in range(len(dxlst))]
plt.clf()
plt.plot(dxlst, dxobt, 'r--o')
plt.plot(dxlst, mij*dxlst + obt0[jbpm,0])
plt.savefig(figname("test_measure_orm_sub1_linearity.png"))
corr.x = x0
def test_orbit_read_l0(self):
self.logger.info("reading orbit")
self.assertGreater(len(ap.getElements('BPM')), 0)
bpm = ap.getElements('BPM')
for i,e in enumerate(bpm):
self.assertGreaterEqual(abs(e.x), 0)
self.assertGreaterEqual(abs(e.y), 0)
v = ap.getOrbit()
self.assertGreater(len(v), 0)
v = ap.getOrbit('*')
self.assertGreater(len(v), 0)
v = ap.getOrbit('p[lhm]*')
self.assertGreater(len(v), 0)
def test_orbit_read(self):
self.logger.info("reading orbit")
self.assertGreater(len(ap.getElements("BPM")), 0)
bpm = ap.getElements("BPM")
for i, e in enumerate(bpm):
self.assertGreaterEqual(abs(e.x), 0)
self.assertGreaterEqual(abs(e.y), 0)
v = ap.getOrbit()
self.assertGreater(len(v), 0)
v = ap.getOrbit("*")
self.assertGreater(len(v), 0)
v = ap.getOrbit("p[lhm]*")
self.assertGreater(len(v), 0)
def test_golden(self):
f = open("golden.txt", "w")
cors = ap.getElements('COR')
for c in cors:
c.x = 0.0
c.y = 0.0
time.sleep(2)
obt0a = ap.getOrbit(spos=True)
for scale in [1.0, 0.9, 0.8, 0.7, 0.6]:
ap.correctOrbit(scale=scale, wait=3)
time.sleep(6)
obt0 = ap.getOrbit(spos=True)
d0 = np.zeros((len(cors), 2), 'd')
for i,c in enumerate(cors):
d0[i,0] = c.x
d0[i,1] = c.y
c.setGolden('x', d0[i,0], unitsys=None)
c.setGolden('y', d0[i,1], unitsys=None)
f.write("{0} x {1}\n".format(c.name, d0[i,0]))
f.write("{0} y {1}\n".format(c.name, d0[i,1]))
f.close()
# now reset the orbit
time.sleep(5)
for c in cors:
c.x = 0.0
c.y = 0.0
for i,c in enumerate(cors):
c.reset('x', data='golden')
c.reset('y', data='golden')
time.sleep(6)
d1 = np.zeros((len(cors), 2), 'd')
for i,c in enumerate(cors):
d1[i,0] = c.x
d1[i,1] = c.y
obt1 = ap.getOrbit(spos=True)
plt.subplot(311)
plt.plot(obt0a[:,-1], obt0a[:,0], 'g-')
plt.plot(obt0[:,-1], obt0[:,0], 'r-')
plt.plot(obt1[:,-1], obt1[:,0], 'b--')
plt.subplot(312)
plt.plot(d1[:,0] - d0[:,0], 'r-')
plt.plot(d1[:,1] - d0[:,1], 'b--')
plt.subplot(313)
plt.plot(obt0[:,-1], obt1[:,0] - obt0[:,0], 'r-x')
plt.plot(obt1[:,-1], obt1[:,1] - obt0[:,1], 'b-o')
plt.savefig(figname("test_golden.png"))
def _random_kick(self, n, vx = 1e-4, vy = 1e-4):
v0 = ap.getOrbit()
hcors = self.lat.getElementList('COR')
for i in range(n):
k = np.random.randint(len(hcors))
v0x, v0y = hcors[k].x, hcors[k].y
self.kickers.append([hcors[k], v0x, v0y])
hcors[k].x = vx
hcors[k].y = vy
ap.hlalib.waitStableOrbit(v0, minwait=3)
def test_corr_orbit_l2(self):
self._random_kick(3)
obt = ap.getOrbit()
bpm = ap.getElements('BPM')[60:101]
trim = ap.getGroupMembers(['*', '[HV]COR'], op='intersection')
v0 = ap.getOrbit('p*', spos=True)
ap.correctOrbit(bpm, trim, repeat=5, scale=0.9)
time.sleep(4)
v1 = ap.getOrbit('p*', spos=True)
import matplotlib.pylab as plt
plt.clf()
ax = plt.subplot(211)
fig = plt.plot(v0[:,-1], v0[:,0], 'r-x', label='X(before)')
fig = plt.plot(v1[:,-1], v1[:,0], 'g-o', label='X(after)')
plt.legend()
ax = plt.subplot(212)
fig = plt.plot(v0[:,-1], v0[:,1], 'r-x', label='Y(before)')
fig = plt.plot(v1[:,-1], v1[:,1], 'g-o', label='Y(after)')
plt.legend()
plt.savefig(figname("test_nsls2_orbit_correct.png"))
def measBackground(ID, output, iiter):
"""measure the background and return saved group name"""
if not nsls2id.putBackground(ID):
print "Failed at setting {0} to background mode".format(ID)
return None
# create background subgroup with index
fid = h5py.File(output)
prefix = "iter_"
iterindex = max([int(g[len(prefix):]) for g in fid[ID.name].keys()
if g.startswith(prefix)] + [-1]) + 1
bkgGroup = "iter_{0:04d}".format(iterindex)
grp = fid[ID.name].create_group(bkgGroup)
orb0 = ap.getOrbit(spos=True)
grp["orbit"] = orb0
tau, I = ap.getLifetimeCurrent()
grp["lifetime"] = tau
grp["current"] = I
grp.attrs["iter"] = iiter
fid.close()
return bkgGroup
def test_local_bump(self):
hcor = ap.getElements('HCOR')
hcor_v0 = [e.x for e in hcor]
vcor = ap.getElements('VCOR')
vcor_v0 = [e.y for e in vcor]
bpm = ap.getElements('BPM')
bpm_v0 = [[e.x, e.y] for e in bpm]
bpm_v1 = [[e.x, e.y] for e in bpm]
for i in range(0, len(bpm)):
bpm_v1[i] = [0, 0]
x1, x2 = 1e-4, 2e-4
bpm_v1[20][0] = x1
bpm_v1[21][0] = x1
bpm_v1[22][0] = x1
bpm_v1[23][0] = x2
bpm_v1[24][0] = x2
bpm_v1[25][0] = x1
bpm_v1[26][0] = x1
bpm_v1[100][1] = x2
bpm_v1[101][1] = x2
bpm_v1[102][1] = x1
bpm_v1[103][1] = x1
bpm_v1[104][1] = x2
bpm_v1[105][1] = x2
ap.setLocalBump(bpm, hcor+vcor, bpm_v1, repeat=10, verbose=3)
import matplotlib.pylab as plt
plt.clf()
v = ap.getOrbit(spos=True)
plt.plot(v[:,-1], v[:,0], '-.')
plt.plot(v[:,-1], v[:,1], '--')
plt.savefig(figname("test_localbump.png"))
hclist = ['cyh1g2c10a', 'cyh2g2c10a', #'cxm1g4c10a', #'cxm1g4c10b', 'cyl1g6c10b', 'cyl2g6c10b'] hcor = ap.getElements(hclist) for h in hcor: print h beta = ap.getBeta(hclist) phi = ap.getPhase(hclist) for h in hcor: h.y = 0 time.sleep(6) x0 = ap.getOrbit(spos=True) #print type(beta), type(phi), type(x) #dphi = (phi - phi[0,:])*(2*np.pi) # the plane, x or y ic = 1 theta = [5e-6, -5e-6, 0, 0] b0, b1, b2, b3 = np.sqrt(beta[:,ic]) sp30 = np.sin((phi[3,ic] - phi[0,ic])*2*np.pi) sp31 = np.sin((phi[3,ic] - phi[1,ic])*2*np.pi) sp20 = np.sin((phi[2,ic] - phi[0,ic])*2*np.pi) sp21 = np.sin((phi[2,ic] - phi[1,ic])*2*np.pi) sp32 = np.sin((phi[3,ic] - phi[2,ic])*2*np.pi) theta[2] = -(b0*theta[0]*sp30 + b1*theta[1]*sp31)/sp32/b2
import aphla as ap
import numpy as np
import matplotlib.pylab as plt
import time
print ap.__path__
ap.initNSLS2V1()
bpms = ap.getElements('BPM')
#trims = ap.getGroupMembers(['*', '[HV]COR'], op='intersection')
trims = ap.getElements('HCOR') + ap.getElements('VCOR')
print "Bpms x Trims: (%d, %d)" % (len(bpms), len(trims))
v0 = ap.getOrbit(spos=True)
n1, n2 = 130, 150
ap.setLocalBump([e.name for e in bpms[n1:n2]], [e.name for e in trims],
np.ones((n2 - n1, 2), 'd') * 1e-5,
scale=0.7,
repeat=6)
#Euclidian norm: ...
time.sleep(4)
v1 = ap.getOrbit(spos=True)
time.sleep(4)
v2 = ap.getOrbit(spos=True)
# plotting
plt.clf()
ax = plt.subplot(211)
ax.annotate("H orbit before/after correction", (0.03, 0.9),
xycoords='axes fraction')
ax.plot(v0[:, -1], v0[:, 0], 'r-')
def saveState(idobj, output, iiter, parnames=None, background=None, extdata={}):
"""
parnames - list of extra fields of idobj to be saved.
background - the group name for its last background.
extdata - extra data dictionary.
returns data group name
"""
t1 = datetime.now()
prefix = "background" if background is None else "iter"
# create background subgroup with index
fid = h5py.File(output)
iterindex = max([int(g[len(prefix) + 1 :]) for g in fid[idobj.name].keys() if g.startswith(prefix)] + [-1]) + 1
groupName = "{0}_{1:04d}".format(prefix, iterindex)
grp = fid[idobj.name].create_group(groupName)
orb0 = ap.getOrbit(spos=True)
grp["orbit"] = orb0
tau, I = ap.getLifetimeCurrent()
grp["lifetime"] = tau
grp["current"] = I
if parnames is None:
parnames = ["gap", "phase", "mode"]
else:
parnames = ["gap", "phase", "mode"] + list(parnames)
parnames = np.unique(parnames).tolist()
fields = idobj.fields()
for par in parnames:
if par in fields:
grp[par] = idobj.get(par, unitsys=None)
grp[par].attrs["unitsymb"] = idobj.getUnit(par, unitsys=None)
for k, v in extdata.items():
grp[k] = v
grp.attrs["iter"] = iiter
if background:
grp.attrs["background"] = background
else:
# Save current ID trim setpoints
elemflds = createCorrectorField(idobj)
_, flds = zip(*elemflds)
trim_sps = [idobj.get(ch, unitsys=None, handle="setpoint") for ch in flds]
grp["trim_sp"] = trim_sps
grp["trim_sp"].attrs["fields"] = flds
# Save current BPM offsets
try:
bpm_offset_pvs = saveState.bpm_offset_pvs
bpm_offset_pv_suffixes = saveState.bpm_offset_pv_suffixes
bpm_offset_fields = saveState.bpm_offset_fields
bpm_names = saveState.bpm_names
except AttributeError:
bpms = ap.getElements("p[uhlm]*")
bpm_names = [b.name for b in bpms]
bpm_pv_prefixes = [b.pv(field="xbba")[0].replace("BbaXOff-SP", "") for b in bpms]
bpm_offset_fields = ["xbba", "ybba", "xref1", "yref1", "xref2", "yref2"]
bpm_offset_pv_suffixes = [bpms[0].pv(field=f)[0].replace(bpm_pv_prefixes[0], "") for f in bpm_offset_fields]
bpm_offset_pvs = []
for suf in bpm_offset_pv_suffixes:
bpm_offset_pvs += [prefix + suf for prefix in bpm_pv_prefixes]
saveState.bpm_offset_pvs = bpm_offset_pvs
saveState.bpm_offset_pv_suffixes = bpm_offset_pv_suffixes
saveState.bpm_offset_fields = bpm_offset_fields
saveState.bpm_names = bpm_names
bpm_offsets = (
np.array([d.real if d.ok else np.nan for d in ap.caget(bpm_offset_pvs, throw=False)])
.reshape((len(bpm_offset_pv_suffixes), -1))
.T
)
grp.create_dataset("bpm_offsets", data=bpm_offsets, compression="gzip")
grp["bpm_offsets"].attrs["fields"] = bpm_offset_fields
grp["bpm_offsets"].attrs["pv_suffixes"] = bpm_offset_pv_suffixes
grp["bpm_offsets"].attrs["bpm_names"] = bpm_names
grp.attrs["state_saved"] = t1.strftime("%Y-%m-%d %H:%M:%S.%f")
fid.close()
return groupName
import aphla as ap
import numpy as np
import matplotlib.pylab as plt
import time
print ap.__path__
ap.initNSLS2V1()
bpms = ap.getElements('BPM')
#trims = ap.getGroupMembers(['*', '[HV]COR'], op='intersection')
trims = ap.getElements('HCOR') + ap.getElements('VCOR')
print "Bpms x Trims: (%d, %d)" % (len(bpms), len(trims) )
v0 = ap.getOrbit(spos=True)
n1, n2 = 130, 150
ap.setLocalBump([e.name for e in bpms[n1:n2]], [e.name for e in trims],
np.ones((n2-n1, 2), 'd')*1e-5, scale=0.7, repeat=6)
#Euclidian norm: ...
time.sleep(4)
v1 = ap.getOrbit(spos=True)
time.sleep(4)
v2 = ap.getOrbit(spos=True)
# plotting
plt.clf()
ax = plt.subplot(211)
ax.annotate("H orbit before/after correction", (0.03, 0.9),
xycoords='axes fraction')
ax.plot(v0[:,-1], v0[:,0], 'r-')
ax.plot(v1[:,-1], v1[:,0], 'g--')
ax.plot(v2[n1:n2,-1], v2[n1:n2,0], 'g-o')
gamma = 3.0e3/.511
eta = alphac - 1/gamma/gamma
# orbit at cell 3-6 BPMs
bpmobj = ap.getElements('p*c0[3-6]*')
bpmnames = [b.name for b in bpmobj]
s1 = [b.sb for b in bpmobj]
eta0 = ap.getDispersion(bpmnames)
print "dispersion:", eta0
# f in MHz
f0 = ap.getRfFrequency()
f = np.linspace(f0 - 1e-5, f0 + 1e-5, 5)
# avoid a bug in virtac
obt0 = ap.getOrbit(bpmnames)
x0, y0 = obt0[:,0], obt0[:,1]
time.sleep(4)
codx = np.zeros((len(f), len(bpmobj)), 'd')
cody = np.zeros((len(f), len(bpmobj)), 'd')
for i,f1 in enumerate(f):
ap.putRfFrequency(f1)
time.sleep(3)
obt1 = ap.getOrbit()
# repeat the put/get in case simulator did not response latest results
ap.putRfFrequency(f1)
time.sleep(6)
obt2 = ap.getOrbit(bpmnames)
print i, obt1[0,:2], obt2[0,:2]
def test_orbit_l0(self):
v = ap.getOrbit()
def saveState(idobj, output, iiter,
parnames=None, background=None, extdata={}):
"""
parnames - list of extra fields of idobj to be saved.
background - the group name for its last background.
extdata - extra data dictionary.
returns data group name
"""
t1 = datetime.now()
prefix = "background" if background is None else "iter"
# create background subgroup with index
fid = h5py.File(output, 'a')
iterindex = max([int(g[len(prefix)+1:]) for g in list(fid[idobj.name])
if g.startswith(prefix)] + [-1]) + 1
groupName = "{0}_{1:04d}".format(prefix, iterindex)
grp = fid[idobj.name].create_group(groupName)
orb0 = ap.getOrbit(spos=True)
grp["orbit"] = orb0
tau, I = ap.getLifetimeCurrent()
grp["lifetime"] = tau
grp["current"] = I
if parnames is None:
parnames = ['gap', 'phase', 'mode']
else:
parnames = ['gap', 'phase', 'mode'] + list(parnames)
parnames = np.unique(parnames).tolist()
fields = idobj.fields()
for par in parnames:
if par in fields:
grp[par] = idobj.get(par, unitsys=None)
grp[par].attrs['unitsymb'] = idobj.getUnit(par, unitsys=None)
for k,v in extdata.items():
grp[k] = v
grp.attrs["iter"] = iiter
if background:
grp.attrs["background"] = background
else:
# Save current ID trim setpoints
elemflds = createCorrectorField(idobj)
_, flds = zip(*elemflds)
trim_sps = [idobj.get(ch, unitsys=None, handle='setpoint') for ch in flds]
grp['trim_sp'] = trim_sps
grp['trim_sp'].attrs['fields'] = flds
# Save current BPM offsets
try:
bpm_offset_pvs = saveState.bpm_offset_pvs
bpm_offset_pv_suffixes = saveState.bpm_offset_pv_suffixes
bpm_offset_fields = saveState.bpm_offset_fields
bpm_names = saveState.bpm_names
except AttributeError:
bpms = ap.getElements('p[uhlm]*')
bpm_names = [b.name for b in bpms]
bpm_pv_prefixes = [b.pv(field='xbba')[0].replace('BbaXOff-SP', '')
for b in bpms]
bpm_offset_fields = ['xbba', 'ybba', 'xref1', 'yref1', 'xref2', 'yref2']
bpm_offset_pv_suffixes = [
bpms[0].pv(field=f)[0].replace(bpm_pv_prefixes[0], '')
for f in bpm_offset_fields]
bpm_offset_pvs = []
for suf in bpm_offset_pv_suffixes:
bpm_offset_pvs += [prefix+suf for prefix in bpm_pv_prefixes]
saveState.bpm_offset_pvs = bpm_offset_pvs
saveState.bpm_offset_pv_suffixes = bpm_offset_pv_suffixes
saveState.bpm_offset_fields = bpm_offset_fields
saveState.bpm_names = bpm_names
bpm_offsets = np.array(
[d.real if d.ok else np.nan
for d in ap.caget(bpm_offset_pvs, throw=False)]).reshape(
(len(bpm_offset_pv_suffixes), -1)).T
grp.create_dataset('bpm_offsets', data=bpm_offsets, compression='gzip')
grp['bpm_offsets'].attrs['fields'] = bpm_offset_fields
grp['bpm_offsets'].attrs['pv_suffixes'] = bpm_offset_pv_suffixes
grp['bpm_offsets'].attrs['bpm_names'] = bpm_names
grp.attrs["state_saved"] = t1.strftime("%Y-%m-%d %H:%M:%S.%f")
fid.close()
return groupName
def test_orbit(self):
v = ap.getOrbit()
gamma = 3.0e3 / .511
eta = alphac - 1 / gamma / gamma
# orbit at cell 3-6 BPMs
bpmobj = ap.getElements('p*c0[3-6]*')
bpmnames = [b.name for b in bpmobj]
s1 = [b.sb for b in bpmobj]
eta0 = ap.getDispersion(bpmnames)
print "dispersion:", eta0
# f in MHz
f0 = ap.getRfFrequency()
f = np.linspace(f0 - 1e-5, f0 + 1e-5, 5)
# avoid a bug in virtac
obt0 = ap.getOrbit(bpmnames)
x0, y0 = obt0[:, 0], obt0[:, 1]
time.sleep(4)
codx = np.zeros((len(f), len(bpmobj)), 'd')
cody = np.zeros((len(f), len(bpmobj)), 'd')
for i, f1 in enumerate(f):
ap.putRfFrequency(f1)
time.sleep(3)
obt1 = ap.getOrbit()
# repeat the put/get in case simulator did not response latest results
ap.putRfFrequency(f1)
time.sleep(6)
obt2 = ap.getOrbit(bpmnames)
print i, obt1[0, :2], obt2[0, :2]
#'cxm1g4c10a',
#'cxm1g4c10b',
'cyl1g6c10b',
'cyl2g6c10b'
]
hcor = ap.getElements(hclist)
for h in hcor:
print h
beta = ap.getBeta(hclist)
phi = ap.getPhase(hclist)
for h in hcor:
h.y = 0
time.sleep(6)
x0 = ap.getOrbit(spos=True)
#print type(beta), type(phi), type(x)
#dphi = (phi - phi[0,:])*(2*np.pi)
# the plane, x or y
ic = 1
theta = [5e-6, -5e-6, 0, 0]
b0, b1, b2, b3 = np.sqrt(beta[:, ic])
sp30 = np.sin((phi[3, ic] - phi[0, ic]) * 2 * np.pi)
sp31 = np.sin((phi[3, ic] - phi[1, ic]) * 2 * np.pi)
sp20 = np.sin((phi[2, ic] - phi[0, ic]) * 2 * np.pi)
sp21 = np.sin((phi[2, ic] - phi[1, ic]) * 2 * np.pi)
sp32 = np.sin((phi[3, ic] - phi[2, ic]) * 2 * np.pi)
theta[2] = -(b0 * theta[0] * sp30 + b1 * theta[1] * sp31) / sp32 / b2
