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Comparison between EM and gradient ascent for tracking a foraging mouse
The code below compares the expectation maximization (EM) and gradient ascent algorithm for tracking a foraging mouse.
import sys
import os.path
import argparse
import configparser
import math
import random
import pickle
import numpy as np
import pandas as pd
import torch
import scipy
import plotly.graph_objects as go
import ssm.learning
Define parameters for estimation
skip_estimation_sigma_a = False
skip_estimation_R = False
skip_estimation_m0 = False
skip_estimation_V0 = False
start_position = 0
# number_positions = 10000
# number_positions = 7500
number_positions = 50
lbfgs_max_iter = 2
lbfgs_tolerance_grad = -1
lbfgs_tolerance_change = 1e-3
lbfgs_lr = 1.0
lbfgs_n_epochs = 100
lbfgs_tol = 1e-3
em_max_iter = 200
Qe_reg_param_ga = None
Qe_reg_param_em = 1e-5
Provide initial conditions
pos_x0 = 0.0
pos_y0 = 0.0
vel_x0 = 0.0
vel_y0 = 0.0
ace_x0 = 0.0
ace_y0 = 0.0
sigma_a0 = 1.0
sigma_x0 = 1.0
sigma_y0 = 1.0
sqrt_diag_V0_value = 0.1
if math.isnan(pos_x0):
pos_x0 = y[0, 0]
if math.isnan(pos_y0):
pos_y0 = y[1, 0]
Get mouse positions
data_filename = "http://www.gatsby.ucl.ac.uk/~rapela/svGPFA/data/positions_session003_start0.00_end15548.27.csv"
data = pd.read_csv(data_filename)
data = data.iloc[start_position:start_position+number_positions,:]
y = np.transpose(data[["x", "y"]].to_numpy())
date_times = pd.to_datetime(data["time"])
dt = (date_times.iloc[1]-date_times.iloc[0]).total_seconds()
Build the matrices of the CWPA model
B, _, Qe, Z, _ = ssm.tracking.utils.getLDSmatricesForKinematics_np(
dt=dt, sigma_a=np.nan, pos_x_R_std=np.nan, pos_y_R_std=np.nan)
m0 = np.array([pos_x0, vel_x0, ace_x0, pos_y0, vel_y0, ace_y0],
dtype=np.double)
vars_to_estimate = {}
if skip_estimation_sigma_a:
vars_to_estimate["sigma_a"] = False
else:
vars_to_estimate["sigma_a"] = True
if skip_estimation_R:
vars_to_estimate["pos_x_R_std"] = False
vars_to_estimate["pos_y_R_std"] = False
vars_to_estimate["R"] = False
else:
vars_to_estimate["pos_x_R_std"] = True
vars_to_estimate["pos_y_R_std"] = True
vars_to_estimate["R"] = True
if skip_estimation_m0:
vars_to_estimate["m0"] = False
else:
vars_to_estimate["m0"] = True
if skip_estimation_V0:
vars_to_estimate["sqrt_diag_V0"] = False
vars_to_estimate["V0"] = False
else:
vars_to_estimate["sqrt_diag_V0"] = True
vars_to_estimate["V0"] = True
Perform gradient ascent optimization
sqrt_diag_R_torch = torch.DoubleTensor([sigma_x0, sigma_y0])
m0_torch = torch.from_numpy(m0.copy())
sqrt_diag_V0_torch = torch.DoubleTensor([sqrt_diag_V0_value
for i in range(len(m0))])
if Qe_reg_param_ga is not None:
Qe_regularized_ga = Qe + Qe_reg_param_ga * np.eye(Qe.shape[0])
else:
Qe_regularized_ga = Qe
y_torch = torch.from_numpy(y.astype(np.double))
B_torch = torch.from_numpy(B.astype(np.double))
Qe_regularized_ga_torch = torch.from_numpy(Qe_regularized_ga.astype(np.double))
Z_torch = torch.from_numpy(Z.astype(np.double))
optim_res_ga = ssm.learning.torch_lbfgs_optimize_SS_tracking_diagV0(
y=y_torch, B=B_torch, Qe=Qe_regularized_ga_torch, Z=Z_torch,
sigma_a0=sigma_a0, pos_x_R_std0=sigma_x0, pos_y_R_std0=sigma_y0, m0_0=m0_torch,
sqrt_diag_V0_0=sqrt_diag_V0_torch, max_iter=lbfgs_max_iter, lr=lbfgs_lr,
vars_to_estimate=vars_to_estimate, tolerance_grad=lbfgs_tolerance_grad,
tolerance_change=lbfgs_tolerance_change, n_epochs=lbfgs_n_epochs,
tol=lbfgs_tol)
print("gradient ascent: " + optim_res_ga["termination_info"])
--------------------------------------------------------------------------------
startup
likelihood: -3948969.481708237
ll=-3948969.481708237, sigma_a=1.0, pos_x_R_std=1.0, pos_y_R_std=1.0, m0=tensor([0., 0., 0., 0., 0., 0.], dtype=torch.float64, requires_grad=True), sqrt_diag_V0=tensor([0.1000, 0.1000, 0.1000, 0.1000, 0.1000, 0.1000], dtype=torch.float64,
requires_grad=True)
ll=-737534.2923452, sigma_a=1.0313226103069837, pos_x_R_std=1.0455456579842255, pos_y_R_std=1.2001321980975206, m0=tensor([2.3505e-04, 5.9404e-05, 8.0036e-06, 4.9398e-04, 1.2692e-04, 1.7218e-05],
dtype=torch.float64, requires_grad=True), sqrt_diag_V0=tensor([0.2250, 0.1080, 0.1001, 0.6519, 0.1364, 0.1007], dtype=torch.float64,
requires_grad=True)
--------------------------------------------------------------------------------
epoch: 0
likelihood: -737534.2923452
sigma_a:
tensor([1.0313], dtype=torch.float64, requires_grad=True)
pos_x_R_std:
tensor([1.0455], dtype=torch.float64, requires_grad=True)
pos_y_R_std:
tensor([1.2001], dtype=torch.float64, requires_grad=True)
m0:
tensor([2.3505e-04, 5.9404e-05, 8.0036e-06, 4.9398e-04, 1.2692e-04, 1.7218e-05],
dtype=torch.float64, requires_grad=True)
sqrt_diag_V0:
tensor([0.2250, 0.1080, 0.1001, 0.6519, 0.1364, 0.1007], dtype=torch.float64,
requires_grad=True)
ll=-737534.2923452, sigma_a=1.0313226103069837, pos_x_R_std=1.0455456579842255, pos_y_R_std=1.2001321980975206, m0=tensor([2.3505e-04, 5.9404e-05, 8.0036e-06, 4.9398e-04, 1.2692e-04, 1.7218e-05],
dtype=torch.float64, requires_grad=True), sqrt_diag_V0=tensor([0.2250, 0.1080, 0.1001, 0.6519, 0.1364, 0.1007], dtype=torch.float64,
requires_grad=True)
ll=-548307.3861159257, sigma_a=1.0342589150317776, pos_x_R_std=1.0624168702824324, pos_y_R_std=1.2054903396696848, m0=tensor([3.8851e-04, 9.8342e-05, 1.3279e-05, 5.6221e-04, 1.4673e-04, 2.0178e-05],
dtype=torch.float64, requires_grad=True), sqrt_diag_V0=tensor([0.3233, 0.1111, 0.1002, 0.7067, 0.1377, 0.1007], dtype=torch.float64,
requires_grad=True)
--------------------------------------------------------------------------------
epoch: 1
likelihood: -548307.3861159257
sigma_a:
tensor([1.0343], dtype=torch.float64, requires_grad=True)
pos_x_R_std:
tensor([1.0624], dtype=torch.float64, requires_grad=True)
pos_y_R_std:
tensor([1.2055], dtype=torch.float64, requires_grad=True)
m0:
tensor([3.8851e-04, 9.8342e-05, 1.3279e-05, 5.6221e-04, 1.4673e-04, 2.0178e-05],
dtype=torch.float64, requires_grad=True)
sqrt_diag_V0:
tensor([0.3233, 0.1111, 0.1002, 0.7067, 0.1377, 0.1007], dtype=torch.float64,
requires_grad=True)
ll=-548307.3861159257, sigma_a=1.0342589150317776, pos_x_R_std=1.0624168702824324, pos_y_R_std=1.2054903396696848, m0=tensor([3.8851e-04, 9.8342e-05, 1.3279e-05, 5.6221e-04, 1.4673e-04, 2.0178e-05],
dtype=torch.float64, requires_grad=True), sqrt_diag_V0=tensor([0.3233, 0.1111, 0.1002, 0.7067, 0.1377, 0.1007], dtype=torch.float64,
requires_grad=True)
ll=-352989.1772245695, sigma_a=1.035773016132182, pos_x_R_std=1.0693196267332854, pos_y_R_std=1.2054940650509616, m0=tensor([6.9201e-04, 1.7613e-04, 2.3952e-05, 7.6842e-04, 2.0977e-04, 2.9846e-05],
dtype=torch.float64, requires_grad=True), sqrt_diag_V0=tensor([0.4829, 0.1125, 0.1002, 0.8413, 0.1387, 0.1007], dtype=torch.float64,
requires_grad=True)
--------------------------------------------------------------------------------
epoch: 2
likelihood: -352989.1772245695
sigma_a:
tensor([1.0358], dtype=torch.float64, requires_grad=True)
pos_x_R_std:
tensor([1.0693], dtype=torch.float64, requires_grad=True)
pos_y_R_std:
tensor([1.2055], dtype=torch.float64, requires_grad=True)
m0:
tensor([6.9201e-04, 1.7613e-04, 2.3952e-05, 7.6842e-04, 2.0977e-04, 2.9846e-05],
dtype=torch.float64, requires_grad=True)
sqrt_diag_V0:
tensor([0.4829, 0.1125, 0.1002, 0.8413, 0.1387, 0.1007], dtype=torch.float64,
requires_grad=True)
ll=-352989.1772245695, sigma_a=1.035773016132182, pos_x_R_std=1.0693196267332854, pos_y_R_std=1.2054940650509616, m0=tensor([6.9201e-04, 1.7613e-04, 2.3952e-05, 7.6842e-04, 2.0977e-04, 2.9846e-05],
dtype=torch.float64, requires_grad=True), sqrt_diag_V0=tensor([0.4829, 0.1125, 0.1002, 0.8413, 0.1387, 0.1007], dtype=torch.float64,
requires_grad=True)
ll=-239770.89278952047, sigma_a=1.0345912248607383, pos_x_R_std=1.0649549949989956, pos_y_R_std=1.192186139945691, m0=tensor([1.0877e-03, 2.7817e-04, 3.7957e-05, 1.1019e-03, 3.1841e-04, 4.6838e-05],
dtype=torch.float64, requires_grad=True), sqrt_diag_V0=tensor([0.6352, 0.1120, 0.1002, 1.0107, 0.1377, 0.1007], dtype=torch.float64,
requires_grad=True)
--------------------------------------------------------------------------------
epoch: 3
likelihood: -239770.89278952047
sigma_a:
tensor([1.0346], dtype=torch.float64, requires_grad=True)
pos_x_R_std:
tensor([1.0650], dtype=torch.float64, requires_grad=True)
pos_y_R_std:
tensor([1.1922], dtype=torch.float64, requires_grad=True)
m0:
tensor([1.0877e-03, 2.7817e-04, 3.7957e-05, 1.1019e-03, 3.1841e-04, 4.6838e-05],
dtype=torch.float64, requires_grad=True)
sqrt_diag_V0:
tensor([0.6352, 0.1120, 0.1002, 1.0107, 0.1377, 0.1007], dtype=torch.float64,
requires_grad=True)
ll=-239770.89278952047, sigma_a=1.0345912248607383, pos_x_R_std=1.0649549949989956, pos_y_R_std=1.192186139945691, m0=tensor([1.0877e-03, 2.7817e-04, 3.7957e-05, 1.1019e-03, 3.1841e-04, 4.6838e-05],
dtype=torch.float64, requires_grad=True), sqrt_diag_V0=tensor([0.6352, 0.1120, 0.1002, 1.0107, 0.1377, 0.1007], dtype=torch.float64,
requires_grad=True)
ll=-158792.43454294148, sigma_a=1.031266253437804, pos_x_R_std=1.0530834420544053, pos_y_R_std=1.1642081151418975, m0=tensor([1.7347e-03, 4.4600e-04, 6.0884e-05, 1.7048e-03, 5.3310e-04, 8.0950e-05],
dtype=torch.float64, requires_grad=True), sqrt_diag_V0=tensor([0.8187, 0.1101, 0.1002, 1.2433, 0.1347, 0.1006], dtype=torch.float64,
requires_grad=True)
--------------------------------------------------------------------------------
epoch: 4
likelihood: -158792.43454294148
sigma_a:
tensor([1.0313], dtype=torch.float64, requires_grad=True)
pos_x_R_std:
tensor([1.0531], dtype=torch.float64, requires_grad=True)
pos_y_R_std:
tensor([1.1642], dtype=torch.float64, requires_grad=True)
m0:
tensor([1.7347e-03, 4.4600e-04, 6.0884e-05, 1.7048e-03, 5.3310e-04, 8.0950e-05],
dtype=torch.float64, requires_grad=True)
sqrt_diag_V0:
tensor([0.8187, 0.1101, 0.1002, 1.2433, 0.1347, 0.1006], dtype=torch.float64,
requires_grad=True)
ll=-158792.43454294148, sigma_a=1.031266253437804, pos_x_R_std=1.0530834420544053, pos_y_R_std=1.1642081151418975, m0=tensor([1.7347e-03, 4.4600e-04, 6.0884e-05, 1.7048e-03, 5.3310e-04, 8.0950e-05],
dtype=torch.float64, requires_grad=True), sqrt_diag_V0=tensor([0.8187, 0.1101, 0.1002, 1.2433, 0.1347, 0.1006], dtype=torch.float64,
requires_grad=True)
ll=-107003.36378827522, sigma_a=1.0265649438188955, pos_x_R_std=1.0345559508769064, pos_y_R_std=1.1272516034940505, m0=tensor([2.7165e-03, 7.0298e-04, 9.5754e-05, 2.6644e-03, 9.2083e-04, 1.4355e-04],
dtype=torch.float64, requires_grad=True), sqrt_diag_V0=tensor([1.0267, 0.1071, 0.1001, 1.5230, 0.1301, 0.1005], dtype=torch.float64,
requires_grad=True)
--------------------------------------------------------------------------------
epoch: 5
likelihood: -107003.36378827522
sigma_a:
tensor([1.0266], dtype=torch.float64, requires_grad=True)
pos_x_R_std:
tensor([1.0346], dtype=torch.float64, requires_grad=True)
pos_y_R_std:
tensor([1.1273], dtype=torch.float64, requires_grad=True)
m0:
tensor([2.7165e-03, 7.0298e-04, 9.5754e-05, 2.6644e-03, 9.2083e-04, 1.4355e-04],
dtype=torch.float64, requires_grad=True)
sqrt_diag_V0:
tensor([1.0267, 0.1071, 0.1001, 1.5230, 0.1301, 0.1005], dtype=torch.float64,
requires_grad=True)
ll=-107003.36378827522, sigma_a=1.0265649438188955, pos_x_R_std=1.0345559508769064, pos_y_R_std=1.1272516034940505, m0=tensor([2.7165e-03, 7.0298e-04, 9.5754e-05, 2.6644e-03, 9.2083e-04, 1.4355e-04],
dtype=torch.float64, requires_grad=True), sqrt_diag_V0=tensor([1.0267, 0.1071, 0.1001, 1.5230, 0.1301, 0.1005], dtype=torch.float64,
requires_grad=True)
ll=-72519.50427712481, sigma_a=1.0212614793416899, pos_x_R_std=1.0076850908683614, pos_y_R_std=1.0897621584560877, m0=tensor([0.0043, 0.0011, 0.0002, 0.0042, 0.0017, 0.0003], dtype=torch.float64,
requires_grad=True), sqrt_diag_V0=tensor([1.2768, 0.1026, 0.1000, 1.8649, 0.1247, 0.1005], dtype=torch.float64,
requires_grad=True)
--------------------------------------------------------------------------------
epoch: 6
likelihood: -72519.50427712481
sigma_a:
tensor([1.0213], dtype=torch.float64, requires_grad=True)
pos_x_R_std:
tensor([1.0077], dtype=torch.float64, requires_grad=True)
pos_y_R_std:
tensor([1.0898], dtype=torch.float64, requires_grad=True)
m0:
tensor([0.0043, 0.0011, 0.0002, 0.0042, 0.0017, 0.0003], dtype=torch.float64,
requires_grad=True)
sqrt_diag_V0:
tensor([1.2768, 0.1026, 0.1000, 1.8649, 0.1247, 0.1005], dtype=torch.float64,
requires_grad=True)
ll=-72519.50427712481, sigma_a=1.0212614793416899, pos_x_R_std=1.0076850908683614, pos_y_R_std=1.0897621584560877, m0=tensor([0.0043, 0.0011, 0.0002, 0.0042, 0.0017, 0.0003], dtype=torch.float64,
requires_grad=True), sqrt_diag_V0=tensor([1.2768, 0.1026, 0.1000, 1.8649, 0.1247, 0.1005], dtype=torch.float64,
requires_grad=True)
ll=-49686.43647528592, sigma_a=1.0172690512410587, pos_x_R_std=0.970620315721213, pos_y_R_std=1.0760647714463025, m0=tensor([0.0067, 0.0018, 0.0002, 0.0066, 0.0031, 0.0005], dtype=torch.float64,
requires_grad=True), sqrt_diag_V0=tensor([1.5801, 0.0963, 0.0999, 2.2741, 0.1195, 0.1004], dtype=torch.float64,
requires_grad=True)
--------------------------------------------------------------------------------
epoch: 7
likelihood: -49686.43647528592
sigma_a:
tensor([1.0173], dtype=torch.float64, requires_grad=True)
pos_x_R_std:
tensor([0.9706], dtype=torch.float64, requires_grad=True)
pos_y_R_std:
tensor([1.0761], dtype=torch.float64, requires_grad=True)
m0:
tensor([0.0067, 0.0018, 0.0002, 0.0066, 0.0031, 0.0005], dtype=torch.float64,
requires_grad=True)
sqrt_diag_V0:
tensor([1.5801, 0.0963, 0.0999, 2.2741, 0.1195, 0.1004], dtype=torch.float64,
requires_grad=True)
ll=-49686.43647528592, sigma_a=1.0172690512410587, pos_x_R_std=0.970620315721213, pos_y_R_std=1.0760647714463025, m0=tensor([0.0067, 0.0018, 0.0002, 0.0066, 0.0031, 0.0005], dtype=torch.float64,
requires_grad=True), sqrt_diag_V0=tensor([1.5801, 0.0963, 0.0999, 2.2741, 0.1195, 0.1004], dtype=torch.float64,
requires_grad=True)
ll=-34046.61543713145, sigma_a=1.0181891658869535, pos_x_R_std=0.9199677343259305, pos_y_R_std=1.1362722752597483, m0=tensor([0.0104, 0.0028, 0.0004, 0.0104, 0.0060, 0.0010], dtype=torch.float64,
requires_grad=True), sqrt_diag_V0=tensor([1.9596, 0.0879, 0.0998, 2.7658, 0.1162, 0.1005], dtype=torch.float64,
requires_grad=True)
--------------------------------------------------------------------------------
epoch: 8
likelihood: -34046.61543713145
sigma_a:
tensor([1.0182], dtype=torch.float64, requires_grad=True)
pos_x_R_std:
tensor([0.9200], dtype=torch.float64, requires_grad=True)
pos_y_R_std:
tensor([1.1363], dtype=torch.float64, requires_grad=True)
m0:
tensor([0.0104, 0.0028, 0.0004, 0.0104, 0.0060, 0.0010], dtype=torch.float64,
requires_grad=True)
sqrt_diag_V0:
tensor([1.9596, 0.0879, 0.0998, 2.7658, 0.1162, 0.1005], dtype=torch.float64,
requires_grad=True)
ll=-34046.61543713145, sigma_a=1.0181891658869535, pos_x_R_std=0.9199677343259305, pos_y_R_std=1.1362722752597483, m0=tensor([0.0104, 0.0028, 0.0004, 0.0104, 0.0060, 0.0010], dtype=torch.float64,
requires_grad=True), sqrt_diag_V0=tensor([1.9596, 0.0879, 0.0998, 2.7658, 0.1162, 0.1005], dtype=torch.float64,
requires_grad=True)
ll=-23031.088729876134, sigma_a=1.0289880255994346, pos_x_R_std=0.8522517630782999, pos_y_R_std=1.3241334500984403, m0=tensor([0.0161, 0.0045, 0.0006, 0.0165, 0.0114, 0.0020], dtype=torch.float64,
requires_grad=True), sqrt_diag_V0=tensor([2.4398, 0.0769, 0.0996, 3.3618, 0.1148, 0.1009], dtype=torch.float64,
requires_grad=True)
--------------------------------------------------------------------------------
epoch: 9
likelihood: -23031.088729876134
sigma_a:
tensor([1.0290], dtype=torch.float64, requires_grad=True)
pos_x_R_std:
tensor([0.8523], dtype=torch.float64, requires_grad=True)
pos_y_R_std:
tensor([1.3241], dtype=torch.float64, requires_grad=True)
m0:
tensor([0.0161, 0.0045, 0.0006, 0.0165, 0.0114, 0.0020], dtype=torch.float64,
requires_grad=True)
sqrt_diag_V0:
tensor([2.4398, 0.0769, 0.0996, 3.3618, 0.1148, 0.1009], dtype=torch.float64,
requires_grad=True)
ll=-23031.088729876134, sigma_a=1.0289880255994346, pos_x_R_std=0.8522517630782999, pos_y_R_std=1.3241334500984403, m0=tensor([0.0161, 0.0045, 0.0006, 0.0165, 0.0114, 0.0020], dtype=torch.float64,
requires_grad=True), sqrt_diag_V0=tensor([2.4398, 0.0769, 0.0996, 3.3618, 0.1148, 0.1009], dtype=torch.float64,
requires_grad=True)
ll=-15520.287365153943, sigma_a=1.0547304947761345, pos_x_R_std=0.7667390521558166, pos_y_R_std=1.612859393851679, m0=tensor([0.0246, 0.0073, 0.0009, 0.0258, 0.0207, 0.0038], dtype=torch.float64,
requires_grad=True), sqrt_diag_V0=tensor([3.0220, 0.0637, 0.0994, 4.0879, 0.1103, 0.1015], dtype=torch.float64,
requires_grad=True)
--------------------------------------------------------------------------------
epoch: 10
likelihood: -15520.287365153943
sigma_a:
tensor([1.0547], dtype=torch.float64, requires_grad=True)
pos_x_R_std:
tensor([0.7667], dtype=torch.float64, requires_grad=True)
pos_y_R_std:
tensor([1.6129], dtype=torch.float64, requires_grad=True)
m0:
tensor([0.0246, 0.0073, 0.0009, 0.0258, 0.0207, 0.0038], dtype=torch.float64,
requires_grad=True)
sqrt_diag_V0:
tensor([3.0220, 0.0637, 0.0994, 4.0879, 0.1103, 0.1015], dtype=torch.float64,
requires_grad=True)
ll=-15520.287365153943, sigma_a=1.0547304947761345, pos_x_R_std=0.7667390521558166, pos_y_R_std=1.612859393851679, m0=tensor([0.0246, 0.0073, 0.0009, 0.0258, 0.0207, 0.0038], dtype=torch.float64,
requires_grad=True), sqrt_diag_V0=tensor([3.0220, 0.0637, 0.0994, 4.0879, 0.1103, 0.1015], dtype=torch.float64,
requires_grad=True)
ll=-10480.990514234054, sigma_a=1.1073379890009312, pos_x_R_std=0.6593231709435864, pos_y_R_std=1.9662619243109694, m0=tensor([0.0372, 0.0122, 0.0016, 0.0401, 0.0357, 0.0070], dtype=torch.float64,
requires_grad=True), sqrt_diag_V0=tensor([3.7193, 0.0482, 0.0991, 4.9804, 0.0970, 0.1026], dtype=torch.float64,
requires_grad=True)
--------------------------------------------------------------------------------
epoch: 11
likelihood: -10480.990514234054
sigma_a:
tensor([1.1073], dtype=torch.float64, requires_grad=True)
pos_x_R_std:
tensor([0.6593], dtype=torch.float64, requires_grad=True)
pos_y_R_std:
tensor([1.9663], dtype=torch.float64, requires_grad=True)
m0:
tensor([0.0372, 0.0122, 0.0016, 0.0401, 0.0357, 0.0070], dtype=torch.float64,
requires_grad=True)
sqrt_diag_V0:
tensor([3.7193, 0.0482, 0.0991, 4.9804, 0.0970, 0.1026], dtype=torch.float64,
requires_grad=True)
ll=-10480.990514234054, sigma_a=1.1073379890009312, pos_x_R_std=0.6593231709435864, pos_y_R_std=1.9662619243109694, m0=tensor([0.0372, 0.0122, 0.0016, 0.0401, 0.0357, 0.0070], dtype=torch.float64,
requires_grad=True), sqrt_diag_V0=tensor([3.7193, 0.0482, 0.0991, 4.9804, 0.0970, 0.1026], dtype=torch.float64,
requires_grad=True)
ll=-7092.864655124649, sigma_a=1.2083100085861398, pos_x_R_std=0.5245917198425245, pos_y_R_std=2.3969283197644358, m0=tensor([0.0560, 0.0219, 0.0028, 0.0619, 0.0596, 0.0125], dtype=torch.float64,
requires_grad=True), sqrt_diag_V0=tensor([4.5623, 0.0303, 0.0989, 6.0756, 0.0667, 0.1041], dtype=torch.float64,
requires_grad=True)
--------------------------------------------------------------------------------
epoch: 12
likelihood: -7092.864655124649
sigma_a:
tensor([1.2083], dtype=torch.float64, requires_grad=True)
pos_x_R_std:
tensor([0.5246], dtype=torch.float64, requires_grad=True)
pos_y_R_std:
tensor([2.3969], dtype=torch.float64, requires_grad=True)
m0:
tensor([0.0560, 0.0219, 0.0028, 0.0619, 0.0596, 0.0125], dtype=torch.float64,
requires_grad=True)
sqrt_diag_V0:
tensor([4.5623, 0.0303, 0.0989, 6.0756, 0.0667, 0.1041], dtype=torch.float64,
requires_grad=True)
ll=-7092.864655124649, sigma_a=1.2083100085861398, pos_x_R_std=0.5245917198425245, pos_y_R_std=2.3969283197644358, m0=tensor([0.0560, 0.0219, 0.0028, 0.0619, 0.0596, 0.0125], dtype=torch.float64,
requires_grad=True), sqrt_diag_V0=tensor([4.5623, 0.0303, 0.0989, 6.0756, 0.0667, 0.1041], dtype=torch.float64,
requires_grad=True)
ll=-4821.532436545909, sigma_a=1.3897246451006247, pos_x_R_std=0.38354405197546165, pos_y_R_std=2.917592575540884, m0=tensor([0.0840, 0.0441, 0.0056, 0.0948, 0.0973, 0.0217], dtype=torch.float64,
requires_grad=True), sqrt_diag_V0=tensor([5.5806e+00, 9.6251e-03, 9.8725e-02, 7.4155e+00, 3.0666e-03, 1.0619e-01],
dtype=torch.float64, requires_grad=True)
--------------------------------------------------------------------------------
epoch: 13
likelihood: -4821.532436545909
sigma_a:
tensor([1.3897], dtype=torch.float64, requires_grad=True)
pos_x_R_std:
tensor([0.3835], dtype=torch.float64, requires_grad=True)
pos_y_R_std:
tensor([2.9176], dtype=torch.float64, requires_grad=True)
m0:
tensor([0.0840, 0.0441, 0.0056, 0.0948, 0.0973, 0.0217], dtype=torch.float64,
requires_grad=True)
sqrt_diag_V0:
tensor([5.5806e+00, 9.6251e-03, 9.8725e-02, 7.4155e+00, 3.0666e-03, 1.0619e-01],
dtype=torch.float64, requires_grad=True)
ll=-4821.532436545909, sigma_a=1.3897246451006247, pos_x_R_std=0.38354405197546165, pos_y_R_std=2.917592575540884, m0=tensor([0.0840, 0.0441, 0.0056, 0.0948, 0.0973, 0.0217], dtype=torch.float64,
requires_grad=True), sqrt_diag_V0=tensor([5.5806e+00, 9.6251e-03, 9.8725e-02, 7.4155e+00, 3.0666e-03, 1.0619e-01],
dtype=torch.float64, requires_grad=True)
ll=-3289.4863324444264, sigma_a=1.7098249459797807, pos_x_R_std=0.4374580016467312, pos_y_R_std=3.5428260154639197, m0=tensor([0.1260, 0.0996, 0.0129, 0.1445, 0.1553, 0.0363], dtype=torch.float64,
requires_grad=True), sqrt_diag_V0=tensor([ 6.7971, -0.0195, 0.0991, 9.0645, -0.1258, 0.1084],
dtype=torch.float64, requires_grad=True)
--------------------------------------------------------------------------------
epoch: 14
likelihood: -3289.4863324444264
sigma_a:
tensor([1.7098], dtype=torch.float64, requires_grad=True)
pos_x_R_std:
tensor([0.4375], dtype=torch.float64, requires_grad=True)
pos_y_R_std:
tensor([3.5428], dtype=torch.float64, requires_grad=True)
m0:
tensor([0.1260, 0.0996, 0.0129, 0.1445, 0.1553, 0.0363], dtype=torch.float64,
requires_grad=True)
sqrt_diag_V0:
tensor([ 6.7971, -0.0195, 0.0991, 9.0645, -0.1258, 0.1084],
dtype=torch.float64, requires_grad=True)
ll=-3289.4863324444264, sigma_a=1.7098249459797807, pos_x_R_std=0.4374580016467312, pos_y_R_std=3.5428260154639197, m0=tensor([0.1260, 0.0996, 0.0129, 0.1445, 0.1553, 0.0363], dtype=torch.float64,
requires_grad=True), sqrt_diag_V0=tensor([ 6.7971, -0.0195, 0.0991, 9.0645, -0.1258, 0.1084],
dtype=torch.float64, requires_grad=True)
ll=-2268.3489998370387, sigma_a=2.1054395181701606, pos_x_R_std=0.2379194880953605, pos_y_R_std=4.2955681882363175, m0=tensor([0.1893, 0.1866, 0.0242, 0.2190, 0.2419, 0.0580], dtype=torch.float64,
requires_grad=True), sqrt_diag_V0=tensor([ 8.3168, -0.0735, 0.0995, 11.0794, -0.3686, 0.1102],
dtype=torch.float64, requires_grad=True)
--------------------------------------------------------------------------------
epoch: 15
likelihood: -2268.3489998370387
sigma_a:
tensor([2.1054], dtype=torch.float64, requires_grad=True)
pos_x_R_std:
tensor([0.2379], dtype=torch.float64, requires_grad=True)
pos_y_R_std:
tensor([4.2956], dtype=torch.float64, requires_grad=True)
m0:
tensor([0.1893, 0.1866, 0.0242, 0.2190, 0.2419, 0.0580], dtype=torch.float64,
requires_grad=True)
sqrt_diag_V0:
tensor([ 8.3168, -0.0735, 0.0995, 11.0794, -0.3686, 0.1102],
dtype=torch.float64, requires_grad=True)
ll=-2268.3489998370387, sigma_a=2.1054395181701606, pos_x_R_std=0.2379194880953605, pos_y_R_std=4.2955681882363175, m0=tensor([0.1893, 0.1866, 0.0242, 0.2190, 0.2419, 0.0580], dtype=torch.float64,
requires_grad=True), sqrt_diag_V0=tensor([ 8.3168, -0.0735, 0.0995, 11.0794, -0.3686, 0.1102],
dtype=torch.float64, requires_grad=True)
ll=-1420.0848234925124, sigma_a=3.0291029023271507, pos_x_R_std=2.471600800500445, pos_y_R_std=5.611907394212267, m0=tensor([0.3166, 0.4308, 0.0547, 0.3693, 0.4151, 0.1008], dtype=torch.float64,
requires_grad=True), sqrt_diag_V0=tensor([10.8086, -0.2959, 0.1011, 14.8299, -0.9118, 0.1125],
dtype=torch.float64, requires_grad=True)
--------------------------------------------------------------------------------
epoch: 16
likelihood: -1420.0848234925124
sigma_a:
tensor([3.0291], dtype=torch.float64, requires_grad=True)
pos_x_R_std:
tensor([2.4716], dtype=torch.float64, requires_grad=True)
pos_y_R_std:
tensor([5.6119], dtype=torch.float64, requires_grad=True)
m0:
tensor([0.3166, 0.4308, 0.0547, 0.3693, 0.4151, 0.1008], dtype=torch.float64,
requires_grad=True)
sqrt_diag_V0:
tensor([10.8086, -0.2959, 0.1011, 14.8299, -0.9118, 0.1125],
dtype=torch.float64, requires_grad=True)
ll=-1420.0848234925124, sigma_a=3.0291029023271507, pos_x_R_std=2.471600800500445, pos_y_R_std=5.611907394212267, m0=tensor([0.3166, 0.4308, 0.0547, 0.3693, 0.4151, 0.1008], dtype=torch.float64,
requires_grad=True), sqrt_diag_V0=tensor([10.8086, -0.2959, 0.1011, 14.8299, -0.9118, 0.1125],
dtype=torch.float64, requires_grad=True)
ll=-1147.9501184695964, sigma_a=3.399261351111765, pos_x_R_std=2.797126297817509, pos_y_R_std=6.3372240583281405, m0=tensor([0.4144, 0.5330, 0.0673, 0.4808, 0.5405, 0.1305], dtype=torch.float64,
requires_grad=True), sqrt_diag_V0=tensor([12.3911, -0.3975, 0.1013, 17.0117, -1.3473, 0.1129],
dtype=torch.float64, requires_grad=True)
--------------------------------------------------------------------------------
epoch: 17
likelihood: -1147.9501184695964
sigma_a:
tensor([3.3993], dtype=torch.float64, requires_grad=True)
pos_x_R_std:
tensor([2.7971], dtype=torch.float64, requires_grad=True)
pos_y_R_std:
tensor([6.3372], dtype=torch.float64, requires_grad=True)
m0:
tensor([0.4144, 0.5330, 0.0673, 0.4808, 0.5405, 0.1305], dtype=torch.float64,
requires_grad=True)
sqrt_diag_V0:
tensor([12.3911, -0.3975, 0.1013, 17.0117, -1.3473, 0.1129],
dtype=torch.float64, requires_grad=True)
ll=-1147.9501184695964, sigma_a=3.399261351111765, pos_x_R_std=2.797126297817509, pos_y_R_std=6.3372240583281405, m0=tensor([0.4144, 0.5330, 0.0673, 0.4808, 0.5405, 0.1305], dtype=torch.float64,
requires_grad=True), sqrt_diag_V0=tensor([12.3911, -0.3975, 0.1013, 17.0117, -1.3473, 0.1129],
dtype=torch.float64, requires_grad=True)
ll=-842.9216932287975, sigma_a=4.091913074964331, pos_x_R_std=3.1989828912614096, pos_y_R_std=7.523208401105215, m0=tensor([0.6478, 0.7656, 0.0955, 0.7454, 0.8368, 0.1987], dtype=torch.float64,
requires_grad=True), sqrt_diag_V0=tensor([15.4074, -0.6133, 0.1020, 21.2251, -2.4562, 0.1129],
dtype=torch.float64, requires_grad=True)
--------------------------------------------------------------------------------
epoch: 18
likelihood: -842.9216932287975
sigma_a:
tensor([4.0919], dtype=torch.float64, requires_grad=True)
pos_x_R_std:
tensor([3.1990], dtype=torch.float64, requires_grad=True)
pos_y_R_std:
tensor([7.5232], dtype=torch.float64, requires_grad=True)
m0:
tensor([0.6478, 0.7656, 0.0955, 0.7454, 0.8368, 0.1987], dtype=torch.float64,
requires_grad=True)
sqrt_diag_V0:
tensor([15.4074, -0.6133, 0.1020, 21.2251, -2.4562, 0.1129],
dtype=torch.float64, requires_grad=True)
ll=-842.9216932287975, sigma_a=4.091913074964331, pos_x_R_std=3.1989828912614096, pos_y_R_std=7.523208401105215, m0=tensor([0.6478, 0.7656, 0.0955, 0.7454, 0.8368, 0.1987], dtype=torch.float64,
requires_grad=True), sqrt_diag_V0=tensor([15.4074, -0.6133, 0.1020, 21.2251, -2.4562, 0.1129],
dtype=torch.float64, requires_grad=True)
ll=-669.453373295344, sigma_a=4.773398117788069, pos_x_R_std=3.2254498589611473, pos_y_R_std=8.451973966071769, m0=tensor([0.9552, 1.0758, 0.1320, 1.0904, 1.2192, 0.2808], dtype=torch.float64,
requires_grad=True), sqrt_diag_V0=tensor([18.5136, -0.8797, 0.1034, 25.6192, -3.9935, 0.1117],
dtype=torch.float64, requires_grad=True)
--------------------------------------------------------------------------------
epoch: 19
likelihood: -669.453373295344
sigma_a:
tensor([4.7734], dtype=torch.float64, requires_grad=True)
pos_x_R_std:
tensor([3.2254], dtype=torch.float64, requires_grad=True)
pos_y_R_std:
tensor([8.4520], dtype=torch.float64, requires_grad=True)
m0:
tensor([0.9552, 1.0758, 0.1320, 1.0904, 1.2192, 0.2808], dtype=torch.float64,
requires_grad=True)
sqrt_diag_V0:
tensor([18.5136, -0.8797, 0.1034, 25.6192, -3.9935, 0.1117],
dtype=torch.float64, requires_grad=True)
ll=-669.453373295344, sigma_a=4.773398117788069, pos_x_R_std=3.2254498589611473, pos_y_R_std=8.451973966071769, m0=tensor([0.9552, 1.0758, 0.1320, 1.0904, 1.2192, 0.2808], dtype=torch.float64,
requires_grad=True), sqrt_diag_V0=tensor([18.5136, -0.8797, 0.1034, 25.6192, -3.9935, 0.1117],
dtype=torch.float64, requires_grad=True)
ll=-526.6241053511125, sigma_a=5.705504727173416, pos_x_R_std=2.3137885463557737, pos_y_R_std=9.076165043268128, m0=tensor([1.4641, 1.6546, 0.1977, 1.6545, 1.8270, 0.3928], dtype=torch.float64,
requires_grad=True), sqrt_diag_V0=tensor([22.5971, -1.3441, 0.1071, 31.4619, -6.5419, 0.1088],
dtype=torch.float64, requires_grad=True)
--------------------------------------------------------------------------------
epoch: 20
likelihood: -526.6241053511125
sigma_a:
tensor([5.7055], dtype=torch.float64, requires_grad=True)
pos_x_R_std:
tensor([2.3138], dtype=torch.float64, requires_grad=True)
pos_y_R_std:
tensor([9.0762], dtype=torch.float64, requires_grad=True)
m0:
tensor([1.4641, 1.6546, 0.1977, 1.6545, 1.8270, 0.3928], dtype=torch.float64,
requires_grad=True)
sqrt_diag_V0:
tensor([22.5971, -1.3441, 0.1071, 31.4619, -6.5419, 0.1088],
dtype=torch.float64, requires_grad=True)
ll=-526.6241053511125, sigma_a=5.705504727173416, pos_x_R_std=2.3137885463557737, pos_y_R_std=9.076165043268128, m0=tensor([1.4641, 1.6546, 0.1977, 1.6545, 1.8270, 0.3928], dtype=torch.float64,
requires_grad=True), sqrt_diag_V0=tensor([22.5971, -1.3441, 0.1071, 31.4619, -6.5419, 0.1088],
dtype=torch.float64, requires_grad=True)
ll=-419.6738967914765, sigma_a=8.206360081964778, pos_x_R_std=-2.3527725535406283, pos_y_R_std=9.271186031228853, m0=tensor([2.4730, 3.1835, 0.3691, 2.7662, 2.9941, 0.5662], dtype=torch.float64,
requires_grad=True), sqrt_diag_V0=tensor([ 29.7736, -2.5397, 0.1201, 41.5404, -11.4699, 0.1018],
dtype=torch.float64, requires_grad=True)
--------------------------------------------------------------------------------
epoch: 21
likelihood: -419.6738967914765
sigma_a:
tensor([8.2064], dtype=torch.float64, requires_grad=True)
pos_x_R_std:
tensor([-2.3528], dtype=torch.float64, requires_grad=True)
pos_y_R_std:
tensor([9.2712], dtype=torch.float64, requires_grad=True)
m0:
tensor([2.4730, 3.1835, 0.3691, 2.7662, 2.9941, 0.5662], dtype=torch.float64,
requires_grad=True)
sqrt_diag_V0:
tensor([ 29.7736, -2.5397, 0.1201, 41.5404, -11.4699, 0.1018],
dtype=torch.float64, requires_grad=True)
ll=-419.6738967914765, sigma_a=8.206360081964778, pos_x_R_std=-2.3527725535406283, pos_y_R_std=9.271186031228853, m0=tensor([2.4730, 3.1835, 0.3691, 2.7662, 2.9941, 0.5662], dtype=torch.float64,
requires_grad=True), sqrt_diag_V0=tensor([ 29.7736, -2.5397, 0.1201, 41.5404, -11.4699, 0.1018],
dtype=torch.float64, requires_grad=True)
ll=-394.7914366586798, sigma_a=8.07425986017163, pos_x_R_std=-1.580002106665833, pos_y_R_std=9.253905387018673, m0=tensor([2.5687, 3.1780, 0.3672, 2.8699, 3.1020, 0.5785], dtype=torch.float64,
requires_grad=True), sqrt_diag_V0=tensor([ 30.3950, -2.5052, 0.1188, 42.6305, -11.8724, 0.1018],
dtype=torch.float64, requires_grad=True)
ll=-378.0699668520697, sigma_a=7.479148360993492, pos_x_R_std=1.9013287565051207, pos_y_R_std=9.176056084851815, m0=tensor([3.0000, 3.1529, 0.3584, 3.3370, 3.5881, 0.6341], dtype=torch.float64,
requires_grad=True), sqrt_diag_V0=tensor([ 33.1945, -2.3498, 0.1129, 47.5413, -13.6855, 0.1017],
dtype=torch.float64, requires_grad=True)
--------------------------------------------------------------------------------
epoch: 22
likelihood: -378.0699668520697
sigma_a:
tensor([7.4791], dtype=torch.float64, requires_grad=True)
pos_x_R_std:
tensor([1.9013], dtype=torch.float64, requires_grad=True)
pos_y_R_std:
tensor([9.1761], dtype=torch.float64, requires_grad=True)
m0:
tensor([3.0000, 3.1529, 0.3584, 3.3370, 3.5881, 0.6341], dtype=torch.float64,
requires_grad=True)
sqrt_diag_V0:
tensor([ 33.1945, -2.3498, 0.1129, 47.5413, -13.6855, 0.1017],
dtype=torch.float64, requires_grad=True)
ll=-378.0699668520697, sigma_a=7.479148360993492, pos_x_R_std=1.9013287565051207, pos_y_R_std=9.176056084851815, m0=tensor([3.0000, 3.1529, 0.3584, 3.3370, 3.5881, 0.6341], dtype=torch.float64,
requires_grad=True), sqrt_diag_V0=tensor([ 33.1945, -2.3498, 0.1129, 47.5413, -13.6855, 0.1017],
dtype=torch.float64, requires_grad=True)
ll=-10249.015952388172, sigma_a=8.424559732631094, pos_x_R_std=0.0035997831962235605, pos_y_R_std=9.176767173887171, m0=tensor([3.3256, 3.6909, 0.4187, 3.6954, 3.9642, 0.6873], dtype=torch.float64,
requires_grad=True), sqrt_diag_V0=tensor([ 35.4868, -2.7734, 0.1179, 50.7121, -15.2745, 0.0993],
dtype=torch.float64, requires_grad=True)
ll=-322.2408296054813, sigma_a=8.108612531533383, pos_x_R_std=0.637802179683593, pos_y_R_std=9.176529534910962, m0=tensor([3.2168, 3.5111, 0.3986, 3.5756, 3.8385, 0.6695], dtype=torch.float64,
requires_grad=True), sqrt_diag_V0=tensor([ 34.7207, -2.6318, 0.1162, 49.6525, -14.7435, 0.1001],
dtype=torch.float64, requires_grad=True)
ll=-292.8137022646379, sigma_a=8.318425519194994, pos_x_R_std=0.21664352049351907, pos_y_R_std=9.17668734527741, m0=tensor([3.2891, 3.6305, 0.4119, 3.6551, 3.9220, 0.6813], dtype=torch.float64,
requires_grad=True), sqrt_diag_V0=tensor([ 35.2294, -2.7258, 0.1173, 50.3562, -15.0961, 0.0996],
dtype=torch.float64, requires_grad=True)
--------------------------------------------------------------------------------
epoch: 23
likelihood: -292.8137022646379
sigma_a:
tensor([8.3184], dtype=torch.float64, requires_grad=True)
pos_x_R_std:
tensor([0.2166], dtype=torch.float64, requires_grad=True)
pos_y_R_std:
tensor([9.1767], dtype=torch.float64, requires_grad=True)
m0:
tensor([3.2891, 3.6305, 0.4119, 3.6551, 3.9220, 0.6813], dtype=torch.float64,
requires_grad=True)
sqrt_diag_V0:
tensor([ 35.2294, -2.7258, 0.1173, 50.3562, -15.0961, 0.0996],
dtype=torch.float64, requires_grad=True)
ll=-292.8137022646379, sigma_a=8.318425519194994, pos_x_R_std=0.21664352049351907, pos_y_R_std=9.17668734527741, m0=tensor([3.2891, 3.6305, 0.4119, 3.6551, 3.9220, 0.6813], dtype=torch.float64,
requires_grad=True), sqrt_diag_V0=tensor([ 35.2294, -2.7258, 0.1173, 50.3562, -15.0961, 0.0996],
dtype=torch.float64, requires_grad=True)
ll=-353.54930497692925, sigma_a=11.079947521958482, pos_x_R_std=-2.8609590164243173, pos_y_R_std=8.897212542001895, m0=tensor([4.2782, 4.8020, 0.5627, 4.7387, 5.0565, 0.8280], dtype=torch.float64,
requires_grad=True), sqrt_diag_V0=tensor([ 41.9839, -3.5720, 0.1267, 60.2272, -19.7491, 0.0940],
dtype=torch.float64, requires_grad=True)
ll=-287.41476612194015, sigma_a=8.729654141556932, pos_x_R_std=-0.241653842398331, pos_y_R_std=9.135069701738502, m0=tensor([3.4364, 3.8050, 0.4344, 3.8165, 4.0909, 0.7032], dtype=torch.float64,
requires_grad=True), sqrt_diag_V0=tensor([ 36.2353, -2.8518, 0.1187, 51.8261, -15.7890, 0.0988],
dtype=torch.float64, requires_grad=True)
ll=-301.34764190185894, sigma_a=8.62261649632766, pos_x_R_std=-0.12236479520853462, pos_y_R_std=9.145902251619903, m0=tensor([3.3980, 3.7595, 0.4285, 3.7745, 4.0469, 0.6975], dtype=torch.float64,
requires_grad=True), sqrt_diag_V0=tensor([ 35.9735, -2.8190, 0.1184, 51.4435, -15.6087, 0.0990],
dtype=torch.float64, requires_grad=True)
ll=-287.1516954426813, sigma_a=8.690740591685477, pos_x_R_std=-0.19828629374761592, pos_y_R_std=9.139007876659502, m0=tensor([3.4224, 3.7884, 0.4323, 3.8012, 4.0749, 0.7011], dtype=torch.float64,
requires_grad=True), sqrt_diag_V0=tensor([ 36.1401, -2.8399, 0.1186, 51.6870, -15.7235, 0.0988],
dtype=torch.float64, requires_grad=True)
ll=-286.9580313447161, sigma_a=8.704812948503571, pos_x_R_std=-0.2139693558417938, pos_y_R_std=9.13758370942512, m0=tensor([3.4275, 3.7944, 0.4330, 3.8067, 4.0807, 0.7018], dtype=torch.float64,
requires_grad=True), sqrt_diag_V0=tensor([ 36.1745, -2.8442, 0.1186, 51.7373, -15.7472, 0.0988],
dtype=torch.float64, requires_grad=True)
--------------------------------------------------------------------------------
epoch: 24
likelihood: -286.9580313447161
sigma_a:
tensor([8.7048], dtype=torch.float64, requires_grad=True)
pos_x_R_std:
tensor([-0.2140], dtype=torch.float64, requires_grad=True)
pos_y_R_std:
tensor([9.1376], dtype=torch.float64, requires_grad=True)
m0:
tensor([3.4275, 3.7944, 0.4330, 3.8067, 4.0807, 0.7018], dtype=torch.float64,
requires_grad=True)
sqrt_diag_V0:
tensor([ 36.1745, -2.8442, 0.1186, 51.7373, -15.7472, 0.0988],
dtype=torch.float64, requires_grad=True)
ll=-286.9580313447161, sigma_a=8.704812948503571, pos_x_R_std=-0.2139693558417938, pos_y_R_std=9.13758370942512, m0=tensor([3.4275, 3.7944, 0.4330, 3.8067, 4.0807, 0.7018], dtype=torch.float64,
requires_grad=True), sqrt_diag_V0=tensor([ 36.1745, -2.8442, 0.1186, 51.7373, -15.7472, 0.0988],
dtype=torch.float64, requires_grad=True)
ll=-277.2848435961711, sigma_a=9.856742774105811, pos_x_R_std=-0.11377958252227706, pos_y_R_std=9.049005823123409, m0=tensor([4.2243, 4.4768, 0.5142, 4.6778, 4.9926, 0.8205], dtype=torch.float64,
requires_grad=True), sqrt_diag_V0=tensor([ 41.6129, -3.2745, 0.1210, 60.0883, -19.4053, 0.0955],
dtype=torch.float64, requires_grad=True)
ll=-273.01236225331905, sigma_a=9.498497597670278, pos_x_R_std=-0.14493816720526453, pos_y_R_std=9.076553161338957, m0=tensor([3.9765, 4.2646, 0.4890, 4.4069, 4.7090, 0.7836], dtype=torch.float64,
requires_grad=True), sqrt_diag_V0=tensor([ 39.9216, -3.1407, 0.1202, 57.4912, -18.2676, 0.0965],
dtype=torch.float64, requires_grad=True)
--------------------------------------------------------------------------------
epoch: 25
likelihood: -273.01236225331905
sigma_a:
tensor([9.4985], dtype=torch.float64, requires_grad=True)
pos_x_R_std:
tensor([-0.1449], dtype=torch.float64, requires_grad=True)
pos_y_R_std:
tensor([9.0766], dtype=torch.float64, requires_grad=True)
m0:
tensor([3.9765, 4.2646, 0.4890, 4.4069, 4.7090, 0.7836], dtype=torch.float64,
requires_grad=True)
sqrt_diag_V0:
tensor([ 39.9216, -3.1407, 0.1202, 57.4912, -18.2676, 0.0965],
dtype=torch.float64, requires_grad=True)
ll=-273.01236225331905, sigma_a=9.498497597670278, pos_x_R_std=-0.14493816720526453, pos_y_R_std=9.076553161338957, m0=tensor([3.9765, 4.2646, 0.4890, 4.4069, 4.7090, 0.7836], dtype=torch.float64,
requires_grad=True), sqrt_diag_V0=tensor([ 39.9216, -3.1407, 0.1202, 57.4912, -18.2676, 0.0965],
dtype=torch.float64, requires_grad=True)
ll=-232.29140859555304, sigma_a=45.76207160943872, pos_x_R_std=-1.0678707739922504, pos_y_R_std=6.183814837522444, m0=tensor([27.9218, 25.1685, 2.9904, 30.5857, 32.1141, 4.3469],
dtype=torch.float64, requires_grad=True), sqrt_diag_V0=tensor([ 2.0334e+02, -1.6452e+01, 1.9790e-01, 3.0782e+02, -1.2833e+02,
-5.9530e-03], dtype=torch.float64, requires_grad=True)
--------------------------------------------------------------------------------
epoch: 26
likelihood: -232.29140859555304
sigma_a:
tensor([45.7621], dtype=torch.float64, requires_grad=True)
pos_x_R_std:
tensor([-1.0679], dtype=torch.float64, requires_grad=True)
pos_y_R_std:
tensor([6.1838], dtype=torch.float64, requires_grad=True)
m0:
tensor([27.9218, 25.1685, 2.9904, 30.5857, 32.1141, 4.3469],
dtype=torch.float64, requires_grad=True)
sqrt_diag_V0:
tensor([ 2.0334e+02, -1.6452e+01, 1.9790e-01, 3.0782e+02, -1.2833e+02,
-5.9530e-03], dtype=torch.float64, requires_grad=True)
ll=-232.29140859555304, sigma_a=45.76207160943872, pos_x_R_std=-1.0678707739922504, pos_y_R_std=6.183814837522444, m0=tensor([27.9218, 25.1685, 2.9904, 30.5857, 32.1141, 4.3469],
dtype=torch.float64, requires_grad=True), sqrt_diag_V0=tensor([ 2.0334e+02, -1.6452e+01, 1.9790e-01, 3.0782e+02, -1.2833e+02,
-5.9530e-03], dtype=torch.float64, requires_grad=True)
ll=-230.95045449243585, sigma_a=45.410933808764845, pos_x_R_std=-1.0446533408115102, pos_y_R_std=6.102408601152707, m0=tensor([27.6899, 24.9597, 2.9658, 30.3318, 31.8475, 4.3104],
dtype=torch.float64, requires_grad=True), sqrt_diag_V0=tensor([ 2.0170e+02, -1.6316e+01, 1.9709e-01, 3.0536e+02, -1.2726e+02,
-4.9107e-03], dtype=torch.float64, requires_grad=True)
ll=-224.65891104742084, sigma_a=43.82905801672904, pos_x_R_std=-0.9400588043322757, pos_y_R_std=5.735673506307042, m0=tensor([26.6454, 24.0191, 2.8548, 29.1880, 30.6462, 4.1460],
dtype=torch.float64, requires_grad=True), sqrt_diag_V0=tensor([ 1.9434e+02, -1.5703e+01, 1.9345e-01, 2.9429e+02, -1.2241e+02,
-2.1530e-04], dtype=torch.float64, requires_grad=True)
ll=-178.88960040929936, sigma_a=35.12258747057533, pos_x_R_std=-0.3643819681799938, pos_y_R_std=3.7172038403635037, m0=tensor([20.8965, 18.8416, 2.2438, 22.8928, 24.0344, 3.2410],
dtype=torch.float64, requires_grad=True), sqrt_diag_V0=tensor([ 1.5380e+02, -1.2332e+01, 1.7344e-01, 2.3332e+02, -9.5739e+01,
2.5628e-02], dtype=torch.float64, requires_grad=True)
ll=-308.7803081074337, sigma_a=-12.798623507040684, pos_x_R_std=2.804196042155922, pos_y_R_std=-7.392637995181446, m0=tensor([-10.7459, -9.6556, -1.1190, -11.7566, -12.3576, -1.7399],
dtype=torch.float64, requires_grad=True), sqrt_diag_V0=tensor([-6.9325e+01, 6.2208e+00, 6.3277e-02, -1.0222e+02, 5.1071e+01,
1.6787e-01], dtype=torch.float64, requires_grad=True)
ll=-161.856606950695, sigma_a=27.07072870462095, pos_x_R_std=0.16801156085771402, pos_y_R_std=1.8504964774447397, m0=tensor([15.5798, 14.0534, 1.6788, 17.0709, 17.9197, 2.4041],
dtype=torch.float64, requires_grad=True), sqrt_diag_V0=tensor([ 1.1631e+02, -9.2150e+00, 1.5493e-01, 1.7694e+02, -7.1072e+01,
4.9527e-02], dtype=torch.float64, requires_grad=True)
ll=-1042.4650396768468, sigma_a=29.445438093760686, pos_x_R_std=0.010994411293587428, pos_y_R_std=2.401038610677753, m0=tensor([17.1479, 15.4656, 1.8454, 18.7879, 19.7231, 2.6509],
dtype=torch.float64, requires_grad=True), sqrt_diag_V0=tensor([ 1.2737e+02, -1.0134e+01, 1.6039e-01, 1.9357e+02, -7.8347e+01,
4.2479e-02], dtype=torch.float64, requires_grad=True)
ll=-178.48279623970024, sigma_a=28.576752562380456, pos_x_R_std=0.06843239786521342, pos_y_R_std=2.1996463949641596, m0=tensor([16.5743, 14.9490, 1.7845, 18.1598, 19.0634, 2.5606],
dtype=torch.float64, requires_grad=True), sqrt_diag_V0=tensor([ 1.2332e+02, -9.7981e+00, 1.5839e-01, 1.8749e+02, -7.5686e+01,
4.5057e-02], dtype=torch.float64, requires_grad=True)
ll=-160.72298901172053, sigma_a=27.74727820892625, pos_x_R_std=0.12327771881756282, pos_y_R_std=2.007344725504646, m0=tensor([16.0266, 14.4557, 1.7263, 17.5601, 18.4335, 2.4744],
dtype=torch.float64, requires_grad=True), sqrt_diag_V0=tensor([ 1.1946e+02, -9.4770e+00, 1.5648e-01, 1.8168e+02, -7.3145e+01,
4.7519e-02], dtype=torch.float64, requires_grad=True)
--------------------------------------------------------------------------------
epoch: 27
likelihood: -160.72298901172053
sigma_a:
tensor([27.7473], dtype=torch.float64, requires_grad=True)
pos_x_R_std:
tensor([0.1233], dtype=torch.float64, requires_grad=True)
pos_y_R_std:
tensor([2.0073], dtype=torch.float64, requires_grad=True)
m0:
tensor([16.0266, 14.4557, 1.7263, 17.5601, 18.4335, 2.4744],
dtype=torch.float64, requires_grad=True)
sqrt_diag_V0:
tensor([ 1.1946e+02, -9.4770e+00, 1.5648e-01, 1.8168e+02, -7.3145e+01,
4.7519e-02], dtype=torch.float64, requires_grad=True)
ll=-160.72298901172053, sigma_a=27.74727820892625, pos_x_R_std=0.12327771881756282, pos_y_R_std=2.007344725504646, m0=tensor([16.0266, 14.4557, 1.7263, 17.5601, 18.4335, 2.4744],
dtype=torch.float64, requires_grad=True), sqrt_diag_V0=tensor([ 1.1946e+02, -9.4770e+00, 1.5648e-01, 1.8168e+02, -7.3145e+01,
4.7519e-02], dtype=torch.float64, requires_grad=True)
ll=-412.31021516342486, sigma_a=-111.85475831568615, pos_x_R_std=10.309414230378485, pos_y_R_std=-36.85376674254815, m0=tensor([-76.2868, -69.0836, -8.1094, -83.5502, -87.8126, -12.1776],
dtype=torch.float64, requires_grad=True), sqrt_diag_V0=tensor([-5.3459e+02, 4.5080e+01, -1.6835e-01, -7.9928e+02, 3.5576e+02,
4.6552e-01], dtype=torch.float64, requires_grad=True)
ll=-85616.51273369906, sigma_a=2.0056478592220426, pos_x_R_std=2.001529406972545, pos_y_R_std=-5.158369982481728, m0=tensor([-0.9954, -0.9483, -0.0873, -1.0839, -1.1576, -0.2273],
dtype=torch.float64, requires_grad=True), sqrt_diag_V0=tensor([-1.1410, 0.5829, 0.0966, 0.7989, 5.9416, 0.1246],
dtype=torch.float64, requires_grad=True)
ll=-340.62430955743326, sigma_a=11.783720261128126, pos_x_R_std=1.2880671768697507, pos_y_R_std=-2.4364414847827005, m0=tensor([5.4705, 4.9030, 0.6016, 5.9981, 6.2842, 0.7990], dtype=torch.float64,
requires_grad=True), sqrt_diag_V0=tensor([ 44.6700, -3.2384, 0.1193, 69.5080, -24.0996, 0.0953],
dtype=torch.float64, requires_grad=True)
ll=-164.44670268876433, sigma_a=26.677610789215112, pos_x_R_std=0.20132656846472255, pos_y_R_std=1.709580696655323, m0=tensor([15.3192, 13.8156, 1.6509, 16.7853, 17.6194, 2.3622],
dtype=torch.float64, requires_grad=True), sqrt_diag_V0=tensor([ 1.1445e+02, -9.0590e+00, 1.5399e-01, 1.7417e+02, -6.9858e+01,
5.0722e-02], dtype=torch.float64, requires_grad=True)
ll=-160.38094014825506, sigma_a=27.532475419466998, pos_x_R_std=0.13895091808432466, pos_y_R_std=1.9475499305816295, m0=tensor([15.8845, 14.3272, 1.7111, 17.4045, 18.2700, 2.4519],
dtype=torch.float64, requires_grad=True), sqrt_diag_V0=tensor([ 1.1845e+02, -9.3930e+00, 1.5598e-01, 1.8017e+02, -7.2485e+01,
4.8163e-02], dtype=torch.float64, requires_grad=True)
--------------------------------------------------------------------------------
epoch: 28
likelihood: -160.38094014825506
sigma_a:
tensor([27.5325], dtype=torch.float64, requires_grad=True)
pos_x_R_std:
tensor([0.1390], dtype=torch.float64, requires_grad=True)
pos_y_R_std:
tensor([1.9475], dtype=torch.float64, requires_grad=True)
m0:
tensor([15.8845, 14.3272, 1.7111, 17.4045, 18.2700, 2.4519],
dtype=torch.float64, requires_grad=True)
sqrt_diag_V0:
tensor([ 1.1845e+02, -9.3930e+00, 1.5598e-01, 1.8017e+02, -7.2485e+01,
4.8163e-02], dtype=torch.float64, requires_grad=True)
ll=-160.38094014825506, sigma_a=27.532475419466998, pos_x_R_std=0.13895091808432466, pos_y_R_std=1.9475499305816295, m0=tensor([15.8845, 14.3272, 1.7111, 17.4045, 18.2700, 2.4519],
dtype=torch.float64, requires_grad=True), sqrt_diag_V0=tensor([ 1.1845e+02, -9.3930e+00, 1.5598e-01, 1.8017e+02, -7.2485e+01,
4.8163e-02], dtype=torch.float64, requires_grad=True)
ll=-150.22891217808984, sigma_a=29.5698747454269, pos_x_R_std=0.13483231718720412, pos_y_R_std=1.4301073203138195, m0=tensor([17.2245, 15.4737, 1.8498, 18.8678, 19.7984, 2.6436],
dtype=torch.float64, requires_grad=True), sqrt_diag_V0=tensor([ 1.2740e+02, -1.0110e+01, 1.6014e-01, 1.9403e+02, -7.8608e+01,
4.2573e-02], dtype=torch.float64, requires_grad=True)
--------------------------------------------------------------------------------
epoch: 29
likelihood: -150.22891217808984
sigma_a:
tensor([29.5699], dtype=torch.float64, requires_grad=True)
pos_x_R_std:
tensor([0.1348], dtype=torch.float64, requires_grad=True)
pos_y_R_std:
tensor([1.4301], dtype=torch.float64, requires_grad=True)
m0:
tensor([17.2245, 15.4737, 1.8498, 18.8678, 19.7984, 2.6436],
dtype=torch.float64, requires_grad=True)
sqrt_diag_V0:
tensor([ 1.2740e+02, -1.0110e+01, 1.6014e-01, 1.9403e+02, -7.8608e+01,
4.2573e-02], dtype=torch.float64, requires_grad=True)
ll=-150.22891217808984, sigma_a=29.5698747454269, pos_x_R_std=0.13483231718720412, pos_y_R_std=1.4301073203138195, m0=tensor([17.2245, 15.4737, 1.8498, 18.8678, 19.7984, 2.6436],
dtype=torch.float64, requires_grad=True), sqrt_diag_V0=tensor([ 1.2740e+02, -1.0110e+01, 1.6014e-01, 1.9403e+02, -7.8608e+01,
4.2573e-02], dtype=torch.float64, requires_grad=True)
ll=-128.56331202099318, sigma_a=47.91344450724506, pos_x_R_std=0.08457435945717082, pos_y_R_std=-2.0479485583659245, m0=tensor([29.0934, 25.6369, 3.0784, 31.8308, 33.3415, 4.3469],
dtype=torch.float64, requires_grad=True), sqrt_diag_V0=tensor([ 2.0695e+02, -1.6500e+01, 1.9701e-01, 3.1674e+02, -1.3290e+02,
-7.6213e-03], dtype=torch.float64, requires_grad=True)
--------------------------------------------------------------------------------
epoch: 30
likelihood: -128.56331202099318
sigma_a:
tensor([47.9134], dtype=torch.float64, requires_grad=True)
pos_x_R_std:
tensor([0.0846], dtype=torch.float64, requires_grad=True)
pos_y_R_std:
tensor([-2.0479], dtype=torch.float64, requires_grad=True)
m0:
tensor([29.0934, 25.6369, 3.0784, 31.8308, 33.3415, 4.3469],
dtype=torch.float64, requires_grad=True)
sqrt_diag_V0:
tensor([ 2.0695e+02, -1.6500e+01, 1.9701e-01, 3.1674e+02, -1.3290e+02,
-7.6213e-03], dtype=torch.float64, requires_grad=True)
ll=-128.56331202099318, sigma_a=47.91344450724506, pos_x_R_std=0.08457435945717082, pos_y_R_std=-2.0479485583659245, m0=tensor([29.0934, 25.6369, 3.0784, 31.8308, 33.3415, 4.3469],
dtype=torch.float64, requires_grad=True), sqrt_diag_V0=tensor([ 2.0695e+02, -1.6500e+01, 1.9701e-01, 3.1674e+02, -1.3290e+02,
-7.6213e-03], dtype=torch.float64, requires_grad=True)
ll=-123.0320870742048, sigma_a=42.53172095314036, pos_x_R_std=0.12147851202649429, pos_y_R_std=-0.9173407591729674, m0=tensor([25.5922, 22.6375, 2.7158, 28.0072, 29.3479, 3.8459],
dtype=torch.float64, requires_grad=True), sqrt_diag_V0=tensor([ 1.8354e+02, -1.4619e+01, 1.8612e-01, 2.8058e+02, -1.1689e+02,
7.1597e-03], dtype=torch.float64, requires_grad=True)
ll=-120.55422824591385, sigma_a=44.19777802025397, pos_x_R_std=0.11005384043646704, pos_y_R_std=-1.2673507689852532, m0=tensor([26.6761, 23.5661, 2.8281, 29.1909, 30.5842, 4.0010],
dtype=torch.float64, requires_grad=True), sqrt_diag_V0=tensor([ 1.9079e+02, -1.5201e+01, 1.8949e-01, 2.9178e+02, -1.2185e+02,
2.5839e-03], dtype=torch.float64, requires_grad=True)
--------------------------------------------------------------------------------
epoch: 31
likelihood: -120.55422824591385
sigma_a:
tensor([44.1978], dtype=torch.float64, requires_grad=True)
pos_x_R_std:
tensor([0.1101], dtype=torch.float64, requires_grad=True)
pos_y_R_std:
tensor([-1.2674], dtype=torch.float64, requires_grad=True)
m0:
tensor([26.6761, 23.5661, 2.8281, 29.1909, 30.5842, 4.0010],
dtype=torch.float64, requires_grad=True)
sqrt_diag_V0:
tensor([ 1.9079e+02, -1.5201e+01, 1.8949e-01, 2.9178e+02, -1.2185e+02,
2.5839e-03], dtype=torch.float64, requires_grad=True)
ll=-120.55422824591385, sigma_a=44.19777802025397, pos_x_R_std=0.11005384043646704, pos_y_R_std=-1.2673507689852532, m0=tensor([26.6761, 23.5661, 2.8281, 29.1909, 30.5842, 4.0010],
dtype=torch.float64, requires_grad=True), sqrt_diag_V0=tensor([ 1.9079e+02, -1.5201e+01, 1.8949e-01, 2.9178e+02, -1.2185e+02,
2.5839e-03], dtype=torch.float64, requires_grad=True)
ll=-124.97495164899436, sigma_a=43.361429607294816, pos_x_R_std=0.10331130687354928, pos_y_R_std=-0.7826698674308084, m0=tensor([26.1215, 23.1048, 2.7714, 28.5866, 29.9560, 3.9276],
dtype=torch.float64, requires_grad=True), sqrt_diag_V0=tensor([ 1.8724e+02, -1.4923e+01, 1.8787e-01, 2.8618e+02, -1.1934e+02,
4.8147e-03], dtype=torch.float64, requires_grad=True)
ll=-120.13707669876071, sigma_a=43.91930369596836, pos_x_R_std=0.10780881617527044, pos_y_R_std=-1.1059692389157907, m0=tensor([26.4915, 23.4125, 2.8092, 28.9897, 30.3750, 3.9766],
dtype=torch.float64, requires_grad=True), sqrt_diag_V0=tensor([ 1.8961e+02, -1.5108e+01, 1.8895e-01, 2.8991e+02, -1.2101e+02,
3.3266e-03], dtype=torch.float64, requires_grad=True)
--------------------------------------------------------------------------------
epoch: 32
likelihood: -120.13707669876071
sigma_a:
tensor([43.9193], dtype=torch.float64, requires_grad=True)
pos_x_R_std:
tensor([0.1078], dtype=torch.float64, requires_grad=True)
pos_y_R_std:
tensor([-1.1060], dtype=torch.float64, requires_grad=True)
m0:
tensor([26.4915, 23.4125, 2.8092, 28.9897, 30.3750, 3.9766],
dtype=torch.float64, requires_grad=True)
sqrt_diag_V0:
tensor([ 1.8961e+02, -1.5108e+01, 1.8895e-01, 2.8991e+02, -1.2101e+02,
3.3266e-03], dtype=torch.float64, requires_grad=True)
ll=-120.13707669876071, sigma_a=43.91930369596836, pos_x_R_std=0.10780881617527044, pos_y_R_std=-1.1059692389157907, m0=tensor([26.4915, 23.4125, 2.8092, 28.9897, 30.3750, 3.9766],
dtype=torch.float64, requires_grad=True), sqrt_diag_V0=tensor([ 1.8961e+02, -1.5108e+01, 1.8895e-01, 2.8991e+02, -1.2101e+02,
3.3266e-03], dtype=torch.float64, requires_grad=True)
ll=-118.17218549398713, sigma_a=45.5920377934972, pos_x_R_std=0.1050403906530122, pos_y_R_std=-1.1127352995430793, m0=tensor([27.5537, 24.3319, 2.9197, 30.1511, 31.5913, 4.1344],
dtype=torch.float64, requires_grad=True), sqrt_diag_V0=tensor([ 1.9689e+02, -1.5698e+01, 1.9233e-01, 3.0102e+02, -1.2590e+02,
-1.2716e-03], dtype=torch.float64, requires_grad=True)
--------------------------------------------------------------------------------
epoch: 33
likelihood: -118.17218549398713
sigma_a:
tensor([45.5920], dtype=torch.float64, requires_grad=True)
pos_x_R_std:
tensor([0.1050], dtype=torch.float64, requires_grad=True)
pos_y_R_std:
tensor([-1.1127], dtype=torch.float64, requires_grad=True)
m0:
tensor([27.5537, 24.3319, 2.9197, 30.1511, 31.5913, 4.1344],
dtype=torch.float64, requires_grad=True)
sqrt_diag_V0:
tensor([ 1.9689e+02, -1.5698e+01, 1.9233e-01, 3.0102e+02, -1.2590e+02,
-1.2716e-03], dtype=torch.float64, requires_grad=True)
ll=-118.17218549398713, sigma_a=45.5920377934972, pos_x_R_std=0.1050403906530122, pos_y_R_std=-1.1127352995430793, m0=tensor([27.5537, 24.3319, 2.9197, 30.1511, 31.5913, 4.1344],
dtype=torch.float64, requires_grad=True), sqrt_diag_V0=tensor([ 1.9689e+02, -1.5698e+01, 1.9233e-01, 3.0102e+02, -1.2590e+02,
-1.2716e-03], dtype=torch.float64, requires_grad=True)
ll=-104.33533277223155, sigma_a=63.09503315804713, pos_x_R_std=0.08659647616457454, pos_y_R_std=-0.8984552915078041, m0=tensor([38.6450, 33.9389, 4.0741, 42.2783, 44.2941, 5.7879],
dtype=torch.float64, requires_grad=True), sqrt_diag_V0=tensor([ 2.7305e+02, -2.1869e+01, 2.2766e-01, 4.1711e+02, -1.7694e+02,
-4.9377e-02], dtype=torch.float64, requires_grad=True)
--------------------------------------------------------------------------------
epoch: 34
likelihood: -104.33533277223155
sigma_a:
tensor([63.0950], dtype=torch.float64, requires_grad=True)
pos_x_R_std:
tensor([0.0866], dtype=torch.float64, requires_grad=True)
pos_y_R_std:
tensor([-0.8985], dtype=torch.float64, requires_grad=True)
m0:
tensor([38.6450, 33.9389, 4.0741, 42.2783, 44.2941, 5.7879],
dtype=torch.float64, requires_grad=True)
sqrt_diag_V0:
tensor([ 2.7305e+02, -2.1869e+01, 2.2766e-01, 4.1711e+02, -1.7694e+02,
-4.9377e-02], dtype=torch.float64, requires_grad=True)
ll=-104.33533277223155, sigma_a=63.09503315804713, pos_x_R_std=0.08659647616457454, pos_y_R_std=-0.8984552915078041, m0=tensor([38.6450, 33.9389, 4.0741, 42.2783, 44.2941, 5.7879],
dtype=torch.float64, requires_grad=True), sqrt_diag_V0=tensor([ 2.7305e+02, -2.1869e+01, 2.2766e-01, 4.1711e+02, -1.7694e+02,
-4.9377e-02], dtype=torch.float64, requires_grad=True)
ll=-95.62930362325272, sigma_a=79.82655176770538, pos_x_R_std=0.09277195281666355, pos_y_R_std=-0.7874243721436601, m0=tensor([49.2385, 43.1059, 5.1761, 53.8607, 56.4254, 7.3648],
dtype=torch.float64, requires_grad=True), sqrt_diag_V0=tensor([ 3.4574e+02, -2.7755e+01, 2.6133e-01, 5.2795e+02, -2.2567e+02,
-9.5278e-02], dtype=torch.float64, requires_grad=True)
--------------------------------------------------------------------------------
epoch: 35
likelihood: -95.62930362325272
sigma_a:
tensor([79.8266], dtype=torch.float64, requires_grad=True)
pos_x_R_std:
tensor([0.0928], dtype=torch.float64, requires_grad=True)
pos_y_R_std:
tensor([-0.7874], dtype=torch.float64, requires_grad=True)
m0:
tensor([49.2385, 43.1059, 5.1761, 53.8607, 56.4254, 7.3648],
dtype=torch.float64, requires_grad=True)
sqrt_diag_V0:
tensor([ 3.4574e+02, -2.7755e+01, 2.6133e-01, 5.2795e+02, -2.2567e+02,
-9.5278e-02], dtype=torch.float64, requires_grad=True)
ll=-95.62930362325272, sigma_a=79.82655176770538, pos_x_R_std=0.09277195281666355, pos_y_R_std=-0.7874243721436601, m0=tensor([49.2385, 43.1059, 5.1761, 53.8607, 56.4254, 7.3648],
dtype=torch.float64, requires_grad=True), sqrt_diag_V0=tensor([ 3.4574e+02, -2.7755e+01, 2.6133e-01, 5.2795e+02, -2.2567e+02,
-9.5278e-02], dtype=torch.float64, requires_grad=True)
ll=-87.79560465369661, sigma_a=132.14156166338873, pos_x_R_std=0.07975240598198552, pos_y_R_std=-0.08773900228658738, m0=tensor([82.3594, 71.7865, 8.6229, 90.0752, 94.3596, 12.3026],
dtype=torch.float64, requires_grad=True), sqrt_diag_V0=tensor([ 5.7320e+02, -4.6181e+01, 3.6676e-01, 8.7464e+02, -3.7808e+02,
-2.3893e-01], dtype=torch.float64, requires_grad=True)
ll=-78.59551191328201, sigma_a=114.89521203002332, pos_x_R_std=0.08404447545165718, pos_y_R_std=-0.318399735142558, m0=tensor([71.4407, 62.3315, 7.4866, 78.1366, 81.8541, 10.6748],
dtype=torch.float64, requires_grad=True), sqrt_diag_V0=tensor([ 4.9821e+02, -4.0107e+01, 3.3200e-01, 7.6034e+02, -3.2784e+02,
-1.9157e-01], dtype=torch.float64, requires_grad=True)
ll=-75.5173950925675, sigma_a=124.90968261949745, pos_x_R_std=0.08155219132279722, pos_y_R_std=-0.18446152940980615, m0=tensor([77.7809, 67.8217, 8.1464, 85.0690, 89.1157, 11.6200],
dtype=torch.float64, requires_grad=True), sqrt_diag_V0=tensor([ 5.4176e+02, -4.3634e+01, 3.5218e-01, 8.2671e+02, -3.5701e+02,
-2.1907e-01], dtype=torch.float64, requires_grad=True)
--------------------------------------------------------------------------------
epoch: 36
likelihood: -75.5173950925675
sigma_a:
tensor([124.9097], dtype=torch.float64, requires_grad=True)
pos_x_R_std:
tensor([0.0816], dtype=torch.float64, requires_grad=True)
pos_y_R_std:
tensor([-0.1845], dtype=torch.float64, requires_grad=True)
m0:
tensor([77.7809, 67.8217, 8.1464, 85.0690, 89.1157, 11.6200],
dtype=torch.float64, requires_grad=True)
sqrt_diag_V0:
tensor([ 5.4176e+02, -4.3634e+01, 3.5218e-01, 8.2671e+02, -3.5701e+02,
-2.1907e-01], dtype=torch.float64, requires_grad=True)
ll=-75.5173950925675, sigma_a=124.90968261949745, pos_x_R_std=0.08155219132279722, pos_y_R_std=-0.18446152940980615, m0=tensor([77.7809, 67.8217, 8.1464, 85.0690, 89.1157, 11.6200],
dtype=torch.float64, requires_grad=True), sqrt_diag_V0=tensor([ 5.4176e+02, -4.3634e+01, 3.5218e-01, 8.2671e+02, -3.5701e+02,
-2.1907e-01], dtype=torch.float64, requires_grad=True)
ll=-55.761944226306, sigma_a=229.18311955796196, pos_x_R_std=0.04988448296175818, pos_y_R_std=0.27735963327432794, m0=tensor([143.8545, 125.0056, 15.0206, 157.3102, 164.7782, 21.4532],
dtype=torch.float64, requires_grad=True), sqrt_diag_V0=tensor([ 9.9503e+02, -8.0339e+01, 5.6227e-01, 1.5179e+03, -6.6097e+02,
-5.0532e-01], dtype=torch.float64, requires_grad=True)
--------------------------------------------------------------------------------
epoch: 37
likelihood: -55.761944226306
sigma_a:
tensor([229.1831], dtype=torch.float64, requires_grad=True)
pos_x_R_std:
tensor([0.0499], dtype=torch.float64, requires_grad=True)
pos_y_R_std:
tensor([0.2774], dtype=torch.float64, requires_grad=True)
m0:
tensor([143.8545, 125.0056, 15.0206, 157.3102, 164.7782, 21.4532],
dtype=torch.float64, requires_grad=True)
sqrt_diag_V0:
tensor([ 9.9503e+02, -8.0339e+01, 5.6227e-01, 1.5179e+03, -6.6097e+02,
-5.0532e-01], dtype=torch.float64, requires_grad=True)
ll=-55.761944226306, sigma_a=229.18311955796196, pos_x_R_std=0.04988448296175818, pos_y_R_std=0.27735963327432794, m0=tensor([143.8545, 125.0056, 15.0206, 157.3102, 164.7782, 21.4532],
dtype=torch.float64, requires_grad=True), sqrt_diag_V0=tensor([ 9.9503e+02, -8.0339e+01, 5.6227e-01, 1.5179e+03, -6.6097e+02,
-5.0532e-01], dtype=torch.float64, requires_grad=True)
ll=-57.1130647333998, sigma_a=206.3852928619817, pos_x_R_std=0.06952602120669439, pos_y_R_std=-0.30048063622517024, m0=tensor([129.4286, 112.5009, 13.5186, 141.5358, 148.2522, 19.2972],
dtype=torch.float64, requires_grad=True), sqrt_diag_V0=tensor([ 8.9581e+02, -7.2296e+01, 5.1625e-01, 1.3668e+03, -5.9457e+02,
-4.4265e-01], dtype=torch.float64, requires_grad=True)
ll=-238.95221768454132, sigma_a=218.707131625971, pos_x_R_std=0.05891010283174217, pos_y_R_std=0.011832231446920286, m0=tensor([137.2255, 119.2595, 14.3304, 150.0616, 157.1842, 20.4625],
dtype=torch.float64, requires_grad=True), sqrt_diag_V0=tensor([ 9.4943e+02, -7.6643e+01, 5.4112e-01, 1.4485e+03, -6.3046e+02,
-4.7652e-01], dtype=torch.float64, requires_grad=True)
ll=-46.13312259302397, sigma_a=222.42277339687192, pos_x_R_std=0.05570888014850713, pos_y_R_std=0.10600995596833532, m0=tensor([139.5767, 121.2976, 14.5752, 152.6325, 159.8777, 20.8139],
dtype=torch.float64, requires_grad=True), sqrt_diag_V0=tensor([ 9.6561e+02, -7.7954e+01, 5.4862e-01, 1.4731e+03, -6.4128e+02,
-4.8674e-01], dtype=torch.float64, requires_grad=True)
--------------------------------------------------------------------------------
epoch: 38
likelihood: -46.13312259302397
sigma_a:
tensor([222.4228], dtype=torch.float64, requires_grad=True)
pos_x_R_std:
tensor([0.0557], dtype=torch.float64, requires_grad=True)
pos_y_R_std:
tensor([0.1060], dtype=torch.float64, requires_grad=True)
m0:
tensor([139.5767, 121.2976, 14.5752, 152.6325, 159.8777, 20.8139],
dtype=torch.float64, requires_grad=True)
sqrt_diag_V0:
tensor([ 9.6561e+02, -7.7954e+01, 5.4862e-01, 1.4731e+03, -6.4128e+02,
-4.8674e-01], dtype=torch.float64, requires_grad=True)
ll=-46.13312259302397, sigma_a=222.42277339687192, pos_x_R_std=0.05570888014850713, pos_y_R_std=0.10600995596833532, m0=tensor([139.5767, 121.2976, 14.5752, 152.6325, 159.8777, 20.8139],
dtype=torch.float64, requires_grad=True), sqrt_diag_V0=tensor([ 9.6561e+02, -7.7954e+01, 5.4862e-01, 1.4731e+03, -6.4128e+02,
-4.8674e-01], dtype=torch.float64, requires_grad=True)
ll=-45.77948959116562, sigma_a=244.56228800562798, pos_x_R_std=0.07828247797814959, pos_y_R_std=0.1863680596281236, m0=tensor([153.5895, 133.4178, 16.0326, 167.9532, 175.9239, 22.8984],
dtype=torch.float64, requires_grad=True), sqrt_diag_V0=tensor([ 1.0617e+03, -8.5735e+01, 5.9311e-01, 1.6197e+03, -7.0574e+02,
-5.4742e-01], dtype=torch.float64, requires_grad=True)
--------------------------------------------------------------------------------
epoch: 39
likelihood: -45.77948959116562
sigma_a:
tensor([244.5623], dtype=torch.float64, requires_grad=True)
pos_x_R_std:
tensor([0.0783], dtype=torch.float64, requires_grad=True)
pos_y_R_std:
tensor([0.1864], dtype=torch.float64, requires_grad=True)
m0:
tensor([153.5895, 133.4178, 16.0326, 167.9532, 175.9239, 22.8984],
dtype=torch.float64, requires_grad=True)
sqrt_diag_V0:
tensor([ 1.0617e+03, -8.5735e+01, 5.9311e-01, 1.6197e+03, -7.0574e+02,
-5.4742e-01], dtype=torch.float64, requires_grad=True)
ll=-45.77948959116562, sigma_a=244.56228800562798, pos_x_R_std=0.07828247797814959, pos_y_R_std=0.1863680596281236, m0=tensor([153.5895, 133.4178, 16.0326, 167.9532, 175.9239, 22.8984],
dtype=torch.float64, requires_grad=True), sqrt_diag_V0=tensor([ 1.0617e+03, -8.5735e+01, 5.9311e-01, 1.6197e+03, -7.0574e+02,
-5.4742e-01], dtype=torch.float64, requires_grad=True)
ll=-41.08393330605275, sigma_a=257.8123300506661, pos_x_R_std=0.07441222964122243, pos_y_R_std=0.13327077032141918, m0=tensor([161.9918, 140.6856, 16.9066, 177.1394, 185.5440, 24.1468],
dtype=torch.float64, requires_grad=True), sqrt_diag_V0=tensor([ 1.1193e+03, -9.0396e+01, 6.1980e-01, 1.7076e+03, -7.4439e+02,
-5.8379e-01], dtype=torch.float64, requires_grad=True)
--------------------------------------------------------------------------------
epoch: 40
likelihood: -41.08393330605275
sigma_a:
tensor([257.8123], dtype=torch.float64, requires_grad=True)
pos_x_R_std:
tensor([0.0744], dtype=torch.float64, requires_grad=True)
pos_y_R_std:
tensor([0.1333], dtype=torch.float64, requires_grad=True)
m0:
tensor([161.9918, 140.6856, 16.9066, 177.1394, 185.5440, 24.1468],
dtype=torch.float64, requires_grad=True)
sqrt_diag_V0:
tensor([ 1.1193e+03, -9.0396e+01, 6.1980e-01, 1.7076e+03, -7.4439e+02,
-5.8379e-01], dtype=torch.float64, requires_grad=True)
ll=-41.08393330605275, sigma_a=257.8123300506661, pos_x_R_std=0.07441222964122243, pos_y_R_std=0.13327077032141918, m0=tensor([161.9918, 140.6856, 16.9066, 177.1394, 185.5440, 24.1468],
dtype=torch.float64, requires_grad=True), sqrt_diag_V0=tensor([ 1.1193e+03, -9.0396e+01, 6.1980e-01, 1.7076e+03, -7.4439e+02,
-5.8379e-01], dtype=torch.float64, requires_grad=True)
ll=-214.28630203764487, sigma_a=308.9968149989999, pos_x_R_std=0.057501200348976385, pos_y_R_std=0.009745853616064226, m0=tensor([194.4460, 168.7612, 20.2824, 212.6215, 222.7033, 28.9702],
dtype=torch.float64, requires_grad=True), sqrt_diag_V0=tensor([ 1.3418e+03, -1.0840e+02, 7.2289e-01, 2.0469e+03, -8.9365e+02,
-7.2427e-01], dtype=torch.float64, requires_grad=True)
ll=-42.33751995177726, sigma_a=290.0794154659185, pos_x_R_std=0.06375138920913558, pos_y_R_std=0.055399731035453426, m0=tensor([182.4511, 158.3847, 19.0347, 199.5076, 208.9695, 27.1875],
dtype=torch.float64, requires_grad=True), sqrt_diag_V0=tensor([ 1.2595e+03, -1.0175e+02, 6.8479e-01, 1.9215e+03, -8.3849e+02,
-6.7235e-01], dtype=torch.float64, requires_grad=True)
ll=-38.94198460474341, sigma_a=275.6126780408463, pos_x_R_std=0.06853110752818437, pos_y_R_std=0.09031270392624456, m0=tensor([173.2783, 150.4494, 18.0806, 189.4789, 198.4668, 25.8242],
dtype=torch.float64, requires_grad=True), sqrt_diag_V0=tensor([ 1.1967e+03, -9.6658e+01, 6.5565e-01, 1.8256e+03, -7.9630e+02,
-6.3264e-01], dtype=torch.float64, requires_grad=True)
--------------------------------------------------------------------------------
epoch: 41
likelihood: -38.94198460474341
sigma_a:
tensor([275.6127], dtype=torch.float64, requires_grad=True)
pos_x_R_std:
tensor([0.0685], dtype=torch.float64, requires_grad=True)
pos_y_R_std:
tensor([0.0903], dtype=torch.float64, requires_grad=True)
m0:
tensor([173.2783, 150.4494, 18.0806, 189.4789, 198.4668, 25.8242],
dtype=torch.float64, requires_grad=True)
sqrt_diag_V0:
tensor([ 1.1967e+03, -9.6658e+01, 6.5565e-01, 1.8256e+03, -7.9630e+02,
-6.3264e-01], dtype=torch.float64, requires_grad=True)
ll=-38.94198460474341, sigma_a=275.6126780408463, pos_x_R_std=0.06853110752818437, pos_y_R_std=0.09031270392624456, m0=tensor([173.2783, 150.4494, 18.0806, 189.4789, 198.4668, 25.8242],
dtype=torch.float64, requires_grad=True), sqrt_diag_V0=tensor([ 1.1967e+03, -9.6658e+01, 6.5565e-01, 1.8256e+03, -7.9630e+02,
-6.3264e-01], dtype=torch.float64, requires_grad=True)
ll=-36.26931118120439, sigma_a=302.12441355943184, pos_x_R_std=0.05723856362196606, pos_y_R_std=0.08488019941425716, m0=tensor([190.0865, 164.9926, 19.8291, 207.8556, 217.7126, 28.3234],
dtype=torch.float64, requires_grad=True), sqrt_diag_V0=tensor([ 1.3119e+03, -1.0599e+02, 7.0907e-01, 2.0014e+03, -8.7361e+02,
-7.0542e-01], dtype=torch.float64, requires_grad=True)
--------------------------------------------------------------------------------
epoch: 42
likelihood: -36.26931118120439
sigma_a:
tensor([302.1244], dtype=torch.float64, requires_grad=True)
pos_x_R_std:
tensor([0.0572], dtype=torch.float64, requires_grad=True)
pos_y_R_std:
tensor([0.0849], dtype=torch.float64, requires_grad=True)
m0:
tensor([190.0865, 164.9926, 19.8291, 207.8556, 217.7126, 28.3234],
dtype=torch.float64, requires_grad=True)
sqrt_diag_V0:
tensor([ 1.3119e+03, -1.0599e+02, 7.0907e-01, 2.0014e+03, -8.7361e+02,
-7.0542e-01], dtype=torch.float64, requires_grad=True)
ll=-36.26931118120439, sigma_a=302.12441355943184, pos_x_R_std=0.05723856362196606, pos_y_R_std=0.08488019941425716, m0=tensor([190.0865, 164.9926, 19.8291, 207.8556, 217.7126, 28.3234],
dtype=torch.float64, requires_grad=True), sqrt_diag_V0=tensor([ 1.3119e+03, -1.0599e+02, 7.0907e-01, 2.0014e+03, -8.7361e+02,
-7.0542e-01], dtype=torch.float64, requires_grad=True)
ll=-39.26596785168318, sigma_a=451.63838707322543, pos_x_R_std=0.01715199089509003, pos_y_R_std=0.037591109652872164, m0=tensor([284.8641, 246.9922, 29.6881, 311.4773, 326.2350, 42.4152],
dtype=torch.float64, requires_grad=True), sqrt_diag_V0=tensor([ 1.9617e+03, -1.5860e+02, 1.0102e+00, 2.9926e+03, -1.3096e+03,
-1.1158e+00], dtype=torch.float64, requires_grad=True)
ll=-31.257233392815955, sigma_a=390.24615743675486, pos_x_R_std=0.03361201814438529, pos_y_R_std=0.05700857672769899, m0=tensor([245.9473, 213.3222, 25.6399, 268.9290, 281.6744, 36.6289],
dtype=torch.float64, requires_grad=True), sqrt_diag_V0=tensor([ 1.6949e+03, -1.3700e+02, 8.8656e-01, 2.5856e+03, -1.1306e+03,
-9.4728e-01], dtype=torch.float64, requires_grad=True)
--------------------------------------------------------------------------------
epoch: 43
likelihood: -31.257233392815955
sigma_a:
tensor([390.2462], dtype=torch.float64, requires_grad=True)
pos_x_R_std:
tensor([0.0336], dtype=torch.float64, requires_grad=True)
pos_y_R_std:
tensor([0.0570], dtype=torch.float64, requires_grad=True)
m0:
tensor([245.9473, 213.3222, 25.6399, 268.9290, 281.6744, 36.6289],
dtype=torch.float64, requires_grad=True)
sqrt_diag_V0:
tensor([ 1.6949e+03, -1.3700e+02, 8.8656e-01, 2.5856e+03, -1.1306e+03,
-9.4728e-01], dtype=torch.float64, requires_grad=True)
ll=-31.257233392815955, sigma_a=390.24615743675486, pos_x_R_std=0.03361201814438529, pos_y_R_std=0.05700857672769899, m0=tensor([245.9473, 213.3222, 25.6399, 268.9290, 281.6744, 36.6289],
dtype=torch.float64, requires_grad=True), sqrt_diag_V0=tensor([ 1.6949e+03, -1.3700e+02, 8.8656e-01, 2.5856e+03, -1.1306e+03,
-9.4728e-01], dtype=torch.float64, requires_grad=True)
ll=-26.754694892115552, sigma_a=487.2457348712854, pos_x_R_std=0.03134052692130207, pos_y_R_std=0.06291893481448813, m0=tensor([307.4198, 266.5029, 32.0342, 336.1379, 352.0624, 45.7690],
dtype=torch.float64, requires_grad=True), sqrt_diag_V0=tensor([ 2.1164e+03, -1.7112e+02, 1.0818e+00, 3.2285e+03, -1.4133e+03,
-1.2134e+00], dtype=torch.float64, requires_grad=True)
--------------------------------------------------------------------------------
epoch: 44
likelihood: -26.754694892115552
sigma_a:
tensor([487.2457], dtype=torch.float64, requires_grad=True)
pos_x_R_std:
tensor([0.0313], dtype=torch.float64, requires_grad=True)
pos_y_R_std:
tensor([0.0629], dtype=torch.float64, requires_grad=True)
m0:
tensor([307.4198, 266.5029, 32.0342, 336.1379, 352.0624, 45.7690],
dtype=torch.float64, requires_grad=True)
sqrt_diag_V0:
tensor([ 2.1164e+03, -1.7112e+02, 1.0818e+00, 3.2285e+03, -1.4133e+03,
-1.2134e+00], dtype=torch.float64, requires_grad=True)
ll=-26.754694892115552, sigma_a=487.2457348712854, pos_x_R_std=0.03134052692130207, pos_y_R_std=0.06291893481448813, m0=tensor([307.4198, 266.5029, 32.0342, 336.1379, 352.0624, 45.7690],
dtype=torch.float64, requires_grad=True), sqrt_diag_V0=tensor([ 2.1164e+03, -1.7112e+02, 1.0818e+00, 3.2285e+03, -1.4133e+03,
-1.2134e+00], dtype=torch.float64, requires_grad=True)
ll=-29.907157979945016, sigma_a=574.2794743734719, pos_x_R_std=0.031996967015306896, pos_y_R_std=0.033106720589132194, m0=tensor([362.5771, 314.2183, 37.7715, 396.4421, 415.2187, 53.9694],
dtype=torch.float64, requires_grad=True), sqrt_diag_V0=tensor([ 2.4945e+03, -2.0173e+02, 1.2571e+00, 3.8054e+03, -1.6670e+03,
-1.4522e+00], dtype=torch.float64, requires_grad=True)
ll=-25.98703100358798, sigma_a=525.8315172324711, pos_x_R_std=0.03163155491510429, pos_y_R_std=0.049701904081530496, m0=tensor([331.8734, 287.6572, 34.5778, 362.8734, 380.0623, 49.4046],
dtype=torch.float64, requires_grad=True), sqrt_diag_V0=tensor([ 2.2840e+03, -1.8469e+02, 1.1595e+00, 3.4843e+03, -1.5258e+03,
-1.3193e+00], dtype=torch.float64, requires_grad=True)
--------------------------------------------------------------------------------
epoch: 45
likelihood: -25.98703100358798
sigma_a:
tensor([525.8315], dtype=torch.float64, requires_grad=True)
pos_x_R_std:
tensor([0.0316], dtype=torch.float64, requires_grad=True)
pos_y_R_std:
tensor([0.0497], dtype=torch.float64, requires_grad=True)
m0:
tensor([331.8734, 287.6572, 34.5778, 362.8734, 380.0623, 49.4046],
dtype=torch.float64, requires_grad=True)
sqrt_diag_V0:
tensor([ 2.2840e+03, -1.8469e+02, 1.1595e+00, 3.4843e+03, -1.5258e+03,
-1.3193e+00], dtype=torch.float64, requires_grad=True)
ll=-25.98703100358798, sigma_a=525.8315172324711, pos_x_R_std=0.03163155491510429, pos_y_R_std=0.049701904081530496, m0=tensor([331.8734, 287.6572, 34.5778, 362.8734, 380.0623, 49.4046],
dtype=torch.float64, requires_grad=True), sqrt_diag_V0=tensor([ 2.2840e+03, -1.8469e+02, 1.1595e+00, 3.4843e+03, -1.5258e+03,
-1.3193e+00], dtype=torch.float64, requires_grad=True)
ll=-25.74660611312993, sigma_a=541.3702650874316, pos_x_R_std=0.03273641171585284, pos_y_R_std=0.05361745732584272, m0=tensor([341.7199, 296.1752, 35.6020, 373.6387, 391.3368, 50.8687],
dtype=torch.float64, requires_grad=True), sqrt_diag_V0=tensor([ 2.3515e+03, -1.9015e+02, 1.1908e+00, 3.5872e+03, -1.5711e+03,
-1.3619e+00], dtype=torch.float64, requires_grad=True)
--------------------------------------------------------------------------------
epoch: 46
likelihood: -25.74660611312993
sigma_a:
tensor([541.3703], dtype=torch.float64, requires_grad=True)
pos_x_R_std:
tensor([0.0327], dtype=torch.float64, requires_grad=True)
pos_y_R_std:
tensor([0.0536], dtype=torch.float64, requires_grad=True)
m0:
tensor([341.7199, 296.1752, 35.6020, 373.6387, 391.3368, 50.8687],
dtype=torch.float64, requires_grad=True)
sqrt_diag_V0:
tensor([ 2.3515e+03, -1.9015e+02, 1.1908e+00, 3.5872e+03, -1.5711e+03,
-1.3619e+00], dtype=torch.float64, requires_grad=True)
ll=-25.74660611312993, sigma_a=541.3702650874316, pos_x_R_std=0.03273641171585284, pos_y_R_std=0.05361745732584272, m0=tensor([341.7199, 296.1752, 35.6020, 373.6387, 391.3368, 50.8687],
dtype=torch.float64, requires_grad=True), sqrt_diag_V0=tensor([ 2.3515e+03, -1.9015e+02, 1.1908e+00, 3.5872e+03, -1.5711e+03,
-1.3619e+00], dtype=torch.float64, requires_grad=True)
ll=-25.693122787594945, sigma_a=565.5208481607478, pos_x_R_std=0.030261452563859335, pos_y_R_std=0.05255148050280519, m0=tensor([357.0263, 309.4173, 37.1941, 390.3734, 408.8631, 53.1445],
dtype=torch.float64, requires_grad=True), sqrt_diag_V0=tensor([ 2.4565e+03, -1.9865e+02, 1.2394e+00, 3.7473e+03, -1.6415e+03,
-1.4282e+00], dtype=torch.float64, requires_grad=True)
--------------------------------------------------------------------------------
epoch: 47
likelihood: -25.693122787594945
sigma_a:
tensor([565.5208], dtype=torch.float64, requires_grad=True)
pos_x_R_std:
tensor([0.0303], dtype=torch.float64, requires_grad=True)
pos_y_R_std:
tensor([0.0526], dtype=torch.float64, requires_grad=True)
m0:
tensor([357.0263, 309.4173, 37.1941, 390.3734, 408.8631, 53.1445],
dtype=torch.float64, requires_grad=True)
sqrt_diag_V0:
tensor([ 2.4565e+03, -1.9865e+02, 1.2394e+00, 3.7473e+03, -1.6415e+03,
-1.4282e+00], dtype=torch.float64, requires_grad=True)
ll=-25.693122787594945, sigma_a=565.5208481607478, pos_x_R_std=0.030261452563859335, pos_y_R_std=0.05255148050280519, m0=tensor([357.0263, 309.4173, 37.1941, 390.3734, 408.8631, 53.1445],
dtype=torch.float64, requires_grad=True), sqrt_diag_V0=tensor([ 2.4565e+03, -1.9865e+02, 1.2394e+00, 3.7473e+03, -1.6415e+03,
-1.4282e+00], dtype=torch.float64, requires_grad=True)
ll=-25.684974135536745, sigma_a=564.296417589708, pos_x_R_std=0.03134897970936324, pos_y_R_std=0.052301325936117395, m0=tensor([356.2497, 308.7452, 37.1133, 389.5243, 407.9739, 53.0290],
dtype=torch.float64, requires_grad=True), sqrt_diag_V0=tensor([ 2.4512e+03, -1.9822e+02, 1.2370e+00, 3.7392e+03, -1.6379e+03,
-1.4248e+00], dtype=torch.float64, requires_grad=True)
--------------------------------------------------------------------------------
epoch: 48
likelihood: -25.684974135536745
sigma_a:
tensor([564.2964], dtype=torch.float64, requires_grad=True)
pos_x_R_std:
tensor([0.0313], dtype=torch.float64, requires_grad=True)
pos_y_R_std:
tensor([0.0523], dtype=torch.float64, requires_grad=True)
m0:
tensor([356.2497, 308.7452, 37.1133, 389.5243, 407.9739, 53.0290],
dtype=torch.float64, requires_grad=True)
sqrt_diag_V0:
tensor([ 2.4512e+03, -1.9822e+02, 1.2370e+00, 3.7392e+03, -1.6379e+03,
-1.4248e+00], dtype=torch.float64, requires_grad=True)
ll=-25.684974135536745, sigma_a=564.296417589708, pos_x_R_std=0.03134897970936324, pos_y_R_std=0.052301325936117395, m0=tensor([356.2497, 308.7452, 37.1133, 389.5243, 407.9739, 53.0290],
dtype=torch.float64, requires_grad=True), sqrt_diag_V0=tensor([ 2.4512e+03, -1.9822e+02, 1.2370e+00, 3.7392e+03, -1.6379e+03,
-1.4248e+00], dtype=torch.float64, requires_grad=True)
ll=-25.684440364580713, sigma_a=563.581055913467, pos_x_R_std=0.03119064976734833, pos_y_R_std=0.05243528783872346, m0=tensor([355.7964, 308.3531, 37.0662, 389.0287, 407.4548, 52.9616],
dtype=torch.float64, requires_grad=True), sqrt_diag_V0=tensor([ 2.4481e+03, -1.9797e+02, 1.2355e+00, 3.7345e+03, -1.6358e+03,
-1.4229e+00], dtype=torch.float64, requires_grad=True)
--------------------------------------------------------------------------------
epoch: 49
likelihood: -25.684440364580713
sigma_a:
tensor([563.5811], dtype=torch.float64, requires_grad=True)
pos_x_R_std:
tensor([0.0312], dtype=torch.float64, requires_grad=True)
pos_y_R_std:
tensor([0.0524], dtype=torch.float64, requires_grad=True)
m0:
tensor([355.7964, 308.3531, 37.0662, 389.0287, 407.4548, 52.9616],
dtype=torch.float64, requires_grad=True)
sqrt_diag_V0:
tensor([ 2.4481e+03, -1.9797e+02, 1.2355e+00, 3.7345e+03, -1.6358e+03,
-1.4229e+00], dtype=torch.float64, requires_grad=True)
gradient ascent: success: converged
Perform EM optimization
sqrt_diag_R = np.array([sigma_x0, sigma_y0])
R_0 = np.diag(sqrt_diag_R)
m0_0 = m0
sqrt_diag_V0 = np.array([sqrt_diag_V0_value for i in range(len(m0))])
V0_0 = np.diag(sqrt_diag_V0)
times = np.arange(0, y.shape[1]*dt, dt)
not_nan_indices_y0 = set(np.where(np.logical_not(np.isnan(y[0, :])))[0])
not_nan_indices_y1 = set(np.where(np.logical_not(np.isnan(y[1, :])))[0])
not_nan_indices = np.array(sorted(not_nan_indices_y0.union(not_nan_indices_y1)))
y_no_nan = y[:, not_nan_indices]
t_no_nan = times[not_nan_indices]
y_interpolated = np.empty_like(y)
tck, u = scipy.interpolate.splprep([y_no_nan[0, :], y_no_nan[1, :]], s=0, u=t_no_nan)
y_interpolated[0, :], y_interpolated[1, :] = scipy.interpolate.splev(times, tck)
if Qe_reg_param_em is not None:
Qe_regularized_em = Qe + Qe_reg_param_em * np.eye(Qe.shape[0])
else:
Qe_regularized_em = Qe
optim_res_em = ssm.learning.em_SS_tracking(
y=y_interpolated, B=B, sigma_a0=sigma_a0,
Qe=Qe_regularized_em, Z=Z, R_0=R_0, m0_0=m0_0, V0_0=V0_0,
vars_to_estimate=vars_to_estimate,
max_iter=em_max_iter)
print("EM: " + optim_res_em["termination_info"])
LogLike[0000]=-1381440.889848
sigma_a=1.000000
R:
[[1. 0.]
[0. 1.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[0.1 0. 0. 0. 0. 0. ]
[0. 0.1 0. 0. 0. 0. ]
[0. 0. 0.1 0. 0. 0. ]
[0. 0. 0. 0.1 0. 0. ]
[0. 0. 0. 0. 0.1 0. ]
[0. 0. 0. 0. 0. 0.1]]
LogLike[0001]=-468.983233
sigma_a=15.498759
R:
[[ 2632.08266461 5451.9175971 ]
[ 5451.9175971 11390.85041816]]
m0:
[186.25895255 44.30023579 5.43377754 390.73095854 97.33426239
12.20335086]
V0:
[[ 0.03201735 -0.0160773 -0.00197267 0. 0. 0. ]
[-0.0160773 0.08961045 -0.00251776 0. 0. 0. ]
[-0.00197267 -0.00251776 0.09901842 0. 0. 0. ]
[ 0. 0. 0. 0.03201735 -0.0160773 -0.00197267]
[ 0. 0. 0. -0.0160773 0.08961045 -0.00251776]
[ 0. 0. 0. -0.00197267 -0.00251776 0.09901842]]
LogLike[0002]=-465.238407
sigma_a=15.680700
R:
[[ 3931.02599865 8087.00016226]
[ 8087.00016226 16717.67074932]]
m0:
[186.30939419 44.25647504 5.42942818 390.72029221 97.36680557
12.21036756]
V0:
[[ 3.14196609e-02 -1.60555858e-02 -1.95092312e-03 2.85630337e-04
-1.11251674e-05 -1.07340039e-05]
[-1.60555858e-02 8.95247919e-02 -2.53259505e-03 -1.11251674e-05
3.91920300e-05 6.19251534e-06]
[-1.95092312e-03 -2.53259505e-03 9.90134505e-02 -1.07340039e-05
6.19251534e-06 1.90506789e-06]
[ 2.85630337e-04 -1.11251674e-05 -1.07340039e-05 3.18785397e-02
-1.60734589e-02 -1.96816781e-03]
[-1.11251674e-05 3.91920300e-05 6.19251534e-06 -1.60734589e-02
8.95877558e-02 -2.52264648e-03]
[-1.07340039e-05 6.19251534e-06 1.90506789e-06 -1.96816781e-03
-2.52264648e-03 9.90165111e-02]]
LogLike[0003]=-464.700912
sigma_a=15.844083
R:
[[ 4127.30830729 8446.86793093]
[ 8446.86793093 17361.82965518]]
m0:
[186.35057479 44.20508546 5.42437781 390.70975568 97.40016282
12.21648708]
V0:
[[ 3.07646560e-02 -1.60195772e-02 -1.92526815e-03 6.02221600e-04
-2.90919212e-05 -2.33900055e-05]
[-1.60195772e-02 8.94324639e-02 -2.54830518e-03 -2.90932889e-05
8.25021060e-05 1.31102542e-05]
[-1.92526815e-03 -2.54830518e-03 9.90083395e-02 -2.33901902e-05
1.31102093e-05 4.02132530e-06]
[ 6.02221600e-04 -2.90932889e-05 -2.33901902e-05 3.17239049e-02
-1.60658546e-02 -1.96251683e-03]
[-2.90919212e-05 8.25021060e-05 1.31102093e-05 -1.60658546e-02
8.95639054e-02 -2.52741913e-03]
[-2.33900055e-05 1.31102542e-05 4.02132530e-06 -1.96251683e-03
-2.52741913e-03 9.90147459e-02]]
LogLike[0004]=-464.405936
sigma_a=16.034073
R:
[[ 4156.95679327 8480.16247418]
[ 8480.16247418 17370.86599603]]
m0:
[186.38421558 44.15133524 5.41940448 390.70242506 97.43451268
12.2224564 ]
V0:
[[ 3.01107018e-02 -1.59776466e-02 -1.89879389e-03 9.20212038e-04
-5.00269693e-05 -3.65116131e-05]
[-1.59776466e-02 8.93379127e-02 -2.56427284e-03 -5.00319421e-05
1.27190134e-04 2.02172933e-05]
[-1.89879389e-03 -2.56427284e-03 9.90032238e-02 -3.65122971e-05
2.02171287e-05 6.16473993e-06]
[ 9.20212038e-04 -5.00319421e-05 -3.65122971e-05 3.15677248e-02
-1.60567139e-02 -1.95658577e-03]
[-5.00269693e-05 1.27190134e-04 2.02171287e-05 -1.60567139e-02
8.95393679e-02 -2.53225255e-03]
[-3.65116131e-05 2.02172933e-05 6.16473993e-06 -1.95658577e-03
-2.53225255e-03 9.90129879e-02]]
LogLike[0005]=-464.178903
sigma_a=16.246166
R:
[[ 4161.13530659 8471.54219664]
[ 8471.54219664 17316.38112822]]
m0:
[186.41297246 44.09666302 5.41457071 390.69740069 97.46935796
12.22834372]
V0:
[[ 2.94759506e-02 -1.59327029e-02 -1.87249568e-03 1.22998362e-03
-7.25046314e-05 -4.95931245e-05]
[-1.59327029e-02 8.92428064e-02 -2.58023866e-03 -7.25155292e-05
1.72309964e-04 2.73521808e-05]
[-1.87249568e-03 -2.58023866e-03 9.89981692e-02 -4.95946386e-05
2.73518181e-05 8.28802166e-06]
[ 1.22998362e-03 -7.25155292e-05 -4.95946386e-05 3.14149979e-02
-1.60467762e-02 -1.95064783e-03]
[-7.25046314e-05 1.72309964e-04 2.73518181e-05 -1.60467762e-02
8.95145629e-02 -2.53710239e-03]
[-4.95931245e-05 2.73521808e-05 8.28802166e-06 -1.95064783e-03
-2.53710239e-03 9.90112408e-02]]
LogLike[0006]=-463.971029
sigma_a=16.475060
R:
[[ 4157.79978866 8453.45580889]
[ 8453.45580889 17255.20549193]]
m0:
[186.43878492 44.04164087 5.40985743 390.69379617 97.50440883
12.23416345]
V0:
[[ 2.88668099e-02 -1.58860618e-02 -1.84676664e-03 1.52793210e-03
-9.58615394e-05 -6.24249084e-05]
[-1.58860618e-02 8.91479237e-02 -2.59607835e-03 -9.58805279e-05
2.17421042e-04 3.44432327e-05]
[-1.84676664e-03 -2.59607835e-03 9.89932066e-02 -6.24275626e-05
3.44425978e-05 1.03721834e-05]
[ 1.52793210e-03 -9.58805279e-05 -6.24275626e-05 3.12677082e-02
-1.60363792e-02 -1.94481541e-03]
[-9.58615394e-05 2.17421042e-04 3.44425978e-05 -1.60363792e-02
8.94897252e-02 -2.54193284e-03]
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LogLike[0007]=-463.766151
sigma_a=16.717430
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LogLike[0008]=-463.558715
sigma_a=16.971457
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m0:
[186.48584935 43.9315167 5.40071597 390.68881144 97.57458315
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LogLike[0009]=-463.346620
sigma_a=17.236287
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LogLike[0010]=-463.128863
sigma_a=17.511664
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m0:
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LogLike[0011]=-462.904770
sigma_a=17.797707
R:
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m0:
[186.55174481 43.76741632 5.38756768 390.68367119 97.6792676
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[[ 2.62198517e-02 -1.56428882e-02 -1.72942129e-03 2.82673833e-03
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LogLike[0012]=-462.673736
sigma_a=18.094781
R:
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m0:
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LogLike[0013]=-462.435138
sigma_a=18.403423
R:
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m0:
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LogLike[0014]=-462.188301
sigma_a=18.724302
R:
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m0:
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LogLike[0015]=-461.932480
sigma_a=19.058200
R:
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m0:
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LogLike[0016]=-461.666843
sigma_a=19.406002
R:
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m0:
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LogLike[0017]=-461.390466
sigma_a=19.768697
R:
[[ 4021.94817817 8121.70243556]
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m0:
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LogLike[0018]=-461.102313
sigma_a=20.147386
R:
[[ 4006.29968796 8084.91247355]
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m0:
[186.69905827 43.39137635 5.35902048 390.67509524 97.91952541
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LogLike[0019]=-460.801224
sigma_a=20.543285
R:
[[ 3990.22622698 8047.07044281]
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m0:
[186.71979339 43.33834912 5.35515604 390.67405257 97.95340665
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LogLike[0020]=-460.485894
sigma_a=20.957739
R:
[[ 3973.72971625 8008.16297455]
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m0:
[186.74049871 43.2854583 5.35133904 390.67303158 97.98718964
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LogLike[0021]=-460.154855
sigma_a=21.392239
R:
[[ 3956.81430447 7968.18025328]
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m0:
[186.76119015 43.23268792 5.34756722 390.67202405 98.02087993
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LogLike[0022]=-459.806452
sigma_a=21.848433
R:
[[ 3939.48735512 7927.11749146]
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m0:
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LogLike[0023]=-459.438812
sigma_a=22.328151
R:
[[ 3921.76033194 7884.97631494]
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m0:
[186.802601 43.12743645 5.34014923 390.67001289 98.08800789
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V0:
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LogLike[0024]=-459.049815
sigma_a=22.833419
R:
[[ 3903.64977528 7841.76640495]
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m0:
[186.82335899 43.07491469 5.33649767 390.66898878 98.1214602
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V0:
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LogLike[0025]=-458.637059
sigma_a=23.366488
R:
[[ 3885.17828771 7797.50719764]
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m0:
[186.8441809 43.0224317 5.33288045 390.66793682 98.15484926
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[[ 2.12292216e-02 -1.49217826e-02 -1.47500200e-03 5.29229599e-03
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LogLike[0026]=-458.197818
sigma_a=23.929857
R:
[[ 3866.37559948 7752.22977717]
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m0:
[186.8650912 42.96996167 5.32929432 390.66684368 98.18818468
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[[ 2.09579074e-02 -1.48669480e-02 -1.45938304e-03 5.42756139e-03
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LogLike[0027]=-457.728996
sigma_a=24.526303
R:
[[ 3847.27969596 7705.97893051]
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m0:
[186.88611703 42.91747625 5.32573577 390.66569445 98.22147721
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LogLike[0028]=-457.227082
sigma_a=25.158906
R:
[[ 3827.93801813 7658.81540741]
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m0:
[186.90728863 42.86494424 5.322201 390.66447236 98.25473881
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[[ 2.04373416e-02 -1.47549785e-02 -1.42872013e-03 5.68777128e-03
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LogLike[0029]=-456.688097
sigma_a=25.831086
R:
[[ 3808.40864962 7610.81823873]
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m0:
[186.9286397 42.81233145 5.31868592 390.66315854 98.28798285
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[[ 2.01869829e-02 -1.46976533e-02 -1.41362690e-03 5.81328655e-03
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LogLike[0030]=-456.107540
sigma_a=26.546624
R:
[[ 3788.76146359 7562.0871058 ]
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m0:
[186.95020787 42.75960043 5.31518609 390.66173169 98.3212242
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LogLike[0031]=-455.480344
sigma_a=27.309699
R:
[[ 3769.07910891 7512.74457758]
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m0:
[186.97203518 42.70671028 5.31169677 390.66016784 98.3544794
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LogLike[0032]=-454.800838
sigma_a=28.124907
R:
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m0:
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LogLike[0033]=-454.062715
sigma_a=28.997277
R:
[[ 3730.00697287 7412.8407434 ]
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m0:
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LogLike[0034]=-453.259041
sigma_a=29.932281
R:
[[ 3710.84994247 7362.6526707 ]
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m0:
[187.03956669 42.54662152 5.30123917 390.65436707 98.45452118
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V0:
[[ 1.90135150e-02 -1.43925889e-02 -1.33950630e-03 6.40598535e-03
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LogLike[0035]=-452.382272
sigma_a=30.935824
R:
[[ 3692.12129342 7312.5988207 ]
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m0:
[187.06295275 42.49261277 5.2977376 390.65195026 98.48803491
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V0:
[[ 1.87909449e-02 -1.43267435e-02 -1.32475601e-03 6.51946606e-03
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LogLike[0036]=-451.424323
sigma_a=32.014232
R:
[[ 3673.96480471 7262.9264473 ]
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m0:
[187.08688731 42.43818545 5.29421788 390.64922535 98.52167446
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V0:
[[ 1.85712504e-02 -1.42588143e-02 -1.30996029e-03 6.63190879e-03
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LogLike[0037]=-450.376641
sigma_a=33.174216
R:
[[ 3656.52917384 7213.89933787]
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m0:
[187.11144577 42.38327691 5.2906735 390.64614616 98.5554688
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V0:
[[ 1.83539356e-02 -1.41885559e-02 -1.29508706e-03 6.74359830e-03
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LogLike[0038]=-449.230292
sigma_a=34.422847
R:
[[ 3639.96231427 7165.7892628 ]
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m0:
[187.13670955 42.32782106 5.2870978 390.64266212 98.58944942
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V0:
[[ 1.81385067e-02 -1.41157002e-02 -1.28010351e-03 6.85482280e-03
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LogLike[0039]=-447.976004
sigma_a=35.767534
R:
[[ 3624.4041785 7118.86434065]
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m0:
[187.16276642 42.27174809 5.28348394 390.63871794 98.62365062
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V0:
[[ 1.79244744e-02 -1.40399568e-02 -1.26497634e-03 6.96587342e-03
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LogLike[0040]=-446.604100
sigma_a=37.216038
R:
[[ 3609.97832197 7073.37432077]
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m0:
[187.18971124 42.21498373 5.2798249 390.63425307 98.65811019
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V0:
[[ 1.77113545e-02 -1.39610125e-02 -1.24967202e-03 7.07704361e-03
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LogLike[0041]=-445.104271
sigma_a=38.776542
R:
[[ 3596.78288426 7029.53376776]
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m0:
[187.21764772 42.15744749 5.2761133 390.62920064 98.69287037
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V0:
[[ 1.74986686e-02 -1.38785295e-02 -1.23415698e-03 7.18862905e-03
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LogLike[0073]=-361.376052
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LogLike[0075]=-360.070431
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6.00453029e-04 9.64035084e-05]
[ 1.27318013e-02 -6.03649174e-03 -8.33451548e-04 2.48334936e-02
-1.28813954e-02 -1.53883494e-03]
[-5.59724753e-03 7.76679184e-03 6.00453029e-04 -1.28813954e-02
8.52534634e-02 -2.91972159e-03]
[-8.16150806e-04 6.22443120e-04 9.64035084e-05 -1.53883494e-03
-2.91972159e-03 9.89316343e-02]]
LogLike[0199]=-346.871708
sigma_a=124.162705
R:
[[ 3143.89725994 5797.42180627]
[ 5797.42180627 10690.59025791]]
m0:
[190.74683915 35.12841032 5.02650043 390.08720559 102.85079316
12.57747815]
V0:
[[ 8.07402195e-03 -5.77767411e-03 -4.74393629e-04 1.27352166e-02
-5.60149211e-03 -8.16455624e-04]
[-5.77767411e-03 7.49427285e-02 -3.72645942e-03 -6.04099350e-03
7.78432632e-03 6.22772608e-04]
[-4.74393629e-04 -3.72645942e-03 9.87988504e-02 -8.33767726e-04
6.00761544e-04 9.64515210e-05]
[ 1.27352166e-02 -6.04099350e-03 -8.33767726e-04 2.48299240e-02
-1.28790921e-02 -1.53865055e-03]
[-5.60149211e-03 7.78432632e-03 6.00761544e-04 -1.28790921e-02
8.52434035e-02 -2.92003274e-03]
[-8.16455624e-04 6.22772608e-04 9.64515210e-05 -1.53865055e-03
-2.92003274e-03 9.89315500e-02]]
EM: success: reached maximum number of iterations
Plot convergence
fig = go.Figure()
trace = go.Scatter(x=optim_res_ga["elapsed_time"], y=optim_res_ga["log_like"],
name="Gradient ascent", mode="lines+markers")
fig.add_trace(trace)
trace = go.Scatter(x=optim_res_em["elapsed_time"], y=optim_res_em["log_like"],
name="EM", mode="lines+markers")
fig.add_trace(trace)
fig.update_layout(xaxis_title="Elapsed Time (sec)",
yaxis_title="Log Likelihood")
fig
Perform smoothing with optimized parameters
Gradient ascent
Perform batch filtering
View source code of ssm.inference.filterLDS_SS_withMissingValues_np
Q_ga = optim_res_ga["estimates"]["sigma_a"].item()**2*Qe
m0_ga = optim_res_ga["estimates"]["m0"].numpy()
V0_ga = np.diag(optim_res_ga["estimates"]["sqrt_diag_V0"].numpy()**2)
R_ga = np.diag([optim_res_ga["estimates"]["pos_x_R_std"].item()**2,
optim_res_ga["estimates"]["pos_y_R_std"].item()**2])
filterRes_ga = ssm.inference.filterLDS_SS_withMissingValues_np(
y=y, B=B, Q=Q_ga, m0=m0_ga, V0=V0_ga, Z=Z, R=R_ga)
Perform batch smoothing
View source code of ssm.inference.smoothLDS_SS
smoothRes_ga = ssm.inference.smoothLDS_SS(
B=B, xnn=filterRes_ga["xnn"], Pnn=filterRes_ga["Pnn"],
xnn1=filterRes_ga["xnn1"], Pnn1=filterRes_ga["Pnn1"], m0=m0_ga, V0=V0_ga)
EM
Perform batch filtering
View source code of ssm.inference.filterLDS_SS_withMissingValues_np
Q_em = optim_res_em["estimates"]["sigma_a"].item()**2*Qe
m0_em = optim_res_em["estimates"]["m0"]
V0_em = optim_res_em["estimates"]["V0"]
R_em = optim_res_em["estimates"]["R"]
filterRes_em = ssm.inference.filterLDS_SS_withMissingValues_np(
y=y, B=B, Q=Q_em, m0=m0_em, V0=V0_em, Z=Z, R=R_em)
Perform batch smoothing
View source code of ssm.inference.smoothLDS_SS
smoothRes_em = ssm.inference.smoothLDS_SS(
B=B, xnn=filterRes_em["xnn"], Pnn=filterRes_em["Pnn"],
xnn1=filterRes_em["xnn1"], Pnn1=filterRes_em["Pnn1"], m0=m0_em, V0=V0_em)
Plot smoothing results
def get_fig_kinematics_vs_time(
time,
measured_x, measured_y,
finite_diff_x, finite_diff_y,
ga_mean_x, ga_mean_y,
ga_ci_x_upper, ga_ci_y_upper,
ga_ci_x_lower, ga_ci_y_lower,
em_mean_x, em_mean_y,
em_ci_x_upper, em_ci_y_upper,
em_ci_x_lower, em_ci_y_lower,
cb_alpha,
color_true,
color_measured,
color_finite_diff,
color_ga_pattern,
color_em_pattern,
xlabel, ylabel):
fig = go.Figure()
if measured_x is not None:
trace_mes_x = go.Scatter(
x=time, y=measured_x,
mode="markers",
marker={"color": color_measured},
name="measured x",
showlegend=True,
)
fig.add_trace(trace_mes_x)
if measured_y is not None:
trace_mes_y = go.Scatter(
x=time, y=measured_y,
mode="markers",
marker={"color": color_measured},
name="measured y",
showlegend=True,
)
fig.add_trace(trace_mes_y)
if finite_diff_x is not None:
trace_fd_x = go.Scatter(
x=time, y=finite_diff_x,
mode="markers",
marker={"color": color_finite_diff},
name="finite difference x",
showlegend=True,
)
fig.add_trace(trace_fd_x)
if finite_diff_y is not None:
trace_fd_y = go.Scatter(
x=time, y=finite_diff_y,
mode="markers",
marker={"color": color_finite_diff},
name="finite difference y",
showlegend=True,
)
fig.add_trace(trace_fd_y)
trace_ga_x = go.Scatter(
x=time, y=ga_mean_x,
mode="markers",
marker={"color": color_ga_pattern.format(1.0)},
name="grad. ascent x",
showlegend=True,
legendgroup="ga_x",
)
fig.add_trace(trace_ga_x)
trace_ga_x_cb = go.Scatter(
x=np.concatenate([time, time[::-1]]),
y=np.concatenate([ga_ci_x_upper, ga_ci_x_lower[::-1]]),
fill="toself",
fillcolor=color_ga_pattern.format(cb_alpha),
line=dict(color=color_ga_pattern.format(0.0)),
showlegend=False,
legendgroup="ga_x",
)
fig.add_trace(trace_ga_x_cb)
trace_ga_y = go.Scatter(
x=time, y=ga_mean_y,
mode="markers",
marker={"color": color_ga_pattern.format(1.0)},
name="grad. ascent y",
showlegend=True,
legendgroup="ga_y",
)
fig.add_trace(trace_ga_y)
trace_ga_y_cb = go.Scatter(
x=np.concatenate([time, time[::-1]]),
y=np.concatenate([ga_ci_y_upper, ga_ci_y_lower[::-1]]),
fill="toself",
fillcolor=color_ga_pattern.format(cb_alpha),
line=dict(color=color_ga_pattern.format(0.0)),
showlegend=False,
legendgroup="ga_y",
)
fig.add_trace(trace_ga_y_cb)
trace_em_x = go.Scatter(
x=time, y=em_mean_x,
mode="markers",
marker={"color": color_em_pattern.format(1.0)},
name="EM x",
showlegend=True,
legendgroup="em_x",
)
fig.add_trace(trace_em_x)
trace_em_x_cb = go.Scatter(
x=np.concatenate([time, time[::-1]]),
y=np.concatenate([em_ci_x_upper, em_ci_x_lower[::-1]]),
fill="toself",
fillcolor=color_em_pattern.format(cb_alpha),
line=dict(color=color_em_pattern.format(0.0)),
showlegend=False,
legendgroup="em_x",
)
fig.add_trace(trace_em_x_cb)
trace_em_y = go.Scatter(
x=time, y=em_mean_y,
mode="markers",
marker={"color": color_em_pattern.format(1.0)},
name="EM y",
showlegend=True,
legendgroup="em_y",
)
fig.add_trace(trace_em_y)
trace_em_y_cb = go.Scatter(
x=np.concatenate([time, time[::-1]]),
y=np.concatenate([em_ci_y_upper, em_ci_y_lower[::-1]]),
fill="toself",
fillcolor=color_em_pattern.format(cb_alpha),
line=dict(color=color_em_pattern.format(0.0)),
showlegend=False,
legendgroup="em_y",
)
fig.add_trace(trace_em_y_cb)
fig.update_layout(xaxis_title=xlabel,
yaxis_title=ylabel,
paper_bgcolor='rgba(0,0,0,0)',
plot_bgcolor='rgba(0,0,0,0)',
)
return fig
N = y.shape[1]
time = np.arange(0, N*dt, dt)
smoothed_means_ga = smoothRes_ga["xnN"]
smoothed_covs_ga = smoothRes_ga["PnN"]
smoothed_std_x_y_ga = np.sqrt(np.diagonal(a=smoothed_covs_ga, axis1=0, axis2=1))
smoothed_means_em = smoothRes_em["xnN"]
smoothed_covs_em = smoothRes_em["PnN"]
smoothed_std_x_y_em = np.sqrt(np.diagonal(a=smoothed_covs_em, axis1=0, axis2=1))
color_true = "blue"
color_measured = "black"
color_finite_diff = "blue"
color_ga_pattern = "rgba(255,0,0,{:f})"
color_em_pattern = "rgba(255,165,0,{:f})"
cb_alpha = 0.3
Gradient ascent
Plot true, measured and smoothed positions (with 95% confidence band)
measured_x = y[0, :]
measured_y = y[1, :]
finite_diff_x = None
finite_diff_y = None
smoothed_mean_x_ga = smoothed_means_ga[0, 0, :]
smoothed_mean_y_ga = smoothed_means_ga[3, 0, :]
smoothed_mean_x_em = smoothed_means_em[0, 0, :]
smoothed_mean_y_em = smoothed_means_em[3, 0, :]
smoothed_ci_x_upper_ga = smoothed_mean_x_ga + 1.96*smoothed_std_x_y_ga[:, 0]
smoothed_ci_x_lower_ga = smoothed_mean_x_ga - 1.96*smoothed_std_x_y_ga[:, 0]
smoothed_ci_y_upper_ga = smoothed_mean_y_ga + 1.96*smoothed_std_x_y_ga[:, 3]
smoothed_ci_y_lower_ga = smoothed_mean_y_ga - 1.96*smoothed_std_x_y_ga[:, 3]
smoothed_ci_x_upper_em = smoothed_mean_x_em + 1.96*smoothed_std_x_y_em[:, 0]
smoothed_ci_x_lower_em = smoothed_mean_x_em - 1.96*smoothed_std_x_y_em[:, 0]
smoothed_ci_y_upper_em = smoothed_mean_y_em + 1.96*smoothed_std_x_y_em[:, 3]
smoothed_ci_y_lower_em = smoothed_mean_y_em - 1.96*smoothed_std_x_y_em[:, 3]
fig = get_fig_kinematics_vs_time(
time=time,
measured_x=measured_x, measured_y=measured_y,
finite_diff_x=finite_diff_x, finite_diff_y=finite_diff_y,
ga_mean_x=smoothed_mean_x_ga, ga_mean_y=smoothed_mean_y_ga,
ga_ci_x_upper=smoothed_ci_x_upper_ga,
ga_ci_y_upper=smoothed_ci_y_upper_ga,
ga_ci_x_lower=smoothed_ci_x_lower_ga,
ga_ci_y_lower=smoothed_ci_y_lower_ga,
em_mean_x=smoothed_mean_x_em, em_mean_y=smoothed_mean_y_em,
em_ci_x_upper=smoothed_ci_x_upper_em,
em_ci_y_upper=smoothed_ci_y_upper_em,
em_ci_x_lower=smoothed_ci_x_lower_em,
em_ci_y_lower=smoothed_ci_y_lower_em,
cb_alpha=cb_alpha,
color_true=color_true, color_measured=color_measured,
color_finite_diff=color_finite_diff,
color_ga_pattern=color_ga_pattern,
color_em_pattern=color_em_pattern,
xlabel="Time (sec)", ylabel="Position (pixels)")
# fig_filename_pattern = "../../figures/smoothed_pos.{:s}"
# fig.write_image(fig_filename_pattern.format("png"))
# fig.write_html(fig_filename_pattern.format("html"))
fig
Plot true and smoothed velocities (with 95% confidence band)
measured_x = None
measured_y = None
finite_diff_x = np.diff(y[0, :])/dt
finite_diff_y = np.diff(y[1, :])/dt
smoothed_mean_x_ga = smoothed_means_ga[1, 0, :]
smoothed_mean_y_ga = smoothed_means_ga[4, 0, :]
smoothed_mean_x_em = smoothed_means_em[1, 0, :]
smoothed_mean_y_em = smoothed_means_em[4, 0, :]
smoothed_ci_x_upper_ga = smoothed_mean_x_ga + 1.96*smoothed_std_x_y_ga[:, 1]
smoothed_ci_x_lower_ga = smoothed_mean_x_ga - 1.96*smoothed_std_x_y_ga[:, 1]
smoothed_ci_y_upper_ga= smoothed_mean_y_ga + 1.96*smoothed_std_x_y_ga[:, 4]
smoothed_ci_y_lower_ga = smoothed_mean_y_ga - 1.96*smoothed_std_x_y_ga[:, 4]
smoothed_ci_x_upper_em = smoothed_mean_x_em + 1.96*smoothed_std_x_y_em[:, 1]
smoothed_ci_x_lower_em = smoothed_mean_x_em - 1.96*smoothed_std_x_y_em[:, 1]
smoothed_ci_y_upper_em= smoothed_mean_y_em + 1.96*smoothed_std_x_y_em[:, 4]
smoothed_ci_y_lower_em = smoothed_mean_y_em - 1.96*smoothed_std_x_y_em[:, 4]
fig = get_fig_kinematics_vs_time(
time=time,
measured_x=measured_x, measured_y=measured_y,
finite_diff_x=finite_diff_x, finite_diff_y=finite_diff_y,
ga_mean_x=smoothed_mean_x_ga, ga_mean_y=smoothed_mean_y_ga,
ga_ci_x_upper=smoothed_ci_x_upper_ga,
ga_ci_y_upper=smoothed_ci_y_upper_ga,
ga_ci_x_lower=smoothed_ci_x_lower_ga,
ga_ci_y_lower=smoothed_ci_y_lower_ga,
em_mean_x=smoothed_mean_x_em, em_mean_y=smoothed_mean_y_em,
em_ci_x_upper=smoothed_ci_x_upper_em,
em_ci_y_upper=smoothed_ci_y_upper_em,
em_ci_x_lower=smoothed_ci_x_lower_em,
em_ci_y_lower=smoothed_ci_y_lower_em,
cb_alpha=cb_alpha,
color_true=color_true, color_measured=color_measured,
color_finite_diff=color_finite_diff,
color_ga_pattern=color_ga_pattern,
color_em_pattern=color_em_pattern,
xlabel="Time (sec)", ylabel="Velocity (pixels/sec)")
# fig_filename_pattern = "../../figures/smoothed_vel.{:s}"
# fig.write_image(fig_filename_pattern.format("png"))
# fig.write_html(fig_filename_pattern.format("html"))
fig
Plot true and smoothed accelerations (with 95% confidence band)
measured_x = None
measured_y = None
finite_diff_x = np.diff(np.diff(y[0, :]))/dt**2
finite_diff_y = np.diff(np.diff(y[1, :]))/dt**2
smoothed_mean_x_ga = smoothed_means_ga[2, 0, :]
smoothed_mean_y_ga = smoothed_means_ga[5, 0, :]
smoothed_mean_x_em = smoothed_means_em[2, 0, :]
smoothed_mean_y_em = smoothed_means_em[5, 0, :]
smoothed_ci_x_upper_ga = smoothed_mean_x_ga + 1.96*smoothed_std_x_y_ga[:, 2]
smoothed_ci_x_lower_ga = smoothed_mean_x_ga - 1.96*smoothed_std_x_y_ga[:, 2]
smoothed_ci_y_upper_ga = smoothed_mean_y_ga + 1.96*smoothed_std_x_y_ga[:, 5]
smoothed_ci_y_lower_ga = smoothed_mean_y_ga - 1.96*smoothed_std_x_y_ga[:, 5]
smoothed_ci_x_upper_em = smoothed_mean_x_em + 1.96*smoothed_std_x_y_em[:, 2]
smoothed_ci_x_lower_em = smoothed_mean_x_em - 1.96*smoothed_std_x_y_em[:, 2]
smoothed_ci_y_upper_em = smoothed_mean_y_em + 1.96*smoothed_std_x_y_em[:, 5]
smoothed_ci_y_lower_em = smoothed_mean_y_em - 1.96*smoothed_std_x_y_em[:, 5]
fig = get_fig_kinematics_vs_time(
time=time,
measured_x=measured_x, measured_y=measured_y,
finite_diff_x=finite_diff_x, finite_diff_y=finite_diff_y,
ga_mean_x=smoothed_mean_x_ga, ga_mean_y=smoothed_mean_y_ga,
ga_ci_x_upper=smoothed_ci_x_upper_ga,
ga_ci_y_upper=smoothed_ci_y_upper_ga,
ga_ci_x_lower=smoothed_ci_x_lower_ga,
ga_ci_y_lower=smoothed_ci_y_lower_ga,
em_mean_x=smoothed_mean_x_em, em_mean_y=smoothed_mean_y_em,
em_ci_x_upper=smoothed_ci_x_upper_em,
em_ci_y_upper=smoothed_ci_y_upper_em,
em_ci_x_lower=smoothed_ci_x_lower_em,
em_ci_y_lower=smoothed_ci_y_lower_em,
cb_alpha=cb_alpha,
color_true=color_true, color_measured=color_measured,
color_finite_diff=color_finite_diff,
color_ga_pattern=color_ga_pattern,
color_em_pattern=color_em_pattern,
xlabel="Time (sec)", ylabel="Acceleration (pixels/sec^2)")
# fig_filename_pattern = "../../figures/smoothed_acc.{:s}"
# fig.write_image(fig_filename_pattern.format("png"))
# fig.write_html(fig_filename_pattern.format("html"))
fig
Total running time of the script: ( 0 minutes 9.448 seconds)
