def Fqz_imag(z):
z_scr = select([z<z_min,z>z_max,z>=z_min] , [z_min,z_max,z])
mask = select( [z<z_min-20*(z_max-z_min), z>z_max+20*(z_max-z_min),
z<z_min, z>z_max, z>=z_min],
[np.exp(-40), np.exp(-40),
np.exp(-2*(z_min-z)/(z_max-z_min)),
np.exp(-2*(z-z_max)/(z_max-z_min)), 1])
return Fqz_imag_raw(z_scr) * mask
def RBFmorph(NCB, knownC, knownD):
# Determine displacement of Base nodes NCB by displacing nodes at coordinates
# knownC by known landmark displacement
#rbfx = Rbf(knownC[:,0],knownC[:,1],knownC[:,2],knownD[:,0],function='gaussian')
#rbfy = Rbf(knownC[:,0],knownC[:,1],knownC[:,2],knownD[:,1],function='gaussian')
#rbfz = Rbf(knownC[:,0],knownC[:,1],knownC[:,2],knownD[:,2],function='gaussian')
#DSx = rbfx(NCB[:,0],NCB[:,1],NCB[:,2])
#DSy = rbfy(NCB[:,0],NCB[:,1],NCB[:,2])
#DSz = rbfz(NCB[:,0],NCB[:,1],NCB[:,2])
#print np.c_[DSx,DSy,DSz]
#print NCB
#NCI = np.c_[DSx,DSy,DSz]+NCB
nrB = np.array([knownC.shape])[0, 0]
shapeN = np.array([NCB.shape])
nrN = shapeN[0, 0]
MATR = np.zeros((nrB, nrB))
knownD = np.r_[knownD, np.zeros((4, 3))]
Pb = np.c_[np.ones((nrB, 1)), knownC]
for i in range(0, nrB):
TEMP = np.array([
np.sqrt(
np.sum(
np.power((np.ones((nrB, 1)) * knownC[i, :] - knownC), 2),
1))
])
##### Thin plate spline:
TEMP = TEMP * TEMP * np.log10(TEMP)
##### Gauss weight:
#TEMP = np.exp(-TEMP*TEMP)
##### CPC2
#TEMP = np.power((1-TEMP),4)*(4*TEMP+1)
MATR[i, :] = TEMP.reshape((1, nrB))
MATR[i, i] = 0
MATR = np.c_[np.r_[MATR, Pb.T], np.r_[Pb, np.zeros((4, 4))]]
#MATR = np.matrix(MATR)
#MATR = np.linalg.pinv(MATR)
#knownD = np.matrix(knownD)
Coeff = np.array(np.linalg.solve(MATR, knownD))
ResDisp = np.zeros((nrN, 3))
for i in range(0, nrN):
TEMP = np.sqrt(
np.sum(np.power((np.ones((nrB, 1)) * NCB[i, :] - knownC), 2), 1))
##### Thin Plate Spline:
TEMPlog10 = np.log10(TEMP)
TEMPlog10 = sp.select([TEMPlog10 < -1000, TEMPlog10 >= 0],
[-1000, TEMPlog10])
TEMP = TEMP * TEMP * TEMPlog10
##### Gauss weight:
#TEMP = np.exp(-TEMP*TEMP)
##### CPC2
#TEMP = np.power((1-TEMP),4)*(4*TEMP+1)
ResDisp[i, :] = np.sum(
Coeff * np.r_[TEMP.reshape((nrB, 1)) * np.ones((1, 3)),
np.array([[1, 1, 1]]),
np.transpose(np.ones((3, 1)) * NCB[i, :])], 0)
NCI = NCB + ResDisp
return NCI
def truean(JD, P, T0=0, Ecc=0):
"""Calculate true anomaly for array of dates."""
Phase = phase(JD, P, T0) # phases
M = 2 * scipy.pi * Phase # mean anomaly
if Ecc <= machep:
return M
eccanV = scipy.vectorize(eccan)
E = eccanV(Ecc, M) % (2 * scipy.pi) # eccentric anomaly
cosE = scipy.cos(E)
cosNu = (cosE - Ecc) / (1 - Ecc * cosE)
Nu = scipy.arccos(cosNu) # true anomaly
Nu = scipy.select([E <= scipy.pi, scipy.ones(len(Nu))], \
[Nu, 2 * scipy.pi - Nu]) # E>pi cases
return Nu
def RBFmorph(NCB, knownC, knownD):
# Determine displacement of Base nodes NCB by displacing nodes at coordinates
# knownC by known landmark displacement
####rbfx = Rbf(knownC[:,0],knownC[:,1],knownC[:,2],knownD[:,0])
####rbfy = Rbf(knownC[:,0],knownC[:,1],knownC[:,2],knownD[:,1])
####rbfz = Rbf(knownC[:,0],knownC[:,1],knownC[:,2],knownD[:,2])
####DSx = rbfx(NCB[:,0],NCB[:,1],NCB[:,2])
####DSy = rbfy(NCB[:,0],NCB[:,1],NCB[:,2])
####DSz = rbfz(NCB[:,0],NCB[:,1],NCB[:,2])
####NCI = NCB + np.c_[DSx,DSy,DSz]
nrB = np.array([knownC.shape])[0, 0]
shapeN = np.array([NCB.shape])
nrN = shapeN[0, 0]
MATR = np.zeros((nrB, nrB))
knownD = np.r_[knownD, np.zeros((4, 3))]
Pb = np.c_[np.ones((nrB, 1)), knownC]
for i in range(0, nrB):
# Thin plate spline:
TEMP = np.array([
np.sqrt(
np.sum(
np.power((np.ones((nrB, 1)) * knownC[i, :] - knownC), 2),
1))
])
TEMP = TEMP * TEMP * np.log10(TEMP)
MATR[i, :] = TEMP.reshape((1, nrB))
MATR[i, i] = 0
MATR = np.c_[np.r_[MATR, Pb.T], np.r_[Pb, np.zeros((4, 4))]]
Coeff = np.array(np.linalg.solve(MATR, knownD))
ResDisp = np.zeros((nrN, 3))
for i in range(0, nrN):
TEMP = np.sqrt(
np.sum(np.power((np.ones((nrB, 1)) * NCB[i, :] - knownC), 2), 1))
TEMPlog10 = np.log10(TEMP)
TEMPlog10 = sp.select([TEMPlog10 < -1000, TEMPlog10 >= 0],
[-1000, TEMPlog10])
TEMP = TEMP * TEMP * TEMPlog10
ResDisp[i, :] = np.sum(
Coeff * np.r_[TEMP.reshape((nrB, 1)) * np.ones((1, 3)),
np.array([[1, 1, 1]]),
np.transpose(np.ones((3, 1)) * NCB[i, :])], 0)
NCI = NCB + ResDisp
return NCI
