# Geodesic Regression on Sphere Manifold # Manifolds import manifolds import numpy as np import StatsModel as sm # Visualization import matplotlib.pyplot as plt # Ground Truth nManifoldDim = 1 p_interp = manifolds.pos_real(nManifoldDim) v_slope = manifolds.pos_real_tVec(nManifoldDim) p_interp_vec = 2.0 p_interp.SetPoint(p_interp_vec) v_slope.SetTangentVector(2.0) ## Random Ground Truth Generation # random_interp = np.random.rand(3) # random_interp_n = np.divide( random_interp, np.linalg.norm( random_interp ) ) # random_tangent_vector = np.random.rand(3) # random_scale = np.random.rand(1) * 2 # random_tangent_vector = np.multiply( random_tangent_vector, random_scale ) # p_interp.SetSpherePt( random_interp_n ) # v_slope.SetTangentVector( random_tangent_vector )
est_pt_list = []
est_t_list = []
base_rad_pt_list = []
tangent_rad_tVec_list = []
for p_i in range(len(point_idx_list)):
pt_idx = point_idx_list[p_i]
k_cmrep = nDimStartlist[a] + pt_idx
base_rad_pt_list.append(base.pt[k_cmrep][1])
tangent_rad_tVec_list.append(tangent.tVector[k_cmrep][1].tVector[0])
base_rad_pt = rsm.FrechetMean(base_rad_pt_list)
tangent_pt = np.average(tangent_rad_tVec_list)
tangent_rad_pt = manifolds.pos_real_tVec(1)
tangent_rad_pt.tVector[0] = tangent_pt
for t in range(nTimePt):
time_pt = (tN - t0) * t / (nTimePt - 1) + t0
v_t = manifolds.pos_real_tVec(1)
v_t.SetTangentVector(np.multiply(tangent_rad_pt.tVector, time_pt).tolist())
mean = base_rad_pt.ExponentialMap(v_t)
est_pt_list.append(mean.pt)
est_t_list.append(time_pt)
########################################
##### Visualization ######
########################################
print( sphere_tVec_r.nDim ) print( sphere_tVec_r.Type ) sphere_pt = manifolds.sphere( 3 ) sphere_pt.SetPoint( [ 0.0, 1.0, 0.0 ] ) sphere_pt.Write( "sphere.rpt" ) sphere_pt_r = manifolds.sphere( 3 ) sphere_pt_r.Read( "sphere.rpt" ) print( sphere_pt_r.pt ) print( sphere_pt_r.nDim ) print( sphere_pt_r.Type ) # Pos Real pos_real_tVec = manifolds.pos_real_tVec( 1 ) pos_real_tVec.SetTangentVector( 2 ) pos_real_tVec.Write( "pos_real_tVec.tvec" ) pos_real_tVec_r = manifolds.pos_real_tVec( 1 ) pos_real_tVec_r.Read( "pos_real_tVec.tvec" ) print( pos_real_tVec_r.tVector ) print( pos_real_tVec_r.nDim ) print( pos_real_tVec_r.Type ) pos_real_pt = manifolds.pos_real( 1 ) pos_real_pt.SetPoint( 4.0 ) pos_real_pt.Write( "pos_real.rpt" )
for n in range( nData ):
pt_list_a.append( CMRepDataList[ n ].pt[ k_cmrep ][ 1 ].pt )
t_list_a.append( ageList[ n ] )
est_pt_list = []
est_t_list = []
for t in range( nTimePt ):
time_pt = ( tN - t0 ) * t / ( nTimePt - 1 ) + t0
base_rad_pt = base.pt[ k_cmrep ][ 1 ]
tangent_rad_pt = tangent.tVector[ k_cmrep ][ 1 ]
v_t = manifolds.pos_real_tVec( 1 )
v_t.SetTangentVector( np.multiply( tangent_rad_pt.tVector, time_pt ).tolist() )
mean = base_rad_pt.ExponentialMap( v_t )
est_pt_list.append( mean.pt )
est_t_list.append( time_pt )
########################################
##### Visualization ######
########################################
font = {'family' : 'normal',
'weight' : 'bold',
'size' : 12}
plt.rc('font', **font)
# Visualization import vtk # Stats Model import statsmodels.api as sm # Pandas import pandas as pd import matplotlib.pyplot as plt # Ground Truth nManifoldDim = 1 p_interp = manifolds.pos_real(nManifoldDim) v_slope = manifolds.pos_real_tVec(nManifoldDim) p_interp_vec = 2.0 p_interp.SetPoint(p_interp_vec) v_slope.SetTangentVector(2.0) ## Random Ground Truth Generation # random_interp = np.random.rand(3) # random_interp_n = np.divide( random_interp, np.linalg.norm( random_interp ) ) # random_tangent_vector = np.random.rand(3) # random_scale = np.random.rand(1) * 2 # random_tangent_vector = np.multiply( random_tangent_vector, random_scale ) # p_interp.SetSpherePt( random_interp_n )