pyerrors/examples/03_fit_example.ipynb
2020-10-13 16:53:00 +02:00

774 lines
196 KiB
Text

{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import sys\n",
"sys.path.append('..')\n",
"import pyerrors as pe\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Read data from the pcac example"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"p_obs = {}\n",
"p_obs['f_P'] = pe.load_object('./data/B1k2_f_P.p')\n",
"\n",
"# f_A can be accesed via p_obs['f_A']\n",
"\n",
"[o.gamma_method() for o in p_obs['f_P']];"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can now define a custom fit function, in this case a single exponential. __Here we need to use the autograd wrapped version of numpy__ (imported as anp) to use automatic differentiation."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"import autograd.numpy as anp\n",
"def func_exp(a, x):\n",
" y = a[1] * anp.exp(-a[0] * x)\n",
" return y"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Fit single exponential to f_P. The kwarg `resplot` generates a figure which visualizes the fit with residuals."
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Fit with 2 parameters\n",
"Method: Levenberg-Marquardt\n",
"`xtol` termination condition is satisfied.\n",
"chisquare/d.o.f.: 0.00287692704517733\n"
]
},
{
"data": {
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\n",
"text/plain": [
"<Figure size 576x355.995 with 2 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Mass, Matrix element:\n",
"[Obs[0.2102(63)], Obs[14.24(66)]]\n"
]
}
],
"source": [
"# Specify fit range for single exponential fit\n",
"start_se = 8\n",
"stop_se = 19\n",
"\n",
"a = pe.fits.standard_fit(np.arange(start_se, stop_se), p_obs['f_P'][start_se:stop_se], func_exp, resplot=True)\n",
"[o.gamma_method() for o in a]\n",
"print('Mass, Matrix element:')\n",
"print(a)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The covariance of the two fit parameters can be computed in the following way"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Covariance: 0.003465486601483565\n",
"Normalized covariance: 0.8360758153764549\n"
]
}
],
"source": [
"cov_01 = pe.fits.covariance(a[0], a[1])\n",
"print('Covariance: ', cov_01)\n",
"print('Normalized covariance: ', cov_01 / a[0].dvalue / a[1].dvalue)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Effective mass"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Calculate the effective mass for comparison"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [],
"source": [
"m_eff_f_P = []\n",
"for i in range(len(p_obs['f_P']) - 1):\n",
" m_eff_f_P.append(np.log(p_obs['f_P'][i] / p_obs['f_P'][i+1]))\n",
" m_eff_f_P[i].gamma_method()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Calculate the corresponding plateau and compare the two results"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Effective mass:\n",
"Obs[0.2114(52)]\n",
"Fitted mass:\n",
"Obs[0.2102(63)]\n"
]
}
],
"source": [
"m_eff_plateau = np.mean(m_eff_f_P[start_se: stop_se]) # Plateau from 8 to 16\n",
"m_eff_plateau.gamma_method()\n",
"print('Effective mass:')\n",
"m_eff_plateau.print(0)\n",
"print('Fitted mass:')\n",
"a[0].print(0)"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"pe.plot_corrs([m_eff_f_P], plateau=[a[0], m_eff_plateau], xrange=[3.5, 19.5], prange=[start_se, stop_se], label=['Effective mass'])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Fitting two exponentials"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can also fit the data with two exponentials where the second term describes the cutoff effects imposed by the boundary."
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [],
"source": [
"def func_2exp(a, x):\n",
" y = a[1] * anp.exp(-a[0] * x) + a[3] * anp.exp(-a[2] * x)\n",
" return y"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can trigger the computation of $\\chi^2/\\chi^2_\\text{exp}$ with the kwarg `expected_chisquare` which takes into account correlations in the data and non-linearities in the fit function and should give a more reliable measure for goodness of fit than $\\chi^2/\\text{d.o.f.}$."
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Fit with 4 parameters\n",
"Method: Levenberg-Marquardt\n",
"`xtol` termination condition is satisfied.\n",
"chisquare/d.o.f.: 0.05399877210985092\n",
"chisquare/expected_chisquare: 0.7915235152326285\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 576x355.995 with 2 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Fit result:\n",
"[Obs[0.2146(65)], Obs[15.15(88)], Obs[0.623(60)], Obs[-9.64(74)]]\n"
]
}
],
"source": [
"# Specify fit range for double exponential fit\n",
"start_de = 2\n",
"stop_de = 21\n",
"\n",
"a = pe.fits.standard_fit(np.arange(start_de, stop_de), p_obs['f_P'][start_de:stop_de], func_2exp, initial_guess=[0.21, 14.0, 0.6, -10], resplot=True, expected_chisquare=True)\n",
"[o.gamma_method() for o in a]\n",
"print('Fit result:')\n",
"print(a)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Fitting with x-errors"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We first generate pseudo data"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(Obs[0.16(35)], Obs[0.15(25)])\n",
"(Obs[2.21(35)], Obs[0.88(25)])\n",
"(Obs[3.72(35)], Obs[-1.70(25)])\n",
"(Obs[6.10(35)], Obs[-1.58(25)])\n",
"(Obs[7.55(35)], Obs[-0.18(25)])\n"
]
}
],
"source": [
"ox = []\n",
"oy = []\n",
"for i in range(0,10,2):\n",
" ox.append(pe.pseudo_Obs(i + 0.35 * np.random.normal(), 0.35, str(i)))\n",
" oy.append(pe.pseudo_Obs(np.sin(i) + 0.25 * np.random.normal() - 0.2 * i + 0.17, 0.25, str(i)))\n",
"\n",
"[o.gamma_method() for o in ox + oy]\n",
"[print(o) for o in zip(ox, oy)];"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"And choose a function to fit"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [],
"source": [
"def func(a, x):\n",
" y = a[0] + a[1] * x + a[2] * anp.sin(x)\n",
" return y"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can then fit this function to the data and get the fit parameter as Obs with the function `odr_fit` which uses orthogonal distance regression."
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Fit with 3 parameters\n",
"Method: ODR\n",
"Sum of squares convergence\n",
"Residual variance: 0.03576834451052203\n",
"Parameter 1 : Obs[0.02(40)]\n",
"Parameter 2 : Obs[-0.225(75)]\n",
"Parameter 3 : Obs[1.59(39)]\n"
]
}
],
"source": [
"beta = pe.fits.odr_fit(ox, oy, func)\n",
"\n",
"pe.Obs.e_tag_global = 1 # Makes sure that the different samples with name length 1 are treated as ensembles and not as replica\n",
"\n",
"for i, item in enumerate(beta):\n",
" item.gamma_method()\n",
" print('Parameter', i + 1, ':', item)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"For the visulization we determine the value of the fit function in a range of x values"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"x_t = np.arange(min(ox).value - 1, max(ox).value + 1, 0.01)\n",
"y_t = func([o.value for o in beta], x_t)\n",
"\n",
"plt.errorbar([e.value for e in ox], [e.value for e in oy], xerr=[e.dvalue for e in ox], yerr=[e.dvalue for e in oy], marker='D', lw=1, ls='none', zorder=10)\n",
"plt.plot(x_t, y_t, '--')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can also take a look at how much the inidividual ensembles contribute to the uncetainty of the fit parameters"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Parameter 0\n"
]
},
{
"data": {
"image/png": 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UM1fYSOn2QzSWGgVcZjqHOL2pe5+aCJCJsPv5eeE8gKa0Pmp1dG66rcEefklbuwX0d1a1c4gPm0Lc3luMfGEkpds/lyGjFjxJOZk9wxrTswBWLlBplDrbdCbXaN0xJZOp+WRDo/pAc8t5A4q/YXAZ8KsiP2ZoSOn2zyWmA4jTG97w6uvAVA1tv74istB0npLTWg9znI0faWpuXG43Lhjm6AtL+GzvQkq3YFK6/SOl61FT9z49EuD1caxtHqQCuwtogKN3Xd3SWvfZBnv6lEzGrV8u73LpeQJJSrdA0ViqEgjlfkLP086hkUe3zge4/6qywE3UEtH60OL2jq0rjjaMfUdH51xgussR5hIfNoa4fdjl5w0EKd3CLSY3EYjwmLOadm9XMLalkk3bp6j5Z76HD2jdMr2ra8NnGhoHXN3Sel4ZXG440WXAI4Yz+JKUbuFk14JHTdm7cjDAoxdGbNNZ+kXr7Oiss/6mxqb2GxubFg3W+mLTkY7zLqR0CyKlWzgpXS/S2h7zZs0CB9780wVqsek4hRjkONve39xy8DMNjXPGZbNe3YUV2P3kpSalWzgvbXWIblWtBzZFtHPJuulqU8ZH8yyUab3vkrb2nZ872jB5bmfXHGCO6UxnsJD4sLOI242mg/iNlG4BorHUbCBwB2iCYNK+Z8s1OA/4YZ4Fre15nZ21n21oHHJ5a9tCBZNMR8pDGbkNjydMB/EbKd3CyAQ3XqR124Q3VltvnsXagyM8Os+C1l0TstmaTzQ0Zj/c3Hxepaa3CWa8bh5SunmT0i3MTNMBxKkGth/ZWOZ0Lnno3RHPnSU4NOts+nBTc/0n7cb5IxzHm78Q8jfNdAA/ktItTHhOKfWRiQf+lumKkH5hrnqH6SwAFVqnl7a07l7RYEendWWCMXTtRFK6BZDSLUzUdABxEq27Ju1//txnFqoNKBU1FUNpfWRRR8fmFUftUUvaO84l2K8VKd0CSOkWRrZ0PWZAV9PG8kzr3IcvL1vk+pNr3X52JlPz6YbGsmubW95RHp7TZKOmA/iRlG6eorFUOf46yhwK499Y3fraeNa1uDXPgtbOCMfZeGNjU/NNdtOCoVpf5Mrzestg4sPGEbcPmg7iJ1K6+ZuMTOfoLVo7U+pWzr7rhrKjpX6qSsd59X0trftubbBnT8xkF5X6+XwgCkjp5kFKN39R0wHEicozbZszylavTiovycGqiNZvLGlr3/65Bnv8go7O2cjoleNNA1abDuEnUrr5i5oOIE409vAr9X+4OFLc17LWzTO7ujbcetQetKy1bVEExhf18YNDDqblSUo3f3IQzWMm7F854vHrVP9Pm9U6MzabXX+z3dT50abmRYO0lvk1zkxKN09SuvmbYjqAOCaS7dyxY8LB+kxZWcHTbA52nC3XNbUc/l+2PW901vHlJDkGyfshT1K6+asyHUAcM7J+077/XBaZne/9yrSuu7y1beeKo/bZs7q65pUiW0hUmg7gN1K6+aswHUAcozuf7Tg8XE3sy22V1g3ndnTW3tZgD7u0rd1SuZEoon/k/ZAnKd38yYvMI5ST2f30ubvGQqTnG2ndOSmTrfmk3aiva2p+RwlWxg07eT/kSUo3f/Ii84jyjtd2vDRHLTvlCq31WY5T+5GmZvsTdpM1zHFkVrjSkQ7Jk/yD5U9K1yO2jVkJSqm3fq7Q+vX3tLTuvu2oPWNqJrPAZLYQkfdDnqR08ycvMg/o0o1dz8/cfIHSHF7c3rHltqP22MUdHXORIUxuk/dDnqR08ycvMg/IDn8x8/XGI6++t6V1Ubn5lXHDTN4PeZLSzZ+8yDxggsPIa1taZUytedIheerlsK/ogZSuB6xx5shpud4g74c8SenmT15kHvCanjBFa1pN5xDyfsiXlG7+5I3uCUq1MHC36RSCrOkAfhPa0lVKvVcptV0ptVMpFcvjriWfs1X0zV499ojpDAL5P8hTKEtXKVUG/Ai4htwy0jcqpfp6/r2UrkdscKbLVpZ59aYD+E0oSxe4ANiptX5Na90JPAx8sI/3ldL1iJecuTL5kHmypZunsJbuJGDvcT/X0fd1z6R0PWKdntWniW5ESUnp5imspdsfh0wHEDl79diJWtNoOkfISenmKaylu48TJ1+e3H1ZX+wvfhxRqCYG7TGdIeT6+r4R3cJaumuAmUqpaUqpAcANwGN9vK+Uroek9XjZ3WNWnekAfhPK0tVaZ4DPAf8DbAV+q7Xe3Me7y292D6lxZmjTGUJOSjdPoSxdAK3141rrWVrr6Vrrb+VxV9nS9ZDVzrwhpjOEnJRunkJbuoVKJ6o7ANmP6BHrnJmy5I45GeCg6RB+I6VbmPWmA4icg4wc62gZxmfIduK2YzqE30jpFqbGdABxjE3V3jPfSpTAWtMB/EhKtzBSuh7ymp7YYDpDSEnpFkBKtzDrTQcQx7zizDQdIaykdAsgpVuAdKJ6NzLRh2e85Mw9y3SGEMogGx8FkdIt3HrTAUROjTNjyplvJYpsM3G73XQIP5LSLdx60wFETj3DRmW1Omw6R8jIroUCSekWTg6mechRhsoIBndJ6RZISrdwUroeslNPajadIWSkdAskpVu4rYB8pPWItc4sZTpDiHQCG02H8Csp3QKlE9UO8LjpHCJntTN3hOkMIfIKcbvTdAi/ktLtnz+aDiBy1jvTZQSDex41HcDPpHT75y/kPmoJw5qoGpbRkQOmc4TEI6YD+JmUbj+kE9VNwCrTOUTOEc6SuY5Lbwtxe4fpEH4mpdt/sovBI7Y7U1pMZwgB2crtJynd/pPS9Yi1zuwy0xlCQEq3n6R0+ymdqE4DfV3qR5TQamfOSNMZAi5N3Jbx6f0kpVscsrXrAbX6nLO1RtZMK50/mA4QBFK6xdHXlYRFCbUysCpDmazZVTqya6EIpHSLIJ2ofhHYYjqHgEMMl2FjpfEG8ILpEEEgpVs895oOIGCbM7XNdIaA+oOsh1YcUrrF8wtAJl0x7GVnTrnpDAH1Y9MBgkJKt0jSiepG4EHTOcLuZWfOGNMZAuhJ4vYm0yGCQkq3uGRrwLDNOnq21mRN5wiY75sOECRSukWUTlRvAp41nSPMOqmo7KJ8j+kcAbIFeMJ0iCCR0i0+2do17IAeedB0hgC5h7gtY5+LSEq3+B4hN7xGGLJZR2XBxOI4jBynKDop3SJLJ6q7gJ+azhFmLztzKk1nCIh7ZcXf4pPSLY0fAa2mQ4TVy86csaYzBEAHudexKDIp3RJIJ6oPAj8wnSOsdujJU7WWyeX76SHi9iHTIYJISrd07gZs0yHCKEN5RQcVu03n8DEH+K7pEEElpVsi6UT1UeA7pnOE1T49+k3TGXzs58RtmUukRKR0S+seQD6iGbBJT+swncGnmoE7TYcIMindEkonqpuBr5vOEUarnTmDTGfwqbuJ2zLksYSkdEvvZ4Cct+6yNc6ccaYz+NA+ZF9uyUnpllg6UZ0FbjedI2x26olTtUbGmObnDuK2DHUsMSldF6QT1U8CKdM5wkQTibRRmTadw0f+Stx+qC83VEpNUUqtVEptUUptVkp9sdThgkRK1z2fR+bbddVePeaI6Qw+0QXclsftM8CXtdbzgAuBFUqpeSVJFkBSui5JJ6pfB75sOkeYbHDO6TKdwSe+T9ze2tcba60PaK1f6f6+CdgKTCpVuKCR0nVROlH9E+DPpnOExct6bpXpDD6wB7ir0DsrpaLAecDqYgUKOild930KqDcdIgzWOLMnmM7gcVngJuJ2SyF3VkoNAX4P/IPWurGoyQJMStdl6UT1AfLbfyYKtFuPm6S17Efvxb8Qt58r5I5KqQpyhfuQ1lqWZs+DlK4B6UT1b4DfmM4RfEo1M0jmYDi9p4FvFXJHpZQC/gvYqrX+XlFThYCUrjm3AftNhwi6PXrsUdMZPOgQud0KhS6pfglwM7BUKbW+++t9xYsXbFK6hqQT1fXAp03nCLoaZ4YsUnkiTa5wCz7VV2v9vNZaaa0XaK0XdX89XsSMgSala1A6Uf1n4D9M5wiyl5x5Q0xn8JgEcftJ0yHCTErXvNuBv5gOEVSvODNl/Ogxf0NmEDNOStewdKI6A3wE2Gw6SxDtZ/R4rWUyeXLDFG8kbsvuFsOkdD0gnai2gWuRuXdLopGqPaYzGJYFbiZu7zUdREjpekY6UZ0GPggyM1axvabHh3kEgwY+RdyWA10eIaXrIelE9UvAJ8i9UUSR1DgzTUcw6cvE7aTpEOIYKV2P6T5x4humcwTJS87coaYzGPIt4vb3TYcQJ5LS9aB0ovqbwIOmcwTFK87MKaYzGHAfcftrpkOIU0npetengcdMhwiCNxk+2tEqTKsDPwysMB1CnJ6UrkelE9WdwIeRORqKooEhdaYzuOQJ4OP9OMVXlJiUrod1j+H9e+B+01n8bqeeGIaxui8AHyZuy+TtHial63HpRLVDbg7eH5nO4mfrnFlBf62/AFwrC0t6X9BfiIGQTlTrdKL6c8DdprP41Wpn7jDTGUro/wFXErfDPB7ZN6R0fSSdqL4D+LrpHH5U48yYajpDiXwb+ChxW06q8QmltYzD95toLHU78F3TOfxmV+XH3ihTerzpHEWSBT5P3L7XdBCRH9nS9aF0ovp7wHLklOG81HNWUCaNbwY+IIXrT1K6PpVOVP8CeBcQlqFQ/bbDmdxkOkMRHAAul7kU/EtK18fSieo1wGKgoMUFw2atnlVmOkM/bQKWELdfMR1EFE5K1+fSieqDwJXAD0xn8brVztwRpjP0w6PApTI9o//JgbQAicZS1wM/B4I8PKpgVbQ1bar81BClUKaz5KENuJ24fZ/pIKI4ZEs3QNKJ6keA84A1prN4UQuDhmaJ+Olg2kZgsRRusEjpBkw6Uf06cCm5EykyhuN4zmGG+6F0NXAPcAFxe4vhLKLIZPdCgEVjqYXAfcCFprN4xf0V/7bq3WUbLjedoxc7gU8St+XgaEDJlm6ApRPVG4BLgM8CDWbTeMMaZ0656Qw9cIB/BxZK4QabbOmGRDSWGgd8H7jRdBaT3qm2b/t95b/MMZ3jJBuBFcTt500HEaUnpRsy0VjqKuDHwAzTWUwYSEfb1spbKpXyxKe83cCdwEMy/214eOGFJ1yUTlQ/CVjANwnhacTtVA7qosz0WNd64MvAbOL2g1K44SJbuiEWjaUmAP8I3AoMNhzHNc8N+MLqKZE3lxh46jZy+20TxO0wTKouTkNKVxCNpUYDtwOfAwK/cu5/Vnx31dVl69wcwZAFHgC+Qdze5+LzCg+S0hVvi8ZSI4AvAF8E/HzKbK8+Vfb4C3dW/PJiF54qA/wBiMt4W/EWKV1ximgsNZTcarK3A2MMxym6BWrXq49V3jmzhE9RB/wU+Blx2w8nYwgXSemKHkVjqcHATcDN5Mb7+mnOgh5VkOncUfnxiFIUc8yuA/wFuBdIEbezRXxsESBSuqJPorHUNI4VcCm3El2xvXL5rkrVNb0ID3WI3CRDPyFuv16ExxMBJ6Ur8haNpZaQK98bgFGG4xRk5YAvvTgtcvCiAu/eCawiV7aPELc7i5dMBJ2UrihYNJaqAK4hV8DvAc4ym6jvfljxg1XXlr2UzwiGNPDn7q9niNstJQkmAk9KVxRFNJYqB5YAy4Crur/36jwH3Fz2l5e+WfFAbxMBdQDP8lbRxu1t7iQTQSelK0qiewTEReSmmbyEXAlXGQ11nDlqz+tPVMamHXdRG7nlcF4GngBWytasKAUpXeGK7i3hBcBccgfiZnT/ORN3xwQ7QLqM7OadlTdvU4oNQA2wXUYcCDdI6QrjorHUSE4s4unAcHKnJp/8Naj7z8rjHqIFONr91dDD93XAdmBnOlHdUdq/kRA9k9IVvhSNpSLkCrgznajuMp1HiL6S0hVCCBfJ1I5CCOEiKV0hhHCRlK4QQrhISlcIIVwkpSuEEC6S0hVCCBdJ6QohhIukdIUQwkVSukII4SIpXSGEcJGUrhBCuEhKVwghXCSlK4QQLpLSFUIIF0npCiGEi6R0hRDCRf8fNNsp10eSxc0AAAAASUVORK5CYII=\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"Parameter 1\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"Parameter 2\n"
]
},
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAV0AAADsCAYAAADXaXXTAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjMuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8vihELAAAACXBIWXMAAAsTAAALEwEAmpwYAAAe2ElEQVR4nO3deZhU1YE28PdUdTe9F3QDsm+y1AUKRFBQBPxQo4lbFo1L1Io6Os+ExIzGTHwSYypjMlHzxfmcqGlAxXYZE4P6GXXiEtxQEBFBL3CLfZd96a7eu6vO/HGbiESgq+ree+7y/p6nH4R03/umod8+feqec4SUEkRE5IyQ6gBEREHC0iUichBLl4jIQSxdIiIHsXSJiBzE0iUichBLlzxBCHGBEGKNEGK9EOIO1XmIciX4nC65nRAiDGAtgPMAbAewFMBVUsrVSoMR5YAjXfKC0wGsl1JulFK2AfgjgEsVZyLKCUuXvKA/gG1H/H57558ReQ5Ll6iLhBC3CiFWCSFWCiGeEUIUq85E3sPSJS/YAWDgEb8f0PlnjhFC9AdwC4BJUsqxAMIArnQyA/kDS5e8YCmAEUKIoUKIIphl9xcFOQoAlAghCgCUAvhMQQbyOJYuuZ6UsgPA9wG8BsAA8KyUcpXDGXYA+L8AtgLYCaBOSvm6kxnIH/jIGFEXCCF6AHgOwBUADgH4M4D5UsqnVOYi7+FIl6hrzgWwSUq5V0rZDuB5AGcqzkQexNIl6pqtAKYIIUqFEALAOTCnOoiywtIl6gIp5RIA8wF8DECH+bUzR2ko8iTO6RIROYgjXSIiBxWoDkAEAEhEBICTAPQC0LPz1yPfegIoh/lvtqBOlh18avdTPQFkAKQBNAOog/lkweG3gwD2AtgCYNOsmpkpx/7/EB0DpxfIWYlIGMBwABqA0Z1vGoAozAUHXdIqCzY+svvPw7K8+0EAmwBsBrAewCcAlgNYM6tmZibLaxHlhKVL9kpE+gKY0fl2JsxyLcr3sjmW7rE0AfgUZgEvA7BwVs3MtRZdm+gLWLpkrURkED4v2RkwR7WWa5UFmx7Z/eehdly7004A7wBYAOCNWTUzt9h4LwoQli7lLxEZD+ByAJcBGOXELR0o3aOtgbkg4rlZNTOXOXhf8hmWLuUmEZmAz4t2hNO3b5MFm+Y6W7pH2ozOAgaweFbNTH4RUZexdKnrEpEhAG6Cuf/AySqjKC7dI20F8CiAx2bVzNyuOgy5H0vXA4QQAwE8AfORKglgjpTyAUdubj7KdR7MXb4uhEue7XZR6R6WBvBXAHMBvDKrZmZacR5yKZauBwgh+gLoK6X8WAhRAfMV9q/bejBjIlIJ4HoA3wMw0rb75KhNFmyeu/vPQ1TnOIbPADwE4OFZNTMPKc5CLsPS9SAhxIsAHpRSvmH5xRORwQB+AuBamIsRXMnlpXtYPYDZAP5zVs3MnarDkDuwdD1GCDEEwLsAxkop6y27sPk87c9gztnm/Ryt3dpkeMvc3fMHq87RRa0wp4fum1Uzc73qMKQWS9dDhBDlMJ8d/bWU8nlLLpqIVAO4A8AsACWWXNMBHivdwzoAzAOQmFUzk0f9BJQrXhShExNCFMJ8ROlpSwo3EYkgEfl3mMtib4eHCreTUB0gBwUwf5JYv2jyxXcYUc210zdkH5auB3Rumv0oAENKeX9eF0tEBBKRGwFsAPBzABX5J6RsdGs5oPeoW/8bAGuNqBY3opoXv4FQjli63jAV5gtbM4UQKzrfvpb1VRIRDcDbAB4BUG1pQocJ89E575EyPU6vOfy57wvgcQBLjKh2hrpQ5CRu7egBUsr3kM+P04lIMYA7AfwYHniRrIs8OTqsTG1ZVNG4Y9pRf3wagEVGVHsCwC1a0qhTEI0cwpGu3yUi58I8XuZn8E/hepOUDbGVc463N8V1AFZw1OtvLF2/SkTKkYjMA/AGbNrpSzHPjXR7712+rFtbXe8TvNsQAAuNqHaXEdXCDsQih7F0/SgROQ3ACgDfVRuE/k5m9mjJJyd18b3DAH4J4C0jqg20MRUpwNL1E/PJhH8D8D4Ub0jjAE+NdAdvfWNNONNWluWHTQPwqRHVLrcjE6nB0vWLRKQKwEsA7gVQqDgNHUFk2jcO2/TSmTl+eHcAzxpR7VEjqmVb2uRCLF0/MKcTPoa5Cxi5zKi1f9onIPOdn70BwDIjqp1qRSZSh6XrdYnItwEsBOC1JbF5EZCemF4oaG/8pN+uxadbdLlRABYbUe0mi65HCrB0vcycv/0jgG6qoyjg/sURUsrYqrlWPwtfBGCOEdV+avF1ySFcHOFF5jHmvwfwL6qjKOT6kW5J854PehxaZ9czt782olo1gNu1pOH+b0D0dxzpek0iUgbgRQS7cN1Pyrbxek1/m+9yG4B5RlTj4MlDWLpekoj0gbm1I18wc7nuh9Z9UNq8Z5ADt4oDeM6IasUO3IsswNL1ikSkP4D3AExUHcUl3Du9IGXd2NWPjHXwjpcAeNWIapUO3pNyxNL1AvNUhzfh/wUPvtB31wcritobqxy+7QwAbxtR7UTLjEkxlq7bJSK9ASyACw+HVMyVI12RSe8Yue6PkxXdfgKA94yoFqjHB72GpetmiUhPmIWrqY5CXTN08yubw5kOlfOrIwC8b0S1YQoz0HGwdN3KXNb7NwBOzg16hnDhSDeUbl0zeOvrbtiWsT+Al42oFlEdhP4RS9eNEpEKAK8DGK86CnWdlnyqQUC65WtKAzCfj5O5j1v+gdBhiUgI5iozPqVwfK5aEFDUWrfspL0fu+3v7FwAD6kOQV/E0nWf3wLI/vyz4HHP9IKUmXErZ7v1gM+bjah2m+oQ9DmWrpskIjfAXGVEJ+SegW55447Flaktbn665LdGVLtEdQgysXTdIhGZBuAPqmN4iDtGulI2x/TZbn9SIATgv42oNkF1EGLpukMiMhTA8+DBkZ5TvX/lhyWtB/qqztEFZQBeMqJaP9VBgo6lq5q5gc1fAPRUHcVj1I90ZWb/GONxL40e+8Ms3lLVQYKMpaveA+CzuJ40YMc7qwrSLV7b7+BUAE+qDhFkLF2VEpFvALhRdQzKnsh0bBm+4Xk3LITIxTd5+oQ6LF1VEpF+AOaqjuFhSqcXhm94fmdIZrx8AOj9RlQbqjpEELF0VUhEBIDHAVQrTkI5CHc0rxq4450pqnPkqRxArRHV2AEO4ydcjR8COE91CC9TuffC2NWPpVXd22LTAPxIdYigYek6LRGJAbhHdQwfULI6orhl/4fVB1aPU3Fvm9xtRLUxqkMECUvXSea+Co8imKf3Ws35ka6UHeP0ml6O39de3QDMNqKa+kfwAoKl66wbAZymOgTlprJ+0+Lyxs/8+OLTVAA3qw4RFCxdpyQiPQD8h+oYlCMpG2Kr5kZVx7DRPUZU66M6RBCwdJ3zK3DVmZUc/XG4955ly7q11fttauFI3WEu1CGbsXSdkIicAuCfVcegHMnMbm3N05NUx3DAt42odoHqEH7H0rWb+UzuQwDCqqP4jGMj3cFbX18bzrSVOXU/xX6tOoDfsXTt9x0AZ6oOQbkJpds3DNv0cpD+/k41otpFqkP4GUvXTolIAYBfqo7hT9KRke6odc8cEJBB+ynlF6oD+BlL117XAHD7Btd0DIVtDSv67loSxEf8JhlRjUdG2YSla5dEJAzgp6pjUI6klGNXzQ3ypvJ3qQ7gVyxd+1wJYITqED5m6/RCadPuxT3q1o+28x4uN9mIauerDuFHLF07mMt9f6Y6BuVIyrZxK2sGqo7hApzbtQFL1x6XA9BUh/A520a6PQ6tWVzavJelC5xhRDXuhmcxlq49OMq1mW2NK2Xd2FWP+WkXsXxxtGsxlq7VEpGzAcRUxwgAW3q3785FKwo7GnvYcW2PmmpEtZmqQ/gJS9d6PHvKo0QmvX3Uume9fiKEHe5QHcBPWLpWSkSqAHxLdYyAsHwT82GbXtoakh3c6/gfnWNEtb6qQ/gFS9da14EblDvF0umFcLrVGLTtDa+e7mu3EMxHIMkCLF1rcWrBozSjtkXluWsecLXqAH7B0rVKIjIVQJAfpneaZQVZ1Hroo977Pplg1fV8apIR1bjYxwIsXetwlOtFUmbGrZwdUR3DIzjatQBL1wqJSDH4AprTLBnpljdsX1SZ2soRXNdcpTqAH7B0rXE+gHLVIShLUjaNWzn7ZNUxPGSUEdUmqg7hdSxda3CU60E99+tLi1sP8lGo7HCKIU8s3TzFamMFdaHQdNU5Aii/6QWZ2TfaqOWLZ9m7wohq7I088JOXv2lnDerfb8ag/svvqer+zraCgu2qA9GJDdz+9uqCdEul6hwe1B/ADNUhvKxAdQAfuBBCFB4Ihyc8HanE05FKFGcya6c2t3x2TV3qpImtrVE+/2mLnD+nItOx+eSNL3AhRO6uBPCW6hBexdLN3z8ca9ISCo1cUFY6ckFZKUJS7hzb2rb+6vpUyXmNTeOKgCCfRuAKI9bP3xWSmSGqc3jY2aoDeJmQ0vIl7IERq40NBrC5yx8gZWpgR8fKb6YaM5elGkZ3z2S4m1WOpETzw7tfKMn24wram/Tp7/+Yu8DlRwLoqSWNA6qDeBFHuvk5K6v3FqJiW2HhGQ9UdccDPSLpSCaz4vzGprpr6lNDhrZ3DLYpIx1hzOrHVEfwAwFgMoC/qg7iRSzd/OQ+LyhEuC4cPuXZygo8W1mBoozcMKWlZfu1dfXVk1tax3Ae2HrFzfuWVB80JqvO4RNngKWbE5Zufizbe7UtJE5+t7Tk5HdLSxCSck+0rW3NlfUNxV9tbBpbLGXWP0YHQHbflKTsGKfX9LYpSxBx3+EccU43R7HaWAmAOgCFtt5IyqZ+HemVlzY0tl1Rn4pWZzI9bb2fR0iJlod3v1Dc1feP1G14d+Ly+/k8tXXqAPTQkgYLJEsc6eZuEuwuXAAQovSzwoLT/9Ajgj90r8xUZKR+blPT/mvqUoNHtrcPtf3+7tX1ka6UqbEr5/KgUGtFYO6qt0p1EK9h6ebO+R+vhAilwiL2QkU5XqgoR6GUm05rbtn6nfpUj7OaW8aGuNjlS52056OPu7Wn+EC/9aaApZs1lm7ulM9ptQsxdFFpydBFpSUQUu4f0daevCLVEL6ooTFWKmWZ6nw269pIV2Z2Rdf892k2ZwmqKQAeVR3Ca1i6uXPVbktSiOq13Yqm3t2tCndX92jpnU4vvaShseXK+oaRJ6XTJ6nOp8qQLa+uD2fasnu0j7pK+cDDi/hCWg5itbEiAM3wwo/zUsoyKVef3dS879q6VL8xbW2+2DtWSrQ9vPuF467uC6Xb1s1YeNvJAtL9f0/elIH5Ylq96iBewpFubobBC4ULAEKIRiHGvFJehlfKy1Ag5dYJLa2bv1OfqpjR1Bwr8O6/gRNOL4xa+0wdC9dWIQCnAHhXcQ5P8eoXnGqe3fi6Q4hBS0uKBy0tKYaQ8tCw9o5Vl6VSoa+nGseWS1mhOp9VCttSy/vu/nCS6hwBMARZlK4QojuARwCMhbmc+AYp5WJbkrkUSzc3ni3dI0khum8oKpx6b3UV7q3q0dYznVn2tcbGxqvrU8P7d6T7qc53Asce6UopYyvndPkZXsrLwCzf/wEAr0opLxNCFAEotSGTq7F0c+OL0v0CIYr2FYQnPhGpxBORSpRkMsnpTc27rqlP9T2ltW2U6njZKG3atbh7/cYzVecIiEFdfUchRATAdADfBQApZRuANntiuRdLNzfDVQewW3MoFH2tvCz6WnkZwlLuGNfauuHq+obycxqbYoVOLAo5sS8f6UrZOl6v6XIRUN6y+VwPBbAXwDwhxHgAywD8UErZaEsyl2Lp5sZ/I93jSAvRf3lxcf/lxcWAlPWDOzo++laqIfPNVMPYSEa66vjyqoPJD0pa9nEhhHOymV4oAHAqgB9IKZcIIR4AcAeAn9uSzKVYurlx+3ynfYSo3FJYeMb9VT1wf4/uHT0ymeUXNDSlrqlPDRvU0TFAaTYpD41Z/dh4pRmCJ5u/8+0Atkspl3T+fj7M0g0UPk6TpVhtLAQet24SouBgODzhmUjF9AsH9hswafCAdbf07vnO0uJuq6X5yrStdz/6D/rtfO+Two6m7jbfl74oYkS1Lg3epJS7AGwTQhx+jeAcAKttS+ZSHOlmrxLc6/ZLtYZCI94qKx3xlnlM0a4xrW1rr0qlSs9vaIoVAd3svLfIpLePXDefK6TUqAKwp4vv+wMAT3c+ubARwPW2pXIplm72eIJsF2SE6KMXd+ujF3fDT3vKhgEd6eVfTzWkv51q0HpkMlUW3OIL3/iGbXpxa0gqnt4Irmp0sXSllCtg7tAXWCzd7LnqhSNPEKJ8e2HBlAeruuNB85iiT89rbDp4bX1qyDALjikKd7QYg7Yt4Om+6ljxTTQwWLrZY+nmwzymaNz8ygrMr6xAkZQbJze3bL2mPtVzSnPL6K5uTynE5yPd0UZtK483UqpadQAvYelmj9MLFmoTYtjC0pJhC83tKfdG29rXXFmfKvpaY1OsK8cUdWs5uLTX/k+5daNa/JrIAks3exzp2kQK0cvoVtTrF72q8YueVc190ukPL001tl6ZSkV7pjO9/vEDZMe4lbN5jL16gVtVlg+WbvbCqgMEghAluwoKTp/dI4LZ3Ssz5Rmpn9PUdOA79akBWlv7yQBQ3rB1cUXDtmmqoxJaVQfwEpZu9vhd3WlChBrCIvZiRTlerChHgZRbJrW0bP7n/z83uItU3IWlmwUujsgeS1exDiEGf1BSMmPOBXX1EkirzkMs3WywdLPXrjoAmRZroYmvThTvq85BaFEdwEtYutnjSNdF5n0lPH1DHyxUnSPgONLNAks3eyxdl7nzuvCUVDE+UZ0jwFi6WWDpZo+l6zLpsCi89ebwgI4QtqvOElAs3SywdLPH0nWh+jJR/fPrws0SaFCdJYBYullg6WZvr+oA9OU29BUjZn81tMqBbSXpi1i6WWDpZm8n+EXtWm+eEpr87ljBI8GdxdLNAks3S3pcbwewT3UOOraHLg7P2F4NPkrmjDSAQJ1xli+Wbm52qA5Ax/eTG8ITm4uCdyqBApu1pNGhOoSXsHRz85nqAHR87QWi+LabwlVpgV2qs/jcGtUBvIalmxuWrgfsrxR97r4qfEByxZSd1qoO4DUs3dxwesEjVg8Wo5+cGfpYdQ4f40g3Syzd3GxTHYC67uXJoTOXjhBvq87hUxzpZomlm5uVqgNQdn77rdCMPREsUZ3DhzjSzRJLNzc6gIzqEJQFIcTt/xQe01qAdaqj+EijljQ41ZYllm4O9LjeBGC96hyUnZYiUX77jeGSDJ+ztgqnFnLA0s0dd7XyoN1VYsC9l4d2SO6LbAWWbg5Yurlj6XrU8uGh8c9NFR+ozuEDnM/NAUs3dyxdD3t2enjaqkHiHdU5PI4j3RywdHPH0vW4u68KnXWwDMtU5/Awfu5yIKTkhlm5itXGdgLoozoH5a6sWdbN+X36QGEaQ1Vn8ZitWtIYrDqEF3Gkm58FqgNQfhpLROQn14chgTrVWTzmNdUBvIqlm5+/qQ5A+dveSwx94NLQeh7nnhWWbo5Yuvl5Q3UAssai0aGJr04U76nO4REd4IAjZyzdPOhxfQeApOocZI15XwnP4HHuXbJESxqcjskRSzd/HO36CI9z7xJOLeSBpZs/lq6PpMOi8Labw/15nPtxsXTzwNLN39sw57jIJ+rKRE8e535M+wF8pDqEl7F086TH9RSAN1XnIGvxOPdj+puWNLjDXh5Yutb4o+oAZL03TwlNXjiGS4WPwqmFPLF0rfECgDbVIch6D14SPntHNRapzuESEizdvLF0LaDH9UMAXlWdg+zxbzeET+Vx7gCABVrS4KGseWLpWudJ1QHIHjzO/e8eUR3AD1i61nkJwEHVIcgePM4d+2FOo1GeWLoW0eN6K/iCmq8F/Dj3J7WkwdctLMDStRZ//PK5lyeHzvxoeCCfaOC/bYuwdC2kx/WPAQTxCzJQ7rssNH1vZaCOc39fSxqrVIfwC5au9X6nOgDZTAjxo5sCdZz7/1MdwE9YutZ7GTywz/cCdJz7FvAFNEuxdC2mx3UJ4D9V5yD7BeQ4999rSYObu1uIpWuPJ+D/ERDBPM79+TN9e5x7A/gCmuVYujbQ43ozgIdV5yBn/GlGeNqqQXhXdQ4bzONm5dZj6drnIQBNqkOQM+6+KjzVZ8e5NwD4D9Uh/IilaxM9ru8Bn2QIjExIhG+7KTy8PYxNqrNY5Dda0gj6smdbsHTtdR+A3apDkDMaS0Tkju/64jj3LQDuVx3Cr1i6NtLjegOAhOoc5JxtvX1xnPsdWtII6h4TtmPp2u8R8MTgQFk0OjTxtVPF+6pz5GixljS4h4iNWLo20+N6B4A7VOcgZz12fnj6Ru8d5y4B3Ko6hN+xdB2gx/UXAc99AVKe7rwuPNljx7k/oyWNIO0poQRL1zm3wtvzfJSljrAouu3mcP+0N45zbwZ/InMES9chelxfBr4iHDh1ZaLnndeGmzxwnPvvtKSxTXWIIGDpOusucDOcwNnQT4ycc4Grj3PfCeAe1SGCgqXrID2utwC4AUBGdRZy1oIJockLxwi3LhW+RUsajapDBAVL12F6XF8E4Peqc5DzHrwkPMOFx7nXaEljvuoQQcLSVeOnADaqDkHO+8n14QkuOs79U/ARMcexdBXQ43oTgBvh3jk+sklboShxyXHujQCu4Moz57F0FdHj+tvgixeB5JLj3L+vJQ2ulFSApavWnQDeUB2CnLd6sBj91P8JqdoK8kktaTyu6N6Bx9JVSI/rGQBXA9iqOgs576UpoakfDRdvO3zbtQC+5/A96QgsXcX0uL4PwGUAWlVnIefdd1loxt5KfOjQ7VoBfFtLGm5fqOFrLF0X0OP6UgA/VJ2DFDCPcx/t0HHuP9KShpf2gvAllq5L6HF9NoDHVecg5x1xnPt+G2/znJY0HrLx+tRFLF13+RdwN7JA2l0lBtx3WWi7Tce5LwRwrQ3XpRywdF2kc5nwxYCntgMki3w8wpbj3D8CcJGWNJotvi7liKXrMnpcrwNwAbhiLZD+NCM8bdVAvGPR5VYBuEBLGvUWXY8sIKTkoig3itXGTgbwHoA+qrOQs0IZma55ML2ieyMm5nGZ9QCm8URf9+FI16X0uL4B5ojX6yfLUpYyIRG+Nb/j3LcBOJeF604sXRfT4/onAC6B2uWipEAex7nvgVm4W+zIRflj6bqcHtffBfBVACnVWchZ23qLof91SWhdFse5HwRwnpY01tqZi/LD0vWAzs1xZgLYpzYJOe39MaFJr50q3uvCuzYA+KqWND61OxPlh6XrEXpc/wjAdMAThxyShR47PzzjBMe51wO4mCf5egOfXvCYWG1sMMydyUaozkLOKUjLtjn/lU6Wt2DcUf/TNgAXaklDV5GLsseRrsfocX0LgGngAopA6QiLoltvDvc76jj3ZQAms3C9haXrQXpc3w1gBoC/qs5CzjnqOPe/AJiuJY2dqnNRdli6HtW5cu0iAL8Cj/0JjA39xMiHLwzdA+AbWtJoUp2Hssc5XR+I1cYuBfAEgErVWchWLQBu0uP6U6qDUO5Yuj4Rq42NAvACAE11FrLFNgDf0OO6qiN+yCKcXvAJPa6vAXA6gOdUZyHLPQtgPAvXHzjS9aFYbewHAO4FUKI6C+WlDsD3OZ3gLyxdn+qcbngC5uiXvOdtAHE9rvPQUp/h9IJPdU43nAnzmHceeukdbQB+DOAcFq4/caQbALHamAbgUQBnqM5Cx7UEwM16XOf+CT7GkW4A6HHdAHAWgFsAHFKbhr7ELgDXAziDhet/HOkGTKw2VgXgLgDfA1CoOE7QtQN4AMDdelznkToBwdL1MCFEGObBgzuklBdl87Gx2thwmE84fNOObHRCrwL41865dwoQlq6HCSFuAzAJQGW2pXtYrDY2DcDvAJxmZTY6puUA7tLj+suqg5AanNP1KCHEAAAXAngkn+vocX0hgMkArgR3LrPTIgAX6nH9VBZusHGk61FCiPkAfgOgAsDtuY50jxarjZ0H85Gl86y4HuFNAL/S4/pbqoOQO7B0PUgIcRGAr0kpvyeEOBsWlu5hsdrYKQBuB3AFgAIrrx0AEsD/APi1HtcXqw5D7sLS9SAhxG8AXAugA0AxzN3FnpdSXmP1vWK1sYEAfgggDqCn1df3mW0A5gGYp8f1zYqzkEuxdD3OrpHu0WK1sUIAF8As+4thlj2ZK8j+AnPxyet6XM8ozkMux9L1OKdK90ix2lgEwOUAroO56EI4dW+XkDCPynkGwJN6XN+rOA95CEuX8hKrjQ2B+azv+TBPK/brCLgJwN8AvATgFT2u85gcyglLlywTq42VwCzer8As4TFqE+VtG4BXALwMYIEe11sU5yEfYOmSbWK1sf4wHz07DcAEAOMBlCoNdWyNMKcMlhx+0+P69uN/CFH2WLrkmFhtLARgJMwCPvwWA9Abzs0LtwHYAmBj59tymCW7So/raYcyUICxdEm5WG2sG4D+AAZ0vg084r97wZwn7nbUr4f/GzDnW5s7f03B3EntYOevn+Hzgt0IYDufMCCVWLpERA7i3gtERA5i6RIROYilS0TkIJYuEZGDWLpERA5i6RIROYilS0TkIJYuEZGDWLpERA5i6RIROYilS0TkIJYuEZGDWLpERA5i6RIROYilS0TkIJYuEZGDWLpERA76X4wY/0lZpzvsAAAAAElFTkSuQmCC\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n"
]
}
],
"source": [
"for i, item in enumerate(beta):\n",
" print('Parameter', i)\n",
" item.plot_piechart()\n",
" print()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Fitting with priors"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"When extracting energy levels and matrix elements from correlation functions one is interested in using as much data is possible in order to decrease the final error estimate and also have better control over systematic effects from higher states. This can in principle be achieved by fitting a tower of exponentials to the data. However, in practice it can be very difficult to fit a function with 6 or more parameters to noisy data. One way around this is to cnostrain the fit parameters with Bayesian priors. The principle idea is that any parameter which is determined by the data is almost independent of the priors while the additional parameters which would let a standard fit collapse are essentially constrained by the priors."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We first generate fake data as a tower of three exponentials with noise which increases with temporal separation."
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"m1 = 0.18\n",
"m2 = 0.5\n",
"m3 = 0.8\n",
"\n",
"A1 = 180\n",
"A2 = 300\n",
"A3 = 500\n",
"\n",
"px = []\n",
"py = []\n",
"for i in range(40):\n",
" px.append(i)\n",
" val = (A1 * np.exp(-m1 * i) + A2 * np.exp(-m2 * i) + A3 * np.exp(-m3 * i))\n",
" err = 0.03 * np.sqrt(i + 1)\n",
" tmp = pe.pseudo_Obs(val * (1 + err * np.random.normal()), val * err, 'e1')\n",
" py.append(tmp)\n",
" \n",
"[o.gamma_method() for o in py];\n",
"\n",
"pe.plot_corrs([py], logscale=True)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"As fit function we choose the sum of three exponentials"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [],
"source": [
"def func_3exp(a, x):\n",
" y = a[1] * anp.exp(-a[0] * x) + a[3] * anp.exp(-a[2] * x) + a[5] * anp.exp(-a[4] * x)\n",
" return y"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can specify the priors in a string format or alternatively input `Obs` from a previous analysis. It is important to choose the priors wide enough, otherwise they can influence the final result."
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [],
"source": [
"priors = ['0.2(4)', '200(500)', \n",
" '0.6(1.2)', '300(550)',\n",
" '0.9(1.8)', '400(700)']"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"It is important to chose a sufficiently large value of `Obs.e_tag_global`, as every prior is given an ensemble id."
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {},
"outputs": [],
"source": [
"pe.Obs.e_tag_global = 5"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The fit can then be performed by calling `prior_fit` which in comparison to the standard fit requires the priors as additional input."
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Fit with 6 parameters\n",
"Method: migrad\n",
"chisquare/d.o.f.: 1.0925587749193326\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 576x355.995 with 2 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"[Obs[0.1861(27)], Obs[210(12)], Obs[0.701(60)], Obs[321(433)], Obs[0.711(51)], Obs[435(433)]]\n"
]
}
],
"source": [
"beta_p = pe.fits.prior_fit(px, py, func_3exp, priors, resplot=True)\n",
"[o.gamma_method() for o in beta_p]\n",
"print(beta_p)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can now observe how far the individual fit parameters are constrained by the data or the priors"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"[o.plot_piechart() for o in beta_p];"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.6.11"
}
},
"nbformat": 4,
"nbformat_minor": 4
}