def linearized_freqs(tref):
astro, ader = ut_astron(tref)
freq = const.freq.copy()
freq[not_shallow] = np.dot(const.doodson[not_shallow, :], ader) / 24
for i0, nshal, k in zip(ishallow, nshallow, kshallow):
ik = i0 + np.arange(nshal)
freq[k] = (freq[shallow.iname[ik] - 1] * shallow.coef[ik]).sum()
return freq
def linearized_freqs(tref):
astro, ader = ut_astron(tref)
freq = const.freq.copy()
freq[not_shallow] = np.dot(const.doodson[not_shallow, :], ader) / 24
for i0, nshal, k in zip(ishallow, nshallow, kshallow):
ik = i0 + np.arange(nshal)
freq[k] = (freq[shallow.iname[ik] - 1] *
shallow.coef[ik]).sum()
return freq
def test_astron():
dns = [694086.000000000, 736094.552430556]
a_expected = np.array([[-0.190238223090586, -0.181487296022524],
[0.308043143259513, 0.867328798490917],
[0.117804920168928, 0.133410946894728],
[0.967220455214981, 0.966971540511103],
[-0.701640310306205, 0.477567604831163],
[0.781185288947374, 0.786679406642858]])
ad_expected = np.array([[9.66136807802411e-01, 9.66136808053116e-01],
[3.66011014627454e-02, 3.66011012649486e-02],
[2.73790926515680e-03, 2.73790931806424e-03],
[3.09455773258269e-04, 3.09453963277675e-04],
[1.47094227256402e-04, 1.47093863142766e-04],
[1.30745790039597e-07, 1.30825941667529e-07]])
a, ad = ut_astron(dns)
np.testing.assert_array_almost_equal(a, a_expected)
np.testing.assert_array_almost_equal(ad, ad_expected)
def FUV(t, tref, lind, lat, ngflgs):
"""
UT_FUV()
compute nodal/satellite correction factors and astronomical argument
inputs
t = times [datenum UTC] (nt x 1)
tref = reference time [datenum UTC] (1 x 1)
lind = list indices of constituents in ut_constants.mat (nc x 1)
lat = latitude [deg N] (1 x 1)
ngflgs = [NodsatLint NodsatNone GwchLint GwchNone] each 0/1
output
F = real nodsat correction to amplitude [unitless] (nt x nc)
U = nodsat correction to phase [cycles] (nt x nc)
V = astronomical argument [cycles] (nt x nc)
UTide v1p0 9/2011 [email protected]
(uses parts of t_vuf.m from t_tide, Pawlowicz et al 2002)
"""
t = np.atleast_1d(t).flatten()
nt = len(t)
nc = len(lind)
# nodsat
if ngflgs[1]:
F = np.ones((nt, nc))
U = np.zeros((nt, nc))
else:
if ngflgs[0]:
tt = np.array([tref])
else:
tt = t
ntt = len(tt)
astro, ader = ut_astron(tt)
if abs(lat) < 5:
lat = np.sign(lat) * 5
slat = np.sin(np.deg2rad(lat))
rr = sat.amprat.copy()
j = sat.ilatfac == 1
rr[j] *= 0.36309 * (1.0 - 5.0 * slat**2) / slat
j = sat.ilatfac == 2
rr[j] *= 2.59808 * slat
# sat.deldood is (162, 3); all other sat vars are (162,)
uu = np.dot(sat.deldood, astro[3:6, :]) + sat.phcorr[:, None]
np.fmod(uu, 1, out=uu) # fmod is matlab rem; differs from % op
mat = rr[:, None] * np.exp(1j * 2 * np.pi * uu)
nfreq = len(const.isat) # 162
F = np.ones((nfreq, ntt), dtype=complex)
iconst = sat.iconst - 1
ind = np.unique(iconst)
for ii in ind:
F[ii, :] = 1 + np.sum(mat[iconst == ii], axis=0)
U = np.angle(F) / (2 * np.pi) # cycles
F = np.abs(F)
for i0, nshal, k in zip(ishallow, nshallow, kshallow):
ik = i0 + np.arange(nshal)
j = shallow.iname[ik] - 1
exp1 = shallow.coef[ik, None]
exp2 = np.abs(exp1)
F[k, :] = np.prod(F[j, :]**exp2, axis=0)
U[k, :] = np.sum(U[j, :] * exp1, axis=0)
F = F[lind, :].T
U = U[lind, :].T
# if ngflgs[0]: # Nodal/satellite with linearized times.
# F = F[np.ones((nt, 1)), :]
# U = U[np.ones((nt, 1)), :]
# Let's try letting broadcasting take care of it.
# gwch (astron arg)
if ngflgs[3]: # None (raw phase lags not Greenwich phase lags).
freq = linearized_freqs(tref)
V = 24 * (t[:, np.newaxis] - tref) * freq[lind]
else:
if ngflgs[2]: # Linearized times.
tt = np.array([tref])
else:
tt = t # Exact times.
ntt = len(tt)
astro, ader = ut_astron(tt)
V = np.dot(const.doodson, astro) + const.semi[:, None]
np.fmod(V, 1, out=V)
for i0, nshal, k in zip(ishallow, nshallow, kshallow):
ik = i0 + np.arange(nshal)
j = shallow.iname[ik] - 1
exp1 = shallow.coef[ik, None]
V[k, :] = np.sum(V[j, :] * exp1, axis=0)
V = V[lind, :].T
if ngflgs[2]: # linearized times
freq = linearized_freqs(tref)
V = V + 24 * (t[:, None] - tref) * freq[None, lind]
return F, U, V
def FUV(t, tref, lind, lat, ngflgs):
"""
UT_FUV()
compute nodal/satellite correction factors and astronomical argument
inputs
t = times [datenum UTC] (nt x 1)
tref = reference time [datenum UTC] (1 x 1)
lind = list indices of constituents in ut_constants.mat (nc x 1)
lat = latitude [deg N] (1 x 1)
ngflgs = [NodsatLint NodsatNone GwchLint GwchNone] each 0/1
output
F = real nodsat correction to amplitude [unitless] (nt x nc)
U = nodsat correction to phase [cycles] (nt x nc)
V = astronomical argument [cycles] (nt x nc)
UTide v1p0 9/2011 [email protected]
(uses parts of t_vuf.m from t_tide, Pawlowicz et al 2002)
"""
t = np.atleast_1d(t).flatten()
nt = len(t)
nc = len(lind)
# nodsat
if ngflgs[1]:
F = np.ones((nt, nc))
U = np.zeros((nt, nc))
else:
if ngflgs[0]:
tt = np.array([tref])
else:
tt = t
ntt = len(tt)
astro, ader = ut_astron(tt)
if abs(lat) < 5:
lat = np.sign(lat) * 5
slat = np.sin(np.deg2rad(lat))
rr = sat.amprat.copy()
j = sat.ilatfac == 1
rr[j] *= 0.36309 * (1.0 - 5.0 * slat**2)/slat
j = sat.ilatfac == 2
rr[j] *= 2.59808 * slat
# sat.deldood is (162, 3); all other sat vars are (162,)
uu = np.dot(sat.deldood, astro[3:6, :]) + sat.phcorr[:, None]
np.fmod(uu, 1, out=uu) # fmod is matlab rem; differs from % op
mat = rr[:, None] * np.exp(1j * 2 * np.pi * uu)
nfreq = len(const.isat) # 162
F = np.ones((nfreq, ntt), dtype=complex)
iconst = sat.iconst - 1
ind = np.unique(iconst)
for ii in ind:
F[ii, :] = 1 + np.sum(mat[iconst == ii], axis=0)
U = np.angle(F) / (2 * np.pi) # cycles
F = np.abs(F)
for i0, nshal, k in zip(ishallow, nshallow, kshallow):
ik = i0 + np.arange(nshal)
j = shallow.iname[ik] - 1
exp1 = shallow.coef[ik, None]
exp2 = np.abs(exp1)
F[k, :] = np.prod(F[j, :]**exp2, axis=0)
U[k, :] = np.sum(U[j, :] * exp1, axis=0)
F = F[lind, :].T
U = U[lind, :].T
# if ngflgs[0]: # Nodal/satellite with linearized times.
# F = F[np.ones((nt, 1)), :]
# U = U[np.ones((nt, 1)), :]
# Let's try letting broadcasting take care of it.
# gwch (astron arg)
if ngflgs[3]: # None (raw phase lags not Greenwich phase lags).
freq = linearized_freqs(tref)
V = 24 * (t[:, np.newaxis] - tref) * freq[lind]
else:
if ngflgs[2]: # Linearized times.
tt = np.array([tref])
else:
tt = t # Exact times.
ntt = len(tt)
astro, ader = ut_astron(tt)
V = np.dot(const.doodson, astro) + const.semi[:, None]
np.fmod(V, 1, out=V)
for i0, nshal, k in zip(ishallow, nshallow, kshallow):
ik = i0 + np.arange(nshal)
j = shallow.iname[ik] - 1
exp1 = shallow.coef[ik, None]
V[k, :] = np.sum(V[j, :] * exp1, axis=0)
V = V[lind, :].T
if ngflgs[2]: # linearized times
freq = linearized_freqs(tref)
V = V + 24*(t[:, None] - tref) * freq[None, lind]
return F, U, V
