.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_examples/tracking/plotEMvsGAcomparisonForagingMouse.py" .. LINE NUMBERS ARE GIVEN BELOW. .. only:: html .. note:: :class: sphx-glr-download-link-note :ref:`Go to the end ` to download the full example code. or to run this example in your browser via Binder .. rst-class:: sphx-glr-example-title .. _sphx_glr_auto_examples_tracking_plotEMvsGAcomparisonForagingMouse.py: 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. .. GENERATED FROM PYTHON SOURCE LINES 11-28 .. code-block:: Python 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 lds.learning .. GENERATED FROM PYTHON SOURCE LINES 29-31 Define parameters for estimation -------------------------------- .. GENERATED FROM PYTHON SOURCE LINES 31-51 .. code-block:: Python 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 .. GENERATED FROM PYTHON SOURCE LINES 52-54 Provide initial conditions -------------------------- .. GENERATED FROM PYTHON SOURCE LINES 54-71 .. code-block:: Python 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] .. GENERATED FROM PYTHON SOURCE LINES 72-74 Get mouse positions ------------------- .. GENERATED FROM PYTHON SOURCE LINES 74-82 .. code-block:: Python 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() .. GENERATED FROM PYTHON SOURCE LINES 83-85 Build the matrices of the CWPA model ------------------------------------ .. GENERATED FROM PYTHON SOURCE LINES 85-116 .. code-block:: Python B, _, Z, _, Qe = lds.tracking.utils.getLDSmatricesForTracking( dt=dt, sigma_a=np.nan, sigma_x=np.nan, sigma_y=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["sqrt_diag_R"] = False vars_to_estimate["R"] = False else: vars_to_estimate["sqrt_diag_R"] = 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 .. GENERATED FROM PYTHON SOURCE LINES 117-119 Perform gradient ascent optimization ------------------------------------ .. GENERATED FROM PYTHON SOURCE LINES 119-143 .. code-block:: Python 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 = lds.learning.torch_lbfgs_optimize_SS_tracking_diagV0( y=y_torch, B=B_torch, sigma_a0=sigma_a0, Qe=Qe_regularized_ga_torch, Z=Z_torch, sqrt_diag_R_0=sqrt_diag_R_torch, 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"]) .. rst-class:: sphx-glr-script-out .. code-block:: none in closure, ll=-4349760.865100649 in closure, ll=-864425.783357166 -------------------------------------------------------------------------------- epoch: 0 likelihood: -4349760.865100649 sigma_a: tensor([1.0474], dtype=torch.float64, requires_grad=True) sqrt_diag_R: tensor([1.0419, 1.1762], dtype=torch.float64, requires_grad=True) m0: tensor([2.2156e-04, 5.9511e-05, 7.5925e-06, 4.6697e-04, 1.2752e-04, 1.6344e-05], dtype=torch.float64, requires_grad=True) sqrt_diag_V0: tensor([0.2254, 0.1090, 0.1001, 0.6569, 0.1415, 0.1007], dtype=torch.float64, requires_grad=True) in closure, ll=-864425.783357166 in closure, ll=-675903.2550139598 -------------------------------------------------------------------------------- epoch: 1 likelihood: -864425.783357166 sigma_a: tensor([1.0546], dtype=torch.float64, requires_grad=True) sqrt_diag_R: tensor([1.0580, 1.1819], dtype=torch.float64, requires_grad=True) m0: tensor([3.6056e-04, 9.6815e-05, 1.2338e-05, 5.2679e-04, 1.4607e-04, 1.8836e-05], dtype=torch.float64, requires_grad=True) sqrt_diag_V0: tensor([0.3178, 0.1123, 0.1002, 0.7057, 0.1428, 0.1007], dtype=torch.float64, requires_grad=True) in closure, ll=-675903.2550139598 in closure, ll=-477237.577875291 -------------------------------------------------------------------------------- epoch: 2 likelihood: -675903.2550139598 sigma_a: tensor([1.0715], dtype=torch.float64, requires_grad=True) sqrt_diag_R: tensor([1.0742, 1.1879], dtype=torch.float64, requires_grad=True) m0: tensor([6.4423e-04, 1.7359e-04, 2.2145e-05, 7.1291e-04, 2.0678e-04, 2.7092e-05], dtype=torch.float64, requires_grad=True) sqrt_diag_V0: tensor([0.4702, 0.1140, 0.1002, 0.8275, 0.1438, 0.1007], dtype=torch.float64, requires_grad=True) in closure, ll=-477237.577875291 in closure, ll=-356966.5981741533 -------------------------------------------------------------------------------- epoch: 3 likelihood: -477237.577875291 sigma_a: tensor([1.1039], dtype=torch.float64, requires_grad=True) sqrt_diag_R: tensor([1.0940, 1.1901], dtype=torch.float64, requires_grad=True) m0: tensor([1.0232e-03, 2.7659e-04, 3.5270e-05, 1.0244e-03, 3.1449e-04, 4.1850e-05], dtype=torch.float64, requires_grad=True) sqrt_diag_V0: tensor([0.6188, 0.1134, 0.1002, 0.9843, 0.1422, 0.1007], dtype=torch.float64, requires_grad=True) in closure, ll=-356966.5981741533 in closure, ll=-263783.7252192787 -------------------------------------------------------------------------------- epoch: 4 likelihood: -356966.5981741533 sigma_a: tensor([1.1846], dtype=torch.float64, requires_grad=True) sqrt_diag_R: tensor([1.1422, 1.2010], dtype=torch.float64, requires_grad=True) m0: tensor([1.6564e-03, 4.4898e-04, 5.7099e-05, 1.6083e-03, 5.3194e-04, 7.1734e-05], dtype=torch.float64, requires_grad=True) sqrt_diag_V0: tensor([0.8021, 0.1110, 0.1002, 1.2044, 0.1371, 0.1006], dtype=torch.float64, requires_grad=True) in closure, ll=-263783.7252192787 in closure, ll=-194897.69144144744 -------------------------------------------------------------------------------- epoch: 5 likelihood: -263783.7252192787 sigma_a: tensor([1.3511], dtype=torch.float64, requires_grad=True) sqrt_diag_R: tensor([1.2445, 1.2457], dtype=torch.float64, requires_grad=True) m0: tensor([2.6471e-03, 7.1836e-04, 9.0867e-05, 2.5812e-03, 9.2699e-04, 1.2594e-04], dtype=torch.float64, requires_grad=True) sqrt_diag_V0: tensor([1.0194, 0.1069, 0.1001, 1.4763, 0.1278, 0.1004], dtype=torch.float64, requires_grad=True) in closure, ll=-194897.69144144744 in closure, ll=-141995.14515118996 -------------------------------------------------------------------------------- epoch: 6 likelihood: -194897.69144144744 sigma_a: tensor([1.6424], dtype=torch.float64, requires_grad=True) sqrt_diag_R: tensor([1.4248, 1.3583], dtype=torch.float64, requires_grad=True) m0: tensor([0.0042, 0.0011, 0.0001, 0.0042, 0.0016, 0.0002], dtype=torch.float64, requires_grad=True) sqrt_diag_V0: tensor([1.2894, 0.1007, 0.1000, 1.8129, 0.1123, 0.1001], dtype=torch.float64, requires_grad=True) in closure, ll=-141995.14515118996 in closure, ll=-105560.15024555809 -------------------------------------------------------------------------------- epoch: 7 likelihood: -141995.14515118996 sigma_a: tensor([2.0430], dtype=torch.float64, requires_grad=True) sqrt_diag_R: tensor([1.6636, 1.5428], dtype=torch.float64, requires_grad=True) m0: tensor([0.0066, 0.0018, 0.0002, 0.0068, 0.0028, 0.0004], dtype=torch.float64, requires_grad=True) sqrt_diag_V0: tensor([1.6078, 0.0926, 0.0999, 2.2095, 0.0883, 0.0997], dtype=torch.float64, requires_grad=True) in closure, ll=-105560.15024555809 in closure, ll=-81571.05497658401 -------------------------------------------------------------------------------- epoch: 8 likelihood: -105560.15024555809 sigma_a: tensor([2.5434], dtype=torch.float64, requires_grad=True) sqrt_diag_R: tensor([1.9304, 1.7680], dtype=torch.float64, requires_grad=True) m0: tensor([0.0103, 0.0027, 0.0003, 0.0109, 0.0048, 0.0006], dtype=torch.float64, requires_grad=True) sqrt_diag_V0: tensor([1.9838, 0.0824, 0.0997, 2.6900, 0.0530, 0.0992], dtype=torch.float64, requires_grad=True) in closure, ll=-81571.05497658401 in closure, ll=-65955.31706052765 -------------------------------------------------------------------------------- epoch: 9 likelihood: -81571.05497658401 sigma_a: tensor([3.1675], dtype=torch.float64, requires_grad=True) sqrt_diag_R: tensor([2.1935, 1.9958], dtype=torch.float64, requires_grad=True) m0: tensor([0.0158, 0.0042, 0.0005, 0.0173, 0.0079, 0.0011], dtype=torch.float64, requires_grad=True) sqrt_diag_V0: tensor([2.4329, 0.0699, 0.0995, 3.2824, 0.0036, 0.0985], dtype=torch.float64, requires_grad=True) in closure, ll=-65955.31706052765 in closure, ll=-55724.821515104406 -------------------------------------------------------------------------------- epoch: 10 likelihood: -65955.31706052765 sigma_a: tensor([3.9680], dtype=torch.float64, requires_grad=True) sqrt_diag_R: tensor([2.3983, 2.1734], dtype=torch.float64, requires_grad=True) m0: tensor([0.0243, 0.0063, 0.0007, 0.0272, 0.0128, 0.0017], dtype=torch.float64, requires_grad=True) sqrt_diag_V0: tensor([ 2.9750, 0.0546, 0.0993, 4.0193, -0.0624, 0.0977], dtype=torch.float64, requires_grad=True) in closure, ll=-55724.821515104406 in closure, ll=-48677.46276967638 -------------------------------------------------------------------------------- epoch: 11 likelihood: -55724.821515104406 sigma_a: tensor([5.0503], dtype=torch.float64, requires_grad=True) sqrt_diag_R: tensor([2.4412, 2.2076], dtype=torch.float64, requires_grad=True) m0: tensor([0.0373, 0.0094, 0.0011, 0.0424, 0.0207, 0.0027], dtype=torch.float64, requires_grad=True) sqrt_diag_V0: tensor([ 3.6442, 0.0358, 0.0990, 4.9566, -0.1490, 0.0967], dtype=torch.float64, requires_grad=True) in closure, ll=-48677.46276967638 in closure, ll=-43126.20433079402 -------------------------------------------------------------------------------- epoch: 12 likelihood: -48677.46276967638 sigma_a: tensor([6.6675], dtype=torch.float64, requires_grad=True) sqrt_diag_R: tensor([2.1361, 1.9359], dtype=torch.float64, requires_grad=True) m0: tensor([0.0579, 0.0141, 0.0016, 0.0659, 0.0344, 0.0044], dtype=torch.float64, requires_grad=True) sqrt_diag_V0: tensor([ 4.5150, 0.0122, 0.0986, 6.2094, -0.2669, 0.0955], dtype=torch.float64, requires_grad=True) in closure, ll=-43126.20433079402 in closure, ll=-38575.54661835186 -------------------------------------------------------------------------------- epoch: 13 likelihood: -43126.20433079402 sigma_a: tensor([9.4357], dtype=torch.float64, requires_grad=True) sqrt_diag_R: tensor([1.6484, 1.3869], dtype=torch.float64, requires_grad=True) m0: tensor([0.0914, 0.0211, 0.0022, 0.1031, 0.0634, 0.0078], dtype=torch.float64, requires_grad=True) sqrt_diag_V0: tensor([ 5.6448, -0.0180, 0.0982, 7.7935, -0.4575, 0.0943], dtype=torch.float64, requires_grad=True) in closure, ll=-38575.54661835186 in closure, ll=-35330.423396786195 -------------------------------------------------------------------------------- epoch: 14 likelihood: -38575.54661835186 sigma_a: tensor([15.3115], dtype=torch.float64, requires_grad=True) sqrt_diag_R: tensor([2.3744, 1.9971], dtype=torch.float64, requires_grad=True) m0: tensor([0.1637, 0.0355, 0.0034, 0.1824, 0.1377, 0.0159], dtype=torch.float64, requires_grad=True) sqrt_diag_V0: tensor([ 7.8777, -0.0843, 0.0971, 10.4573, -0.9780, 0.0917], dtype=torch.float64, requires_grad=True) in closure, ll=-35330.423396786195 in closure, ll=-32321.736077543555 -------------------------------------------------------------------------------- epoch: 15 likelihood: -35330.423396786195 sigma_a: tensor([18.5797], dtype=torch.float64, requires_grad=True) sqrt_diag_R: tensor([1.9159, 1.2629], dtype=torch.float64, requires_grad=True) m0: tensor([0.2029, 0.0433, 0.0041, 0.2259, 0.1783, 0.0203], dtype=torch.float64, requires_grad=True) sqrt_diag_V0: tensor([ 9.0688, -0.1161, 0.0967, 12.1607, -1.2467, 0.0905], dtype=torch.float64, requires_grad=True) in closure, ll=-32321.736077543555 in closure, ll=-28041.283336008222 -------------------------------------------------------------------------------- epoch: 16 likelihood: -32321.736077543555 sigma_a: tensor([35.9907], dtype=torch.float64, requires_grad=True) sqrt_diag_R: tensor([-1.4661, -1.1189], dtype=torch.float64, requires_grad=True) m0: tensor([0.4041, 0.0831, 0.0075, 0.4475, 0.4111, 0.0448], dtype=torch.float64, requires_grad=True) sqrt_diag_V0: tensor([15.4072, -0.2725, 0.0943, 20.5471, -2.9635, 0.0843], dtype=torch.float64, requires_grad=True) in closure, ll=-28041.283336008222 in closure, ll=-60845.44854412978 in closure, ll=-28016.72369289751 in closure, ll=-27642.86961457806 -------------------------------------------------------------------------------- epoch: 17 likelihood: -28041.283336008222 sigma_a: tensor([35.4827], dtype=torch.float64, requires_grad=True) sqrt_diag_R: tensor([-1.3597, -0.9811], dtype=torch.float64, requires_grad=True) m0: tensor([0.3985, 0.0820, 0.0074, 0.4413, 0.4046, 0.0441], dtype=torch.float64, requires_grad=True) sqrt_diag_V0: tensor([15.2323, -0.2681, 0.0944, 20.2934, -2.9165, 0.0845], dtype=torch.float64, requires_grad=True) in closure, ll=-27642.86961457806 in closure, ll=-50348.9578325196 in closure, ll=-28031.70882471392 in closure, ll=-27294.53614617836 -------------------------------------------------------------------------------- epoch: 18 likelihood: -27642.86961457806 sigma_a: tensor([35.6823], dtype=torch.float64, requires_grad=True) sqrt_diag_R: tensor([-1.3666, -0.7355], dtype=torch.float64, requires_grad=True) m0: tensor([0.4014, 0.0825, 0.0075, 0.4445, 0.4081, 0.0444], dtype=torch.float64, requires_grad=True) sqrt_diag_V0: tensor([15.3370, -0.2703, 0.0943, 20.3412, -2.9506, 0.0843], dtype=torch.float64, requires_grad=True) in closure, ll=-27294.53614617836 in closure, ll=-26992.066136108533 -------------------------------------------------------------------------------- epoch: 19 likelihood: -27294.53614617836 sigma_a: tensor([37.1363], dtype=torch.float64, requires_grad=True) sqrt_diag_R: tensor([-1.1797, -0.7222], dtype=torch.float64, requires_grad=True) m0: tensor([0.4197, 0.0861, 0.0078, 0.4646, 0.4266, 0.0465], dtype=torch.float64, requires_grad=True) sqrt_diag_V0: tensor([15.8772, -0.2868, 0.0941, 21.0349, -3.0763, 0.0837], dtype=torch.float64, requires_grad=True) in closure, ll=-26992.066136108533 in closure, ll=-26167.47437272276 -------------------------------------------------------------------------------- epoch: 20 likelihood: -26992.066136108533 sigma_a: tensor([44.6102], dtype=torch.float64, requires_grad=True) sqrt_diag_R: tensor([-0.9844, -0.6663], dtype=torch.float64, requires_grad=True) m0: tensor([0.5111, 0.1042, 0.0093, 0.5653, 0.5243, 0.0570], dtype=torch.float64, requires_grad=True) sqrt_diag_V0: tensor([18.6658, -0.3660, 0.0929, 24.5325, -3.7736, 0.0806], dtype=torch.float64, requires_grad=True) in closure, ll=-26167.47437272276 in closure, ll=-24700.283777922232 -------------------------------------------------------------------------------- epoch: 21 likelihood: -26167.47437272276 sigma_a: tensor([61.7582], dtype=torch.float64, requires_grad=True) sqrt_diag_R: tensor([-1.0137, -0.5894], dtype=torch.float64, requires_grad=True) m0: tensor([0.7194, 0.1455, 0.0129, 0.7946, 0.7500, 0.0811], dtype=torch.float64, requires_grad=True) sqrt_diag_V0: tensor([25.0668, -0.5439, 0.0901, 32.5239, -5.4040, 0.0736], dtype=torch.float64, requires_grad=True) in closure, ll=-24700.283777922232 in closure, ll=-23851.18246110244 -------------------------------------------------------------------------------- epoch: 22 likelihood: -24700.283777922232 sigma_a: tensor([81.8113], dtype=torch.float64, requires_grad=True) sqrt_diag_R: tensor([-0.9371, -0.6384], dtype=torch.float64, requires_grad=True) m0: tensor([0.9630, 0.1937, 0.0170, 1.0629, 1.0134, 0.1093], dtype=torch.float64, requires_grad=True) sqrt_diag_V0: tensor([32.5313, -0.7526, 0.0869, 41.9016, -7.2929, 0.0654], dtype=torch.float64, requires_grad=True) in closure, ll=-23851.18246110244 in closure, ll=-23494.35249912862 in closure, ll=-23197.13638543685 -------------------------------------------------------------------------------- epoch: 23 likelihood: -23851.18246110244 sigma_a: tensor([107.4640], dtype=torch.float64, requires_grad=True) sqrt_diag_R: tensor([-0.8749, -0.4626], dtype=torch.float64, requires_grad=True) m0: tensor([1.2749, 0.2554, 0.0223, 1.4063, 1.3513, 0.1455], dtype=torch.float64, requires_grad=True) sqrt_diag_V0: tensor([42.1096, -1.0195, 0.0828, 53.8506, -9.7275, 0.0548], dtype=torch.float64, requires_grad=True) in closure, ll=-23197.13638543685 in closure, ll=-22650.26086579791 -------------------------------------------------------------------------------- epoch: 24 likelihood: -23197.13638543685 sigma_a: tensor([134.3731], dtype=torch.float64, requires_grad=True) sqrt_diag_R: tensor([-0.8753, -0.4871], dtype=torch.float64, requires_grad=True) m0: tensor([1.6015, 0.3200, 0.0278, 1.7659, 1.7053, 0.1834], dtype=torch.float64, requires_grad=True) sqrt_diag_V0: tensor([ 5.2132e+01, -1.2988e+00, 7.8562e-02, 6.6417e+01, -1.2273e+01, 4.3807e-02], dtype=torch.float64, requires_grad=True) in closure, ll=-22650.26086579791 in closure, ll=-22253.747573382083 -------------------------------------------------------------------------------- epoch: 25 likelihood: -22650.26086579791 sigma_a: tensor([179.0867], dtype=torch.float64, requires_grad=True) sqrt_diag_R: tensor([-0.8171, -0.4377], dtype=torch.float64, requires_grad=True) m0: tensor([2.1447, 0.4275, 0.0370, 2.3639, 2.2936, 0.2463], dtype=torch.float64, requires_grad=True) sqrt_diag_V0: tensor([ 6.8797e+01, -1.7635e+00, 7.1441e-02, 8.7286e+01, -1.6503e+01, 2.5486e-02], dtype=torch.float64, requires_grad=True) in closure, ll=-22253.747573382083 in closure, ll=-22052.708890079248 -------------------------------------------------------------------------------- epoch: 26 likelihood: -22253.747573382083 sigma_a: tensor([218.3609], dtype=torch.float64, requires_grad=True) sqrt_diag_R: tensor([-0.7963, -0.4390], dtype=torch.float64, requires_grad=True) m0: tensor([2.6215, 0.5219, 0.0451, 2.8890, 2.8104, 0.3016], dtype=torch.float64, requires_grad=True) sqrt_diag_V0: tensor([ 8.3429e+01, -2.1713e+00, 6.5191e-02, 1.0562e+02, -2.0219e+01, 9.4132e-03], dtype=torch.float64, requires_grad=True) in closure, ll=-22052.708890079248 in closure, ll=-21962.3996258442 -------------------------------------------------------------------------------- epoch: 27 likelihood: -22052.708890079248 sigma_a: tensor([258.2953], dtype=torch.float64, requires_grad=True) sqrt_diag_R: tensor([-0.7783, -0.4232], dtype=torch.float64, requires_grad=True) m0: tensor([3.1064, 0.6178, 0.0533, 3.4229, 3.3360, 0.3578], dtype=torch.float64, requires_grad=True) sqrt_diag_V0: tensor([ 9.8310e+01, -2.5860e+00, 5.8836e-02, 1.2426e+02, -2.3999e+01, -6.9359e-03], dtype=torch.float64, requires_grad=True) in closure, ll=-21962.3996258442 in closure, ll=-21934.28696190734 in closure, ll=-22043.622258688818 in closure, ll=-21953.372906392866 in closure, ll=-21932.374703323203 in closure, ll=-21940.424137954924 in closure, ll=-21935.742710205144 in closure, ll=-21933.88841178075 in closure, ll=-21933.08817943135 in closure, ll=-21932.720493706052 in closure, ll=-21932.544848530142 in closure, ll=-21932.459086793122 in closure, ll=-21932.416722561076 in closure, ll=-21932.39566979108 in closure, ll=-21932.38517576563 in closure, ll=-21932.3799368494 in closure, ll=-21932.377319418145 in closure, ll=-21932.376011200173 in closure, ll=-21932.375357218676 in closure, ll=-21932.375030254232 in closure, ll=-21932.374866781967 in closure, ll=-21932.374785051157 in closure, ll=-21932.374744187 in closure, ll=-21932.37472374585 in closure, ll=-21932.37471354182 in closure, ll=-21932.374708425283 in closure, ll=-21932.37470588156 -------------------------------------------------------------------------------- epoch: 28 likelihood: -21962.3996258442 sigma_a: tensor([320.1212], dtype=torch.float64, requires_grad=True) sqrt_diag_R: tensor([-0.7416, -0.4207], dtype=torch.float64, requires_grad=True) m0: tensor([3.8572, 0.7664, 0.0660, 4.2495, 4.1506, 0.4449], dtype=torch.float64, requires_grad=True) sqrt_diag_V0: tensor([ 1.2134e+02, -3.2280e+00, 4.8998e-02, 1.5313e+02, -2.9853e+01, -3.2238e-02], dtype=torch.float64, requires_grad=True) in closure, ll=-21932.374703323203 gradient ascent: nan generated .. GENERATED FROM PYTHON SOURCE LINES 144-146 Perform EM optimization ----------------------- .. GENERATED FROM PYTHON SOURCE LINES 146-176 .. code-block:: Python 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 = lds.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"]) .. rst-class:: sphx-glr-script-out .. code-block:: none LogLike[0000]=-1532961.666165 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]=-56083.466132 sigma_a=2.320011 R: [[25.16113242 31.90946823] [31.90946823 77.90941043]] m0: [188.93507296 47.02895603 5.48547484 397.12406422 103.86097823 12.3310036 ] V0: [[ 0.03106149 -0.01705374 -0.00199045 0. 0. 0. ] [-0.01705374 0.08734047 -0.00277441 0. 0. 0. ] [-0.00199045 -0.00277441 0.09897246 0. 0. 0. ] [ 0. 0. 0. 0.03106149 -0.01705374 -0.00199045] [ 0. 0. 0. -0.01705374 0.08734047 -0.00277441] [ 0. 0. 0. -0.00199045 -0.00277441 0.09897246]] LogLike[0002]=-54472.593838 sigma_a=2.564253 R: [[ 35.37688641 48.73015339] [ 48.73015339 121.26331529]] m0: [189.70957688 47.30563329 5.54917522 398.61986099 104.90457137 12.54064585] V0: [[ 2.95260918e-02 -1.74339463e-02 -2.02991792e-03 5.99137707e-04 1.06471579e-04 3.69656031e-06] [-1.74339463e-02 8.63039357e-02 -3.07862433e-03 1.06471579e-04 2.48348818e-04 4.79567735e-05] [-2.02991792e-03 -3.07862433e-03 9.88222388e-02 3.69656031e-06 4.79567735e-05 1.14329137e-05] [ 5.99137707e-04 1.06471579e-04 3.69656031e-06 3.05165026e-02 -1.72579423e-02 -2.02380728e-03] [ 1.06471579e-04 2.48348818e-04 4.79567735e-05 -1.72579423e-02 8.67144713e-02 -2.99934889e-03] [ 3.69656031e-06 4.79567735e-05 1.14329137e-05 -2.02380728e-03 -2.99934889e-03 9.88411381e-02]] LogLike[0003]=-53853.778108 sigma_a=2.770890 R: [[ 35.76653521 49.25133189] [ 49.25133189 124.70669138]] m0: [190.3200895 47.5038523 5.59217624 399.5385031 105.60763469 12.68412762] V0: [[ 2.84831892e-02 -1.76810358e-02 -2.05250346e-03 9.91916125e-04 1.70366217e-04 4.10256195e-06] [-1.76810358e-02 8.55151446e-02 -3.31461774e-03 1.70345195e-04 4.35952348e-04 8.50568293e-05] [-2.05250346e-03 -3.31461774e-03 9.87026266e-02 4.09686528e-06 8.50555086e-05 2.05726882e-05] [ 9.91916125e-04 1.70345195e-04 4.09686528e-06 3.01697537e-02 -1.73909794e-02 -2.04543390e-03] [ 1.70366217e-04 4.35952348e-04 8.50555086e-05 -1.73909794e-02 8.62571640e-02 -3.16978380e-03] [ 4.10256195e-06 8.50568293e-05 2.05726882e-05 -2.04543390e-03 -3.16978380e-03 9.87376695e-02]] LogLike[0004]=-53310.596369 sigma_a=2.973903 R: [[ 34.40528734 47.75760647] [ 47.75760647 121.10214082]] m0: [190.92662984 47.68113641 5.62804419 400.40124977 106.24206749 12.80940523] V0: [[ 2.75804672e-02 -1.78646596e-02 -2.06370956e-03 1.31914998e-03 2.09393020e-04 6.60751004e-07] [-1.78646596e-02 8.48322773e-02 -3.51616528e-03 2.09380593e-04 5.91914558e-04 1.15038698e-04] [-2.06370956e-03 -3.51616528e-03 9.86006011e-02 6.57059727e-07 1.15037747e-04 2.78999454e-05] [ 1.31914998e-03 2.09380593e-04 6.57059727e-07 2.98635810e-02 -1.75021065e-02 -2.06252654e-03] [ 2.09393020e-04 5.91914558e-04 1.15037747e-04 -1.75021065e-02 8.58571112e-02 -3.31694979e-03] [ 6.60751004e-07 1.15038698e-04 2.78999454e-05 -2.06252654e-03 -3.31694979e-03 9.86489247e-02]] LogLike[0005]=-52791.362708 sigma_a=3.182133 R: [[ 32.83707195 46.32121238] [ 46.32121238 116.66827267]] m0: [191.53414901 47.83481226 5.65743723 401.26345954 106.84225309 12.92287915] V0: [[ 2.67344819e-02 -1.80018071e-02 -2.06527408e-03 1.62002464e-03 2.30378860e-04 -6.17290606e-06] [-1.80018071e-02 8.42152691e-02 -3.69371198e-03 2.30426741e-04 7.30651050e-04 1.40696434e-04] [-2.06527408e-03 -3.69371198e-03 9.85116762e-02 -6.16169426e-06 1.40698766e-04 3.40763450e-05] [ 1.62002464e-03 2.30426741e-04 -6.16169426e-06 2.95696166e-02 -1.75991701e-02 -2.07619387e-03] [ 2.30378860e-04 7.30651050e-04 1.40698766e-04 -1.75991701e-02 8.54930843e-02 -3.44769062e-03] [-6.17290606e-06 1.40696434e-04 3.40763450e-05 -2.07619387e-03 -3.44769062e-03 9.85712583e-02]] LogLike[0006]=-52288.500863 sigma_a=3.398887 R: [[ 31.3297926 45.03311803] [ 45.03311803 112.29577869]] m0: [192.13917459 47.96276156 5.68059404 402.13288377 107.41514769 13.02611575] V0: [[ 2.59192207e-02 -1.80988532e-02 -2.05829312e-03 1.90775855e-03 2.36118264e-04 -1.60128416e-05] [-1.80988532e-02 8.36470512e-02 -3.85236840e-03 2.36266355e-04 8.58750260e-04 1.63469429e-04] [-2.05829312e-03 -3.85236840e-03 9.84333826e-02 -1.59774015e-05 1.63477211e-04 3.94740993e-05] [ 1.90775855e-03 2.36266355e-04 -1.59774015e-05 2.92801339e-02 -1.76842103e-02 -2.08679352e-03] [ 2.36118264e-04 8.58750260e-04 1.63477211e-04 -1.76842103e-02 8.51575895e-02 -3.56495322e-03] [-1.60128416e-05 1.63469429e-04 3.94740993e-05 -2.08679352e-03 -3.56495322e-03 9.85027694e-02]] LogLike[0007]=-51798.997842 sigma_a=3.626353 R: [[ 29.93105007 43.82732987] [ 43.82732987 108.09165489]] m0: [192.73955908 48.06527691 5.69799317 403.01057423 107.96301222 13.1198701 ] V0: [[ 2.51261820e-02 -1.81594408e-02 -2.04374856e-03 2.18694758e-03 2.28104430e-04 -2.85065748e-05] [-1.81594408e-02 8.31179458e-02 -3.99541631e-03 2.28363686e-04 9.79638791e-04 1.84174441e-04] [-2.04374856e-03 -3.99541631e-03 9.83640070e-02 -2.84449230e-05 1.84188233e-04 4.43118006e-05] [ 2.18694758e-03 2.28363686e-04 -2.84449230e-05 2.89926875e-02 -1.77580967e-02 -2.09456778e-03] [ 2.28104430e-04 9.79638791e-04 1.84188233e-04 -1.77580967e-02 8.48464289e-02 -3.67065440e-03] [-2.85065748e-05 1.84174441e-04 4.43118006e-05 -2.09456778e-03 -3.67065440e-03 9.84421158e-02]] LogLike[0008]=-51322.712710 sigma_a=3.865215 R: [[ 28.64157747 42.65967457] [ 42.65967457 104.048869 ]] m0: [193.33419196 48.1438379 5.71022775 403.8966386 108.48688104 13.20466052] V0: [[ 2.43531660e-02 -1.81864630e-02 -2.02259315e-03 2.45894926e-03 2.07439553e-04 -4.33071072e-05] [-1.81864630e-02 8.26214051e-02 -4.12525731e-03 2.07784144e-04 1.09539469e-03 2.03339096e-04] [-2.02259315e-03 -4.12525731e-03 9.83022460e-02 -4.32257855e-05 2.03357557e-04 4.87312993e-05] [ 2.45894926e-03 2.07784144e-04 -4.32257855e-05 2.87065542e-02 -1.78214071e-02 -2.09973501e-03] [ 2.07439553e-04 1.09539469e-03 2.03357557e-04 -1.78214071e-02 8.45566260e-02 -3.76625484e-03] [-4.33071072e-05 2.03339096e-04 4.87312993e-05 -2.09973501e-03 -3.76625484e-03 9.83882490e-02]] LogLike[0009]=-50860.320623 sigma_a=4.115591 R: [[ 27.453166 41.5083522 ] [ 41.5083522 100.15512917]] m0: [193.92246832 48.2004204 5.71792202 404.79118026 108.98740988 13.28091799] V0: [[ 2.36003593e-02 -1.81826955e-02 -1.99576339e-03 2.72383439e-03 1.75151626e-04 -6.00675309e-05] [-1.81826955e-02 8.21523719e-02 -4.24381815e-03 1.75515616e-04 1.20747115e-03 2.21343334e-04] [-1.99576339e-03 -4.24381815e-03 9.82470326e-02 -5.99816255e-05 2.21363154e-04 5.28329430e-05] [ 2.72383439e-03 1.75515616e-04 -5.99816255e-05 2.84216434e-02 -1.78746681e-02 -2.10250956e-03] [ 1.75151626e-04 1.20747115e-03 2.21363154e-04 -1.78746681e-02 8.42857360e-02 -3.85298070e-03] [-6.00675309e-05 2.21343334e-04 5.28329430e-05 -2.10250956e-03 -3.85298070e-03 9.83402879e-02]] LogLike[0010]=-50411.286925 sigma_a=4.378348 R: [[26.35515438 40.36278475] [40.36278475 96.40150097]] m0: [194.5040394 48.23715251 5.72168108 405.69436238 109.46507985 13.34902548] V0: [[ 2.28689800e-02 -1.81509837e-02 -1.96417690e-03 2.98107411e-03 1.32301389e-04 -7.84406456e-05] [-1.81509837e-02 8.17067571e-02 -4.35269067e-03 1.32578804e-04 1.31694008e-03 2.38470481e-04] [-1.96417690e-03 -4.35269067e-03 9.81974724e-02 -7.83730480e-05 2.38486463e-04 5.66894049e-05] [ 2.98107411e-03 1.32578804e-04 -7.83730480e-05 2.81381612e-02 -1.79184211e-02 -2.10310532e-03] [ 1.32301389e-04 1.31694008e-03 2.38486463e-04 -1.79184211e-02 8.40316530e-02 -3.93189234e-03] [-7.84406456e-05 2.38470481e-04 5.66894049e-05 -2.10310532e-03 -3.93189234e-03 9.82974748e-02]] LogLike[0011]=-49976.250935 sigma_a=4.653379 R: [[25.33435536 39.21675759] [39.21675759 92.77505604]] m0: [195.07875561 48.25610179 5.7220514 406.606318 109.92019052 13.40931576] V0: [[ 2.21606863e-02 -1.80942464e-02 -1.92871726e-03 3.22983980e-03 8.00039719e-05 -9.80830091e-05] [-1.80942464e-02 8.12813329e-02 -4.45316519e-03 8.00519711e-05 1.42456654e-03 2.54926069e-04] [-1.92871726e-03 -4.45316519e-03 9.81528281e-02 -9.80630848e-05 2.54931336e-04 6.03516482e-05] [ 3.22983980e-03 8.00519711e-05 -9.80630848e-05 2.78564811e-02 -1.79532241e-02 -2.10173176e-03] [ 8.00039719e-05 1.42456654e-03 2.54931336e-04 -1.79532241e-02 8.37926049e-02 -4.00388883e-03] [-9.80830091e-05 2.54926069e-04 6.03516482e-05 -2.10173176e-03 -4.00388883e-03 9.82591695e-02]] LogLike[0012]=-49555.159033 sigma_a=4.940840 R: [[24.37981546 38.06990831] [38.06990831 89.26990104]] m0: [195.64670731 48.25917907 5.71950856 407.52719934 110.35302292 13.4621071 ] V0: [[ 2.14770471e-02 -1.80154584e-02 -1.89021620e-03 3.46926175e-03 1.94225051e-05 -1.18664541e-04] [-1.80154584e-02 8.08734404e-02 -4.54632245e-03 1.90667752e-05 1.53090937e-03 2.70860693e-04] [-1.89021620e-03 -4.54632245e-03 9.81124715e-02 -1.18726474e-04 2.70846964e-04 6.38556381e-05] [ 3.46926175e-03 1.90667752e-05 -1.18726474e-04 2.75770072e-02 -1.79796685e-02 -2.09859358e-03] [ 1.94225051e-05 1.53090937e-03 2.70846964e-04 -1.79796685e-02 8.35670239e-02 -4.06976083e-03] [-1.18664541e-04 2.70860693e-04 6.38556381e-05 -2.09859358e-03 -4.06976083e-03 9.82248138e-02]] LogLike[0013]=-49147.635814 sigma_a=5.240908 R: [[23.4816108 36.92413184] [36.92413184 85.88016681]] m0: [196.20819013 48.24807083 5.71444779 408.45709109 110.76382463 13.50770193] V0: [[ 2.08193543e-02 -1.79175658e-02 -1.84943611e-03 3.69854102e-03 -4.82631316e-05 -1.39876459e-04] [-1.79175658e-02 8.04809326e-02 -4.63305743e-03 -4.92215893e-05 1.63635419e-03 2.86379984e-04] [-1.84943611e-03 -4.63305743e-03 9.80758718e-02 -1.40057484e-04 2.86337886e-04 6.72256916e-05] [ 3.69854102e-03 -4.92215893e-05 -1.40057484e-04 2.73001309e-02 -1.79983592e-02 -2.09388575e-03] [-4.82631316e-05 1.63635419e-03 2.86337886e-04 -1.79983592e-02 8.33535444e-02 -4.13019612e-03] [-1.39876459e-04 2.86379984e-04 6.72256916e-05 -2.09388575e-03 -4.13019612e-03 9.81939251e-02]] LogLike[0014]=-48753.439932 sigma_a=5.553402 R: [[22.6315643 35.78291829] [35.78291829 82.60084329]] m0: [196.76367367 48.22421279 5.70718599 409.39600935 111.15283137 13.54639034] V0: [[ 2.01884563e-02 -1.78033894e-02 -1.80705300e-03 3.91705022e-03 -1.21899686e-04 -1.61440463e-04] [-1.78033894e-02 8.01020679e-02 -4.71411399e-03 -1.23677767e-04 1.74115855e-03 3.01555907e-04] [-1.80705300e-03 -4.71411399e-03 9.80425784e-02 -1.61779271e-04 3.01475271e-04 7.04778354e-05] [ 3.91705022e-03 -1.23677767e-04 -1.61779271e-04 2.70261759e-02 -1.80098952e-02 -2.08778884e-03] [-1.21899686e-04 1.74115855e-03 3.01475271e-04 -1.80098952e-02 8.31509707e-02 -4.18579405e-03] [-1.61440463e-04 3.01555907e-04 7.04778354e-05 -2.08778884e-03 -4.18579405e-03 9.81660859e-02]] LogLike[0015]=-48371.770562 sigma_a=5.878519 R: [[21.82388511 34.65115173] [34.65115173 79.42975805]] m0: [197.31374436 48.18880282 5.69797288 410.34392512 111.52030033 13.57845591] V0: [[ 1.95846995e-02 -1.76755541e-02 -1.76364849e-03 4.12438364e-03 -2.00397408e-04 -1.83114693e-04] [-1.76755541e-02 7.97353972e-02 -4.79012112e-03 -2.03224100e-04 1.84549470e-03 3.16437009e-04] [-1.76364849e-03 -4.79012112e-03 9.80122037e-02 -1.83650182e-04 3.16307104e-04 7.36226471e-05] [ 4.12438364e-03 -2.03224100e-04 -1.83650182e-04 2.67553661e-02 -1.80148542e-02 -2.08046640e-03] [-2.00397408e-04 1.84549470e-03 3.16307104e-04 -1.80148542e-02 8.29582346e-02 -4.23708354e-03] [-1.83114693e-04 3.16437009e-04 7.36226471e-05 -2.08046640e-03 -4.23708354e-03 9.81409313e-02]] LogLike[0016]=-48001.728909 sigma_a=6.216529 R: [[21.05401648 33.53328233] [33.53328233 76.36413188]] m0: [197.85903004 48.14282651 5.68700222 411.30074309 111.86647655 13.60416876] V0: [[ 1.90079967e-02 -1.75364373e-02 -1.71971077e-03 4.32034475e-03 -2.82755331e-04 -2.04694633e-04] [-1.75364373e-02 7.93797321e-02 -4.86160669e-03 -2.86867299e-04 1.94946742e-03 3.31054044e-04] [-1.71971077e-03 -4.86160669e-03 9.79844162e-02 -2.05465023e-04 3.30863744e-04 7.66668336e-05] [ 4.32034475e-03 -2.86867299e-04 -2.05465023e-04 2.64878322e-02 -1.80137739e-02 -2.07206295e-03] [-2.82755331e-04 1.94946742e-03 3.30863744e-04 -1.80137739e-02 8.27743947e-02 -4.28452647e-03] [-2.04694633e-04 3.31054044e-04 7.66668336e-05 -2.07206295e-03 -4.28452647e-03 9.81181454e-02]] LogLike[0017]=-47642.238892 sigma_a=6.567981 R: [[20.31864825 32.43337726] [32.43337726 73.40164863]] m0: [198.4001516 48.08709392 5.67442475 412.26632852 112.19159167 13.62378437] V0: [[ 1.84578941e-02 -1.73881475e-02 -1.67564010e-03 4.50492692e-03 -3.68076481e-04 -2.26012235e-04] [-1.73881475e-02 7.90340880e-02 -4.92901718e-03 -3.73715293e-04 2.05313564e-03 3.45425600e-04] [-1.67564010e-03 -4.92901718e-03 9.79589316e-02 -2.27054560e-04 3.45163477e-04 7.96146484e-05] [ 4.50492692e-03 -3.73715293e-04 -2.27054560e-04 2.62236149e-02 -1.80071429e-02 -2.06270380e-03] [-3.68076481e-04 2.05313564e-03 3.45163477e-04 -1.80071429e-02 8.25986166e-02 -4.32852733e-03] [-2.26012235e-04 3.45425600e-04 7.96146484e-05 -2.06270380e-03 -4.32852733e-03 9.80974544e-02]] LogLike[0018]=-47292.640797 sigma_a=6.933031 R: [[19.61520342 31.35467726] [31.35467726 70.53971233]] m0: [198.93768297 48.0222764 5.66035913 413.24051268 112.49584819 13.63754083] V0: [[ 1.79336686e-02 -1.72325256e-02 -1.63175892e-03 4.67827451e-03 -4.55570735e-04 -2.46932357e-04] [-1.72325256e-02 7.86976539e-02 -4.99273045e-03 -4.62981467e-04 2.15652390e-03 3.59561638e-04] [-1.63175892e-03 -4.99273045e-03 9.79355055e-02 -2.48282232e-04 3.59215996e-04 8.24687417e-05] [ 4.67827451e-03 -4.62981467e-04 -2.48282232e-04 2.59626827e-02 -1.79953954e-02 -2.05249604e-03] [-4.55570735e-04 2.15652390e-03 3.59215996e-04 -1.79953954e-02 8.24301634e-02 -4.36943939e-03] [-2.46932357e-04 3.59561638e-04 8.24687417e-05 -2.05249604e-03 -4.36943939e-03 9.80786212e-02]] LogLike[0019]=-46952.053478 sigma_a=7.312255 R: [[18.94215735 30.30038201] [30.30038201 67.77762472]] m0: [199.47213635 47.94894641 5.64490262 414.22312702 112.77944388 13.64566375] V0: [[ 1.74344028e-02 -1.70711695e-02 -1.58832338e-03 4.84064836e-03 -5.44549232e-04 -2.67348726e-04] [-1.70711695e-02 7.83697400e-02 -5.05307334e-03 -5.53980022e-04 2.25963643e-03 3.73466848e-04] [-1.58832338e-03 -5.05307334e-03 9.79139251e-02 -2.69040301e-04 3.73025711e-04 8.52309095e-05] [ 4.84064836e-03 -5.53980022e-04 -2.69040301e-04 2.57049432e-02 -1.79789164e-02 -2.04153105e-03] [-5.44549232e-04 2.25963643e-03 3.73025711e-04 -1.79789164e-02 8.22683693e-02 -4.40757616e-03] [-2.67348726e-04 3.73466848e-04 8.52309095e-05 -2.04153105e-03 -4.40757616e-03 9.80614383e-02]] LogLike[0020]=-46619.973878 sigma_a=7.705835 R: [[18.29802926 29.27261023] [29.27261023 65.11366679]] m0: [200.00394531 47.86760315 5.6281367 415.21397284 113.04254819 13.6483639 ] V0: [[ 1.69590830e-02 -1.69054623e-02 -1.54553603e-03 4.99237964e-03 -6.34412304e-04 -2.87178347e-04] [-1.69054623e-02 7.80497802e-02 -5.11032541e-03 -6.46114299e-04 2.36245529e-03 3.87141379e-04] [-1.54553603e-03 -5.11032541e-03 9.78940059e-02 -2.89244321e-04 3.86592467e-04 8.79022450e-05] [ 4.99237964e-03 -6.46114299e-04 -2.89244321e-04 2.54502726e-02 -1.79580440e-02 -2.02988676e-03] [-6.34412304e-04 2.36245529e-03 3.86592467e-04 -1.79580440e-02 8.21126435e-02 -4.44321326e-03] [-2.87178347e-04 3.87141379e-04 8.79022450e-05 -2.02988676e-03 -4.44321326e-03 9.80457251e-02]] LogLike[0021]=-46295.744729 sigma_a=8.114308 R: [[17.68180408 28.27330521] [28.27330521 62.54713209]] m0: [200.53347708 47.77869472 5.61013245 416.21285101 113.28532855 13.64584219] V0: [[ 1.65066360e-02 -1.67366000e-02 -1.50355471e-03 5.13384846e-03 -7.24640396e-04 -3.06358027e-04] [-1.67366000e-02 7.77372956e-02 -5.16473089e-03 -7.38867952e-04 2.46494919e-03 4.00582732e-04] [-1.50355471e-03 -5.16473089e-03 9.78755856e-02 -3.08829704e-04 3.99913422e-04 9.04835206e-05] [ 5.13384846e-03 -7.38867952e-04 -3.08829704e-04 2.51985215e-02 -1.79330765e-02 -2.01762993e-03] [-7.24640396e-04 2.46494919e-03 3.99913422e-04 -1.79330765e-02 8.19624497e-02 -4.47659666e-03] [-3.06358027e-04 4.00582732e-04 9.04835206e-05 -2.01762993e-03 -4.47659666e-03 9.80313224e-02]] LogLike[0022]=-45978.812161 sigma_a=8.538173 R: [[17.09225844 27.30349521] [27.30349521 60.076146 ]] m0: [201.06103352 47.68262877 5.59095254 417.21953488 113.5079379 13.63828917] V0: [[ 1.60759797e-02 -1.65656167e-02 -1.46250140e-03 5.26545768e-03 -8.14782645e-04 -3.24840267e-04] [-1.65656167e-02 7.74318948e-02 -5.21650117e-03 -8.31793441e-04 2.56707202e-03 4.13786075e-04] [-1.46250140e-03 -5.21650117e-03 9.78585227e-02 -3.27747590e-04 4.12983368e-04 9.29752280e-05] [ 5.26545768e-03 -8.31793441e-04 -3.27747590e-04 2.49495339e-02 -1.79042764e-02 -2.00481806e-03] [-8.14782645e-04 2.56707202e-03 4.12983368e-04 -1.79042764e-02 8.18173089e-02 -4.50794417e-03] [-3.24840267e-04 4.13786075e-04 9.29752280e-05 -2.00481806e-03 -4.50794417e-03 9.80180908e-02]] LogLike[0023]=-45668.772842 sigma_a=8.977763 R: [[16.5281429 26.36371688] [26.36371688 57.69844484]] m0: [201.58686797 47.57977842 5.57065274 418.23378474 113.71052549 13.6258871 ] V0: [[ 1.56660352e-02 -1.63934005e-02 -1.42246766e-03 5.38762367e-03 -9.04450698e-04 -3.42590950e-04] [-1.63934005e-02 7.71332524e-02 -5.26582146e-03 -9.24505916e-04 2.66876872e-03 4.26745394e-04] [-1.42246766e-03 -5.26582146e-03 9.78426924e-02 -3.45962546e-04 4.25795879e-04 9.53777793e-05] [ 5.38762367e-03 -9.24505916e-04 -3.45962546e-04 2.47031489e-02 -1.78718738e-02 -1.99150065e-03] [-9.04450698e-04 2.66876872e-03 4.25795879e-04 -1.78718738e-02 8.16767889e-02 -4.53744981e-03] [-3.42590950e-04 4.26745394e-04 9.53777793e-05 -1.99150065e-03 -4.53744981e-03 9.80059079e-02]] LogLike[0024]=-45365.286692 sigma_a=9.433329 R: [[15.98826146 25.45422336] [25.45422336 55.41173061]] m0: [202.11119744 47.47048769 5.54928347 419.25535662 113.89324965 13.60881247] V0: [[ 1.52757365e-02 -1.62207110e-02 -1.38351948e-03 5.50076895e-03 -9.93312250e-04 -3.59587298e-04] [-1.62207110e-02 7.68410901e-02 -5.31285639e-03 -1.01667671e-03 2.76998023e-03 4.39454343e-04] [-1.38351948e-03 -5.31285639e-03 9.78279840e-02 -3.63450504e-04 4.38344166e-04 9.76916479e-05] [ 5.50076895e-03 -1.01667671e-03 -3.63450504e-04 2.44592040e-02 -1.78360709e-02 -1.97772049e-03] [-9.93312250e-04 2.76998023e-03 4.38344166e-04 -1.78360709e-02 8.15404954e-02 -4.56528781e-03] [-3.59587298e-04 4.39454343e-04 9.76916479e-05 -1.97772049e-03 -4.56528781e-03 9.79946651e-02]] LogLike[0025]=-45067.882889 sigma_a=9.905405 R: [[15.47139878 24.57493915] [24.57493915 53.21342126]] m0: [202.63421137 47.35507494 5.52689051 420.28400208 114.05628402 13.5872376 ] V0: [[ 1.49040407e-02 -1.60481944e-02 -1.34570166e-03 5.60531541e-03 -1.08108474e-03 -3.75815969e-04] [-1.60481944e-02 7.65551647e-02 -5.35775365e-03 -1.10802694e-03 2.87064629e-03 4.51906736e-04] [-1.34570166e-03 -5.35775365e-03 9.78142987e-02 -3.80196849e-04 4.50621569e-04 9.99174347e-05] [ 5.60531541e-03 -1.10802694e-03 -3.80196849e-04 2.42175378e-02 -1.77970462e-02 -1.96351481e-03] [-1.08108474e-03 2.87064629e-03 4.50621569e-04 -1.77970462e-02 8.14080660e-02 -4.59161524e-03] [-3.75815969e-04 4.51906736e-04 9.99174347e-05 -1.96351481e-03 -4.59161524e-03 9.79842658e-02]] LogLike[0026]=-44776.082758 sigma_a=10.394594 R: [[14.97613319 23.72522413] [23.72522413 51.09993006]] m0: [203.15607795 47.23383223 5.50351491 421.31946073 114.19981053 13.56132998] V0: [[ 0.01454994 -0.01587639 -0.00130904 0.00570168 -0.00116753 -0.00039127] [-0.01587639 0.07627526 -0.00540065 -0.00119832 0.00297071 0.0004641 ] [-0.00130904 -0.00540065 0.09780155 -0.00039619 0.00046262 0.00010206] [ 0.00570168 -0.00119832 -0.00039619 0.02397799 -0.01775495 -0.00194892] [-0.00116753 0.00297071 0.00046262 -0.01775495 0.08127917 -0.00461657] [-0.00039127 0.0004641 0.00010206 -0.00194892 -0.00461657 0.09797462]] LogLike[0027]=-44489.579638 sigma_a=10.901122 R: [[14.50099108 22.90412569] [22.90412569 49.06719813]] m0: [203.67695389 47.10702528 5.4791932 422.36147482 114.32401996 13.53125198] V0: [[ 0.01421244 -0.01570576 -0.00127355 0.00579027 -0.00125245 -0.00040595] [-0.01570576 0.07600119 -0.00544165 -0.00128737 0.00307011 0.00047602] [-0.00127355 -0.00544165 0.09778966 -0.00041144 0.00047434 0.00010411] [ 0.00579027 -0.00128737 -0.00041144 0.02374042 -0.01770993 -0.00193395] [-0.00125245 0.00307011 0.00047434 -0.01770993 0.0811535 -0.00464029] [-0.00040595 0.00047602 0.00010411 -0.00193395 -0.00464029 0.09796567]] LogLike[0028]=-44207.824156 sigma_a=11.425807 R: [[14.04468668 22.11074994] [22.11074994 47.11159858]] m0: [204.19699177 46.97489802 5.45395855 423.40981104 114.4291221 13.4971621 ] V0: [[ 0.0138906 -0.01553665 -0.00123923 0.00587149 -0.0013357 -0.00041987] [-0.01553665 0.07573277 -0.00548089 -0.00137502 0.0031688 0.00048767] [-0.00123923 -0.00548089 0.09777855 -0.00042595 0.00048577 0.00010607] [ 0.00587149 -0.00137502 -0.00042595 0.02350466 -0.01766209 -0.00191864] [-0.0013357 0.0031688 0.00048577 -0.01766209 0.08103077 -0.00466288] [-0.00041987 0.00048767 0.00010607 -0.00191864 -0.00466288 0.09795732]] LogLike[0029]=-43930.345885 sigma_a=11.969322 R: [[13.60574902 21.34372401] [21.34372401 45.22859432]] m0: [204.71633594 46.83767282 5.4278404 424.46423821 114.51532734 13.45921323] V0: [[ 0.01358349 -0.01536935 -0.00120606 0.00594574 -0.00141714 -0.00043304] [-0.01536935 0.0754698 -0.00551845 -0.00146115 0.00326675 0.00049905] [-0.00120606 -0.00551845 0.09776816 -0.00043973 0.00049691 0.00010796] [ 0.00594574 -0.00146115 -0.00043973 0.02327056 -0.01761152 -0.00190302] [-0.00141714 0.00326675 0.00049691 -0.01761152 0.08091071 -0.00468445] [-0.00043304 0.00049905 0.00010796 -0.00190302 -0.00468445 0.09794953]] LogLike[0030]=-43656.658116 sigma_a=12.532441 R: [[13.18282448 20.60167382] [20.60167382 43.41385221]] m0: [205.2351314 46.69555252 5.40086498 425.52455395 114.58284817 13.41755211] V0: [[ 0.01329025 -0.0152041 -0.00117403 0.00601338 -0.00149668 -0.00044546] [-0.0152041 0.07521211 -0.00555444 -0.00154568 0.00336392 0.00051016] [-0.00117403 -0.00555444 0.09775844 -0.00045278 0.00050777 0.00010976] [ 0.00601338 -0.00154568 -0.00045278 0.02303796 -0.0175583 -0.00188708] [-0.00149668 0.00336392 0.00050777 -0.0175583 0.08079307 -0.00470509] [-0.00044546 0.00051016 0.00010976 -0.00188708 -0.00470509 0.09794225]] LogLike[0031]=-43386.234493 sigma_a=13.116125 R: [[12.77463475 19.88318091] [19.88318091 41.6631466 ]] m0: [205.75352321 46.54872364 5.3730557 426.5905852 114.63189368 13.37231893] V0: [[ 0.01301002 -0.01504104 -0.0011431 0.00607478 -0.00157425 -0.00045717] [-0.01504104 0.07495953 -0.00558894 -0.00162854 0.0034603 0.000521 ] [-0.0011431 -0.00558894 0.09774933 -0.00046514 0.00051833 0.00011148] [ 0.00607478 -0.00162854 -0.00046514 0.02280673 -0.0175025 -0.00187086] [-0.00157425 0.0034603 0.00051833 -0.0175025 0.0806776 -0.0047249 ] [-0.00045717 0.000521 0.00011148 -0.00187086 -0.0047249 0.09793541]] LogLike[0032]=-43118.576195 sigma_a=13.721353 R: [[12.3799549 19.18677521] [19.18677521 39.97232163]] m0: [206.27165705 46.39735843 5.34443327 427.66218872 114.66266221 13.32364671] V0: [[ 0.01274202 -0.01488031 -0.00111326 0.00613029 -0.00164981 -0.00046817] [-0.01488031 0.07471187 -0.00562204 -0.00170968 0.00355588 0.00053156] [-0.00111326 -0.00562204 0.09774078 -0.00047681 0.0005286 0.00011312] [ 0.00613029 -0.00170968 -0.00047681 0.0225767 -0.01744415 -0.00185436] [-0.00164981 0.00355588 0.0005286 -0.01744415 0.08056408 -0.00474394] [-0.00046817 0.00053156 0.00011312 -0.00185436 -0.00474394 0.09792898]] LogLike[0033]=-42853.108744 sigma_a=14.349476 R: [[11.99767834 18.51105721] [18.51105721 38.33756351]] m0: [206.78968135 46.2416172 5.31501599 428.73925798 114.67533787 13.27166097] V0: [[ 0.01248549 -0.01472198 -0.00108446 0.00618024 -0.00172332 -0.0004785 ] [-0.01472198 0.07446895 -0.00565381 -0.0017891 0.00365064 0.00054186] [-0.00108446 -0.00565381 0.09773276 -0.00048782 0.00053859 0.00011469] [ 0.00618024 -0.0017891 -0.00048782 0.02234773 -0.0173833 -0.00183758] [-0.00172332 0.00365064 0.00053859 -0.0173833 0.08045228 -0.00476231] [-0.0004785 0.00054186 0.00011469 -0.00183758 -0.00476231 0.09792293]] LogLike[0034]=-42589.346361 sigma_a=15.001709 R: [[11.62672985 17.85459047] [17.85459047 36.75512332]] m0: [207.30774582 46.0816493 5.28481963 429.82171552 114.67008134 13.21647925] V0: [[ 0.01223973 -0.01456608 -0.00105668 0.00622494 -0.00179477 -0.00048816] [-0.01456608 0.07423061 -0.00568433 -0.00186678 0.0037446 0.0005519 ] [-0.00105668 -0.00568433 0.09772522 -0.00049819 0.00054829 0.00011618] [ 0.00622494 -0.00186678 -0.00049819 0.02211967 -0.01731995 -0.00182054] [-0.00179477 0.0037446 0.00054829 -0.01731995 0.080342 -0.00478006] [-0.00048816 0.0005519 0.00011618 -0.00182054 -0.00478006 0.09791721]] LogLike[0035]=-42326.772153 sigma_a=15.679544 R: [[11.26620362 17.2161289 ] [17.2161289 35.22183214]] m0: [207.82600513 45.91759502 5.25385769 430.90952514 114.64703002 13.15821113] V0: [[ 0.01200407 -0.01441266 -0.00102986 0.00626466 -0.00186416 -0.00049719] [-0.01441266 0.07399665 -0.00571366 -0.00194273 0.00383777 0.00056167] [-0.00102986 -0.00571366 0.09771812 -0.00050793 0.00055771 0.0001176 ] [ 0.00626466 -0.00194273 -0.00050793 0.02189236 -0.01725412 -0.00180325] [-0.00186416 0.00383777 0.00055771 -0.01725412 0.08023302 -0.00479725] [-0.00049719 0.00056167 0.0001176 -0.00180325 -0.00479725 0.0979118 ]] LogLike[0036]=-42064.905449 sigma_a=16.384541 R: [[10.91526741 16.59449025] [16.59449025 33.73479152]] m0: [208.34461626 45.74958678 5.22214145 432.00268104 114.60629282 13.09695855] V0: [[ 0.01177789 -0.0142617 -0.00100398 0.00629967 -0.00193147 -0.0005056 ] [-0.0142617 0.07376692 -0.00574187 -0.00201696 0.00393014 0.00057119] [-0.00100398 -0.00574187 0.09771145 -0.00051707 0.00056686 0.00011895] [ 0.00629967 -0.00201696 -0.00051707 0.02166567 -0.0171858 -0.0017857 ] [-0.00193147 0.00393014 0.00056686 -0.0171858 0.08012515 -0.00481395] [-0.0005056 0.00057119 0.00011895 -0.0017857 -0.00481395 0.09790666]] LogLike[0037]=-41803.313024 sigma_a=17.118285 R: [[10.57320316 15.98863239] [15.98863239 32.29152309]] m0: [208.86373982 45.57774961 5.18967997 433.10120919 114.54794858 13.03281598] V0: [[ 0.01156062 -0.0141132 -0.00097899 0.00633022 -0.00199672 -0.00051341] [-0.0141132 0.07354125 -0.00576902 -0.00208949 0.00402175 0.00058046] [-0.00097899 -0.00576902 0.09770515 -0.00052564 0.00057572 0.00012023] [ 0.00633022 -0.00208949 -0.00052564 0.02143944 -0.01711498 -0.00176789] [-0.00199672 0.00402175 0.00057572 -0.01711498 0.0800182 -0.00483021] [-0.00051341 0.00058046 0.00012023 -0.00176789 -0.00483021 0.09790177]] LogLike[0038]=-41541.578533 sigma_a=17.882516 R: [[10.23941402 15.39767496] [15.39767496 30.89000159]] m0: [209.38353987 45.40220191 5.15648025 434.20516506 114.47204611 12.96587106] V0: [[ 0.01135174 -0.01396713 -0.00095488 0.00635653 -0.00205992 -0.00052065] [-0.01396713 0.07331948 -0.00579516 -0.00216035 0.00411261 0.00058949] [-0.00095488 -0.00579516 0.09769922 -0.00053363 0.00058432 0.00012144] [ 0.00635653 -0.00216035 -0.00053363 0.02121354 -0.01704164 -0.00174984] [-0.00205992 0.00411261 0.00058432 -0.01704164 0.07991198 -0.00484608] [-0.00052065 0.00058949 0.00012144 -0.00174984 -0.00484608 0.09789712]] LogLike[0039]=-41279.289629 sigma_a=18.679211 R: [[ 9.91338871 14.82085581] [14.82085581 29.52853379]] m0: [209.90418259 45.2230554 5.12254725 435.31462603 114.37860357 12.89620525] V0: [[ 0.01115074 -0.01382346 -0.00093158 0.00637879 -0.00212107 -0.00052732] [-0.01382346 0.07310148 -0.00582033 -0.00222954 0.00420272 0.00059827] [-0.00093158 -0.00582033 0.09769362 -0.00054108 0.00059264 0.00012259] [ 0.00637879 -0.00222954 -0.00054108 0.02098782 -0.01696575 -0.00173154] [-0.00212107 0.00420272 0.00059264 -0.01696575 0.07980631 -0.0048616 ] [-0.00052732 0.00059827 0.00012259 -0.00173154 -0.0048616 0.09789267]] LogLike[0040]=-41016.084028 sigma_a=19.510403 R: [[ 9.59467623 14.25750074] [14.25750074 28.2056652 ]] m0: [210.42583543 45.04041434 5.08788383 436.42968469 114.26760758 12.82389445] V0: [[ 0.01095718 -0.01368218 -0.00090909 0.00639718 -0.00218017 -0.00053345] [-0.01368218 0.07288711 -0.0058446 -0.00229709 0.0042921 0.00060681] [-0.00090909 -0.0058446 0.09768834 -0.000548 0.0006007 0.00012368] [ 0.00639718 -0.00229709 -0.000548 0.02076216 -0.01688729 -0.001713 ] [-0.00218017 0.0042921 0.0006007 -0.01688729 0.07970102 -0.00487682] [-0.00053345 0.00060681 0.00012368 -0.001713 -0.00487682 0.0978884 ]] LogLike[0041]=-40751.669528 sigma_a=20.378070 R: [[ 9.28290993 13.70706373] [13.70706373 26.92025358]] m0: [210.94866765 44.8543747 5.05249084 437.55044817 114.13901475 12.74900952] V0: [[ 0.01077064 -0.01354325 -0.00088737 0.00641187 -0.00223723 -0.00053905] [-0.01354325 0.07267625 -0.00586799 -0.00236301 0.00438076 0.00061512] [-0.00088737 -0.00586799 0.09768334 -0.0005544 0.00060848 0.0001247 ] [ 0.00641187 -0.00236301 -0.0005544 0.02053644 -0.01680621 -0.0016942 ] [-0.00223723 0.00438076 0.00060848 -0.01680621 0.07959593 -0.00489178] [-0.00053905 0.00061512 0.0001247 -0.0016942 -0.00489178 0.09788431]] LogLike[0042]=-40485.798004 sigma_a=21.284247 R: [[ 8.97781348 13.16913834] [13.16913834 25.67148479]] m0: [211.47284997 44.66502369 5.0163673 438.67703594 113.9927554 12.67161716] V0: [[ 0.01059074 -0.01340664 -0.00086638 0.00642298 -0.00229224 -0.00054414] [-0.01340664 0.07246879 -0.00589055 -0.00242732 0.00446869 0.00062319] [-0.00086638 -0.00589055 0.09767863 -0.00056029 0.000616 0.00012566] [ 0.00642298 -0.00242732 -0.00056029 0.02031053 -0.01672249 -0.00167517] [-0.00229224 0.00446869 0.000616 -0.01672249 0.07949089 -0.00490651] [-0.00054414 0.00062319 0.00012566 -0.00167517 -0.00490651 0.09788037]] LogLike[0043]=-40218.256874 sigma_a=22.231053 R: [[ 8.67916635 12.64340877] [12.64340877 24.4587525 ]] m0: [211.99855327 44.47243861 4.97951049 439.80957279 113.82873711 12.59178082] V0: [[ 0.01041711 -0.01327234 -0.0008461 0.00643063 -0.00234519 -0.00054872] [-0.01327234 0.07226464 -0.00591232 -0.00249001 0.00455589 0.00063102] [-0.0008461 -0.00591232 0.09767416 -0.00056569 0.00062326 0.00012656] [ 0.00643063 -0.00249001 -0.00056569 0.02008432 -0.01663609 -0.00165588] [-0.00234519 0.00455589 0.00062326 -0.01663609 0.07938573 -0.00492106] [-0.00054872 0.00063102 0.00012656 -0.00165588 -0.00492106 0.09787658]] LogLike[0044]=-39948.866309 sigma_a=23.220691 R: [[ 8.3867795 12.12961543] [12.12961543 23.28156775]] m0: [212.52594828 44.27668498 4.94191606 440.94818369 113.64684796 12.50956152] V0: [[ 0.01024944 -0.01314031 -0.00082651 0.00643494 -0.00239607 -0.00055282] [-0.01314031 0.07206372 -0.00593332 -0.00255108 0.00464235 0.00063862] [-0.00082651 -0.00593332 0.09766994 -0.0005706 0.00063024 0.0001274 ] [ 0.00643494 -0.00255108 -0.0005706 0.01985771 -0.01654697 -0.00163636] [-0.00239607 0.00464235 0.00063024 -0.01654697 0.07928031 -0.00493545] [-0.00055282 0.00063862 0.0001274 -0.00163636 -0.00493545 0.09787291]] LogLike[0045]=-39677.495752 sigma_a=24.255328 R: [[ 8.10047964 11.62753223] [11.62753223 22.13949793]] m0: [213.05520589 44.07781417 4.90357799 442.09299059 113.44695975 12.42501842] V0: [[ 0.01008742 -0.01301055 -0.00080757 0.00643597 -0.00244486 -0.00055642] [-0.01301055 0.07186597 -0.00595359 -0.00261052 0.00472804 0.00064599] [-0.00080757 -0.00595359 0.09766595 -0.00057503 0.00063694 0.00012819] [ 0.00643597 -0.00261052 -0.00057503 0.01963061 -0.01645509 -0.00161659] [-0.00244486 0.00472804 0.00063694 -0.01645509 0.07917448 -0.00494971] [-0.00055642 0.00064599 0.00012819 -0.00161659 -0.00494971 0.09786936]] LogLike[0046]=-39404.042189 sigma_a=25.337171 R: [[ 7.82011112 11.13696915] [11.13696915 21.03216474]] m0: [213.58649858 43.87586086 4.86448863 443.24411299 113.22893165 12.33820926] V0: [[ 0.00993077 -0.01288305 -0.00078928 0.00643381 -0.00249153 -0.00055956] [-0.01288305 0.07167133 -0.00597316 -0.00266831 0.00481293 0.00065311] [-0.00078928 -0.00597316 0.09766216 -0.00057899 0.00064338 0.00012891] [ 0.00643381 -0.00266831 -0.00057899 0.01940292 -0.01636042 -0.00159659] [-0.00249153 0.00481293 0.00064338 -0.01636042 0.07906809 -0.00496387] [-0.00055956 0.00065311 0.00012891 -0.00159659 -0.00496387 0.09786591]] LogLike[0047]=-39128.437210 sigma_a=26.468374 R: [[ 7.54551546 10.65774228] [10.65774228 19.95917512]] m0: [214.12000115 43.67084032 4.82463873 444.4016661 112.99261351 12.24919079] V0: [[ 0.00977923 -0.0127578 -0.0007716 0.00642851 -0.00253604 -0.00056222] [-0.0127578 0.07147978 -0.00599204 -0.00272441 0.00489697 0.00066 ] [-0.0007716 -0.00599204 0.09765858 -0.00058248 0.00064953 0.00012958] [ 0.00642851 -0.00272441 -0.00058248 0.01917458 -0.01626293 -0.00157634] [-0.00253604 0.00489697 0.00064953 -0.01626293 0.07896103 -0.00497796] [-0.00056222 0.00066 0.00012958 -0.00157634 -0.00497796 0.09786256]] LogLike[0048]=-38850.588060 sigma_a=27.651363 R: [[ 7.27653203 10.18967451] [10.18967451 18.92011794]] m0: [214.65589279 43.46274533 4.78401739 445.56576296 112.7378487 12.15801895] V0: [[ 0.00963255 -0.01263478 -0.00075452 0.00642012 -0.00257836 -0.00056443] [-0.01263478 0.07129127 -0.00601026 -0.00277879 0.00498013 0.00066664] [-0.00075452 -0.00601026 0.09765519 -0.0005855 0.00065539 0.00013018] [ 0.00642012 -0.00277879 -0.0005855 0.0189455 -0.0161626 -0.00155587] [-0.00257836 0.00498013 0.00065539 -0.0161626 0.07885315 -0.004992 ] [-0.00056443 0.00066664 0.00013018 -0.00155587 -0.004992 0.09785929]] LogLike[0049]=-38570.428827 sigma_a=28.888455 R: [[ 7.01296193 9.73254374] [ 9.73254374 17.9144515 ]] m0: [215.19435766 43.251543 4.74261198 446.73651091 112.46447499 12.06474907] V0: [[ 0.00949051 -0.012514 -0.00073801 0.00640866 -0.00261844 -0.00056618] [-0.012514 0.0711058 -0.00602785 -0.00283139 0.00506234 0.00067303] [-0.00073801 -0.00602785 0.09765197 -0.00058806 0.00066096 0.00013073] [ 0.00640866 -0.00283139 -0.00058806 0.01871564 -0.01605939 -0.00153517] [-0.00261844 0.00506234 0.00066096 -0.01605939 0.07874434 -0.00500601] [-0.00056618 0.00067303 0.00013073 -0.00153517 -0.00500601 0.0978561 ]] LogLike[0050]=-38287.879057 sigma_a=30.182082 R: [[ 6.75460466 9.28613508] [ 9.28613508 16.9416094 ]] m0: [215.73558907 43.03717133 4.70040802 447.91402056 112.17232485 11.96943549] V0: [[ 0.00935287 -0.01239545 -0.00072206 0.00639417 -0.00265623 -0.00056747] [-0.01239545 0.07092336 -0.00604483 -0.00288216 0.00514352 0.00067916] [-0.00072206 -0.00604483 0.09764892 -0.00059015 0.00066623 0.00013122] [ 0.00639417 -0.00288216 -0.00059015 0.01848493 -0.01595328 -0.00151425] [-0.00265623 0.00514352 0.00066623 -0.01595328 0.07863449 -0.00502002] [-0.00056747 0.00067916 0.00013122 -0.00151425 -0.00502002 0.09785298]] LogLike[0051]=-38002.815762 sigma_a=31.534959 R: [[ 6.50124719 8.85022489] [ 8.85022489 16.00096912]] m0: [216.27979061 42.81953667 4.65738915 449.09840652 111.86122544 11.87213144] V0: [[ 0.00921943 -0.01227912 -0.00070664 0.00637665 -0.00269168 -0.00056832] [-0.01227912 0.07074394 -0.00606121 -0.00293104 0.00522362 0.00068503] [-0.00070664 -0.00606121 0.09764603 -0.00059179 0.00067119 0.00013166] [ 0.00637665 -0.00293104 -0.00059179 0.01825332 -0.01584426 -0.00149311] [-0.00269168 0.00522362 0.00067119 -0.01584426 0.07852349 -0.00503403] [-0.00056832 0.00068503 0.00013166 -0.00149311 -0.00503403 0.09784993]] LogLike[0052]=-37715.098574 sigma_a=32.949873 R: [[ 6.25265721 8.42457107] [ 8.42457107 15.09183222]] m0: [216.8271774 42.59851101 4.61353706 450.28978792 111.53099687 11.77288897] V0: [[ 0.00908997 -0.012165 -0.00069173 0.00635612 -0.00272473 -0.00056873] [-0.012165 0.07056753 -0.00607701 -0.00297796 0.00530253 0.00069063] [-0.00069173 -0.00607701 0.09764329 -0.00059296 0.00067584 0.00013203] [ 0.00635612 -0.00297796 -0.00059296 0.01802076 -0.01573229 -0.00147175] [-0.00272473 0.00530253 0.00067584 -0.01573229 0.07841122 -0.00504808] [-0.00056873 0.00069063 0.00013203 -0.00147175 -0.00504808 0.09784693]] LogLike[0053]=-37424.546970 sigma_a=34.429850 R: [[ 6.00861133 8.00895175] [ 8.00895175 14.21350338]] m0: [217.37797871 42.37392972 4.56883145 451.48829499 111.18144954 11.67175839] V0: [[ 0.0089643 -0.01205306 -0.00067731 0.00633258 -0.00275532 -0.0005687 ] [-0.01205306 0.07039415 -0.00609226 -0.00302284 0.00538017 0.00069596] [-0.00067731 -0.00609226 0.09764069 -0.00059367 0.00068016 0.00013235] [ 0.00633258 -0.00302284 -0.00059367 0.01778721 -0.01561737 -0.00145019] [-0.00275532 0.00538017 0.00068016 -0.01561737 0.07829758 -0.00506217] [-0.0005687 0.00069596 0.00013235 -0.00145019 -0.00506217 0.09784398]] LogLike[0054]=-37130.931391 sigma_a=35.978224 R: [[ 5.76889852 7.60316878] [ 7.60316878 13.36530057]] m0: [217.93243826 42.14559019 4.52325007 452.69406981 110.81238181 11.56878824] V0: [[ 0.00884221 -0.01194328 -0.00066337 0.00630602 -0.00278339 -0.00056823] [-0.01194328 0.07022377 -0.00610697 -0.0030656 0.00545645 0.00070099] [-0.00066337 -0.00610697 0.09763822 -0.00059392 0.00068416 0.00013261] [ 0.00630602 -0.0030656 -0.00059392 0.01755261 -0.01549946 -0.00142842] [-0.00278339 0.00545645 0.00068416 -0.01549946 0.07818248 -0.00507633] [-0.00056823 0.00070099 0.00013261 -0.00142842 -0.00507633 0.09784108]] LogLike[0055]=-36833.978861 sigma_a=37.598627 R: [[ 5.53332625 7.20705453] [ 7.20705453 12.54657119]] m0: [218.49081405 41.91325076 4.47676886 453.90726632 110.42357728 11.46402515] V0: [[ 0.0087235 -0.01183563 -0.00064988 0.00627644 -0.00280887 -0.00056733] [-0.01183563 0.07005641 -0.00612115 -0.00310616 0.00553127 0.00070574] [-0.00064988 -0.00612115 0.09763587 -0.0005937 0.00068781 0.00013282] [ 0.00627644 -0.00310616 -0.0005937 0.01731692 -0.01537853 -0.00140646] [-0.00280887 0.00553127 0.00068781 -0.01537853 0.0780658 -0.00509056] [-0.00056733 0.00070574 0.00013282 -0.00140646 -0.00509056 0.09783822]] LogLike[0056]=-36533.363878 sigma_a=39.295110 R: [[ 5.30173326 6.82048722] [ 6.82048722 11.75672494]] m0: [219.05337794 41.67663023 4.42936208 455.12805053 110.01480199 11.35751394] V0: [[ 0.00860799 -0.01173007 -0.00063681 0.00624382 -0.0028317 -0.000566 ] [-0.01173007 0.06989204 -0.00613484 -0.00314442 0.00560453 0.00071018] [-0.00063681 -0.00613484 0.09763364 -0.00059302 0.00069112 0.00013296] [ 0.00624382 -0.00314442 -0.00059302 0.01708009 -0.01525457 -0.0013843 ] [-0.0028317 0.00560453 0.00069112 -0.01525457 0.07794745 -0.00510488] [-0.000566 0.00071018 0.00013296 -0.0013843 -0.00510488 0.0978354 ]] LogLike[0057]=-36228.723407 sigma_a=41.072062 R: [[ 5.07399212 6.4433919 ] [ 6.4433919 10.9952391 ]] m0: [219.62041381 41.43540796 4.38100263 456.35659732 109.58580255 11.24929789] V0: [[ 0.00849548 -0.01162655 -0.00062416 0.00620815 -0.00285182 -0.00056424] [-0.01162655 0.06973066 -0.00614804 -0.0031803 0.0056761 0.00071431] [-0.00062416 -0.00614804 0.09763152 -0.00059188 0.00069407 0.00013305] [ 0.00620815 -0.0031803 -0.00059188 0.01684206 -0.01512753 -0.00136195] [-0.00285182 0.0056761 0.00069407 -0.01512753 0.07782731 -0.0051193 ] [-0.00056424 0.00071431 0.00013305 -0.00136195 -0.0051193 0.09783261]] LogLike[0058]=-35919.653939 sigma_a=42.934308 R: [[ 4.85002005 6.07575212] [ 6.07575212 10.26168377]] m0: [220.19221583 41.18922416 4.33166235 457.59308817 109.13630473 11.13941905] V0: [[ 0.00838578 -0.01152501 -0.00061188 0.0061694 -0.00286915 -0.00056205] [-0.01152501 0.06957224 -0.00616078 -0.00321369 0.0057459 0.00071813] [-0.00061188 -0.00616078 0.09762951 -0.00059026 0.00069666 0.00013309] [ 0.0061694 -0.00321369 -0.00059026 0.01660279 -0.01499737 -0.00133941] [-0.00286915 0.0057459 0.00069666 -0.01499737 0.07770528 -0.00513383] [-0.00056205 0.00071813 0.00013309 -0.00133941 -0.00513383 0.09782986]] LogLike[0059]=-35605.712575 sigma_a=44.887182 R: [[4.62977829 5.71760596] [5.71760596 9.55571748]] m0: [220.76908526 40.93768081 4.28131247 458.83770506 108.6660138 11.02791897] V0: [[ 0.0082787 -0.01142538 -0.00059998 0.00612756 -0.00288362 -0.00055944] [-0.01142538 0.06941675 -0.00617308 -0.0032445 0.00581378 0.00072161] [-0.00059998 -0.00617308 0.09762758 -0.00058818 0.00069888 0.00013306] [ 0.00612756 -0.0032445 -0.00058818 0.01636221 -0.01486405 -0.00131669] [-0.00288362 0.00581378 0.00069888 -0.01486405 0.07758125 -0.00514849] [-0.00055944 0.00072161 0.00013306 -0.00131669 -0.00514849 0.09782712]] LogLike[0060]=-35286.435152 sigma_a=46.936413 R: [[4.41326879 5.36903871] [5.36903871 8.87707612]] m0: [221.35132666 40.68034267 4.22992415 460.09062268 108.17461603 10.91483956] V0: [[ 0.00817405 -0.01132761 -0.00058841 0.00608259 -0.00289516 -0.00055641] [-0.01132761 0.06926417 -0.00618495 -0.00327261 0.00587965 0.00072476] [-0.00058841 -0.00618495 0.09762575 -0.00058563 0.00070072 0.00013298] [ 0.00608259 -0.00327261 -0.00058563 0.01612028 -0.01472752 -0.00129378] [-0.00289516 0.00587965 0.00070072 -0.01472752 0.07745511 -0.00516329] [-0.00055641 0.00072476 0.00013298 -0.00129378 -0.00516329 0.09782442]] LogLike[0061]=-34961.339388 sigma_a=49.088176 R: [[4.20053675 5.03018308] [5.03018308 8.22557528]] m0: [221.9392445 40.41673841 4.177469 461.35200171 107.66178136 10.800224 ] V0: [[ 0.00807167 -0.0112316 -0.00057716 0.00603449 -0.00290369 -0.00055296] [-0.0112316 0.06911445 -0.00619642 -0.00329793 0.00594336 0.00072756] [-0.00057716 -0.00619642 0.097624 -0.0005826 0.00070216 0.00013284] [ 0.00603449 -0.00329793 -0.0005826 0.01587695 -0.01458773 -0.0012707 ] [-0.00290369 0.00594336 0.00070216 -0.01458773 0.07732673 -0.00517824] [-0.00055296 0.00072756 0.00013284 -0.0012707 -0.00517824 0.09782173]] LogLike[0062]=-34629.919774 sigma_a=51.349225 R: [[3.99166469 4.70120871] [4.70120871 7.60109325]] m0: [222.53313858 40.14636197 4.1239198 462.62197905 107.12716822 10.68411793] V0: [[ 0.00797135 -0.01113728 -0.0005662 0.00598321 -0.00290914 -0.0005491 ] [-0.01113728 0.06896755 -0.0062075 -0.00332033 0.00600478 0.00073 ] [-0.0005662 -0.0062075 0.09762233 -0.00057911 0.00070321 0.00013264] [ 0.00598321 -0.00332033 -0.00057911 0.01563218 -0.01444462 -0.00124745] [-0.00290914 0.00600478 0.00070321 -0.01444462 0.07719601 -0.00519335] [-0.0005491 0.00073 0.00013264 -0.00124745 -0.00519335 0.09781907]] LogLike[0063]=-34291.671039 sigma_a=53.726691 R: [[3.78676009 4.38230417] [4.38230417 7.00354068]] m0: [223.13329861 39.86867419 4.06925124 463.90065529 106.57043025 10.56657087] V0: [[ 0.00787294 -0.01104455 -0.00055553 0.00592873 -0.00291143 -0.00054482] [-0.01104455 0.06882342 -0.00621822 -0.0033397 0.00606377 0.00073208] [-0.00055553 -0.00621822 0.09762074 -0.00057514 0.00070386 0.00013239] [ 0.00592873 -0.0033397 -0.00057514 0.01538591 -0.01429815 -0.00122403] [-0.00291143 0.00606377 0.00070386 -0.01429815 0.07706281 -0.00520863] [-0.00054482 0.00073208 0.00013239 -0.00122403 -0.00520863 0.09781642]] LogLike[0064]=-33946.084942 sigma_a=56.228175 R: [[3.5859547 4.0736744 ] [4.0736744 6.43285716]] m0: [223.74000011 39.58310403 4.01344065 465.1880855 105.99122356 10.44763745] V0: [[ 0.00777627 -0.01095333 -0.0005451 0.00587103 -0.00291047 -0.00054014] [-0.01095333 0.06868201 -0.0062286 -0.00335591 0.00612019 0.00073379] [-0.0005451 -0.0062286 0.0976192 -0.00057069 0.00070409 0.00013209] [ 0.00587103 -0.00335591 -0.00057069 0.01513814 -0.01414825 -0.00120045] [-0.00291047 0.00612019 0.00070409 -0.01414825 0.07692702 -0.00522409] [-0.00054014 0.00073379 0.00013209 -0.00120045 -0.00522409 0.09781379]] LogLike[0065]=-33592.651489 sigma_a=58.861776 R: [[3.38939444 3.77552734] [3.77552734 5.88898907]] m0: [224.35349871 39.28905038 3.95646893 466.48426606 105.38921667 10.32737897] V0: [[ 0.00768116 -0.01086352 -0.00053491 0.00581009 -0.00290618 -0.00053505] [-0.01086352 0.06854326 -0.00623865 -0.00336884 0.00617387 0.0007351 ] [-0.00053491 -0.00623865 0.09761774 -0.00056578 0.0007039 0.00013172] [ 0.00581009 -0.00336884 -0.00056578 0.01488883 -0.01399488 -0.00117671] [-0.00290618 0.00617387 0.0007039 -0.01399488 0.07678851 -0.00523974] [-0.00053505 0.0007351 0.00013172 -0.00117671 -0.00523974 0.09781117]] LogLike[0066]=-33230.866673 sigma_a=61.636032 R: [[3.19723089 3.48806365] [3.48806365 5.37187263]] m0: [224.97402424 38.98588397 3.89832148 467.78912064 104.76410202 10.20586501] V0: [[ 0.00758747 -0.01077502 -0.00052494 0.00574589 -0.00289849 -0.00052955] [-0.01077502 0.06840712 -0.0062484 -0.00337835 0.00622465 0.00073603] [-0.00052494 -0.0062484 0.09761632 -0.00056039 0.00070328 0.00013131] [ 0.00574589 -0.00337835 -0.00056039 0.01463799 -0.01383798 -0.00115283] [-0.00289849 0.00622465 0.00070328 -0.01383798 0.07664718 -0.00525557] [-0.00052955 0.00073603 0.00013131 -0.00115283 -0.00525557 0.09780857]] LogLike[0067]=-32860.236772 sigma_a=64.559895 R: [[3.00961798 3.21147405] [3.21147405 4.88142882]] m0: [225.60177468 38.67294951 3.83898923 469.10248615 104.1156089 10.08317508] V0: [[ 0.00749504 -0.01068771 -0.00051515 0.00567842 -0.00288729 -0.00052367] [-0.01068771 0.06827352 -0.00625787 -0.0033843 0.00627235 0.00073654] [-0.00051515 -0.00625787 0.09761497 -0.00055453 0.00070222 0.00013084] [ 0.00567842 -0.0033843 -0.00055453 0.01438564 -0.01367754 -0.00112881] [-0.00288729 0.00627235 0.00070222 -0.01367754 0.0765029 -0.00527161] [-0.00052367 0.00073654 0.00013084 -0.00112881 -0.00527161 0.09780598]] LogLike[0068]=-32480.277530 sigma_a=67.642802 R: [[2.82671077 2.94594004] [2.94594004 4.41756274]] m0: [226.23690899 38.34956872 3.77846985 470.42409669 103.44351881 9.95940039] V0: [[ 0.00740372 -0.01060151 -0.00050554 0.00560768 -0.00287252 -0.00051739] [-0.01060151 0.06814238 -0.00626708 -0.00338656 0.00631677 0.00073665] [-0.00050554 -0.00626708 0.09761365 -0.00054821 0.00070072 0.00013031] [ 0.00560768 -0.00338656 -0.00054821 0.01413182 -0.01351351 -0.00110468] [-0.00287252 0.00631677 0.00070072 -0.01351351 0.07635556 -0.00528784] [-0.00051739 0.00073665 0.00013031 -0.00110468 -0.00528784 0.0978034 ]] LogLike[0069]=-32090.530209 sigma_a=70.894523 R: [[2.64866551 2.69163666] [2.69163666 3.98016443]] m0: [226.87953777 38.01504479 3.71676913 471.75356339 102.74768423 9.83464597] V0: [[ 0.00731339 -0.01051628 -0.00049609 0.00553367 -0.0028541 -0.00051074] [-0.01051628 0.06801364 -0.00627605 -0.00338499 0.00635773 0.00073633] [-0.00049609 -0.00627605 0.09761239 -0.00054143 0.00069877 0.00012974] [ 0.00553367 -0.00338499 -0.00054143 0.01387659 -0.0133459 -0.00108044] [-0.0028541 0.00635773 0.00069877 -0.0133459 0.07620509 -0.00530428] [-0.00051074 0.00073633 0.00012974 -0.00108044 -0.00530428 0.09780084]] LogLike[0070]=-31690.574363 sigma_a=74.325142 R: [[2.47564777 2.44874461] [2.44874461 3.5691219 ]] m0: [227.52971234 37.6686689 3.65390268 473.09035229 102.02805077 9.70903287] V0: [[ 0.0072239 -0.01043193 -0.00048678 0.00545641 -0.00283193 -0.00050371] [-0.01043193 0.06788721 -0.0062848 -0.00337943 0.00639501 0.00073557] [-0.00048678 -0.0062848 0.09761116 -0.0005342 0.00069636 0.00012912] [ 0.00545641 -0.00337943 -0.0005342 0.01362006 -0.0131747 -0.00105611] [-0.00283193 0.00639501 0.00069636 -0.0131747 0.07605138 -0.00532092] [-0.00050371 0.00073557 0.00012912 -0.00105611 -0.00532092 0.0977983 ]] LogLike[0071]=-31280.050009 sigma_a=77.945006 R: [[2.30784184 2.21746239] [2.21746239 3.18433108]] m0: [228.18740951 37.30973044 3.58989802 474.43375529 101.28468563 9.58270101] V0: [[ 0.00713514 -0.01034833 -0.00047759 0.00537593 -0.00280597 -0.00049633] [-0.01034833 0.067763 -0.00629336 -0.00336974 0.00642839 0.00073438] [-0.00047759 -0.00629336 0.09760997 -0.00052653 0.00069351 0.00012845] [ 0.00537593 -0.00336974 -0.00052653 0.01336235 -0.01299996 -0.00103172] [-0.00280597 0.00642839 0.00069351 -0.01299996 0.07589438 -0.00533775] [-0.00049633 0.00073438 0.00012845 -0.00103172 -0.00533775 0.09779577]] LogLike[0072]=-30858.706142 sigma_a=81.764407 R: [[2.14546191 1.99801832] [1.99801832 2.82570218]] m0: [228.85251131 36.93753254 3.52479722 475.78285318 100.51781396 9.45581248] V0: [[ 0.00704701 -0.01026537 -0.00046851 0.0052923 -0.00277614 -0.0004886 ] [-0.01026537 0.06764092 -0.00630174 -0.00335579 0.00645767 0.00073274] [-0.00046851 -0.00630174 0.09760882 -0.00051843 0.00069019 0.00012773] [ 0.0052923 -0.00335579 -0.00051843 0.01310365 -0.01282173 -0.00100729] [-0.00277614 0.00645767 0.00069019 -0.01282173 0.07573404 -0.00535478] [-0.0004886 0.00073274 0.00012773 -0.00100729 -0.00535478 0.09779326]] LogLike[0073]=-30426.464821 sigma_a=85.793222 R: [[1.98876715 1.79068314] [1.79068314 2.49316362]] m0: [229.5247794 36.55141459 3.4586601 477.13647225 99.72786419 9.32855539] V0: [[ 0.0069594 -0.01018293 -0.00045953 0.00520558 -0.00274241 -0.00048054] [-0.01018293 0.06752085 -0.00630996 -0.00333745 0.0064826 0.00073064] [-0.00045953 -0.00630996 0.09760769 -0.00050992 0.00068642 0.00012697] [ 0.00520558 -0.00333745 -0.00050992 0.01284417 -0.01264012 -0.00098287] [-0.00274241 0.0064826 0.00068642 -0.01264012 0.07557036 -0.00537198] [-0.00048054 0.00073064 0.00012697 -0.00098287 -0.00537198 0.09779077]] LogLike[0074]=-29983.502208 sigma_a=90.040493 R: [[1.83807324 1.59577388] [1.59577388 2.18665111]] m0: [230.20382272 36.15078436 3.391568 478.493132 98.91552505 9.20114808] V0: [[ 0.00687224 -0.01010089 -0.00045063 0.00511589 -0.00270476 -0.00047218] [-0.01010089 0.06740268 -0.00631806 -0.00331461 0.00650297 0.0007281 ] [-0.00045063 -0.00631806 0.0976066 -0.00050103 0.00068221 0.00012617] [ 0.00511589 -0.00331461 -0.00050103 0.01258421 -0.01245529 -0.00095847] [-0.00270476 0.00650297 0.00068221 -0.01245529 0.07540337 -0.00538934] [-0.00047218 0.0007281 0.00012617 -0.00095847 -0.00538934 0.09778831]] LogLike[0075]=-29530.364110 sigma_a=94.513604 R: [[1.69375513 1.41364325] [1.41364325 1.90607593]] m0: [230.88905781 35.73516185 3.32362811 479.85098448 98.08181556 9.07384375] V0: [[ 0.00678547 -0.01001914 -0.00044182 0.00502338 -0.00266319 -0.00046353] [-0.01001914 0.06728628 -0.00632603 -0.00328718 0.00651859 0.0007251 ] [-0.00044182 -0.00632603 0.09760552 -0.00049177 0.00067755 0.00012533] [ 0.00502338 -0.00328718 -0.00049177 0.01232412 -0.01226746 -0.00093416] [-0.00266319 0.00651859 0.00067755 -0.01226746 0.07523317 -0.00540684] [-0.00046353 0.0007251 0.00012533 -0.00093416 -0.00540684 0.09778587]] LogLike[0076]=-29068.094619 sigma_a=99.217284 R: [[1.55624068 1.24465476] [1.24465476 1.65127665]] m0: [231.57966545 35.30423505 3.2549779 481.20775335 97.22816444 8.94693455] V0: [[ 0.00669906 -0.00993758 -0.00043308 0.00492824 -0.00261777 -0.00045463] [-0.00993758 0.06717152 -0.00633391 -0.00325511 0.00652926 0.00072166] [-0.00043308 -0.00633391 0.09760448 -0.00048219 0.00067247 0.00012447] [ 0.00492824 -0.00325511 -0.00048219 0.01206435 -0.01207691 -0.00090997] [-0.00261777 0.00652926 0.00067247 -0.01207691 0.0750599 -0.00542444] [-0.00045463 0.00072166 0.00012447 -0.00090997 -0.00542444 0.09778347]] LogLike[0077]=-28598.363905 sigma_a=104.152466 R: [[1.42598923 1.08913999] [1.08913999 1.42195365]] m0: [232.2745469 34.85792686 3.18578905 482.56067926 96.35649433 8.82075428] V0: [[ 0.006613 -0.00985613 -0.00042441 0.00483073 -0.00256859 -0.00044551] [-0.00985613 0.06705826 -0.00634171 -0.00321841 0.00653483 0.00071777] [-0.00042441 -0.00634171 0.09760345 -0.00047232 0.000667 0.00012357] [ 0.00483073 -0.00321841 -0.00047232 0.01180542 -0.01188405 -0.00088598] [-0.00256859 0.00653483 0.000667 -0.01188405 0.07488383 -0.00544211] [-0.00044551 0.00071777 0.00012357 -0.00088598 -0.00544211 0.0977811 ]] LogLike[0078]=-28123.586254 sigma_a=109.314756 R: [[1.30345561 0.94734222] [0.94734222 1.21759611]] m0: [232.97228631 34.39646889 3.11627003 483.9064832 95.4693011 8.69567864] V0: [[ 0.00652734 -0.00977473 -0.00041583 0.00473116 -0.00251582 -0.00043622] [-0.00977473 0.06694636 -0.00634943 -0.00317713 0.00653524 0.00071348] [-0.00041583 -0.00634943 0.09760245 -0.00046221 0.00066115 0.00012265] [ 0.00473116 -0.00317713 -0.00046221 0.01154797 -0.01168935 -0.00086224] [-0.00251582 0.00653524 0.00066115 -0.01168935 0.0747053 -0.00545981] [-0.00043622 0.00071348 0.00012265 -0.00086224 -0.00545981 0.09777878]] LogLike[0079]=-27646.983378 sigma_a=114.692996 R: [[1.18904696 0.8193585 ] [0.8193585 1.03741985]] m0: [233.67112924 33.92047353 3.04666625 485.24136537 94.56971121 8.57212155] V0: [[ 0.00644215 -0.00969335 -0.00040733 0.00462991 -0.0024597 -0.00042679] [-0.00969335 0.06683571 -0.00635709 -0.00313142 0.00653044 0.00070878] [-0.00040733 -0.00635709 0.09760148 -0.00045192 0.00065497 0.00012172] [ 0.00462991 -0.00313142 -0.00045192 0.01129274 -0.01149344 -0.00083884] [-0.0024597 0.00653044 0.00065497 -0.01149344 0.07452478 -0.00547747] [-0.00042679 0.00070878 0.00012172 -0.00083884 -0.00547747 0.09777651]] LogLike[0080]=-27172.578420 sigma_a=120.267773 R: [[1.08307849 0.70508975] [0.70508975 0.88032802]] m0: [234.36898524 33.43099385 2.97725686 486.56105087 93.66150079 8.4505266 ] V0: [[ 0.00635753 -0.009612 -0.00039894 0.00452745 -0.00240055 -0.00041728] [-0.009612 0.06672621 -0.00636469 -0.00308151 0.00652054 0.00070373] [-0.00039894 -0.00636469 0.09760052 -0.0004415 0.0006485 0.00012077] [ 0.00452745 -0.00308151 -0.0004415 0.01104054 -0.01129703 -0.00081584] [-0.00240055 0.00652054 0.0006485 -0.01129703 0.07434287 -0.00549503] [-0.00041728 0.00070373 0.00012077 -0.00081584 -0.00549503 0.0977743 ]] LogLike[0081]=-26705.090330 sigma_a=126.010207 R: [[0.98573851 0.60421082] [0.60421082 0.74490718]] m0: [235.06346251 32.92955837 2.90834756 487.86089389 92.74905731 8.33135327] V0: [[ 0.00627365 -0.00953074 -0.00039066 0.00442427 -0.00233877 -0.00040775] [-0.00953074 0.06661778 -0.00637222 -0.00302773 0.00650569 0.00069836] [-0.00039066 -0.00637222 0.09759959 -0.00043103 0.00064179 0.00011983] [ 0.00442427 -0.00302773 -0.00043103 0.01079226 -0.01110096 -0.00079335] [-0.00233877 0.00650569 0.00064179 -0.01110096 0.07416028 -0.00551242] [-0.00040775 0.00069836 0.00011983 -0.00079335 -0.00551242 0.09777216]] LogLike[0082]=-26249.717125 sigma_a=131.881150 R: [[0.89706754 0.51616444] [0.51616444 0.62945976]] m0: [235.75193796 32.41816913 2.84025946 489.13604246 91.83727123 8.21505838] V0: [[ 0.00619068 -0.00944964 -0.00038252 0.00432093 -0.00227484 -0.00039825] [-0.00944964 0.06651037 -0.00637969 -0.0029705 0.0064862 0.00069271] [-0.00038252 -0.00637969 0.09759869 -0.00042057 0.00063491 0.00011889] [ 0.00432093 -0.0029705 -0.00042057 0.01054882 -0.01090614 -0.00077142] [-0.00227484 0.0064862 0.00063491 -0.01090614 0.07397785 -0.00552956] [-0.00039825 0.00069271 0.00011889 -0.00077142 -0.00552956 0.09777008]] LogLike[0083]=-25811.804138 sigma_a=137.831213 R: [[0.81695227 0.44017829] [0.44017829 0.53206745]] m0: [236.43166184 31.89925444 2.77331466 490.38165716 90.9313532 8.10207415] V0: [[ 0.00610883 -0.00936886 -0.00037455 0.00421802 -0.0022093 -0.00038883] [-0.00936886 0.06640399 -0.00638707 -0.00291033 0.00646246 0.00068685] [-0.00037455 -0.00638707 0.09759781 -0.00041019 0.00062792 0.00011795] [ 0.00421802 -0.00291033 -0.00041019 0.01031114 -0.01071355 -0.00075016] [-0.0022093 0.00646246 0.00062792 -0.01071355 0.07379647 -0.00554637] [-0.00038883 0.00068685 0.00011795 -0.00075016 -0.00554637 0.09776808]] LogLike[0084]=-25396.427680 sigma_a=143.801721 R: [[0.74513142 0.37530021] [0.37530021 0.45067523]] m0: [237.09988962 31.37557371 2.70781978 491.59316622 90.03658649 7.99278514] V0: [[ 0.00602833 -0.00928856 -0.00036675 0.00411612 -0.00214273 -0.00037956] [-0.00928856 0.06629868 -0.00639435 -0.00284781 0.00643498 0.00068082] [-0.00036675 -0.00639435 0.09759696 -0.00039996 0.00062089 0.00011704] [ 0.00411612 -0.00284781 -0.00039996 0.01008008 -0.01052414 -0.00072961] [-0.00214273 0.00643498 0.00062089 -0.01052414 0.0736171 -0.00556278] [-0.00037956 0.00068082 0.00011704 -0.00072961 -0.00556278 0.09776616]] LogLike[0085]=-25007.948400 sigma_a=149.726863 R: [[0.68121082 0.32044672] [0.32044672 0.38318515]] m0: [237.75402986 30.85007846 2.64404946 492.76653094 89.15803803 7.88750679] V0: [[ 0.00594938 -0.00920894 -0.00035916 0.00401579 -0.00207572 -0.00037048] [-0.00920894 0.06619451 -0.00640152 -0.00278354 0.00640434 0.00067469] [-0.00035916 -0.00640152 0.09759614 -0.00038994 0.00061387 0.00011615] [ 0.00401579 -0.00278354 -0.00038994 0.0098564 -0.01033883 -0.00070984] [-0.00207572 0.00640434 0.00061387 -0.01033883 0.07344064 -0.00557872] [-0.00037048 0.00067469 0.00011615 -0.00070984 -0.00557872 0.09776433]] LogLike[0086]=-24649.616234 sigma_a=155.537059 R: [[0.62468581 0.27445944] [0.27445944 0.32754846]] m0: [238.39179069 30.32574361 2.58223168 493.89848695 88.30026576 7.78646833] V0: [[ 0.0058722 -0.00913021 -0.00035179 0.00391754 -0.00200885 -0.00036164] [-0.00913021 0.06609159 -0.00640855 -0.00271817 0.00637115 0.00066852] [-0.00035179 -0.00640855 0.09759536 -0.00038018 0.00060692 0.00011529] [ 0.00391754 -0.00271817 -0.00038018 0.00964071 -0.01015843 -0.00069089] [-0.00200885 0.00637115 0.00060692 -0.01015843 0.07326795 -0.00559413] [-0.00036164 0.00066852 0.00011529 -0.00069089 -0.00559413 0.09776258]] LogLike[0087]=-191385.912354 sigma_a=161.163137 R: [[0.57496949 0.23616374] [0.23616374 0.28184554]] m0: [239.01130467 29.80539128 2.52253721 494.98672426 87.46706754 7.68980274] V0: [[ 0.00579694 -0.00905256 -0.00034465 0.00382179 -0.00194264 -0.00035306] [-0.00905256 0.06599005 -0.00641544 -0.0026523 0.00633606 0.00066234] [-0.00034465 -0.00641544 0.0975946 -0.00037073 0.0006001 0.00011445] [ 0.00382179 -0.0026523 -0.00037073 0.00943343 -0.0099836 -0.00067277] [-0.00194264 0.00633606 0.0006001 -0.0099836 0.07309973 -0.00560897] [-0.00035306 0.00066234 0.00011445 -0.00067277 -0.00560897 0.09776092]] EM: log likelihood decreased .. GENERATED FROM PYTHON SOURCE LINES 177-179 Plot convergence ---------------- .. GENERATED FROM PYTHON SOURCE LINES 179-191 .. code-block:: Python 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 .. raw:: html


.. GENERATED FROM PYTHON SOURCE LINES 192-194 Perform smoothing with optimized parameters ------------------------------------------- .. GENERATED FROM PYTHON SOURCE LINES 196-198 Gradient ascent ~~~~~~~~~~~~~~~ .. GENERATED FROM PYTHON SOURCE LINES 200-204 Perform batch filtering ####################### View source code of `lds.inference.filterLDS_SS_withMissingValues_np `_ .. GENERATED FROM PYTHON SOURCE LINES 204-213 .. code-block:: Python 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"]["sqrt_diag_R"].numpy()**2) filterRes_ga = lds.inference.filterLDS_SS_withMissingValues_np( y=y, B=B, Q=Q_ga, m0=m0_ga, V0=V0_ga, Z=Z, R=R_ga) .. GENERATED FROM PYTHON SOURCE LINES 214-218 Perform batch smoothing ####################### View source code of `lds.inference.smoothLDS_SS `_ .. GENERATED FROM PYTHON SOURCE LINES 218-223 .. code-block:: Python smoothRes_ga = lds.inference.smoothLDS_SS( B=B, xnn=filterRes_ga["xnn"], Vnn=filterRes_ga["Vnn"], xnn1=filterRes_ga["xnn1"], Vnn1=filterRes_ga["Vnn1"], m0=m0_ga, V0=V0_ga) .. GENERATED FROM PYTHON SOURCE LINES 224-226 EM ~~ .. GENERATED FROM PYTHON SOURCE LINES 228-232 Perform batch filtering ####################### View source code of `lds.inference.filterLDS_SS_withMissingValues_np `_ .. GENERATED FROM PYTHON SOURCE LINES 232-241 .. code-block:: Python 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 = lds.inference.filterLDS_SS_withMissingValues_np( y=y, B=B, Q=Q_em, m0=m0_em, V0=V0_em, Z=Z, R=R_em) .. GENERATED FROM PYTHON SOURCE LINES 242-246 Perform batch smoothing ####################### View source code of `lds.inference.smoothLDS_SS `_ .. GENERATED FROM PYTHON SOURCE LINES 246-251 .. code-block:: Python smoothRes_em = lds.inference.smoothLDS_SS( B=B, xnn=filterRes_em["xnn"], Vnn=filterRes_em["Vnn"], xnn1=filterRes_em["xnn1"], Vnn1=filterRes_em["Vnn1"], m0=m0_em, V0=V0_em) .. GENERATED FROM PYTHON SOURCE LINES 252-254 Plot smoothing results ---------------------- .. GENERATED FROM PYTHON SOURCE LINES 256-258 Define function for plotting ############################ .. GENERATED FROM PYTHON SOURCE LINES 258-398 .. code-block:: Python 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 .. GENERATED FROM PYTHON SOURCE LINES 399-401 Set variables for plotting ########################## .. GENERATED FROM PYTHON SOURCE LINES 401-417 .. code-block:: Python N = y.shape[1] time = np.arange(0, N*dt, dt) smoothed_means_ga = smoothRes_ga["xnN"] smoothed_covs_ga = smoothRes_ga["VnN"] 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["VnN"] 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 .. GENERATED FROM PYTHON SOURCE LINES 418-420 Gradient ascent ~~~~~~~~~~~~~~~ .. GENERATED FROM PYTHON SOURCE LINES 422-424 Plot true, measured and smoothed positions (with 95% confidence band) ##################################################################### .. GENERATED FROM PYTHON SOURCE LINES 424-468 .. code-block:: Python 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 .. raw:: html


.. GENERATED FROM PYTHON SOURCE LINES 469-471 Plot true and smoothed velocities (with 95% confidence band) ############################################################ .. GENERATED FROM PYTHON SOURCE LINES 471-515 .. code-block:: Python 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 .. raw:: html


.. GENERATED FROM PYTHON SOURCE LINES 516-518 Plot true and smoothed accelerations (with 95% confidence band) ############################################################### .. GENERATED FROM PYTHON SOURCE LINES 518-562 .. code-block:: Python 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 .. raw:: html


.. rst-class:: sphx-glr-timing **Total running time of the script:** (8 minutes 2.825 seconds) .. _sphx_glr_download_auto_examples_tracking_plotEMvsGAcomparisonForagingMouse.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: binder-badge .. image:: images/binder_badge_logo.svg :target: https://mybinder.org/v2/gh/joacorapela/lds_python/gh-pages?filepath=notebooks/auto_examples/tracking/plotEMvsGAcomparisonForagingMouse.ipynb :alt: Launch binder :width: 150 px .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plotEMvsGAcomparisonForagingMouse.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plotEMvsGAcomparisonForagingMouse.py ` .. container:: sphx-glr-download sphx-glr-download-zip :download:`Download zipped: plotEMvsGAcomparisonForagingMouse.zip ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_