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Update fitting hands-on #12

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Update fitting hands-on #12

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78 changes: 26 additions & 52 deletions smd_handson_fitting.ipynb
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Original file line number Diff line number Diff line change
Expand Up @@ -7,24 +7,6 @@
"<span style=\"font-size: 3rem; font-weight: bold;\">SMD Hands-On Estimators / Fitting</span>"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"%%javascript\n",
"$.getScript('https://kmahelona.github.io/ipython_notebook_goodies/ipython_notebook_toc.js')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h1 id=\"tocheading\">Table of Contents</h1>\n",
"<div id=\"toc\"></div>"
]
},
{
"cell_type": "code",
"execution_count": null,
Expand Down Expand Up @@ -133,28 +115,25 @@
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"scrolled": false
},
"metadata": {},
"outputs": [],
"source": [
"# create some randomized example data points\n",
"rng = np.random.default_rng(1337)\n",
"\n",
"N = 100\n",
"true_parameters = np.array([2, 1, 0.5])\n",
"y_unc = rng.uniform(0.1, 0.4, N)\n",
"\n",
"x = np.linspace(0, 4 * np.pi, N)\n",
"y = linear_combination(x, funcs, true_parameters)\n",
"\n",
"# add some noise for to simulate measurement uncertainty\n",
"y_unc = rng.uniform(0.1, 0.4, N)\n",
"y += rng.normal(0, y_unc)\n",
"\n",
"plt.figure()\n",
"plt.errorbar(x, y, yerr=y_unc, ls='', marker='.', color='k')\n",
"plt.xlabel('x')\n",
"plt.ylabel('y')"
"plt.ylabel('y');"
]
},
{
Expand Down Expand Up @@ -213,7 +192,7 @@
"\n",
"fig, ax = plt.subplots()\n",
"plot = ax.matshow(W)\n",
"fig.colorbar(plot)"
"fig.colorbar(plot);"
]
},
{
Expand All @@ -239,7 +218,7 @@
"outputs": [],
"source": [
"def solve_linear_least_squares(A, W, y):\n",
" \"\"\"Solve the linear least sqaures problem\n",
" \"\"\"Solve the linear least squares problem\n",
" \n",
" Parameters\n",
" ----------\n",
Expand Down Expand Up @@ -378,7 +357,7 @@
")\n",
"\n",
"\n",
"ax.legend()"
"ax.legend();"
]
},
{
Expand All @@ -389,10 +368,9 @@
"source": [
"corr = cov_to_corr(cov)\n",
"\n",
"fig = plt.figure(constrained_layout=True)\n",
"ax = fig.add_subplot(1, 1, 1)\n",
"fig, ax = plt.subplots()\n",
"m = ax.matshow(corr, cmap='RdBu_r', vmin=-1, vmax=1)\n",
"fig.colorbar(m)"
"fig.colorbar(m);"
]
},
{
Expand Down Expand Up @@ -469,7 +447,7 @@
")\n",
"\n",
"\n",
"ax.legend()"
"ax.legend();"
]
},
{
Expand Down Expand Up @@ -512,9 +490,7 @@
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"scrolled": false
},
"metadata": {},
"outputs": [],
"source": [
"df = pd.read_csv('resources/spalt.csv')\n",
Expand Down Expand Up @@ -547,9 +523,7 @@
" xlabel=r'$\\varphi \\,\\, / \\,\\, \\mathrm{rad}$',\n",
" ylabel=r'$I \\,\\, / \\,\\, \\mathrm{A}$',\n",
")\n",
"ax.legend(loc='best')\n",
"\n",
"None # to not have mpl objects in the output"
"ax.legend(loc='best');"
]
},
{
Expand Down Expand Up @@ -583,10 +557,10 @@
"E_MAX = 175\n",
"\n",
"# normally distributed signal\n",
"higgs_signal = np.random.normal(126, 5, 500)\n",
"higgs_signal = rng.normal(126, 5, 500)\n",
"\n",
"# exponentially distributed background\n",
"background = np.random.exponential(50, size=20000)\n",
"background = rng.exponential(50, size=20000)\n",
"\n",
"# combine signal and background\n",
"measured = np.append(higgs_signal, background)\n",
Expand All @@ -598,7 +572,7 @@
"\n",
"fig, ax = plt.subplots()\n",
"ax.hist(measured, bins=100)\n",
"ax.set_xlabel('$m \\,/\\, \\mathrm{GeV}$')\n",
"ax.set_xlabel(r'$m \\,/\\, \\mathrm{GeV}$')\n",
"ax.margins(x=0)\n",
"None"
]
Expand Down Expand Up @@ -714,7 +688,9 @@
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"metadata": {
"scrolled": true
},
"outputs": [],
"source": [
"from scipy.optimize import minimize\n",
Expand Down Expand Up @@ -768,7 +744,6 @@
"metadata": {},
"outputs": [],
"source": [
"\n",
"e = np.linspace(E_MIN, E_MAX, 1000)\n",
"\n",
"\n",
Expand All @@ -778,7 +753,7 @@
"ax.plot(e, pdf(e, *result.x))\n",
"ax.axvline(result.x[0], color='C2', lw=2)\n",
"\n",
"ax.set_xlabel('$m \\,/\\, \\mathrm{GeV}$')\n",
"ax.set_xlabel(r'$m \\,/\\, \\mathrm{GeV}$')\n",
"ax.margins(x=0)"
]
},
Expand Down Expand Up @@ -904,9 +879,7 @@
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"scrolled": false
},
"metadata": {},
"outputs": [],
"source": [
"N = np.genfromtxt(\"resources/muon_data.txt\")\n",
Expand Down Expand Up @@ -1000,17 +973,18 @@
"source": [
"plt.figure()\n",
"\n",
"plt.axvline(m.values['tau'], color='C1')\n",
"plt.axvline(m.values['tau'], color='C1', label=\"Fit-Result\")\n",
"plt.plot(m.values['tau'], m.fval, color='C1', marker='o', zorder=3)\n",
"\n",
"plt.axvline(m.values['tau'] + m.merrors['tau'].lower, color='C2')\n",
"plt.axvline(m.values['tau'] + m.merrors['tau'].upper, color='C2')\n",
"plt.axhline(m.fval + 1, color='C3')\n",
"plt.axvline(m.values['tau'] + m.merrors['tau'].lower, color='C2', label=\"Lower Error\")\n",
"plt.axvline(m.values['tau'] + m.merrors['tau'].upper, color='C2', label=\"Upper Error\")\n",
"plt.axhline(m.fval + 1, color='C3', label=\"NLL + 1\")\n",
"plt.axvline(pdg_reference, color='k', label='PDG')\n",
"plt.plot(tau, ts)\n",
"\n",
"plt.xlabel('τ / µs')\n",
"plt.ylabel('NLL')\n",
"plt.legend()\n",
"None"
]
},
Expand All @@ -1021,7 +995,7 @@
"outputs": [],
"source": [
"plt.figure()\n",
"m.draw_mncontour('tau', 'p', size=250)"
"m.draw_mncontour('tau', 'p', size=250);"
]
},
{
Expand All @@ -1048,7 +1022,7 @@
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.10.6"
"version": "3.12.7"
}
},
"nbformat": 4,
Expand Down