def _apply_function(func, arg):
# type: (QuilParser.FunctionContext, Any) -> Any
if isinstance(arg, Expression):
if func.SIN():
return parameters.quil_sin(arg)
elif func.COS():
return parameters.quil_cos(arg)
elif func.SQRT():
return parameters.quil_sqrt(arg)
elif func.EXP():
return parameters.quil_exp(arg)
elif func.CIS():
return parameters.quil_cis(arg)
else:
raise RuntimeError("Unexpected function to apply: " + func.getText())
else:
if func.SIN():
return sin(arg)
elif func.COS():
return cos(arg)
elif func.SQRT():
return sqrt(arg)
elif func.EXP():
return exp(arg)
elif func.CIS():
return cos(arg) + complex(0, 1) * sin(arg)
else:
raise RuntimeError("Unexpected function to apply: " + func.getText())
def compute_linear_ss(model_type: ModelType, e_op):
"""
Computes the A and B matrices of the linear state space model at the specified operating point for all control
algorithms that require it.
:param model_type: the type that should be linearized
:param e_op: elevation angle (rad) of the desired operating point
:return: A, B
"""
Vf_op, Vb_op = compute_feed_forward_static([e_op, 0, 0, 0, 0],
[0, 0, 0, 0, 0])
Vs_op = Vf_op + Vb_op
if model_type == ModelType.EASY:
A = np.array([[0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 1, 0],
[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0],
[0, -L2 * sin(e_op) / Je, 0, 0, 0, 0],
[L4 * Vs_op * cos(e_op) / Jl, 0, 0, 0, 0, 0]])
elif model_type == ModelType.FRICTION or model_type == ModelType.CENTRIPETAL:
A = np.array(
[[0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1],
[0, 0, 0, -mc.mu_phi / Jp, 0,
0], [0, -L2 * sin(e_op) / Je, 0, 0, -mc.mu_eps / Je, 0],
[L4 * Vs_op * cos(e_op) / Jl, 0, 0, 0, 0, -mc.mu_lamb / Jl]])
else:
# TODO: Implement for remaining model types
print("Unsupported model type while trying to linearize system")
A = np.zeros((6, 6))
B = np.array([[0, 0], [0, 0], [0, 0], [L1 / Jp, -L1 / Jp],
[L3 / Je, L3 / Je], [0, 0]])
return A, B
def gen_xy(self):
for i in range(-7, 8):
y_min = -abs(abs(i) - 7) * cos(pi / 3)
y_max = abs(abs(i) - 7) * cos(pi / 3)
for j in np.linspace(y_min, y_max, abs(abs(i) - 7) + 1):
self.xs.append(int(self.s_x / 2 + i * scale))
self.ys.append(int(self.s_y / 2 + j * scale))
self.points[int(self.s_x / 2 + i * scale)] = int(self.s_y / 2 +
j * scale)
return
def _apply_function(func, arg):
# type: (QuilParser.FunctionContext, Any) -> Any
if func.SIN():
return sin(arg)
elif func.COS():
return cos(arg)
elif func.SQRT():
return sqrt(arg)
elif func.EXP():
return exp(arg)
elif func.CIS():
return cos(arg) + complex(0, 1) * sin(arg)
else:
raise RuntimeError("Unexpected function to apply: " + str(func))
def getVectorDpsi(traj):
dpsi = traj.getMaskedPosture(traj.dpsi)
if float(len(dpsi.compressed()))/float(len(dpsi)) > 0.2:
vdpsi = ma.array([ma.cos(dpsi), ma.sin(dpsi)]).T
return vdpsi
else:
return ma.zeros((len(dpsi), 2))*ma.masked
def getVectorDpsi(traj):
dpsi = traj.getMaskedPosture(traj.dpsi)
if float(len(dpsi.compressed())) / float(len(dpsi)) > 0.2:
vdpsi = ma.array([ma.cos(dpsi), ma.sin(dpsi)]).T
return vdpsi
else:
return ma.zeros((len(dpsi), 2)) * ma.masked
def get_wind_components(speed, wdir):
r'''Calculate the U, V wind vector components from the speed and
direction.
Parameters
----------
speed : array_like
The wind speed (magnitude)
wdir : array_like
The wind direction in degrees, specified as the direction from which the
wind is blowing.
Returns
-------
u, v : tuple of array_like
The wind components in the X (East-West) and Y (North-South)
directions, respectively.
See Also
--------
get_speed_dir
'''
wdir = np.deg2rad(wdir)
u = -speed * sin(wdir)
v = -speed * cos(wdir)
return u, v
def get_wind_components(speed, wdir):
r'''Calculate the U, V wind vector components from the speed and
direction.
Parameters
----------
speed : array_like
The wind speed (magnitude)
wdir : array_like
The wind direction in degrees, specified as the direction from which the
wind is blowing.
Returns
-------
u, v : tuple of array_like
The wind components in the X (East-West) and Y (North-South)
directions, respectively.
See Also
--------
get_speed_dir
'''
wdir = np.deg2rad(wdir)
u = -speed * sin(wdir)
v = -speed * cos(wdir)
return u, v
def test_testUfuncs1(self):
# Test various functions such as sin, cos.
(x, y, a10, m1, m2, xm, ym, z, zm, xf, s) = self.d
assert_(eq(np.cos(x), cos(xm)))
assert_(eq(np.cosh(x), cosh(xm)))
assert_(eq(np.sin(x), sin(xm)))
assert_(eq(np.sinh(x), sinh(xm)))
assert_(eq(np.tan(x), tan(xm)))
assert_(eq(np.tanh(x), tanh(xm)))
with np.errstate(divide='ignore', invalid='ignore'):
assert_(eq(np.sqrt(abs(x)), sqrt(xm)))
assert_(eq(np.log(abs(x)), log(xm)))
assert_(eq(np.log10(abs(x)), log10(xm)))
assert_(eq(np.exp(x), exp(xm)))
assert_(eq(np.arcsin(z), arcsin(zm)))
assert_(eq(np.arccos(z), arccos(zm)))
assert_(eq(np.arctan(z), arctan(zm)))
assert_(eq(np.arctan2(x, y), arctan2(xm, ym)))
assert_(eq(np.absolute(x), absolute(xm)))
assert_(eq(np.equal(x, y), equal(xm, ym)))
assert_(eq(np.not_equal(x, y), not_equal(xm, ym)))
assert_(eq(np.less(x, y), less(xm, ym)))
assert_(eq(np.greater(x, y), greater(xm, ym)))
assert_(eq(np.less_equal(x, y), less_equal(xm, ym)))
assert_(eq(np.greater_equal(x, y), greater_equal(xm, ym)))
assert_(eq(np.conjugate(x), conjugate(xm)))
assert_(eq(np.concatenate((x, y)), concatenate((xm, ym))))
assert_(eq(np.concatenate((x, y)), concatenate((x, y))))
assert_(eq(np.concatenate((x, y)), concatenate((xm, y))))
assert_(eq(np.concatenate((x, y, x)), concatenate((x, ym, x))))
def test_testUfuncs1(self):
# Test various functions such as sin, cos.
(x, y, a10, m1, m2, xm, ym, z, zm, xf, s) = self.d
assert_(eq(np.cos(x), cos(xm)))
assert_(eq(np.cosh(x), cosh(xm)))
assert_(eq(np.sin(x), sin(xm)))
assert_(eq(np.sinh(x), sinh(xm)))
assert_(eq(np.tan(x), tan(xm)))
assert_(eq(np.tanh(x), tanh(xm)))
with np.errstate(divide='ignore', invalid='ignore'):
assert_(eq(np.sqrt(abs(x)), sqrt(xm)))
assert_(eq(np.log(abs(x)), log(xm)))
assert_(eq(np.log10(abs(x)), log10(xm)))
assert_(eq(np.exp(x), exp(xm)))
assert_(eq(np.arcsin(z), arcsin(zm)))
assert_(eq(np.arccos(z), arccos(zm)))
assert_(eq(np.arctan(z), arctan(zm)))
assert_(eq(np.arctan2(x, y), arctan2(xm, ym)))
assert_(eq(np.absolute(x), absolute(xm)))
assert_(eq(np.equal(x, y), equal(xm, ym)))
assert_(eq(np.not_equal(x, y), not_equal(xm, ym)))
assert_(eq(np.less(x, y), less(xm, ym)))
assert_(eq(np.greater(x, y), greater(xm, ym)))
assert_(eq(np.less_equal(x, y), less_equal(xm, ym)))
assert_(eq(np.greater_equal(x, y), greater_equal(xm, ym)))
assert_(eq(np.conjugate(x), conjugate(xm)))
assert_(eq(np.concatenate((x, y)), concatenate((xm, ym))))
assert_(eq(np.concatenate((x, y)), concatenate((x, y))))
assert_(eq(np.concatenate((x, y)), concatenate((xm, y))))
assert_(eq(np.concatenate((x, y, x)), concatenate((x, ym, x))))
def result(traj):
psi = unwrapma(traj.getMaskedPosture(traj.psi))
if float(len(psi.compressed()))/float(len(psi)) > 0.2:
sel = ~ma.getmaskarray(psi)
p = np.polyfit(traj.t[sel], psi[sel], 1)
psi_corr = psi - np.polyval(p, xrange(psi.shape[0]))
return dotacf(ma.array([ma.cos(psi),ma.sin(psi)]).T, lags, traj.excluded)
else:
return ma.zeros((len(lags),))*ma.masked
def compute_feed_forward_static(e_and_derivatives, lambda_and_derivatives):
e = e_and_derivatives[0]
Vs = -L2 / L3 * cos(e)
Vd = 0
Vf = (Vs + Vd) / 2
Vb = (Vs - Vd) / 2
return Vf, Vb
def transform_non_affine(self, a):
# With safeguards
# TODO: Can improve this?
a = np.deg2rad(a) # convert to radians
m = ma.masked_where((a < -self._thresh) | (a > self._thresh), a)
if m.mask.any():
return ma.log(np.abs(ma.tan(m) + 1 / ma.cos(m)))
else:
return np.log(np.abs(np.tan(a) + 1 / np.cos(a)))
def delta(lon, lat):
_dLon = transformLon(lon - 105, lat - 35)
_dLat = transformLat(lon - 105, lat - 35)
radLat = lat / 180 * PI
magic = sin(radLat)
magic = 1 - _ee * magic * magic
sqrtMagic = sqrt(magic)
dLon = (_dLon * 180) / (_a / sqrtMagic * cos(radLat) * PI)
dLat = (_dLat * 180) / ((_a * (1 - _ee)) / (magic * sqrtMagic) * PI)
return [dLon, dLat]
def calc_PA(self):
"""Calculates the telescope PA. requires LST to be either a field or
previously calculated array
Outputs an array of PA values for each time in radians.
This requires the fields Ra = 'CRVAL2', Dec = 'CRVAL3' and 'DATE-OBS'
to be set.
"""
self.PA = sp.zeros(self.dims[0])
for ii in range(self.dims[0]):
RA = self.field['CRVAL2'][ii]
DEC = self.field['CRVAL3'][ii]
LST = utils.LSTatGBT(self.field['DATE-OBS'][ii])
H = LST - RA
Latit = 38.0 + 26.0 / 60
tanPA = ma.sin(H * sp.pi / 180) / (
ma.cos(DEC * sp.pi / 180) * ma.tan(Latit * sp.pi / 180) -
ma.sin(DEC * sp.pi / 180) * ma.cos(H * sp.pi / 180))
self.PA[ii] = ma.arctan(tanPA)
def result(traj):
psi = unwrapma(traj.getMaskedPosture(traj.psi))
if float(len(psi.compressed())) / float(len(psi)) > 0.2:
sel = ~ma.getmaskarray(psi)
p = np.polyfit(traj.t[sel], psi[sel], 1)
psi_corr = psi - np.polyval(p, xrange(psi.shape[0]))
return dotacf(
ma.array([ma.cos(psi), ma.sin(psi)]).T, lags,
traj.excluded)
else:
return ma.zeros((len(lags), )) * ma.masked
def LinearizedSingleJointModel(self, exoskeletonGeneratedTorque, humanGeneratedTorque, position, velocity, restPosition, referencePosition):
self.exoskeletonGeneratedTorque = exoskeletonGeneratedTorque
self.humanGeneratedTorque = humanGeneratedTorque
self.position = position
self.referencePosition = referencePosition
self.velocity = velocity
self.restPosition = restPosition
self.acceleration = 1 / self.inertia * (self.exoskeletonGeneratedTorque + self.humanGeneratedTorque - (
self.damping * self.velocity + self.stiffness*(
self.position - self.restPosition) + self.gravitationnalTorque * cos(self.referencePosition - self.restPosition)*(self.referencePosition - self.restPosition)))
return self.acceleration
def polar2cart(rho, theta):
"""
Convert polar coordinates to cartesian coordinated.
:param rho: polar rho coordinate
:param theta: polar theta coordinate in degrees
:return:
"""
x = rho * ma.cos(theta)
y = rho * ma.sin(theta)
return x, y
def kinematicEquations(self, velocity):
dq = np.zeros(10)
dq[0] = velocity * cos(self.q[2]) * self.matrices.rearWheelRadius
dq[1] = velocity * sin(self.q[2]) * self.matrices.rearWheelRadius
dq[2] = (velocity * (self.q[6] / self.matrices.wheelBase)) * np.cos(self.matrices.frontFrameTilt)
dq[3] = self.q[4]
dq[9] = (velocity * (self.q[8] / self.matrices.wheelBase)) * np.cos(self.matrices.frontFrameTilt)
return dq
def polar2cart(rho, theta):
"""
Convert polar coordinates to cartesian coordinated.
:param rho: polar rho coordinate
:param theta: polar theta coordinate in degrees
:return:
"""
x = rho * ma.cos(theta)
y = rho * ma.sin(theta)
return x, y
def drunken_walk(N, step=1, x0=0, y0=0):
""" Simulates a random walker
For N iterations, it turns in any direction, equally distributed. Each
time moves one step
"""
rad = random(N) * 2 * np.pi
dx = ma.sin(rad) * step
dy = ma.cos(rad) * step
x = dx.cumsum() + x0
y = dy.cumsum() + y0
return x, y
def drunken_walk(N, step=1, x0=0, y0=0):
""" Simulates a random walker
For N iterations, it turns in any direction, equally distributed. Each
time moves one step
"""
rad = random(N)*2*np.pi
dx = ma.sin(rad)*step
dy = ma.cos(rad)*step
x = dx.cumsum() + x0
y = dy.cumsum() + y0
return x, y
def fitBearingDiffusion(self, trajectory, windowSize=None, plotFit=False):
lags = np.round(
np.linspace(0, np.round(100. * trajectory.frameRate),
200)).astype(int)
tau = lags / trajectory.frameRate
if windowSize is None:
psi = unwrapma(trajectory.getMaskedPosture(trajectory.psi))
sel = ~ma.getmaskarray(psi)
p = np.polyfit(trajectory.t[sel], psi[sel], 1)
psi_corr = psi - np.polyval(p, xrange(psi.shape[0]))
C = dotacf(
ma.array([ma.cos(psi), ma.sin(psi)]).T, lags,
trajectory.excluded)
else:
def result(traj):
psi = unwrapma(traj.getMaskedPosture(traj.psi))
if float(len(psi.compressed())) / float(len(psi)) > 0.2:
sel = ~ma.getmaskarray(psi)
p = np.polyfit(traj.t[sel], psi[sel], 1)
psi_corr = psi - np.polyval(p, xrange(psi.shape[0]))
return dotacf(
ma.array([ma.cos(psi), ma.sin(psi)]).T, lags,
traj.excluded)
else:
return ma.zeros((len(lags), )) * ma.masked
C = ma.array(
[result(traj) for traj in trajectory.asWindows(windowSize)]).T
C = C.mean(axis=1)
p, pcov = opt.curve_fit(self._bearingDiffusionFitFunction, tau, C,
[-1.])
self.D_psi = 10**p[0]
if plotFit:
plt.plot(tau, C, 'k.')
plt.plot(tau, self._bearingDiffusionFitFunction(tau, p[0]), 'r-')
plt.xlabel(r'$\tau$ (s)')
plt.ylabel(
r'$\langle \cos \left( \psi(\tau) - \psi(0)\right) \rangle$')
textstr = '$D_\psi=%.2f \mathrm{rad}^2/\mathrm{s}$' % (self.D_psi)
props = dict(boxstyle='round', facecolor='wheat', alpha=0.5)
# place a text box in lower left in axes coords
ax = plt.gca()
ax.text(0.95,
0.95,
textstr,
transform=ax.transAxes,
fontsize=14,
horizontalalignment='right',
verticalalignment='top',
bbox=props)
plt.show()
def transform_non_affine(self, a):
# NOTE: Critical to truncate valid range inside transform *and*
# in limit_range_for_scale or get weird duplicate tick labels. This
# is not necessary for positive-only scales because it is harder to
# run up right against the scale boundaries.
with np.errstate(divide='ignore', invalid='ignore'):
m = ma.masked_where((a <= -90) | (a >= 90), a)
if m.mask.any():
m = np.deg2rad(m)
return ma.log(ma.abs(ma.tan(m) + 1 / ma.cos(m)))
else:
a = np.deg2rad(a)
return np.log(np.abs(np.tan(a) + 1 / np.cos(a)))
def getBodyBearingAutocorrelation(self, maxT=50., windowSize=100.):
lags = np.round(np.linspace(0, np.round(maxT*self.frameRate), 200)).astype(int)
if windowSize is None:
psi = self.getMaskedPosture(self.psi)
C = dotacf(ma.array([ma.cos(psi),ma.sin(psi)]).T, lags, self.excluded)
else:
def result(traj):
psi = traj.getMaskedPosture(traj.psi)
return dotacf(ma.array([ma.cos(psi),ma.sin(psi)]).T, lags, traj.excluded)
C = ma.array([result(traj)
for traj in self.asWindows(windowSize)]).T
C = C.mean(axis=1)
tau = lags / self.frameRate
return tau, C
def transform_non_affine(self, a):
"""
This transform takes a numpy array and returns a transformed copy.
Since the range of the Mercator scale is limited by the
user-specified threshold, the input array must be masked to
contain only valid values. Matplotlib will handle masked arrays
and remove the out-of-range data from the plot. However, the
returned array *must* have the same shape as the input array, since
these values need to remain synchronized with values in the other
dimension.
"""
masked = ma.masked_where((a < -self.thresh) | (a > self.thresh), a)
if masked.mask.any():
return ma.log(np.abs(ma.tan(masked) + 1 / ma.cos(masked)))
else:
return np.log(np.abs(np.tan(a) + 1 / np.cos(a)))
def calc_PA(self) :
"""Calculates the telescope PA. requires LST to be either a field or
previously calculated array
Outputs an array of PA values for each time in radians.
This requires the fields Ra = 'CRVAL2', Dec = 'CRVAL3' and 'DATE-OBS'
to be set.
"""
self.PA = sp.zeros(self.dims[0])
for ii in range(self.dims[0]) :
RA = self.field['CRVAL2'][ii]
DEC = self.field['CRVAL3'][ii]
LST = utils.LSTatGBT(self.field['DATE-OBS'][ii])
H = LST-RA
Latit = 38.0+26.0/60
tanPA = ma.sin(H*sp.pi/180)/(ma.cos(DEC*sp.pi/180)*ma.tan(Latit*sp.pi/180)-ma.sin(DEC*sp.pi/180)*ma.cos(H*sp.pi/180))
self.PA[ii] = ma.arctan(tanPA)
def fitReversals(self, trajectory, windowSize=None, plotFit=False):
lags = np.arange(0, np.round(10.*trajectory.frameRate))
if windowSize is None:
dpsi = trajectory.getMaskedPosture(trajectory.dpsi)
vdpsi = ma.array([ma.cos(dpsi), ma.sin(dpsi)]).T
C = dotacf(vdpsi, lags, trajectory.excluded)
else:
def getVectorDpsi(traj):
dpsi = traj.getMaskedPosture(traj.dpsi)
if float(len(dpsi.compressed()))/float(len(dpsi)) > 0.2:
vdpsi = ma.array([ma.cos(dpsi), ma.sin(dpsi)]).T
return vdpsi
else:
return ma.zeros((len(dpsi), 2))*ma.masked
C = ma.array([dotacf(getVectorDpsi(traj), lags, traj.excluded)
for traj in trajectory.asWindows(windowSize)]).T
C = C.mean(axis=1)
tau = lags / trajectory.frameRate
# do the bounded fit
params = lmfit.Parameters()
params.add('log_tau_eff', value=0.)
params.add('Cinf', value=0.5, min=0., max=1.)
if C.compressed().shape[0]>0:
p = lmfit.minimize(self._reversalFitResidual, params, args=(tau, C))
f_rev = 0.5 - np.sqrt(params['Cinf']/4.)
self.tau_rev = 10**params['log_tau_eff']/(1.-f_rev)
self.tau_fwd = 10**params['log_tau_eff']/f_rev
else:
self.tau_rev = ma.masked
self.tau_fwd = ma.masked
if plotFit:
plt.plot(tau, C, 'k.')
plt.plot(tau, self._reversalFitFunction(tau, params['log_tau_eff'], params['Cinf']), 'r-')
plt.xlabel(r'$\tau$ (s)')
plt.ylabel(r'$\langle \cos\left(\Delta\psi(\tau) - \Delta\psi(0)\right) \rangle$')
textstr = '$\\tau_{\mathrm{rev}}=%.2f$ s\n$\\tau_{\mathrm{fwd}}=%.2f$ s'%(self.tau_rev, self.tau_fwd)
props = dict(boxstyle='round', facecolor='wheat', alpha=0.5)
# place a text box in lower left in axes coords
ax = plt.gca()
ax.text(0.95, 0.95, textstr, transform=ax.transAxes, fontsize=14,
horizontalalignment='right', verticalalignment='top', bbox=props)
plt.show()
def transform_non_affine(self, a):
"""
This transform takes an Nx1 ``numpy`` array and returns a
transformed copy. Since the range of the Mercator scale
is limited by the user-specified threshold, the input
array must be masked to contain only valid values.
``matplotlib`` will handle masked arrays and remove the
out-of-range data from the plot. Importantly, the
``transform`` method *must* return an array that is the
same shape as the input array, since these values need to
remain synchronized with values in the other dimension.
"""
masked = ma.masked_where((a < -self.thresh) | (a > self.thresh), a)
if masked.mask.any():
return ma.log(np.abs(ma.tan(masked) + 1.0 / ma.cos(masked)))
else:
return np.log(np.abs(np.tan(a) + 1.0 / np.cos(a)))
def transform(self, a):
"""
This transform takes an Nx1 ``numpy`` array and returns a
transformed copy. Since the range of the Mercator scale
is limited by the user-specified threshold, the input
array must be masked to contain only valid values.
``matplotlib`` will handle masked arrays and remove the
out-of-range data from the plot. Importantly, the
``transform`` method *must* return an array that is the
same shape as the input array, since these values need to
remain synchronized with values in the other dimension.
"""
masked = ma.masked_where((a < -self.thresh) | (a > self.thresh), a)
if masked.mask.any():
return ma.log(np.abs(ma.tan(masked) + 1.0 / ma.cos(masked)))
else:
return np.log(np.abs(np.tan(a) + 1.0 / np.cos(a)))
def get_wind_components(speed, wdir):
'''
Calculate the U, V wind vector components from the speed and
direction (from which the wind is blowing).
speed : scalar or array
The wind speed (magnitude)
wdir : scalar or array
The wind direction in degrees
Returns : tuple of scalars or arrays
The tuple (U,V) corresponding to the wind components in the
X (East-West) and Y (North-South) directions, respectively.
'''
wdir = wdir * degree
u = -speed * sin(wdir)
v = -speed * cos(wdir)
return u, v
def get_wind_components(speed, wdir):
"""
Calculate the U, V wind vector components from the speed and
direction (from which the wind is blowing).
speed : scalar or array
The wind speed (magnitude)
wdir : scalar or array
The wind direction in degrees
Returns : tuple of scalars or arrays
The tuple (U,V) corresponding to the wind components in the
X (East-West) and Y (North-South) directions, respectively.
"""
wdir = wdir * degree
u = -speed * sin(wdir)
v = -speed * cos(wdir)
return u, v
def getBodyBearingAutocorrelation(self, maxT=50., windowSize=100.):
lags = np.round(np.linspace(0, np.round(maxT * self.frameRate),
200)).astype(int)
if windowSize is None:
psi = self.getMaskedPosture(self.psi)
C = dotacf(
ma.array([ma.cos(psi), ma.sin(psi)]).T, lags, self.excluded)
else:
def result(traj):
psi = traj.getMaskedPosture(traj.psi)
return dotacf(
ma.array([ma.cos(psi), ma.sin(psi)]).T, lags,
traj.excluded)
C = ma.array([result(traj)
for traj in self.asWindows(windowSize)]).T
C = C.mean(axis=1)
tau = lags / self.frameRate
return tau, C
def rebin_velocity(
self,
time: np.ndarray,
time_new: np.ndarray,
folding_velocity: Union[float, np.ndarray],
sequence_indices: list,
) -> None:
"""Rebins Doppler velocity in polar coordinates.
Args:
time: 1D time array.
time_new: 1D new time array.
folding_velocity: Folding velocity (m/s). Can be float when it's the same for all
altitudes, or np.ndarray when it matches difference altitude regions
(defined in `sequence_indices`).
sequence_indices: List containing indices of different folding regions,
e.g. [[0, 1, 2, 3], [4, 5, 6, 7], [8, 9, 10]].
"""
def _get_scaled_vfold() -> np.ndarray:
vfold_scaled = math.pi / folding_velocity
if isinstance(vfold_scaled, float):
vfold_scaled = np.array([float(vfold_scaled)])
return vfold_scaled
def _scale_by_vfold(data_in: np.ndarray, fun) -> np.ndarray:
data_out = ma.copy(data_in)
for i, ind in enumerate(sequence_indices):
data_out[:, ind] = fun(data_in[:, ind], folding_velocity_scaled[i])
return data_out
folding_velocity_scaled = _get_scaled_vfold()
data_scaled = _scale_by_vfold(self.data, np.multiply)
vel_x = ma.cos(data_scaled)
vel_y = ma.sin(data_scaled)
vel_x_mean, _ = utils.rebin_2d(time, vel_x, time_new)
vel_y_mean, _ = utils.rebin_2d(time, vel_y, time_new)
mean_vel_scaled = np.arctan2(vel_y_mean, vel_x_mean)
self.data = _scale_by_vfold(mean_vel_scaled, np.divide)
def compute_pitch_and_inputs_flatness_simple(e_and_derivatives,
lambda_and_derivatives):
e = e_and_derivatives[0]
de1 = e_and_derivatives[1]
de2 = e_and_derivatives[2]
de3 = e_and_derivatives[3]
de4 = e_and_derivatives[4]
l = lambda_and_derivatives[0]
dl1 = lambda_and_derivatives[1]
dl2 = lambda_and_derivatives[2]
dl3 = lambda_and_derivatives[3]
dl4 = lambda_and_derivatives[4]
b = L3 * Jl * dl2
c = L4 * cos(e)
d = Je * de2 - L2 * cos(e)
a = b * c / d
db1 = L3 * Jl * dl3
db2 = L3 * Jl * dl4
dc1 = -L4 * sin(e) * de1
dc2 = -L4 * (cos(e) * de1**2 + sin(e) * de2)
dd1 = Je * de3 + L2 * sin(e) * de1
dd2 = Je * de4 + L2 * (cos(e) * de1**2 + sin(e) * de2)
f = db1 * c * d
g = dc1 * d + c * dd1
h = c * c * d * d
da1 = (f - b * g) / h
df1 = db2 * c * d + db1 * g
dg1 = dc2 * d + 2 * dc1 * dd1 + c * dd2
dh1 = 2 * c * dc1 * d**2 + 2 * c**2 * d * dd1
da2 = ((df1 - (db1 * g + b * dg1)) * h - (f - b * g) * dh1) / h**2
p = arctan(a)
dp1 = da1 / (1 + a**2)
dp2 = (da2 * (1 + a**2) - 2 * a * da1**2) / (1 + a**2)**2
Vs = ((Jl * dl2 / (L4 * cos(e)))**2 +
((Je * de2 - L2 * cos(e)) / L3)**2)**(1 / 2)
Vd = Jp * dp2 / L1
Vf = (Vs + Vd) / 2
Vb = (Vs - Vd) / 2
return np.array([p, dp1, dp2]), np.array([Vf, Vb])
def _vec2comp(wdir, wspd):
'''
Underlying function that converts a vector to its components
Parameters
----------
wdir : number, masked_array
Angle in meteorological degrees
wspd : number, masked_array
Magnitudes of wind vector
Returns
-------
u : number, masked_array (same as input)
U-component of the wind
v : number, masked_array (same as input)
V-component of the wind
'''
u = wspd * ma.sin(np.radians(wdir % 360.)) * -1
v = wspd * ma.cos(np.radians(wdir % 360.)) * -1
return u, v
def _vec2comp(wdir, wspd):
'''
Underlying function that converts a vector to its components
Parameters
----------
wdir : number, masked_array
Angle in meteorological degrees
wspd : number, masked_array
Magnitudes of wind vector
Returns
-------
u : number, masked_array (same as input)
U-component of the wind
v : number, masked_array (same as input)
V-component of the wind
'''
u = wspd * ma.sin(np.radians(wdir)) * -1
v = wspd * ma.cos(np.radians(wdir)) * -1
return u, v
def fitBearingDiffusion(self, trajectory, windowSize=None, plotFit=False):
lags = np.round(np.linspace(0, np.round(100.*trajectory.frameRate), 200)).astype(int)
tau = lags/trajectory.frameRate
if windowSize is None:
psi = unwrapma(trajectory.getMaskedPosture(trajectory.psi))
sel = ~ma.getmaskarray(psi)
p = np.polyfit(trajectory.t[sel], psi[sel], 1)
psi_corr = psi - np.polyval(p, xrange(psi.shape[0]))
C = dotacf(ma.array([ma.cos(psi),ma.sin(psi)]).T, lags, trajectory.excluded)
else:
def result(traj):
psi = unwrapma(traj.getMaskedPosture(traj.psi))
if float(len(psi.compressed()))/float(len(psi)) > 0.2:
sel = ~ma.getmaskarray(psi)
p = np.polyfit(traj.t[sel], psi[sel], 1)
psi_corr = psi - np.polyval(p, xrange(psi.shape[0]))
return dotacf(ma.array([ma.cos(psi),ma.sin(psi)]).T, lags, traj.excluded)
else:
return ma.zeros((len(lags),))*ma.masked
C = ma.array([result(traj)
for traj in trajectory.asWindows(windowSize)]).T
C = C.mean(axis=1)
p, pcov = opt.curve_fit(self._bearingDiffusionFitFunction, tau, C, [-1.])
self.D_psi = 10**p[0]
if plotFit:
plt.plot(tau, C, 'k.')
plt.plot(tau, self._bearingDiffusionFitFunction(tau, p[0]), 'r-')
plt.xlabel(r'$\tau$ (s)')
plt.ylabel(r'$\langle \cos \left( \psi(\tau) - \psi(0)\right) \rangle$')
textstr = '$D_\psi=%.2f \mathrm{rad}^2/\mathrm{s}$'%(self.D_psi)
props = dict(boxstyle='round', facecolor='wheat', alpha=0.5)
# place a text box in lower left in axes coords
ax = plt.gca()
ax.text(0.95, 0.95, textstr, transform=ax.transAxes, fontsize=14,
horizontalalignment='right', verticalalignment='top', bbox=props)
plt.show()
def get_p_and_first_derivative_simple(model_type: ModelType, e_and_derivatives,
lambda_and_derivatives):
"Computes p and dp from the flat output and its derivatives."
if model_type != ModelType.EASY:
print("model_type = " + str(model_type))
raise NotImplementedError(
"get_p_and_first_derivative is not implemented for other model types than EASY."
)
p = np.arctan(
(Jl * L3 * lambda_and_derivatives[2]) /
(L4 * cos(e_and_derivatives[0]) *
(Je * e_and_derivatives[2] - L2 * cos(e_and_derivatives[0]))))
# the following part is partly copied from compute_feed_forward_flatness
e = e_and_derivatives[0]
de1 = e_and_derivatives[1]
de2 = e_and_derivatives[2]
de3 = e_and_derivatives[3]
de4 = e_and_derivatives[4]
l = lambda_and_derivatives[0]
dl1 = lambda_and_derivatives[1]
dl2 = lambda_and_derivatives[2]
dl3 = lambda_and_derivatives[3]
dl4 = lambda_and_derivatives[4]
b = L3 * Jl * dl2
c = L4 * cos(e)
d = Je * de2 - L2 * cos(e)
a = b * c / d
db1 = L3 * Jl * dl3
db2 = L3 * Jl * dl4
dc1 = -L4 * sin(e) * de1
dc2 = -L4 * (cos(e) * de1**2 + sin(e) * de2)
dd1 = Je * de3 + L2 * sin(e) * de1
dd2 = Je * de4 + L2 * (cos(e) * de1**2 + sin(e) * de2)
f = db1 * c * d
g = dc1 * d + c * dd1
h = c * c * d * d
da1 = (f - b * g) / h
dp = (1 / (1 + a * a)) * da1
return p, dp
def drunken_drive(cfg):
""" Simulates a standard normal change in course
For N iterations it changes the course with a normal probability around
the previous course. Each time moves one step distance. On the drunken
drive there is a memory on the course followed, different from the
drunken walk, and so it is more similar to real sensors (ships, drifters
etc).
Variance between -90 to 90 deg.
"""
N = cfg['montecarlo']['Nsamples']
Rlimit = cfg['montecarlo']['Rlimit']
x0 = Rlimit * (random(1)[0] - 0.5) * 2
y0 = Rlimit * (random(1)[0] - 0.5) * 2
rad = 0.25 * np.pi * randn(N)
rad[0] = random(1) * 2 * np.pi
rad = rad.cumsum()
step = cfg['montecarlo']['dt'] * cfg['montecarlo']['VSampler']
dx = ma.sin(rad) * step
dy = ma.cos(rad) * step
x = dx.cumsum() + x0
y = dy.cumsum() + y0
return x, y
def drunken_drive(cfg):
""" Simulates a standard normal change in course
For N iterations it changes the course with a normal probability around
the previous course. Each time moves one step distance. On the drunken
drive there is a memory on the course followed, different from the
drunken walk, and so it is more similar to real sensors (ships, drifters
etc).
Variance between -90 to 90 deg.
"""
N = cfg['montecarlo']['Nsamples']
Rlimit = cfg['montecarlo']['Rlimit']
x0 = Rlimit*(random(1)[0]-0.5)*2
y0 = Rlimit*(random(1)[0]-0.5)*2
rad = 0.25*np.pi*randn(N)
rad[0] = random(1)*2*np.pi
rad = rad.cumsum()
step = cfg['montecarlo']['dt'] * cfg['montecarlo']['VSampler']
dx = ma.sin(rad)*step
dy = ma.cos(rad)*step
x = dx.cumsum() + x0
y = dy.cumsum() + y0
return x, y
def fun_dct1(x, i, n):
return cos(pi*x*i/n)
def getBearingAutocorrelation(self, maxT=100):
n = int(np.round(maxT*self.frameRate))
tau = range(n)/self.frameRate
psi = self.getMaskedPosture(self.psi)
C = dotacf(ma.array([ma.cos(psi), ma.sin(psi)]), n)
return tau, C
def fun_dct2(x, i, n):
return cos(pi*x*(i+1/2)/n)
def scale_by_cal(Data, scale_t_ave=True, scale_f_ave=False, sub_med=False,
scale_f_ave_mod=False, rotate=False) :
"""Puts all data in units of the cal temperature.
Data is put into units of the cal temperature, thus removing dependence on
the gain. This can be done by dividing by the time average of the cal
(scale_t_ave=True, Default) thus removing dependence on the frequency-
dependant gain. Alternatively, you can scale by the frequency average to
remove the time-dependent gain (scale_f_ave=True). Data is then in units of
the frequency averaged cal temperture. You can also do both (recommended).
After some scaling the data ends up in units of the cal temperture as a
funciton of frequency.
Optionally you can also subtract the time average of the data off here
(subtract_time_median), since you might be done with the cal information at
this point.
"""
on_ind = 0
off_ind = 1
if (Data.field['CAL'][on_ind] != 'T' or
Data.field['CAL'][off_ind] != 'F') :
raise ce.DataError('Cal states not in expected order.')
if tuple(Data.field['CRVAL4']) == (-5, -7, -8, -6) :
# Here we check the polarizations and cal indicies
xx_ind = 0
yy_ind = 3
xy_inds = [1,2]
# A bunch of calculations used to test phase closure. Not acctually
# relevant to what is being done here.
#a = (Data.data[5, xy_inds, on_ind, 15:20]
# - Data.data[5, xy_inds, off_ind, 15:20])
#a /= sp.sqrt( Data.data[5, xx_ind, on_ind, 15:20]
# - Data.data[5, xx_ind, off_ind, 15:20])
#a /= sp.sqrt( Data.data[5, yy_ind, on_ind, 15:20]
# - Data.data[5, yy_ind, off_ind, 15:20])
#print a[0,:]**2 + a[1,:]**2
diff_xx = Data.data[:,xx_ind,on_ind,:] - Data.data[:,xx_ind,off_ind,:]
diff_yy = Data.data[:,yy_ind,on_ind,:] - Data.data[:,yy_ind,off_ind,:]
if scale_t_ave :
# Find the cal means (in time) and scale by them.
# Means work much better than medians. Medians seems to bias the
# result by up to 10%. This seems to be discretization noise. Cal
# switches fast enough that we shouldn't need this anyway.
cal_tmed_xx = ma.mean(diff_xx, 0)
cal_tmed_yy = ma.mean(diff_yy, 0)
cal_tmed_xx[sp.logical_or(cal_tmed_xx<=0, cal_tmed_yy<=0)] = ma.masked
cal_tmed_yy[cal_tmed_xx.mask] = ma.masked
Data.data[:,xx_ind,:,:] /= cal_tmed_xx
Data.data[:,yy_ind,:,:] /= cal_tmed_yy
Data.data[:,xy_inds,:,:] /= ma.sqrt(cal_tmed_yy*cal_tmed_xx)
if scale_f_ave :
# The frequency gains have have systematic structure to them,
# they are not by any approximation gaussian distributed. Use
# means, not medians across frequency.
operation = ma.mean
cal_fmea_xx = operation(diff_xx, -1)
cal_fmea_yy = operation(diff_yy, -1)
# Flag data with wierd cal power. Still Experimental.
cal_fmea_xx[sp.logical_or(cal_fmea_xx<=0,cal_fmea_yy<=0)] = ma.masked
cal_fmea_yy[cal_fmea_xx.mask] = ma.masked
cal_xx = ma.mean(cal_fmea_xx)
cal_yy = ma.mean(cal_fmea_yy)
cal_fmea_xx[sp.logical_or(abs(cal_fmea_xx.anom()) >= 0.1*cal_xx,
abs(cal_fmea_yy.anom()) >= 0.1*cal_yy)] = ma.masked
cal_fmea_yy[cal_fmea_xx.mask] = ma.masked
ntime = len(cal_fmea_xx)
cal_fmea_xx.shape = (ntime, 1, 1)
cal_fmea_yy.shape = (ntime, 1, 1)
Data.data[:,xx_ind,:,:] /= cal_fmea_xx
Data.data[:,yy_ind,:,:] /= cal_fmea_yy
cal_fmea_xx.shape = (ntime, 1, 1, 1)
cal_fmea_yy.shape = (ntime, 1, 1, 1)
Data.data[:,xy_inds,:,:] /= ma.sqrt(cal_fmea_yy*cal_fmea_xx)
if scale_f_ave_mod :
# The frequency gains have have systematic structure to them,
# they are not by any approximation gaussian distributed. Use
# means, not medians across frequency.
operation = ma.mean
cal_fmea_xx = operation(diff_xx, -1)
cal_fmea_yy = operation(diff_yy, -1)
cal_fmea_xx_off = operation(Data.data[:,xx_ind,off_ind,:], -1)
cal_fmea_yy_off = operation(Data.data[:,yy_ind,off_ind,:], -1)
sys_xx = cal_fmea_xx_off/cal_fmea_xx
sys_yy = cal_fmea_yy_off/cal_fmea_yy
percent_ok = 0.03
sys_xx_tmed = ma.median(sys_xx)
sys_yy_tmed = ma.median(sys_yy)
maskbad_xx = (sys_xx > sys_xx_tmed + sys_xx_tmed*percent_ok)|(sys_xx < sys_xx_tmed - sys_xx_tmed*percent_ok)
maskbad_yy = (sys_yy > sys_yy_tmed + sys_yy_tmed*percent_ok)|(sys_yy < sys_yy_tmed - sys_yy_tmed*percent_ok)
cal_fmea_xx[sp.logical_or(cal_fmea_xx<=0,cal_fmea_yy<=0)] = ma.masked
cal_fmea_yy[cal_fmea_xx.mask] = ma.masked
cal_fmea_xx[maskbad_xx] = ma.masked
cal_fmea_yy[maskbad_yy] = ma.masked
cal_xx = ma.mean(cal_fmea_xx)
cal_yy = ma.mean(cal_fmea_yy)
ntime = len(cal_fmea_xx)
cal_fmea_xx.shape = (ntime, 1, 1)
cal_fmea_yy.shape = (ntime, 1, 1)
Data.data[:,xx_ind,:,:] /= cal_fmea_xx
Data.data[:,yy_ind,:,:] /= cal_fmea_yy
cal_fmea_xx.shape = (ntime, 1, 1, 1)
cal_fmea_yy.shape = (ntime, 1, 1, 1)
Data.data[:,xy_inds,:,:] /= ma.sqrt(cal_fmea_yy*cal_fmea_xx)
if scale_f_ave and scale_t_ave :
# We have devided out t_cal twice so we need to put one factor back
# in.
cal_xx = operation(cal_tmed_xx)
cal_yy = operation(cal_tmed_yy)
Data.data[:,xx_ind,:,:] *= cal_xx
Data.data[:,yy_ind,:,:] *= cal_yy
Data.data[:,xy_inds,:,:] *= ma.sqrt(cal_yy*cal_xx)
if scale_f_ave_mod and scale_t_ave :
#Same divide out twice problem.
cal_xx = operation(cal_tmed_xx)
cal_yy = operation(cal_tmed_yy)
Data.data[:,xx_ind,:,:] *= cal_xxcal_imag_mean
Data.data[:,yy_ind,:,:] *= cal_yy
Data.data[:,xy_inds,:,:] *= ma.sqrt(cal_yy*cal_xx)
if scale_f_ave and scale_f_ave_mod :
raise ce.DataError("time averaging twice")
if rotate:
# Define the differential cal phase to be zero and rotate all data
# such that this is true.
cal_real_mean = ma.mean(Data.data[:,1,0,:] - Data.data[:,1,1,:], 0)
cal_imag_mean = ma.mean(Data.data[:,2,0,:] - Data.data[:,2,1,:], 0)
# Get the cal phase angle as a function of frequency.
cal_phase = -ma.arctan2(cal_imag_mean, cal_real_mean)
# Rotate such that the cal phase is zero. Imperative to have a
# temporary variable.
New_data_real = (ma.cos(cal_phase) * Data.data[:,1,:,:]
- ma.sin(cal_phase) * Data.data[:,2,:,:])
New_data_imag = (ma.sin(cal_phase) * Data.data[:,1,:,:]
+ ma.cos(cal_phase) * Data.data[:,2,:,:])
Data.data[:,1,:,:] = New_data_real
Data.data[:,2,:,:] = New_data_imag
elif tuple(Data.field['CRVAL4']) == (1, 2, 3, 4) :
# For the shot term, just devide everything by on-off in I.
I_ind = 0
cal_I_t = Data.data[:,I_ind,on_ind,:] - Data.data[:,I_ind,off_ind,:]
cal_I = ma.mean(cal_I_t, 0)
Data.data /= cal_I
else :
raise ce.DataError("Unsupported polarization states.")
# Subtract the time median if desired.
if sub_med :
Data.data -= ma.median(Data.data, 0)
def diff(j, x, N):
theta_j = theta(j, N)
theta_j_1 = theta(j+1, N)
a1 = (cos(x) - cos(theta_j)) / (cos(theta_j_1 - theta_j))
a2 = (x - theta_j) / (theta_j_1 - theta_j)
return a1 - a2
def angleToVector(alpha):
return ma.array([ma.cos(alpha), ma.sin(alpha)]).T
def calibrate_pol(Data, m_total, flux_status):
"""Subtracts a Map out of Data."""
# Data is a DataBlock object. It holds everything you need to know about
# the data in a single scan and IF. You should get to know them very well.
# Data.data is a numpy masked array (see numpy documentation) and holds the
# acctual data. It is a 4 dimensional array. The demensions are (in
# order): (time, pol, cal, freq). Each dimension can be any length which
# you can figure out by looking at Data.dims = sp.shape(Data.data).
# Data.field is a python dictionary that holds all the other data that you
# might care about from the origional fits file. For instance,
# Data.field['CAL'] is an array with length dims[2]. It normally has
# values ['T', 'F']. Data.field['CRVAL4'] tells you about the polarization
# axis of Data.data. By SDfits convension each polarization is represented
# by an integer: 1=I, 2=Q, 3=U, 4=V, -5=XX, -6=YY, -7=XY, -8=YX.
# Also this depends on having the polarizations rotated correctly to IQUV.
# Some code to do this has been hacked together in the rotate_pol module,
# but I don't trust it yet.
# Some dimension checks.
# We expect 4 polarizations.
if not Data.dims[1] == 4:
raise ce.DataError('Require 4 polarizations.')
# We expect polarizations to be in order IQUV.
if (Data.field['CRVAL4'][0] != 1 or Data.field['CRVAL4'][1] != 2
or Data.field['CRVAL4'][2] != 3 or Data.field['CRVAL4'][3] != 4):
raise ce.DataError('Expected the polarization basis to be IQUV.')
# A useful function that might need:
Data.calc_freq()
# Now data has an atribute Data.freq which is an array that gives the
# frequency along the last axis.
# Data.field['CRVAL1'] is center frequency in Hz.
# Data.data 4 dim array 2nd index polarization, 4th index frequency.
# Need to get parallactic angle:
Data.calc_PA()
# This gives an array (Data.PA) of PA values of length = time dim.
for time_index in range(0, Data.dims[0]):
#Generate a sky matrix for this time index:
m_sky = sp.zeros((4, 4))
m_sky[0, 0] = 1
m_sky[1, 1] = ma.cos(2 * Data.PA[time_index] * sp.pi / 180)
m_sky[1, 2] = ma.sin(2 * Data.PA[time_index] * sp.pi / 180)
m_sky[2, 1] = -ma.sin(2 * Data.PA[time_index] * sp.pi / 180)
m_sky[2, 2] = ma.cos(2 * Data.PA[time_index] * sp.pi / 180)
m_sky[3, 3] = 1
M_sky = sp.mat(m_sky)
M_sky = M_sky.I
# print M_sky
for cal_index in range(0, Data.dims[2]):
# Determines the Mueller Matrix to use
for freq in range(0, Data.dims[3]):
# Tells which mueller matrix to use.
freq_limit = len(m_total[0, 0, :])
frequency = int(Data.freq[freq] / 1000)
# print frequency
bin = int((900000 - frequency) * freq_limit / 200000)
# print bin
# if freq_limit == 200:
# bin = 900-frequency
#Not setup to work with spectrometer data.
# elif freq_limit == 260:
# bin = 929-frequency
# print bin
# Converts files into matrix format
STOKES = Data.data[time_index, :, cal_index, freq]
# print STOKES
MUELLER = sp.mat(m_total[:, :, bin])
# print MUELLER
# Next there is a matrix multiplication that will generate
# a new set of stokes values.
stokesmod = STOKES
if flux_status == 'False':
stokesmod = np.dot(MUELLER, stokesmod)
stokesmod = np.dot(M_sky, stokesmod)
# You always want to include the M_sky matrix transformation, but you if you just want the flux cal, coment out the MUELLER, STOKES dot product above and include the flux multiplication below instead.
if flux_status == 'True':
stokesmod[0] = stokesmod[0] * MUELLER[0, 0]
stokesmod[1] = stokesmod[1] * MUELLER[0, 0]
stokesmod[2] = stokesmod[2] * MUELLER[0, 0]
stokesmod[3] = stokesmod[3] * MUELLER[0, 0]
# print stokesmod
for i in range(0, Data.dims[1]):
Data.data[time_index, i, cal_index, freq] = stokesmod[i]
def result(traj):
psi = traj.getMaskedPosture(traj.psi)
return dotacf(ma.array([ma.cos(psi),ma.sin(psi)]).T, lags, traj.excluded)
def least_squares(obs, navs, init_pos='', vmf_coeffs=()):
"""
x = (A^TA)^{-1}A^T l
Takes an observation ``obs`` and all the data ``nav`` from navigation file.
If we have a-priori information about rover's position,
then we can filter low satellites and use troposperic correction
:return: rover's position in ecef [m]
"""
c = 299792428 # speed of light
elev_mask = 8 # satellite elevation mask
now = obs.date
# Find all possible satellites N
sats = []
for r in obs.PRN_number:
# print r, "Data:", obs.obs_data['C1'][obs.prn(r)], obs.obs_data['P2'][obs.prn(r)]
if obs.obs_data['C1'][obs.prn(r)] and obs.obs_data['P2'][obs.prn(r)] and ('G' in r): # iono-free
# if obs.obs_data['C1'][obs.prn(r)] and obs.obs_data['P1'][obs.prn(r)] and ('R' in r): # iono-free
# if obs.obs_data['C1'][i] and ('G' in r): # C1 only
nnt = nav_nearest_in_time(now, navs[r])
if len(init_pos):
sat_coord = nnt.eph2pos(now)
if sat_elev(init_pos, sat_coord) < elev_mask:
# print "\tSatellite %s excluded" % r
continue
sats += [(r, nnt)]
# Form matrix if N >= 4:
if len(sats) > 3:
# observed [iono-free] pseudoranges
# P = np.array([obs.ionofree_pseudorange(s[0]) for s in sats]) # iono-free
P = np.array([obs.obs_data['C1'][obs.prn(s[0])] for s in sats]) # C1 only
# get XYZ-coords of satellites
XYZs = np.array([s[1].eph2pos(now) for s in sats]) # len(XYZs[0]) = 3
# print "XYZs =",XYZs
# elif len(sats) <= 3 and len(init_pos): # FIXME: rewise this logic
elif len(sats) <= 3: # FIXME: rewise this logic
print "\n\tWarning: too few satellites:", len(sats)
return None
# else:
# print "\n\tWarning: bad measurement!"
# print "sats:", sats, init_pos
# return None
# if err == {}: err = {s[0]:0. for s in sats}
xyzt = [1e-10, 1e-10, 1e-10, 0.] # initial point
if len(init_pos):
xyzt = init_pos + [0.]
# print "initial position:", lla_string(ecef_to_lat_lon_alt(xyzt)), tuple(xyzt[:3])
for itr in range(10):
# print "\n*** iter = %d ***" % itr
# geometrical ranges
lla = ecef_to_lat_lon_alt(xyzt, deg=False)
## rho is geometric ranges i.e. distances between current position and every satellite in `sats`
rho = np.array([np.sqrt(sum([(x - xyzt[i]) ** 2 for i, x in enumerate(XYZs[j])])) for j in xrange(len(sats))])
# print "ρ =", rho
# form l-vector (sometimes `l` is denoted as `b`)
# print "cδt =", xyzt[3]
# l = np.matrix([P[i] - rho[i] + c * s[1].time_offset(now + dt.timedelta(seconds=xyzt[3]))
# print "time_offset(now + xyzt[3]) =",[s[1].time_offset(now + xyzt[3]) for s in sats]
l = np.matrix([P[i] - rho[i] + c * s[1].time_offset(now + xyzt[3])
- tropmodel(lla, sat_elev(xyzt[:3], XYZs[i], deg=False), vmf_coeffs)
for i, s in enumerate(sats)]).transpose()
# from A-matrix
A = np.matrix([np.append((xyzt[:3] - XYZs[i]) / rho[i], [c]) for i in xrange(len(sats))])
AT = A.transpose()
# form x-vector
x_hat_matrix = ((AT * A).I * AT * l)
x_hat = x_hat_matrix.flatten().getA()[0]
x_hat[3] /= c
# x_hat[3] *= 1e9 # time in seconds again
# print "(x,y,z,cδt) ="," m, ".join(map(lambda x: "%.f" %x, x_hat[:3])),"m, %.1e" % x_hat[3]
xyzt += x_hat
# print lla_string(ecef_to_lat_lon_alt(xyzt)),"%.4f"%xyzt[3]
delta = np.sqrt(sum(map(lambda k: k ** 2, x_hat[:3])))
if delta < 1.:
# print "1 meter accuracy achieved, break"
break
# now += dt.timedelta(seconds=x_hat[3])
# XYZs = np.array([s[1].eph2pos(now + dt.timedelta(seconds=x_hat[3])) for s in sats])
XYZs = np.array([s[1].eph2pos(now + x_hat[3]) for s in sats])
phi, t, h = ecef_to_lat_lon_alt(xyzt, deg=False)
R = np.matrix([[-sin(phi) * cos(t), -sin(phi) * sin(t), cos(phi)],
[-sin(t), cos(t), 0],
[cos(phi) * cos(t), cos(phi) * sin(t), sin(phi)]])
Q = (AT * A).I
# S_T = R * Q[0:3, 0:3] * R.transpose()
# GDOP = sqrt(sum(S_T.diagonal().getA()[0]) + Q[3, 3])
# print "GDOP = %.3f, VDOP = %.3f" % (GDOP,sqrt(S_T[2,2]))
return xyzt[:3]
def angleToVector(alpha):
return ma.array([ma.cos(alpha), ma.sin(alpha)]).T
def outlier_detector_cmean(np_ma, Vny, Nprf_arr, Nmin=2):
data = np_ma.data
mask = np_ma.mask
f_arr = np.ones(Nprf_arr.shape)
f_arr[np.where(Nprf_arr == np.min(Nprf_arr))] = -1
Vny_arr = Vny / Nprf_arr
kH, kL = np.zeros((5, 5)), np.zeros((5, 5))
kH[1::2] = 1
kL[::2] = 1
# Array with the number of valid neighbours at each point
Nval_arr_H = local_valid(mask, kernel=kH)
Nval_arr_L = local_valid(mask, kernel=kL)
# Convert to angles and calculate trigonometric variables
ang_ma = (np_ma * pi / Vny)
cos_ma = ma.cos(ang_ma * Nprf_arr)
sin_ma = ma.sin(ang_ma * Nprf_arr)
# Average trigonometric variables in local neighbourhood
dummy_cos = cos_ma.data * (~mask).astype(int)
dummy_sin = sin_ma.data * (~mask).astype(int)
ncols, cos_conv = dummy_cols(dummy_cos, kH, val=0)
ncols, sin_conv = dummy_cols(dummy_sin, kH, val=0)
cos_sumH = ndimage.convolve(cos_conv, weights=kH, mode='wrap')
cos_sumL = ndimage.convolve(cos_conv, weights=kL, mode='wrap')
sin_sumH = ndimage.convolve(sin_conv, weights=kH, mode='wrap')
sin_sumL = ndimage.convolve(sin_conv, weights=kL, mode='wrap')
# Remove added columns
cos_sumH = cos_sumH[:, :int(cos_sumL.shape[1] - ncols)]
cos_sumL = cos_sumL[:, :int(cos_sumL.shape[1] - ncols)]
sin_sumH = sin_sumH[:, :int(sin_sumL.shape[1] - ncols)]
sin_sumL = sin_sumL[:, :int(sin_sumL.shape[1] - ncols)]
# Average angle in local neighbourhood
cos_avgH_ma = ma.array(data=cos_sumH, mask=mask) / Nval_arr_H
cos_avgL_ma = ma.array(data=cos_sumL, mask=mask) / Nval_arr_L
sin_avgH_ma = ma.array(data=sin_sumH, mask=mask) / Nval_arr_H
sin_avgL_ma = ma.array(data=sin_sumL, mask=mask) / Nval_arr_L
BH = ma.arctan2(sin_avgH_ma, cos_avgH_ma)
BL = ma.arctan2(sin_avgL_ma, cos_avgL_ma)
# Average velocity ANGLE of neighbours (reference ANGLE for outlier detection):
angref_ma = f_arr * (BL - BH)
angref_ma[angref_ma < 0] = angref_ma[angref_ma < 0] + 2 * pi
angref_ma[angref_ma > pi] = -(2 * pi - angref_ma[angref_ma > pi])
angobs_ma = ma.arctan2(ma.sin(ang_ma), ma.cos(ang_ma))
# Detector array (minimum ANGLE difference between observed and reference):
diff = angobs_ma - angref_ma
det_ma = (Vny / pi) * ma.arctan2(ma.sin(diff), ma.cos(diff))
out_mask = np.zeros(det_ma.shape)
out_mask[abs(det_ma) > 0.8 * Vny_arr] = 1
out_mask[(Nval_arr_H < Nmin) | (Nval_arr_L < Nmin)] = 0
# CORRECTION (2 STEP)
# Convolution kernel
kernel = np.ones(kH.shape)
new_mask = (mask) | (out_mask.astype(bool))
# Array with the number of valid neighbours at each point (outliers removed)
Nval_arr = local_valid(new_mask, kernel=kernel)
out_mask[Nval_arr < Nmin] = 0
ref_arr = ref_val(data, new_mask, kernel, method='median')
ref_ma = ma.array(data=ref_arr, mask=mask)
return ref_ma, out_mask
def calibrate_pol(Data, m_total,RM_dir,R_to_sky,DP_correct,RM_correct) :
"""Subtracts a Map out of Data."""
# Data is a DataBlock object. It holds everything you need to know about
# the data in a single scan and IF. You should get to know them very well.
# Data.data is a numpy masked array (see numpy documentation) and holds the
# acctual data. It is a 4 dimensional array. The demensions are (in
# order): (time, pol, cal, freq). Each dimension can be any length which
# you can figure out by looking at Data.dims = sp.shape(Data.data).
# Data.field is a python dictionary that holds all the other data that you
# might care about from the origional fits file. For instance,
# Data.field['CAL'] is an array with length dims[2]. It normally has
# values ['T', 'F']. Data.field['CRVAL4'] tells you about the polarization
# axis of Data.data. By SDfits convension each polarization is represented
# by an integer: 1=I, 2=Q, 3=U, 4=V, -5=XX, -6=YY, -7=XY, -8=YX.
# Also this depends on having the polarizations rotated correctly to IQUV.
# Some code to do this has been hacked together in the rotate_pol module,
# but I don't trust it yet.
# Some dimension checks.
# We expect 4 polarizations.
if not Data.dims[1] == 4 :
raise ce.DataError('Require 4 polarizations.')
# We expect polarizations to be in order IQUV.
if (Data.field['CRVAL4'][0] != -5 or Data.field['CRVAL4'][1] != -7 or
Data.field['CRVAL4'][2] != -8 or Data.field['CRVAL4'][3] != -6) :
raise ce.DataError('Expected the polarization basis to be XY.')
# A useful function that might need:
Data.calc_freq()
# Now data has an atribute Data.freq which is an array that gives the
# frequency along the last axis.
# Data.field['CRVAL1'] is center frequency in Hz.
# Data.data 4 dim array 2nd index polarization, 4th index frequency.
# Need to get parallactic angle:
Data.calc_PA()
# This gives an array (Data.PA) of PA values of length = time dim.
# print Data.dims[0]
# This segment of the code is for Rotation Measure Component
# Since the RM Tables have half hour time divisions and scans are shorter, we can do 1 selection.
if RM_correct==True:
Comp_Time = 0.0
Full_date = Data.field['DATE-OBS'][Data.dims[0]/2]
Date = Full_date.split('T')[0]
Year = Date.split('-')[0]
Month = Date.split('-')[1]
Day = Date.split('-')[2]
Full_time = Full_date.split('T')[1]
Hour = Full_time.split(':')[0]
Min = Full_time.split(':')[1]
Sec = Full_time.split(':')[2]
if int(Min)<=15:
Comp_Time = float(Hour)+0.0
elif int(Min)<=45:
Comp_Time = float(Hour)+0.5
else :
Comp_Time = float(Hour)+1.0
#Victor's tables have time in format Hour (xx.xx), Az (deg), El (deg), RM
# Angle phi = RM*(wavelength)^2 where phi is in radians and wavelength is in meters
RM_file_name = RM_dir + Year + Month + Day + '_RM.txt'
RM_data = np.loadtxt(RM_file_name)
RA_RM = sp.zeros(len(RM_data[:,0]))
DEC_RM = sp.zeros(len(RM_data[:,0]))
for i in range(0,len(RM_data[:,0])):
RM_Hr = int(RM_data[i,0])
if RM_data[i,0]%1 == 0 :
RM_Min = '00'
minutes = 0.0
else:
RM_Min = '30'
minutes = 0.5
Test = float(RM_Hr)+minutes
if str(Comp_Time) == str(Test):
UT_RM = Year+'-'+Month+'-'+Day+'T'+str(RM_Hr)+':'+RM_Min+':00.00'
EL_RM = RM_data[i,2]
AZ_RM = RM_data[i,1]
RA_RM[i], DEC_RM[i] = utils.elaz2radecGBT(EL_RM,AZ_RM,UT_RM)
#Now have tables of RA/DEC to compare to actual RA/DEC
RM = 0
#This segment of the code is for Differential Phase Correction Generation
# Can determine the differential phase prior to the loop:
if DP_correct==True:
# Set up a table of data to examine (calon-caloff to get Tcal)
Tcal = ma.mean(Data.data[:,:,0,:],axis=0)-ma.mean(Data.data[:,:,1,:],axis=0)
# Tcal = ma.mean(Data.data[:,:,0,:]-Data.data[:,:,1,:],axis=0)
# This version was if we arbitrarily set 4 possible phases and found closest match. There seems to be
# enough variability in the phase within the four categories that this doesn't quite work.
# Randomly pick frequency bin near one of the zero crossings to compare U's
# U_test = Tcal[1,230]/sp.sqrt(Tcal[1,230]**2+Tcal[2,230]**2)
# print Tcal[:,191]
# print Tcal[1,:]
# U_test = Tcal[1,191]
# print U_test
# chi_sq =sp.zeros(4)
# dp_dat = sp.zeros((4,2))
# dp_dat[0] = [0.1354,2.341]
# dp_dat[1] = [0.0723, 2.4575]
# dp_dat[1] = [0.0730,2.611] #calculated specifically for sess 81
# dp_dat[2] = [0.1029,0.045]
# dp_dat[3] = [0,0]
# dp_dat[3] = [0.1669,5.609] # giving problems because closer for sess 81 at given freq
# min = 10
# val = 5
# for i in range(0,4):
# chi_sq[i] = U_test-sp.cos(dp_dat[i,0]*Data.freq[230]/1000000+dp_dat[i,1])/sp.sqrt(Tcal[1,230]**2+Tcal[2,230]**2)
# print sp.cos(dp_dat[i,0]*Data.freq[191]/1000000+dp_dat[i,1])
# chi_sq[i] = U_test-sp.cos(dp_dat[i,0]*Data.freq[191]/1000000+dp_dat[i,1])
# if abs(chi_sq[i]) < min:
# min = abs(chi_sq[i])
# val = i
# val tells which of the correction functions to use.
# print chi_sq
# print val
# print Data.freq[191]
# Alternate code for solving differential phase for each scan.
fitfunc = lambda p,x: sp.cos(p[0]*x+p[1])
errfunc = lambda p,x,y: fitfunc(p,x)-y
freqs = sp.zeros(Data.dims[3])
U_data = sp.zeros(Data.dims[3])
V_data = sp.zeros(Data.dims[3])
R_data = sp.zeros(Data.dims[3])
for i in range(0,Data.dims[3]):
freqs[i] = Data.freq[Data.dims[3]-i-1]/1000000
U_data[i] = Tcal[1,Data.dims[3]-i-1]
V_data[i] = Tcal[2,Data.dims[3]-i-1]
R_data[i] = U_data[i]/sp.sqrt(U_data[i]**2+V_data[i]**2)
# print np.any(np.isnan(R_data))
# print np.any(np.isinf(R_data))
# print freqs
for j in range(0,Data.dims[3]):
if int(freqs[j])==710:
mask_num = j
if int(freqs[j])==740:
mask_num2 = j
Datain = R_data[mask_num:mask_num2]
fin = freqs[mask_num:mask_num2]
bad_pts = np.logical_or(np.isnan(Datain),np.isinf(Datain))
good_ind = np.where(np.logical_not(bad_pts))
Datain = Datain[good_ind]
fin = fin[good_ind]
R0 = [0.18,1.0]
if len(good_ind[0])>1:
# print good_ind[0]
R,success = optimize.leastsq(errfunc,R0[:],args=(fin,Datain),maxfev=10000)
R[1] = R[1]%(2*sp.pi)
print R
else:
R=[0.0,0.0]
print "Not able to resolve a noise cal phase, setting phase to zero."
# This starts the actual data processing for the given scan
for time_index in range(0,Data.dims[0]):
# Extra data needed for Rotation Measure Correction
if RM_correct==True:
RA = Data.field['CRVAL2'][time_index]
DEC = Data.field['CRVAL3'][time_index]
# print RA
# print DEC
RM = 0
valid = []
for i in range(0,len(RA_RM)):
if RA_RM[i] != 0:
if abs(RA-RA_RM[i])<10.0:
if abs(DEC-DEC_RM[i])<10.0:
RM = RM_data[i,3]
valid.append(i)
RA_M = 10.0
DEC_M = 10.0
for j in range(0,len(valid)):
if abs(RA-RA_RM[valid[j]])<RA_M:
if abs(DEC-DEC_RM[valid[j]])<DEC_M:
RM = RM_data[valid[j],3]
# print RM
#Generate a sky matrix for this time index (assumes a XY basis):
m_sky = sp.zeros((4,4))
m_sky[0,0] = 0.5*(1+ma.cos(2*Data.PA[time_index]*sp.pi/180))
m_sky[0,1] = -ma.sin(2*Data.PA[time_index]*sp.pi/180)
m_sky[0,3] = 0.5*(1-ma.cos(2*Data.PA[time_index]*sp.pi/180))
m_sky[1,0] = 0.5*ma.sin(2*Data.PA[time_index]*sp.pi/180)
m_sky[1,1] = ma.cos(2*Data.PA[time_index]*sp.pi/180)
m_sky[1,3] = -0.5*ma.sin(2*Data.PA[time_index]*sp.pi/180)
m_sky[2,2] = 1
m_sky[3,0] = 0.5*(1-ma.cos(2*Data.PA[time_index]*sp.pi/180))
m_sky[3,1] = ma.sin(2*Data.PA[time_index]*sp.pi/180)
m_sky[3,3] = 0.5*(1+ma.cos(2*Data.PA[time_index]*sp.pi/180))
M_sky = sp.mat(m_sky)
M_sky = M_sky.I
# print M_sky
# for cal_index in range(0,Data.dims[2]):
for cal_index in range(0,2):
# Determines the Gains to use
for freq in range(0,Data.dims[3]):
# Tells which mueller matrix to use.
freq_limit = len(m_total[0,:])
frequency = int(Data.freq[freq]/1000)
# print frequency
bin = int((900000-frequency)*freq_limit/200000)
# print bin
# if freq_limit == 200:
# bin = 900-frequency
#Not setup to work with spectrometer data.
# elif freq_limit == 260:
# bin = 929-frequency
# print bin
#Generate a sky matrix for this time index:
#With faraday rotation sky matrix now frequency dependent
if RM_correct==True:
wavelength = 300000.0/float(frequency) # should be in meters given that frequency is in kHz
# print wavelength
Phi = RM*wavelength*wavelength
# print Phi
m_sky = sp.zeros((4,4))
m_sky[0,0] = 0.5*(1+ma.cos(2*Data.PA[time_index]*sp.pi/180+Phi))
m_sky[0,1] = -ma.sin(2*Data.PA[time_index]*sp.pi/180+Phi)
m_sky[0,3] = 0.5*(1-ma.cos(2*Data.PA[time_index]*sp.pi/180+Phi))
m_sky[1,0] = 0.5*ma.sin(2*Data.PA[time_index]*sp.pi/180+Phi)
m_sky[1,1] = ma.cos(2*Data.PA[time_index]*sp.pi/180+Phi)
m_sky[1,3] = -0.5*ma.sin(2*Data.PA[time_index]*sp.pi/180+Phi)
m_sky[2,2] = 1
m_sky[3,0] = 0.5*(1-ma.cos(2*Data.PA[time_index]*sp.pi/180+Phi))
m_sky[3,1] = ma.sin(2*Data.PA[time_index]*sp.pi/180+Phi)
m_sky[3,3] = 0.5*(1+ma.cos(2*Data.PA[time_index]*sp.pi/180+Phi))
M_sky = sp.mat(m_sky)
M_sky = M_sky.I
# print M_sky
# Converts files into vector format
XY_params = Data.data[time_index,:,cal_index,freq]
# Next there is a matrix multiplication that will generate
# a new set of xy values. (Differential gain correction)
XY_params[0] = XY_params[0]*m_total[0,bin]
XY_params[3] = XY_params[3]*m_total[1,bin]
XY_params[1] = XY_params[1]*sp.sqrt(m_total[0,bin]*m_total[1,bin])
XY_params[2] = XY_params[2]*sp.sqrt(m_total[0,bin]*m_total[1,bin])
# Add in correction for differential phase
if DP_correct==True:
XY_params[1] = XY_params[1]*sp.cos(R[0]*frequency/1000+R[1])-XY_params[2]*sp.sin(R[0]*frequency/1000+R[1])
XY_params[2] = XY_params[1]*sp.sin(R[0]*frequency/1000+R[1])+XY_params[2]*sp.cos(R[0]*frequency/1000+R[1])
#Rotate to sky coordinates (and RM correct if set)
if R_to_sky==True:
XY_params = np.dot(M_sky,XY_params)
#Write corrected data to the new file.
for i in range(0,Data.dims[1]):
Data.data[time_index,i,cal_index,freq] = XY_params[i]
def calibrate_pol(Data, m_total) :
"""Subtracts a Map out of Data."""
# Data is a DataBlock object. It holds everything you need to know about
# the data in a single scan and IF. You should get to know them very well.
# Data.data is a numpy masked array (see numpy documentation) and holds the
# acctual data. It is a 4 dimensional array. The demensions are (in
# order): (time, pol, cal, freq). Each dimension can be any length which
# you can figure out by looking at Data.dims = sp.shape(Data.data).
# Data.field is a python dictionary that holds all the other data that you
# might care about from the origional fits file. For instance,
# Data.field['CAL'] is an array with length dims[2]. It normally has
# values ['T', 'F']. Data.field['CRVAL4'] tells you about the polarization
# axis of Data.data. By SDfits convension each polarization is represented
# by an integer: 1=I, 2=Q, 3=U, 4=V, -5=XX, -6=YY, -7=XY, -8=YX.
# Also this depends on having the polarizations rotated correctly to IQUV.
# Some code to do this has been hacked together in the rotate_pol module,
# but I don't trust it yet.
# Some dimension checks.
# We expect 4 polarizations.
if not Data.dims[1] == 4 :
raise ce.DataError('Require 4 polarizations.')
# We expect polarizations to be in order IQUV.
if (Data.field['CRVAL4'][0] != 1 or Data.field['CRVAL4'][1] != 2 or
Data.field['CRVAL4'][2] != 3 or Data.field['CRVAL4'][3] != 4) :
raise ce.DataError('Expected the polarization basis to be IQUV.')
# A useful function that might need:
Data.calc_freq()
# Now data has an atribute Data.freq which is an array that gives the
# frequency along the last axis.
# Data.field['CRVAL1'] is center frequency in Hz.
# Data.data 4 dim array 2nd index polarization, 4th index frequency.
# Need to get parallactic angle:
Data.calc_PA()
# This gives an array (Data.PA) of PA values of length = time dim.
for time_index in range(0,Data.dims[0]):
#Generate a sky matrix for this time index:
m_sky = sp.zeros((4,4))
m_sky[0,0] = 1
m_sky[1,1] = ma.cos(2*Data.PA[time_index]*sp.pi/180)
m_sky[1,2] = ma.sin(2*Data.PA[time_index]*sp.pi/180)
m_sky[2,1] = -ma.sin(2*Data.PA[time_index]*sp.pi/180)
m_sky[2,2] = ma.cos(2*Data.PA[time_index]*sp.pi/180)
m_sky[3,3] = 1
M_sky = sp.mat(m_sky)
M_sky = M_sky.I
# print M_sky
for cal_index in range(0,Data.dims[2]):
# Determines the Inverse Mueller Matrix to use
# CenterFrequency = int(Data.field['CRVAL1']/1000000)
for freq in range(0,Data.dims[3]):
# if Data.freq[freq] in range(669,699):
# bin = 0
# elif Data.freq[freq] in range(700,729):
# bin = 1
# elif Data.freq[freq] in range(730,759):
# bin = 2
# elif Data.freq[freq] in range(760,789):
# bin = 3
# elif Data.freq[freq] in range(790,819):
# bin = 4
# elif Data.freq[freq] in range(820,849):
# bin = 5
# elif Data.freq[freq] in range(850,879):
# bin = 6
# elif Data.freq[freq] in range(880,929):
# bin = 7
# else :
# raise ce.DataError('The frequency outside viable window')
# Tells which mueller matrix to use. Assumes at least 1 MHz bins.
frequency = int(Data.freq[freq]/1000)
freq_limit=len(m_total[0,0,:])
bin = int((900000-frequency)*freq_limit/200000)
# if freq_limit == 200:
# bin = 900-frequency
# elif freq_limit == 260:
# bin = 929-frequency
# print bin
# Converts files into matrix format
STOKES = Data.data[time_index,:,cal_index,freq]
# print STOKES
MUELLER = sp.mat(m_total[:,:,bin])
# print MUELLER
# Next there is a matrix multiplication that will generate
# a new set of stokes values.
stokesmod = np.dot(MUELLER,STOKES)
stokesmod = np.dot(M_sky,stokesmod)
# print stokesmod
for i in range(0,Data.dims[1]):
Data.data[time_index,i,cal_index,freq] = stokesmod[i]
