def eop_pm(dset):
"""Calculate the partial derivative of the polar motion Earth Orientation Parameters
Args:
data: A Dataset containing model data.
Returns:
Tuple: Array of partial derivatives, and list of names of derivatives
"""
column_names = ["xp", "yp"]
partials = np.zeros((dset.num_obs, 2))
src_dir = dset.src_dir.unit_vector[:, None, :]
baseline = (dset.site_pos_2.itrs_pos - dset.site_pos_1.itrs_pos)[:, :, None]
# x-pole
partials[:, 0] = -(
src_dir @ rotation.Q(dset.time) @ rotation.R(dset.time) @ rotation.dW_dxp(dset.time) @ baseline
)[:, 0, 0]
# y-pole
partials[:, 1] = -(
src_dir @ rotation.Q(dset.time) @ rotation.R(dset.time) @ rotation.dW_dyp(dset.time) @ baseline
)[:, 0, 0]
return partials, column_names, "meter per radian"
def itrs2gcrs_dot(self):
"""The derivative of ITRS to GCRS transformation matrix for the given times
Returns:
Numpy-float array with transformation matrices, shape is (len(self), 3, 3).
"""
return rotation.Q(self) @ rotation.dR_dut1(self) @ rotation.W(self)
def itrs2gcrs(self):
"""The ITRS to GCRS transformation matrix for the given times
Returns:
Numpy-float array with transformation matrices, shape is (len(self), 3, 3).
"""
return rotation.Q(self) @ rotation.R(self) @ rotation.W(self)
def eop_lod(dset):
"""Calculate the partial derivative of the Earth Orientation Parameter Length of Day
Args:
data: A Dataset containing model data.
Returns:
Tuple: Array of partial derivatives, and list of names of derivatives
"""
unit_vector = dset.sat_pos.gcrs.pos.val - dset.site_pos.gcrs.val
unit_vector = unit_vector / np.linalg.norm(unit_vector)
# Use only core sites for EOP estimation
core_sites = config.tech.core_sites.list
is_core_station = np.in1d(dset.station, core_sites)
column_name = ["lod"]
sat_dir = unit_vector[:, None, :]
dR_dut1 = rotation.dR_dut1(dset.time)
dt = (dset.time.jd - dset.time.mean.jd)[:, None, None]
# lod = - ut1_rate * 1 day -> lod_partial = - ut1_rate_partial / 1 day
pick_relevant_data = np.zeros((dset.num_obs, 3, 3))
for j in range(0, dset.num_obs):
if is_core_station[j]:
pick_relevant_data[j] += np.eye(3)
partials = (sat_dir @ rotation.Q(dset.time) @ dR_dut1 @ rotation.W(
dset.time) @ dset.site_pos.trs.val[:, :, None] @ dt)[:, :, 0]
return partials, column_name, "meter * radians / seconds"
def eop_pm(dset):
"""Calculate the partial derivative of the polar motion Earth Orientation Parameters
Args:
data: A Dataset containing model data.
Returns:
Tuple: Array of partial derivatives, and list of names of derivatives
"""
# Use only core sites for EOP estimation
core_sites = config.tech.core_sites.list
is_core_station = np.in1d(dset.station, core_sites)
column_names = ["xp", "yp"]
partials = np.zeros((dset.num_obs, 2))
unit_vector = dset.sat_pos.gcrs.pos.val - dset.site_pos.gcrs.val
unit_vector = unit_vector / np.linalg.norm(unit_vector)
sat_dir = unit_vector[:, None, :]
pick_relevant_data = np.zeros((dset.num_obs, 3, 3))
for j in range(0, dset.num_obs):
if is_core_station[j]:
pick_relevant_data[j] += np.eye(3)
# x-pole
partials[:, 0] = -(
sat_dir
@ rotation.Q(dset.time)
@ rotation.R(dset.time)
@ rotation.dW_dxp(dset.time)
@ pick_relevant_data
@ dset.site_pos.trs.val[:, :, None]
)[:, 0, 0]
# y-pole
partials[:, 1] = -(
sat_dir
@ rotation.Q(dset.time)
@ rotation.R(dset.time)
@ rotation.dW_dyp(dset.time)
@ pick_relevant_data
@ dset.site_pos.trs.val[:, :, None]
)[:, 0, 0]
return partials, column_names, "meter per radian"
def eop_pm_rate(dset):
"""Calculate the partial derivative of the rate of the polar motion Earth Orientation Parameters
Args:
data: A Dataset containing model data.
Returns:
Tuple: Array of partial derivatives, and list of names of derivatives
"""
column_names = ["dxp", "dyp"]
partials = np.zeros((dset.num_obs, 2))
time = dset.time
src_dir = dset.src_dir.unit_vector[:, None, :]
baseline = (dset.site_pos_2.trs.pos - dset.site_pos_1.trs.pos).mat
dt = (time.jd - time.mean.jd)[:, None, None]
# x-pole
partials[:, 0] = -(src_dir @ rotation.Q(time) @ rotation.R(time) @ rotation.dW_dxp(time) @ baseline @ dt)[:, 0, 0]
# y-pole
partials[:, 1] = -(src_dir @ rotation.Q(time) @ rotation.R(time) @ rotation.dW_dyp(time) @ baseline @ dt)[:, 0, 0]
return partials, column_names, "meter * days / radian"
def eop_dut1(dset):
"""Calculate the partial derivative of the dUT1 Earth Orientation Parameter
Args:
data: A Dataset containing model data.
Returns:
Tuple: Array of partial derivatives, and list of names of derivatives
"""
column_name = ["dut1"]
src_dir = dset.src_dir.unit_vector[:, None, :]
baseline = (dset.site_pos_2.trs.pos - dset.site_pos_1.trs.pos).mat
dR_dut1 = rotation.dR_dut1(dset.time)
partials = -(src_dir @ rotation.Q(dset.time) @ dR_dut1 @ rotation.W(
dset.time) @ baseline)[:, :, 0]
return partials, column_name, "meter * (radians per second)"
def eop_dut1_rate(dset):
"""Calculate the partial derivative of the rate of the dUT1 Earth Orientation Parameter
Args:
data: A Dataset containing model data.
Returns:
Tuple: Array of partial derivatives, and list of names of derivatives
"""
column_name = ["ddut1"]
src_dir = dset.src_dir.unit_vector[:, None, :]
baseline = (dset.site_pos_2.itrs_pos - dset.site_pos_1.itrs_pos)[:, :, None]
dR_dut1 = rotation.dR_dut1(dset.time)
dt = (dset.time.jd - dset.time.mean.jd)[:, None, None]
partials = -(src_dir @ rotation.Q(dset.time) @ dR_dut1 @ rotation.W(dset.time) @ baseline @ dt)[:, :, 0]
return partials, column_name, "meter * radians * days / seconds"
def eop_lod(dset):
"""Calculate the partial derivative of the Earth Orientation Parameter Length of Day
Args:
data: A Dataset containing model data.
Returns:
Tuple: Array of partial derivatives, and list of names of derivatives
"""
column_name = ["lod"]
src_dir = dset.src_dir.unit_vector[:, None, :]
baseline = (dset.site_pos_2.trs.pos - dset.site_pos_1.trs.pos).mat
dR_dut1 = rotation.dR_dut1(dset.time)
dt = (dset.time.jd - dset.time.mean.jd)[:, None, None]
# lod = - ut1_rate * 1 day -> lod_partial = - ut1_rate_partial / 1 day
partials = (src_dir @ rotation.Q(dset.time) @ dR_dut1 @ rotation.W(
dset.time) @ baseline @ dt)[:, :, 0]
return partials, column_name, "meter * radians / seconds"
def eop_dut1(dset):
"""Calculate the partial derivative of the dUT1 Earth Orientation Parameter
Args:
data: A Dataset containing model data.
Returns:
Tuple: Array of partial derivatives, and list of names of derivatives
"""
unit_vector = dset.sat_pos.gcrs.pos.val - dset.site_pos.gcrs.val
unit_vector = unit_vector / np.linalg.norm(unit_vector)
# Use only core sites for EOP estimation
core_sites = config.tech.core_sites.list
is_core_station = np.in1d(dset.station, core_sites)
column_name = ["dut1"]
partials = np.zeros(dset.num_obs)
sat_dir = unit_vector[:, None, :]
dR_dut1 = rotation.dR_dut1(dset.time)
pick_relevant_data = np.zeros((dset.num_obs, 3, 3))
for j in range(0, dset.num_obs):
if is_core_station[j]:
pick_relevant_data[j] += np.eye(3)
partials = (
sat_dir
@ rotation.Q(dset.time)
@ dR_dut1
@ rotation.W(dset.time)
@ pick_relevant_data
@ dset.site_pos.trs.val[:, :, None]
)[:, :, 0]
return partials, column_name, "meter * (radians per second)"
