def comp_a(dert__, rng):
"""
Compute and compare a over predetermined range.
"""
# Unpack dert__:
if len(dert__) in (5, 12): # idert or full dert with m.
i__, g__, m__, dy__, dx__ = dert__[:5]
else: # idert or full dert without m.
i__, g__, dy__, dx__ = dert__[:4]
if len(dert__) > 10: # if ra+:
a__ = dert__[-7:-5] # Computed angle (use reverse indexing to avoid m check).
day__ = dert__[-4:-2] # Accumulated day__.
dax__ = dert__[-2:] # Accumulated day__.
else: # if fa:
# Compute angles:
a__ = ma.stack((dy__, dx__), axis=0) / g__
a__.mask = g__.mask
# Initialize dax, day:
day__, dax__ = [ma.zeros((2,) + i__.shape) for _ in range(2)]
# Compute angle differences:
da__ = translated_operation(a__, rng, angle_diff)
comp_field = central_slice(rng)
# Decompose and add to corresponding day and dax:
day__[comp_field] = (da__ * Y_COEFFS[rng]).mean(axis=-1)
dax__[comp_field] = (da__ * X_COEFFS[rng]).mean(axis=-1)
# Apply mask:
msq = np.ones(a__.shape, dtype=int) # Rim mask.
msq[comp_field] = a__.mask[comp_field] + da__.mask.sum(axis=-1) # Summed d mask.
imsq = msq.nonzero()
day__[imsq] = dax__[imsq] = ma.masked # Apply mask.
# Compute ga:
ga__ = ma.hypot(
ma.arctan2(*day__),
ma.arctan2(*dax__)
)[np.newaxis, ...] * SCALER_ga
try: # dert with m is more common:
return ma.concatenate( # Concatenate on the first dimension.
(
ma.stack((i__, g__, m__, dy__, dx__), axis=0),
a__, ga__, day__, dax__,
),
axis=0,
)
except NameError: # m doesn't exist:
return ma.concatenate( # Concatenate on the first dimension.
(
ma.stack((i__, g__, dy__, dx__), axis=0),
a__, ga__, day__, dax__,
),
axis=0,
)
def comp_a(gdert__, rng):
"""
Compute and compare a over predetermined range.
"""
# Unpack dert__:
try:
g, gg, m, dy, dx = gdert__
except ValueError: # Initial dert doesn't contain m.
g, gg, dy, dx = gdert__
# Initialize dax, day:
day, dax = [ma.zeros((2, ) + g.shape) for _ in range(2)]
# Compute angles:
a = ma.stack((dy, dx), axis=0) / gg
a.mask = gg.mask
# Compute angle differences:
da = translated_operation(a, rng, angle_diff)
comp_field = central_slice(rng)
# Decompose and add to corresponding day and dax:
day[comp_field] = (da * Y_COEFFS[rng]).mean(axis=-1)
dax[comp_field] = (da * X_COEFFS[rng]).mean(axis=-1)
# Apply mask:
msq = np.ones(a.shape, dtype=int) # Rim mask.
msq[comp_field] = a.mask[comp_field] + da.mask.sum(
axis=-1) # Summed d mask.
imsq = msq.nonzero()
day[imsq] = dax[imsq] = ma.masked # Apply mask.
# Compute ga:
ga = ma.hypot(ma.arctan2(*day), ma.arctan2(*dax))[np.newaxis,
...] * SCALER_ga
try:
return ma.concatenate( # Concatenate on the first dimension.
(
ma.stack((g, gg, m), axis=0),
ga,
day,
dax,
),
axis=0,
)
except NameError: # m doesn't exist.
return ma.concatenate( # Concatenate on the first dimension.
(
ma.stack((g, gg), axis=0),
a,
ga,
day,
dax,
),
axis=0,
)
def _compare(self):
dy, dx = compare_slices(self._i, self._rng, operator=angle_diff)
self._derts[1:][central_slice(self._rng)] += np.concatenate((dy, dx))
self._derts[0] = ma.hypot(
ma.arctan2(*self.dy),
ma.arctan2(*self.dx),
)
self._derts[rim_mask(self._i.shape, rng)] = ma.masked
return self
def _angles(self, U, V, eps=0.001):
xy = self.ax.transData.transform(self.XY)
uv = ma.hstack((U[:, np.newaxis], V[:, np.newaxis])).filled(0)
xyp = self.ax.transData.transform(self.XY + eps * uv)
dxy = xyp - xy
ang = ma.arctan2(dxy[:, 1], dxy[:, 0])
return ang
def calculatePosturalMeasurements(self):
self.Xhead = ma.array(ma.squeeze(self.skeleton[:, 0, :]))
self.Xhead = ((self.Xhead + self.h5ref['boundingBox'][:, :2]) /
self.pixelsPerMicron)
self.Xhead[np.logical_not(self.orientationFixed), :] = ma.masked
self.Xtail = ma.array(np.squeeze(self.skeleton[:, -1, :]))
self.Xtail = ((self.Xtail + self.h5ref['boundingBox'][:, :2]) /
self.pixelsPerMicron)
self.Xtail[np.logical_not(self.orientationFixed), :] = ma.masked
self.psi = ma.arctan2(self.Xhead[:, 0]-self.X[:, 0],
self.Xhead[:, 1]-self.X[:, 1])
dpsi = self.phi - self.psi
self.dpsi = ma.mod(dpsi+np.pi, 2*np.pi)-np.pi
self.psi[np.logical_not(self.orientationFixed)] = ma.masked
self.dpsi[np.logical_or(np.logical_not(self.orientationFixed),
self.badFrames)] = ma.masked
self.Xhead[np.logical_or(np.logical_not(self.orientationFixed),
self.badFrames), :] = ma.masked
self.Xtail[np.logical_or(np.logical_not(self.orientationFixed),
self.badFrames), :] = ma.masked
skeleton = ma.array(self.skeleton)
skeleton[np.logical_not(self.orientationFixed), :, :] = ma.masked
posture = ma.array(self.posture)
posture[np.logical_not(self.orientationFixed), :] = ma.masked
missing = np.any(posture.mask, axis=1)
if np.all(missing):
self.Ctheta = None
self.ltheta = None
self.vtheta = None
else:
posture = posture[~missing, :].T
self.Ctheta = np.cov(posture)
self.ltheta, self.vtheta = LA.eig(self.Ctheta)
def _generate_dbc(lane_to_follow: Lane, dbe_file_name: str) -> str:
from numpy.ma import arctan2
from numpy import rad2deg, pi, sin, cos, array
goal = lane_to_follow[-1]
current = lane_to_follow[0]
current_pos = array([current["x"], current["y"]])
next = lane_to_follow[1]
next_pos = array([next["x"], next["y"]])
delta = next_pos - current_pos
initial_orientation_rad = arctan2(delta[1], delta[0])
initial_orientation_deg = float("{0:.2f}".format(
rad2deg(initial_orientation_rad)))
r2 = 0.25 * current["width"]
theta2 = initial_orientation_rad - 0.5 * pi
offset = array([
2.5 * cos(initial_orientation_rad), 2.5 * sin(initial_orientation_rad)
])
temp = current_pos + offset
initial_position = temp + array([r2 * cos(theta2), r2 * sin(theta2)])
initial_state = {"x": initial_position[0], "y": initial_position[1]}
return TEMPLATE_ENV.get_template(DBC_TEMPLATE_NAME) \
.render(initial_state=initial_state,
initial_orientation=initial_orientation_deg,
lane=lane_to_follow,
dbe_file_name=dbe_file_name,
goal=goal)
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 calculateCentroidMeasurements(self):
self.X[self.badFrames, :] = ma.masked
if not self.useSmoothingFilterDerivatives:
self.v[1:-1] = (self.X[2:, :] - self.X[0:-2])/(2.0/self.frameRate)
else:
# use a cubic polynomial filter to estimate the velocity
self.v = ma.zeros(self.X.shape)
halfWindow = int(np.round(self.filterWindow/2.*self.frameRate))
for i in xrange(halfWindow, self.v.shape[0]-halfWindow):
start = i-halfWindow
mid = i
finish = i+halfWindow+1
if not np.any(self.X.mask[start:finish,:]):
px = np.polyder(np.polyfit(self.t[start:finish]-self.t[mid],
self.X[start:finish, 0], 3))
py = np.polyder(np.polyfit(self.t[start:finish]-self.t[mid],
self.X[start:finish, 1], 3))
self.v[i,:] = [np.polyval(px, 0), np.polyval(py, 0)]
else:
self.v[i,:] = ma.masked
self.s = ma.sqrt(ma.sum(ma.power(self.v, 2), axis=1))
self.phi = ma.arctan2(self.v[:, 1], self.v[:, 0])
self.t[self.badFrames] = ma.masked
self.X[self.badFrames, :] = ma.masked
self.v[self.badFrames, :] = ma.masked
self.s[self.badFrames] = ma.masked
self.phi[self.badFrames] = ma.masked
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 _angles(self, U, V, eps=0.001):
xy = self.ax.transData.transform(self.XY)
uv = ma.hstack((U[:,np.newaxis], V[:,np.newaxis])).filled(0)
xyp = self.ax.transData.transform(self.XY + eps * uv)
dxy = xyp - xy
ang = ma.arctan2(dxy[:,1], dxy[:,0])
return ang
def DD_FF(u,v):
''' calculates wind/current speed and direction from u and v components
#
if u and v are easterly and northerly components,
DD is heading direction of the wind.
to get meteorological-standard, call DD_FF(-u, -v)
'''
DD = ma.arctan2(u, v)*180/sp.pi
DD[DD < 0] = 360 + DD[DD < 0]
FF = ma.sqrt(u**2 + v**2)
return DD, FF
def DD_FF(u,v):
''' calculates wind/current speed and direction from u and v components
#
if u and v are easterly and northerly components,
DD is heading direction of the wind.
to get meteorological-standard, call DD_FF(-u, -v)
'''
DD = ma.arctan2(u, v)*180/sp.pi
DD[DD < 0] = 360 + DD[DD < 0]
FF = ma.sqrt(u**2 + v**2)
return DD, FF
def cart2polar(x, y, degrees=True):
"""
Convert cartesian X and Y to polar RHO and THETA.
:param x: x cartesian coordinate
:param y: y cartesian coordinate
:param degrees: True = return theta in degrees, False = return theta in
radians. [default: True]
:return: r, theta
"""
rho = ma.sqrt(x**2 + y**2)
theta = ma.arctan2(y, x)
if degrees:
theta *= (180 / math.pi)
return rho, theta
def cart2polar(x, y, degrees=True):
"""
Convert cartesian X and Y to polar RHO and THETA.
:param x: x cartesian coordinate
:param y: y cartesian coordinate
:param degrees: True = return theta in degrees, False = return theta in
radians. [default: True]
:return: r, theta
"""
rho = ma.sqrt(x ** 2 + y ** 2)
theta = ma.arctan2(y, x)
if degrees:
theta *= (180 / math.pi)
return rho, theta
def DD_FF(u,v,met=True):
''' calculates wind/current speed and direction from u and v components
#
if u and v are easterly and northerly components,
returns:
FF : wind speed
DD : wind direction in meteorological standard (directions the wind is coming from)
call with met=False for oceanographic standard
'''
if met==False:
u,v = -u, -v
DD = ma.arctan2(-u, -v)*180/sp.pi
DD[DD < 0] = 360 + DD[DD < 0]
FF = ma.sqrt(u**2 + v**2)
return DD, FF
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 _make_barbs(self, u, v, nflags, nbarbs, half_barb, empty_flag, length,
pivot, sizes, fill_empty, flip):
'''
This function actually creates the wind barbs. *u* and *v*
are components of the vector in the *x* and *y* directions,
respectively.
*nflags*, *nbarbs*, and *half_barb*, empty_flag* are,
*respectively, the number of flags, number of barbs, flag for
*half a barb, and flag for empty barb, ostensibly obtained
*from :meth:`_find_tails`.
*length* is the length of the barb staff in points.
*pivot* specifies the point on the barb around which the
entire barb should be rotated. Right now, valid options are
'head' and 'middle'.
*sizes* is a dictionary of coefficients specifying the ratio
of a given feature to the length of the barb. These features
include:
- *spacing*: space between features (flags, full/half
barbs)
- *height*: distance from shaft of top of a flag or full
barb
- *width* - width of a flag, twice the width of a full barb
- *emptybarb* - radius of the circle used for low
magnitudes
*fill_empty* specifies whether the circle representing an
empty barb should be filled or not (this changes the drawing
of the polygon).
*flip* is a flag indicating whether the features should be flipped to
the other side of the barb (useful for winds in the southern
hemisphere.
This function returns list of arrays of vertices, defining a polygon for
each of the wind barbs. These polygons have been rotated to properly
align with the vector direction.
'''
spacing = length * sizes.get('spacing', 0.125)
full_height = length * sizes.get('height', 0.4)
full_width = length * sizes.get('width', 0.25)
empty_rad = length * sizes.get('emptybarb', 0.15)
pivot_points = dict(tip=0.0, middle=-length/2.)
if flip: full_height = -full_height
endx = 0.0
endy = pivot_points[pivot.lower()]
angles = -(ma.arctan2(v, u) + np.pi/2)
circ = CirclePolygon((0,0), radius=empty_rad).get_verts()
if fill_empty:
empty_barb = circ
else:
empty_barb = np.concatenate((circ, circ[::-1]))
barb_list = []
for index, angle in np.ndenumerate(angles):
if empty_flag[index]:
barb_list.append(empty_barb)
continue
poly_verts = [(endx, endy)]
offset = length
for i in range(nflags[index]):
if offset != length: offset += spacing / 2.
poly_verts.extend([[endx, endy + offset],
[endx + full_height, endy - full_width/2 + offset],
[endx, endy - full_width + offset]])
offset -= full_width + spacing
for i in range(nbarbs[index]):
poly_verts.extend([(endx, endy + offset),
(endx + full_height, endy + offset + full_width/2),
(endx, endy + offset)])
offset -= spacing
if half_barb[index]:
if offset == length:
poly_verts.append((endx, endy + offset))
offset -= 1.5 * spacing
poly_verts.extend([(endx, endy + offset),
(endx + full_height/2, endy + offset + full_width/4),
(endx, endy + offset)])
poly_verts = transforms.Affine2D().rotate(-angle).transform(
poly_verts)
barb_list.append(poly_verts)
return barb_list
def _OSGB36toWGS84(self):
""" Convert between OSGB36 and WGS84. If we already have values available, we just return them.
:rtype: float, float
"""
if self.easting is None or self.northing is None:
return False
#E, N are the British national grid coordinates - eastings and northings
a, b = 6377563.396, 6356256.909 #The Airy 180 semi-major and semi-minor axes used for OSGB36 (m)
F0 = 0.9996012717 #scale factor on the central meridian
lat0 = 49 * pi / 180 #Latitude of true origin (radians)
lon0 = -2 * pi / 180 #Longtitude of true origin and central meridian (radians)
N0, E0 = -100000, 400000 #Northing & easting of true origin (m)
e2 = 1 - (b * b) / (a * a) #eccentricity squared
n = (a - b) / (a + b)
#Initialise the iterative variables
lat, M = lat0, 0
while self.northing - N0 - M >= 0.00001: #Accurate to 0.01mm
lat += (self.northing - N0 - M) / (a * F0)
M1 = (1 + n + (5. / 4) * n**2 + (5. / 4) * n**3) * (lat - lat0)
M2 = (3 * n + 3 * n**2 +
(21. / 8) * n**3) * sin(lat - lat0) * cos(lat + lat0)
M3 = ((15. / 8) * n**2 +
(15. / 8) * n**3) * sin(2 * (lat - lat0)) * cos(2 *
(lat + lat0))
M4 = (35. / 24) * n**3 * sin(3 * (lat - lat0)) * cos(3 *
(lat + lat0))
#meridional arc
M = b * F0 * (M1 - M2 + M3 - M4)
#transverse radius of curvature
nu = a * F0 / sqrt(1 - e2 * sin(lat)**2)
#meridional radius of curvature
rho = a * F0 * (1 - e2) * (1 - e2 * sin(lat)**2)**(-1.5)
eta2 = nu / rho - 1
secLat = 1. / cos(lat)
VII = tan(lat) / (2 * rho * nu)
VIII = tan(lat) / (24 * rho * nu**3) * (5 + 3 * tan(lat)**2 + eta2 -
9 * tan(lat)**2 * eta2)
IX = tan(lat) / (720 * rho * nu**5) * (61 + 90 * tan(lat)**2 +
45 * tan(lat)**4)
X = secLat / nu
XI = secLat / (6 * nu**3) * (nu / rho + 2 * tan(lat)**2)
XII = secLat / (120 * nu**5) * (5 + 28 * tan(lat)**2 +
24 * tan(lat)**4)
XIIA = secLat / (5040 * nu**7) * (
61 + 662 * tan(lat)**2 + 1320 * tan(lat)**4 + 720 * tan(lat)**6)
dE = self.easting - E0
#These are on the wrong ellipsoid currently: Airy1830. (Denoted by _1)
lat_1 = lat - VII * dE**2 + VIII * dE**4 - IX * dE**6
lon_1 = lon0 + X * dE - XI * dE**3 + XII * dE**5 - XIIA * dE**7
#Want to convert to the GRS80 ellipsoid.
#First convert to cartesian from spherical polar coordinates
H = 0 #Third spherical coord.
x_1 = (nu / F0 + H) * cos(lat_1) * cos(lon_1)
y_1 = (nu / F0 + H) * cos(lat_1) * sin(lon_1)
z_1 = ((1 - e2) * nu / F0 + H) * sin(lat_1)
#Perform Helmut transform (to go between Airy 1830 (_1) and GRS80 (_2))
s = -20.4894 * 10**-6 #The scale factor -1
tx, ty, tz = 446.448, -125.157, +542.060 #The translations along x,y,z axes respectively
rxs, rys, rzs = 0.1502, 0.2470, 0.8421 #The rotations along x,y,z respectively, in seconds
rx, ry, rz = rxs * pi / (180 * 3600.), rys * pi / (
180 * 3600.), rzs * pi / (180 * 3600.) #In radians
x_2 = tx + (1 + s) * x_1 + (-rz) * y_1 + (ry) * z_1
y_2 = ty + (rz) * x_1 + (1 + s) * y_1 + (-rx) * z_1
z_2 = tz + (-ry) * x_1 + (rx) * y_1 + (1 + s) * z_1
#Back to spherical polar coordinates from cartesian
#Need some of the characteristics of the new ellipsoid
a_2, b_2 = 6378137.000, 6356752.3141 #The GSR80 semi-major and semi-minor axes used for WGS84(m)
e2_2 = 1 - (b_2 * b_2) / (a_2 * a_2
) #The eccentricity of the GRS80 ellipsoid
p = sqrt(x_2**2 + y_2**2)
#Lat is obtained by an iterative proceedure:
lat = arctan2(z_2, (p * (1 - e2_2))) #Initial value
latold = 2 * pi
while abs(lat - latold) > 10**-16:
lat, latold = latold, lat
nu_2 = a_2 / sqrt(1 - e2_2 * sin(latold)**2)
lat = arctan2(z_2 + e2_2 * nu_2 * sin(latold), p)
#Lon and height are then pretty easy
lon = arctan2(y_2, x_2)
H = p / cos(lat) - nu_2
#Convert to degrees
self.lat = lat * 180 / pi
self.lon = lon * 180 / pi
return True
def _WGS84toOSGB36(self):
"""Perform conversion from WGS84 to OSGB36. If the OSGB36 co-ords are available,
just return those.
"""
if self.lat is None or self.lon is None:
return False
#First convert to radians
#These are on the wrong ellipsoid currently: GRS80. (Denoted by _1)
lat_1 = self.lat * pi / 180
lon_1 = self.lon * pi / 180
#Want to convert to the Airy 1830 ellipsoid, which has the following:
a_1, b_1 = 6378137.000, 6356752.3141 #The GSR80 semi-major and semi-minor axes used for WGS84(m)
e2_1 = 1 - (b_1 * b_1) / (a_1 * a_1
) #The eccentricity of the GRS80 ellipsoid
nu_1 = a_1 / sqrt(1 - e2_1 * sin(lat_1)**2)
#First convert to cartesian from spherical polar coordinates
H = 0 #Third spherical coord.
x_1 = (nu_1 + H) * cos(lat_1) * cos(lon_1)
y_1 = (nu_1 + H) * cos(lat_1) * sin(lon_1)
z_1 = ((1 - e2_1) * nu_1 + H) * sin(lat_1)
#Perform Helmut transform (to go between GRS80 (_1) and Airy 1830 (_2))
s = 20.4894 * 10**-6 #The scale factor -1
tx, ty, tz = -446.448, 125.157, -542.060 #The translations along x,y,z axes respectively
rxs, rys, rzs = -0.1502, -0.2470, -0.8421 #The rotations along x,y,z respectively, in seconds
rx, ry, rz = rxs * pi / (180 * 3600.), rys * pi / (
180 * 3600.), rzs * pi / (180 * 3600.) #In radians
x_2 = tx + (1 + s) * x_1 + (-rz) * y_1 + ry * z_1
y_2 = ty + rz * x_1 + (1 + s) * y_1 + (-rx) * z_1
z_2 = tz + (-ry) * x_1 + rx * y_1 + (1 + s) * z_1
#Back to spherical polar coordinates from cartesian
#Need some of the characteristics of the new ellipsoid
a, b = 6377563.396, 6356256.909 #The GSR80 semi-major and semi-minor axes used for WGS84(m)
e2 = 1 - (b * b) / (a * a
) #The eccentricity of the Airy 1830 ellipsoid
p = sqrt(x_2**2 + y_2**2)
#Lat is obtained by an iterative proceedure:
lat = arctan2(z_2, (p * (1 - e2))) #Initial value
latold = 2 * pi
while abs(lat - latold) > 10**-16:
lat, latold = latold, lat
nu = a / sqrt(1 - e2 * sin(latold)**2)
lat = arctan2(z_2 + e2 * nu * sin(latold), p)
#Lon and height are then pretty easy
lon = arctan2(y_2, x_2)
H = p / cos(lat) - nu
#E, N are the British national grid coordinates - eastings and northings
F0 = 0.9996012717 #scale factor on the central meridian
lat0 = 49 * pi / 180 #Latitude of true origin (radians)
lon0 = -2 * pi / 180 #Longtitude of true origin and central meridian (radians)
N0, E0 = -100000, 400000 #Northing & easting of true origin (m)
n = (a - b) / (a + b)
#meridional radius of curvature
rho = a * F0 * (1 - e2) * (1 - e2 * sin(lat)**2)**(-1.5)
eta2 = nu * F0 / rho - 1
M1 = (1 + n + (5 / 4) * n**2 + (5 / 4) * n**3) * (lat - lat0)
M2 = (3 * n + 3 * n**2 +
(21 / 8) * n**3) * sin(lat - lat0) * cos(lat + lat0)
M3 = ((15 / 8) * n**2 +
(15 / 8) * n**3) * sin(2 * (lat - lat0)) * cos(2 * (lat + lat0))
M4 = (35 / 24) * n**3 * sin(3 * (lat - lat0)) * cos(3 * (lat + lat0))
#meridional arc
M = b * F0 * (M1 - M2 + M3 - M4)
I = M + N0
II = nu * F0 * sin(lat) * cos(lat) / 2
III = nu * F0 * sin(lat) * cos(lat)**3 * (5 - tan(lat)**2 +
9 * eta2) / 24
IIIA = nu * F0 * sin(lat) * cos(lat)**5 * (61 - 58 * tan(lat)**2 +
tan(lat)**4) / 720
IV = nu * F0 * cos(lat)
V = nu * F0 * cos(lat)**3 * (nu / rho - tan(lat)**2) / 6
VI = nu * F0 * cos(lat)**5 * (5 - 18 * tan(lat)**2 + tan(lat)**4 + 14 *
eta2 - 58 * eta2 * tan(lat)**2) / 120
N = I + II * (lon - lon0)**2 + III * (lon - lon0)**4 + IIIA * (lon -
lon0)**6
E = E0 + IV * (lon - lon0) + V * (lon - lon0)**3 + VI * (lon - lon0)**5
self.easting = E
self.northing = N
return True
def _make_barbs(self, u, v, nflags, nbarbs, half_barb, empty_flag, length,
pivot, sizes, fill_empty, flip):
"""Monkey-patch _make_barbs. Allows pivot to be a float value."""
# These control the spacing and size of barb elements relative to the
# length of the shaft
spacing = length * sizes.get('spacing', 0.125)
full_height = length * sizes.get('height', 0.4)
full_width = length * sizes.get('width', 0.25)
empty_rad = length * sizes.get('emptybarb', 0.15)
# Controls y point where to pivot the barb.
pivot_points = dict(tip=0.0, middle=-length / 2.)
# Check for flip
if flip:
full_height = -full_height
endx = 0.0
try:
endy = float(pivot)
except ValueError:
endy = pivot_points[pivot.lower()]
# Get the appropriate angle for the vector components. The offset is
# due to the way the barb is initially drawn, going down the y-axis.
# This makes sense in a meteorological mode of thinking since there 0
# degrees corresponds to north (the y-axis traditionally)
angles = -(ma.arctan2(v, u) + np.pi / 2)
# Used for low magnitude. We just get the vertices, so if we make it
# out here, it can be reused. The center set here should put the
# center of the circle at the location(offset), rather than at the
# same point as the barb pivot; this seems more sensible.
circ = CirclePolygon((0, 0), radius=empty_rad).get_verts()
if fill_empty:
empty_barb = circ
else:
# If we don't want the empty one filled, we make a degenerate
# polygon that wraps back over itself
empty_barb = np.concatenate((circ, circ[::-1]))
barb_list = []
for index, angle in np.ndenumerate(angles):
# If the vector magnitude is too weak to draw anything, plot an
# empty circle instead
if empty_flag[index]:
# We can skip the transform since the circle has no preferred
# orientation
barb_list.append(empty_barb)
continue
poly_verts = [(endx, endy)]
offset = length
# Add vertices for each flag
for i in range(nflags[index]):
# The spacing that works for the barbs is a little to much for
# the flags, but this only occurs when we have more than 1
# flag.
if offset != length:
offset += spacing / 2.
poly_verts.extend(
[[endx, endy + offset],
[endx + full_height, endy - full_width / 2 + offset],
[endx, endy - full_width + offset]])
offset -= full_width + spacing
# Add vertices for each barb. These really are lines, but works
# great adding 3 vertices that basically pull the polygon out and
# back down the line
for i in range(nbarbs[index]):
poly_verts.extend(
[(endx, endy + offset),
(endx + full_height, endy + offset + full_width / 2),
(endx, endy + offset)])
offset -= spacing
# Add the vertices for half a barb, if needed
if half_barb[index]:
# If the half barb is the first on the staff, traditionally it
# is offset from the end to make it easy to distinguish from a
# barb with a full one
if offset == length:
poly_verts.append((endx, endy + offset))
offset -= 1.5 * spacing
poly_verts.extend(
[(endx, endy + offset),
(endx + full_height / 2, endy + offset + full_width / 4),
(endx, endy + offset)])
# Rotate the barb according the angle. Making the barb first and
# then rotating it made the math for drawing the barb really easy.
# Also, the transform framework makes doing the rotation simple.
poly_verts = transforms.Affine2D().rotate(-angle).transform(
poly_verts)
barb_list.append(poly_verts)
return barb_list
def _WGS84toOSGB36(self):
"""Perform conversion from WGS84 to OSGB36. If the OSGB36 co-ords are available,
just return those.
"""
if self.lat is None or self.lon is None:
return False
#First convert to radians
#These are on the wrong ellipsoid currently: GRS80. (Denoted by _1)
lat_1 = self.lat * pi / 180
lon_1 = self.lon * pi / 180
#Want to convert to the Airy 1830 ellipsoid, which has the following:
a_1, b_1 =6378137.000, 6356752.3141 #The GSR80 semi-major and semi-minor axes used for WGS84(m)
e2_1 = 1 - (b_1*b_1) / (a_1 * a_1) #The eccentricity of the GRS80 ellipsoid
nu_1 = a_1/sqrt(1-e2_1*sin(lat_1)**2)
#First convert to cartesian from spherical polar coordinates
H = 0 #Third spherical coord.
x_1 = (nu_1 + H)*cos(lat_1)*cos(lon_1)
y_1 = (nu_1 + H)*cos(lat_1)*sin(lon_1)
z_1 = ((1-e2_1)*nu_1 + H)*sin(lat_1)
#Perform Helmut transform (to go between GRS80 (_1) and Airy 1830 (_2))
s = 20.4894*10**-6 #The scale factor -1
tx, ty, tz = -446.448, 125.157, -542.060 #The translations along x,y,z axes respectively
rxs, rys, rzs = -0.1502, -0.2470, -0.8421#The rotations along x,y,z respectively, in seconds
rx, ry, rz = rxs*pi/(180*3600.), rys*pi/(180*3600.), rzs*pi/(180*3600.) #In radians
x_2 = tx + (1+s)*x_1 + (-rz)*y_1 + ry * z_1
y_2 = ty + rz * x_1 + (1+s)*y_1 + (-rx)*z_1
z_2 = tz + (-ry) * x_1 + rx * y_1 +(1+s)*z_1
#Back to spherical polar coordinates from cartesian
#Need some of the characteristics of the new ellipsoid
a, b = 6377563.396, 6356256.909 #The GSR80 semi-major and semi-minor axes used for WGS84(m)
e2 = 1 - (b*b)/(a*a) #The eccentricity of the Airy 1830 ellipsoid
p = sqrt(x_2**2 + y_2**2)
#Lat is obtained by an iterative proceedure:
lat = arctan2(z_2,(p*(1-e2))) #Initial value
latold = 2*pi
while abs(lat - latold)>10**-16:
lat, latold = latold, lat
nu = a/sqrt(1 - e2 * sin(latold) ** 2)
lat = arctan2(z_2 + e2 * nu * sin(latold), p)
#Lon and height are then pretty easy
lon = arctan2(y_2,x_2)
H = p/cos(lat) - nu
#E, N are the British national grid coordinates - eastings and northings
F0 = 0.9996012717 #scale factor on the central meridian
lat0 = 49*pi/180#Latitude of true origin (radians)
lon0 = -2*pi/180#Longtitude of true origin and central meridian (radians)
N0, E0 = -100000, 400000#Northing & easting of true origin (m)
n = (a-b)/(a+b)
#meridional radius of curvature
rho = a*F0*(1-e2)*(1-e2*sin(lat)**2)**(-1.5)
eta2 = nu*F0/rho-1
M1 = (1 + n + (5/4)*n**2 + (5/4)*n**3) * (lat-lat0)
M2 = (3*n + 3*n**2 + (21/8)*n**3) * sin(lat-lat0) * cos(lat+lat0)
M3 = ((15/8)*n**2 + (15/8)*n**3) * sin(2*(lat-lat0)) * cos(2*(lat+lat0))
M4 = (35/24)*n**3 * sin(3*(lat-lat0)) * cos(3*(lat+lat0))
#meridional arc
M = b * F0 * (M1 - M2 + M3 - M4)
I = M + N0
II = nu*F0*sin(lat)*cos(lat)/2
III = nu*F0*sin(lat)*cos(lat)**3*(5- tan(lat)**2 + 9*eta2)/24
IIIA = nu*F0*sin(lat)*cos(lat)**5*(61- 58*tan(lat)**2 + tan(lat)**4)/720
IV = nu*F0*cos(lat)
V = nu*F0*cos(lat)**3*(nu/rho - tan(lat)**2)/6
VI = nu*F0*cos(lat)**5*(5 - 18* tan(lat)**2 + tan(lat)**4 + 14*eta2 - 58*eta2*tan(lat)**2)/120
N = I + II*(lon-lon0)**2 + III*(lon- lon0)**4 + IIIA*(lon-lon0)**6
E = E0 + IV*(lon-lon0) + V*(lon- lon0)**3 + VI*(lon- lon0)**5
self.easting = E
self.northing = N
return True
def _make_barbs(self, u, v, nflags, nbarbs, half_barb, empty_flag, length,
pivot, sizes, fill_empty, flip):
"""Monkey-patch _make_barbs. Allows pivot to be a float value."""
# These control the spacing and size of barb elements relative to the
# length of the shaft
spacing = length * sizes.get('spacing', 0.125)
full_height = length * sizes.get('height', 0.4)
full_width = length * sizes.get('width', 0.25)
empty_rad = length * sizes.get('emptybarb', 0.15)
# Controls y point where to pivot the barb.
pivot_points = dict(tip=0.0, middle=-length / 2.) # noqa: C408
# Check for flip
if flip:
full_height = -full_height
endx = 0.0
try:
endy = float(pivot)
except ValueError:
endy = pivot_points[pivot.lower()]
# Get the appropriate angle for the vector components. The offset is
# due to the way the barb is initially drawn, going down the y-axis.
# This makes sense in a meteorological mode of thinking since there 0
# degrees corresponds to north (the y-axis traditionally)
angles = -(ma.arctan2(v, u) + np.pi / 2)
# Used for low magnitude. We just get the vertices, so if we make it
# out here, it can be reused. The center set here should put the
# center of the circle at the location(offset), rather than at the
# same point as the barb pivot; this seems more sensible.
circ = CirclePolygon((0, 0), radius=empty_rad).get_verts()
if fill_empty:
empty_barb = circ
else:
# If we don't want the empty one filled, we make a degenerate
# polygon that wraps back over itself
empty_barb = np.concatenate((circ, circ[::-1]))
barb_list = []
for index, angle in np.ndenumerate(angles):
# If the vector magnitude is too weak to draw anything, plot an
# empty circle instead
if empty_flag[index]:
# We can skip the transform since the circle has no preferred
# orientation
barb_list.append(empty_barb)
continue
poly_verts = [(endx, endy)]
offset = length
# Add vertices for each flag
for _ in range(nflags[index]):
# The spacing that works for the barbs is a little to much for
# the flags, but this only occurs when we have more than 1
# flag.
if offset != length:
offset += spacing / 2.
poly_verts.extend(
[[endx, endy + offset],
[endx + full_height, endy - full_width / 2 + offset],
[endx, endy - full_width + offset]])
offset -= full_width + spacing
# Add vertices for each barb. These really are lines, but works
# great adding 3 vertices that basically pull the polygon out and
# back down the line
for _ in range(nbarbs[index]):
poly_verts.extend([(endx, endy + offset),
(endx + full_height,
endy + offset + full_width / 2),
(endx, endy + offset)])
offset -= spacing
# Add the vertices for half a barb, if needed
if half_barb[index]:
# If the half barb is the first on the staff, traditionally it
# is offset from the end to make it easy to distinguish from a
# barb with a full one
if offset == length:
poly_verts.append((endx, endy + offset))
offset -= 1.5 * spacing
poly_verts.extend([(endx, endy + offset),
(endx + full_height / 2,
endy + offset + full_width / 4),
(endx, endy + offset)])
# Rotate the barb according the angle. Making the barb first and
# then rotating it made the math for drawing the barb really easy.
# Also, the transform framework makes doing the rotation simple.
poly_verts = transforms.Affine2D().rotate(-angle).transform(
poly_verts)
barb_list.append(poly_verts)
return barb_list
def _OSGB36toWGS84(self):
""" Convert between OSGB36 and WGS84. If we already have values available, we just return them.
:rtype: float, float
"""
if self.easting is None or self.northing is None:
return False
#E, N are the British national grid coordinates - eastings and northings
a, b = 6377563.396, 6356256.909 #The Airy 180 semi-major and semi-minor axes used for OSGB36 (m)
F0 = 0.9996012717 #scale factor on the central meridian
lat0 = 49 * pi / 180 #Latitude of true origin (radians)
lon0 = -2 * pi / 180 #Longtitude of true origin and central meridian (radians)
N0, E0 = -100000, 400000 #Northing & easting of true origin (m)
e2 = 1 - (b*b)/(a*a) #eccentricity squared
n = (a-b) / (a+b)
#Initialise the iterative variables
lat, M = lat0, 0
while self.northing - N0 - M >= 0.00001: #Accurate to 0.01mm
lat += (self.northing - N0 - M) / (a * F0)
M1 = (1 + n + (5./4)*n**2 + (5./4)*n**3) * (lat-lat0)
M2 = (3*n + 3*n**2 + (21./8)*n**3) * sin(lat-lat0) * cos(lat+lat0)
M3 = ((15./8)*n**2 + (15./8)*n**3) * sin(2*(lat-lat0)) * cos(2*(lat+lat0))
M4 = (35./24)*n**3 * sin(3*(lat-lat0)) * cos(3*(lat+lat0))
#meridional arc
M = b * F0 * (M1 - M2 + M3 - M4)
#transverse radius of curvature
nu = a * F0 / sqrt(1 - e2 * sin(lat) ** 2)
#meridional radius of curvature
rho = a * F0 * (1 - e2) * (1 - e2 * sin(lat) ** 2) ** (-1.5)
eta2 = nu / rho-1
secLat = 1./cos(lat)
VII = tan(lat)/(2*rho*nu)
VIII = tan(lat)/(24*rho*nu**3)*(5+3*tan(lat)**2+eta2-9*tan(lat)**2*eta2)
IX = tan(lat)/(720*rho*nu**5)*(61+90*tan(lat)**2+45*tan(lat)**4)
X = secLat/nu
XI = secLat/(6*nu**3)*(nu/rho+2*tan(lat)**2)
XII = secLat/(120*nu**5)*(5+28*tan(lat)**2+24*tan(lat)**4)
XIIA = secLat/(5040*nu**7)*(61+662*tan(lat)**2+1320*tan(lat)**4+720*tan(lat)**6)
dE = self.easting - E0
#These are on the wrong ellipsoid currently: Airy1830. (Denoted by _1)
lat_1 = lat - VII*dE**2 + VIII*dE**4 - IX*dE**6
lon_1 = lon0 + X*dE - XI*dE**3 + XII*dE**5 - XIIA*dE**7
#Want to convert to the GRS80 ellipsoid.
#First convert to cartesian from spherical polar coordinates
H = 0 #Third spherical coord.
x_1 = (nu/F0 + H)*cos(lat_1)*cos(lon_1)
y_1 = (nu/F0+ H)*cos(lat_1)*sin(lon_1)
z_1 = ((1-e2)*nu/F0 +H)*sin(lat_1)
#Perform Helmut transform (to go between Airy 1830 (_1) and GRS80 (_2))
s = -20.4894*10**-6 #The scale factor -1
tx, ty, tz = 446.448, -125.157, + 542.060 #The translations along x,y,z axes respectively
rxs,rys,rzs = 0.1502, 0.2470, 0.8421 #The rotations along x,y,z respectively, in seconds
rx, ry, rz = rxs*pi/(180*3600.), rys*pi/(180*3600.), rzs*pi/(180*3600.) #In radians
x_2 = tx + (1+s)*x_1 + (-rz)*y_1 + (ry)*z_1
y_2 = ty + (rz)*x_1 + (1+s)*y_1 + (-rx)*z_1
z_2 = tz + (-ry)*x_1 + (rx)*y_1 + (1+s)*z_1
#Back to spherical polar coordinates from cartesian
#Need some of the characteristics of the new ellipsoid
a_2, b_2 =6378137.000, 6356752.3141 #The GSR80 semi-major and semi-minor axes used for WGS84(m)
e2_2 = 1- (b_2*b_2)/(a_2*a_2) #The eccentricity of the GRS80 ellipsoid
p = sqrt(x_2**2 + y_2**2)
#Lat is obtained by an iterative proceedure:
lat = arctan2(z_2,(p*(1-e2_2))) #Initial value
latold = 2 * pi
while abs(lat - latold)>10**-16:
lat, latold = latold, lat
nu_2 = a_2/sqrt(1-e2_2*sin(latold)**2)
lat = arctan2(z_2+e2_2*nu_2*sin(latold), p)
#Lon and height are then pretty easy
lon = arctan2(y_2,x_2)
H = p/cos(lat) - nu_2
#Convert to degrees
self.lat = lat*180/pi
self.lon = lon*180/pi
return True
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 _make_barbs(self, u, v, nflags, nbarbs, half_barb, empty_flag, length,
pivot, sizes, fill_empty, flip):
'''
This function actually creates the wind barbs. *u* and *v*
are components of the vector in the *x* and *y* directions,
respectively.
*nflags*, *nbarbs*, and *half_barb*, empty_flag* are,
*respectively, the number of flags, number of barbs, flag for
*half a barb, and flag for empty barb, ostensibly obtained
*from :meth:`_find_tails`.
*length* is the length of the barb staff in points.
*pivot* specifies the point on the barb around which the
entire barb should be rotated. Right now, valid options are
'head' and 'middle'.
*sizes* is a dictionary of coefficients specifying the ratio
of a given feature to the length of the barb. These features
include:
- *spacing*: space between features (flags, full/half
barbs)
- *height*: distance from shaft of top of a flag or full
barb
- *width* - width of a flag, twice the width of a full barb
- *emptybarb* - radius of the circle used for low
magnitudes
*fill_empty* specifies whether the circle representing an
empty barb should be filled or not (this changes the drawing
of the polygon).
*flip* is a flag indicating whether the features should be flipped to
the other side of the barb (useful for winds in the southern
hemisphere.
This function returns list of arrays of vertices, defining a polygon
for each of the wind barbs. These polygons have been rotated to
properly align with the vector direction.
'''
#These control the spacing and size of barb elements relative to the
#length of the shaft
spacing = length * sizes.get('spacing', 0.125)
full_height = length * sizes.get('height', 0.4)
full_width = length * sizes.get('width', 0.25)
empty_rad = length * sizes.get('emptybarb', 0.15)
#Controls y point where to pivot the barb.
pivot_points = dict(tip=0.0, middle=-length / 2.)
#Check for flip
if flip:
full_height = -full_height
endx = 0.0
endy = pivot_points[pivot.lower()]
# Get the appropriate angle for the vector components. The offset is
# due to the way the barb is initially drawn, going down the y-axis.
# This makes sense in a meteorological mode of thinking since there 0
# degrees corresponds to north (the y-axis traditionally)
angles = -(ma.arctan2(v, u) + np.pi / 2)
# Used for low magnitude. We just get the vertices, so if we make it
# out here, it can be reused. The center set here should put the
# center of the circle at the location(offset), rather than at the
# same point as the barb pivot; this seems more sensible.
circ = CirclePolygon((0, 0), radius=empty_rad).get_verts()
if fill_empty:
empty_barb = circ
else:
# If we don't want the empty one filled, we make a degenerate
# polygon that wraps back over itself
empty_barb = np.concatenate((circ, circ[::-1]))
barb_list = []
for index, angle in np.ndenumerate(angles):
#If the vector magnitude is too weak to draw anything, plot an
#empty circle instead
if empty_flag[index]:
#We can skip the transform since the circle has no preferred
#orientation
barb_list.append(empty_barb)
continue
poly_verts = [(endx, endy)]
offset = length
# Add vertices for each flag
for i in range(nflags[index]):
# The spacing that works for the barbs is a little to much for
# the flags, but this only occurs when we have more than 1
# flag.
if offset != length:
offset += spacing / 2.
poly_verts.extend(
[[endx, endy + offset],
[endx + full_height, endy - full_width / 2 + offset],
[endx, endy - full_width + offset]])
offset -= full_width + spacing
# Add vertices for each barb. These really are lines, but works
# great adding 3 vertices that basically pull the polygon out and
# back down the line
for i in range(nbarbs[index]):
poly_verts.extend(
[(endx, endy + offset),
(endx + full_height, endy + offset + full_width / 2),
(endx, endy + offset)])
offset -= spacing
# Add the vertices for half a barb, if needed
if half_barb[index]:
# If the half barb is the first on the staff, traditionally it
# is offset from the end to make it easy to distinguish from a
# barb with a full one
if offset == length:
poly_verts.append((endx, endy + offset))
offset -= 1.5 * spacing
poly_verts.extend(
[(endx, endy + offset),
(endx + full_height / 2, endy + offset + full_width / 4),
(endx, endy + offset)])
# Rotate the barb according the angle. Making the barb first and
# then rotating it made the math for drawing the barb really easy.
# Also, the transform framework makes doing the rotation simple.
poly_verts = transforms.Affine2D().rotate(-angle).transform(
poly_verts)
barb_list.append(poly_verts)
return barb_list
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)