# Geodesic Regression on Sphere Manifold # Manifolds import manifolds import numpy as np import StatsModel as sm import matplotlib.pyplot as plt # Visualization import vtk # Parameters nDimManifold = 3 # Ground Truth p_interp = manifolds.sphere(nDimManifold) v_slope = manifolds.sphere_tVec(nDimManifold) p_interp.SetPoint([0.0, 0.0, 1.0]) v_slope.SetTangentVector([0, np.pi * 0.25, 0]) # Generating sphere manifolds. distributed over time perturbed by Gaussian random # Time t0 = 0 t1 = 2.0 # Generate a random point on the manifold nData = 500 dim = nDimManifold sigma = 0.1 pt_list = []
# Generating sphere manifolds. distributed over time perturbed by Gaussian random # Time t0 = 0 t1 = 2 # Generate a random point on the manifold # Parameters nDimManifold = 3 nData = 200 dim = nDimManifold sigma = 0.15 # Ground Truth p_interp = manifolds.sphere(nDimManifold) v_slope = manifolds.sphere_tVec(nDimManifold) p_interp.SetPoint([0.0, 0.0, 1.0]) v_slope.SetTangentVector([0, np.pi * 0.25, 0]) # Point List # Base Function ( Geodesic ) pt_list = [] # Projected sin on the base point function at time t pt_list_proj_sin = [] # Time List t_list = [] # Points Generation over a sin function
nDimManifold = 3 nData_1 = 300 nData_2 = 300 nData = nData_1 + nData_2 # Data Noise Parameter pt_sigma = 0.05 ## Time t0 = 0.0 t1 = 1.0 # Ground Truth beta0 = manifolds.sphere(nDimManifold) beta1 = manifolds.sphere_tVec(nDimManifold) beta2 = manifolds.sphere_tVec(nDimManifold) # Intercept Point # beta0.SetPoint( [ 0.94644084, 0.00146423, -0.32287396 ] ) # beta0.SetPoint( [ np.sqrt( 0.28 ), 0.6, 0.6 ] ) beta0.SetPoint([1.0, 0.0, 0.0]) # A tangent vector for different sex beta1.SetTangentVector([0.0, 0.5, 0.0]) # A slope tangent vector for age beta2.SetTangentVector([0.0, 0.0, 0.5]) # # Visualize group level grount truth # Curve Visualization Parameter
arrow_transform.Scale(length, length, length)
arrow_transform.Update()
transformPD = vtk.vtkTransformPolyDataFilter()
transformPD.SetInputData(arrowBase.GetOutput())
transformPD.SetTransform(arrow_transform)
transformPD.Update()
return transformPD.GetOutput()
# Base Intercept Point
beta0 = manifolds.sphere(nDimManifold)
beta0.SetPoint([1, 0, 0])
gamma1 = manifolds.sphere_tVec(nDimManifold)
gamma1.SetTangentVector([0.0, -0.3, 0.0])
tVec_to_f_i = manifolds.sphere_tVec(nDimManifold)
tVec_to_f_i.SetTangentVector([0.0, -1.0, 0.0])
f_i = beta0.ExponentialMap(tVec_to_f_i)
# f_i.SetPoint( [ 0, 1, 0 ] )
gamma1_f_i = beta0.ParallelTranslateAtoB(beta0, f_i, gamma1)
pt_sigma = 0.15
# Draw beta0 to f_i - Main Geodesic
nLineTimePt = 100
t1 = 1.0
# Parameters nDimManifold = 3 nData_1 = 500 nData_2 = 500 nData_g = 100 nData = nData_1 + nData_2 # Data Noise Parameter pt_sigma = 0.05 # Ground Truth beta0 = manifolds.sphere(nDimManifold) beta1 = manifolds.sphere_tVec(nDimManifold) beta2 = manifolds.sphere_tVec(nDimManifold) beta3 = manifolds.sphere_tVec(nDimManifold) beta4 = manifolds.sphere_tVec(nDimManifold) # Intercept Point # beta0.SetPoint( [ 0.94644084, 0.00146423, -0.32287396 ] ) beta0.SetPoint([1.0, 0.0, 0.0]) ## Time t0 = 0.0 t1 = 60.0 ## CAG Repeath Length c0 = 0.0 c1 = 20.0
import manifolds import numpy as np import StatsModel as sm # Visualization import vtk # Time import time # Parameters nDimManifold = 3 # Ground Truth p_interp = manifolds.sphere(nDimManifold) v_slope = manifolds.sphere_tVec(nDimManifold) p_interp.SetPoint([0.0, 0.0, 1.0]) v_slope.SetTangentVector([0, np.pi * 0.25, 0]) # Generating sphere manifolds. distributed over time perturbed by Gaussian random # Time t0 = 0 t1 = 2 # Generate a random point on the manifold nData = 15 dim = nDimManifold sigma = 0.15 pt_list = []
import manifolds
import numpy as np
import StatsModel as sm
# Visualization
import vtk
# Parameters
nDimManifold = 3
# Mean Interpolation Point
p_interp = manifolds.sphere(nDimManifold)
p_interp.SetPoint([0.0, 0.0, 1.0])
# Mean Slope Tangent Vector
v_slope = manifolds.sphere_tVec(nDimManifold)
v_slope.SetTangentVector([0, np.pi * 0.25, 0])
# Mean Interpolation Point / Mean Slope Tangent Vector - VTK PolyData Line
nTimePt = 100
t1 = 1.0
t0 = 0
meanLinePointsArr = []
for n in range(nTimePt):
time_pt = (t1 - t0) * n / (nTimePt - 1) + t0
# Generate a random Gaussians with polar Box-Muller Method
v_t = manifolds.sphere_tVec(nDimManifold)
v_t.SetTangentVector([
##################################################### # Generating sphere manifolds. distributed over time perturbed by Gaussian random # Time t0 = 0 t1 = 2 # Generate a random point on the manifold # Parameters nDimManifold = 3 nData = 200 dim = nDimManifold sigma = 0.15 # Population Bias p_bias = manifolds.sphere(nDimManifold) v_bias = manifolds.sphere_tVec(nDimManifold) p_bias.SetPoint([0.0, 0.0, 1.0]) v_bias.SetTangentVector([0, np.pi * 0.1, 0]) bias_param_t0 = 0.0 bias_param_t1 = 3.0 nSubj = 10 bias_step = (bias_param_t1 - bias_param_t0) / float(nSubj - 1) # Subject-wise Ground Truth subj_t0 = -0.5 subj_t1 = 0.5 v_subj_slope_base = manifolds.sphere_tVec(nDimManifold)
import manifolds import numpy as np import StatsModel as sm import matplotlib.pyplot as plt # Visualization import vtk # Parameters nDimManifold = 3 # Group Level Parameters ## Ground Truth p0 = manifolds.sphere( nDimManifold ) v0 = manifolds.sphere_tVec( nDimManifold ) ## Random interpolation - mean # p0.SetPoint( [ -1.0, 0.0, 0.0 ] ) # p0 = sm.GaussianNoisePerturbation( p0, 2.0 ) # Mean Interpolation Point - Fixed for Experiment p0.SetPoint( [ 0.94644084, 0.00146423, -0.32287396 ] ) print( p0.pt ) ## Time t0 = 0.0 t1 = 60.0
print( eucl_tVec_r.nDim ) print( eucl_tVec_r.Type ) eucl_pt = manifolds.euclidean( 3 ) eucl_pt.SetPoint( [ 3, 1, 5 ] ) eucl_pt.Write( "eucl.rpt" ) eucl_pt_r = manifolds.euclidean( 3 ) eucl_pt_r.Read( "eucl.rpt" ) print( eucl_pt_r.pt ) print( eucl_pt_r.nDim ) print( eucl_pt_r.Type ) # Sphere sphere_tVec = manifolds.sphere_tVec( 3 ) sphere_tVec.SetTangentVector( [ 0, 0.8192, 0 ] ) sphere_tVec.Write( "sphere_tVec.tvec" ) sphere_tVec_r = manifolds.sphere_tVec( 3 ) sphere_tVec_r.Read( "sphere_tVec.tvec" ) print( sphere_tVec_r.tVector ) 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" )
# Generating sphere manifolds. distributed over time perturbed by Gaussian random # Time t0 = 0 t1 = 2 # Generate a random point on the manifold # Parameters nDimManifold = 3 nData = 500 dim = nDimManifold sigma = 0.15 # Ground Truth p_interp = manifolds.sphere( nDimManifold ) v_slope = manifolds.sphere_tVec( nDimManifold ) p_interp.SetPoint( [ 0.0, 0.0, 1.0 ] ) v_slope.SetTangentVector( [ 0, np.pi * 0.25, 0 ] ) # Point List # Base Function ( Geodesic ) pt_list = [] # Added sin on the first axis pt_list_add_sin = [] # Projected sin on the base point function at time t pt_list_proj_sin = [] ## Point List - Sin Function: Parallel Transported
# Time Interval t_int0 = 0.5 t_int1 = 2 # Number of Observations nObs0 = 2 nObs1 = 5 # # Visualize group level grount truth # Curve Visualization Parameter nLineTimePt = 100 # Ground Truth # Intercept Coefficeints beta0 = manifolds.sphere(nDimManifold) beta1 = manifolds.sphere_tVec(nDimManifold) beta2 = manifolds.sphere_tVec(nDimManifold) # Intercept Point beta0.SetPoint([1.0, 0.0, 0.0]) # A tangent vector for different sex beta1.SetTangentVector([0.0, 0.2, 0.0]) # A tangent vector for CAG repeat length # beta2.SetTangentVector( [ 0.0, 0.05, 0.0 ] ) beta2.SetTangentVector([0.0, 0.0, 0.15]) # beta2.SetTangentVector( [ 0.0, 0.0, -0.2 ] ) # Slope Coefficients
import numpy as np import StatsModel as sm import matplotlib.pyplot as plt # Visualization import vtk # Parameters nDimManifold = 3 # Group Level Parameters ## Ground Truth p0 = manifolds.sphere( nDimManifold ) v0 = manifolds.sphere_tVec( nDimManifold ) v1 = manifolds.sphere_tVec( nDimManifold ) ## Random interpolation - mean # p0.SetPoint( [ -1.0, 0.0, 0.0 ] ) # p0 = sm.GaussianNoisePerturbation( p0, 2.0 ) # Mean Interpolation Point - Fixed for Experiment p0.SetPoint( [ np.sqrt( 0.28 ), 0.6, 0.6 ] ) print( p0.pt ) ## Time t0 = 0.0 t1 = 60.0
