def calculateBasisOffset(self,x1,x2,basis):
dx = [(x2[j] - x1[j]) for j in range(len(x1))] # Calculate the difference between the master and slave position vectors
z_offset = MM.dotProduct(dx,basis.getVelocityVector()) # Calculate the length of the projection of the difference in position and the "velocity" component
v_offset = MM.dotProduct(dx,basis.getPositionVector())
c_offset = MM.dotProduct(dx,basis.getCrossTrackVector())
return z_offset,v_offset,c_offset
def fitDoppler(self):
"""Read in a Doppler file, remove outliers and then perform a quadratic fit"""
self._wrap()
unw = self._unwrap()
self.pixelIndex = range(len(self.fractionalDoppler))
(self.linear['a'], self.linear['b'], self.linear['stdDev']) = MathModule.linearFit(self.pixelIndex, unw)
(pixels, unw) = self._cullPoints(self.pixelIndex,unw)
(self.linear['a'], self.linear['b'], self.linear['stdDev']) = MathModule.linearFit(pixels, unw)
(pixels, unw) = self._cullPoints(pixels,unw)
(a,b,c) = MathModule.quadraticFit(pixels,unw)
self.quadratic['a'] = a
self.quadratic['b'] = b
self.quadratic['c'] = c
def parameterize(self):
"""
Read in Doppler estimates, remove outliers and then perform a quadratic fit
"""
self.pixelIndex = range(len(self.fractionalDoppler))
(self.linear['a'], self.linear['b'],
self.linear['stdDev']) = MathModule.linearFit(self.pixelIndex,
self.unw)
(pixels, self.unw) = self._cullPoints(self.pixelIndex, self.unw)
(self.linear['a'], self.linear['b'],
self.linear['stdDev']) = MathModule.linearFit(pixels, self.unw)
(pixels, self.unw) = self._cullPoints(pixels, self.unw)
(a, b, c) = MathModule.quadraticFit(pixels, self.unw)
self.quadratic['a'] = a
self.quadratic['b'] = b
self.quadratic['c'] = c
def __initialize(self):
s = self.sch[0] / self.peg.getRadiusOfCurvature()
c = self.sch[1] / self.peg.getRadiusOfCurvature()
schxyzp = [[0 for i in range(3)] for j in range(3)]
schxyzp[0][0] = -math.sin(s)
schxyzp[0][1] = -math.sin(c) * math.cos(s)
schxyzp[0][1] = math.cos(s) * math.cos(c)
schxyzp[1][0] = math.cos(s)
schxyzp[1][1] = -math.sin(c) * math.sin(s)
schxyzp[1][2] = math.sin(s) * math.cos(c)
schxyzp[2][0] = 0.0
schxyzp[2][1] = math.cos(c)
schxyzp[2][2] = math.sin(c)
self.sch2xyz = MM.multiplyMatrices(self.M, schxyzp)
self.xyz2sch = MM.matrixTranspose(self.sch2xyz)
def calculateBasis(self,orbit,time):
sv = orbit.interpolateOrbit(time, method='hermite')
x1 = sv.getPosition()
v = sv.getVelocity()
r = MM.normalizeVector(x1) # Turn the position vector into a unit vector
v = MM.normalizeVector(v) # Turn the velocity vector into a unit vector
c = MM.crossProduct(r,v) # Calculate the vector perpendicular to the platform position and velocity, this is the c, or cross-track vector
c = MM.normalizeVector(c)
v = MM.crossProduct(c,r) # Calculate a the "velocity" component that is perpendicular to the cross-track direction and position
basis = BaselineBasis()
basis.setPositionVector(r)
basis.setVelocityVector(v)
basis.setCrossTrackVector(c)
return basis
def _integrateBVector(self, date, coordinate, k):
"""
Integrate the B-field estimates through the ionosphere at the specified date and location
@param date (\a datetime.datetime) date at which to calculate the B-field
@param coordinate (\a isceobj.Location.Coordinate) the coordinate at which to calculate the B-field.
@param k (\a list) the look vector of the radar
@return (\a float) the integrated value of the B-field at the specified date and location in gauss
"""
kdotb = []
n_altitude = int((self.top - self.bottom) / self.step) + 1
altitude = [self.bottom + i * self.step for i in range(n_altitude)]
for h in altitude:
coordinate.setHeight(h)
bvector = self._calculateBVector(date, coordinate)
kdotb.append(MM.dotProduct(k, bvector))
meankdotb = MM.mean(kdotb)
return meankdotb
def sch_to_xyz(self, sch):
radcur = self.peg.getRadiusOfCurvature(
) # Get the radius of curvature at the peg point
ellipsoid = Ellipsoid(a=radcur, e2=0.0)
xyz = [0 for i in range(3)]
llh = [0 for i in range(3)]
llh[0] = math.degrees(sch[1] / radcur)
llh[1] = math.degrees(sch[0] / radcur)
llh[2] = sch[2]
schv = ellipsoid.llh_to_xyz(llh)
schvt = MM.matrixVectorProduct(self.M, schv)
for i in range(3):
xyz[i] = schvt[i] + self.r_ov[i]
return xyz
def xyz_to_sch(self, xyz):
radcur = self.peg.getRadiusOfCurvature(
) # Get the radius of curvature at the peg point
ellipsoid = Ellipsoid(a=radcur, e2=0.0)
schvt = [0 for i in range(3)]
rschv = [0 for i in range(3)]
for i in range(3):
schvt[i] = xyz[i] - self.r_ov[i]
schv = MM.matrixVectorProduct(self.invM, schvt)
llh = ellipsoid.xyz_to_llh(schv)
rschv[0] = radcur * math.radians(llh[1])
rschv[1] = radcur * math.radians(llh[0])
rschv[2] = llh[2]
return rschv
def frToTEC(self, date, corners, lookAngle, lookDirection, fc):
"""
Given a list of geodetic coordinates, a list of lookAngles and a list of lookDirections,
calculate the average value of the B-field in the radar line-of-sight. Look angles are
calculated in degrees from the nadir and look directions are calculated in degrees from
the perpendicular to the flight direction.
@param date (\a datetime.datetime) the date on which to calculate the B-field
@param corners (\a list) a list of Location.Coordinate objects specifying the corners of the radar image
@param lookAngle (\a list) a list of the look angles (in degrees) to each corner of the radar image
@param lookDirection (\a list) a list of the look directions (in degrees) to each corner of the radar image
@param fc (\a float) the radar carrier frequency in Hz
@return (\a float) the mean value of the B-field in the look direction of the radar in gauss
"""
kdotb = []
# Calculate the integrated B vector for each of the four corners of the interferogram
# Need to get the date from any of the Frame objects associated with one of the polarities
for i, coordinate in enumerate(corners):
k = self._calculateLookVector(lookAngle[i], lookDirection[i])
kdotb.append(self._integrateBVector(date, coordinate, k))
# Use this value to convert from Faraday rotation to TEC
meankdotb = MM.mean(kdotb)
self.logger.info("Creating TEC Map")
self._scaleFRToTEC(meankdotb, fc)
# Create a resource file for the TEC output file
rsc = ResourceFile(self.tecOutput + '.rsc')
rsc.write('WIDTH', self.samples)
rsc.write('FILE_LENGTH', self.lines)
rsc.write('MEAN_K_DOT_B', meankdotb)
rsc.write('LOOK_DIRECTION', lookDirection[0])
for i in range(len(corners)):
lattag = 'LAT_CORNER_' + str((i + 1))
lontag = 'LON_CORNER_' + str((i + 1))
looktag = 'LOOK_ANGLE_' + str((i + 1))
rsc.write(lattag, corners[i].getLatitude())
rsc.write(lontag, corners[i].getLongitude())
rsc.write(looktag, lookAngle[i])
rsc.close()
return meankdotb
def initializeRotationMatrix(self):
lat = math.radians(self.peg.getLatitude())
lon = math.radians(self.peg.getLongitude())
heading = math.radians(self.peg.getHeading())
self.M[0][0] = math.cos(lat) * math.cos(lon)
self.M[0][1] = -math.sin(heading) * math.sin(lon) - math.sin(
lat) * math.cos(lon) * math.cos(heading)
self.M[0][2] = math.sin(lon) * math.cos(heading) - math.sin(
lat) * math.cos(lon) * math.sin(heading)
self.M[1][0] = math.cos(lat) * math.sin(lon)
self.M[1][1] = math.cos(lon) * math.sin(heading) - math.sin(
lat) * math.sin(lon) * math.cos(heading)
self.M[1][2] = -math.cos(lon) * math.cos(heading) - math.sin(
lat) * math.sin(lon) * math.sin(heading)
self.M[2][0] = math.sin(lat)
self.M[2][1] = math.cos(lat) * math.cos(heading)
self.M[2][2] = math.cos(lat) * math.sin(heading)
self.invM = MM.matrixTranspose(self.M)
def polynomialFit(self, xRef, yRef):
size = len(xRef)
if not (len(xRef) == len(yRef)):
print("Error. Expecting input vectors of same length.")
raise Exception
if not (size == 3):
print("Error. Expecting input vectors of length 3.")
raise Exception
Y = [0] * size
A = [0] * size
M = [[0 for i in range(size)] for j in range(size)]
for j in range(size):
for i in range(size):
M[j][i] = math.pow(xRef[j], i)
Y[j] = yRef[j]
MInv = MM.invertMatrix(M)
for i in range(size):
for j in range(size):
A[i] += MInv[i][j] * Y[j]
return A
def testMean(self):
ans = 2
mean = MM.mean(self.V)
self.assertAlmostEquals(mean, ans)
def testMatrixVectorProduct(self):
ans = [14, 32, 50]
mV = MM.matrixVectorProduct(self.M, self.V)
for i in range(3):
self.assertAlmostEquals(mV[i], ans[i], 5)
def testMatrixTranspose(self):
ans = [[1, 4, 7], [2, 5, 8], [3, 6, 9]]
mT = MM.matrixTranspose(self.M)
for i in range(3):
for j in range(3):
self.assertAlmostEquals(mT[i][j], ans[i][j], 5)
def testMultiplyMatrices(self):
ans = [[6, 12, 18], [15, 30, 45], [24, 48, 72]]
mM = MM.multiplyMatrices(self.M, self.N)
for i in range(3):
for j in range(3):
self.assertAlmostEquals(mM[i][j], ans[i][j], 5)
def xyz_to_localsch(self, xyz):
sch = MM.matrixVectorProduct(self.xyz2sch, xyz)
return sch
def calculateScalarVelocity(self, orbit, time):
sv = orbit.interpolateOrbit(time)
v = sv.getVelocity()
normV = MM.norm(v)
return normV
def localsch_to_xyz(self, sch):
xyz = MM.matrixVectorProduct(self.sch2xyz, sch)
return xyz