{
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"cell_type": "code",
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"shell.execute_reply": "2021-11-16T10:25:17.136868Z"
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"slideshow": {
"slide_type": "slide"
},
"tags": [
"hide_input",
"hide_output"
]
},
"outputs": [
{
"data": {
"text/html": [
"\n",
" \n",
" \n",
" \n",
" > \n",
" \n",
" \n",
" \n",
" \n",
" \n",
" \n",
" "
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""
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"source": [
"### BEGIN hide_toggle\n",
"### Update 30/10-'20\n",
"def hide_toggle_code(off=0):\n",
" \"\"\"This function generates HTML code to toggle the display of an input\n",
" cell.\n",
" \n",
" The output of the cell will still be displayed. This can be used\n",
" to hide (from immediate view) some code to generate data or the\n",
" like. It can also be used to hide other notebook explicit\n",
" implementations - e.g., C++ processing, or the like.\n",
" \n",
" Note, calling this function alone will not enable toggling.\n",
" Instead, we must wrap the generated code in an\n",
" `IPython.display.HTML` object and return that as the cell value.\n",
" This will let IPython evaluate the HTML code and pass it on to the\n",
" browser.\n",
" \n",
" If all one wants is to toggle a cell one can use the function\n",
" `hide_toggle` below. However, we can also combine the code\n",
" generated here with other HTML code - for example _style_\n",
" declarations and pass that along embedded in an HTML object.\n",
" \n",
" Parameters\n",
" ----------\n",
" off : int \n",
" Offset of cell to hide relative to the cell calling this function \n",
" \n",
" Returns\n",
" -------\n",
" code : str \n",
" HTML code to enable toggling of the cell\n",
"\n",
" \"\"\"\n",
" from random import randint \n",
" from IPython.display import HTML \n",
" \n",
" jp_cell = 'document.getElementsByClassName(\"jp-Cell jp-mod-selected\")[0]'\n",
" jq_cell = '$(\"div.cell.code_cell.rendered.selected\")'\n",
" toggle_text = 'Please close'\n",
" cell_id = str(randint(1,2**64))\n",
" func_name = f'code_toggle_{cell_id}'\n",
" \n",
" scr1 = f'''\n",
" \n",
" '''\n",
" but = f'''\n",
" \n",
" > \n",
" \n",
" '''\n",
" scr2 = f'''\n",
" \n",
" '''\n",
" return scr1+but+scr2 \n",
"\n",
"def hide_toggle(off=0,cnt=None):\n",
" \"\"\"This will wrap the HTML code returned from the above function\n",
" in an `IPython.display.HTML` object so that the notebook will \n",
" evaluate the HTML code. \n",
" \n",
" This function is what we will use most of the time. However, \n",
" the function `hide_toggle_code` can be combined with other code \n",
" and then be put into an HTML object to let the notebook evaluate\n",
" all the code. \n",
"\n",
" Parameters \n",
" ----------\n",
" off : int \n",
" Cell offset relative to calling cell which we should toggle \n",
" cnt : int or None \n",
" If not None, set the execution count to this number \n",
" (currently broken)\n",
" \n",
" Returns\n",
" -------\n",
" object : IPython.display.HTML \n",
" HTML object wrapping code to toggle cell \n",
" \"\"\"\n",
" from IPython.display import HTML\n",
" if cnt is not None:\n",
" get_ipython().execution_count = cnt\n",
" return HTML(hide_toggle_code(off))\n",
"### END hide_toggle\n",
"\n",
"### BEGIN show_all\n",
"def _show_all():\n",
" try:\n",
" from IPython.core.interactiveshell import InteractiveShell\n",
" InteractiveShell.ast_node_interactivity = \"all\"\n",
" except:\n",
" pass \n",
"### END show_all\n",
" \n",
"### BEGIN setup_matplotlib\n",
"### Update 30/10-'20\n",
"def _setup_matplotlib():\n",
" \"\"\"Set-up Matplotlib parameters. \n",
" \n",
" We specify that we want both PDF and PNG images, and \n",
" that the default image size should be 8 by 8 inches \n",
" \n",
" We also disable warnings about too many open figures \n",
" \"\"\"\n",
" %matplotlib inline \n",
" from matplotlib import rcParams \n",
" \n",
" rcParams['figure.max_open_warning'] = 0\n",
" rcParams['font.serif'] = ['Palatino'] + rcParams['font.serif']\n",
" rcParams['font.family'] = ['serif']\n",
" rcParams['mathtext.fontset'] = 'dejavuserif'\n",
" rcParams['axes.formatter.use_mathtext'] = True\n",
"\n",
" f = None\n",
" try:\n",
" # IPython >= 7.23 depcrates set_matplotlib_formats\n",
" from matplotlib_inline.backend_inline import set_matplotlib_formats\n",
" f = set_matplotlib_formats\n",
" \n",
" except Exception as e:\n",
" try:\n",
" from IPython.display import set_matplotlib_formats\n",
" f = set_matplotlib_formats\n",
" except Exception as e:\n",
" pass \n",
"\n",
" if f is not None:\n",
" set_matplotlib_formats('png','pdf')\n",
" \n",
"_setup_matplotlib()\n",
"### END setup_matplotlib\n",
"_setup_matplotlib()\n",
"\n",
"### BEGIN css_styling\n",
"### Update 30/10-'20\n",
"def css_styling_code():\n",
" \"\"\"This function returns HTML code to customize the CSS \n",
" of the notebook \n",
" \n",
" - The text font to be Palatino (serif)\n",
" - Headers are oblique (italic)\n",
" - Extra spacing below H1 headers \n",
" - Extra spacing spacing above H1 headers \n",
" - Headers have larger fonts, and is set in normal weight\n",
" - Remove padding around code cells \n",
" - Code uses the fint \"Source Code Pro\" (or monospace)\n",
" - Code background is changed to light yellow \n",
" - Output background is set to lavender\n",
" \n",
" The function combines these CSS declarations with the HTML \n",
" code from `hide_toggle_code` above so what we automatically \n",
" hide this code from the user. \n",
" \"\"\"\n",
" styles = '''\n",
" \n",
" \n",
" '''\n",
" return styles\n",
"\n",
"def css_styling():\n",
" from IPython.display import HTML \n",
" \n",
" return HTML(hide_toggle_code()+css_styling_code())\n",
"### END css_styling\n",
"css_styling()"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "-"
},
"tags": [
"title"
]
},
"source": [
"### Christian Holm Christensen \n",
"\n",
"# `nbi_stat` Examples \n",
"## Complete examples with some explanations \n",
"## 0.1 - December 2019 \n",
"\n",
"> In this note, we will show some examples of using the module `nbi_stat` available from the [NBI-Python](https://cholmcc.gitlab.io/nbi-python/statistics/#Statistik) page. For motivation, arguments, and statistical considerations, we refer you to the full text of [Statistics Overview - Using Python](https://cholmcc.gitlab.io/nbi-python/statistics/#Statistik). \n",
">\n",
"> The module `nbi_stat` is a Python module with various numerical and statistical tools to ease various tasks, such as \n",
">\n",
"> - Presentation of data in tables and visually\n",
"> - Reporting results \n",
"> - Calculating statistical quantities \n",
"> - Histogramming\n",
"> - Random samplling\n",
"> - Propagation of uncertainties \n",
"> - Curve fitting \n",
">\n",
"> The module is built on top of [_SciPy_](https://scipy.org) and [_NumPy_](https://numpy.org) and is throughly [documented](https://cholmcc.gitlab.io/nbi-python/statistics/nbi_stat/). \n",
">\n",
"> This document is available in many formats at https://cholmcc.gitlab.io/nbi-python\n",
"\n",
"### Niels Bohr Institutet "
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
},
"toc": false
},
"source": []
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Introduction\n",
"\n",
"If you haven't already, you should install the `nbi_stat` module. Just do as [we would normally do with any other Python package](https://pip.pypa.io/en/stable/quickstart/) \n",
"\n",
" > pip install nbi_stat \n",
" \n",
"If you have already installed the module, you can check for updates with \n",
"\n",
" > pip install --upgrade nbi_stat \n",
" \n",
"First, we will load our module. We alias it to `nbi` to save a few key-strokes here and there. "
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"execution": {
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"shell.execute_reply": "2021-11-16T10:25:17.224398Z"
}
},
"outputs": [],
"source": [
"import nbi_stat as nbi"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We may need to import more modules or packages later on. We will do so when needed. "
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"You can get help on any part of the module by, for example "
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:25:17.234360Z",
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"shell.execute_reply": "2021-11-16T10:25:17.238896Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Help on function chi2nu in module nbi_stat:\n",
"\n",
"chi2nu(x, y, f, theta, delta=None, deltax=None, df=None, df_step=None)\n",
" Calculate the chi-square over the sample (x,y)\n",
" for the model f with parameters p. \n",
" \n",
" Note, points where delta<=0 are explicitly ignored\n",
" \n",
" Parameters\n",
" ----------\n",
" x : array-like \n",
" Independent variable, N long \n",
" y : array-like \n",
" Dependent variable, N long \n",
" delta : array-like (optional)\n",
" Uncertainty on y or None\n",
" f : callable\n",
" Our model function with signature f(x,a...)\n",
" p : array-like \n",
" Model parameters \n",
" deltax : array-like \n",
" Uncertainty in X. If this is specified then the \n",
" effective variance is calculated and used instead of the \n",
" y variance (given in delta)\n",
" df : callable \n",
" The derivative of f with respect to x (only relevant if deltax is not\n",
" None)\n",
" df_step : float \n",
" The step size for numerical differentation of f with respect to x\n",
" - (only relevant if deltax is not None)\n",
" \n",
" \n",
" Returns\n",
" -------\n",
" chi2 : float \n",
" Calculated schi-square \n",
" nu : int\n",
" Number degrees of freedom\n",
" \n",
" See also\n",
" --------\n",
" lsq_fit\n",
"\n"
]
}
],
"source": [
"help(nbi.chi2nu)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"Similarly, \n",
"\n",
" help(nbi)\n",
" \n",
"will print out documentation of the whole module. "
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"## Further reading \n",
"\n",
"**Python specific**\n",
"\n",
"- [Documentation of the application programming interface of `nbi_stat`](https://cholmcc.gitlab.io/nbi-python/statistics/nbi_stat)\n",
"- [Statistics Overview - with Python](https://cholmcc.gitlab.io/nbi-python/statistics/#Statistik)\n",
"- [A short lecture on Statistics](https://cholmcc.gitlab.io/nbi-python/statistics/#Lecture)\n",
"- [An example lab-report using Jupyter and `nbi_stat`](https://cholmcc.gitlab.io/nbi-python/misc/#NewtonSecondLaw)\n",
"\n",
"**General on statistics**\n",
"\n",
"- L.Wasserman [All of Statistics](http://www.stat.cmu.edu/~larry/all-of-statistics/), Springer, 2005\n",
"- H.Cramér [Mathematical Methods of Statistics](https://press.princeton.edu/titles/391.html), Princeton University Press, 1999\n",
"- A.Stuart [Kendall's Advanced Theory of Statistics](https://www.wiley.com/en-us/Kendall%27s+Advanced+Theory+of+Statistics%2C+3+Volume+Set%2C+6th+Edition-p-9780470669549), Wiley, 2010\n",
"- S.Ditlevsen og H.Sørensen [Introduktion til Statistik](http://web.math.ku.dk/noter/filer/ss18.pdf), IMF, 2018\n",
"- [Wikipedia](http://wikipedia.org) - scientific articles are generally good.\n",
"\n",
"**Data analysis**\n",
"\n",
"- P.Bevington og D.K.Robinson [Data Reduction and Error Analysis for the Physical Sciences](https://www.mheducation.com/highered/product/data-reduction-error-analysis-physical-sciences-bevington-robinson/M0072472278.html), McGraw-Hill, 2003\n",
"- R.J.Barlow [Statitics - A Guide to the Use of Statistical Methods in the Physical Sciences](https://www.wiley.com/en-us/Statistics%3A+A+Guide+to+the+Use+of+Statistical+Methods+in+the+Physical+Sciences-p-9780471922957), Wiley, 1993\n",
"- G.Cowan [Statistical Data Analysis](https://global.oup.com/academic/product/statistical-data-analysis-9780198501558?cc=dk&lang=en&), Oxford Univeristy Press, 1998\n",
"- O.Behnke _et al_ [Data Analysis in High Energy Physics](https://onlinelibrary.wiley.com/doi/book/10.1002/9783527653416), Wiley-VCH, 2013"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Tabulation of data "
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"## `format_data_table`\n",
"Using the function `format_data_table` we can easily tabulate data and display it. "
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:25:17.260438Z",
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},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"| || |\n",
"|:---:|:---:|:---:\n",
"| 1|2|3 |\n",
"| 4|5|6 |\n",
"| 7|8|9 |\n",
"| 10|10|10 |\n",
"\n"
]
}
],
"source": [
"data = [[1, 2, 3],\n",
" [4, 5, 6],\n",
" [7, 8, 9],\n",
" [10,11,12]]\n",
"print(nbi.format_data_table(data,mode='markdown'))"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"Off-hand this does not look like much, but if we load the `display` module of `IPython`, we can format the output better"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:25:17.277805Z",
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"shell.execute_reply": "2021-11-16T10:25:17.281863Z"
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},
"outputs": [
{
"data": {
"text/markdown": [
"| || |\n",
"|:---:|:---:|:---:\n",
"| 1|2|3 |\n",
"| 4|5|6 |\n",
"| 7|8|9 |\n",
"| 10|11|12 |\n"
],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from IPython.core.display import Latex, HTML, Markdown\n",
"display(Markdown(nbi.format_data_table(data,nsig=None,mode='markdown')))"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"execution": {
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},
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [
{
"data": {
"text/html": [
"1 2 3 \n",
"4 5 6 \n",
"7 8 9 \n",
"10 11 12 \n",
"
"
],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"display(HTML(nbi.format_data_table(data,mode='html',nsig=None)))"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"execution": {
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"shell.execute_reply": "2021-11-16T10:25:17.310869Z"
},
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [
{
"data": {
"text/latex": [
"$\\begin{array}{|ccc|}\n",
"\\hline\n",
"1&2&3\\\\\n",
"4&5&6\\\\\n",
"7&8&9\\\\\n",
"10&11&12\\\\\n",
"\\hline\n",
"\\end{array}$"
],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"display(Latex(nbi.format_data_table(data,mode='latex',nsig=None)))"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"The $\\mathrm{\\LaTeX}$ formatting is especially useful if you are generating a final PDF to hand in as a lab-report or the like. See also [this example lab-report](https://cholmcc.gitlab.io/nbi-python/misc/#NewtonSecondLaw) for how to make a lab-report (or similar) in Jupyter. \n",
"\n",
"We can customize the table by various keywords. Let's illustrate a few "
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:25:17.327681Z",
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}
},
"outputs": [
{
"data": {
"text/latex": [
"$\\begin{array}{|c|ccc|}\n",
"\\hline\n",
"One&A&B&C\\\\\n",
"\\hline\n",
"I&1&2&3\\\\\n",
"II&4&5&6\\\\\n",
"III&7&8&9\\\\\n",
"IV&10&11&12\\\\\n",
"\\hline\n",
"\\end{array}\\quad \\begin{array}{ccc}\n",
"\\hline\n",
"a&b&c\\\\\n",
"\\hline\n",
"1&2&3\\\\\n",
"4&5&6\\\\\n",
"7&8&9\\\\\n",
"10&11&12\\\\\n",
"\\hline\n",
"\\end{array}\\quad \\begin{array}{|r|cc|}\n",
"\\hline\n",
"a&b&c\\\\\n",
"\\hline\n",
"1&2&3\\\\\n",
"4&5&6\\\\\n",
"7&8&9\\\\\n",
"10&11&12\\\\\n",
"\\hline\n",
"\\end{array}$"
],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"display(Latex('$'+nbi.format_data_table(data,mode='latex',nsig=None,\n",
" dollar=False,title='One',\n",
" columns=['A','B','C'],\n",
" rows=['I','II','III','IV'])+r'\\quad'\n",
" ' '+nbi.format_data_table(data,mode='latex',nsig=None,\n",
" dollar=False,title='Two',\n",
" columns=['a','b','c'],\n",
" borders='TBH')+r'\\quad'\n",
" ' '+nbi.format_data_table(data,mode='latex',nsig=None,\n",
" dollar=False,title='Three',\n",
" columns=['a','b','c'],\n",
" fmt='|r|cc|',borders='TBH')+\n",
" '$'))"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"If the data entries are tuples, then they are interpreted as results with uncertainties. The keyword `nsig` determines how many significant digits to round to. "
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:25:17.345261Z",
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"outputs": [
{
"data": {
"text/latex": [
"$$\\begin{array}{|ccc|}\n",
"\\hline\n",
"1.0\\pm0.1&2.0\\pm0.2&3.0\\pm0.3\\\\\n",
"12.34\\pm1.234\\pm0.1234&0\\pm1&10000000.0\\pm300000.0\\\\\n",
"\\hline\n",
"\\end{array}$$"
],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"data = [[(1,0.1), (2,0.2), (3,0.3)],\n",
" [(12.34,1.234,0.1234), (0,1), (1e7,3e5)]]\n",
"display(Latex(nbi.format_data_table(data,mode='latex',nsig=None,dollar='$$')))"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Visualisation of data "
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"## One-dimensional samples \n",
"\n",
"### `hist`\n",
"\n",
"If we have a number of observations and we want to visually represent empirical probability of a given observation, we will _histogram_ the data (see also [Statistics Overview](https://cholmcc.gitlab.io/nbi-python/statistics/#Statistik)). Although _Matplotlib_ provides the function `hist` its use is discouraged - it rarely does what we want. In particular, it does not represent the uncertainties on the measurements, and the counts are not normalised properly (_Matplotlib_'s `hist` is really a bar chart mostly suitable for _discrete_ random variables). "
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"The module `nbi_stat` therefor provides a drop-in replacement function `hist` to represent a one-dimensional data sample. "
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:25:17.361718Z",
"iopub.status.busy": "2021-11-16T10:25:17.360562Z",
"iopub.status.idle": "2021-11-16T10:25:19.891798Z",
"shell.execute_reply": "2021-11-16T10:25:19.893263Z"
}
},
"outputs": [
{
"data": {
"application/pdf": 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\n",
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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"from numpy.random import normal \n",
"from matplotlib.pyplot import xlabel, ylabel, title\n",
"\n",
"data = normal(size=1000)\n",
"nbi.hist(data,bins=30,fmt='none')\n",
"xlabel('$x$')\n",
"ylabel('$P(x)$')\n",
"title('Distribution of data');"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"We can choose the bins by passing the `bin` keyword. For example, for data roughly exponentially distributed - like the decay of a radioactive source, we often get very few counts at high values, and thus we would like to make the bins _wider_, resulting in non-equidistant bin edges. "
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:25:19.910566Z",
"iopub.status.busy": "2021-11-16T10:25:19.901171Z",
"iopub.status.idle": "2021-11-16T10:25:21.311605Z",
"shell.execute_reply": "2021-11-16T10:25:21.312307Z"
}
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/home/cholm/Work/nbi-python/statistics/nbi_stat.py:351: RuntimeWarning: invalid value encountered in true_divide\n",
" h = h/w/s\n"
]
},
{
"data": {
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\n",
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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"from numpy.random import exponential\n",
"from numpy import linspace, hstack\n",
"from matplotlib.pyplot import yscale\n",
"\n",
"data = exponential(size=1000)\n",
"bins = hstack((linspace(0,2,20,endpoint=True), linspace(2,5,7)))\n",
"nbi.hist(data,bins=bins)\n",
"yscale('log')\n",
"xlabel('$x$')\n",
"ylabel('$P(x)$')\n",
"title('Distribution of data');"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"If we need to plot the data in a sub-plot we can pass the keyword `ax` to select the `Axes` object to plot in"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:25:21.351367Z",
"iopub.status.busy": "2021-11-16T10:25:21.348083Z",
"iopub.status.idle": "2021-11-16T10:25:23.266675Z",
"shell.execute_reply": "2021-11-16T10:25:23.266058Z"
}
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/home/cholm/Work/nbi-python/statistics/nbi_stat.py:351: RuntimeWarning: invalid value encountered in true_divide\n",
" h = h/w/s\n"
]
},
{
"data": {
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\n",
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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"from matplotlib.pyplot import subplots \n",
"\n",
"fig, ax = subplots(ncols=2)\n",
"\n",
"data = normal(size=1000)\n",
"nbi.hist(data,bins=30,ax=ax[0],fmt='s')\n",
"ax[0].set_xlabel('$x$')\n",
"ax[0].set_ylabel('$y$')\n",
"ax[0].set_title(r'Data ($X\\sim \\mathcal{N}[0,1]$)')\n",
"\n",
"data = exponential(size=1000)\n",
"nbi.hist(data,bins=bins,ax=ax[1],fmt='o')\n",
"ax[1].set_xlabel('$x$')\n",
"ax[1].set_ylabel('$y$')\n",
"ax[1].set_yscale('log')\n",
"ax[1].set_title(r'Data ($X\\sim \\mathcal{E}[1]$)')\n",
"\n",
"fig.suptitle('Measurements',y=0)\n",
"fig.tight_layout()"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"## Multi-dimensional samples \n",
"\n",
"### `corner_plot`\n",
"\n",
"Generally it is difficult to visualize samples in 2 or more dimensions. For 2 dimensions one may use _NumPy_'s [`histogram2d`](https://docs.scipy.org/doc/numpy/reference/generated/numpy.histogram2d.html) in combination with for example _Matplotlib_'s [`pcolormesh`](https://matplotlib.org/api/_as_gen/matplotlib.axes.Axes.pcolormesh.html), or even [`hist2d`](https://matplotlib.org/api/_as_gen/matplotlib.axes.Axes.hist2d.html). However, one has to be careful in these cases \n",
"- We cannot easily visualize the uncertainties \n",
"- We must be careful to pass `density=True` in all cases to properly normalize the histogram (if not, it is not really a histogram but a bar-chart which isn't really suitable for a continuous varible). "
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"The module `nbi_stat` provides an alternative representation via the function `corner_plot`. It is best illustrated by an example "
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:25:23.311487Z",
"iopub.status.busy": "2021-11-16T10:25:23.273243Z",
"iopub.status.idle": "2021-11-16T10:25:27.977285Z",
"shell.execute_reply": "2021-11-16T10:25:27.977845Z"
}
},
"outputs": [
{
"data": {
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YQAgJV9vbyE8DG8PAZYTdt8Rl4AesA9rGXGJ3adBEfvJGs7rT5nenokI/JG+sdoL9g2sxqdgPpCxx3oL9jL5lqGI/TKxpoMYGa849exX8IU4fICFgb7lkpYM/kUFtnHq+oV9N7IeEA6scxlN0DSYV/On0CDr4AkaR+3Ad/IkrLw2EA+Xm6kEd/HnOBNTTrEyW8ajcxn9iBRUOcIlvpqj4D+2hBqEBk9b1OHT8B1TbJiHqljxBqOM/GEvnBGYN1uKdpor/wMeCaZt91tHBH8oiyDX0X16T01+Hf9A9t8QUtuLrVxX+KVTOsGZxAi5Z6fBPoosN7VpTc102Ff4ZkIPYSkzF3WwV/gErEKOldvA5XkV/lozFsDCOnA1rFcj4DwyaSrsX6s21UEwACBYK+BNKDT6yay2pCNCEEQ5ahIyI45bNIQNAtJQZhun0s9z+KgBUuI3Yw5ina7qpCBAU/xLoJJVbIuUaAYKNPWOirVpch9pEgLArVFr4Z3fZ3kSAEtON6OzXGx6hjgCt8DO9N4blfQNIRIAmUQeIn5bVgX5K/EcBbKIVbPoGr6n4j+ovm/UAEefREJ5s10MkGkfQCEepwX3R7IL74RgPaVcCyWVPgSEeD3GKbV6A/Hthj+/QI+w7/vaPtxF4FkY8/+Lrb377H3/9zdd//uPvn1/++Ke//uV1209xCohYmNbQsnopovl+nALu2MYUrpj7nof90VAWzGtwf2QxhprI0fxOTA2KF9oiLffl3VDWnQhSIgQCv77pmJpofmciDazeyLDwbN8NIfmRm2X3MnJD0B4aoxbY7Uvjvz2s7S/ToZuvPjV0o5nLR6M1en4L774diHkIIf9QsOfB0I2agAD81QRuxQ5uvf6K0V871B2KvwPUp9tA/RPX8b2A+qfbIz4I1CfoFSyDmCT9aA+oTxZqAqHCcAsgfxeoT1bhwosM0D6puji96s7E4lgGFSicVAeo1w+vk9g7zgxas7hIfTJ6C/4sDmr5bA5Un4xtNpm6wwRTB6g3MyECS88DCqV6QH3S1iqNWuYGwEg8A/V6SyqB4NEgHaBfHZze2RL6evRAXKA+acNv9FEDhG/wcHrVFxtWFxBIG8jB6VVnOBIFEwFV0dBycHo97R4pT+dygV2Y3lBVXXKaG5GKg9PrY6ffCDpiMqKD0usnNyYg08vv1cPodefMnG/mamVGOc4gve7NagyQKzVp9kB6s0QoJbjGdI+ri9GbNYIBmSY89vxYC9Eb8hsdlh2M9hxdgF71hr2TVnUSvDwPn9c0QvGJGcPbWOUqJ3heL3JsdKphUMMO8eB5syVxgbS1LufLwef1loBnI+gaHqEPz1vZUOvAZAKcbw+eNycPv4AFeiCk4cDzujOMQsgoeqPw2114Xh8Pc+TgJAdCrx48rxltMmafIbHhNnnovJ7L5MsH3CNmOHvwvJXHmajIXJm8Dj5vlAO83wgnZi4J4SH0qj9cQUbE4DLN5iD05vCZibpQq0AXxUHoLSNDjhUI5J6jg9BbYQXFEArz27sH0BsZ23jgjM2FmhyEXquRSsirs6whDg+gPy1zBFZ+Qo8kF6DX/IaHD3h1mcC1g89rYU/vGMIHXl7tHj5vmBNzzXRJmdrlwPMnRQ9/FNOOtAsceN4yZygwMvpkmtQZnjfyqtL15ZFkD5033MYoBHkd05kOPG9IsIFEJ0TEKic6g/NGWxKdZbVZGh42b3Ta1mCHRGhJxu5P4LymQEI/jD12Jro66LzZbJx0oQpbmIoDzxtpRQM1xw53vVQXnz8pQdaLgmxb9PB5fTqd+b8NShOi1YHnzeksHLzTSJ3TBehPZFUWcA6zcHgQ/ckwAEnR4mFs5ozRayJcVTs4oMqZexC94bXRqQihJbqH0Js9hySGjAWZ5jY9iF4LWlAe1BieBVPageiNAIKjWaES4CBmF6I3806weXOljnUAetO3EjvDw2FeOvi8YR6KhwxR1jx03swZc8QEWXMyPXRebwcDRDBeYDJOD5u3dmnuMEk4DxebP2ljPLxS/BBgPKPzlotrpyKAyTRdcN7KtciEdcwW5Oqg8ydZRXATRiy9BgedN0YeDiLPOqaLzGtRRagSSj5wKh40b2R9hC6GE5tWYbEHzmtxlSEhSqXAR3cHnDdnP8hZkGiJAQ4HndfLBKPRmWax5hmet0cP/V9X+VV30fmTIIRggJtR5iwuPH86zVYxU+zz8OB58/TKrCccX44+Pm+0GsNDFEArw8Pi84ZQNspUKI/C8NMJoDfMs5KKYWvCRPfgeWtB0HsHdffoofN2HhV+ADakt+mC8/rZgXXf3GByhIfOGzqhNgDRgf7huHjovOnfN7igLNAuVCYOPK/6T/hUjYlgCy5w8PmzqUwjY8Cwry5Er/2kQq06icqzFPyM0Bsd22l+QWb3HKML0eutpGyAC9tLr8lD6E9mZKFwplzMDkSfHoToRQ6yxvhku4bQRQ6yRuVkuxly5CDrIbLdYPsS+xNIfWw8NdtuhyhEXAw5QeJiiMSu5RALXoshEmWWQwzM/G6e9aOArA98Ppo0/RCG+rHU7Hso7q1JF2bMTUomPQPRfisx/4zi3iVylurkxksv9BaIZk18q/aGyc16gGw2AypxpRrtANFsBgzmuVKTmBGy3TCRS0UfIAl/419ubvwdwrt1hndqAu685bFs/dwXQm3ue7q2fnszPuGGM9xM/evDfkI5+pEeTZuE064XjGSrU2SOPnQvEVt6Ct3rblL0oT7hocLwwuu8x6sUfWzrWg0mNr3OOkU/QmijO3y92r3e+mqmQBdyQHW1t3JVs0yVof9c4IvB6i7laoGa7jpFP/UN5seok2aFOxeRo79SIDsR0HEF/7M1KUWWPkFMTJulysWbjM7Sx8xYoU5DO3lT0Un6vBgHPIF1dH8q+nYmYpSQPj2l7D1bp+kTi0u8iii9YXWnPRRZ+mFV1tMCdR+tc/TLtnI5GnO2/XmIHH1QPAzV2dq4olJmIjpHn2X70NPYkejSikrSJ4IMRwKMf8XR9eHoJH0QQobT1FMOLl2ZJP3OjA44HhX77fXXSfpEBGgZd6JTN+hKJukXvKyAT+l/RG+hOkkfggBmKEz/2t1tNEn6mE2CHc98wuHtjM7Sb4yGY6PiESPUT9dZ+p05ZTMSUHdpy2Tpw6WDMBzE9ae3Up2mz2J/xhAgXbK3Up2mT3sT588ooftsm6ffmRmVQASELzyKUXn6vL4GwppJts19us7TJ0iEf4Gp4K/mG3x0JOrDzc6V6fXgVI/UVaJ+pBRjAmrt0yNGlahPlB+cCqva3RSVpv9cFtxNoeXut8nTx1lF5pP22LwVmhuaCjRQCbyiokd3A3Wefm68H5ACLLzhu/rsVZ5+phqg5i/Tl3EmUR+iqNY64d3W6QouJ1OftyBO3r7k0YrK1GdNPoTvAOm656MS9bFNZD0QYnC30STqg24CJgLJP6OrKEyiPjMiW2YoM3rbqBP1+8ZoKjgw+cpZJ+rT4Wd8PtOu8EhcZeo3/sU7y2po7pabVH1IsZgh4aBeusueOlU/bmlCcgQ23Jj6NVUf1FID5EBi5qJvsRy5+uu6R+4hMxe9R+tkfWY5wACACXK9f9CQuUzWh1EXed1anlesWc9E5eq3FeKGxvKnbVL1SeQp0aJs16Cr6q+S9UEok/HuiO3090Td08SEAV6vABvTtflUsn5khCTwAivfnrTZ+pl3Y8FEjMyc9nZcZ+tDO46Zc83B1VgmW39SN4Pd4g0yVNn63MPGGwgh8dyF2nz9sqLiE3TvsoTJ15+0+QuDHsGV+ipfnxKxpiVybzkIIl0fYwlCThoBrvGk8/XRG4yNiVdXW53y9WFijBqh3/p0qUUl7HeoRrjOKbZUPb2iE/bHWBbGBNlP377RGfsRU2F4Pobk6RWVsD+IETP2hb9umtlHwj5oAdIKBj1NY/f0TcJ+goAEQ8Oid2W5StiH3dU7lG31PRuVrk+PuBHapp/l7aBK18e0GTyYy1n0piHT9Wl0w3FDZ1+1qWz9shDizNCBSyYmX7/QLIZYoT/hSiyVr8+9n7BZIBjdNapsfcg6KK0xJjPV3amIbH2IiNqZMBKnS64qWX9ujP7x2l7XutJ3NdEimiuW1l3HwEnXT0yEaFyHbxuIdH3mcBA9iLQMfWtc5+vvN9zxbrnpHrxK16eqgnfdcfS+b62y9QkKkG6XT+t2l8n6e44dLOE0XI9GpupzlbDCwf9YpEuCIlcf+1loLTUoRV+/qlR9Cq6QGa3Hf13trXL1oep7gZAb84aG1Zn6ePisDYtu17s+rQUkUvUxdUb4IHXLkMv8lFx9Aa8dbTjHcuveHTo97BUSJTWzzVYG+985G/6oEhALEI33VjDh5rMbpHisagXh1sRPSfCi5kAClKL13gwi/XX2g5yHY/TQFJLMOj+exAgHMzhh8cE3mKSm1128l3X+29u59KxzgOrTl0JdG+8XSbTI4HvkPff1H1sjwRIHGsG6IOBovV8PMOFwMccxko8/mTYE8MysEahvGESq6ORofqdSgxFtJgpC8oVPoZDTRBoV1mTunK5+uTa/MxFmlw1eVT3TR6+2uhZI4BToDMHCXaDAvYutfvep1RFSnPn4v454+dGF23UO70YjPlRH8WBVhHi5CLeIl9+K8t169a2KCD8gcqcW4scYEDG1EF5ApFg4T9ZCnAMixVozohTCiYeo7roUwgmI6IfrUggnIlKMWSAqIZyQSDF271EJ4QREzEx0KYQTECnaFRC1EF5ARO+KqoZw4iHOrlyrIZyASNGGtSiGcOIhqrOuhnDiIaq3Loc4x0P0tFU1xDkcYshK1UKc4yH64EUthBMN0U9WtRBOLET3VsUQTjBE99bFEOdgiFmjKoZwYiFmkaIYwgmFGPqTxRBOIET11sUQ5ziIJhFdDOGEQfQqVTWEEwYxe6KrIc5xEL0nuhrCCYNYASHKIZwwiDl7WQ7hhEF0b1MP4YRB9AmpeggnDKI5TdVDeFEQPRldEOGEQaxUFgURThzEaAhVEHGOhKjeqhzCiYSY41f1EOdIiGVlUQ3hRUKstBL1EE4gxEhZVQ/hREK0NtEFEU4g5LRQWxFhAiGa6WRFxDkOogW+Kohw4iCGP2VBhBMGOal7WRBxDoNY/hQFEecwiJFZsiDCiYIYflMVEU4YxJChLIlwgiBGZ8qSiHMMxCg2WRLhBEE0FaqaCC8KYjZcFUU4YRAjs1RRhBMHOSnDoybiHAfR56NKIrwwiDkgVRThBEJOlCVrIpxQyMlCEEURTixEU6KuinBCIYbfZFXEORJiNl1XRZxDIVraqqoILxRiBJGuiziHQszMRV3EORBi+oq6iHMcxDCQKItwoiBmzqou4hwF0Rui6yLOMRBroorCCCcGclLLsjDCiYJYZpaVEecgiJVvojDCiYKcRJYojHCiIMbgE4UR5wiIFliqMOIUAjESX5dFOEEQLbFUWYQTBDFHL8sinCiIXqOqijiHQezJy7oIJwpykoWiLuIcBjkd5VEV4YRBzLNlVYQTBzGaTRRFnOMghkhkUYQXCDG8Y8oibBjEmhFHWYQXBbFTkXUR5yCIfrYuizhHQQyZqKoIJwpiuquiiHMYRPXWJRFeHORsLR81EU4oRHtLqiTCi4QYHatqIs6hEL2LuiLCiYSc7EhREuGEQsqDoRBR+yDRPdF6F8pvvGSd/RIjpR+LJohaConxidZ7U4AxshJd6PSk9snRhNcpHLUZcgqi9e4UoI3y6leo+h+aQnEDGonsA+MWRkRfsdNTQOOdDyC8xmcOxFMENETRholoHN1l5ED0t6EDgahKkF/Wq1iUX4KwAo5XJS4aj3+3kuQx+NoDix8tCXkXc/5Y0cmDFSQSzj8KCcTbb1Uk3Hr1FfG+dmA2zE+kBADW4QZTZca0TGQP8a7WTuisfH3NkDsj3ro79oLlG/BNW/Yhb9W/RAJHMDtgugwP8q5WoNMHTjQPugd5q+7EGZgCTB0+PMhb9Z4btS02MdN5P0PeeiaFkSp+tIvojQt563XSmk1paU4X8tYThwPW+P3mwhttz4j3eVMGP5KGg8we4q2fTRccZlFhXNmDvM2mMNWId13k7iHeqvPiA7jX5JfpIN562pUfM6q8e4iFdGfIW/VmWnRhrnvLHuBtzmbhf5UWTvYgb7N9y4qA17GwKQfz1ttH/K8zFSPU6WHeekf4zela+Y3LNjzM20y8b4QtB0NswwW9NVHxA7S8+4M5/R7qbVhzvR77XWJzYW899bgy9Hl8sLUc3NuICbiacHrg4UWmMDrAt+oPl22QXmm5Vw/4Nme0q0lIoTyjB3zr7pPMy++Cd34m0wG+9UoTv7qJI4ToHB7wrXrDlGPAreVlr55xb3OicYEfTK8isuLg3vpE6R7yazXro5EO7m2YkxhfWNiKC3ubI2J/5t3yO5Me7K1PiIDXWFcvNhf2NsTV6RfAZebnxB3Y23AznHHqz/3mtBPsbQ6f9zgR24cDORzY2xxP571W/P65j3prbm7bAlUH86s81Fv1xqroAff1yV8H89bT7rR2e2L+anQxb3M6MIHpIbcwyZ4O5q2JlknahZ9g4+0iZ9Bb73df38GGH0z00AG99VQaZGBkkAEeYfFQ75P+wUw6aHZ9/sGBvfXMC2/c4dcjS/ay/83DN7jsYKEei49762czLgod3/m9bwf1PjEEC/7AyIVlRQ7ubbecn8JtzACeHvCtn864IQikL0fZAb41t0EJDYZp+XwX+DbsxttZx5gsKvRwb9ObBwqyrjA5kod7a6YgEAcLDCZWyg7ubWQQI4C8/mdWF/Y2xwk5gg3rGAN56MDehhK5K+R75qJ7qLfqTnWYeN1O32Eni3mfNiVCs/I6H5KWA3pbmyzz67W84LF4qLemFe5LoaXAVGoH9DbycNAsCPAgXMjbbAqOBFq+JoJwHuRtOYhYJy95DNUDve0qsST4E5EZkifQ+6Rmec1N64RSPdjbWuOjM7QzeNWNA3sb5twG46hhrruyz7C33W5+CRsSkB/OdmDvkzmBg4TfRvjNQ72NpQrBAIEWWVPmwt6qe880wHk3zroo8Ax7m7nQF+BXi6GYu4t7m33hV9lzATv3kF3sW88Gi8NpZsrYeMa+jcqavKGSn6Wlme1h35psCd1OgqC82c7Bvs3MaVpDHpODXfBbH+nKAGSyMbwCB/w+u528k5b1HMVFv03/upv5WO7w0G9tlcGdhshvvNUne+i3eXaBQ4GpUsS68LcxWHCYlQQ1mgN/ay3BlNNEZZz9MoCzsOU9axWGcnTxb82gDAPTOoRUHC4AfrJYYPpQzWcWtp8RcK0o+M3oSf3a+AmdEwB+tpupa4kldw8APzlOOEHY/Lyu3AHANdlWGpz8gDFdPA8AN+uEowoySm1ZFQ4Ars+IaU6Tyng/pDMAfqJEVsPWRmf2jH9bmxIu8KRXzW9eOPi3IS2aQmHJOQ/9rg+i38etKBLpOxrvor5jGarwkis9wX9ULcBxT4tYgmi8twR+TTnTD2O056Pw/XHvi5zA0Xh3AjURKokkovTppQCvEziukZEzEK13pzDgpbEfnIL54BR88D4XflmAhagUkg9XI3x1CkYc6K1A70lu1bTuMPnRXaL3or9B7yU6LNF7McKi9wpQFui9HPIQev/JYLwHfD96Fc+7+PnHLvu5e3OPO93Kyw9CJRoo3i5ab90JdUbv79c1ZeYL0n5Waxetd2ub8gr6LVVX+j9MoMEF4gfNicnLRYjWu4tovIOB/RJDFh8TaTUQvK9GL8jWu1OYYyurH2+o+5hMqyuJoc84NR0drfdmUImvrX6ECr+PTOO285sCqTOX99GA5KOFK5/K2x4fvdzko5vSw2fHO5eF3XlDWOt7ZUbG08V3u4kHMR9mr3+Zb3FO0e7G1BnHOqpRSlrxL1aW7bdsP0DK6ybQDAOU2iawy8+29QMcmb6upc/XH87FfWIFjdcBlmQXcG1+ZP4EnyqDSXPEdz9z8878iWeb+Z9YR8y/BgJ4lXi2WoBof2QFc66bWHkl/uff/3Jv/vA8YbznnMz8j/YH5g/VD4cTkqvB/P4BKKgdK9A3yx0fqGeu9qcEly/x6RumKd4LGp8+GWOEC94NToY/CC9/S4W37JCVJxOZMz8scTTvwuX4hTngEaYM7SgIwLHHFUTzGiB+gVBIsCIq3zCY6cs0Ytm8BohfmEwEdoCL+PIEdyNBU7Qkm9eA45eaCOEyQElKCOW17FW278kI4qdAxptjXfFJ6G0ViIvmfcDxC9QrpB9rqDCAtw8HXgohmvcB4pdKN7zG/RbRzFQgWKVdtu9DxE/8jEJlMSWHlMnLJNqQzfsI7xeyANGyQk1kR/yIKK+yHg37w28gEiylb0/KO5oJKLVKDHrNHQzPUCQc41Lg4afI7NkX2dygpiK/ffNKee318wXYasy1N2akvcjmzsujA4vtdspjsv/gkTGWyrA0D/lonaT9xAvLdrobTM+E9bCohZBZJN2JZuK++Fd+IzvijoTHccKDl7Lwbu5Fd9f2ymtmerxOKTLMEDOt0lJhXzbevLwo72gf/KoRtuCN9HLilYB4HDYqYsbMB31RzS2tMtvx9hKCjrMRttXaWLRjdCIu9DaESOJgcrQZItrNkM9Ge+npV3uyzPeiP0lpUvQJepKSTFCNlFcHcUihJEhASh55zkK+yLMUUkQemBQV6rQEe6sjObP92+bREru6Q7dKpI/TUUXSsNbhXvBWkVNSlxqhlLMecuMd/pPMCPGsu++w1qa6d7ZuzAbdby+e6c0vF+0uijWbzATjLbUzrxjWHvz7oa1N6a5HXgTOu/f1CkT7AyvIrExOzP6IzNX54e1NuQLGXUNhaoBewdH+yArAtJAYEdouf1+D+RGDUy6g4fhnInCoF3C0P7KAyjg8s59mfND5/qC9eV4AhFUY/GSGWcDR/sgCRlhJPrxw7cFPhN4hobF/t+VYwLizALjTjGHPZthYtD+wgBIS8/CYcNHftfjj9+Fi5/6E46ZrXoXySV+U/P7Kb2Wu9xYC76YjBh3C7r7SLGlMrpHtu6wXPxUCLCwu45BJN5ehcNm+D5E/MYYWlyWSQoXuY5xINO8wo/gFAipB7Kc1gmVNMNgZkz7a9yHip7BuR5+1rcR4xg+ZIy7b9yHipwinj0G0NQQGeE91vfzavI84flHvKAtAYsbn6R3uTxjSmFY3IazPQ9yfmF8PKg2Bd72dhsifMgO9c4mkkZnLCt9dNF8NgR8XHXbwTRzrNlUYRy0wBvci24k2dd4yl9/okGZwroFfD0yr11xej2iv/MAm8b9XMpzMveK3FzJzAfOsu60q2ivLI/KVDuO65XkwKhL6+pLGosKjlSYbr+wrbyRFg2AwDTPNzp/6ihUczZAZK/Te4xtJYZ+ZU8Ave0d+CI9W5ItqJ53Gla38SlPMHuQ1nvolR/PpJbVuLOtk3Y4ccTSfRrTGA4u8VFSOOJpPI3BUY1XwYAQFNLN7Ftle23Pg5xJLGOOHoMJ0+SzugCRFLRIPupLyTVKPkGKSSKSoUqQguFjRgZA66lRlf3l2sl2ekGyXx3CSBQ84Bbc+/XHHYr/1nQepwM2QD3xg5Jbzcect1jGQSDYhfNDYcuEL4Z5Tu3/T3Xx9AoiDuDcv2+QLWWP+d3AM5KczQl6XEy8MSKxAtD+wghT4MbWSmKyW+udfQby3gsz8d166aFZwtD+ygswUqh5fkyJ+aMdGzp9YZ2jMB9bzP9ofmX/rW4j8aEAq75uln34CWZulpsjp3ofO7+Ayn8ccSJN5WwX6Anw3+amSGsjSOTB3sE4oFtG+WFr8lPiRy9HGEtt0hwPM1dxk+z5E/BRZzwTxmFY6yMpJzLJ1H3D9ocKqY0L5Sp2Au1oq0+1l+z7A/Yn5HmHPfejnIeInftihRF59giGNReAs2JLt+xDxk1p6z6xk3m//NEs/fqJxPqDtyrr+EI5fWp//k+37EPGTlJGwojZ+vm4kIyN/o35i3khZ6UpgicDM1TB598bRflVGPyZKxGto/DCPmFvWYlkrEM2j8XqvWq9EFbcCZc9Mq7DfE5bWNol2fpdiXdz8RlZpay0XVgbBEyWCu79EtDO9c7D645WumAHIjyjil7k+ZJjHIsWjHWb0SiV9O4tS15Uqs5ohot0OIe7JSw2YWQ5ZWl5jm7J98ENC6+L0V1Jk+UfAGZnVi3a7emamgrBGw16uQF0Yi0eO9sQwTeYH099IEdY7bykxlOg179AhLaGwvjIQ+WHOPlmF+KLaJz+WOF9Bp89NiJ/JNpXUKMWioC3J6JKApCiTZCLFj6QF1S4OXMoeearqveJIpRS5cUDyFBxx8IBt+lP60pm1TUU2BePYpJu8kiwGbAnT7Ga3lPQ6nkYDg9vwZMIgBf4d7FIxe2bjr2vL9OyP5vdnz8sRWcUb215m+UPbpDKTBf5/fXUFxeyP5vdnH2GA95DXZ2HD982NeMQkldPnwbPMopj5H+0PLCDX/XvgkFDzB8DajUV6MMmyhz9Sdv85MiMibyZhOR7v9hpEQhYHM10cpnnPovk1TnX9BXJzcF5L15TAegEsVzTvA45fJqV02ePHDFZDwjbRuHc/t6Mz80krsb5T9+OXyBI+foNujYA905mrNmT7PkT8xGQEzK0uZxLSmd/L5vWHR/s+RPzEIpwaV1otRPkGgc9q3qN5H3D8MgZvZ2krqxaktj7zE6do3hNOjl9qWjdEdcaNKuvYWYeRRfM+QPwizoHZfj2s+3TMOfyIaI5l1lAbJSqZL5rNWkvmvYC86pafWWAEZe3+0Uq13UZ9MyALNH3vTGThJ0rG+rjBi2zlfRCB32fJb0SHBfMiwaQGHK2nAW1ssdL3eb13nrXMi1CPdtBQy7G8mc6FdzIWUnZk8fXsdZ2waObN4pWXGb7REEQPrzzAgYS5qrEWzR2thXh9OEiIVaTwqPulF37rjd+ifpHNEfZ359eU+hsNUc7yA1UX7A1vGVu8I5o5JdZhvPZfH13IzM0Q5yBazTl8LpL7TKkQku6krDvoSLKMIBcpcwRRqGZx8FLeiOOVMkWeopAc4qykfJAHIjhDbLzD649kQvzEcm7XvTIwKr/48rI0daKmJtDE8svl5FTS7Xytu/jZL377v+vzD5ellP8fJMJMBgplbmRzdHJlYW0KZW5kb2JqCjExIDAgb2JqCjExNjM2CmVuZG9iagoyMiAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDIzMSA+PgpzdHJlYW0KeJxdUDGSxCAM63mFPnAzyDYG3pObrXL/b08mu80WRIoxkuWxEx3u+KFjeNcJ/LJ5Ohbx15wbXLB8WrgfvBp9HLYNiQxEqKjPJCTBHgdOtUjKZYBzwiUo16ulOkmQptpS0RBj6cLUPPrSWEPzOEIDFEp/+mGD6jBVbYvvuvH6w90G8016Rbvlvh58It2NeshIhSs2U8MRYTCJCeQ/exHvsq8pFJIVQ200h0uFFVO7MI+3eeSW9hebOjYQS6/2Pigdn4eZdCqwnYi9droGXOGpACbP2rH1Z9uqlm/NnoZPhqu9/gGm3VPoCmVuZHN0cmVhbQplbmRvYmoKMjMgMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCAyOTMgPj4Kc3RyZWFtCnicNVFLbkQhDNu/U/gClYhJ+Jxnqq6m99/WhukCxUog/jCyoSGJr+ioOTBHw3c8sRpmW/h9dh7wfqLlmb4fenhRLGT3lBnI2cChjt5wL1Q0vJ5OIRb6SFTvyHbr60ndNaoolDgqB7KWJjWEmEdRX5/az8ToaO3gmijt4DBPFRHTrBsRRI6NQdO4QfFfl1bm+npYF1Hqvgpsga12zAlxR23kQuiscFtK7Tlv+U9ISKTsqaxiUlv0RkHEqltHnZ1C3R2d8HRgeyubvPh9+RcopuQJbRp0PZa5vnV72goHrCNTlpaSHv3j3m655Vq5dH5qOrGDpu/qNE3siycYWXHeGf67edhcRa/IjI4e7WdZlydkSI7+t0lWzqOC61q8Mbyfnz+swW+5CmVuZHN0cmVhbQplbmRvYmoKMjQgMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCAyNjkgPj4Kc3RyZWFtCnicVVG7bUQxDOs9hRYIoL/teV6Q6rJ/G1IXBEhhULBpiaSqVVTS5cNCClgR8mkrb4pVy/fKrWIKThypI3FbQuVZUWCgzPnqeQafZfvdzKxx5Ki04RrsWxxk6EM4B7co3NA7xSOlVLzZuzGDHDVJPRCyJYt8p0rc+D6jlCKIkHN6qjS8+AVfgZycx6T4D2pK4TDR9WxqgkR2eK3s+FdBIhHnjWSzSoUH8DJyAmGNF8O8nRLwlKegvQeh9+6pnA7gyp0Z0Ild9L2Itq9EMOz6NW+IkjxLHK6B2POHVWzcXERr+HPl2mRO8+KKXoiSa8qZzhwlGAcA6+ycqEJOjhcz6vFZ9fO39Nf6+gHKnmOJCmVuZHN0cmVhbQplbmRvYmoKMjUgMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCAyOTQgPj4Kc3RyZWFtCnicPZFLbgQxCET3PkVdIJL5Gfs8jrKauf82BZ3JogXNp4Dn5RMTOvElhjUFuSa+Zaw5230PD2PFa9j6s7mxpZxw+IZpQh16Egd36Ep8BdS0JeU89g7R3d6eEEVMLGXUJk7UfLHH7IpqrbSg2jpsVK5yhzvMuWLCZ1KFNrKkGQlG1Bxhxl12W8rb41lOhAbssEJaSzacf24LzqzzFGf1HVGnz80LXeLjsbdwvP7BMMZMTXy3lu7oOoVRv+qNc9uS020F2xVhlp3eVTXPiMipaEu4SbI/2hbL056SkgdnzOopQMKM7QVx1hOR1NXNSLS4MaMFPx+b3VOea3MT4Wd8scYX9fRETxr6DOtHyFWOCZHxmQn/SK2b3qJ2OCQFHwx3/PwCiHhtNAplbmRzdHJlYW0KZW5kb2JqCjIwIDAgb2JqCjw8IC9CYXNlRm9udCAvRGVqYVZ1U2VyaWYtSXRhbGljIC9DaGFyUHJvY3MgMjEgMCBSCi9FbmNvZGluZyA8PCAvRGlmZmVyZW5jZXMgWyA5NyAvYSAvYiAvYyAvZCBdIC9UeXBlIC9FbmNvZGluZyA+PgovRmlyc3RDaGFyIDAgL0ZvbnRCQm94IFsgLTg0MCAtMzQ3IDE2NDUgMTExMCBdIC9Gb250RGVzY3JpcHRvciAxOSAwIFIKL0ZvbnRNYXRyaXggWyAwLjAwMSAwIDAgMC4wMDEgMCAwIF0gL0xhc3RDaGFyIDI1NSAvTmFtZSAvRGVqYVZ1U2VyaWYtSXRhbGljCi9TdWJ0eXBlIC9UeXBlMyAvVHlwZSAvRm9udCAvV2lkdGhzIDE4IDAgUiA+PgplbmRvYmoKMTkgMCBvYmoKPDwgL0FzY2VudCA5MjkgL0NhcEhlaWdodCAwIC9EZXNjZW50IC0yMzYgL0ZsYWdzIDk2Ci9Gb250QkJveCBbIC04NDAgLTM0NyAxNjQ1IDExMTAgXSAvRm9udE5hbWUgL0RlamFWdVNlcmlmLUl0YWxpYwovSXRhbGljQW5nbGUgMCAvTWF4V2lkdGggMTM0MiAvU3RlbVYgMCAvVHlwZSAvRm9udERlc2NyaXB0b3IgL1hIZWlnaHQgMCA+PgplbmRvYmoKMTggMCBvYmoKWyA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMAo2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDMxOCA0MDIgNDYwIDgzOCA2MzYKOTUwIDg5MCAyNzUgMzkwIDM5MCA1MDAgODM4IDMxOCAzMzggMzE4IDMzNyA2MzYgNjM2IDYzNiA2MzYgNjM2IDYzNiA2MzYgNjM2CjYzNiA2MzYgMzM3IDMzNyA4MzggODM4IDgzOCA1MzYgMTAwMCA3MjIgNzM1IDc2NSA4MDIgNzMwIDY5NCA3OTkgODcyIDM5NQo0MDEgNzQ3IDY2NCAxMDI0IDg3NSA4MjAgNjczIDgyMCA3NTMgNjg1IDY2NyA4NDMgNzIyIDEwMjggNzEyIDY2MCA2OTUgMzkwCjMzNyAzOTAgODM4IDUwMCA1MDAgNTk2IDY0MCA1NjAgNjQwIDU5MiAzNzAgNjQwIDY0NCAzMjAgMzEwIDYwNiAzMjAgOTQ4IDY0NAo2MDIgNjQwIDY0MCA0NzggNTEzIDQwMiA2NDQgNTY1IDg1NiA1NjQgNTY1IDUyNyA2MzYgMzM3IDYzNiA4MzggNjAwIDYzNiA2MDAKMzE4IDM3MCA1MTggMTAwMCA1MDAgNTAwIDUwMCAxMzQyIDY4NSA0MDAgMTEzNyA2MDAgNjk1IDYwMCA2MDAgMzE4IDMxOCA1MTEKNTExIDU5MCA1MDAgMTAwMCA1MDAgMTAwMCA1MTMgNDAwIDk4OSA2MDAgNTI3IDY2MCAzMTggNDAyIDYzNiA2MzYgNjM2IDYzNgozMzcgNTAwIDUwMCAxMDAwIDQ3NSA2MTIgODM4IDMzOCAxMDAwIDUwMCA1MDAgODM4IDQwMSA0MDEgNTAwIDY1MCA2MzYgMzE4CjUwMCA0MDEgNDcwIDYxMiA5NjkgOTY5IDk2OSA1MzYgNzIyIDcyMiA3MjIgNzIyIDcyMiA3MjIgMTAwMSA3NjUgNzMwIDczMAo3MzAgNzMwIDM5NSAzOTUgMzk1IDM5NSA4MDcgODc1IDgyMCA4MjAgODIwIDgyMCA4MjAgODM4IDgyMCA4NDMgODQzIDg0MyA4NDMKNjYwIDY3NiA2NjggNTk2IDU5NiA1OTYgNTk2IDU5NiA1OTYgOTQwIDU2MCA1OTIgNTkyIDU5MiA1OTIgMzIwIDMyMCAzMjAgMzIwCjYwMiA2NDQgNjAyIDYwMiA2MDIgNjAyIDYwMiA4MzggNjAyIDY0NCA2NDQgNjQ0IDY0NCA1NjUgNjQwIDU2NSBdCmVuZG9iagoyMSAwIG9iago8PCAvYSAyMiAwIFIgL2IgMjMgMCBSIC9jIDI0IDAgUiAvZCAyNSAwIFIgPj4KZW5kb2JqCjMwIDAgb2JqCjw8IC9GaWx0ZXIgL0ZsYXRlRGVjb2RlIC9MZW5ndGggMTY2ID4+CnN0cmVhbQp4nEWPuxUDIQwEc6rYEgT6QT32c8T1n1rLvbMTdkACDVMGBO61pBlyLLx7G5bwgaupTsJupoPg4shV/YGuilcLKZqJqPoIO6nhrBRZBNjhpueOr6wKHwkX8M3IBIcwX2cuaT8Gux21i3G23eYf7tYq/YD+u6k9ZNkPeSzEomblEU+5T/lryztvcdIovZSJHlL9EyvoHRP8VEopcYbwkLHb5wv6uT5LCmVuZHN0cmVhbQplbmRvYmoKMzEgMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCAzMTEgPj4Kc3RyZWFtCnicPVJJbsQwDLvnFfxAAe2235Oip5n/X0spnR4CErZkUlTyFAQp+FJH1ka641svPxtajvcwW47XZds+zNcwk4CxSvsmAvelJTALKJ/Ukw9m9U0z41eKo2xxLOG5SSIo4Ql/lAj35SpNPARx4BRZ1se7wGfHnv0h7+4rNosp/B6WRpczzocIsas/SE8kq5vgSaNBRqHWEMdXD2iTitFGI0fYT07qHBsq0s33VYWyzlAZx/+8JCYHdWBzxdl2z6tR6OFMlO05Mo332Gr2GHTm9LBoIc4dTqRS5CRBW7HomqKx+Q7rG5mo5TA9ixUF5Rc12sla7kmDtb0Lp5fdcR8Z8moSp3esphyG3UlU4iZax2B0n8zK/MzvYrUG29Nz4nwhlS6cOuv0ephDhGPWdAyfdd3Xzy9+enflCmVuZHN0cmVhbQplbmRvYmoKMzIgMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCAzODEgPj4Kc3RyZWFtCnicNVJBkgQhCLvPK/jAVgmC6Htma2/z/+smsefQRVohCeCay4atth+fVutYZ9ivv3It83PsIxTlljUtDmK0zRj2fuVwm3lsrryfb8X3K9qFYpYyYpynxvdl8R5iZaQOboiyjRk+lmq6SQaS3CbOR4QaUkyjCdzSlbJpk+VqAHTfRnCTywq3n4sO7lC/Zlh62CpWz31sbQjVtnWuGiNbuihQy4yIfGoCDsjiZ4hVETpoiWjAOj32VE0mvZAl8UdWqlOHEQ7qOYETZhDfGroli9yD9dsPas5E/lZnmM4elocLgHqAKeiytL67Yw6e8c5FaOIE04KdGpChk2S9zbP1NuiQkfu4r8W7cO+cH9OhzxG1uBhEDkC1HRJ3EsmOZ8qg75bhyNsChwZ0sLTCiJwCaCe5AqezDkNvhcfBoPYBluMp4eNGHHoLZ6Ry6yiQt941e2iZpRQRiZmRO5+aevZaWWJlvDJC0K3pslGjHmPZR1YzXda/+3i//v4B2j+hEAplbmRzdHJlYW0KZW5kb2JqCjMzIDAgb2JqCjw8IC9GaWx0ZXIgL0ZsYXRlRGVjb2RlIC9MZW5ndGggMTA1ID4+CnN0cmVhbQp4nEWOuxHAMAhDe6ZgBJufk31yqfD+bYD47AbeAUIyNmzIPYpehkMInw4sN5IMnEXGig69tZr53jqoSQgnEFN0r660Tjb0O/XhsYHkStBWhg4S3w6t3xHn0C/N7aEyyAgbMsP7AapsKLAKZW5kc3RyZWFtCmVuZG9iagozNCAwIG9iago8PCAvQkJveCBbIC03NzAgLTM0NyAyMTA2IDExMTAgXSAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDM3Ci9TdWJ0eXBlIC9Gb3JtIC9UeXBlIC9YT2JqZWN0ID4+CnN0cmVhbQp4nOMyNDBTMDY1VsjlMjc2ArNywCwjcxMgCySLYEFk0wABBQoICmVuZHN0cmVhbQplbmRvYmoKMzUgMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCA4MyA+PgpzdHJlYW0KeJxNzbENwDAIBMCeKRgBY/zE+0Sp7P3bAIqSNHBC+gcdLNxUY9o0dlM+GzXLw649lBcp5geMI5Shgf4I6qEuUhUh+E8Vzf4Xkrn6sui6AayDGa0KZW5kc3RyZWFtCmVuZG9iagozNiAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDEyNCA+PgpzdHJlYW0KeJwtTskNwzAM+2cKLhBAlO04mqdFf93/W1IpYIAGL3HwRqAmTg5kTpAX3jzELOJrvAqMwG0tURuvgzaG+Bkd4KpGKXs/TGU7MtYTSW5X+IQKDeoXrc/QZal6di+3KH2a2b3L9UYJOtiMYjZoUPu1T3GNHYn6V39+aDooVwplbmRzdHJlYW0KZW5kb2JqCjM3IDAgb2JqCjw8IC9GaWx0ZXIgL0ZsYXRlRGVjb2RlIC9MZW5ndGggMzMwID4+CnN0cmVhbQp4nDVSy20lMQy7uwo1sID1t+uZRU5J/9eQmhdgAHH0pSiXl2ypln/qku3SYfJfl1uLh/wshw8g9pHcEu5yQp4V2aJ6JHqLVo0134wQXRdmeOiUeCcj6BH7CluGlXAG7bPs7EEWMRlmG1mNiF7kwauYardf66wh0lZhhpqiRuVMs0hJ/B8l8c8iyC9OV6ykl9NSTFMCvS3IdkrRL5Dn27ARiv2MBXfdgxiNNAzYo8mzEn9eMeL5zrGvEkSKvgnhQD0Z9NHuClS4d0R387EkroMUmys+CNeccC7w5ZEMy9Qr67MAyAZSJ6Bi6/JXspbeSMYyvKYjSvssv+99A/I2OkYc2DlNF9Aejg1CCW8PKaJE3fcKHOmDkF0QMMql+CrQs4pUA0eok8JJdSEgHgEtlvt4LFDLJwLxy+xzyIS0PFDuLX+HetbXLwl+fOsKZW5kc3RyZWFtCmVuZG9iagozOCAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDE3MSA+PgpzdHJlYW0KeJxNkEsOAzEIQ/c5hS9QKUDI5zxTdTW9/7Z2Ru10xYsJlqFVR4UvPCwQq6HPiqcVqxOtD7wLe4JTkLYI6t2kAdL6p6sbHLvpMlH3JosvrYAzSm9wM6TjKM7RxmyRCMo5VShP228ZkSpTJeXg774QnliUvcNcLtpJxBDUR0OMKdvgFEf4IRwPp9/YN/Csux47lsi6scKUxaQbDShz9+m7aI3jd7KzvD5QfEA6CmVuZHN0cmVhbQplbmRvYmoKMzkgMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCAzNDYgPj4Kc3RyZWFtCnicPVLLrRwxDLtPFWzgAdbXdj0bvNOm/2tI7SKHgWjJpkRqOhoLu/FjgWrHTscfe+5G34O/j0Vhm8O2YXvAV2OH4fV4MhMHvnNexaqJryfIJ5RBPm/kdrI1K0Wm7kKx0u4Tq48qQp4oO8izkXchS5XkVOnMsnuug9iBuFMJonPJfxG9IfYITVBZcGqQIi+faDyzIuSXnS+22pBUajJ5m2w+Tvj9OEKVnGEyvvBzYSd5ZN7yoGFy5sg/2vR6GI2kb7pm/1FOP6uFS7h5e4mXPmbD+fGGUw8DrcsBIQco2VpDajo+1YsiU37jOCrkRRGZM3UaX7sqwVGjqIn6gj1d50/vOIPeg9IHjctCYXdQKEMdMZuQvNRu6LV8L/aZ2P7dRC9m3NCxZz/da/6FRNNVTdE3ZyuKcjY+GbL2CerhzWEzzta8b9VoW4zc4Eyulc7g3//z/fz+A6Zmg/YKZW5kc3RyZWFtCmVuZG9iago0MCAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDIyMiA+PgpzdHJlYW0KeJxFUblxBDEMy1UFShB/qp7zODr3nxrUes7BLjAiBQJUWmIjm7+wRrniS5ZoIyLws8oueQ/JHiK7UNsgbC0pSPGaFl5LxVBWUH+EtPXia1k8Jy7Ta/BUqs2d2IkMDufE3A+G3QqZZ8Cpb71hRG0ZtdpQ+jFWldYtheisSBXY+l7Oxg+RGjbx/tlgfiCMqH0o62RGA6bKkfyS/NDybg5wcbgfuNLY0YuP3cs6GZHR1Gl5gt3wOQtmAHbk8RtikAszv0wOw3NZMkuOM0G8kHwaMaptRvh7kNf6/gVtdFHbCmVuZHN0cmVhbQplbmRvYmoKNDEgMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCAyMTEgPj4Kc3RyZWFtCnicNVDJccQwDPurCjSQGVG8pHqc2d/2/w1BOS/BJi4yNDARgR9ReE6kLfzKUNlQw3doNLDpCIHphEjgGeYGKb5FYrn2q2GcFLIsSTHcszUhixOaVBY94xgYwvcZ6/2zyC3GmvFqZEu7SJx25XtziJhMBptQc7u1i2Dd6u8qT+/ENb9FuEiSURBd2BTuDfHFcywzdFMKC9hW1NRLQHZYd6uvnBu0490YkD3Rk43MTzN86qtxy3bhrWnK96YQMZYMtqBm31MftqQnS/+v8YzPH2qKUxoKZW5kc3RyZWFtCmVuZG9iagoyOCAwIG9iago8PCAvQmFzZUZvbnQgL0RlamFWdVNlcmlmIC9DaGFyUHJvY3MgMjkgMCBSCi9FbmNvZGluZyA8PAovRGlmZmVyZW5jZXMgWyA0NiAvcGVyaW9kIDQ4IC96ZXJvIC9vbmUgL3R3byAvdGhyZWUgL2ZvdXIgNTQgL3NpeCA1NiAvZWlnaHQgNjggL0QgOTcgL2EKMTE2IC90IF0KL1R5cGUgL0VuY29kaW5nID4+Ci9GaXJzdENoYXIgMCAvRm9udEJCb3ggWyAtNzcwIC0zNDcgMjEwNiAxMTEwIF0gL0ZvbnREZXNjcmlwdG9yIDI3IDAgUgovRm9udE1hdHJpeCBbIDAuMDAxIDAgMCAwLjAwMSAwIDAgXSAvTGFzdENoYXIgMjU1IC9OYW1lIC9EZWphVnVTZXJpZgovU3VidHlwZSAvVHlwZTMgL1R5cGUgL0ZvbnQgL1dpZHRocyAyNiAwIFIgPj4KZW5kb2JqCjI3IDAgb2JqCjw8IC9Bc2NlbnQgOTI5IC9DYXBIZWlnaHQgMCAvRGVzY2VudCAtMjM2IC9GbGFncyAzMgovRm9udEJCb3ggWyAtNzcwIC0zNDcgMjEwNiAxMTEwIF0gL0ZvbnROYW1lIC9EZWphVnVTZXJpZiAvSXRhbGljQW5nbGUgMAovTWF4V2lkdGggMTM0MiAvU3RlbVYgMCAvVHlwZSAvRm9udERlc2NyaXB0b3IgL1hIZWlnaHQgMCA+PgplbmRvYmoKMjYgMCBvYmoKWyA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMAo2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDMxOCA0MDIgNDYwIDgzOCA2MzYKOTUwIDg5MCAyNzUgMzkwIDM5MCA1MDAgODM4IDMxOCAzMzggMzE4IDMzNyA2MzYgNjM2IDYzNiA2MzYgNjM2IDYzNiA2MzYgNjM2CjYzNiA2MzYgMzM3IDMzNyA4MzggODM4IDgzOCA1MzYgMTAwMCA3MjIgNzM1IDc2NSA4MDIgNzMwIDY5NCA3OTkgODcyIDM5NQo0MDEgNzQ3IDY2NCAxMDI0IDg3NSA4MjAgNjczIDgyMCA3NTMgNjg1IDY2NyA4NDMgNzIyIDEwMjggNzEyIDY2MCA2OTUgMzkwCjMzNyAzOTAgODM4IDUwMCA1MDAgNTk2IDY0MCA1NjAgNjQwIDU5MiAzNzAgNjQwIDY0NCAzMjAgMzEwIDYwNiAzMjAgOTQ4IDY0NAo2MDIgNjQwIDY0MCA0NzggNTEzIDQwMiA2NDQgNTY1IDg1NiA1NjQgNTY1IDUyNyA2MzYgMzM3IDYzNiA4MzggNjAwIDYzNiA2MDAKMzE4IDM3MCA1MTggMTAwMCA1MDAgNTAwIDUwMCAxMzQyIDY4NSA0MDAgMTEzNyA2MDAgNjk1IDYwMCA2MDAgMzE4IDMxOCA1MTEKNTExIDU5MCA1MDAgMTAwMCA1MDAgMTAwMCA1MTMgNDAwIDk4OSA2MDAgNTI3IDY2MCAzMTggNDAyIDYzNiA2MzYgNjM2IDYzNgozMzcgNTAwIDUwMCAxMDAwIDQ3NSA2MTIgODM4IDMzOCAxMDAwIDUwMCA1MDAgODM4IDQwMSA0MDEgNTAwIDY1MCA2MzYgMzE4CjUwMCA0MDEgNDcwIDYxMiA5NjkgOTY5IDk2OSA1MzYgNzIyIDcyMiA3MjIgNzIyIDcyMiA3MjIgMTAwMSA3NjUgNzMwIDczMAo3MzAgNzMwIDM5NSAzOTUgMzk1IDM5NSA4MDcgODc1IDgyMCA4MjAgODIwIDgyMCA4MjAgODM4IDgyMCA4NDMgODQzIDg0MyA4NDMKNjYwIDY3NiA2NjggNTk2IDU5NiA1OTYgNTk2IDU5NiA1OTYgOTQwIDU2MCA1OTIgNTkyIDU5MiA1OTIgMzIwIDMyMCAzMjAgMzIwCjYwMiA2NDQgNjAyIDYwMiA2MDIgNjAyIDYwMiA4MzggNjAyIDY0NCA2NDQgNjQ0IDY0NCA1NjUgNjQwIDU2NSBdCmVuZG9iagoyOSAwIG9iago8PCAvRCAzMCAwIFIgL2EgMzEgMCBSIC9laWdodCAzMiAwIFIgL2ZvdXIgMzMgMCBSIC9vbmUgMzUgMCBSCi9wZXJpb2QgMzYgMCBSIC9zaXggMzcgMCBSIC90IDM4IDAgUiAvdGhyZWUgMzkgMCBSIC90d28gNDAgMCBSIC96ZXJvIDQxIDAgUgo+PgplbmRvYmoKMyAwIG9iago8PCAvRjEgMjggMCBSIC9GMiAyMCAwIFIgPj4KZW5kb2JqCjQgMCBvYmoKPDwgL0ExIDw8IC9DQSAwIC9UeXBlIC9FeHRHU3RhdGUgL2NhIDEgPj4KL0EyIDw8IC9DQSAxIC9UeXBlIC9FeHRHU3RhdGUgL2NhIDEgPj4gPj4KZW5kb2JqCjUgMCBvYmoKPDwgPj4KZW5kb2JqCjYgMCBvYmoKPDwgPj4KZW5kb2JqCjcgMCBvYmoKPDwgL0YxLURlamFWdVNlcmlmLW1pbnVzIDM0IDAgUiAvTTAgMTIgMCBSIC9NMSAxMyAwIFIgL00yIDE0IDAgUgovTTMgMTUgMCBSIC9NNCAxNiAwIFIgL001IDE3IDAgUiA+PgplbmRvYmoKMTIgMCBvYmoKPDwgL0JCb3ggWyAtOCAtOCA4IDggXSAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDEzMSAvU3VidHlwZSAvRm9ybQovVHlwZSAvWE9iamVjdCA+PgpzdHJlYW0KeJxtkEEOhCAMRfc9RS/wSUtFZevSa7iZTOL9twNxQEzdNNC+PH5R/pLwTqXA+CQJS06z5HrTkNK6TIwY5tWyKMegUS3WznU4qM/QcGN0i7EUptTW6Hijm+k23pM/+rBZIUY/HA6vhHsWQyZcKTEGh98LL9vD/xGeXtTAH6KNfmNaQ/0KZW5kc3RyZWFtCmVuZG9iagoxMyAwIG9iago8PCAvQkJveCBbIC04IC04IDggOCBdIC9GaWx0ZXIgL0ZsYXRlRGVjb2RlIC9MZW5ndGggMTMxIC9TdWJ0eXBlIC9Gb3JtCi9UeXBlIC9YT2JqZWN0ID4+CnN0cmVhbQp4nG2QQQ6EIAxF9z1FL/BJS0Vl69JruJlM4v23A3FATN000L48flH+kvBOpcD4JAlLTrPketOQ0rpMjBjm1bIox6BRLdbOdTioz9BwY3SLsRSm1NboeKOb6Tbekz/6sFkhRj8cDq+EexZDJlwpMQaH3wsv28P/EZ5e1MAfoo1+Y1pD/QplbmRzdHJlYW0KZW5kb2JqCjE0IDAgb2JqCjw8IC9CQm94IFsgLTggLTggOCA4IF0gL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCAxMzEgL1N1YnR5cGUgL0Zvcm0KL1R5cGUgL1hPYmplY3QgPj4Kc3RyZWFtCnicbZBBDoQgDEX3PUUv8ElLRWXr0mu4mUzi/bcDcUBM3TTQvjx+Uf6S8E6lwPgkCUtOs+R605DSukyMGObVsijHoFEt1s51OKjP0HBjdIuxFKbU1uh4o5vpNt6TP/qwWSFGPxwOr4R7FkMmXCkxBoffCy/bw/8Rnl7UwB+ijX5jWkP9CmVuZHN0cmVhbQplbmRvYmoKMTUgMCBvYmoKPDwgL0JCb3ggWyAtOCAtOCA4IDggXSAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDEzMSAvU3VidHlwZSAvRm9ybQovVHlwZSAvWE9iamVjdCA+PgpzdHJlYW0KeJxtkEEOhCAMRfc9RS/wSUtFZevSa7iZTOL9twNxQEzdNNC+PH5R/pLwTqXA+CQJS06z5HrTkNK6TIwY5tWyKMegUS3WznU4qM/QcGN0i7EUptTW6Hijm+k23pM/+rBZIUY/HA6vhHsWQyZcKTEGh98LL9vD/xGeXtTAH6KNfmNaQ/0KZW5kc3RyZWFtCmVuZG9iagoxNiAwIG9iago8PCAvQkJveCBbIC04IC04IDggOCBdIC9GaWx0ZXIgL0ZsYXRlRGVjb2RlIC9MZW5ndGggMTMxIC9TdWJ0eXBlIC9Gb3JtCi9UeXBlIC9YT2JqZWN0ID4+CnN0cmVhbQp4nG2QQQ6EIAxF9z1FL/BJS0Vl69JruJlM4v23A3FATN000L48flH+kvBOpcD4JAlLTrPketOQ0rpMjBjm1bIox6BRLdbOdTioz9BwY3SLsRSm1NboeKOb6Tbekz/6sFkhRj8cDq+EexZDJlwpMQaH3wsv28P/EZ5e1MAfoo1+Y1pD/QplbmRzdHJlYW0KZW5kb2JqCjE3IDAgb2JqCjw8IC9CQm94IFsgLTggLTggOCA4IF0gL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCAxMzEgL1N1YnR5cGUgL0Zvcm0KL1R5cGUgL1hPYmplY3QgPj4Kc3RyZWFtCnicbZBBDoQgDEX3PUUv8ElLRWXr0mu4mUzi/bcDcUBM3TTQvjx+Uf6S8E6lwPgkCUtOs+R605DSukyMGObVsijHoFEt1s51OKjP0HBjdIuxFKbU1uh4o5vpNt6TP/qwWSFGPxwOr4R7FkMmXCkxBoffCy/bw/8Rnl7UwB+ijX5jWkP9CmVuZHN0cmVhbQplbmRvYmoKMiAwIG9iago8PCAvQ291bnQgMSAvS2lkcyBbIDEwIDAgUiBdIC9UeXBlIC9QYWdlcyA+PgplbmRvYmoKNDIgMCBvYmoKPDwgL0NyZWF0aW9uRGF0ZSAoRDoyMDIxMTExNjExMjUyNyswMicwMCcpCi9DcmVhdG9yIChNYXRwbG90bGliIHYzLjMuNCwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZykKL1Byb2R1Y2VyIChNYXRwbG90bGliIHBkZiBiYWNrZW5kIHYzLjMuNCkgPj4KZW5kb2JqCnhyZWYKMCA0MwowMDAwMDAwMDAwIDY1NTM1IGYgCjAwMDAwMDAwMTYgMDAwMDAgbiAKMDAwMDAyMjE5MSAwMDAwMCBuIAowMDAwMDIwMzY3IDAwMDAwIG4gCjAwMDAwMjA0MTAgMDAwMDAgbiAKMDAwMDAyMDUwOSAwMDAwMCBuIAowMDAwMDIwNTMwIDAwMDAwIG4gCjAwMDAwMjA1NTEgMDAwMDAgbiAKMDAwMDAwMDA2NSAwMDAwMCBuIAowMDAwMDAwNDAxIDAwMDAwIG4gCjAwMDAwMDAyMDggMDAwMDAgbiAKMDAwMDAxMjExMiAwMDAwMCBuIAowMDAwMDIwNjY3IDAwMDAwIG4gCjAwMDAwMjA5MjEgMDAwMDAgbiAKMDAwMDAyMTE3NSAwMDAwMCBuIAowMDAwMDIxNDI5IDAwMDAwIG4gCjAwMDAwMjE2ODMgMDAwMDAgbiAKMDAwMDAyMTkzNyAwMDAwMCBuIAowMDAwMDE0MDQzIDAwMDAwIG4gCjAwMDAwMTM4MzYgMDAwMDAgbiAKMDAwMDAxMzUxMyAwMDAwMCBuIAowMDAwMDE1MDk4IDAwMDAwIG4gCjAwMDAwMTIxMzQgMDAwMDAgbiAKMDAwMDAxMjQzOCAwMDAwMCBuIAowMDAwMDEyODA0IDAwMDAwIG4gCjAwMDAwMTMxNDYgMDAwMDAgbiAKMDAwMDAxOTE1NSAwMDAwMCBuIAowMDAwMDE4OTU1IDAwMDAwIG4gCjAwMDAwMTg1ODEgMDAwMDAgbiAKMDAwMDAyMDIxMCAwMDAwMCBuIAowMDAwMDE1MTYwIDAwMDAwIG4gCjAwMDAwMTUzOTkgMDAwMDAgbiAKMDAwMDAxNTc4MyAwMDAwMCBuIAowMDAwMDE2MjM3IDAwMDAwIG4gCjAwMDAwMTY0MTUgMDAwMDAgbiAKMDAwMDAxNjU4NCAwMDAwMCBuIAowMDAwMDE2NzM5IDAwMDAwIG4gCjAwMDAwMTY5MzYgMDAwMDAgbiAKMDAwMDAxNzMzOSAwMDAwMCBuIAowMDAwMDE3NTgzIDAwMDAwIG4gCjAwMDAwMTgwMDIgMDAwMDAgbiAKMDAwMDAxODI5NyAwMDAwMCBuIAowMDAwMDIyMjUxIDAwMDAwIG4gCnRyYWlsZXIKPDwgL0luZm8gNDIgMCBSIC9Sb290IDEgMCBSIC9TaXplIDQzID4+CnN0YXJ0eHJlZgoyMjQwOAolJUVPRgo=\n",
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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"data1 = normal(size=(100,1))\n",
"data2 = exponential(size=(100,1))\n",
"data3 = data1+data2 \n",
"data4 = data1-normal(size=(100,1))\n",
"data = hstack((data1,data2,data3,data4))\n",
"\n",
"fig, *_ = nbi.corner_plot(data,names='auto',fig_kw={'figsize':(8,8)})\n",
"fig.tight_layout()\n",
"fig.suptitle('Data');"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"For the four-dimensional sample we see \n",
"\n",
"- On the diagonal, the distribution in each dimension \n",
"- In the off-diagonal elements, the correlation between all dimensions. \n",
"\n",
"While representation does not show the \"full\" distribution, it does illustrate important features of the data. For example, it is clear from the plot above that variables $a$ and $c$ are correlated. However, for many variables the rendering of the plot can take some time. \n",
"\n",
"We can customize `corner_plot` in many ways. For example, we can specify a different drawing method for the diagonal and off-diagonal elements. In general \n",
"\n",
"- `diag=`_f_ uses the _callable_ _f_ (typically a function) to draw on the diagonal. The function will get the sample of a single variable and must plot in the current `Axes`. It will also receive optional keyword arguments specified by the keyword `dia_kw`. \n",
"- `off`=_f_ uses the _callable_ _f_ (typically a function) to draw in the off-diagonal. The function will get the sample of two variables as well as keyword arguments specified by `off_kw`. The callable must draw in the current `Axes` object. \n",
"\n",
"Many functions in _Matplotlib_ fits these requirements. For example, one can use `hist2d` for `off`. However, if needed, one can define a function which illustrates the data best possible. "
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:25:27.995593Z",
"iopub.status.busy": "2021-11-16T10:25:27.994336Z",
"iopub.status.idle": "2021-11-16T10:25:34.351769Z",
"shell.execute_reply": "2021-11-16T10:25:34.352857Z"
},
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"data": {
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\n",
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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"def scathist(x,y,**kwargs):\n",
" from numpy import histogram2d, meshgrid\n",
" from matplotlib.pyplot import scatter\n",
" \n",
" nbins = kwargs.get('nbins',10)\n",
" h, xb, yb = histogram2d(x,y,bins=nbins,density=True)\n",
" xc = (xb[1:]+xb[:-1])/2\n",
" yc = (yb[1:]+yb[:-1])/2\n",
" xx, yy = meshgrid(xc,yc)\n",
" scatter(xx,yy,1000/nbins*h,h)\n",
" \n",
"fig, *_ = nbi.corner_plot(data,names='auto',off=scathist,off_kw={'nbins':5},\n",
" dia_kw={'fmt':'o'},fig_kw=dict(figsize=(8,8)))\n",
"fig.tight_layout()\n",
"fig.suptitle('Custom off-diagonal plottig');"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"It is also possible to plot several data sets together. Each data set can be customized by a `dict` following the data. "
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:25:34.364674Z",
"iopub.status.busy": "2021-11-16T10:25:34.363359Z",
"iopub.status.idle": "2021-11-16T10:25:40.636080Z",
"shell.execute_reply": "2021-11-16T10:25:40.635048Z"
}
},
"outputs": [
{
"data": {
"application/pdf": 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\n",
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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"from matplotlib.pyplot import hist2d, scatter\n",
"\n",
"data1 = normal(size=(100,3))\n",
"data2 = normal(.5,.5,size=(100,3))\n",
"fig, *_ = nbi.corner_plot(data1,{'off':hist2d,'label':'A','off_kw':{'cmap':'Greys'}},\n",
" data2,'B',{'dia_kw':{'bins':3}},legend=True,names='Alpha',\n",
" fig_kw=dict(figsize=(8,8)))\n",
"fig.tight_layout()\n",
"fig.suptitle('Two datasets');"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Rounding results "
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"## `print_result`\n",
"\n",
"Generally, we do not want to give too many digits on the uncertainty of a result. Typically we want _one_ significant digit on the least uncertainty and the result given to the same precision (least power of 10 rounded to). \n",
"\n",
"Suppose we get the value \n",
"\n",
" 12.3456\n",
" \n",
"with the uncertainties \n",
"\n",
" 1.23456 0.123456 0.0123456\n",
" \n",
"from our calculations. To print the result correctly we can do "
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:25:40.646551Z",
"iopub.status.busy": "2021-11-16T10:25:40.645358Z",
"iopub.status.idle": "2021-11-16T10:25:40.656669Z",
"shell.execute_reply": "2021-11-16T10:25:40.655525Z"
},
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" 12.35 +/- 1.23 +/- 0.12 +/- 0.01\n"
]
}
],
"source": [
"value = 12.3456\n",
"uncer = [1.23456, 0.123456, 0.012345]\n",
"nbi.print_result(value,uncer)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"## `format_result` \n",
"\n",
"If we one to _pretty-print_ using $\\mathrm{\\LaTeX}$ and give the measured quantity a name we can do "
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:25:40.669864Z",
"iopub.status.busy": "2021-11-16T10:25:40.664386Z",
"iopub.status.idle": "2021-11-16T10:25:40.678101Z",
"shell.execute_reply": "2021-11-16T10:25:40.678972Z"
}
},
"outputs": [
{
"data": {
"text/latex": [
"$x=12.35\\pm1.23\\pm0.12\\pm0.01$"
],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"display(Latex('$'+nbi.format_result(value,uncer,name='x',latex=True)+'$'))"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"To avoid extracting a common exponent we can add `expo=False`. We can also set a unit by passing `unit=`, as well as give labels to each uncertainty "
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:25:40.690087Z",
"iopub.status.busy": "2021-11-16T10:25:40.683639Z",
"iopub.status.idle": "2021-11-16T10:25:40.699595Z",
"shell.execute_reply": "2021-11-16T10:25:40.698711Z"
}
},
"outputs": [
{
"data": {
"text/latex": [
"$$x=\\left(12.35\\pm1.23\\mathrm{(stat)}\\pm0.12\\mathrm{(sys)}\\pm0.01\\mathrm{(theory)}\\right)\\,\\mathrm{u}$$"
],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"display(Latex('$$'+nbi.format_result(value,uncer,name='x',latex=True,expo=False,unit='u',\n",
" dnames=['stat','sys','theory'])+'$$'))"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"More fine-grained control can be done with `nbi.round_result` and `nbi.round`. "
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Mean, variance, and covariance on the fly "
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"## `welford_init`, `west_init`, `welford_update`, `west_update` \n",
"To calculate the mean \n",
"\n",
"$$\\overline{x} = \\frac{1}{N}\\sum_{i=1}^{N} x_i\\quad,$$ \n",
"\n",
"and variance \n",
"\n",
"$$s^2_x = \\frac{1}{N-1}\\sum_{i=1}^{N} (x_i - \\overline{x})^2\\quad,$$ \n",
"\n",
"or covariance \n",
"\n",
"$$c_{x,y} = \\frac{1}{N-1}\\sum_{i=1}^{N} (x_i - \\overline{x})(y_i - \\overline{y})\\quad,$$ \n",
"\n",
"robustly (i.e., with minimal rounding errors due to machine precision) and on-the-fly (i.e., using a _single_ pass over data), we can use one of the `welford` or `west` families of functions \n",
"\n",
"- `welford_init` or `west_init` to initialize an appropriate data structure, and one of \n",
"- `welford_update` or `west_update` to update the mean and (co)variance, or \n",
"\n",
"The `welford...` functions must be used for _unweighted_ samples, while the `west...` functions are used for _weighted_ samples. Here, we will illustrate the use of both families using the `welford` family. "
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"First, we initialise our data structure. We will have 3 variables $x,y,z$ and each observation in our sample will consist of such a 3-tuple. We will have two data structures - one that has the means and variances, and one with the means and covariances. "
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:25:40.707370Z",
"iopub.status.busy": "2021-11-16T10:25:40.704207Z",
"iopub.status.idle": "2021-11-16T10:25:40.711908Z",
"shell.execute_reply": "2021-11-16T10:25:40.712712Z"
}
},
"outputs": [],
"source": [
"from numpy.random import normal, uniform, exponential\n",
"from numpy import array \n",
"\n",
"mean_var = nbi.welford_init(3,False)\n",
"mean_covar = nbi.welford_init(3,True)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"Now let us fill in random observations "
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:25:40.723741Z",
"iopub.status.busy": "2021-11-16T10:25:40.722392Z",
"iopub.status.idle": "2021-11-16T10:25:40.737415Z",
"shell.execute_reply": "2021-11-16T10:25:40.738629Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Means: [-0.10274929 0.49175404 1.02384517]\n",
"Variances: [0.77153254 0.08887651 1.2050375 ]\n",
"Means: [-0.10274929 0.49175404 1.02384517]\n",
"Covariance:\n",
"[[ 0.77153254 -0.01793416 0.10483751]\n",
" [-0.01793416 0.08887651 0.00944052]\n",
" [ 0.10483751 0.00944052 1.2050375 ]]\n"
]
}
],
"source": [
"n = 100\n",
"for x,y,z in zip(normal(size=n),uniform(size=n),exponential(size=n)):\n",
" obs = array((x,y,z))\n",
" mean_var = nbi.welford_update(obs,*mean_var, ddof=1)\n",
" mean_covar = nbi.welford_update(obs,*mean_covar,ddof=1)\n",
" \n",
"print(f'Means: {mean_var[0]}')\n",
"print(f'Variances: {mean_var[1]}')\n",
"print(f'Means: {mean_covar[0]}')\n",
"print(f'Covariance:\\n{mean_covar[1]}')"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"The _NumPy_ functions [`numpy.mean`](https://docs.scipy.org/doc/numpy/reference/generated/numpy.mean.html) and [`numpy.var`](https://docs.scipy.org/doc/numpy/reference/generated/numpy.var.html) similarly calculates the mean and variance of sample but requires that the _whole_ sample is available, while the above methods allow for incremental updates. The two _NumPy_ function will be faster for a _whole_ sample, but does not provide more accurate calculations. "
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"## `Welford`, `West` \n",
"\n",
"The module `nbi_stat` also provides Object Oriented statistical calculations through the classes `Welford` and `West` "
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:25:40.747643Z",
"iopub.status.busy": "2021-11-16T10:25:40.746602Z",
"iopub.status.idle": "2021-11-16T10:25:40.765834Z",
"shell.execute_reply": "2021-11-16T10:25:40.766786Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[[-0.21374692 0.11019054 1.21419551]\n",
" [ 0.50323772 0.02671057 0.07134547]\n",
" [ 1.02074505 0.10955489 1.20022749]] 100\n",
"[[-0.21374692 0.11019054 1.21419551 -0.0114984 -0.00248777]\n",
" [ 0.50323772 0.02671057 -0.0114984 0.07134547 -0.02755563]\n",
" [ 1.02074505 0.10955489 -0.00248777 -0.02755563 1.20022749]]\n"
]
}
],
"source": [
"mean_var = nbi.Welford(3)\n",
"mean_covar = nbi.Welford(3,True)\n",
"\n",
"n = (100,1)\n",
"data = hstack((normal (size=n),\n",
" uniform (size=n),\n",
" exponential(size=n)))\n",
"for obs in data:\n",
" mean_var.update(obs)\n",
"\n",
"mean_covar += data\n",
"print(mean_var,mean_var.n)\n",
"print(mean_covar)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Histogramming "
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"The _NumPy_ function [`histogram`](https://docs.scipy.org/doc/numpy/reference/generated/numpy.histogram.html) is a bit cumbersome in that it \n",
"\n",
"- Returns the bin count or bin density, but not the uncertainties, leaving that task to the user. \n",
" while it is not difficult to do, it is something that is easy to mess up \n",
"- Returns the bin edges rather than the bin centres and possible widths. Again, it is not difficult to \n",
" calculate the bin centres and widths, but it is easy to mess it up. \n",
"- While _NumPy_'s `histogram` allows for weight, it _only_ allows for _frequency_ weights (for more, see [Statistics Overview](https://cholmcc.gitlab.io/nbi-python/statistics/#Statistik)), which makes it less attractive for cases where the weights may represent efficiencies or the like. "
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"## `histogram` \n",
"\n",
"For these reasons `nbi_stat` define the drop-in function `histogram`. This function differs from the _NumPy_'s version by \n",
"\n",
"- The histogram bin values are _always_ normalized to the bin width so that the bin integral (area) \n",
" is proportional to the probability. \n",
"- The function returns \n",
" - bin values $h_i$\n",
" - bin centres $b_i$ \n",
" - bin widths $w_i$\n",
" - bin uncertainties $e_i$ \n",
" (_NumPy_'s `histogram` returns bin values and bin edges only)\n",
"- Allows for non-frequency weights (and calculates the uncertainties) \n",
"- The histogram values are _not_ normalised to the number of observations $N$, meaning that the total integral\n",
"\n",
" $$N_{\\mathrm{acc}} = \\sum_{i=1}^{n} h_i w_i\\quad,$$\n",
" \n",
" is equal to the number of observations within the range of the histogram - that is, the histogram\n",
" represents a _number density_. If one want to normalise to this histogram one should pass the option\n",
" `normalize=True` thus turning the histogram into a _probability density_. "
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"We will illustrate this. First, a simple histogram with no weights and equidistant bins "
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:25:40.777831Z",
"iopub.status.busy": "2021-11-16T10:25:40.776627Z",
"iopub.status.idle": "2021-11-16T10:25:42.248133Z",
"shell.execute_reply": "2021-11-16T10:25:42.249557Z"
}
},
"outputs": [
{
"data": {
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\n",
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"from matplotlib.pyplot import errorbar \n",
"\n",
"data = normal(size=1000)\n",
"h, b, w, e = nbi.histogram(data,30)\n",
"\n",
"errorbar(b,h,e,w/2,fmt='o')\n",
"\n",
"xlabel('$x$')\n",
"ylabel('$\\mathrm{d}N/\\mathrm{d}x$')\n",
"title('Number density');"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"We can calculate the integral and uncertainty easily "
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:25:42.258945Z",
"iopub.status.busy": "2021-11-16T10:25:42.258021Z",
"iopub.status.idle": "2021-11-16T10:25:42.264617Z",
"shell.execute_reply": "2021-11-16T10:25:42.265986Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" 1000 +/- 30\n"
]
}
],
"source": [
"from numpy import sqrt \n",
"\n",
"i = (h*w).sum()\n",
"ie = sqrt(((e*w)**2).sum())\n",
"\n",
"nbi.print_result(i, [ie])"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"Let us do the same, but this time normalising to the integral "
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:25:42.275259Z",
"iopub.status.busy": "2021-11-16T10:25:42.273881Z",
"iopub.status.idle": "2021-11-16T10:25:43.748326Z",
"shell.execute_reply": "2021-11-16T10:25:43.749200Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" 1.00 +/- 0.03\n"
]
},
{
"data": {
"application/pdf": 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\n",
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"h, b, w, e = nbi.histogram(data,30,normalize=True)\n",
"\n",
"errorbar(b,h,e,w/2,fmt='o')\n",
"\n",
"xlabel('$x$')\n",
"ylabel('$1/N\\,\\mathrm{d}N/\\mathrm{d}x$')\n",
"title('Probability density')\n",
"\n",
"i = (h*w).sum()\n",
"ie = sqrt(((e*w)**2).sum())\n",
"nbi.print_result(i, [ie])"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"Finally, we will do an example with _non_-frequency weights "
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:25:43.772984Z",
"iopub.status.busy": "2021-11-16T10:25:43.756423Z",
"iopub.status.idle": "2021-11-16T10:25:45.595871Z",
"shell.execute_reply": "2021-11-16T10:25:45.596706Z"
}
},
"outputs": [
{
"data": {
"application/pdf": 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\n",
"image/png": "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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"from matplotlib.pyplot import bar \n",
"from numpy.random import random\n",
"\n",
"weights = random(len(data))\n",
"h, b, w, e = nbi.histogram(data,bins=[-4,-2,-1,0,1,2,4],weights=weights,frequency=False)\n",
"bar(b,h,yerr=e,xerr=w/2,width=w,alpha=.2)\n",
"xlabel(r\"$x$\")\n",
"ylabel(r\"$\\mathrm{d}N/\\mathrm{d}x$\");"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"## `init_histogram`, `fill_histogram`, `fini_histogram` \n",
"\n",
"Both the _NumPy_ and `nbi_stat` functions `histogram` assumes that the full sample is available for calculations. However, often we are accumulating histograms _on-line_ meaning we _fill_ new observations into the histogram and then immediately forget about the number. For long-run programs or large data sets we can gain a bit by doing on-line updates. \n",
"\n",
"The function `init_histogram` is a litle like `histogram`, exept it does not do any updating. It declares the structures need, though "
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:25:45.606596Z",
"iopub.status.busy": "2021-11-16T10:25:45.605410Z",
"iopub.status.idle": "2021-11-16T10:25:45.611929Z",
"shell.execute_reply": "2021-11-16T10:25:45.613228Z"
}
},
"outputs": [],
"source": [
"hist = nbi.init_histogram(linspace(-3,3,31))"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"We then fill observations into the histogram with `fill_histogram`. We can fill with weights. However, to fill with _non_-frequency weights we must initialize with the option `weights=True`. Continuing from above, we fill without weights "
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:25:45.648677Z",
"iopub.status.busy": "2021-11-16T10:25:45.634178Z",
"iopub.status.idle": "2021-11-16T10:25:45.653287Z",
"shell.execute_reply": "2021-11-16T10:25:45.652089Z"
}
},
"outputs": [],
"source": [
"for _ in range(1000):\n",
" hist = nbi.fill_histogram(normal(),*hist)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"To finalize the histogram and extract \n",
"- bin values $h_i$ \n",
"- bin centres $b_i$\n",
"- bin widths $w_i$ \n",
"- bin uncertainties $e_i$\n",
"we call `fini_histogram`. "
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:25:45.661167Z",
"iopub.status.busy": "2021-11-16T10:25:45.660023Z",
"iopub.status.idle": "2021-11-16T10:25:45.663064Z",
"shell.execute_reply": "2021-11-16T10:25:45.664058Z"
}
},
"outputs": [],
"source": [
"h, b, w, e = nbi.fini_histogram(*hist)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"Let us plot it"
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:25:45.732732Z",
"iopub.status.busy": "2021-11-16T10:25:45.671789Z",
"iopub.status.idle": "2021-11-16T10:25:47.180722Z",
"shell.execute_reply": "2021-11-16T10:25:47.182430Z"
},
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [
{
"data": {
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\n",
"image/png": "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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"errorbar(b,h,e,w/2,\".\",label=\"Data\")\n",
"xlabel(r\"$x$\")\n",
"ylabel(r\"$\\mathrm{d}N/\\mathrm{d}x$\");"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"With weights, we need to make the histogram with structure with the option `weight=True`"
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:25:47.194035Z",
"iopub.status.busy": "2021-11-16T10:25:47.192731Z",
"iopub.status.idle": "2021-11-16T10:25:48.690779Z",
"shell.execute_reply": "2021-11-16T10:25:48.691447Z"
}
},
"outputs": [
{
"data": {
"application/pdf": 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\n",
"image/png": "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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"from numpy import array \n",
"\n",
"hist = nbi.init_histogram([-6,-3,-1,0,1,3,6],weighted=True)\n",
"for x,w in zip(normal(size=1000),random(size=1000)):\n",
" hist = nbi.fill_histogram(x,*hist,w)\n",
"\n",
"h, b, w, e = nbi.fini_histogram(*hist)\n",
"errorbar(b,h,e,w/2,\".\",label=\"Data\")\n",
"xlabel(r\"$x$\")\n",
"ylabel(r\"$\\mathrm{d}N/\\mathrm{d}x$\");"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"## `Histogram` \n",
"\n",
"Sometimes it can feel more comfortable to have a full object for complicated such as histograms. For that reason, the `nbi_stat` defines the class `Histogram`. It is similar to the function `init_histogram`, `fill_histogram`, and `fini_histogram` (in fact, those functions are used behind the scenes). An example to illustrate its use "
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:25:48.718430Z",
"iopub.status.busy": "2021-11-16T10:25:48.717117Z",
"iopub.status.idle": "2021-11-16T10:25:49.700365Z",
"shell.execute_reply": "2021-11-16T10:25:49.699767Z"
},
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"data": {
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\n",
"image/png": "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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"from numpy import zeros_like\n",
"from matplotlib.pyplot import fill_between\n",
"\n",
"hist = nbi.Histogram(linspace(-3,3,31),True)\n",
"for _ in range(1000):\n",
" hist.fill(normal(), random())\n",
"hist.finalize()\n",
"fill_between(hist.centers,\n",
" zeros_like(hist.heights),\n",
" hist.heights,\n",
" step='mid',alpha=.5)\n",
"errorbar(hist.centers,\n",
" hist.heights,\n",
" hist.uncertainties,\n",
" hist.widths/2,\n",
" '.', label='Non-frequency weighted')\n",
"xlabel('$x$')\n",
"ylabel('$\\mathrm{d}N/\\mathrm{d}x$');"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Sampling a probability density function "
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"## `eval_cdf` \n",
"\n",
"Suppose we have some function $f:\\mathbb{X}\\rightarrow\\mathbb{Y}$ from which we would like to draw random samples. If the function is one of the regular distributions we can often find it in _NumPy_'s `numpy.random` or _SciPy_'s `scipy.stats` packages. \n",
"\n",
"Sometimes, however, the distribution $f$ we are interested in does not exist in some readily available package. In that case one can use `nbi_stat`'s `eval_cdf` and `sample_pdf` to draw such random numbers. `eval_cdf` evaluates the _cumulative distribution function_ (CDF) $F$ defined by \n",
"\n",
"$$F(x) = \\int_a^x\\mathrm{d}x'\\,f(x')\\quad,$$ \n",
"\n",
"where $a$ is the lower bound of $X$ and $f$ is the _probability density function_ (PDF). `eval_cdf` build up the CDF numerically by integrating $f$ in steps \n",
"\n",
"$$I_n = \\int_{x_{n-1}}^{x_{n}}\\mathrm{d}x'\\,f(x')\\quad,$$ \n",
"\n",
"and then calculate the cumulative sum to give \n",
"\n",
"$$F_n = \\sum_{i=0}^{n} I_i\\quad.$$ \n",
"\n",
"Typically, one would require $f$ to be normalized on $X$ \n",
"\n",
"$$\\int_X\\mathrm{d}x\\,f(x) = 1\\quad,$$ \n",
"\n",
"but we relax that requirement in `eval_cdf` since we will normalize explicitly by dividing all $F_n$ by $F_N$ where $N$ is the last point. "
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"As an example, take the function that describes invariant mass of a resonance decay over some background \n",
"\n",
"$$f(E;a_1,a_2,a_3,A,\\Gamma,E_0) =\n",
"a_1+a_2x+a_3x^2+A\\frac{\\Gamma/(2\\pi)}{(E-E_0)^2+(\\Gamma/2)^2}\\quad,$$\n",
"\n",
"with \n",
"\n",
"$$\n",
"\\begin{split}\n",
"a_1 &= -0.3\\\\\n",
"a_2 &= 73\\\\\n",
"a_3 &= -18\\\\\n",
"A &= 33.8\\\\\n",
"\\Gamma &= 0.138\\,\\mathrm{Ge\\!V}\\\\\n",
"E_0 &= 0.9667\\,\\mathrm{Ge\\!V}\\quad.\n",
"\\end{split}\n",
"$$ \n",
"\n",
"We want to sample this distribution over $E\\in[0,3]\\,\\mathrm{Ge\\!V}$ in 51 steps. "
]
},
{
"cell_type": "code",
"execution_count": 32,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:25:49.711176Z",
"iopub.status.busy": "2021-11-16T10:25:49.709599Z",
"iopub.status.idle": "2021-11-16T10:25:49.713640Z",
"shell.execute_reply": "2021-11-16T10:25:49.714425Z"
},
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [],
"source": [
"from numpy import pi \n",
"def pdf(E,a1=-.3,a2=73,a3=-18,A=33.8,Gamma=0.138,E0=0.9667):\n",
" return a1+a2*E+a3*E**2+A*(Gamma/(2*pi))/((E-E0)**2+(Gamma/2)**2)\n",
"\n",
"x = linspace(0,3,51)\n",
"cdf = nbi.eval_cdf(pdf,x)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"We can choose as many steps as we want, but in general we should choose _just_ enough that we have enough resolution in the CDF to do reasonable sampling. That is, the PDF should be roughly linear between sampling points. Some trial-and-error may be involved when choosing the number of steps. In `sample_pdf` we will do linear interpolation between the sample points. \n",
"\n",
"Let us draw up the PDF and the CDF "
]
},
{
"cell_type": "code",
"execution_count": 33,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:25:49.745872Z",
"iopub.status.busy": "2021-11-16T10:25:49.744013Z",
"iopub.status.idle": "2021-11-16T10:25:51.378358Z",
"shell.execute_reply": "2021-11-16T10:25:51.379073Z"
}
},
"outputs": [
{
"data": {
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\n",
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MUODXwM9V9b+BfCIBMCEsoJmk62npmE4iwvCSXFu52uyQhkKsv/wKNlzza1yj90Cys23xzf5zisjCbl/Tt3r9MGC1qkanVWEucNJWx3gBP1AU3S4AlsWtxFuxJkeTVOGwstnrpzy/5z40iDQ72nyOpifdB0q7hg6l4sorKJ82jfbFi21C4f4LqurEHbw+GGjptt0c3ddFVZujTY5PisgGYB2wIuYl3Q4LaCapmto753HcfgZjZUkOb32WuevYmZ3T9sEHrLngQlBF3G5GPPJwV/CyCYXjohYo7LZdFN3XRUTGA78CDlLVoIjcA/wGuCoRBbQmR5NU9dFZQrbX5AiRGtqmVh/+YDhRxTIpruOTT1h/xZUQCkE4jAYC1lcWf+8DI0WksznlcOAFABEZFd03HGhQ1WB0ewOQk6gCWg3NJFXXPI69NDmqwsbmjm0WATUDi4ZC1D/8MJvu/SNZBQWIy4WGw9ZXlgCq6hWRi4F7RWQTsFhVXxcRB/CWiBwNvAR8J1ozawTGAZclqowW0ExSdc4SsqMmx+5j0SygDUydfWXh9nbqH3yQwuOPZ+hNN+Jftcr6yhJIVV8FXt1qX5hImn6n/5fIMnVnAc0kVV1b5zyOO25yBBuLNlB1TSocCCBuNxW/vJLyCy5ARHCWllogM10soJmkaog2OZbuoIY2rDjSBG8BbeAJtbRQc/PNX08qHAhAKIyIJLlkJhVZUohJqvo2H8W5LlxZ2/+nmOPKYlCBm/U2Fm1A8S5axMpTT8O3/DNwOm1cmemV1dBMUtW3bX+WkO4qS3KthjYAeD0evPPm4V+zlqZnn8VVWcnI//s/EKyvzPTKAppJqvpWX59m0a8szuXLTa0JKJFJFq/Hw5rzp6H+SDN0/uGHM/z3vyOroADAApnplTU5mqRq2MG0V9111tBsoc/MpKo0PPpYJJiFwyBC3sSJXcHMmL6wgGaSKjLT/vbHoHWqLMmhzR+iqd0W+sw0oZYWqn/5K1peeglErK/M7DRrcjRJEw4rDW3+Habsd+o+Fq2kh5WtTXryLvJQ/atfEaipoeLSX5A3aRLehR9aX5nZKQkNaNGlBW4BDlTVQ7rt/wDoTGELqeqU6P5e194x6auxPUBYdzyoutPXY9E62K/SFvpMd16Ph81PPknzc//GNXw4o/7vH10LcOYdfHByC2fSVqJraEcAzwHjt9r/UnR9nS7d1t7ZT1V9IjJLRKao6us9nTi61MF0ALfbPsGng/rWznkce29yHF4araFt9sa1TCb+vIs8rJkWTf5wOBh6801dwcyYXZHQPjRVncmWyw902l9ErhaRG0Wkc32dvqy90/3cM1R1oqpOdDqtJTUd1Ld1zuPY+weQ8nw32U6HLSOT5ppffJH1V1zxdfIH0LFkaZJLZTJFqvzlv1NV54tIFvC2iLTQh7V3THrryzyOnWyhz/QWbmuj5pZbaXrmGdxjxiCbN6PBoCV/mJhKiYCmqvOj30Mi8g5wDPAuvay9Y9Lb102OfWsiHl6ayzqroaUVr8dD03+ep/WNNwhu3Ej5xT+l4mc/o33pUhsobWIu6QFNRMYCh6vqX6O79gSeptvaO9Fmx8OB+5NUTBMHnU2OpX3MWqwszuXTDfaZJl10DZTuiNSqh9xwA2VnnwXYApwmPhKd5XgUcA4wTESuB+4h0pQ4VUQqidTC1gKPq2q4p7V3ElleE1/1rX5K8nY8j2N3w0tzqWv10REIkePKinPpzK4I1NbSOuftrlk/yHIQbrWZXkx8JTSgqeocYM5Wu9uB07Zz/DZr75jMERlU3feM1M6xaBuaOth9UH68imV2Ucubb7Lh2uvIHjsWcbsjy75YX5lJgKQ3OZqBq67Vx6A+zBLSqfu6aBbQUk/Y56P2rrvZ/I9/kD12LEOvv45Qc7P1lZmEsYBmkqahzc/oir7P1VfVNRbNEkNSTfPs2dTcehuhujpKzz2HwVdeiSM78mHFAplJFJvL0SRNQ5ufsj5mOAIMKcpBBMt0TDFej4fqa35NqK4OcbkoOvHErmBmTCJZDc0kRSisNHj9DOpHH5rb6WBIYY6ti5YiQk1NNDz2d8TljKwkDWg4HGlitFqZSQKroZmkaPT60T7O49jd8NJca3JMAd6FC/nq1NOo+/OfySopRdxumyXfJJ3V0ExSdE171Yd5HLurLMll8brGOJTI9IV34UI2/ek+vPPm4dptN0Y9/k9y99+f7L33suQPk3QW0ExS1Lf2fR7H7oaX5PLy0hrCYcXhkHgUzWyH1+Nh9bk/jszB6HAw9MYbyd1/f8AGSpvUYE2OJinq2yLTXvUnKQRgeEkO/lCYTa2+3g82MdPZN9ZFhI4lS5JXIGN6YDU0kxQNXTPt96/JsWsZmcZ2hhTlxLxcZkvh9nY23nY74nZTNPUkGyhtUpoFNJMUnU2OpXmufr1veEkeEBmLdtCI0piXy0R4PR6aX3iRljffJFhdTfmFF5I7fjwjHnnY+spMyrKAZpKivs1HaZ4LZx/ncexUWRKplVnqfvx4F3lYfe65EAwCMOTaX1N27rmA9ZWZ1GZ9aCYpapo6GFzY/ybDwhwXRTlOW+gzjlreeL0rmOFwEG63NehMerCAZpJidb2XEeV5O/XeyhIbixYPHZ99hqpSOGXK1+PK3G7rKzNpwwKaSThVZU2Dl5FlOxfQqkpzrYYWQxoIUHvP71h56mm0zJ5N3oQJjHj0b1T84heMeORha2I0acP60EzCbWrx4QuGd7qGNrwkl3krG2JcqoGp+aWX2HjHnQRraij5r/+i4JhjAOsrM+nJAppJuNUNXgBG7GQNrbIkl5aOIM0dAYpy+pclab626YEHqfvf/wVAXC6KTzsVR25ukktlzM6zgGYSbk39rgW0zrFo1Y3tFA21gLaz/CtXdv1skwqbvhCRY4HTgVpAVfWmHo7ZG/ghkcWbjwJuVNX5iSif9aGZhFvd4EUEqkp3voYGti7azmhfvJjGmTMBKP3hD5CcHJtU2HRyisjCbl/Tu78oInnAg8DlqnojcICITNnqmCzgd8DNqnoncAGwkgSxGppJuLUNXiqLc3E7d+7zVFW3latN77weD9558wnU1NA4cyau4ZUUnXxyJPnDBkqbrwVVdeIOXj8MWK2qnfPOzQVOAl7vdswhgAA/jwbAeuAv8ShsTyygmYRbXd/GbmU731czqCAbd5bDFvrsA6/Hw5rzzkd9kb9Bed/4BlX3/i8Od2QOTUv+MP0wGGjptt0c3dfdSCKB74eq2iQi/wD8wN8SUUBrcjQJt6ahnZFl+Tv9fodDGFaSY02OfdD27rtdwQwR8icfRlZxcXILZdJVLVDYbbsouq+7ZmC5qjZFt98Fjo5/0SIsoJmEavMFqWv17XTKfqfhJbnW5LgDGgoBkH/EEeB0gsOBZGeTN2lSkktm0tj7wEgR6ZxR/HDgBQARGRXdNw8oj/alQaTG9nmiCmhNjiah1m7etQzHTpUlubzzxaZYFCnjdHz2GdW//CWDr76GgiMOZ+TfH7N+MrPLVNUrIhcD94rIJmCxqr4uIg7gLRE5WlVXicjVwB+ix1QANyeqjBbQTELtasp+p+EludS2+PAHwzudXJJpvIs81M+YQeu775JVWoI4Ix+SrZ/MxIqqvgq8utW+MDCq2/YzwDOJLVmEBTSTUGuig6pH7mqTY2kuqpFJjne1+TITtMyZw7qLf9a1mvSwW24l/9BDk10sYxLKPtqahFrT4KUwx0lx7q4NiB4eTd1f1+iNRbHSXuO//hUJZgAi+JYvT26BjEkCC2gmoVbXexlZnoeI7NJ5hneNRRu4S5uEfT7alywBoHzaBUh2tg2SNgOaNTmahFrb4GXssMLeD+zF0OLIWmoDMXXf6/HQPHs2rW/NIbR5M2Nee5W8gyYw4m+PWPKHGdAsoJmECYWVtZu9HLffkF0+V44ri4rC7AGXur/1atKDr7qqa1yZJX+YTCAiQ4BcoFpV/f15b7+bHEVkiIiMEhF3f99rBraa5g4CId2lQdXdDS8ZWOuiqd/Phuuu22I1aQ0EklsoY2JARBwi8j8iUg18TGRA9kYReUZERvT1PH0KaLG6mBnYVte3Abuest9poAU0cbvJHjMmMlDaVpM2meV2YBGwh6oOVdUqVS0FbgL+R0RK+nKSvjY53g58ANyqql298CIyPnqxS1W1sR+FNwPQ2hil7HcaXprLq59uRFV3OckkFXk9Htreew/fihUMmj6dnH32oeqP90YmG7a+MpMhogOz71PVNVu/pqofRWf9LwcaeztXrwEterE/qeraXb2YGdjWNHhxOoRh0YSOXTW8JBd/MExdq5+Kwuze35BGvB4Pa358HuqPdCE4y8oZesP1gPWVmcyiqmERqdvB6z6gui/n6rXJMToK/GkROa37fhFxdV5MVft0MTOwra73Mrw0F2dWbEaLdK2LlmHNjhoOU/fAg13BDIcD5+CtJzU3JqPM2V6M6Y++/mV5XlWfEZH7ReR6EZkEHC0iz/f3gmbgWtvgjVn/GXQfi5ZZAa1x1iza3n4bHI7IpMLWV2YyX0xiTF/70BRAVX8mIg8Cjao6P3pRY/pkdYOX7+w/LGbnG55hK1cHN2/GWVpKySmnkFVYiHPwELwLrK/MDAgxiTF9DWjda3JeVe1cDkD7czEzcDW1B2j0BhgZwxpaUa6Tgmxn2jc5tr73PrV3301wwwZGvzSbrOJiik44AYC8gyyQmQEhJjGmr02O14jIahF5AThcRE4Vkcr+XMgMbJ0ZjrFschSRtE/d3/zEk6y94AJ8n3xCqKUZ3+dfJLtIxiRDTGJMXwPaJcBkYAbwCvAT4CPghv5e0AxMnbPsx3pm/Mo0Xblag0Fqf/8Ham66CTT6IVTBu2hRcgtmTHLEJMb0qclRVR+K/rgeeK5zv4jc0p+LichQ4BbgQFU9pNv+Y4HTiSznrap60472m/SzJg41NIiMRfOsbYzpORMiK4uOZcvIP/JIvB98gAaDNqmwGZCiQ8OeUdV6eogxEhlkWhZ9fYf6Og6tdDsnu6M/FwOOiBZ2fLfz5wEPAvupqk9EZonIFCLLfW+zX1Vf78N1TIpZXe+lLN9NYc6uLRuztcqSXBq9Adp8QfKzU3tqUu8iD/V/fYjiU0+l6LjjqLr/Phxutw2UNgNadBza9SIyS1Xf3erlB6Nfv+nLufo6Du16ETmih5eLohfra01vJtCy1e7DgNXRwXMAc4GTdrC/RyIyXUQWisjCYOdcdyZlrG3wsluMa2cAoysKAPh4XWPMzx1Lza+/weof/YjW199g/WWX4/V4cLgj06HmTZjAoJ9Mt2BmBrJrgR+LSLWILBERj4isAZ4iMrHHxr6cpK8fae8CbhKRp4B6IAiUEake/qSvF9uOwWwZ5Jqj+7a3v0eqOoNI+yv5+fmWfZliVje0MX630pif95t7DiLXlcWLSzYwefSgmJ8/Fppfepnqq6/+egFOiNTILIAZ02mwql4kIvnAaCAbWKuqNf05SV+TQh4ELgb2BM4GpgPfUNXJqrqkPxfsQS3QfYGsoui+7e03aSYQClPd2BHTlP1OeW4n39pnMLOX1BAMhXt/Q4I1zpzJ+ssuwzV8OOJ22wKcxvTsHyJyqqq2qepiVV3Q32AGfa+hLVLVoIhcpaq39fcivXgfGCki2dHmxcOB+3ew36SZ6sZ2QmGNeUJIp6n7D+OFxRuYt7KBw8ckv5bm9Xhoe/998g87jMITTiDU1EzZuefQvnSp9ZUZ07PXVPVZEfkTEABeVNVX+3uSvga0XBH5D4CIfAv4UFWb+nsxETkKOAcYJiLXA/eoqldELgbuFZFNwOLOxI/t7TfpJV4p+52OGTuYPHcWzy+uTnpAa5s/nzXnT4NQiPoZMxjxyCOUXzANsEmFjdmBzplCLhGRewHPzpykr8kcV4vIBOC3RALS76MTR34MvAM8oqq9DgZS1TnAnB72vwpsE423t9+kl9X18UnZ75TjyuLYfYbw0tIabj5lHK4YTX7cX+3LlrH+ssshFAJAA0HrKzOmb7r/pw2q6nZn3+/rSXZIVT3ANFU9X1UPBA4G7gVygP/dmYubgWFtgxd3loOhRbFZNqYnUw8YxmZvgPe+7MvokdjSYJC6Bx5g1fd/AKqIy2V9Zcb0z9YzhZwsIhUicnV/TtKvgTvd10SL1sjeB96PjhszpkdrGrxUleXicMRvEc4j96qgMNvJ8x9Xc9ReFXG7Tndd48cOmkDzK69S9O1vM/SG6/GtXGl9Zcb0zyXAbGBi9Oti4C9AHnBnX08Sk5Go1rdldmR1fWyXjelJjiuL4/YdwsvLarj1tP1xO+Pb7Ohd5GH1j8+FUBhxu6m6/z4KJk8GrK/MmP6K1WxUyelsMAOGqrK2wRuXlP2tTT1wGM0dQd5dsSmu1wnU1FB9zTUQCEI4jAYCdCxZGtdrGjNA3dGfgy2gmbja7A3Q4gvGZZaQrR0xpoKiHCfPL94Ql/OrKk3//jdfffdkAjU14HRaX5kxcaSqrf05PrUnvzNprzNlf2R5ftyv5XY6+PZ+Q3lpaQ0dgRA5rqyYnLezryywYQONTzxB7oQJVN5xO8GGBusrMyaFWEAzcbW6vg2IX8r+1k46YBj/+nAd73xRx3H7Dtnl83k9Htacfz7qDyAuF6Vnn82Qa3+NZGXhHjnSApkxKcSaHE1cxWNhzx05fMwgSvJcPL+4epfPFWptpeaWW9EOX6SvLBjEOXgwkhWbmp8xJrYsoJm4Wl3vpaIwm1x3YoKAK8vBCfsN5bVPNtIRCO30edrmzWflyafg++QTyMqyvjJjiKxRKSL3i8iNIvLfOzguV0QWi8jdiSyfNTmauFqyvokx0SVeEmXqAZU8sWAtb31WywnjhvXrveGODjb9/g80PPoorpEjGPnP/wOwvjIz4G1v7crtDNu6hZ2cvmpXWEAzcbOyro3lNS3cMHXfhF730D3KKM9385/FG/oV0LweD23vvEvTCy9QetZZDP7llTjyIk2lFsjMAOAUkYXdtmdEl+XqtL01KrcIaCJyTvS1A4CEfpq1gGbiZvbSSPr8CeOGJvS6ziwHJ4wbytOL1vdpJWsNBtl4z+9ofPyfXckfRd+d2hXMjBkggqo6cQev97pGpYjsC+yjqteKyAFxKOMOWR+aiZvZS2o4cLcShpfkJvzapx9URXsgxJVPfUwovP31Xv2rVrHq7LPZ/MgjqM/flfzhnb8ggaU1Ji30ZY3K04AOEbkGOAKYJCKXJaZ4FtBMnKxt8LJkfRPfSXDtrNPBI0u5Yeq+vLSshuueWYLqlkFNVdn8xBN8ddrp+FetZtAvfo5kZ1vyhzHb17VGZXT7cOAFABEZBaCqt6rqzap6B/AuMF9V/5CoAlqTo4mLl5ZGFps9sZ9JGbF0wRG7s7nNz5/eXEFZvpurThgLRPrKau+6m/ZFi8ifPJlht9+Ga8gQ8g87zJI/jNmO7a1dKSIO4C0ROVpVVwGIyBnAkYBbRH6oqo8nooyy9SfXTJCfn69tbW3JLsaAdvr9c/EFw7zwi28mtRyqynXPLuWf89Zw/Un7cFbeZtZccCHq94PDwcjHHiXvoIOSWkZjUoGIeFU1/lP6xJHV0EzMbWhqZ9GaRn55/F7JLgoiwv+cMo6WplYabruV5VpLrj/SV4YI3gULLaAZkyEsoJmYezna3NjfMWDxEvjicy79160EVn7Jm1UTOMrpwhEKDvi+MlXFFwzjC4TxBUORn4Nh/MHIdiiskS9VwmEIa+RnIfJBwSHgEOnadmUJriwHriwHbqfgzsrC5RRynFnkurPIdjoQid+aeMZYQDMx9+LSGvYaUsCYwYkdUN1dZELh+QQbNtP4+OM4ioqoeODPvLTMwUvLljAtv4GDTpmS1n1l7f4Qm71+Nnv9NHoDXd9bOoI0dwRo6QjQ3B6kpSOyr80fot3f+T1Emz9IInscHAJ5bie57izy3VkU5DgpynFFvnKjP+e6KMlzUZrnpjzfTVmBm7J8N6V5blxZlsNmdswCmompTS0+Fqxq4Off2jNpZYhMKDwt0k8WDpM7fjxV9/0JZ3k5jxzi4+pZOVy+fCPyYj3HrlzIuYeNYvLo8riuqN0XobBS3+ZjU4uPulY/m1p81Lf6qG/zU9fqo6HNT32rv2ufLxje7rmcDqEo10VhNGgU5jgpyXOTn51FnttJXjSo5LqdZDsdZLscuLMcuJ0Osp2R2lSWQ8hyCA7p/E7X70hVUYWwRmpuYY3U5gKhSA3PH1ICwTD+UJiOQAhvNIh6/SHaA0G8/hCt0cC7sq6N5o4ATe0BvP7tT1dWkudiSGEOg4uyGVKUw9CiHIZEf64syaWqNJfiXJfVAgcwC2gmpl5eVoMqfGf/5KTrA7S88kpXMMPhoOCYo3GWlwNQXpDNQz+eyNoGL/+cv4YnF6zllU82svugfM7+xggmjipjRFkepXmx+cPoD4bZ7N0yIEUCViRwbWr1dW3Xt/l7rDG5nQ4qCrIpy3dTXuBmryGFlOW7KMmL1FxK86I/57soyXVTnOsix5WezXuBUJhGb4CGNn+3r8jvZlOLj9oWH7XNHayobaW2xbfNGMN8dxaVJbkML40EuFHl+Ywsz2dUeR67leXFbEkhk5osy9HE1I8emsf6xnbeuPKopPxBbXz6GTb85jeRDVXE5WLEIw9vt2nRFwwxe0kNj72/ikVrGrv2F2Y72a0sjxFleYwozyPXlRXpL5JI01nnvfmCYVo7grT6ArT6grR0RL6a2gPUtfpo6Qj2eN3OIDWoMJuKgmwqCt1bbHd+Ly9wU5DtTMvgFG+hsNLQ5qemqYP1jV7WbW5nfWM766Pf1zZ4ae72+xeBYUU5jBqUz+iKSJN459fgwuwB/zvOhCxHC2gmZja3+Zl462v85Mg9usZ8JYr6/dTcfjuNjz9B3qGHUnb++fiWL+/XmLKVdW18WdvK6gYvaxu8rGnwsrq+jbWb2/Fvp3lPBArcTgpynBRkf/29ONfFoGitqiw/2h+U76a8IJuKwmyKcixIJUKj18+q+shzXFUX+f5V9Dm3+L4OdoU5TsYMLmDs0CL2GVbI2KFF7D20kOJcVxJLn1gW0FKUBbTkeGrBWq6atZj/XHIE+1cVJ+SaXo+HljfepPXNN/GvWEHZBdMYfPnliDO2relf9xkpSvS7gjvLkfS+N9N/qkpti48Vta1dX1/UtrC8poVGb6DruOEluYwdWsh+w4vZf3gxB1QVM6QoJ4klj59MCGjWh2Zi5sWlG6gqzWXc8KKEXK8r+cPnA1UGXXopFRf/NC7Xks7mRix4ZQIRYUhRDkOKcjh8zKCu/arKxmYfn9Y08+mGZpZvaOGTDc28+Vktnd11FYXZ7D+8mHHDi5mwWwkTRpRQkudO0p2Y7iygmZhoag8wd0Ud500elbCmtLa3344kf6hG5mB0WFq32TUiwtDiHIYW53DM3l9PJO/1B/mkupkl65tYsq6JJeubeKtbkNtjUD4TRpQyYUQkwI0dWkSW1dwTzgKaiYnXP91IIKScuH9iBlO3zZtP/d8eRbKyUJEBP0jaxFee28nEUWVMHFXWta/NF2TxuiY8azezaHUjcz6vZdaidUAkqeigkaVM2r2MSbuXcUBVMdlOy7CMN+tDMzFx/iPz+XRDC+9d86249ym1zp3Luv93Ca6q4VRccQX+L1bYhMIm6VSVdZvb+XD1ZhasamDBqgY+39gKRLJax+9WwqF7lHP46HLGjyhJuQCXCX1oFtDMLnvni02c89f5XH7sXlx6bHwHVLfOmcO6n/8C9+67M+Lhv3aNLzMmFTW0+SPBbWUD81Y2sKy6ibBCjsvBIaPKOHzMICaPLme/yuKkN1FaQEtRFtASpyMQ4vjfv43TIbx46TfjNnDV6/HQ/NLLbP7HP8jZe292++tDOEtL43ItY+KlqT3AB1/V8/6X9cxdUccXtZEaXEmei2/uWcFRe1Vw5J6DGJyETMpMCGjWh2Z2yR/f+II1DV7+edE34hrMuqaycjiouOIKC2YmLRXnuvj2fkP59n6RmXRqWzp4/8t63v68jjmfb+I/H1cDsM+wIo7aq4Kj965g4shSnDaPZZ9YQDM77bOaFv485yvOOKiKyaMH9f6GndSVzRhd8qVj2TIKjjg8btczJlEGF+ZwyvjhnDJ+OOGw8mlNM3M+38Sczzbx0Dtf8eCcLynOdXH03hVM2WcIR+1VMaAGe/eXBTSzU8Jh5dpnllCY4+S6k/aJ67W8i5dEgllWlmUzmozlcAj7VRazX2UxPzt6DC0dAd79oo7XPq3lzc9qee6japwO4ZBRZRy37xC+PW4ow0tyk13slGJ9aGan/HPeGq59Zgl3f+9Azjy4Km7XaX71Vdb//BcUn3kG7t1GWDajGZBCYeWjtZt57dNaXv90Y1f25AFVxXx7v6GcMG4ooyt2bbmmTOhDs4Bm+q22pYMp98xhXGUx/7zoG3EbSB3cvJmvpn4X55DB7P7kk4jLmlqMgci8oy8vq+GlpTV8tLYRgD0HF3DCuKFc8q0xOzUkwAJairKAFl8/f9zDy0treOmyb7LHLn4q3JH1V1xB86uvsfvMf5Gz995xu44x6WxDUzuvLNvIS0tr2Njcwes7udJFJgQ060Mz/fLWZ7X85+NqLj92r7gGMw0GySopoeL//cyCmTE7MKw4lx9PHsWPJ4/CFwwN6FUcrIZm+mx9YztnPvAeee4sXrz0mwmZ6UBVB/R/UGMSJRNqaDa4wfRJbXMHZ//lA1p9Qe794YS4BTOvx8PqH53D5n/9C8CCmTGmz6zJ0fRqc5ufH/11HrUtPv5+wST2q4zPWmdej4c15/4YDQTwfvQR2WPGWEajMabPUiagicgHQEd0M6SqU6L7jwVOB2oBVdWbklTEAam5I8C5D89nVb2Xv513CAePLOv9TTvJO28eGogurqiKd/4CC2jGmD5LmYAGvKSqN3bfISJ5wIPAfqrqE5FZIjJFVV9PSgkHGK8/yPmPLGB5TTMzzpnI5DHxmw0EQAPByA8Ohw2gNsb0WyoFtP1F5GogF1igqi8AhwGrVdUXPWYucBKwTUATkenAdAC321aP3VUdgRAXPbYQz5rN/Omsgzhm7ODe37QLNBSiefZsXFVVlJx5JnnfmGS1M2NMv6RSQLtTVeeLSBbwtoi0AIOBlm7HNEf3bUNVZwAzIJLlGO/CZjKvP8gl//Qwd0U993zvQL6TiEU7w2FKf/B9XCNGUHj00fG/njEm46RMQFPV+dHvIRF5BzgGeBco7HZYEZG+NBMnaxu8XPTYQj7f2MKtp43jjDhOa9WduFyUnXtuQq5ljMlMKZG2LyJjReSCbrv2BFYA7wMjRSQ7uv9w4IVEl2+g+OCrek65by7rG9t55PxJnP2NkQm5bus779A4cyYaDCbkesaYzJQqNbRmYKqIVBKpha0FHlfVsIhcDNwrIpuAxZYQEnuqyj8+WM1N//mEkeV5/OXciXGdBWSLa4fD1N51NxoMUnzaaQm5pjEmM6VEQFPVaqDHv2aq+irwamJLNHD4g2H++9/LeHz+Gr41djB/+MF4inISNwlwy2uv4fv8cyrv+i2SFf+ZR4wxmSslAppJjurGdi59wsOCVZv52dGjufL4vclyJG5mDlWl7v4HcI8aRdF3vpOw6xpjdk5v44JFZDRwC7AIqALqVfXmRJXPAtoA9Z+Pq7numSWEwsq9P5zAyQdWJrwMrW+8gW/5cobdcbvVzoxJPqeILOy2PSOaPQ70eVxwGfCEqj4Xfc8nIvKCqn6YkBtIxEVM6mjpCPDfzy3jac96Jowo4Q/fH8/I8sTPR+r1eGh5401yJ06keOrUhF/fGLONoKpO3MHrvY4LVtUFW73HASRspngLaAPIwlUNXPbkR2xo6uCyY/fkkmPG4MxKfKKr1+NhzfnTUL8fcbtpX7LEBlEbk/r6PC4YQEROA15W1eXxLlgnC2gDgD8Y5o9vfMF9b66gqjSPp35yGAePLE1aeVrnvI36fKAamYjY5mw0Jh3U0sdxwSJyDJGxxJfFv1hfs4CW4Rava+SqmYtZXtPCmQdXcePJ+1GQnbzHrqEQbXPngqrN2WhMeukaFxxtdjwcuB9AREap6qrozycB3wQuBYaJyEhVfT8RBbSAlqE6AiH+8NoXzHj7SyoKs3no3Ikcu++QZBeLuvvuo2PJEsouvJCswkLyJh1itTNj0oCqensaFywiDuAtETkaKAeeBBYCbwL5wH1EgmHc2YrVGWjhqgaumrmYr+ra+P7E3bj2pH0ozk3c2LLtaXnzTdZd/DOKzzidYbfcYot3GpNCMmHFagtoGaTNF+Sulz/j0fdXUVmcyx1n7M8396xIdrEAUL+fFSecgLOklJH//D8cOTnJLpIxphsLaClqIAa0N5Zv5IZnl7G+sZ0fHzaSq04YS34S+8p64vtqJeJ2464anuyiGGO2kgkBLbX+4pl+q23p4Kb/fMILizew5+ACZv70MCaOit+q0v3lXeShcebMyBpnB1lfmTEmfqyGlqbCYeXJhWu5/cVP6QiG+cW3xjD9yNG4nSmxgAIQGW+2+pxzIRhEXC5GPPaoJYAYk6KshmaSYkVtC9c+vZT5qxo4dI8ybjtt/4TNjt9XGgyy8c7fQnRJGA2HbbyZMSauLKClkY5AiPvfXMEDc74kz+3kt2cewPcOrkq5bMHg5s2sv+IKOj76CKJzNNp4M2NMvFlASxNzV9Rx/bNLWVnXxmkThnPdSfswqCC79zcmge+LL2j/6GOG3X477lEjIzUzG29mjIkz60NLcfWtPm598VOeXrSekeV53Hrq/hyx56BkF2sbXo+HlldepfD448ibMIFgQwPOstRJTjHG7Fgm9KFZQEtRqsq/PlzHbS9+SpsvyE+OHM0l3xpDjiv1llnxLljA6vOnRZI/3C5GPGrJH8akm0wIaNbkmIK+3NTKtU8vYd7KBiaOLOW20/dnryGFvb8xCbyLFrHu0su+Tv4IWfKHMSY5LKClEF8wxANvfcn9b35JjsvB7afvz/cn7oYjgatI98fG395Fw8MPkzWoHHG50HDYkj+MMUljTY4pYt5X9Vz7zBK+3NTGdw+s5Iap+zC4MPWmh/Iu8uBdMJ+8SZPwLV+Of/UaKn5+CR2ff27JH8aksUxocrSAlmRN3gC3vfgpTy5cS1VpLrecOo6j997umnlJ1fjMM2y47npQRbKzGfHIwxa8jMkQmRDQrMkxSVSV5xdv4Kb/fMJmr5+fHLkHlx67J3nu1Hsk/lWr2HTvvTS/OLtrny3MaYxJNan313MAWN/Yzg3PLuWN5bXsP7yYv51/COOGFye7WFvwejx45y8gUF1N48yZiNtN0amn0DL7JTQ6lZX1lRljUok1OSZQKKw8+t4q7n7lM1ThyuP34rzJo3Bmpc78iwDNr79B9RVXoIEAkpVFwTHHMPSG63FWVHQFOusrMyazWJOj6bPPalq4etZiPlrbyFF7VXDLqePYrSwv2cXagu+rr6j/619peuZZUAVVVISc/fbDWRFZVy1vwgQLZMaYlGQBLc78wTD3vbmC+99aQUG2kz98fzynjK9MmfkXvR4PTc8+h+/LL2lfuBDJzqZwyhRa337bmhaNMWnFAlocedZs5upZi/l8YyunjK/kN1P3pTxF5l/UUIj2xYtZc/40tKMDgOLTT2PwL3+Js6zMmhaNMWnHAloceP1B7nnlcx6eu5KhRTk8fN5EvjV2SHLLFA1Q7j12p2PZMppmPU3RSSehfn/kgKws3CNHdc2/aE2Lxph0YwEtxt7/sp6rZy1mTYOXHx06gqtPGEthjiupZfJ++CFrzjsfDQS69hUccww5++2LuN2R5A9rWjTGpDkLaDHS6gtyx+xP+ccHaxhZnseT0w/lG3uUJ7VM4bY2HPn5tL079+tgJkLZtPMZ8qtfAeCqqrKmRWNMRrCAFgPvflHH1bMWU93UzgVH7M4vj9+bXHdyZsVvefttGh9/Av/q1WQVFTHqicfJP/Kb1P/1r2gohLhcFB57bNfx1rRojMkUFtB2QXNHgNtf/JTH569lj0H5zPzpYRw8MjlrgLW+8w6b/nQfHR9/HNkhQumPfoSqkjdhAiMe/ZvVxIwxGc0C2k5654tNXD1zMTXNHfzkyD24/Li9ErZWmdfjofWtt9BgkPILLsBZVkZg3Tr8q1aBSGQMmcOBc9CgruEBVhMzxmQ6C2j91OYLcnu0r2yPinxmXjyZg0aUxuVa3VPncw88kI5ln7D5qSdpmjkrErQAR04OFT//OSXf+x7Ze49lzbRpluRhjBmQLKD1w7yv6vnVzMWs3ezlgiN251ff3jtutTKvx9OVmShuN5X33M36/3fJlgc5HIjbDYA4neQdNIERjzxsTYvGmAHJAlofdARC3PXyZzw8dyW7lebx5PTDmLR77PrKOmti2fuMRTs68M5fQPNLL6E+HxCZ2d6/4kuq7vsTOF2sv/TSbrWwSVucy5oWjTEDlQW0Xny8tpHLn/qIrza1cc6hI7nmxLHkZ+/cr22LJsQDDsD35Ze0vv02dX+6LzLAOTp/ouTmkj1mDKHGRui2CnRnoLJamDHGbMtm29+OYCjMfW9+yb1vfMHgwmzuOvNAjthzUJ/e29O0UV6PhzU/Pu/r8WBuN/h8kJUVCWThMDgclHzvewy97lrE7bbpp4wxCWOz7Weorza1cvlTH/Px2kZOHV/JTaeMozh329k+tg44odY2ml96iY033YQGgyCCc9gwdv/XU3jnL4gEs+gHiJx99qHsrB9ClpMN113X1YRYfOopXf1i1nxojDF9ZwGtG+8iD3NnvcKfNhexasho/nTWBE4aN5R2j4e6hR+Svc9YCAYJ1tXRsXQpjbOehlAIcbsZ8ejf8K9aTc311399QlUcOTmEve3kTTokMs1UdAb7IVdf1RWsXJXDrCZmjEl5InIscDpQC6iq3rQzx8StfKne5Lgzv5ydaXKsm7eQDdOmkRWKNAlKUTGOYICw1wsuVyRwOZ1fT+bbncNBxaWXUnzKyTQ9/zx19/6xa1aOEY88vEWzowUuY0wq6q3JUUTygMXAfqrqE5FZwP2q+np/jomnlK6hRX85D9LtlyMiU3r65YjIdGA6gDvaZNcf6vkQRzhI5yplOSNHkHfwwXR8+ineBQsgHEZDIUrO+iGDLrwQ/7p1rJ3+ky3GfLmGDmXQhReSd/DBPQYua0I0xqQwp4gs7LY9Q1VndNs+DFitqr7o9lzgJOD1fh4TNykd0OjHLyf6i58BkRpafy+U/41JZGVndwWoIdf+mrwJEyLJHOd/PVi5+LvfxVVZiauycrvZhha4jDFpKKiqE3fw+mCgpdt2c3Rff4+Jm1QPaAn75eRN6HlQ8vb2d75mgcsYM0DUAoXdtoui+/p7TNykekBL6C9newHKApcxxvA+MFJEsqOtZocD9wOIyChVXbWjYxIh1QNaUn85xhhjIlTVKyIXA/eKyCZgsaq+LiIO4C0ROVpVV/V0TKLKmA5ZjscBZwKbgEC8shyNMWYgy4SB1Skf0HaGBTRjjOmfTAhojmQXwBhjjIkFC2jGGGMyggU0Y4wxGSEj+9BEJAy07+TbnUAwhsVJpky5l0y5D7B7SUWZch+wa/eSq6ppXcnJyIC2K0RkYS+j5dNGptxLptwH2L2koky5D8ise9kZaR2NjTHGmE4W0IwxxmQEC2jbmtH7IWkjU+4lU+4D7F5SUabcB2TWvfSb9aEZY4zJCFZDM8YYkxEsoBljjMkIFtCMMcZkBAtoxhhjMkKqr4cWFyJyLHA6kcVCtaclafpyTCro4718AHREN0OqOiWBRewzERkK3AIcqKqHbOeYlH8ufbyPlH8mIjKayH0sAqqAelW9uYfj0uGZ9PVe0uG5OID/APMANzAamKaq7Vsdl/LPJeZUdUB9AXnACiA7uj0LmNLfY1Lhq6/lBG5Mdln7eD9nAt8FFu7K/Sb7q7f7SJdnAhwCnNJt+xPg4DR9Jr3eSxo9Fwdwfbft54Cz0/G5xPprIDY5Hgas1sgK2ABzgZN24phU0Ndy7i8iV4vIjSKSivcBgKrOBFp2cEhaPJc+3AekwTNR1QWq+ly3XQ5g64UG0+WZ9OVeID2eS1hVbwEQESeRGudnWx2WFs8l1gZik+Ngtvxj0xzd199jUkFfy3mnqs4XkSzgbRFpUdW3E1LC2EqX59IXafVMROQ04GVVXb7VS2n3THZwL5BGz0VEvg1cDjyvqgu3ejntnkssDMQaWi1Q2G27KLqvv8ekgj6VU1XnR7+HgHeAYxJSuthLl+fSq3R6JiJyDJHyXd7Dy2n1THq5l7R6Lqr6sqqeAOwuIj/b6uW0ei6xMhAD2vvASBHJjm4fDrwAICKjejsmxfR6LyIyVkQu6PaePYm0raeNNHwuPUrHZxJtdvs2cCkwVEQOi+4fFT0kbZ5Jb/eSLs9FRPbdqjl0JbBH9LVR0X1p81xiaUBOfSUixxHpuN8EBFT1pmjm0FfA0aq6qqdjklfi7evtXgA/cB+R7K4iwAVcoarh5JR4+0TkKOBc4ATgAeAewEeaPZfe7oM0eSYicjAwB+hszsonUu7HSL9n0uu9kD7PZTRwF5FyuoB9gF8QqYGl1XOJtQEZ0IwxxmSegdjkaIwxJgNZQDPGGJMRLKAZY4zJCBbQjDHGZAQLaMYYYzKCBTRjjDEZwQKaMcaYjGABzZg4iM4FmPLnNCaTWEAzpg9E5CIR8YnIzdGZ2G8UkQ9FpGCr4/JE5A9AWXR7mIjcIyI3RN/zuIjc3sP5C0Tk7yJSJyIndNt/sYi8JyLjgSoR+W10hnVjzFbsP4YxfTMbqFXV33TuEJElqtq61XH3Ao+p6qboPHr/Bk5X1bXR97iBf259clVtFZHpQDWRufk6NQHXqepH0fd/ANwIXB+rGzMmU9jUV8b0gYicCvxEVU+Mbj+gqhdvdUwB8AVQqaoqImcAP1DV7+3gvDcT+WAZIrLcxwjAp6pXRl+fEb2uRrdziczXNzzV5hg0JtmshmZM30wEBkWbE3OB9T0cMxpo0K8/Je4B1HS+KCIjgR8Smfn858DewKGqenz09beA3wBPi8i1wEjg827nQ1Xbo31pQ4ANsbxBY9KdBTRj+mYicIeqzhKRsUBJD8dkA8Fu218C3+jcUNXVwB0isgooAA4A8kTkmugha6PnWAGcAewH/KGH6wSIBFVjTDeWFGJM3xwMzAOIrnRc1G2tqU5riSaDRL0AjOq2RlWnzv93HxPpl7tDVe8AHgE+A2YAlwDFqrqp+xtFRIgEw+pdviNjMozV0IzZAREpBK4hsj7WeZF4AsBkVX2l+7GqukFE1otIlaquU1WfiHwXuFpENgNZwBjgUWClqi4VkUnRrMcgkBO91hPA74AbeijSgcBbqtoR+7s1Jr1ZUogxMSQiBxDpH/upqoZifO4c4C/ADaq6KpbnNiYTWEAzJsZEZBgQ3Lq5MAbnHQ60q2pDLM9rTKawgGaMMSYjWFKIMcaYjGABzRhjTEawgGaMMSYjWEAzxhiTESygGWOMyQgW0IwxxmSE/w928kRdUk9jWgAAAABJRU5ErkJggg==\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"from matplotlib.pyplot import gca \n",
"\n",
"ax = gca()\n",
"lp = ax.plot(x,pdf(x),label='PDF');\n",
"tax = gca().twinx()\n",
"lc = tax.plot(x,cdf,'.--',label='CDF',color='C3')\n",
"\n",
"ax.set_xlabel(r'$E\\ (\\mathrm{Ge\\!V})$')\n",
"ax.set_ylabel(r'$f(E)$')\n",
"\n",
"tax.set_ylabel(r'$F(E)$')\n",
"\n",
"ax.legend([lp[0],lc[0]],[lp[0].get_label(),lc[0].get_label()],\n",
" loc='upper left');"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"To draw random variables from $f$ we will pick a uniform random number $r\\sim\\mathcal{U}[0,1]$ and then solve \n",
"\n",
"$$F(E) - r = 0\\quad.$$\n",
"\n",
"Of course, we will do so numerically by look-up in our calculated CDF. "
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"## `sample_pdf` \n",
"\n",
"Let us generate 2000 samples from the PDF above "
]
},
{
"cell_type": "code",
"execution_count": 34,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:25:51.385441Z",
"iopub.status.busy": "2021-11-16T10:25:51.384328Z",
"iopub.status.idle": "2021-11-16T10:25:51.388923Z",
"shell.execute_reply": "2021-11-16T10:25:51.389552Z"
}
},
"outputs": [],
"source": [
"samples = nbi.sample_pdf(random(2000),x,cdf)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"Let us draw this with a histogram "
]
},
{
"cell_type": "code",
"execution_count": 35,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:25:51.414269Z",
"iopub.status.busy": "2021-11-16T10:25:51.412114Z",
"iopub.status.idle": "2021-11-16T10:25:53.024283Z",
"shell.execute_reply": "2021-11-16T10:25:53.025013Z"
}
},
"outputs": [
{
"data": {
"application/pdf": 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\n",
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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"ax = gca()\n",
"ha = nbi.hist(samples,bins=linspace(0,3,101),fmt='none',\n",
" label='Samples')\n",
"tax = ax.twinx()\n",
"lp = tax.plot(x,pdf(x),label='PDF',color='C1')\n",
"\n",
"ax.set_xlabel(r'$E\\ (\\mathrm{Ge\\!V})$')\n",
"ax.set_ylabel(r'$\\mathrm{d}N/\\mathrm{d}E$')\n",
"\n",
"tax.set_ylabel(r'$f(E)$')\n",
"\n",
"ax.legend([lp[0],ha],[lp[0].get_label(),ha.get_label()],\n",
" loc='upper left');"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"Note, in the plot above, the two ordinate ($y$) scales are independent and we should _not_ expect the PDF line to lie on top of the sample points. However, we _should_ expect the curves to have the same shape, which they do. Note, that we have made a finer binning in our histogram than what we determined our CDF with, but we still get reasonable samples. That is because `sample_pdf` does linear interpolation between the determined CDF points. \n",
"\n",
"If our PDF has distinct features in some region of the domain (e.g., sharp peaks or the like), one can define the CDF evaluation points to be closer in the region of that feature. For example "
]
},
{
"cell_type": "code",
"execution_count": 36,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:25:53.035066Z",
"iopub.status.busy": "2021-11-16T10:25:53.034029Z",
"iopub.status.idle": "2021-11-16T10:25:55.203245Z",
"shell.execute_reply": "2021-11-16T10:25:55.204058Z"
},
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"data": {
"application/pdf": 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\n",
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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"x = hstack((linspace(0,.5,5,endpoint=False),\n",
" linspace(.5,1.5,40,endpoint=False),\n",
" linspace(1.5,3,16)))\n",
"cdf = nbi.eval_cdf(pdf,x)\n",
"\n",
"ax = gca()\n",
"lp = ax.plot(x,pdf(x),label='PDF');\n",
"tax = gca().twinx()\n",
"lc = tax.plot(x,cdf,'.--',label='CDF',color='C3')\n",
"\n",
"ax.set_xlabel(r'$E\\ (\\mathrm{Ge\\!V})$')\n",
"ax.set_ylabel(r'$f(E)$')\n",
"\n",
"tax.set_ylabel(r'$F(E)$')\n",
"\n",
"ax.legend([lp[0],lc[0]],[lp[0].get_label(),lc[0].get_label()],\n",
" loc='upper left');"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"In this way, our sampling near the peak will be much more fine grained "
]
},
{
"cell_type": "code",
"execution_count": 37,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:25:55.215305Z",
"iopub.status.busy": "2021-11-16T10:25:55.213914Z",
"iopub.status.idle": "2021-11-16T10:25:57.179355Z",
"shell.execute_reply": "2021-11-16T10:25:57.180186Z"
}
},
"outputs": [
{
"data": {
"application/pdf": 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\n",
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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"samples = nbi.sample_pdf(random(2000),x,cdf)\n",
"\n",
"ax = gca()\n",
"ha = nbi.hist(samples,bins=linspace(0,3,101),fmt='none',\n",
" label='Samples')\n",
"tax = ax.twinx()\n",
"lp = tax.plot(x,pdf(x),label='PDF',color='C1')\n",
"\n",
"ax.set_xlabel(r'$E\\ (\\mathrm{Ge\\!V})$')\n",
"ax.set_ylabel(r'$\\mathrm{d}N/\\mathrm{d}E$')\n",
"\n",
"tax.set_ylabel(r'$f(E)$')\n",
"\n",
"ax.legend([lp[0],ha],[lp[0].get_label(),ha.get_label()],\n",
" loc='upper left');"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Propagation of uncertainties "
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"## `propagate_uncertainty` \n",
"\n",
"Generally, if we measure the quantities $x_1,\\ldots,x_n$ and determine some estimator $y$ as \n",
"\n",
"$$y = f(x_1,...,x_n)\\quad,$$ \n",
"\n",
"we need to propagate the uncertainties of the measured quantities $\\delta_1,\\ldots,\\delta_n$ to get the final uncertainty $\\delta_y$ on $y$. The standard formula is given by \n",
"\n",
"$$\\delta_y^2 = \\sum_{i=1}^{n}\\left(\\frac{\\partial f}{\\partial x_i}\\right)^2\\delta_i^2\\quad,$$ \n",
"\n",
"where we explicitly ignore correlations between the measured quantities $x_1,\\ldots,x_n$. "
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"The module `nbi_stat` allows us to evaluate this formula _numerically_ using the function `propagate_uncertainty` Let us take the example of \n",
"\n",
"\\begin{align*}\n",
" x_1 &= 1.3\\pm0.1\\\\\n",
" x_2 &= 0.22\\pm0.05\\\\\n",
"\\end{align*}\n",
"\n",
"and \n",
"\n",
"$$ y = f(x_1,x_2) = x_1^{x_2}\\quad.$$"
]
},
{
"cell_type": "code",
"execution_count": 38,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:25:57.191859Z",
"iopub.status.busy": "2021-11-16T10:25:57.190130Z",
"iopub.status.idle": "2021-11-16T10:25:57.194979Z",
"shell.execute_reply": "2021-11-16T10:25:57.194076Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" 1.06 +/- 0.02\n"
]
}
],
"source": [
"x = [1.3, 0.22]\n",
"dx = [0.1, 0.05]\n",
"y = x[0]**x[1]\n",
"dy2 = nbi.propagate_uncertainty(lambda x: x[0]**x[1],x,dx)\n",
"nbi.print_result(y,sqrt(dy2))"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"Note, that `propagate_uncertainty` returns the _square_ uncertainty. "
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"An alternative to this numerical evaluation is to evaluate the derivatives _symbolically_ using [_SymPy_](https://sympy.org). Let us do that for the above "
]
},
{
"cell_type": "code",
"execution_count": 39,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:25:57.205284Z",
"iopub.status.busy": "2021-11-16T10:25:57.204077Z",
"iopub.status.idle": "2021-11-16T10:25:58.863661Z",
"shell.execute_reply": "2021-11-16T10:25:58.864253Z"
}
},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle d_{y}^{2} = x_{1}^{2 x_{2} - 2} \\left(d_{1}^{2} x_{2}^{2} + d_{2}^{2} x_{1}^{2} \\log{\\left(x_{1} \\right)}^{2}\\right)$"
],
"text/plain": [
"Eq(d_y**2, x_1**(2*x_2 - 2)*(d_1**2*x_2**2 + d_2**2*x_1**2*log(x_1)**2))"
]
},
"execution_count": 39,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"from sympy import symbols, Eq, latex\n",
"x1, x2 = symbols('x_1 x_2',real=True)\n",
"d1, d2 = symbols('d_1 d_2',real=True)\n",
"y = x1**x2 \n",
"dy2 = (y.diff(x1))**2*d1**2 + (y.diff(x2))**2*d2**2 \n",
"Eq(symbols('d_y')**2, dy2.simplify())"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"We can turn this expression into something we can use numerically using _SymPy_'s `lambdify` function. We do that here for both `dy2` and `y` to evaluate our result "
]
},
{
"cell_type": "code",
"execution_count": 40,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:25:58.871214Z",
"iopub.status.busy": "2021-11-16T10:25:58.870060Z",
"iopub.status.idle": "2021-11-16T10:25:59.054443Z",
"shell.execute_reply": "2021-11-16T10:25:59.055021Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" 1.06 +/- 0.02\n"
]
}
],
"source": [
"from sympy import lambdify\n",
"ny = lambdify((x1,x2),y)\n",
"ndy2 = lambdify((x1,x2,d1,d2),dy2)\n",
"ry = ny(*x)\n",
"rdy2 = ndy2(*x,*dx)\n",
"nbi.print_result(ry,sqrt(rdy2))"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"We see that our numerical evaluation using `propagate_uncertainty` gave the same answer as by direct evaluation of the formulas. Behind the scenes, `propagate_uncertainty` uses a simple formula for evaluating the derivatives numerically \n",
"\n",
"$$\\frac{\\partial f(x_1,\\ldots,x_i,\\ldots,x_n)}{\\partial x_i} \\approx \n",
"\\frac{f(x_1,\\ldots,x_i+s_i,\\ldots,x_n) - f(x_1,\\ldots,x_i-s_i,\\ldots,x_n)}{2s_i}\\quad,$$ \n",
"\n",
"where $s_i$ is the step size normally set to $d_i$. However, if the step size is too small or too large, this approximation may not be stable. We can therefor supply another step size should that be needed. "
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"If any $x_i,x_j$ are correlated, then we must add \n",
"\n",
"$$\\frac{\\partial f}{\\partial x_i}\\frac{\\partial f}{\\partial x_j}\\delta_i\\delta_j\\rho_{ij}\\quad,$$ \n",
"\n",
"to the above sum. Here, $\\rho_{ij}$ is the correlation coefficient between the $x_i$ and $x_j$ \n",
"\n",
"\\begin{align*}\n",
"\\rho_{ij} \n",
"&= \\frac{\\sum_{k=1}^N (x_{i_k} - \\overline{x}_i)(x_{j_k} - \\overline{x}_j)}{\n",
" \\sqrt{\\sum_{k=1}^N (x_{i_k}-\\overline{x}_i)^2}\\sqrt{\\sum_{k=1}^{N}(x_{j_k}-\\overline{x}_j)^2}}\\\\\n",
"&= \\frac{c_{ij}}{\\sqrt{s^2_i s^2_j}}\\quad,\n",
"\\end{align*}\n",
"\n",
"where $c_ij$ is the covariance between $x_i$ and $x_j$ and $s^2_i,s^2_j$ are the variances of $x_i,x_j$, respectively. Since $\\delta_i^2=s_i^2$, and with the _Jacobian_ given by \n",
"\n",
"$$J_i = \\frac{\\partial f}{\\partial x_i}\\quad,$$ \n",
"\n",
"we can write up propagation of uncertainty in matrix form as \n",
"\n",
"$$\\delta^2 = J^T C J \n",
"= \n",
"\\begin{bmatrix}\n",
" \\frac{\\partial f}{\\partial x_1}&\n",
" \\frac{\\partial f}{\\partial x_2}&\n",
" \\cdots&\n",
" \\frac{\\partial f}{\\partial x_n}\n",
"\\end{bmatrix}\n",
"\\begin{bmatrix} \n",
" c_{11} & c_{12} & \\cdots c_{1n}\\\\\n",
" c_{21} & c_{22} & \\cdots c_{2n}\\\\\n",
" \\vdots & \\vdots & \\ddots \\vdots\\\\\n",
" c_{n1} & c_{n2} & \\cdots c_{nn}\n",
"\\end{bmatrix}\n",
"\\begin{bmatrix}\n",
" \\frac{\\partial f}{\\partial x_1}\\\\\n",
" \\frac{\\partial f}{\\partial x_2}\\\\\n",
" \\vdots\\\\\n",
" \\frac{\\partial f}{\\partial x_n}\n",
"\\end{bmatrix}\n",
"\\quad,$$ \n",
"\n",
"where $J$ is the Jacobian vector and $C$ is the covariance matrix. "
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"`propagate_uncertainty` can handle this case as well. Let us continue the example from above, with the additional information that \n",
"\n",
"$$\\rho_{12} = 0.4\\quad.$$ \n",
"\n",
"Our covariance matrix is then \n",
"\n",
"$$C = \\begin{bmatrix} 0.01 & 0.001\\\\ 0.001 & 0.0025\\end{bmatrix}\\quad,$$ \n",
"\n",
"which we pass to the function "
]
},
{
"cell_type": "code",
"execution_count": 41,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:25:59.066059Z",
"iopub.status.busy": "2021-11-16T10:25:59.065211Z",
"iopub.status.idle": "2021-11-16T10:25:59.071952Z",
"shell.execute_reply": "2021-11-16T10:25:59.072758Z"
},
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" 1.06 +/- 0.03\n"
]
}
],
"source": [
"rho = 0.4\n",
"c = [[dx[0]**2, rho*dx[0]*dx[1]],\n",
" [rho*dx[1]*dx[0], dx[1]**2]]\n",
"dy2 = nbi.propagate_uncertainty(lambda x:x[0]**x[1],x,c)\n",
"nbi.print_result(x[0]**x[1],sqrt(dy2))"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"Let us calculate the same symbolicly "
]
},
{
"cell_type": "code",
"execution_count": 42,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:25:59.094657Z",
"iopub.status.busy": "2021-11-16T10:25:59.093516Z",
"iopub.status.idle": "2021-11-16T10:25:59.146114Z",
"shell.execute_reply": "2021-11-16T10:25:59.152009Z"
}
},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle d_{y} = x_{1}^{x_{2}} \\left(\\frac{d_{1} d_{2} \\rho x_{1}^{x_{2}} x_{2}}{x_{1}} + d_{2}^{2} x_{1}^{x_{2}} \\log{\\left(x_{1} \\right)}\\right) \\log{\\left(x_{1} \\right)} + \\frac{x_{1}^{x_{2}} x_{2} \\left(\\frac{d_{1}^{2} x_{1}^{x_{2}} x_{2}}{x_{1}} + d_{1} d_{2} \\rho x_{1}^{x_{2}} \\log{\\left(x_{1} \\right)}\\right)}{x_{1}}$"
],
"text/plain": [
"Eq(d_y, x_1**x_2*(d_1*d_2*rho*x_1**x_2*x_2/x_1 + d_2**2*x_1**x_2*log(x_1))*log(x_1) + x_1**x_2*x_2*(d_1**2*x_1**x_2*x_2/x_1 + d_1*d_2*rho*x_1**x_2*log(x_1))/x_1)"
]
},
"execution_count": 42,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"from sympy import Matrix\n",
"rho = symbols('rho',real=True)\n",
"C = Matrix([[d1**2, rho*d1*d2],\n",
" [rho*d2*d1, d2**2]])\n",
"J = Matrix([[y.diff(x1)],[y.diff(x2)]])\n",
"Eq(symbols('d_y'),(J.T * C * J)[0])"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"Again, we will use `lambdify` to evaluate this numerically "
]
},
{
"cell_type": "code",
"execution_count": 43,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:25:59.167959Z",
"iopub.status.busy": "2021-11-16T10:25:59.165099Z",
"iopub.status.idle": "2021-11-16T10:25:59.195922Z",
"shell.execute_reply": "2021-11-16T10:25:59.197103Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" 1.06 +/- 0.03\n"
]
}
],
"source": [
"ndy2 = lambdify((x1,x2,d1,d2,rho),(J.T * C * J)[0])\n",
"dy2 = ndy2(*x,*dx,0.4)\n",
"nbi.print_result(x[0]**x[1],sqrt(dy2)) "
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"Similarly, we can evalutate the uncertainty on a function $f$ over some range $x\\in X$ with the parameters $p$ due to the uncertainty in the parameters $p$. \n",
"\n",
"Here, we will take \n",
"\n",
"\\begin{align*}\n",
" f(x) &= a+bx\\\\\n",
" a &= 1 \\pm 0.1\\\\\n",
" b &= 1 \\pm 0.2\\\\\n",
" x &\\in [0,1]\\quad.\n",
"\\end{align*}"
]
},
{
"cell_type": "code",
"execution_count": 44,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:25:59.215663Z",
"iopub.status.busy": "2021-11-16T10:25:59.214142Z",
"iopub.status.idle": "2021-11-16T10:26:00.716648Z",
"shell.execute_reply": "2021-11-16T10:26:00.717509Z"
},
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"data": {
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\n",
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AVfbJF+aHSKgLMYlUQn9zreGPB+pY3uPj3X43TdUJ/uKyfdx8ThDXJA7zQyTUhZgkYrE9BAKryra/udbwxr56lvX4eD9QS0tNgq9dvpebzgnisGmzyysZEupCVLhkMkIw+BRDQ+vLcl9QQ8Mf9jSwrMfH9lAN7e4431i4h+vPDuGwSpgfTUJdiAqVTo8zOPgyweBTgC67fUENDb/d1cjyHh+7ItVMqRvnm4t2c+3MMDYJ82OSUBeiwmhtMDy8Ab//UVKpwbIbN08b8JudHlb0+Ng7WMW0hhh/f9Uurj4zjNVidnWlT0JdiAoSi+3C73+UWGxH2Y2bpw14aUcTj/Z42T9URVfjGN+5ZieLZkQkzE9CzqGulGoHHgbmaK0XHOOYB4EuIATMBO7VWpf+ViFClLlkMkww+CRDQ7/Daq3F6ewqm3HzZFrxwvYmVm700ht1cUbTGN+9dgcLpw9gKY9LKCknc6d+BbAOmDvRh9nQ/xbQrLU2lFLrgNuAR0+3SCHExNLpGJHIi4TDvwTA6exEqfK4rU2kFc990MzKjV78I07Obhnl4eu3c1nnIGXy91FJyjnUtdZrlFKLj3PIGJAA6oBBoBbYOtGBSqn7gPsAOjo6ci1BCJGldZpo9I8EAitJpYaz4+YOs8vKSTyleOb9FlZt8hIadXBu6wgPLNzLxdOGJMzzIG9j6lrraHb45XGlVB9wANhxjGMfAR4BmD9/vjzGFuIkjI1tx+9fwfj4Huz2FlyuTrNLykksaeHpbS08vrmdyJiD2e3D/N3i3XRPiUqY51HeQl0pNRd4EOjWWqeUUj8CHgK+ma9zCDGZJRIBgsG1RKNvYLXWlc24+VjCwrr3Wlm9uZ3BcTvzfFG+c80u5vqGzS6tIp12qCulurTWe4ApQERrfahRcR8gYytCnKZ0eoxI5DnC4V8B1rIZNx+JW3lqaytPvNNONG5jwdQhll7YywXtI2aXZirDiJNIBFBKYbFU5f3rn8zsl0XAUsCrlPo28CMgDryaHWt/DvhU9g59EDgfeCC/5QoxeWidZmjodQKBxzCMMex2LxaL3eyyTmg4bmXtljbWbmljJGHj0o5Bll7Yy6zWUbNLM43WmlQqQjo9jNVaTXPzzdTXX4bD0Zb3c53Mg9L1wPoJPuo67L//4nQLEmKy01oTi31If/9y4vF92O1t2O3NZpd1QkMxG09saeMX77YxlrRyRdcAS7t7OatlzOzSTGMYcZLJAFqnqa4+C4/ny9TUnF/Qh9qy+EiIEhKP9xMMPsHw8NtYrfW4XDPMLumEBmI2Vm9u56mtrcRTFq6ckQnzM5om5xKVzF35AOl0FIvFhcdzA/X1V+B0eotyfgl1IUpAKjVMOPwMAwMvoJS9LB6ChkftPLa5nae3tZBMW7jqjAh3d/fS1ThudmmmMIwEyaQfrdNUVZ2Bx7OU2trZRW/RIKEuhIkMI8ng4O8IBlejdRyHw4dSpf3HMjhiZ9UmL796v4W0obh2ZpgvzOtlWkPc7NKKLnNXPkg6PYTF4qSxcQn19QtxOqeY9pdyaf/uEaJCaa0ZHd1Cf/8KkskAdnsbVmv+Z0LkU/+wg1WbvPz6/WYM4Iazwnx+Xh++uskX5oaRzI6VJ3G5Omlru4va2rlYreZv1C2hLkSRjY/vzW7y/F5ZbPJ8cMjJyk1env+wCQtw4zkh7prbR7s7YXZpRaW1Jp2OkkoNoJSDhoZFNDRcmd0KsHSGyiTUhSiSZHKAUOgpBgdfxWKpLvlNnvcPOlmx0cdL25uwWTR/cm6Qu+b00VKbNLu0otI6RTLpxzCSOJ1TaWn5DG73PKzWarNLm5CEuhAFlk6PMzDwEqHQUwAlv1nFngEXy3t8vLrTg91qcPsFfu6c3U9TzeQJ88xd+TCpVASlbNTXL6Sh4UpcrtJ/gC2hLkSBaG0Qjb5FILCKVGoIh8NX0k23doarWN7j47e7GnHaDO6c088ds/tprEqd+BdXiMxdeQDDSOBwePF6v4zbPR+rtcbs0nImoS5EnmUWD+3A73+U8fHd2aZbXWaXdUwfBqtZ3uPjd3saqXGkuLu7j9sv6KfelTa7tKJJpQ7dlVuoq7uMxsbFuFwzSv6ufCIS6kLkUSLhJxBYw/DwWyXfdOs9fw3Le3y8sa+BWkeKL114kNsu8ON2To4w1zr90V253d5Ce/s9uN3zsdncZpd2WiTUhciDVGqESOTXhMO/xmKxlXTTrS39tSzb4OPtA/XUuZLcu+AAt57vp8ZhmF1aUaTTo6RSIUDhdl9MY+NVVFWdWbLfr5MloS7EaTCMJENDvycQeBzDiGc3qyi9pltaw+Y+N8s2+NjYW0eDK8mfXbyfT58XoMpe+WGutUEyGcQwYtjtHlpbP09d3UXYbPVml5Z3EupCnILM4qF38fsfJZHox25vw+EovcVDWsOGg3Us3+DjnX43nuoEf37pPm6ZFcQ1CcI8nR4jmQySuSufR2PjEqqrzyrp2UenS0JdiJM0Pr6fQOAxRke3YLN5SvIhqNbw1v56lm3w8V6glpaaBF+7fC+fOieI01bZm41l7srDGMYoNls9ra2foa7uUux2j9mlFYWEuhA5SiYHCYd/ycDAK1itVTidpbd4SGv4w94Glvf4+CBYQ1ttnL9auIcbzg7hsFZ2mBvGeHbpvqam5nw8nuuorp6FxTK5Ym5yXa0QpyCdHmdw8DeEQk+itc4uCy+tH98NDa/tbmR5j4+d4Wp8deM8uGg3180MY6vgMD9y84kampo+TX39pTgcrWaXZhoJdSGOQWuD4eEN+P2PkkoNZh+CFreN6omkDVi/y8PyHi97BqqZVh/jW1ft4pozw1grYzLHhA5vc1tdfTYezw3U1JxX0ou7ikVCXYijHFo8FAisIhbbic3WXHLj5mkDXt7RxIqNXvYPVtHZGOPb1+xk8YxIxYb5kW1uD20+cTlOp8/s0kqKhLoQh8nsPLSG4eE/YrW6S27xUCqteHF7Jsx7oy5meMb47rU7WDh9AEvplJlXmTa3frRO4XJNp63tC9TWzi6JNrelSEJdCCCVihIOP0sk8jwWi73kFg8l0ornP2hm5SYv/cNOZjaP8j+v385lnYMVGeafbHN7VbbN7dSS+ku2FEmoi0nNMBIMDq4nGFyD1snsjjWl88cikVI8834LqzZ5CY46mNU6wtcu38slHUNUYraVW5vbUlQ6v3uFKKLMQ9CNBAKPkkxGcDjasVhK58f58aSFX21r4bHN7YTHHJzfPsyDi3Yzf2q0IsM801ArnG1zezkNDYvLos1tKcop1JVS7cDDwByt9YJjHHM2cBcQAxYB39Vav5WvQoXIl7GxHQQCKxkb21FyHRRjSQu/fK+Vxze3MxCzM9cX5R+u3sVc33DFhfnhDbUcjlba27+UbahVa3ZpZS3XO/UrgHXA3Ik+VJlJu/8C3KK1NpRSy4BjNmFWSt0H3AfQ0dFxMvUKccqO7KDoLqmdh0YTFp7a2sbqd9qIjtuZP3WIpd29zPaOmF1a3qXToySTIZRSuN0X0dh4dUU11DJbTqGutV6jlFp8nEMWAAr4S6VUNRAG/vM4X+8R4BGA+fPnV+7KCFESUqlhIpFnCYefL7kOiiNxK2vfbWPtljaG4zYu7hjknu5ezm0bNbu0vMos3Q9hGGPYbI20tn6OurqLsdsbzC6t4uRrTL0TuBS4S2s9pJRaASSAn+fp6wtx0jIPQX+bfQiawOn0lcxD0KFxK2u3tPPku62MJmxc3jXA0u5ezm4ZM7u0vDq0dB80NTWzaWy8lpqaWSW3IreS5Ot3eBR4X2s9lH39O2AxEurCBKX8EHQwZmP1O+08tbWVWNLKldMjLO3u5czmmNml5c3ES/cvw+FoMbu0SeG0Ql0p1aW13gO8CTQppaxa6zSZO/cP81CfECclFtuJ37+SWGx7Sa0EjYzZeHyzl1++10I8ZeGqMyLc3d3HdE/lhPnHS/cNqqtn4vF8hZqa80uyv3wly3X2yyJgKeBVSn0b+BEQB15VSi3WWu9RSv0t8K9KqSDQAny/UEULcbREIkAwuIZo9I3sStDSeAgaHLXz2CYvv9rWQspQXHNmmLvn9dHROG52aXmRWSQ0RCo1iMXipLHxOhoaFsrSfRPl+qB0PbB+go+6DjvmF8Av8lOWELnJPAT9NeHwc9mHoF0l8RDUP+xg5SYvv36/GQO4bmaYL8zrY0p93OzS8uLwRUIuVyetrZ+jtnauLN0vAaXx1EiIk1SqD0F7o05WbvTy/IdNANxwdojPz+3DW5cwubL8yCwSiqCUlfr6hTQ0LMLl6iyJn4pEhvl/CoQ4CZmHoJuyD0HD2O1tWK3mbyO3f9DJoxt9vLi9CatFc/OsIHfN7ae1tvzD/ONFQnEcjjba278oi4RKmIS6KBuZh6CriMU+LJmHoHsHXKzo8fHKTg82i+a28/3cOaef5pqk2aWdtk8uErqGqqozSmJ4SxybhLooeZmHoE8Sjb6OxVJbEg9Bd4WrWN7jY/2uRpw2gzsu6Oezc/rxVB9zIXVZOHKRUIMsEipDEuqiZGUegj5HJPJrwFoSK0G3h6pZvsHHa3saqbanuWtuH3fM9tNQVd5hfvQiocz+nufIIqEyJKEuSo5hxBkYWE8otBatk9jtXtPnOm8L1LB8g4/X9zVQ40hxT/dBbr/AT50rbWpdpyOzSGiAdDqaXST0J9TXXy6LhMqchLooGVqniUb/SCDwWHZPUPNXgr7bX8vyHi9v7W/A7UzxlQUHuPW8ALXO8g3zw3cSqqo6E4/ni9TWXiD7e1YICXVhOq01Y2Pb8PtXEo/vw2Yzvx3u5t5alvX46DlYT70ryX0X7+fT5waodhim1nWqMouEhkmnBwBbdiehRdlNQWQ6YiWRUBemGh/fRyCwmtHRLVit9bhcM0yrRWvoOehmWY+Pd/rqaKxK8tVL9nHLuUGq7OUa5mkSiQBax3E4vLS0fAW3+0LZSaiCSagLUyQSIUKhdQwN/RartdrUDZ61hj/ur2NZzxS2+mtprk5w/2V7uXlWEKetPDtDp9NjJJPB7HTEiw+bjih35ZVOQl0UVSo1wsDAC4TDvwIsOJ0dps2w0Bpe31vPsp4pfBCsobU2zgNX7OHGs0M4yjDMMw8+M9MRrdZ6WlvvpK7uEpmOOMlIqIuiyCzrf41g8Ins9mXmzWgxNPxudyMrNnrZHqrB6x7nb67czXVnhbFbyy/MDSNOIhEA0tTUnI/Hcz3V1bOwWOSP92Qk33VRUJll/T0EAitJJiPY7W04HOYs608bsH6XhxUbveyOVDO1fpy/XbyLJWdGsJVZmGfuygdJp4ewWqtobr4pOx2xzezShMkk1EVBaK2JxT7E73+U8fE9ps5oSRvwyk4PK3p87BusorMhxj9cvZOrzohgLbMV70d2R+yire0LuN1zsFicZpcmSoSEusi78fEDBINPMDKyCau1zrRl/am04qUdmTA/GHUx3TPGQ0t2cOX0gbIL80x3xDBK2aivv5LGxkXZ5xHy4FMcSUJd5E0yGSEU+iWDg69isbhMm9GSTCue/7CJlRu99A27OLNplO9ft53LuwaxlFEGZvqwBDCMcez2VtrbvyTdEcUJSaiL05ZOjxKJvJid0QJO5zRTZrQkUopnP2hm1SYvgREn57SM8JeXf8glHUOU0w1tOh0jlQoC4HZfSGPjEqqqZpre90aUBwl1ccoMI8nQ0O8JBldn7ybbTVlqHk8pnt7WyuOb2gmNOTivbZi/vnIPC6ZGyybMj9ys2U1z823U11+G3e4xuzRRZiTUxUn7eKOKlSSTIez2Nuz21qLXEUtaePq9Fh7b7GUgZmeON8q3rt7FPN9w2YT54X1YqqvPks2axWmTUBc5y8xo2UEgsIpYbCc2W5MpM1rGEhae2trK6nfaGRq30z1liIe6+5jrGy56Lafq4wefdunDIvJKQl3kJB7vJRhcw/Dw29kZLcV/CDoSt/Lku62s3dJONG7jommDLO3u4/z2kaLWcao+fvAZx+Foxev9Mm73fKzWGrNLExVEQl0cVzIZJhR6OjujxWnK9MTouJU1W9p48t02RhM2LuscYGl3H+e0jha1jlN1aAMKrTVu94V4PNfKg09RMDmFulKqHXgYmKO1XnCc46qAN4EXtNZ/k58ShRkyuw69QCTyLKBMmdEyGLPxxDtt/GJrG7GklYXTIyzt7mNm81hR6zgVn9yA4k9paLgcu73J7NJEhcv1Tv0KYB0w9wTHPQxsPNEXU0rdB9wH0NHRkWMJohjS6XEGB39DKPQUhpE0pUdLZMzG6s3trHuvlXjKwuIzItw9r48ZTbGi1nEqtE6RSPjROpndgOIeamtnywYUomhyCnWt9Rql1OLjHaOUWgr8HpgNHHd1hNb6EeARgPnz55dX040KZRhJotHXCQafIJUaNmXXodConcc2tfP0tlZShuLqMyLc3d1LZ+N4Ues4Fen0CMlkGKWsNDRcSUPD4uxPN/LgUxRXXsbUlVLnArO01n+vlJqdj68piiMzPXEjgcBjJJMB7PZWXK7iDhH4hx2s2tTOsx+0kDYU180M8YXuPqbWx4tax8nKPPgMYhgx7PZm2truoa5ugaz4FKbK14PSW4FxpdTfkRmqcSilHtBa/2uevr7Is8wWcu8TCKxifHxvdnri9KLW0Bd18OhGL89/2AzA9WeF+Py8fnx1pR3mhhEnmfQDmpqauXg811FdfbY8+BQl4bRCXSnVpbXeo7X+wWHvuYBaCfTSFYvtIRh8gtHRd02ZnnhgyMmjPV5e2N6MVWluOifIXXP7aXMnilbDyTqy1W01TU23UF9/BQ5Hi9mlCXGEXGe/LAKWAl6l1LeBHwFx4FWl1GKt9Z7scbcDV5K5U79La72qMGWLUxGP9xEK/YJo9E0sluJvIbdvwMWKjV5e3tGEzaK59Tw/d87tp6UmWbQaTtaRrW47pdWtKHm5PihdD6yf4KOuo45bC6w9/bJEPiWTEcLhZxgcfAWl7DidnUUdKtgdqWJ5j5dXd3pw2gzuuKCfz87px1OdKloNJyudHiWVCgFW6usvo6HhalyuTnnwKUqeLD6qYJn9QD/unuhwTC3qXPMdoSqW9fh4bbeHKnuau+b2c8fsfhqqSjPMM0MsYdLpEWy2RlpbP09d3cXYbHVmlyZEziTUK5BhxBkYWE8o9GR2Sbq3qPOk3w/UsLzHyx/2NlLjSLG0+yCfucBPnStdtBpOxuFNtWpqZuHx3Eh19bmyx6coS/K7toIYRopo9E2CwdWkUkNFn2u+tb+G5T0+3tzfgNuZ4svzD3Db+QFqnaUZ5pm55aFsU62rs7sJTTG7LCFOi4R6BdDaYGRkM37/quxc8+aidk/c3FvL8h4fGw7WU+9K8n9dtJ9PnxegxmEUrYZcZeaWhzCMMez2Ztrbv0hd3UXSVEtUDAn1MnZoc+dA4DFisV3YbJ6ihbnWsLHXzbINPjb31dFYleSrl+zjlnODVNlLL8wNI5EdYklTWzsbj+d6qqvPMWWHJiEKSUK9TI2P7yMYXMPIyGasVnfRpidqDX88UMeyDT62+t00Vyf4i8v2cfM5QVwlGOapVJRUKoLF4qCx8bps3/J2s8sSomAk1MtMIuEnFHqKoaE/YLFUFTXM39hXz7INPt4P1tJaG+frV+zhU2eHcNhKq33P4cv3HY52vN57s33Lq8wuTYiCk1AvE5m55s8yMPAyStmKNtfc0PD7PQ0s7/GxPVRDuzvOX1+5m+vPCmO3llaYZ5bvBwCD2tp5NDZeR3X1WbJ8X0wqEuolLpUaIhJ5nkjkBUBntzwr/LctbcBvdzeyosfHrkg1U+rG+dvFu1hyZgRbCYW51pp0OkoqNYDVWkVT003U1y+U5fti0pJQL1GZhUMvE4n8Cq3T2O3F6WueNuA3Oz2s6PGxd7CKjoYYf3/1Tq4+I4K1hG54tU5/tDWc0zmF1tY7qK3txmotbrtgIUqNhHqJSadjDA6+Sii0rqgLh9IGvLi9iUc3+jgw5GK6Z4zvXLOTRTNKK8wPbQ0H4HYvoLFxCVVVZ8ryfSGyJNRLhGHEGRz8PaHQWtLpMRyOtqIsHEqmFS982MTKTV56oy7OaBrje9fu4IrpA1hKJCeP7JB4aGu4K7DbPWaXJkTJkVA3WWbHoTcIBteQSg1ht7dhtxd+PDiRVjz3QTMrN3rxjzg5u2WUH1z/IZd2DlEqN72HD7F83CFxrmwNJ8RxSKibROs00ejbBIOrSSZD2R2Hugp+3nhK8cz7Laza5CU06uDc1hG+sXAPC6ZFSybMjxxiuQSPZwku13QZYhEiBxLqRZbZPm4TweBqEok+bLbmouw4FEtaeHpbC49vbicy5mB2+zB/t3g33VNKI8yPnMVSLUMsQpwiCfUi0VozOrqVYHB1dvu4xqKE+VjCwrr3Wlm9uZ3BcTvzfFG+c80u5vqGC37uXHy8UGgsO4vls7jd3bIJhRCnSEK9wD7uz7KaWGwHVmt9UVaBjsStPLW1lSfeaScat7Fg6hBLL+zlgvaRgp43Vx/3YjFwu+fh8dxAVdVMGWIR4jRJqBeI1prx8d0Eg2uze4EWpz/LcNzK2i1trN3SxkjCxqUdgyy9sJdZraMFPW+u0ukRUqkwStnxeG6goWERDker2WUJUTEk1Asg02zrF4yM9GCx1BQlzIdiNp7Y0sYv3m1jLGllYdcAd3f3clbLWEHPm4vMlMQQ6fQIdnsLbW2H2t1Wm12aEBVHQj2PMhs7ryMafQOLxVWUMI+M2Vj9TjvrtrYST1lYNCMT5mc0xQp63lxonSKR6M/uKHQeHs+N1NTMkna3QhSQhHoeJBJBwuGnGRx8DYvFjtPZUfAmUuFRO49tbufpbS0k0xauOiPC3d29dDWOF/S8uUinx0ilgoCVhoYraWy8RnYUEqJIcg51pVQ78DAwR2u9YILPz8h+3gNMBcJa6+/nq9BSlOmc+GsGB18GLDidhd/YOThiZ9UmL796v4W0obh2ZpgvzOtlWkO8oOc9kcwQywDpdBSbrZ6Wlruor78Um81tal1CTDYnc6d+BbAOmHuMzz3AY1rrdQBKqfeUUs9orTecXomlJ5WKEom8QCTyHFprnE5fwTsn9g87WLnRy3MfNGMAN5wV5vPz+vDVmR3maZJJP4aRoKpqBk1NX6am5gLZtFkIk+T8J09rvUYptfg4n//xqLcswIRTLpRS9wH3AXR0dORagulSqWi2c+KzReuceHDIyaMbvbywvQkLcOM5Ie6a20e7O1HQ857I4as+6+oupbHxWlyuTpmSKITJCnI7pZS6FXhea/3+RJ9rrR8BHgGYP39+6TTnPoZPhnl7wfuP7Bt08ehGLy9tb8Jm0fzJuUHumtNHS22yoOc9nqNXfTY330p9/RXY7Y2m1SSEOFLeQ10pdRVwFfBAvr92sZkR5rsjLlZs9PHqTg92q8HtF/i5c3Y/TTVmhrmRbawVw+mcRmvr57KNtWTVpxCl5rRDXSnVpbXek/3vm4CFwNcBr1KqU2v9+umeo9gOD3PDSONwFD7Md4SrWNHj47e7GnHaDO6c088ds/tprEoV9LzHYxhJksl+tE7jdnfLqk8hysDJzH5ZBCwlE9bfBn4ExIFXs2PtTcDjwNvAb4Aa4KdA2YS6GWH+QbCa5T0+fr+nkRpHii/M6+MzF/ipNzHM0+kYqVQApWw0Ni6hsfFqHI420+oRQuTuZB6UrgfWT/BRV/bfe4Da0y+p+MwI8/f8NSzv8fHGvgZqHSm+dOFBbrvAj9uZLuh5jyUzXj5EKjWI1eqmpeVO6usvlymJQpSZST3vzIww39JXy7IeH28fqKfOmeLeBQe49Xw/NQ6joOc9Fq31UV0SPy8bUQhRxiZlqGfC/BUikWeKEuZaw+Y+N8s2+NjYW0eDK8mfXbyfT58XoMpuVph/vIS/tnY2TU03UVV1loyXC1HmJlWomxHmGw7WsWyDjy39bjzVCf780n3cMiuIy6QwN4xxEgk/SlloaFhEY+MSnE6fKbUIIfJvUoS6GWH+5v56lm/w8V6glpaaBF+7fC+fOieI02bOtPxUKkoqFcFqraal5XYaGhZis9WbUosQonAqOtRTqeHsmHnxwvz3extYvsHHh6Ea2mrj/NXCPdxwdgiHtfhh/nHL21EcjnZ8vvtwuy+U+eVCVLCKDPVih7mh4bXdjSzv8bEzXI2vbpwHF+3muplhbKaEeZpksh/DSFBTcy5NTbdQXX1OwTtHCiHMV1Gh/nGYP4thpAoe5mkD1u/ysLzHy56BaqbVx/jWVbu45swwVhPy0zDiJJN+AOrrr8j2Y5lW/EKEEKapiFDPhPmhMfPihPnLO5pYsdHL/sEqOhtjfPuanSyeETElzFOpYVKpMBZLFU1Nf0pDw0LpxyLEJFXWoV7sME+lFS9sb+LRjV56oy5meMb47rU7WDh9AEuRZwJmxssjpNNR7PYWvN6v4HZfhNXqKm4hQoiSUrahbhhxdu/+NqnUcMHDPJFWPP9BMys3eekfdjKzeZT/ef12LuscNCHMD+9fPpPm5vuoqTlXtogTQgBlHeoJ0ulhXK7C9WNPpBTPvN/Cqk1egqMOZrWO8LXL93JJxxDFXqNjGEkSiX5AU1d3CR7PddK/XAjxCWUb6oU0nrTwq20tPLa5nfCYg/Pbh3lw0W7mT40WPcwPb67V1HQDDQ1X4XA0F7cIIUTZkFA/TCxpYd3WVla/085AzM5cX5R/uHoXc33DRQ/zQw8/rdYaWlo+S339FdJcSwhxQhLqwGjCwlNb21j9ThvRcTvzpw6xtLuX2d6RotaRefg5SDo9mH34+T+oq1sgi4WEEDmb1KE+Erey9t021m5pYzhu4+KOQe7p7uXctgm3Vi2YjzsljuJydeH1fona2tny8FMIcdImZagPjVtZu6WdJ99tZTRh4/KuAZZ293J2y1hR6/h4JkucmpoLaG6+RTolCiFOy6QK9cGYjdXvtPPU1lZiSSuLZkS4u7uXM5tiRa3j423iDOrrL8XjuaGgs3iEEJPHpAj1yJiNxzd7+eV7LcRTFq46M8Ld83qZ7hkvah0ft7210th4LY2N1+BwtBS1BiFEZavoUA+O2nlsk5dfbWshZSiuOTPM3fP66Ggsbpin0yMkk6HD2t5eic1WV9QahBCTQ0WGun/YwcpNXn79fjMGcN3MMF+Y18eU+njRajh8z0+bzYPX+2Xc7otlGb8QoqAqKtR7o05WbvTy/IdNANx4dojPz+uj3Z0oWg2ZmSwhDGMEp3MabW1Lqa2dg8VSUf+rhRAlqiKSZv+gk0c3+nhxexNWi+aWWUE+N7ef1tpihrlx2EyWQz3Mz5Ye5kKIosop1JVS7cDDwByt9YJjHLMEuA0IAFpr/b28VXkM+wbdrH53Bq/s9GC3Gtx2vp875/TTXJMs9Kk/cmgmCxi43RfT1HQjTmeHTEsUQpgi1zv1K4B1wNyJPlRKVQM/A87TWseVUmuVUtdorV/OT5lHSqUNvv74Np7dci1Om8Eds/v57Ox+PNWpQpxuQoYRJ5HoRykrDQ3X4PFcg8PRVrTzCyHERHIKda31GqXU4uMccimwV2t96Enk74GbgAlDXSl1H3AfQEfHyc/PtlktOKyKO2d/wOfmxqivKl6Yp9NjJJMBLJYqWlpuy85kkQ2chRClIV9j6q3A8GGvo9n3JqS1fgR4BGD+/PmntInn//rMOezY8X9wOouzaOfjaYlu2truob7+UqzWqqKcWwghcpWvUA8Ah7cQrMu+V/ZSqSipVBibrQmv917q6i6SBltCiJJ1WqGulOrSWu8BXgc6lVLO7BDM5cD/zkN9pjiyW2IbPt+f43Z3Y7HYzS5NCCGOK9fZL4uApYBXKfVt4EdAHHhVKbVYa71HKfVV4N+UUkHgnUI9JC2kw/f9dDqn0d7+RdzuOdItUQhRNnJ9ULoeWD/BR12HHfMi8GJ+yiquw1vfVlWdSXPzn2X3/ZQ55kKI8lIRi49OVWbBUADDiFFTcx7NzZ+W1rdCiLI2KUM9E+b9GEac2tpumptvweWaLmEuhCh7kyrUtU6TSPSjdZK6uktoaroJl2ua2WUJIUTeTIpQ1zqVDXODhoYr8HhuxOn0ml2WEELkXUWHumEksn1ZLDQ0XI3Hc61sSiGEqGgVGeqH+rJYLDY8nptobLwau73R7LKEEKLgKirU0+kYyaQfi8WV7cuySHYYEkJMKhUR6un0KMlkEKu1htbWz9PQcDlWa43ZZQkhRNGVdahrnWJ8fA82Wz3t7V+iru4S2S5OCDGplW2oWywOamouoK7uMurqFmCxOMwuSQghTFfGoe6ko+NBs8sQQoiSIs1NhBCigkioCyFEBZFQF0KICiKhLoQQFURCXQghKoiEuhBCVBAJdSGEqCAS6kIIUUGU1trcAjIbVe89xV/eDITyWE45kGueHCbbNU+264XTu+ZOrfWEfcRND/XToZR6W2s93+w6ikmueXKYbNc82a4XCnfNMvwihBAVREJdCCEqSLmH+iNmF2ACuebJYbJd82S7XijQNZf1mLoQQogjlfuduhBCiMNIqAshRAWRUBdCiAoioS6EEBWk5LezU0otAW4DAoDWWn/vVI4pJye6HqXUGcDDQA8wFQhrrb9f9ELzKNfvoVKqCngTeEFr/TdFLDHvcvy9fTZwFxADFgHf1Vq/VdRC8yjHa34Q6CKz2nImcK/WOlbMOvNJKdVO5s/rHK31gmMck78M01qX7D9ANbADcGZfrwWuOdljyumfHK95AfDpw16/B1xodu2FvObDjv0R8P8B/6/ZdRfh+2wFngEs2ddeoMXs2gt8ze1A5LBrXgd8wezaT/O6PwPcArx9qv9fTuafUh9+uRTYq7WOZ1//HrjpFI4pJye8Hq31H7XW6w57ywKMFqm+Qsjpe6iUWpr9bHcRayuUXK55AaCAv1RKfYtMMJRzf5RcrnkMSAB12de1wNbilFcYWus1wPBxDslrhpX68EsrR/7PiGbfO9ljyslJXY9S6lbgea31+4UurIBOeM1KqXOBWVrrv1dKzS5mcQWSy/e5k8wf+Lu01kNKqRVkAu/nRakw/054zVrraHb45XGlVB9wgMxdbCXLa4aV+p16AHAf9rou+97JHlNOcr4epdRVwFXAXxWhrkLK5ZpvBcaVUn8HXAFcpJR6oDjlFUQu1xwF3tdaD2Vf/w5YXPjSCuaE16yUmgs8CNyktf4SmZ9MHipSfWbJa4aVeqi/DnQqpZzZ15eTGWNEKdV1omPKVC7XjFLqJuB64OtAu1Lq0iLXmU8nvGat9Q+01t/XWv8zmXB7S2v9rybUmi+5fJ/fBJqUUtbs607gw2IWmWe5XPMUIKK1TmVf9wGuYhZZLIXKsJJvE6CUupbMg4YgkNRaf08pZQF2AYu11nsmOsa8ik/fia4ZaALWA29nf0kN8FOt9c+LX21+5PJ9zh53O/AXgIPMNa8yqeTTluPv7VuBq7PHdAB/qct7JsiJfm/vB/4NGAcGgfOBB7TWfaYUnAdKqUXAPcANwP8h87A/ToEyrORDXQghRO5KffhFCCHESZBQF0KICiKhLoQQFURCXQghKoiEuhBCVBAJdSGEqCAS6kIIUUEk1IU4jFLqIqXUNqXUJdnX31JKTTe7LiFyJYuPhDiKUuoGMv1G1gK/0lp/YHJJQuRM7tSFOIrW+jnAA8Ql0EW5kTt1IY6ilPoG4Cdzt36+1jppcklC5Ezu1IU4jFLqfuAVrfWjZLrn/ddh3fOEKHlypy6EEBVE7tSFEKKCSKgLIUQFkVAXQogKIqEuhBAVREJdCCEqiIS6EEJUEAl1IYSoIP8/MJntd6rtINQAAAAASUVORK5CYII=\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"def f(x,a,b):\n",
" return a + b * x \n",
"\n",
"a, b, da, db = 1, 1, .1, .2 \n",
"x = linspace(0,1,11)\n",
"y = f(x,a,b)\n",
"dy2 = nbi.propagate_uncertainty(lambda p : f(x,*p),[a,b],[da,db])\n",
"\n",
"from matplotlib.pyplot import plot, legend\n",
"\n",
"plot(x,y,label='$f(x)$')\n",
"fill_between(x,y-sqrt(dy2),y+sqrt(dy2),label=r'$\\delta f(x)$',\n",
" color='y',alpha=.5)\n",
"xlabel(r'$x$')\n",
"legend();"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"We will use this feature later in the function `plot_fit` "
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Curve fitting "
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"Curve fitting is procedure by which we adjust parameters of a function so that it comes closest possible to the data. Note, we say we \n",
"\n",
"> fit a function to data \n",
"\n",
"_not_ the converse (_fit data to a function_), since data by definition is _true_ and the function is our _hypothesis_.\n",
"\n",
"In general, there are three types of curve fitting \n",
"\n",
"- Maximum-Likelihood fit of $f$ to observed samples (not binned) \n",
"- Linear _least squares_ fit of $f$ to a distribution of observations (typically binned) \n",
"- Non-linear _least squares_ fit of $f$ to a distribution of observations (typically binnned) \n",
"\n",
"We will give a few more details on each type of fit below. \n",
"\n",
"[_SciPy_](https://scipy.org) and _NumPy_ provides a number of ways to perform curve fits. \n",
"\n",
"- For Maximum-Likelihood fits we can use `scipy.optimize.minimize` \n",
"- For linear least squares we can use `numpy.linalg.lstsq` \n",
"- For non-linear least squares we can use `scipy.optimize.curve_fit` "
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"Each of these have their own caveats and thus `nbi_stat` provides \n",
"\n",
"- `mle_fit` for Maximum-Likelihood fits \n",
"- `lin_fit` for linear least squares fits \n",
"- `lsg_fit` for non-linear least squares fits (aliased to `curve_fit`)\n",
"\n",
"as well as the unified interface `fit` which can perform all of the above. In general, we want the fit procedure to yield the values of the adjusted parameters $p$ _and_ the uncertainties $\\delta p$ on these. The uncertainties of the parameters $p$ are given by the diagonal of the _covariance matrix_ (or inverse Hessian matrix) of the fit. The off-diagonal elements represents the _correlation_ between the parameters. Thus, for each type of procedure we want to get two outputs \n",
"\n",
"- `p` the adjusted parameter values \n",
"- `cov` the covariance matrix of the parameters \n",
"\n",
"The three `nbi_stat` functions mentioned above, as well as the interface `fit`, all return these values. \n",
"\n",
"Let us look at some examples. "
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"## `lin_fit` \n",
"\n",
"A linear function, for the purpose of curve fitting, is a function that is _linear in the parameters $p$_. That is, any function that we can write on the form \n",
"\n",
"$$f(x) = \\sum_{i=1}^{n} p_i f_i(x)\\quad,$$ \n",
"\n",
"where _non_ of the $n$ $f_i$ depend on $p$. Note, we have made no claim about linearity in terms of the independent variable $x$ - that is not relevant to curve fitting. \n",
"\n",
"For linear functions there exists an _exact_ solution to curve fitting (see also [Statistics Overview](https://cholmcc.gitlab.io/nbi-python/statistics/#Statistik)) which is calculated by `lin_fit`. That function expects the function to fit to the data to be given in terms of the term functions $f_i$. "
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"Let us consider the function \n",
"\n",
"$$f(x;a,b) = a + bx\\quad,$$ \n",
"\n",
"with the free parameters $a$ and $b$. Let us fit that to some generated data. First, we generate our data and take a look at it."
]
},
{
"cell_type": "code",
"execution_count": 45,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:26:00.734768Z",
"iopub.status.busy": "2021-11-16T10:26:00.733721Z",
"iopub.status.idle": "2021-11-16T10:26:02.302330Z",
"shell.execute_reply": "2021-11-16T10:26:02.301214Z"
}
},
"outputs": [
{
"data": {
"application/pdf": 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\n",
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"x = linspace(0,1,11)\n",
"e = normal(.5,.1,size=len(x))\n",
"y = 5*x + 10 + normal(0,.5,size=len(x))\n",
"errorbar(x,y,e,fmt='o',label='Generated data')\n",
"legend();"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"We perform our linear fit to the data and print out the resulting parameter values and uncertainties. Note, we specify our function in terms of the individual term functions $f_i$, which are \n",
"\n",
"$$ f_a(x) = 1\\quad f_b(x) = x$$"
]
},
{
"cell_type": "code",
"execution_count": 46,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:26:02.314903Z",
"iopub.status.busy": "2021-11-16T10:26:02.307356Z",
"iopub.status.idle": "2021-11-16T10:26:02.330240Z",
"shell.execute_reply": "2021-11-16T10:26:02.331407Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"a=9.5 +/- 0.2\n",
"b=5.5 +/- 0.4\n"
]
}
],
"source": [
"from numpy import ones_like,diagonal\n",
"f = [lambda x: ones_like(x), lambda x : x]\n",
"p, cov = nbi.lin_fit(f,x,y,e)\n",
"for pv, pe, pn in zip(p,sqrt(diagonal(cov)),['a','b']):\n",
" print(nbi.format_result(pv,[pe],name=pn,expo=None,latex=False))"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"We can use the function `format_data_table` to print out the parameters "
]
},
{
"cell_type": "code",
"execution_count": 47,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:26:02.340879Z",
"iopub.status.busy": "2021-11-16T10:26:02.339624Z",
"iopub.status.idle": "2021-11-16T10:26:02.352067Z",
"shell.execute_reply": "2021-11-16T10:26:02.354377Z"
}
},
"outputs": [
{
"data": {
"text/latex": [
"$\\begin{array}{|c|c|}\n",
"\\hline\n",
"Fit&\\mathrm{Found}\\\\\n",
"\\hline\n",
"a&9.46\\pm0.05\\\\\n",
"b&5.5\\pm0.2\\\\\n",
"\\hline\n",
"\\end{array}$"
],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"out = [[(pv,pe)] for pv,pe in zip(p,diagonal(cov))]\n",
"display(Latex(nbi.format_data_table(out,rows=['a','b'],title='Fit',\n",
" columns=[r'\\mathrm{Found}'])))"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"## `chi2nu` \n",
"\n",
"To evaluate the _goodness-of-fit_ of a least-squares (linear or non-linear) we must evaluate \n",
"\n",
"\\begin{align*}\n",
" \\chi^2 &= \\sum_{i=1}^{N} \\frac{\\left(y_i - f(x_i;p)\\right)^2}{\\delta_i^2}\\\\\n",
" \\nu &= N-n\\quad,\n",
"\\end{align*}\n",
"where $n$ is the number of parameters $p$. \n",
"\n",
"This is the _square_ in least square - the $\\chi^2$, and $\\nu$ is the number of degrees of freedom (sometimes denoted n.d.f. or similar). The module `nbi_stat` defines the function `chi2nu` to evaluate this "
]
},
{
"cell_type": "code",
"execution_count": 48,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:26:02.363725Z",
"iopub.status.busy": "2021-11-16T10:26:02.362596Z",
"iopub.status.idle": "2021-11-16T10:26:02.375023Z",
"shell.execute_reply": "2021-11-16T10:26:02.374150Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"chi^2: 5.7\n",
"nu: 9\n"
]
}
],
"source": [
"from numpy import dot, sum \n",
"\n",
"ff = lambda x,*p : dot(p, [fi(x) for fi in f])\n",
"chi2, nu = nbi.chi2nu(x,y,ff,p,e)\n",
"print(f'chi^2: {chi2:.1f}\\nnu: {nu}')"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"As a rule-of-thumb, we say \n",
"\n",
"$$\\chi^2/\\nu \\approx 1\\quad,$$ \n",
"\n",
"signifies a good fit. "
]
},
{
"cell_type": "code",
"execution_count": 49,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:26:02.381921Z",
"iopub.status.busy": "2021-11-16T10:26:02.380898Z",
"iopub.status.idle": "2021-11-16T10:26:02.392840Z",
"shell.execute_reply": "2021-11-16T10:26:02.393846Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"chi^2/nu: 0.63\n"
]
}
],
"source": [
"print(f'chi^2/nu: {chi2/nu:.2f}')"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"In this example we see $\\chi^2\\nu < 1$ which typically indicates and overestimation of the uncertainties on data. \n",
"\n",
"A more _correct_ way of evaluating the goodness-of-fit is to calculate the $\\chi^2$ probability for the given $\\nu$. Without going into further details (see [Statistics Overview](https://cholmcc.gitlab.io/nbi-python/statistics/#Statistik)) we state we can calculate this probability by `scipy.stats.chi2.sf` and that we expect this to be around $50\\%$ for a good fit."
]
},
{
"cell_type": "code",
"execution_count": 50,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:26:02.410421Z",
"iopub.status.busy": "2021-11-16T10:26:02.408643Z",
"iopub.status.idle": "2021-11-16T10:26:02.994075Z",
"shell.execute_reply": "2021-11-16T10:26:02.995171Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"P(chi^2;nu) = 77.1%\n"
]
}
],
"source": [
"from scipy.stats import chi2 as schi2\n",
"\n",
"print(f'P(chi^2;nu) = {schi2.sf(chi2,nu)*100:.1f}%')"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"We can add this information to the table above "
]
},
{
"cell_type": "code",
"execution_count": 51,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:26:03.001818Z",
"iopub.status.busy": "2021-11-16T10:26:02.999839Z",
"iopub.status.idle": "2021-11-16T10:26:03.017499Z",
"shell.execute_reply": "2021-11-16T10:26:03.027150Z"
}
},
"outputs": [
{
"data": {
"text/latex": [
"$\\begin{array}{|c|c|}\n",
"\\hline\n",
"&\\mathrm{Found}\\\\\n",
"\\hline\n",
"a&9.46\\pm0.05\\\\\n",
"b&5.5\\pm0.2\\\\\n",
"\\chi^2/\\nu&0.6\\\\\n",
"p&0.8\\\\\n",
"\\hline\n",
"\\end{array}$"
],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"out += [[chi2/nu],[schi2.sf(chi2,nu)]]\n",
"display(Latex(nbi.format_data_table(out,rows=['a','b',r'\\chi^2/\\nu','p'],\n",
" columns=[r'\\mathrm{Found}'])))"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"## `plot_fit` \n",
"\n",
"We can plot our data, the fit, and some summary information using the function `plot_fit` (or the alias `fit_plot`) from the `nbi_stat` module. "
]
},
{
"cell_type": "code",
"execution_count": 52,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:26:03.035383Z",
"iopub.status.busy": "2021-11-16T10:26:03.034243Z",
"iopub.status.idle": "2021-11-16T10:26:06.060426Z",
"shell.execute_reply": "2021-11-16T10:26:06.061430Z"
}
},
"outputs": [
{
"data": {
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\n",
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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"nbi.plot_fit(x,y,e,ff,p,cov,\n",
" band=True,\n",
" data={'fmt':'o','label':'Data'},\n",
" fit={'label':'Fit'},\n",
" table={'loc':'upper left'},\n",
" legend={'loc':'lower right'},\n",
" parameters=['a','b']);\n",
"xlabel('$x$')\n",
"ylabel('$y$');"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"Here, we will not go into all the possible ways to customize the appearance of the plot. We will, however, use this function to illustrate fits, and various examples will be given. \n",
"\n",
"The individual parts of the plot is drawn by the function `plot_fit_func` and `plot_fit_table` which can be used on their own too. "
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"## `plot_nsigma_contour` \n",
"\n",
"To further investigate the result or our fits, we may want to draw the _parameter contours_. We can use the function `plot_nsigma_contour` to do so "
]
},
{
"cell_type": "code",
"execution_count": 53,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:26:06.111766Z",
"iopub.status.busy": "2021-11-16T10:26:06.097279Z",
"iopub.status.idle": "2021-11-16T10:26:07.493613Z",
"shell.execute_reply": "2021-11-16T10:26:07.495220Z"
}
},
"outputs": [
{
"data": {
"application/pdf": 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\n",
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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"nbi.plot_nsigma_contour(p,cov,[1,2,3],pnames=['a','b'])\n",
"gca().set_aspect(1)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"The plot above shows the contours where the value of $\\chi^2$ would change by one, two or three units. In other words, within a contour the fit give more or less equivalent results. From this, we see that the incline of the ellipse is related to how correlated the parameter values are. For full correlation, these ellipse collapse to more or less to a line, while for no correlation the shapes are more circular. \n",
"\n",
"Before we go on to the next topic, we will store the fitted function and the data for later use (see [below](#LLSQ))."
]
},
{
"cell_type": "code",
"execution_count": 54,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:26:07.500316Z",
"iopub.status.busy": "2021-11-16T10:26:07.499059Z",
"iopub.status.idle": "2021-11-16T10:26:07.505159Z",
"shell.execute_reply": "2021-11-16T10:26:07.506225Z"
}
},
"outputs": [],
"source": [
"llsq = dict(x=x,y=y,ey=e,f=f,g=ff)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"## Linear functions are more than you think\n",
"\n",
"As stated earlier, a linear function is any function that is linear in the parameters \n",
"\n",
"$$f(x;p) = \\sum_{i=1}^{n} p_i f_i(x)\\quad,$$ \n",
"\n",
"which means that sometimes we can manipulate our functional expression so that it can be written on this form. \n",
"\n",
"As an example, consider the function \n",
"\n",
"$$f(x;a,b) = ax^b\\quad,$$ \n",
"\n",
"which off-hand does not seem linear in the parameters. However, if we take the logarithm on both sides we find \n",
"\n",
"$$\\log f(x) = \\log a + b\\log x = g(\\log x,\\log a,b)\\quad,$$ \n",
"\n",
"which is clearly linear in $\\log a$ and $b$. First, we generate some data over $x\\in[1,10]$ with \n",
"\n",
"\\begin{align*}\n",
" b &= 0.3\\\\\n",
" a &= \\frac{b+1}{10^{b+1}-1}\\quad.\n",
"\\end{align*}"
]
},
{
"cell_type": "code",
"execution_count": 55,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:26:07.515774Z",
"iopub.status.busy": "2021-11-16T10:26:07.510355Z",
"iopub.status.idle": "2021-11-16T10:26:07.520896Z",
"shell.execute_reply": "2021-11-16T10:26:07.522032Z"
}
},
"outputs": [],
"source": [
"l = 10\n",
"b = 0.3\n",
"a = (b+1)/(l**(b+1)-1)\n",
"x = linspace(1,l,20)\n",
"r = ((a+(b+1)*random(size=8000))/a)**(1/(b+1))"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"We histogram our 8000 samples "
]
},
{
"cell_type": "code",
"execution_count": 56,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:26:07.530619Z",
"iopub.status.busy": "2021-11-16T10:26:07.529055Z",
"iopub.status.idle": "2021-11-16T10:26:07.536015Z",
"shell.execute_reply": "2021-11-16T10:26:07.534753Z"
}
},
"outputs": [],
"source": [
"h,c,w,e = nbi.histogram(r,linspace(1,l,20+1),normalize=True)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"Next, we define our function $g$ in terms of terms. Our terms are \n",
"\n",
"$$g_a(\\log x) = 1\\quad g_b(\\log x) = \\log x\\quad.$$"
]
},
{
"cell_type": "code",
"execution_count": 57,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:26:07.545754Z",
"iopub.status.busy": "2021-11-16T10:26:07.544478Z",
"iopub.status.idle": "2021-11-16T10:26:07.547386Z",
"shell.execute_reply": "2021-11-16T10:26:07.548440Z"
}
},
"outputs": [],
"source": [
"g = [lambda logx: ones_like(logx), lambda logx: logx]"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"We are now ready to perform our fit, passing the histogram bin centres $c_i$, values $h_i$, and uncertainties $e_i$ as our data. "
]
},
{
"cell_type": "code",
"execution_count": 58,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:26:07.566656Z",
"iopub.status.busy": "2021-11-16T10:26:07.554767Z",
"iopub.status.idle": "2021-11-16T10:26:10.689796Z",
"shell.execute_reply": "2021-11-16T10:26:10.691421Z"
},
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [
{
"data": {
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\n",
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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"from numpy import log, ones_like, exp\n",
"\n",
"p, cov = nbi.lin_fit(g,log(c),log(h),e)\n",
"\n",
"f = lambda x,loga,b: exp(loga)*x**b\n",
"x = linspace(c[0]-w[0],c[-1]+w[-1],20)\n",
"y = f(x,*p)\n",
"nbi.plot_fit(c,h,e,f,p,cov,\n",
" band=False,\n",
" parameters=[r'\\log(a)', 'b'],\n",
" xeval=x,\n",
" data=dict(fmt='none',xerr=w/2),\n",
" table=dict(loc='upper left'))\n",
" \n",
"dly2 = nbi.propagate_uncertainty(lambda p: dot(p,[gi(log(x)) for gi in g]),p,cov)\n",
"fill_between(x,y+sqrt(dly2),y-sqrt(dly2),color='y',alpha=0.5,label='Uncertainty');"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"Note, we have turned off the automatic band drawing (`band=False`) here, since the calculate uncertainty band would be wrong due to our transformation of variable ($x\\rightarrow\\log x$). We do draw it ourselves though using the function `propagate_uncertainty` from the `nbi_stat` module. "
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"## `lsq_fit` \n",
"\n",
"The _SciPy_ function `scipy.optimize.curve_fit` does the right thing in most cases, and we could often just use that. However, it does have one significant short-coming which we will get to in a minute. For this reason, we have the drop-in function `lsq_fit` - aliased as `curve_fit` - in `nbi_stat` which we will use here. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"A non-linear least squares fit is performed by minimizing the $\\chi^2$ (see [above](#chi2nu)). If our fitted function is _not_ linear in the parameters there is in general _no_ analytic solution to the problem and we must use numerical methods to solve it. The exact algorithms used for the $\\chi^2$ minimization are many and will be treated as _black-box_ here, but users are encouraged to familiarize themselves with a least one such algorithm to get a idea about what is going on (an example of one such algorithm _gradient descent_ is available in [Statistics Overview](https://cholmcc.gitlab.io/nbi-python/statistics/#Statistik)). "
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"Let us do an example. Here, we assume we have measurements of the invariant mass \n",
"\n",
"$$E_0^2 = (E_1 + E_2)^2 - \\|p_1 + p_2\\|^2\\quad,$$ \n",
"\n",
"in a two-particle decay where $(E,p)$ is the energy and momentum of the decay products. We want to estimate the rest mass $E_0$ and width $\\Gamma$ of a resonance using the function \n",
"\n",
"$$f(x;a_1,a_2,a_3,A_0,\\Gamma,E_0) = a_1+a_2x+a_3x^2+A_0\\frac{\\Gamma/(2\\pi}{(E_0-x)^2+(\\Gamma/2)^2}\\quad,$$ \n",
"\n",
"where the first three terms model the background and the last term is the Cauchy (or Lorentzian) distribution. Let us first draw the data we want to fit to. "
]
},
{
"cell_type": "code",
"execution_count": 59,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:26:10.710245Z",
"iopub.status.busy": "2021-11-16T10:26:10.700241Z",
"iopub.status.idle": "2021-11-16T10:26:12.027559Z",
"shell.execute_reply": "2021-11-16T10:26:12.028575Z"
},
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [
{
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\n",
"image/png": "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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"y = [ 7, 2, 6, 12, 15, 18, 31, 29, 27, 27, 41, 35,\n",
" 37, 37, 63, 71, 102, 95, 115, 202, 190, 113, 86, 68,\n",
" 74, 79, 75, 79, 68, 62, 69, 81, 79, 85, 87, 68,\n",
" 70, 89, 77, 70, 71, 62, 85, 62, 73, 70, 59, 61,\n",
" 77, 61, 62, 73, 67, 71, 75, 66, 73, 71, 71, 49]\n",
"x = linspace(0,3,len(y),endpoint=False)\n",
"ey = sqrt(y)\n",
"ex = (x[-1]-x[0])/len(x)/2\n",
"errorbar(x,y,ey,ex,'.',label='Data')\n",
"legend();"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"Next, we define the function to fit to the data. "
]
},
{
"cell_type": "code",
"execution_count": 60,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:26:12.038822Z",
"iopub.status.busy": "2021-11-16T10:26:12.037643Z",
"iopub.status.idle": "2021-11-16T10:26:12.043345Z",
"shell.execute_reply": "2021-11-16T10:26:12.044246Z"
}
},
"outputs": [],
"source": [
"from numpy import pi \n",
"\n",
"def f(x,a1,a2,a3,a0,gamma,e0):\n",
" return a1+a2*x+a3*x**2+a0*(gamma/(2*pi))/((x-e0)**2+(gamma/2)**2)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"To use `curve_fit` we need to make an initial guess at the parameter values $p_0$. Typically, it doesn't matter much what this guess is _as long as we do not give values that result in infinities or not defined_. However, if one has quickly oscillating data some care has to be taken to get, for example, the frequency right. Here, we will give conservative estimates for the parameters based on visual inspection of the data above \n",
"\n",
"\\begin{align*}\n",
" a_1 &= 0 & a_2 &= 0 & a_3 &= 0\\\\\n",
" A_2 &= 1 & \\Gamma &= 0.1 & E_0 &= 1\\quad.\n",
"\\end{align*}\n",
"\n",
"Note, we also define some settings for the parameters in the dictionary `pars` "
]
},
{
"cell_type": "code",
"execution_count": 61,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:26:12.054916Z",
"iopub.status.busy": "2021-11-16T10:26:12.053085Z",
"iopub.status.idle": "2021-11-16T10:26:12.056114Z",
"shell.execute_reply": "2021-11-16T10:26:12.056988Z"
}
},
"outputs": [],
"source": [
"p0 = [0,0,0,1,.1,1]\n",
"pars = [\"a_1\",\"a_2\",\"a_3\",\"A_0\",\n",
" {'label':r'\\Gamma','unit':'GeV'},\n",
" {'label':'E_0', 'unit':'GeV'}] "
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"We are now ready to perform our fit "
]
},
{
"cell_type": "code",
"execution_count": 62,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:26:12.091729Z",
"iopub.status.busy": "2021-11-16T10:26:12.090189Z",
"iopub.status.idle": "2021-11-16T10:26:16.958529Z",
"shell.execute_reply": "2021-11-16T10:26:16.970124Z"
}
},
"outputs": [
{
"data": {
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\n",
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"p, cov = nbi.lsq_fit(f,x,y,p0,ey) # or nbi.curve_fit\n",
"nbi.plot_fit(x,y,ey,f,p,cov,nsig=1,\n",
" parameters=pars,\n",
" legend=False,\n",
" data={\"label\":\"Data\",\"fmt\":\".\",'xerr':ex},\n",
" fit={\"label\":\"Fit\"})\n",
"plot(x,p[0]+p[1]*x+p[2]*x**2,'--',color='grey',label='Background')\n",
"xlabel(\"$E$ (GeV)\")\n",
"ylabel(\"Events\")\n",
"legend(loc='upper left');"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"Let us plot the parameter contours of this fit "
]
},
{
"cell_type": "code",
"execution_count": 63,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:26:16.996235Z",
"iopub.status.busy": "2021-11-16T10:26:16.978130Z",
"iopub.status.idle": "2021-11-16T10:26:22.732093Z",
"shell.execute_reply": "2021-11-16T10:26:22.732699Z"
}
},
"outputs": [
{
"data": {
"application/pdf": 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\n",
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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"nbi.plot_nsigma_contour(p,cov,[1,2],parameters=pars,\n",
" fig_kw={'figsize':(8,8)})"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"## Residuals \n",
"\n",
"Suppose we would like to see the residuals \n",
"\n",
"$$r_i = \\frac{y_i-f(x_i;p)}{\\delta_i}\\quad,$$ \n",
"\n",
"of the fit. We can easily evaluate these "
]
},
{
"cell_type": "code",
"execution_count": 64,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:26:22.739632Z",
"iopub.status.busy": "2021-11-16T10:26:22.737838Z",
"iopub.status.idle": "2021-11-16T10:26:22.740402Z",
"shell.execute_reply": "2021-11-16T10:26:22.740958Z"
}
},
"outputs": [],
"source": [
"r = (y - f(x,*p)) / ey "
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"Now, we would like to plot these at below our fit plot and show the uncertainties of the fitted function too. First, let us propagate the uncertainties of the fit using `propagate_uncertainty`. Note, we divide the uncertainty by the data uncertainty in each point \n",
"\n",
"$$\\frac{\\delta_{f(x_i)}}{\\delta_i}\\quad,$$ \n",
"\n",
"so that we can compare to the residuals in a meaningful way. "
]
},
{
"cell_type": "code",
"execution_count": 65,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:26:22.749016Z",
"iopub.status.busy": "2021-11-16T10:26:22.747280Z",
"iopub.status.idle": "2021-11-16T10:26:22.749700Z",
"shell.execute_reply": "2021-11-16T10:26:22.750246Z"
}
},
"outputs": [],
"source": [
"from numpy import sqrt\n",
"\n",
"df = sqrt(nbi.propagate_uncertainty(lambda p : f(x,*p), p, cov)) / ey"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"Let us plot the fit as before, but put a small axes below with the residuals and the uncertainty on $f(x)$ scaled by the uncertainty $\\delta$. We will show the residuals as points and the uncertainty on $f(x)$ as a band. "
]
},
{
"cell_type": "code",
"execution_count": 66,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:26:22.761903Z",
"iopub.status.busy": "2021-11-16T10:26:22.760862Z",
"iopub.status.idle": "2021-11-16T10:26:27.277480Z",
"shell.execute_reply": "2021-11-16T10:26:27.279116Z"
}
},
"outputs": [
{
"data": {
"application/pdf": 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\n",
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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"fig, ax = subplots(nrows=2,sharex=True,\n",
" gridspec_kw=dict(hspace=0,height_ratios=(3,1)))\n",
"nbi.plot_fit(x,y,ey,f,p,cov,nsig=1,\n",
" ax=ax[0],\n",
" parameters=pars,\n",
" legend=False,\n",
" data={\"label\":\"Data\",\"fmt\":\".\",'xerr':ex},\n",
" fit={\"label\":\"Fit\"})\n",
"ax[0].set_ylabel(r'$\\mathrm{d}N/\\mathrm{d}E\\ (\\mathrm{Ge\\!V}^{-1})$')\n",
"ax[0].legend(loc='upper left')\n",
"\n",
"ax[1].plot(x,r,'.',label='Residuals')\n",
"ax[1].fill_between(x,df,-df,color='y',alpha=.5,label=r'$\\delta f(x)/\\delta y$')\n",
"ax[1].set_xlabel(r'$E\\ (\\mathrm{Ge\\!V})$')\n",
"ax[1].set_ylabel(r'$(y-f(x))/\\delta$')\n",
"ax[1].legend();"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"We _expect_, that roughly $65\\%$ of residuals $r_i$ to be in the interval $[-1,1]$, and around $95\\%$ to be within $[-2,2]$, if the measurements are normally distributed around $f(x_i)$ (the assumption of a least-squares fit). We can easily evaluate these ratios "
]
},
{
"cell_type": "code",
"execution_count": 67,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:26:27.291459Z",
"iopub.status.busy": "2021-11-16T10:26:27.290039Z",
"iopub.status.idle": "2021-11-16T10:26:27.299006Z",
"shell.execute_reply": "2021-11-16T10:26:27.297853Z"
},
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" 58.3% (35 out of 60) of the residuals are within +/-1\n",
" 96.7% (58 out of 60) of the residuals are within +/-2\n"
]
}
],
"source": [
"for n in [1,2]:\n",
" s = sum(abs(r)"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"from matplotlib.pyplot import figure\n",
"\n",
"fig = figure(figsize=(10,6))\n",
"ax = fig.subplots(nrows=2,sharex=True,squeeze=False ,\n",
" gridspec_kw=dict(wspace=0,hspace=0,right=.5,height_ratios=(3,1)))\n",
"\n",
"nbi.plot_fit(x,y,ey,f,p,cov,ax=ax[0,0] ,\n",
" parameters=pars, xeval=linspace(0,3,100),\n",
" data={\"label\":\"Data\",\"fmt\":\".\"},\n",
" fit={\"label\":\"Fit\"},\n",
" legend={\"loc\":\"upper left\"})\n",
"ax [0 ,0].set_ylabel(\" Events \")\n",
"\n",
"nbi.plot_residual(x,y,f,p,cov,ey,ax=ax[1,0],residuals={'marker':'.','ls':'none'})\n",
"ax [1,0].set_xlabel (\"$E$ (GeV)\")\n",
"ax [1,0].set_ylabel ('Residuals ')\n",
"\n",
"nbi.plot_nsigma_contour(p,cov,[1 ,2],colors ='auto',\n",
" gridspec_kw =dict(left=.6,top =.7) , # adjust\n",
" legend=True, clabel=True, parameters=pars)\n",
"\n",
"fig.suptitle('A very complete plot of a fit');"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"Again, before we go on, we store the function and the data for later use (see [below](#NLSQ)). "
]
},
{
"cell_type": "code",
"execution_count": 69,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:26:44.125661Z",
"iopub.status.busy": "2021-11-16T10:26:44.124400Z",
"iopub.status.idle": "2021-11-16T10:26:44.127389Z",
"shell.execute_reply": "2021-11-16T10:26:44.128396Z"
}
},
"outputs": [],
"source": [
"nlsq = dict(x=x,y=y,ey=ey,ex=ex,f=f,p0=p0)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"## Including $x$ uncertainties \n",
"\n",
"The `SciPy` function `scipy.optimize.curve_fit` does not take the uncertainty in the independent variable into account when fitting. In most cases, that is indeed the correct thing to do. However, in some cases, when the \"indepedent\" variable is a measured quantity with its own uncertainty, we should take that uncertainty into account. The function `curve_fit` (and `chi2nu`) of `nbi_stat` can do that. \n",
"\n",
"There is no straight forward way of including the uncertainties on the independent variable. The method employed by `curve_fit` is that of _effective variance_ which relies on an iterative procedure to propagate uncertainties on the independent variable to the dependent variable (see also [Statistics Overview](https://cholmcc.gitlab.io/nbi-python/statistics/#Statistik)). "
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"Let us consider the following example. The goal is to determine the inductance $L$ and resistance $R$ of a _Little Henry_ box by measuring the phase shift $\\theta$ of a sine voltage across the box as a function of the wavelength $\\omega$ of the sine wave\n",
"\n",
"$$\\cot\\theta = \\frac{L}{R}\\omega - \\frac{1}{RC}\\frac1{\\omega}\\quad,$$\n",
"where $C$ is a known capacitance. We determine several correlated values of ($\\cot\\omega,\\theta$) and calculate the mean and uncertainty of each variable. We end up with data"
]
},
{
"cell_type": "code",
"execution_count": 70,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:26:44.171678Z",
"iopub.status.busy": "2021-11-16T10:26:44.143301Z",
"iopub.status.idle": "2021-11-16T10:26:45.833540Z",
"shell.execute_reply": "2021-11-16T10:26:45.832436Z"
},
"slideshow": {
"slide_type": "-"
}
},
"outputs": [
{
"data": {
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\n",
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAYgAAAEGCAYAAAB/+QKOAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjMuNCwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8QVMy6AAAACXBIWXMAAAsTAAALEwEAmpwYAAATAUlEQVR4nO3df5BdZX3H8fc3sLoo65CEYKxpNso4BqtUJiuTWAdBU6PG2kEawo/ROtUJVocSLCDYqoHGaWmxkzhDDdHBH6OjQVMHazr80GhBCeKuOjoy6CDtTiN0WEIgGZIlG/LtH/cGNuHZzW6y9567975fMxnOj+fe833mhnzuc55zz4nMRJKkw82ougBJUmsyICRJRQaEJKnIgJAkFRkQkqSi46su4GidfPLJuWDBgqrLkKRpY2Bg4LHMnDPR9tM2IBYsWEB/f3/VZUjStBERg5Np7ykmSVKRASFJKjIgJElF03YOomRkZITt27czPDxcdSkN193dzbx58+jq6qq6FEltqq0CYvv27fT09LBgwQIioupyGiYz2bFjB9u3b+cVr3hF1eVIalNtdYppeHiY2bNnt3U4AEQEs2fP7oiRkqTqtFVAAJMOh5U3bWPlTdsaVE3jtHsISqpe2wWEJGlqtNUcRNXuu+8+rrrqKvbt28fb3vY29u7dC8A111zDSSedNObr1q1bx+rVq5tTpKRjcvCMw6ZLllRcSeN1/Ahi9/AIv39iLwODO4/5vc4880zOPvts3vjGN7JmzRquv/56zj77bN7ylrewf//+MV+3bt26Yz62JE21jhtBjJ5v2D08wv2P7AZgxYZ7WDi3h57u2mWjU/Xt4B3veAfXXnstt912G5/73Oc466yz+M1vfsNFF13E0qVLueWWW3jiiSdYs2YNCxcu5F3vehcrV658XjtJaraOC4jRdg0/963+QNbWDwbEVOrt7eWhhx7i8ssvZ+nSpTz++OMsW7aMpUuXcv7553PVVVexZs0aAPbs2VNsJ0nN1nEBMXpkMDC4kxUb7uFAQnfXDNZfcAaLemdO+TEHBwd53/vexw9/+EO2bdtGV1cXQ0NDxbaZOaF2ktRoHRcQoy3qncnCuT3sGt7fsHC48847GR4e5sEHH+Thhx/m5ptvZmRkhA0bNjzb5rjjjiMz+cUvfsFdd901ZjtJaqaODgiAnu4uerq7piQc+vv7ueuuu9i3bx9r165lz549jIyMsHXrVh599FG+9a1vceWVVzJr1iyefPJJNm/ezHnnncfy5cu54ooreOaZZ/jQhz40ZjtJaqaOD4ip1NfXx9atW4v7Zs2axd133/3s+jXXXPPs8mc/+9lD2o7VTpKaqeMDohOuZZako9Hxv4OQJJW1xAgiIq4EFgCPAa8CPpCZe4/mvTKzI+5TlJlVlyCpzVU+goiIucA1wKWZ+SngxcB7jua9uru72bFjR9v/43nwdt/d3d1VlyKpjbXCCGIPsA94CfAEcCLw61LDiFgFrAKYP3/+8/bPmzeP7du3d8RvBw4+MEiSGqXygMjMXfVTTJsi4hFgO/DgGG03AhsB+vr6njdM6Orq8gE6kjRFWuEU0+uBK4Hlmfl+avMQn6yyJklSCwQE8HLg8cw8eGOkRwBPrktSxSo/xQTcBrwzIj5DbQ7itcDqKguSJLVAQGTmM8BHqq5DknSoVjjFJElqQQaEJKnIgJAkFRkQkqQiA0KSVGRASJKKDAhJUpEBIUkqMiAkSUUGhCRNwu7hEX7/xF4GBndWXUrDVX6rDUk6Witv2tbU4+0eHuH+R3YDsGLDPSyc20NPd1dTa9h0yZKmHcsRhCRN0K7h/c8uH8hD19uRIwhJ01Yzv00DDAzuZMWGeziQ0N01g/UXnMGi3plNraGZDAhJmqBFvTNZOLeHXcP72z4cwICQpEnp6e6ip7ur7cMBnIOQJI3BgJAkFRkQkqQiA0KSVGRASJKKDAhJUpEBIUkqaonfQUTEq4ELgb3Am4E1mXlftVVJUmerPCAi4jjgX4E/y8wDEfEVoHiDk4hYBawCmD9/fvOKlKQOVHlAAG8AArg0Il4E7AA+X2qYmRuBjQB9fX3ZtAolqQO1QkD0AkuACzPzyYj4KrAP+FKlVUlSh2uFSepdwAOZ+WR9/UfA2dWVI0mC1giInwCz63MRUBtR/LbCeiRJtMAppsx8PCI+BqyLiCFgDnBdxWVJUserPCAAMvPbwLerrkOS9JxWOMUkSWpBBoQkqciAkCQVGRCSpCIDQpJUZEBIkooMCElSkQEhSSoyICRJRS3xS2pJmi42XbKk6hKaxhGEJKnIgJAkFRkQkqQiA0KSVGRASJKKDAhJUpEBIUkqMiAkSUUGhCSpyICQJBUZEJKkIgNCklTUMgERESdExC8j4oaqa5EktVBAAGuBn4/XICJWRUR/RPQPDQ01qSxJ6kwtERAR8V7gx8B/j9cuMzdmZl9m9s2ZM6c5xUlSh6o8ICLiNcBpmfnvVdciSXpO5QEBnAsMR8TVwJuAMyNidbUlSZIqf6JcZn764HJEdAMnZua66iqSJEFrjCAAiIjzgLOAxRFxYdX1SFKnq3wEcVBmbgY2V12HJKmmZUYQkqTWYkBIkooMCElSkQEhSSoyICRJRQaEJKnIgJAkFRkQkqQiA0KSVGRASJKKDAhJUpEBIUkqMiAkSUVHvJtrRJwCfAR4GfA/wK2Z+esG1yVJqthERhBrgd8B9wJvBzZFxJfrD/eRJLWpiQTEvZn5lcy8GdiSma8Fvghc3djSJElVmkhA/GFEnFVfToDM/CEw2KiiJEnVm8gT5f4ZuCki/g14PCIeB/YDi6mNJCRJbeiIAZGZe4H3RcRpwLuBPuAR4BMNrk2SVKHJPJP6dZl5PUBEvJ7aHMRHG1GUJKl6k/kdxMKDC5n5C+DAlFcjSWoZE/kdxGXAauCkiHg/ENTmILZMRQERcSq1S2l/BswDdmTmdVPx3pKkozeROYj1wPqIWJGZ32xADbOAb2TmrQARcX9EbMnMgQYcS5I0QROeg8jMb0bEUuCPgZ9n5tapKCAzf3rYphnAU6W2EbEKWAUwf/78qTi8JGkME56DiIhPUJuU7gWurK9PqYg4F7g9Mx8o7c/MjZnZl5l9c+bMmerDS5JGmcxVTC/IzHceXImIf5zKQiLiHOAcavMdkqSKTeYqpmcOW5+yq5giYjmwDLgMmBsRS6bqvSVJR2cyI4j9EfEd4CHgVOAnU1FARCwCNgH9wA+AFwM3Atum4v0lSUdnMpPUayPibcDpwHcz83tTUUD9aqUTp+K9JElTZzKT1LcAL8/MG6jdwO/DjStLUpXeuf4u3nT9VgYGd1Zdiio0mVNMv8rMLwJk5hcj4pMNqknSKCtvau7Z1t3DI9z/yG4AVmy4h4Vze+jp7mra8Tdd4hRkq5jMJPXhf0NeOJWFSGoNu4b3P7t8IA9dV2eZzAhiJCK+CzzIFE5SSxpfs79RDwzu5OIv3MvI/gN0HT+D9RecwaLemU2tQa1hMpPU/zBqknpLZt7ZuLIkVWVR70y+9sHF3PvQDha/crbh0MEmM4IgM+8A7mhQLZJaxKLemQaDJjUHIUnqIAaEJKnIgJAkFRkQkqQiA0KSVGRASJKKDAhJUpEBIUkqMiAkSUUGhCSpyICQJBUZEJKkIgNCklRkQEiSigwISVKRASFJKprUA4MaJSKWAu8BHgUyM6+tuCRJ6niVB0REvAjYAPxRZj4dEZsj4q2Z+f2qa5OkTtYKp5iWAIOZ+XR9/cfA8lLDiFgVEf0R0T80NNS0AiWpE7VCQJwC7B61vqu+7Xkyc2Nm9mVm35w5c5pSnCR1qlYIiEeBnlHrL6lvkyRVqBUCYhvQGxEvrK//CbClwnokSbTAJHVm7omIvwY+GxFDwC+doJak6lUeEACZeSdwZ9V1SJKe0wqnmCRJLciAkCQVGRCSpCIDQpJUZEBIkooMCElSkQEhSSoyICRJRQaEJKnIgFDHGhjcyY0/eJCBwZ1VlyK1pJa41YZ00MqbtjXlOLuHR7j/kdpd5mcELJzbQ093V1OOvemSJU05jnSsHEGoI+0a3v/s8oE8dF1SjSMItZRmfbseGNzJxV+4l5H9B+g6fgbrLziDRb0zm3JsabowINSRFvXO5GsfXMy9D+1g8StnGw5SgQGhjrWod6bBII3DOQhJUpEBIUkqMiAkSUUGhCSpyICQJBUZEJKkIgNCklRU+e8gIuJUYC3wM2AesCMzr6u2KklS5QEBzAK+kZm3AkTE/RGxJTMHDm8YEauAVQDz589vbpWS1GEqP8WUmT89GA51M4Cnxmi7MTP7MrNvzpw5zSlQkjpUU0YQEXE78NLCrk9m5ndGtTsXuD0zH2hGXZKksTUlIDJz2ZHaRMQ5wDnA6oYXJEk6ospPMQFExHJgGXAZMDcifKKKJFWs8oCIiEXAJmAx8APgVuDVlRYlSar+Kqb61UonVl2HJOlQlY8gJEmtyYDQEa28aRsrb9pWdRmSmsyAkCQVGRA6ot3DI/z+ib0MDO6suhRJTVT5JLWOTaNP/eweHuH+R3YDsGLDPSyc20NPd1dDj7npEq9yllqBIwiNa9fw/meXD+Sh65LamyOIaa7R37YHBneyYsM9HEjo7prB+gvOYFHvzIYeU1JrMCA0rkW9M1k4t4ddw/sNB6nDGBA6ov+87KyqS5BUAecgJElFBoQkqciAkCQVGRCSpCIDQpJUZEBIkooMCElSkQHRAN4eW1I7MCAkSUUGhCSpyICQJBUZEJKkIgOiAXwCm6R20BJ3c42IE4CfAHdk5hWNPl4jrzBq5hPYfPKapEZqlRHEWuDnR2oUEasioj8i+oeGhppQ1uT5BDZJ7SIys9oCIt4LPAWcDpw40RFEX19f9vf3N7S2o3H4E9i+9sHFPmRHUkuIiIHM7Jto+4afYoqI24GXFnZ9EngQOC0zPx4Rpze6lmbwCWyS2kXDAyIzl421LyL+DhiOiKuBNwEviIjVmbmu0XU1Uk93Fz3dXYaDpGmt0knqzPz0weWI6KZ2imlddRVJkg5qiUnqiDgPOAtYHBEXVl2PJKlFLnPNzM3A5qrrkCQ9pyVGEJKk1tMSI4h24w/YJLUDRxCSpCIDQpJUZEBIkooMCElSkQEhSSoyICRJRQaEJKnIgJAkFRkQkqSiyh8YdLQiYggYrLqOcZwMPFZ1EQ3U7v0D+9gO2r1/MLk+9mbmnIm+8bQNiFYXEf2TeXLTdNPu/QP72A7avX/Q2D56ikmSVGRASJKKDIjG2Vh1AQ3W7v0D+9gO2r1/0MA+OgchSSpyBCFJKjIgJElFBoQkqciAkCQV+UzqMUTEqcBa4GfAPGBHZl431vb6a5YC7wEeBTIzrx31fsV9472m0cbp4wzgP4CfAC8ATgX+KjP3Tqc+jvdZ1fefQK2Pd2TmFUeqtdX6Vz/2eH8f7wWG602fycy3HqneadjHVwMXAnuBNwNrMvO+duljRCwAvg/8b73pS4BfZub7m9LHzPRP4Q/wBuDPR63fDywaZ/uLgAeBF9a3bwbeWl8u7hvvNRX3cQbw96O23wpcPN36OFb/Rq1/BvgycMN4fWjV/h2pj9T+sTy8fdv0ETgO2ALMqG9/GTCnzfo4G1g6avu1wJua1UdHEGPIzJ8etmkG8FRmPlDaDiwBBjPz6fr2HwPLqaX/WPsY5zUNN04fD1D7NkNEHE/tG81vmGZ9HKt/ABHx3notpwMn1vdPq/7B+H0EXhcRHwNOAH6amVtorz6+AQjg0oh4EbAD+DzwlnHqnVZ9zMwdwPcAIuKFQF9mfioi3jpOvVPWRwNiAiLiXOD2w8Nh9PaIOAPYPWr3LuCU+vIpY+wba3vTlfoYEcuAy4HvZmZ/RFzINO3jYZ/Va4DTMvPjEXH6qGbj1drS/YPiZ3h91k63HAfcFRG7aaM+RsRKav8YXpiZT0bEV4F9wNO0SR8P23UR8PX6clM+RyepjyAizgHOofYP5XjbHwV6RjV5SX3bePvGe03TjNXHzLw9M98OvCIiPsw07WOhf+cCwxFxNbXh+pkRsZpp2j8of4aZeV/9v88Ad9f3t1MfdwEPZOaT9fUfAWfTXn0cbQWwqb7cnD426xzbdPxDbfj1T9SGsX8ALBlrO9PwvOc4fXkNsHxUm2uBG6ZjH8f6DEftX8M0noMY5zNcCHxgVJvNTMN5pCP0cRbwW+C4ept/BD7eTn0cte8cDp0XbEofvdXGGCJiEfBfQH9904uBG4FflbZn5pci4k+BvwCGgJE89KqC4r7xXtNo4/TxbuBfqF1R0QWcBvxNZv7fdOrjWP3LzC/V958HfITalVo3ZubXp1P/6sce6zO8o/7fn1H7ptgFfDQzD7RLH+v/z51Lbc5hCJgPXJq1q+3apo/1/V+n1rfHRr2m4X00ICRJRc5BSJKKDAhJUpEBIUkqMiAkSUUGhCSpyICQJBUZEJKkIgNCmgIR8bcR8anDtt0YERdXVZN0rAwI6RhFxGJqt2S+NiLmR8S767tuBv6ywtKkY2JASMfuPJ67ZfLbqd3HH+BVVHDDN2mqGBDSsZsJPF5fXgr8rr58PnBLJRVJU8B7MUnHKCJOAz4NDAAPU7uF+BDwu8z8fJW1ScfCgJAkFXmKSZJUZEBIkooMCElSkQEhSSoyICRJRQaEJKnIgJAkFf0/1k8r2xKS4PQAAAAASUVORK5CYII=\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"data = array([[22000 , 440, -4.017 , 0.5],\n",
" [22930 , 470, -2.742 , 0.25], \n",
" [23880 , 500, -1.1478, 0.08],\n",
" [25130 , 530, 1.491 , 0.09],\n",
" [26390 , 540, 6.873 , 1.90]])\n",
"\n",
"errorbar(data[:,0],data[:,2],data[:,3],data[:,1],'.',label='Data')\n",
"xlabel(r'$\\omega$')\n",
"ylabel(r'$\\cot\\theta$')\n",
"legend(loc='upper left');"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"Next, we define our function, parameter names, and initial value $p_0$"
]
},
{
"cell_type": "code",
"execution_count": 71,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:26:45.844045Z",
"iopub.status.busy": "2021-11-16T10:26:45.842509Z",
"iopub.status.idle": "2021-11-16T10:26:45.845280Z",
"shell.execute_reply": "2021-11-16T10:26:45.846189Z"
}
},
"outputs": [],
"source": [
"def f(x,a,b): \n",
" return a * x + b / x \n",
"pnames = ['a','b']\n",
"p0 = (1,1)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"Next, we do the fit. We do so with and without the uncertainties in the independent variable to illustrate the difference. "
]
},
{
"cell_type": "code",
"execution_count": 72,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:26:45.863476Z",
"iopub.status.busy": "2021-11-16T10:26:45.862330Z",
"iopub.status.idle": "2021-11-16T10:26:49.932403Z",
"shell.execute_reply": "2021-11-16T10:26:49.932967Z"
}
},
"outputs": [
{
"data": {
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\n",
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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"p, cov = nbi.lsq_fit(f,data[:,0],data[:,2],p0,data[:,3],data[:,1])\n",
"p2, cov2 = nbi.lsq_fit(f,data[:,0],data[:,2],p0,data[:,3])\n",
"nbi.plot_fit(data[:,0],data[:,2],data[:,3],f,p,cov,data[:,1],\n",
" data={'fmt':'none','label':'Data'},\n",
" parameters=dict(scale='auto'),\n",
" fit=dict(color='C1',label='With $x$ uncer.'),\n",
" band={'color':'C1','alpha':.3},\n",
" table=dict(loc='upper left',\n",
" title={'label':'With $x$ uncer.','color':'C1'}))\n",
"nbi.plot_fit(data[:,0],data[:,2],data[:,3],f,p2,cov2,\n",
" data=False,\n",
" parameters=dict(scale='auto'),\n",
" fit=dict(color='C2',label='No $x$ uncer.'),\n",
" band={'color':'C2','alpha':.3},\n",
" table=dict(loc='lower right',\n",
" title={'label':'No $x$ uncer.','color':'C2'}))\n",
"xlabel(r'$\\omega$')\n",
"ylabel(r'$\\cot\\theta$')\n",
"legend(loc='center left');"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"## `mle_fit` \n",
"\n",
"Maksimum likelihood fits are obtained by, well, maximizing the likelihood \n",
"\n",
"$$\\mathcal{L} = \\prod_{i=1}^{n} f(x_i;p)\\quad,$$ \n",
"\n",
"where $f$ is the _probability density function_ (PDF). For this to be valid, the PDF _must_ be normalized over the measured range $X$ \n",
"\n",
"$$\\int_X\\mathrm{d}x\\,f(x;p) = 1\\quad.$$ \n",
"\n",
"However, instead of maximizing $\\mathcal{L}$ we will _minimize_ $-\\log\\mathcal{L}$ \n",
"\n",
"$$-\\ell = \\log\\mathcal{L} = -\\log\\left(\\prod_{i=1}^{n}f(x_i;p)\\right) = -\\sum_{i=1}^{n}\\log\\left(f(x_i;p)\\right)\\quad.$$ \n",
"\n",
"Here the sum runs over the $n$ _samples_ - not bins or the like. In fact, maximum likelihood fits are not really applicable for binned data (on _can_ do it, but then it becomes a different answer to a different question). \n",
"\n",
"Thus, the requirements of a maximum likelihood fit become \n",
"\n",
"- We have a sample of size $n$ \n",
"- We have a _normalized_ PDF $f$ for which we want to adjust the parameters \n",
" - Alternatively, we can use the logarithm of the PDF $\\log f$. "
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"_SciPy_ has no general maximum likelihood fit procedure. However, the general minimizer routine `scipy.optimize.minimize` can be used to minimize $-\\ell$. The module `nbi_stat` provides the function `mle_fit` that uses `scipy.optimize.minimize` to do a maximum likelihood parameter estimate (Maximum Likelihood Estimate - MLE) given the _normalized_ PDF $f$ or the logarithm of the PDF $\\log f$ and the samples $x_i$. "
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"As an example consider samples drawn from an exponential - for example the time between decays of a radioactive source. "
]
},
{
"cell_type": "code",
"execution_count": 73,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:26:49.940586Z",
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"outputs": [],
"source": [
"t = exponential(size=100)\n",
"t = t[t<3]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"were we have limited the observations to $3$ simulating finite acceptance of our measurements."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"Our PDF is given by \n",
"\n",
"$$f(t;\\tau) = A \\frac1{\\tau}e^{-t/\\tau}\\quad,$$ \n",
"\n",
"where $\\tau>0$ is the half-life of the source, and $A$ is the normalization factor. The normalization must be over the range of samples. Let us find this constant by solving \n",
"\n",
"$$\\int_{0}^{a}\\mathrm{d}t\\,f(f;\\tau) - 1 = 0\\quad.$$"
]
},
{
"cell_type": "code",
"execution_count": 74,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:26:49.953118Z",
"iopub.status.busy": "2021-11-16T10:26:49.952033Z",
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"shell.execute_reply": "2021-11-16T10:26:50.189843Z"
}
},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle A = \\frac{e^{\\frac{a}{\\tau}}}{e^{\\frac{a}{\\tau}} - 1}$"
],
"text/plain": [
"Eq(A, exp(a/tau)/(exp(a/tau) - 1))"
]
},
"execution_count": 74,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"from sympy import exp as syexp, solve, Function\n",
"\n",
"tt, a, A = symbols('t a A',real=True,positive=True)\n",
"tau = symbols('tau',real=True,positive=True)\n",
"f = A*syexp(-tt/tau)/tau\n",
"s = solve(f.integrate((tt,0,a))-1,A)[0]\n",
"Eq(A,s)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"Thus, our PDF becomes "
]
},
{
"cell_type": "code",
"execution_count": 75,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:26:50.229528Z",
"iopub.status.busy": "2021-11-16T10:26:50.228455Z",
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"shell.execute_reply": "2021-11-16T10:26:50.232984Z"
}
},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle f{\\left(t,\\tau \\right)} = \\frac{e^{\\frac{a}{\\tau}} e^{- \\frac{t}{\\tau}}}{\\tau \\left(e^{\\frac{a}{\\tau}} - 1\\right)}$"
],
"text/plain": [
"Eq(f(t, tau), exp(a/tau)*exp(-t/tau)/(tau*(exp(a/tau) - 1)))"
]
},
"execution_count": 75,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"ff = f.subs(A,s)\n",
"Eq(Function('f')(tt,tau),ff)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"Alternatively, we can use the logarithm of this "
]
},
{
"cell_type": "code",
"execution_count": 76,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:26:50.260421Z",
"iopub.status.busy": "2021-11-16T10:26:50.246998Z",
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"shell.execute_reply": "2021-11-16T10:26:50.266634Z"
}
},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\log{\\left(f{\\left(t,\\tau \\right)} \\right)} = \\frac{a}{\\tau} - \\frac{t}{\\tau} - \\log{\\left(\\tau \\right)} - \\log{\\left(e^{\\frac{a}{\\tau}} - 1 \\right)}$"
],
"text/plain": [
"Eq(log(f(t, tau)), a/tau - t/tau - log(tau) - log(exp(a/tau) - 1))"
]
},
"execution_count": 76,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"from sympy import log as sylog \n",
"lff = sylog(ff).expand(log=True,force=True)\n",
"Eq(sylog(Function('f')(tt,tau)),lff)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"We turn this into substitute in the numerical expression we can evaluate over our sample. Also, we bind the upper limit $a$ to the maximum of our sample "
]
},
{
"cell_type": "code",
"execution_count": 77,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:26:50.289435Z",
"iopub.status.busy": "2021-11-16T10:26:50.288081Z",
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"shell.execute_reply": "2021-11-16T10:26:50.292060Z"
}
},
"outputs": [],
"source": [
"g = lambdify((tt,tau),ff.subs(a,t.max()))\n",
"lg = lambdify((tt,tau),lff.subs(a,t.max()))"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"We are now ready to perform our fit. As with non-linear least squares fits (see [above](#lsq_fit)), we need to provide an initial guess of the parameters $p_0$. Here, we choose a small value"
]
},
{
"cell_type": "code",
"execution_count": 78,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:26:50.306579Z",
"iopub.status.busy": "2021-11-16T10:26:50.305786Z",
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"shell.execute_reply": "2021-11-16T10:26:50.311701Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[1.03483183] [[0.02782399]]\n"
]
}
],
"source": [
"p, cov = nbi.mle_fit(g,t,[.9])\n",
"print(p, cov)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"Alternatively, we can use the logarithm of the PDF"
]
},
{
"cell_type": "code",
"execution_count": 79,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:26:50.329560Z",
"iopub.status.busy": "2021-11-16T10:26:50.327375Z",
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"shell.execute_reply": "2021-11-16T10:26:50.333453Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[1.03483189] [[0.02782012]]\n"
]
}
],
"source": [
"lp, lcov = nbi.mle_fit(lg,t,[.9],logpdf=True,bounds=[(1e-3,None)])\n",
"print(lp,lcov)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"Since our data in this case is the samples themselves, we need to generate a histogram of the density to illustrate our data and fits "
]
},
{
"cell_type": "code",
"execution_count": 80,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:26:50.340009Z",
"iopub.status.busy": "2021-11-16T10:26:50.338974Z",
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"shell.execute_reply": "2021-11-16T10:26:50.343030Z"
}
},
"outputs": [],
"source": [
"h,c,w,e = nbi.histogram(t,linspace(0,3,10),normalize=True)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"Below we draw use `plot_fit` _and_ `plot_fit_table` to show both results. Since the fits are practically on top of each other, there's no reason to draw the second plot, but we would like to see the parameter values though. "
]
},
{
"cell_type": "code",
"execution_count": 81,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:26:50.352236Z",
"iopub.status.busy": "2021-11-16T10:26:50.351258Z",
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"shell.execute_reply": "2021-11-16T10:26:53.859450Z"
},
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [
{
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\n",
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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"nbi.plot_fit(c,h,e,g,p,cov,w/2,\n",
" parameters=[r'\\tau'],\n",
" data=dict(xerr=w/2,fmt='.',label='Data'),\n",
" fit={'ls':'--','label':'Fit (PDF)','color':'C1'},\n",
" table={'title':'PDF'},\n",
" band={'alpha':.2,'color':'C1'},\n",
" legend=False)\n",
"lchi2nu = nbi.chi2nu(c,h,g,lp,e)\n",
"nbi.plot_fit_table(lp,diagonal(lcov),chi2nu=lchi2nu,\n",
" pvalue=True, parameters=[r'\\tau'],\n",
" loc='center right',\n",
" title='log-PDF');"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "-"
}
},
"source": [
"We also store this function and data for later use (see [below](#MLE)). "
]
},
{
"cell_type": "code",
"execution_count": 82,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:26:53.866635Z",
"iopub.status.busy": "2021-11-16T10:26:53.865235Z",
"iopub.status.idle": "2021-11-16T10:26:53.868114Z",
"shell.execute_reply": "2021-11-16T10:26:53.868683Z"
}
},
"outputs": [],
"source": [
"mle = dict(t=t,f=g,p0=[.9],x=c,y=h,ey=e,ex=w/2)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"## `fit` "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Above, we used 3 different functions to do \n",
"\n",
"- `lin_fit` for Linear least squares (LLSQ)\n",
"- `lsq_fit` for Non-linear least squares (NLSQ) \n",
"- `mle_fit` for Maximum likelihood (MLE)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"However, there is something to be said for having a simple interface. The module `nbi_stat` therefore provides the function `fit` which will do one of the 3 procedures depend on the input given. \n",
"\n",
"- If a function of the form \n",
"\n",
" $$f(x;p) = \\sum_{i=1} p_i f_i(x)\\quad,$$ \n",
" \n",
" is given via a sequence of $f_i$ - for example \n",
" \n",
" f = [lambda x:ones_like(x), lambda x:x, lambda x: sin(x)]\n",
" \n",
" for the function \n",
" \n",
" $$f(x;p) = p_0 + p_1 x + p_2\\sin(x)\\quad,$$ \n",
" \n",
" then `lin_fit` is called and a linear least squares fit is performed (LLSQ mode).\n",
" \n",
"- If any other function is given, _and_ both independent and dependent variable valus ($x$ and $y$), then \n",
" we call `lsq_fit` and perform a non-linear least squares fit (NLSQ mode).\n",
" \n",
"- If any kind of function is given and only independent samples $x$ is given, then we call `mle_fit` and perform a maximum likelihood fit (MLE mode). "
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"Each of the three modes have different requirements with respect to the remaining arguments to `fit` \n",
"\n",
"- Linear least squares requires (in order)\n",
" - A linear function given as a sequence of term functions ($f_i$'s)\n",
" - Independent variable values ($x$)\n",
" - Dependent variable values ($y$) \n",
" - Uncertainties on the dependent variable ($\\delta_y$)\n",
"- Non-linear least squares requires (in order)\n",
" - A function given as a callable (a `def ...` for example)\n",
" - Independent variable values ($x$)\n",
" - Dependent variable values ($y$) \n",
" - An initial guess at the parameter values ($p_0$)\n",
" - Uncertainties on the dependent variable ($\\delta_y$)\n",
"- Maximum likelihood estimate requires (in order)\n",
" - A probability density function (PDF) or the logarithm of the PDF. Note, the PDF _must_ \n",
" be normalized and single valued. \n",
" - A sample of independent variable values ($x$)\n",
" - An initial guess at the parameter values ($p_0$)\n",
" \n",
"In addition, any other valid arguments for the function (`lin_fit`, `lsq_fit`, or `mle_fit`) can be passed. \n",
"\n",
"In any case, the estimated parameter values and their covariance matrix is returned. \n",
"\n",
"Below, we will redo some of the fits we did above using the `fit` interface. "
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"### LLSQ\n",
"\n",
"Here, we re-do the linear least squares fit done earlier (see [above](#lin_fit)). Remember that we defined the function `f` as a list of term functions. "
]
},
{
"cell_type": "code",
"execution_count": 83,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:26:53.906434Z",
"iopub.status.busy": "2021-11-16T10:26:53.881698Z",
"iopub.status.idle": "2021-11-16T10:26:56.325247Z",
"shell.execute_reply": "2021-11-16T10:26:56.326095Z"
}
},
"outputs": [
{
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\n",
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BGgKBSuz2fqSkXE9ExPEnqTuCBHIhxGlHa82GAzV8vLmEjzYXU1DhQqEZlOqkV7Qmwhxk1vRdJNn9mIzh4WVjXS0Ja5cSVbATf1QMledNpjyrD7RhPDsYdOH3OzCbU8nM/DFRUcNOaBz8REkgF+I05na7uf322/n222+54YYb2LJlCxaLhWeffZannnqKgoICXnrppS5v14EDB/D6vDz66Md4vV6efPLJZoFv3LhxjUsjjUYjCxcubPWewZBmzb5KPt5cwidbSiiu8WAywPBeNVw+bieT+gRIijLywPvhlPq06PCyPxUMELt5HbGbVgOaquHj2RCZyJbNO4jcG14KOnnylCbPqqqq5IsvvqBXrxR8vhLM5iguueT/iIk5B4PB3AE/ofaRQC7EaSwiIoKRI0cSExPDT37yEyC88fDPfvYzpk+fzvPPP3/ce1xzzTUtZnY+8sgjTJw4sd1t+uabbyhxlJA/Kp/H776Jq6++mvnz53PllU2TxKdPn85jjz3W6r18gRBf7i7nky0lfLrFQUW9D7MB0lUFj15kZ1D8J8TZrQ2TmUfVjtUae+EeEtYsxlxXS33OWVTmT8JtjeD9F57nnnvuwWg08Z//zGXv3j3k5R0eJnG56hkyJJ2cnBwSE+/jggt+Rv/+UYwa1fVBHCSQC3HaW7t2LT/84Q8B8Pv9eDweoqOjaeuKtY6utbJz505s1sNJSL1792bhwoXNAvmmTZt46qmncLvdjB49unFzZLcvyJJvy/hkSwmfb3Pg9ASItBg5b0AqFw1KxVT6X8pLXmZU2kCs1gyUaqHsQbCE1M/fxV5UgC82geILr8aTHt4r4cDePcTGxmI0hq/Lzs5m586d5OX1bpjIdJCYGKRPn+tJSroCszkRj+dnREa2f9efjiKBXIjT3Lp16xqr7M2bN48LL7yQhIQEamtr23R9R9daGT16NPUfzycUCqG1Zu3atY0lY4/08MMPM2bMGILBIBOnXsCmWhv7AnEs/rYUjz9EnN3M9EFpXDwkjXP6JHHNlVNYOrCYpKQKKiqC7NrlAMJVHlNSUgFQPi+3uN7mMu8XGN1GKkZPprb/MDgie7O+vh6r9fB6cqvVSn19PX5/FcFgFZGRQ0lJuQ6bLdzmd999l4suuoj+/fu3+2fRUSSQC3Eaq66uxmaz8dZbb1FTU0NpaSkvv/xyu+7R0bVWcnNzObvf2RQUFPDMM2sYNGgQcXFxzc7rM3AYc9fs56PNJTjO+TEvbPCQEl3Fd0ZlcfHgNMbkJWAyGgiFAlRXf8Ef/tAfpQZQXOxl376CpuPaWhO1Zxvx65aR63XxueUczpo5mFBE87foyMhIvF5v42e/v5akpAAmUxQZGXdjtw9oHM9ftGgRixYt4umnn+7Qn1F7SSAX4jS2bt06Ro8eza9//esmx7XWzJ07lx07drB+/XpGjhzZpe0ymUzk5eXxwN03cNNNN3HvvfcCsHrzTrbVmnl79W42lbjRKLISIkiu2sLMUbk8fMcMDIbDk6LhzMx/4PXub8zMTE6ux26PajzHUuEgcdUibGXFeBNT+Znpf9hpyuPpiB0tti0zM4uamhr8/nqCwTKKiw8wZMh95OXdS0FBIbm54ecvWLCAZcuW8cwzz1BcXExBQQHjx3d9ghNIIBfitLZu3boWg7RSiocffpiHH364G1oFu3btIjY2lt/85jMmTr+SpaUWfv7Fcr4prAEgL8FGavnXjMuMwFTmIBDh5+E7HmoM4uEys+9RVfUJRmM0Nlse//73v5qM+0foEOdpFyPxErJFUHbOBdT1HcTOD469vyaAyaS45JIxLF36IbW1w6mr+y7Tpt1HKBRiypQpLF68mIqKCq677jry8/OZOnUq9fX13HvvvRLIhRAd76GHHuruJrRo8JChlNR6+dKWyfbNTti8nSEZsfz0orO5aFAafVOigOZlew+XmX2VQKAOqzUbpcLj2zfd9L3wSaEQ0d9uJP7rLzH4fdT2H0H18HGELK1XedQ6hN9fgtZ+Bg26mcmTL8Fkim383mAwsG/fPiA8PNTSvEF3kUAuhOhye8rrqXL5GZ0bz68uHchFg1LJjG9eDOxIPl8ZDscbOJ3rMZuTsdmym51jKzlAwupFWKvKcadlUTFmCv74pFbvq7UmEKggGHQSHT2a5OSrsVqPvWPSqUgCuRCiS+10OKly+ekVZ2PeD8457vnhycxFlJbORSlDY5nZIxnrnSSsXUbUvh0EIqNxTLkUV3bf42ZlBgK1BAIVRET0ISXlfiIi+nZpRmZHkUAuhOhSzy/ZjUFBWszxN7Rwu/c0TGYWtlxmNhggdut64jaugpCmathYagaPRptaT8zROoTHsw+zOZGMjPuIjh6BUj13nx0J5EKILlNY6eK9b4pIibZiPrps4BEO7ZlZVfVp42Tm0SIK95C4ZjFmZw31WX2oHD2ZQHRsC3c7LBTyEwp5UcpAaurNxMVNxGCwtHpNR+nMkr0SyIU4TR2rzkpb0vI7y0tL92BQUF64i6oDmilTft6kjkp4MnM9DserzJ8/B5fLjtYKpRQ333wLAKbaKhJXL8F+cC++2ARKzr8Kd0ZOq8/VOoTPVwyEeOXGkSQkXITJFNXiuZ9//jnvvPMOKSkpKKV49NFHWzzP7XYzduxYLrzwQv7whz+c+A+lA0ggF+I0daw6K+PGjcPhcOD3++nXrx/f+c53Wr1PR9VaKXV6mLu2kGtGZfLFmhpyc3OZ+9wPG78/cjLTYkkhOXlQk6Qe5fcRt3EVsVvXo40mKvInUdt/OBib1lApKNjHvn37mDx5SkNKfRmhUD2xseeQlHQVFkvyMdvocrn4wQ9+wJYtW7BarVx99dUsXLiwxY2vH3nkEUaMGNHm/ncmCeRCnMZaqrNy/vnnk5GRQU1NDbfffvtxA3lH1Vp5ZfleAsEQd0/qwweLV1NYWMhjj33C6NEjGDfORlnZvCaTmQ6HgxUrlhPw+xlpgYEHdmJy1+PsM5CqkRMI2lt+oz4kXBu8Aru9f0Nt8NbXjwOsXLmSnJycxhT9CRMmsGDBgmaB/F//+hcTJkxg48aNp8QyRAnkQpzGWqqzkpGRAYRrhDz44IPHvUdH1Fqpcfn598oCLh3ai9ykSLKzs4mOjubBG4fzf/93HpGRg8jKGtlkMnPChInkRVhIWPUFEQVFOKPicF58Hd6UXi0+4/XXX0NrTTDowmp1MXfubjZtSuGXv3yQnJzjB3GA0tJSoqOjGz/HxMRQWlra5JytW7eybds2fve737Fx48Y23bezSSAX4jTVWp2VBQsW0Lt378ag3pqOqLXy2sp91PuC/HBKHwCiouz4fA4KC1+gd+9U9u3zkpNzOIgbPG6GFm4n+ttNhCw2lsVnsCcmmUnHCOIAN910Az5fEQ5HFd98E8d9973c7trgKSkpOJ3Oxs+1tbWkpKQ0Oefdd9/FZrPx+9//nuXLl+Pz+Xj66ad54IEH2vWsjtSmQK6USgNmAcO01qOP+i4CWAV8qrU+/j/vQogucaw6K/Pnz+epp55i2LBhOJ1O3njjjU5tR703wD9W7OX8ASn0T4tm48b/UFFRid1uw2rNpqRkNQMGhCcrq6sqySotJG7dcox+H7X9h1M9fDxfvvceA/Ja3m4tPJFZBGiSki4jIWEkKSmuE9rgYfz48RQUFOD1erFaraxYsYJ77rkHgH379pGbm8svf/nLxvM9Hg91dXXdGsSh7W/kE4H3gOEtfDcL+Lq1i5VSdwF3Qbi2rxCi8x2rzsrMmTOZOXNml7Vj9ur9VLv83DkhnsLCP+L3f4XHM5FgED7/fCGxsbEMHjwES8kBkhfMI8kEdUlpzK0NYPIa8C5d2njOkcITmaWEQi5iY8/lnnveoK7uuWbPf/rppxk8eHCb2mq323n++ee57777SE5OZujQoUybNq1JnZXc3FwA3n77bZYuXYrP52P27Nlcf/31J/2zOlGqrcXllVJTgD9orfOPOPY9oB4YCkS15Y08Pz9fr1279oQaK4ToWbyBIJP+dxFZsR5mTXsXpUyYzWn8+INw7e6nL9+B0VVHwrplRO3ZTsAeReXoSdTn9Gs1KzMQqG7Y5HggqanXY7O1vvzwdKCUWndk/D3SCY+RK6UGAgO01r9QSg094dYJIU5bc75ah6PWy/1jl2I2pzZJvjHpALGb1xC3YRUqFKJ6yBiqh4xBm489JBLe5LgUiyWNrKyfEhk5uEem1He0k5nsvBLwKKV+RnjoxaKUekBr/XSHtEwI0WMFAjUUlczjhSVRnJ0UYlyevckL9oujPiFh9WIs66qoz+wdzsqMiTvm/UIhH35/MQZDJOnptzVscixrNQ454Z+E1vqJQ/9fKWUjPLTydEc0SgjRM2kdoqZmBQ7Hm3yxO5Vi52juGb+zMYibaqtJWLOEyAN78MfEUTJtJu7MYy8N1DrYkJEJiYkzSUi4AKOx9SqJZ6K2rlqZDHwPSFdKPQL8UWvtbvjuamAS4Tfy67XWszuttUKIU5bHcwCH4zVcrh0YTWn8Z/MgcuLdnJNbjfL7idu0mtgt69AGA5WjJlIzYGSzrMxDwqVlSwkG3cTFTSYp6XLM5pZXrYg2BnKt9RJgyTG+ext4uyMbJYToOYJBDxUVC6is/BCDIQKrNY+VBXHsrbTzi6m7id63g4S1SzG56qjr3Z/KUee2mpUZ3uS4msjIwQ2bHMtKt+ORQSYhxAnRWlNXtwmH41X8/qqGMrNmtIZ/f92L9EgX1+95mWjHfrwJyZROnoE35dgJSMFgfcNEZgYZGXdhtw+Uicw2kkAuhGg3v78Ch2MOtbWrMJuTmiz/21BgZVtpFLPM/8BeXUr5uPNwnjUEDC2XrQ2FfPh8xZhMUaSn30lMzDiZyGwn+WkJIdosvFvPEsrK5qK1brpbTyhE9K4tvLVsLMlUcVH/Sg6MvJWQLaLFe4UnMosARXLy1cTHT8NobPlc0ToJ5EKINnG791Jc/E+83gIslnQMhsM7/FhLi0hcvYhtZdGsCNzGvUO3UTd+cov3CWdkOgiFPMTHTyUx8XLM5viu6sZpSQK5EKJV4d163qOq6pNmu/UY3fXEr1tG9O5tBCIi+XPsT4iuDTBjlKvFe4UnMquIjBzWMJGZ2VXdOK1JIBdCtCi8W886HI7XCATqsVqzUaphuWAwSMz2b4jf8BUqGKB68Gi+zprMknezuWXUQeyWUJN7yURm55JALoRoxudzUFLyb+rrN2A2p2CzHV7DHXGwgIQ1i7HUVOLKyKNizGQCMfG8+UU2NlOQKwc7Gs9tmpF5BzEx42UisxPIT1QI0SgU8lFV9RllZe+glAmr9fBkpslZE87KLNyNPzqWkvOuwJ3VG4CiWisLdyVyzRAHsbbgEaVlJSOzK0ggF0IA4HJ9S3HxP/D5ShrWhIcLXKmAn9jNa4jdvBaUonLkBGoGjgTj4fAxd0MaRqW5ZkgxPp+DUMhNbOxEkpOvlIzMLiCBXIgzXCBQS2npW9TULMZojMdmyw1/oTX2gp0krl2Kqd5JXd7Z4azMyOgm11fUm/loexIX9isiyvgtNttAUlK+S0REbpf35UwlgVyIM1S4wNWXOBxvoLUPqzUXpcJJO+aqchJXLyaipBBvfBJlE6fjSWt5hcncDYkENVw39CDZ2Q8SGTlEJjK7mARyIc5AHk8hJSWv4XbvxGxObRy/Nvg8xH3zFTHbvyFktlA+dirOfkNbzMoMhfxUOMv4YNsIpg8wM3H4r05oezVx8iSQC3EGCQZdVFR8SEXFfzEY7A1v4Qq0JmrXFhLWr8DgceHsN4SqERNazMoMT2QWAyE+3Xc5noCJ+y+cIEG8G0kgF+IMEF4T/jUOx2sEg06s1kyUCv/1t5SVkLTqC6wVDjzJ6VScPxNfYmqL9/D7ywmF6oiJGU9EzEzmzd3IBQMTODstutn5outIIBfiNOfzOXA43sDp/AazORmrNVwW1uCuJ2H9CqJ3bSEQYads4kXU9R7Q4l6ZgUAtgUA5ERH9SE29gYiI3ry0dDc1bj/3TOnT1V0SR5FALsRpKhTyUVn5KeXl4U2PGwtchYLEbN9A/Dcrw1mZg0ZRPXQs2mJt4R4efL4SzOZEMjIeIDp6OEoZ8PiDvLxsLxP6JjIiW+qkdDcJ5EKcZrTWuFzbKS7+Z0Na/OE14bbi/SSuWhTOyuyVQ+WYKfhjE1q4RwCfrwilLKSm3kRc3KQmGye/te4AZU4vz1w3vKu6JVohgVyI04jfX0Vp6Vxqa7/EZEpoXBNuqqslYe1SIgt24o+KwTH1clxZvZsNo2gdwu8vQesA8fEXkph4CSZT0/HvQDDEC0t2MzwrjvF9JNnnVCCBXIjTQLhO+DLKyuagdahxTbgKBIjdspbYTWsAqBp+DjWDR6GNTf/qh/fIrCAYdBIdPZrk5GuwWtNafNYHG4s4UOXmscsGyXrxU4QEciF6OLd7D8XFr+L17sdiSQvXCdcae8EuEtYuwVxXS11uv3BWZlRMs+sDASeBQDk2Wx6ZmfcTEdH3mAE6FNI8t2g3/dOiOa9/Smd3TbSRBHIhutl1L64EYO7d49t1XSDgpLx8PlVVnzfUCc8FwFxTScLqxdiLCvDFJVJ84TV40rOaXR8KeRu2WIsjI+NeoqPzGzM7j+WzbQ52ltbxzHeHYzDI2/ipQgK5ED2M1iFqa1fhcPybUMjTWCdc+bzEb1hFzLavCZnMVIyZQu3Zw5plZR7aYk0pAykp1xIfPw2DofmKlebP1Ty3aBc5iXYuGZLeWd0TJ0ACuRA9iNd7kJKS13G5tmE2p2I2JzdmZcavW47R46LurMFUjphAKKJp2dhwQk8poZCbuLgpJCVd0a4t1lbsqmDDgRqevGoIJmPrb+6ia0kgF6IHCAbdVFT8l8rKDzEYbI11wi0VDhJXLcJWVownKQ3HtCvwJTWfpAwEavD7K4iMHEhq6g3YbNntbsPfFu0iNcbKVSMzOqJLogO1OZArpdKAWcAwrfXohmMG4ANgFWAB+gC3aa3dndBWIc44Wmvq6jZQUvIqwWANZnMvDAYzBo+L+PUriN65mZDNTtmEC6nrM7DZcsJwQk8xZnMKWVn/j6iooSe00mRdQRUr91TwyCUDsJqMHdU90UHa80Y+EXgPGH7U8ZVa61kASqn3gKuANzqkdUKcwXy+MkpL38TpXIfJlITVmgOhEDHbvibum5UY/H5qB46kati4ZlmZTRN6bm5I6DnxolbPL95FvN3M9WPa/yYvOl+bA7nW+i2l1JSjjoUIv6WjwhV4MoEdR1+rlLoLuAsgO1v+IAjRmvB2awspK3sbpQyNwyi2kkISVy/GUlWOOz2bijFT8Mc1TcgJj4OXoLXviISe5ksO22NbcS2fbyvlJxf0I9Iqo7Gnog75XVFKXQT8GPhQa7326O+11i8BLwHk5+frjnimEKcjl2sHxcX/bLLdmrHeScLapUTt+xZ/ZAyOKZfiyu7bbBjF768iEKgiOnoEKSnXYbX26pA2Pb94N5EWI7eMz+2Q+4mO1yGBXGv9CfCJUup1pdQ9WuvnOuK+QpwptA5QVPQyNTXLMRrjsNlyUcEAMRtXEbdpNWhN1bBx1AwejTY1/WsbDLrw+x1YLBlkZNyN3T6gwzIu95XX8+HGIu6c1JtYu9QbP1WdVCBXSg0E8rTWCxoO7QV6n3SrhDhDhEIBAoFq/P5SamtXYbXmoFBEFO4mcfUSzHU11Gf3pXL0JAJRsUdd68fnK8JotJOefjsxMedgMHTs0MeLS3djMhq4fWJeh95XdKz2rFqZDHwPSFdKPQL8EfACtyulRgBmYABwX2c0VIjTjcu1i5KSV/H5+mAwWLBaMzHVVJG4ZjH2g/vwxSZQfMFVeHrlNLnucGGrIImJl5KYOB2jMfKE2tBaVmlJjYe31h3gu6OzSYm2ndD9Rddoz2TnEmDJUYd3E16lIoRoI7+/mrKyt6mpWYrRGIPBYCNCe4hft4zYrevRRhMV+ZOpHTAMDIeX+oULW1USDNYSHT2GlJTvYLF0Xr2Tl5ftIaThrknyH9mnOpmCFqKLNK1QGGwcRpnsXcWt7neIq67B2WcglaMmEopo+oYdDNbh95dhs+WSmXlfq4WtOkJlvY83V+3niuG9yEqwH/8C0a0kkAvRBQ4No3i9hVgs6RgMNiwVpRxctos91WO4RM/ion7lXDrCTWKEv/G6UMjXUNgqhl69fkhMzGiU6vyEnFdX7MUTCMo2bj2EBHIhOtHRwyg2Wx7a5ebrpYW8WTiItaFLsCg/FjO8tiOBf+/UnNe3kmsGF5MdswtQJCdfRXz8+RiNzXe07wxOj59Xv9zHRQPT6Jsimyr3BBLIhegETYdRAlitObi9Bj5dEmDungEU6mQyLNX8z4jdLNqXjNEAD07ex9ubUvl4RyKffpvEyIx+3DVlKP0S+nRpydg3Vu2n1hPgnqnyNt5TSCAXooMdOYxiNqdR7orl/eV2PtidgVPbGWndyw9GFTJ2UBCjAZbuTwYgLbKMu/O3c8fYASzeP40319Tygzd2kJd0gO9PyOXqkZmdnlnp8Qf5+7K9nHtWEkMz4zr1WaLjSCAXosGJbvBwyNHDKPtqB/PW+kQWFyQDmumW9Vw1ooLewxKOysrUhEJelIKMjPuJjh7O4H4G7p4a4uPNJfx9+V5+/d4W/vDJDq4fm80t43PpFdc5wyzz1hZSXufl3qkjOuX+onNIIBfiJB05jBIIBlhbPJy3NqaxyRFDFC6+b/qYKweVEDmqP9p8uDaK1iF8viK0zsNiSaF37yebbPBgNhq4bFgvLh2azvr9VbyyfC8vL93D35ftZcaQdG6fmMfwrLgO64c/GOKFJXsYlRPP2LyEDruv6HwSyIU4CeFhlNeoriti4d6hvLslk6JaGxmGCn5lep1Ls/fjGzeWQPQQDhUZChe2KicUqiM2dhI2W2+UMh1zlx6lFKNyEhiVk0BhpYvXvtzH3DWFfLChiPyceG6fmMeFg9IwnuQ4+vvfFHGw2s1vZ8qmyj2NBHIhTsChYZRdRWv4cMcg/rsjnzqfieG2Ah4xv8uUuN3Ujp2EK+OiJteF14OXEhHRj9TUG4mIyEOplW1+blaCnUcuHcj955/FvLUH+OeXe/nhG+vJjI/g1nNyuW50FtG29tdECYU0zy3eRf+0aKaeLZsq9zQSyIVoh1AoQE3NclZs/S9vb8lj6d5L0Cimxe3kB2o2I0x7qB41DseAG8FoPOK6I9eD39uwHvzEt0uLtpm5bWIet5yTy2dbS3hl+V5mLdjG05/v5LrRWdx6Tm67Enk+3VrC7rJ6nr1+hLyN90ASyIVoI2fdTuav/oC5G+LZ7JiM3Rzk2uwd3F39OrnuApx9BnBg1K0E7VGN14THwYuBEElJM0lIuLBD14MbDYrpg9OZPjidjQeqeWX5Xl77ch//XLGXiwalcfvEPEblxLcanLXW/G3RbnIT7cyQTZV7JAnkQhxHrauS15Z8wuz1iiLn2aRGefnRsG3cXDmbFMcuvAkpFJ13Ld6UpntZ+v2VBIM1DXVRrsViSe7Udg7NjOOZ747gZxf35/WVBby5aj8fbS5hWGYst5/bm4sHp2FuYdPkGneAHQ4nT1095KTH2UX3kEAuxDEUVdXx8pIvmbe+njpfDP2T67hz5DYur/6QhG+/IWSxUj5uGs6zBoPhcIA8VB/cas0iM/NHRESc1aXDFemxETw8vT//c15f3l53gH+s2Md9s78mPdbGLefkcv3o7Ca1xYtq3KTH2rhyRGaXtVF0LAnkQhxl88EaXly8kf9urkYDE3JquHZoKeNqV5Hw9QoMPg/OfkOpGnEOIevh8q5aB/B6izAaI0hPv4OYmPEdXh+8PewWE98bn8uNY3NYtKOUV5bv5fcfbecvC3dyzahMvj8hD6fHj9MT4Mfn98NiOvExe9G9JJAL0aDG7edgtYtLn11OhMnP5QMP8p2hNeR69pG4ehHWilI8KRlUjJ2KL+HwMMmR+2QmJl5MQsIMTKaoVp7UtQwGxbQBqUwbkMrWolr+sWIvc1YX8q+vCjAqhcmg+O6YrO5upjgJSuuu3UIzPz9fr13bbFtPIbqNLxDi9x9t5R8rCjAbgtw6ciuXDfYSF6ojft0yondvI2CPonLUudTnnd0kKzMQqCYQqCIqahgpKd/tsH0yO1up08O/v9rP84t30Ss2giUPTe3uJonjUEqt01rnt/SdvJGLM1pBRT33/HslW4q9JEa4SI/xccPwemK2fU38xlWoYJDqIaOpHjIGbbY0XhcKefD5SjCbU8jK+imRkT0riSYl2sZPLujHqj0V3d0U0QEkkIsz1nvrd/CL+d+iCPDr87by3rbeDPdvJ+P9f2GprcKVmUfF6MkEYuIbr9E6iM9XhFImUlNvIi5uMgaDbEosupcEcnHGcXnq+dW7X/D2BgP9k6v59fkFZKkKBq75hHH+Dfij4yiZdgXuzMNbnIXHwcsIhVzEx59HUtIVmEyxrTxFiK4jgVycMbTWbNy3mh/P28ueymiuHXqAu0YVkrhlNbGb15IcMvK6bSbnXpEFxsN/NQIBJ4FAGXb7AFJTb8Bmy2nlKUJ0PQnk4ozg8RTy+tIF/GlpGhajlSen7+A8vZbE95diqndSl3c291XeSoUhnnONO4BDafVFmExxDeVlR5xUWr0QnUUCuTitBQJOCos/4HcfV/LZ7jyGptfy+Ki19N/8CRElhXjjkyibOB1PWiYV74fHwg+Vlw1vs3ZNwzZrttYfJEQ3kkAuTkuhUIDa2i/5atuH/G7xCAprcrlleAH3MY+EhV8TMlsoH3sezn5DmmRlau3H6y0gNnYCyclXYz6ifrgQpyoJ5OK043LtpLj4dd7bbOKF1ROJsgT56/BPmL5vHgaPG2e/IVSNmEDIdrh4VTDoIhTyYDDYyMn5FXZ7327sgRDt0+ZArpRKA2YBw7TWoxuO9Wk4th7IBCq01r/pjIYKcTx+fwVlZW9RVLaav341nsV70xmdUsbThr+QsX03nuR0Ks6/El9iauM14eWEBzEYbFgs6ZhMMRLERY/TnjfyicB7wPAjjiUAc7TW7wEopbYqpRZordd1XBOFaF0o5KWq6nPKyuazszyWJ5fOwOG0cn/qIu6v/jshu53SidOp792/MSuz6XLCC0hKuhyTaXM390SIE9PmQK61fkspNeWoY2uOOs0A1B99rVLqLuAugOzs7HY3Upw52rMBstaauroNOBz/wu+v5MNvR/LiqlwSTS7etP2RMc5t1AweSfWwcU2yMsO79JRht/cjNfV72GzZbX6mEKeiDhsjV0pdCXyitd5+9Hda65eAlyBca6WjninOXF5vEQ7HbOrqNuAOpfHn5dNYvi+eqZZN/Ek9izU9kYNjvoc/9vAmwloH8PmKMBoj6dXrnpPepUeIU0WHBHKl1FRgKvBAR9xPiGMJBuupqFhAZeVHKGVld80QZn2WR4XLzCOmf3Fz9JdUjTmP6qzeRw2jONDaS0LCDBITL8FobPs2aEKc6k46kCulLgHOBe4H0pVSOVrrtu8mK0QbaB2ktnYVDscbBINuzJYM5n3Ti7+vyaKXKmee7W/kjEimaNDN6BayMiMjh5CaemOPqU4oRHu0Z9XKZOB7hIP1I8AfgYHAXGAtsAiIBP4GSCAXHcbt3kNJyet4PHsxm1Oo96fxm3fTWFneixmGVfyqzxf4x06mJjK68ZpQyN+YlZmZ+WOioob3qOqEQrRHeyY7lwBLjjq8Djh1KuiL04rfX0VZ2TvU1CzFaIzGas1l806YtbQP1cEIHo+ZwwWTLXh6nd94TXgYpRitgyQlXdmw2bFkZYrTmyQEiVOQprLyM8rK5qF1CKs1B+31M+8jPy8WjyfH4OCZkZ+RNioP7xFZmYFADYFABdHRo0hJuR6LJaUb+9AzyEqd04MEcnHK0FoTDNbj8zlwOD7DYknHoCy4t+7lN18N5avAAC6N28S9M6qxRR+uQBgKefH5ijGbk8nKeqjHbfIgxMmSQC5OCR7PAUpLZ+P1JqGUGZstF0t5CVuXFPOz8utwKRu/GPU1548KoFR4qCRc3KoYgJSU7xIffx4Gg6W1xwhxWpJALrpVIFBDefkHVFV9jtEYgcGQSUzISeyKhby8bQDPB++iT2QVf5ixg9yEQON1fn8lwWANMTHjSUn5jhS3Emc0CeSiW4RCfqqrlzSMgwewWrNQWnGJZxFTXSu4s+wO1oX6cVm/Yu499yBWk264zoPPV4zFkkFm5r1ERPSTYRRxxpNALrqU1pr6+k2UlPwLv78MiyUNg8GGraQQy8qVhJwjuDLwOCGTmV9N3c15fSsbrgvi8xWjlJHU1FuIi5uEwSB/fIUACeSiCx0aB6+v34TJlIjNloux3klg5Wpe3XcWb4R+Q52OIMri56WrtpIR60VrTSBQQTDoJC5uCklJV2I2x3V3V4Q4pUggF53u6HFwqzUPQyhI5Vc7mL0li/mB+wliYErvSgprg9jNITJivQSDLvx+BzZbLllZPyYiok93d0WIU5IEctFpWhwHx8DujTXMWZ/M576bsCkfl/Ur5upRVfSK8fLA+2cD4PXux2CwkZ5+B7Gx56CUsZt7I8SpSwK5aFF7yskeraVxcJSNNduMzF2TwHrPGOJUPbf128pl47zERQQar9Paj9ZB4uKmNdQIjz7O04QQEshFhzp6HNxozuPT7bHMWxPPHk8SvVQ5D/ZewXmTzERYD682CQZd+HwlKDUAqzWVtLSp3dgLIXoWCeSiQwQCtZSXv09V1ecYDDaCqg/vb0nh7a8TKfVG0l8V8GTmcsZMiccQebiEbHg1ShFKWejV605sNiMgywmFaA8J5OKkHD0OXh/szTsb0nl/SzJ1fjPjDVt4InE5Ayel40vJaHKt319BMFhLXNxUkpOvwmSKQQpnCtF+EsjFCQmPg29uGAcvpdSdy7xNOXy6Iwl/SDHdsJq7oj4lc0wmdX1H4DsiaedQUo/Vmk1W1gOyGkWIkySBXLTbkePgu6rymLdpGsv2xmNWQa42LeFO8wckDkynevgU6iyHS8iGa6MUNST13Epc3LmS1CNEB5C/RaLNDo2DV1Z+zvribN7afDHfFMcQbfZxd+Rn3BZ4l+j0GCrGXEBlfFKTa/3+KoLBamJjJ5KcfA1mc3w39UKI048EcnFch8bBix1vsXhPGm9vmcGeykiS7R5+mvIJt9TMxWYzU5E/iZKcsxr3ygxf622ojZJGZuY92O1nd2NPhDg9SSAXraqr28Tewjf4cGsU7267gNI6GzlxLh7v+znXFb+Jpc5PzbB8yoeMRpvMjdc1LTF7fUOJWfOxHiOEOAkSyEWLQiEvbk8pT7y/jw93jMXptTA0zclD/Vdz2b65WA9UUZ/Vh4OjJxGIjmtybSBQg99fQUzMGFJSvovFktTyQ1ogO9YI0X4SyEUTfn81jtL32Vdmo9xlZ4tjIBNyq7nxrK+ZvPd97Jv34ouJp+T8q3Bn5DS5NhTy4fMVYTYnkZPzMHb7QCkxK0QXkEAuAAgGPVRXL2Lz3o95cnE+Za5I4iN8PH3xZobtX0LsivVog4GKUedSO2AEGA/XPglveFyC1gGSk68hIeECDAZrN/ZGiDOLBPIznNYhnM61OBxvsmR3JE9/eR4ayImr5zLjV0xYPBeTqw5nnwFUjZxI0B7V5PpAoBa/v5zo6JGkpl6PxZLaPR0R4gwmgfwM5nLtxOF4g9r6Av6xfizvbc2if3Idv8lfQ+SyRQzy7MKbkELp5EvwpvRqcm0o5MfnK8JkiiUr6ydERQ2TYRQhuokE8jOQz+egtPQtnM7VlNSl8sTii9lVEcm1gw7wsGE2CYu/wYmdv9lvZMYlSWAwNF4bHkZxoLWPpKTLSUi4GKPR1srThBCdTQL5GSQQqKOy8iMqKz9CKRPLC0fyp2V5mA0h/jT4U64onIPB56X27GH8sPh71BsimWHY0Xh9MFiH31+K3T6YtLSbsFp7tfI0IURXaXMgV0qlAbOAYVrr0cc7Lk4doZCfmpoVlJbOJRTyEDJk8tzKPizYnszQhAr+Yn6W3F3f4k7NoGLMVPwJydS/H9l4vdYBvN6DmExRZGTcR3T0KBlGEeIU0p438onAe8DwNh4X3axpYSsHZnMaRfU5PP5ZHwqqIrgzaRkPO1+ESDulk2ZQn9uvSVYmhIdhQiE3iYkXk5h4KUZj5DGeJoToLm0O5Frrt5RSU9p6/EhKqbuAuwCys7Pb1UBxYjye/Tgcc3C5NmMyJWC15vHxjiSeWZ5NpMHLq7Y/MMm1kZqh+VQPGYM2N8261DqE1j5stkxSU2/GZsvqpp4IIY6nS8bItdYvAS8B5Ofn66545pnK76+ivHw+1dWLMRjsWK15uP1Gnl6aw2c7kxhn3sFfDM8QlRnPgdE3E4iJa3J9eKOHg0BvrNZ0srNvQSlDi88SQpwaZLLzNBEMeqiq+pzy8vkAWK3ZKGVkV3kEv/k0j4POCH5imsddcYupHjMFR2Zes3v4/ZUEg9XExZ2HzdYbpYwSxIXoASSQ93BaB6mtXUNp6WwCgRoslnQMBitaw/sbE/jbVznEU8sbEc9w9og4igfeBMamv+3hCoVFWCwZZGb+D3b7WSglO/UI0VO0Z9XKZOB7QLpS6hHgj1pr97GOd05zxSFaa9zucEKPx7MPszkZmy0XgDqPgT9/nMQXjhymGL7hN30+h7HjqYmManYPv78YrUOkpNzQpEKhFK8Soudoz2TnEmBJW4+LjnHdi+E34yMDq9dbQlnZWzidazAaY7BacxuXA+7a7efxxWdTEojlpzHvccVUjT9tcrP7BgK1BALlREePIiXlBiyW5K7pkBCiw8nQSg8SCDiprPyIioqPMBgsWK05jWPYyuvhw0/9PFM0iWRVzUvD/0ve6DT8hqZj3FoH8PkOYjTGkpkpqfVCnA4kkPcImsrKLygr+w9a+7BaM1Cq4bdOawJbd/LkV4P4IjCc82K+5SczyomMTW96B63x+0sJhTwkJl5KYuIMjMaIbuiLEKKjSSA/hWmtCQbr8PlKcTg+w2xObRJ8rWXF7F26jwfLb6ScWB4YvoXLx7hQquma8GDQhd9fgt1+Nqmpt2CzZXZ1V4QQnUgC+SnK7d5LaekcvN40lDI3TmQCGN31xK5dzr+/7cufAveSHlHPs9O3c3ZK0znm8HZrB1HKQnr6XcTGniPLCYU4DUkgP8X4fGWUl79LTc0KDIZIDIbcw1+GgsRs+4bA11u5130ny0NDOC+vjJ9M2U+kJdTkPofWhMfGTiEl5WpMptiu7YgQostIID9FBIP1VFZ+QkXFh4CxyUQmgK2ogMTVi1lTmc79oVnUqkgenLSXGf3Lm5RHObwmvBeZmT/Cbu/X9Z0RQnQpCeTd7FBlwrKy/xAMurFYejXZbT4lWM5t7rdI/nQjfzZcz3P+GWTHeXjq/G30Tjw8lNJ0Tfj1xMdPk13rhThDSCDvJuHKhBspKXmjoTJhKmZzSuP3KhAgdvMa/lq7jhIdz7WWp1jvzGD62WXcN2E/EebDQymBgBO/v6xhu7UbZU24EGcYCeTdwO3eR2npbOrrt2E2J2KzHVH3RGvs+3eRsGYp5vpa/qqu4RnvFRiD8POpe7iwX8URpwbw+YowGmPIyvoxUVHDZU24EGcgCeRdyOcrb5jIXI7BEInNltck8JqrK0hcvZiI4v3UxKUzK/1B5u3ti80U5MWrt5Id5wEODaOUEQq5SEy8hMTESzAa7d3VLSFEN5NA3gUOT2QuAAzNJjKVz0v8hq+I2fYNIbOZpQO+wy/3TKewJIIku5f0GG9jEA8G3fh8xdjt/UhLuxmbTeq7C3Gmk0DeiUIhP7W1X1Ja+h+CQVeziUy0JmrXVhLWL8fgcVHVdwjPmq7n9Q3ZJEQE+MMlO/jX+vSGU0P4fEUoZaJXrzsb1oQbu6lnQohTiQTyThCeyNxEScm/j5jIbDoBaSkvIXHVImzlJXiS0/l6zA08/s0YtpdGcX7fCu6fWECUNci/1qc37JlZQGzsuaSkfEfWhAshmpBA3sHCE5lzqK/fitmc0HQiEzC4XSR8vYKonZsJ2uyUTriINzyTeeGLLCxGza/P38XUPlUAhEI+QiEPBoOFnJxfYLef3R1dEkKc4iSQd5DjTWQSChGzYwNxX6/EEPBTO3AUO886l6dWnM2aA7GMzqzhp1P2khzpb5jMLEHrABbLBEymeAniQohjkkB+ksITmZ82ZGSqZhOZALbiQhJXL8JSXYE7PZuKMVP4rKIvf56fizeouH/iPq4YWIZS4fv5/Q4iI4eSlvY9TEv2dE/HhBA9hgTyExQKBaitXUFp6X8IhdyYzenNMimNdbUkrF1KVMFO/FExOKZeRmlKP55ZkcvnuxLpn1zHz8/bS3acB62DeL0HMRjsZGT8iOjo0Q1v9BLIhRCtk0DeBkfu0nNoItPheAOfr6TFiUwVDBC7eR2xm1YDmqrh46kZlM/aknieeqs3FS4zt446yI0jijEZNX5/BcFgLfHx55OUdCUmU1QLrRBCiJZJIG8Hj6cAh2M2Ltc2TKb4ZhOZaI29cA8JaxZjrqulPucsKvMnUW+L5eVVmby9OY2sODd/m7mL/in1hEJePJ4irNZMsrIeICKiT/d0TAjRo0kgbwOt/fj95ezd+yIGQ0STPTIPMddUkrB6MfaiAnyxCRRfeDWe9Gx2lNl5ckFvCqojuHKQg7vGHsBqCuLztbzpsRBCtFePCuQtbUTcmQ5lZLrdtQBYrdnNJjKVz0vcxlXEbv0abTJRMXoytf2HEcTI7PXpvLquF/G2AP87Ywejs2oJBJx4PG0vcCW72QshjqdHBfKucri07DyCQRcGwwWAahrEtSZqzzbi1y3D5Hbh7DuIypETCUXYOVhj5Xdf9GZraRTn9Qkn90RbfXg8BzGZosjMfIDo6BFS4EoI0SEkkB9B6xB1dRtwON7E7y/FbE5rmMhsGnAtFY5wVmZZMZ6kNBxTr8CXnIbW8MHWZJ5fmYXJoHlk2m6m9a3E7y/H63WSkDCdpKTLMRoju6eDQojTkgTyBm73bkpL5+ByfYvJ1DwjE8DgcRP/9Qqiv91EyGan7JwLqes7EJSiot7M/y3NZdX+OPIza3ho8l4S7U48nmJstlyysh4kIiK36zsmhDjttSmQK6XSgFnAMK316COOnw9cBZQCWmv9eKe0shP5fA7Kyt6htvYrDIaoFicyDTrIdO8yMt99F4PfR+2AEVQPH0fIYgNgyZ54/rQsB4/fyP9MKOCKgQ4C/iICAUVq6s3ExU3GYJB/M4UQnaOt0WUi8B4w/NABpZQdeAEYpLX2KqXeVkpN01ov7PhmdrxAwEll5UdUVn6MUqYWMzIBbCUH+JPzP+QFD+JOy6JizBT88UkA1HmN/GVFNp/tTKJfUj2/PG8PvaJL8fvKiY4eQ2rq9ZjNiV3dNSHEGaZNgVxr/ZZSaspRh8cDBVprb8PnFcAlQLNArpS6C7gLIDu7e+tnh0JeqquXUlb2Nlr7sFh6oVTzH4Ox3knCumVE7d1BqSGB30fexXUX2jm00/HXB6N5anEeZfUWbh55kJtGFhIKHABiycz8f0RFDZXJTCFElziZ/95PAZxHfK5tONaM1vol4CWA/Px8fRLPPGFah3A611FaOhu/vxKLJQ2Dwdb8xGCA2K3ridu4GkIhqoaN5d6CG/EpC9epHfgCipdXZ/LWpjQyYz08e8VW+sbvI+g/tFvPpRiNEV3fQSHEGetkAnkpEH3E55iGY6cUrTVu904cjjfxePZgMiVjs+W2eG5E4R4S1yzG7KyhPqsPlaMnE4iOxbffAsDOcju/+yKPfVV2rhjo4I7ROzFxEKu1L2lpt8puPUKIbnEygXwlkKOUsjYMr0wAnuuYZnUMr7eIsrJ5OJ3rMRpjsFrzWhzuMNVWkbh6CfaDe/HFJlBy/lW4M3Iav9caSust3PPuAGJtAX5/8XaGp25HKQMpKbcRF3eu7NYjhOg2bV21Mhn4HpCulHoE+KPW2qWU+iHwF6VUGbDxVJno9PurqahYQHX15yhlbnElCoDy+4jbuJrYrevRRiMV+ZOoOXs4pe4Itu+JZHtpJDvKItnsiCakFZN7V3Lf+E1EGEuIjj6HlJTrMJvju6GHQghxWFsnO5cAS1o4/hnwWUc36kQFgx6qq7+gvPxdtA5hsWS0OJGJ1kTu3UHC2qXUugx8lDqDtfHj2LY/nu3rIqlyh+uemAwh+iS6iY/wE2318/DEhVgsiaSnP4zdPlAmM4UQp4TTYnGz1kFqa1dTWjqHQKC2YSLT2uw8t9/A3j0+Cr4pZ0ttXzaoizkQTIL9oPZrsuM8jMmq4ezkevqn1NMn0YXZEOKB9/ugdYjk5MtJSJiB0djCJKkQQnSTHh3Itda4XNtwON7A6z2A2ZyMzRYe2/YHFXsqI9heGsn2skh2OOwUVEcQIrxWPN3mpF+6jxkphQxIqeespHoiLaEm9w8G3Xg8xRgMA7FYUklOntLVXRRCiOPqsYHc4ymktPQ/1NdvRBlicbgHsH1/JDtKI9lWFsnucjv+UDhox5ndDNM7udy0k75ZmqwxmcTGHXtyUusQPl8RSpno1etOrNYe+2MSQpwBelyECoX8fL3jNdbs+ZadFSnsrJzOt2WRuPzhwBxhDtIvqZ6rBjsYbC3knIKP6F2zA09aJhVjpzZmZR5LIFBDIFBOTMwEUlK+i9kcR3iBjhBCnJp6TCCvcfnZUVJDndfPlf9MApIaJyMvOKuc/in1nJ1cT3acB4unLpyV+e12AvYoyqbMoD6nX2NWZktCIT8+30HM5kSys3+O3T5AJjOFED1Cjwnk0TYT/mCIKIuPm0c5GJBST+9EFxbjEYmiwWA4K3PDKlQoRPWQMVQPGYM2H3v3Ha01fn8pWntISpLJTCFEz9NjArnBoBiYbsPjKeXKwc0TSCMO7CVhzRIstVXUZ/YOZ2XGxLV6z2DQjc9XjN3eryEzM7OTWi+EEJ2nxwTyYzHVVpOwZgmRB/bgj4mjZNpM3JnNa4kfqelk5h3Exk6QzEwhRI/VYwO58vuJ27SamC3rwGCgctREagaMBGPrATk8mVlBTMz4hslMycwUQvRsPS+QH5GVaXLVUde7P5WjziVoj2r1svBkZhFmczzZ2ZKZKYQ4ffSoQJ7tL+CW+r+SsnQX3oRkSifPwJuS0eo14cnMMkIhN0lJl8lkphDitNNzAnnNQZ6q/H+4lJXycefhPGsIGJrv6HOkYNCN319CRMRZpKXdgs2W1UWNFUKIrtNzAnlsBs/F/IivdCpPnF3W6qnhycxilDKQlvZ9KTMrhDit9ZxADiyLmILHsx84diAPBGrw+yuIje24ycy5d48/6XsIIURn6VGBvDVaB/B6DzZMZj5EZOQgmcwUQpwRenwgP3IyMzHxUhITL5HJTCHEGaVHB/LwZGYxERF9SUv7vkxmCiHOSD0ykB/OzDSSliZ7Zgohzmw9MJCH8Hj2ERMzjtTU6yUzUwhxxuthgdyAwWAjO/unREYOlslMIYSghwVyg8GKzZZHVNSQ7m6KEEKcMlpPjRRCCHHK61Fv5JKYI4QQzckbuRBC9HASyIUQooc76aEVpdSPgQygHrACP9da69avEkII0VFOKpArpYYDt2ithzd8fhuYCbx71Hl3AXcBZGdnn8wjhRBCHOVkh1bOAgqP+LwHmHb0SVrrl7TW+Vrr/OTk5JN8pBBCiCOdbCBfAwxQStlUODsnH4g5+WYJIYRoq5MaWtFa72sYNvkV4SLhW4DqDmiXEEKINuqIdeSVWutfAiil/g38rQPuKYQQoo06IpD/RSm1DPAC87XW2zrgnkIIIdpIdfVKQaVUGVBwErdIAso7qDk9xZnW5zOtvyB9PlOcTJ9ztNYtrhbp8kB+spRSa7XW+d3djq50pvX5TOsvSJ/PFJ3VZ8nsFEKIHk4CuRBC9HA9MZC/1N0N6AZnWp/PtP6C9PlM0Sl97nFj5EIIIZrqiW/kQgghjiCBXAghejgJ5EII0cNJIBdCiB7ulNyzUyl1PnAVUAporfXjJ3JOT3K8/iil+gCzgPVAJlChtf5Nlze0A7X191ApFQGsAj7VWj/YhU3scG38s302cD3gBiYDj2mtV3dpQztQG/v8UyCXcNbjWcDtWmt3V7azoyil0gj/XR2mtR59jHM6Nn5prU+pX4Ad2AVYGz6/DUxr7zk96Vcb+zwauOKIz1uBUd3d9s7s8xHn/hF4DfhDd7e7C36fjcACwNDwOR1I7u62d3Kf04DKI/r8HnBjd7f9JPp8DXAZsPZEfybt/XUqDq2MBwq01t6GzyuAS07gnJ7kuP3RWq/RWr93xCED4e31eqo2/R4qpb7X8N3eLmxbZ2lLn0cDCvgfpdTPCQeEnlyPpC19dgE+Du9lEEW4JHaPpLV+C3C2ckqHx69TcWglhaY/hNqGY+09pydpV3+UUlcCn2itt3d2wzrRcfuslBoIDNBa/0IpNbQrG9dJ2vL7nEP4L/r1WuuahtLQPuDVLmlhxztun7XWtQ1DK3OVUsXAAcJvrKerDo9fp+IbeSkQfcTnmIZj7T2nJ2lzf5RSU4GpwI+7oF2dqS19vhLwKKV+BkwExiilHuia5nWKtvS5Ftiuta5p+LwcmNL5Tes0x+1zw96/PwUu0VrfSvi/QH7dRe3rDh0ev07FQL4SyFFKWRs+TyA8ZohSKvd45/RQbekzSqlLgIuA+4E0pdT4Lm5nRzpun7XWT2itf6O1/j3hgLZaa/10N7S1o7Tl93kVkKiUMjZ8zgG+7cpGdrC29DmD8AY1gYbPxYCtKxvZFTozfp2SKfpKqQsITxiUAX6t9eNKKQPhzZ2n6PAWc83O6b4Wn7zj9RlIBJYAaxsuiQT+prV+tetb2zHa8vvccN7VwL2AhXCfZ3dTk09aG/9sXwmc13BONvA/uoeu4IA2/dkuBP4CeAhvFTkYeEBrXdwtDT5JSqnJwM3AdOB5wpP1Xjoxfp2SgVwIIUTbnYpDK0IIIdpBArkQQvRwEsiFEKKHk0AuhBA9nARyIYTo4SSQCyFEDyeBXAgherj/D59pKRxc+/DoAAAAAElFTkSuQmCC\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"p, cov = nbi.fit(llsq['f'],llsq['x'],llsq['y'],llsq['ey'])\n",
"\n",
"g = lambda x,*p: dot(p,[fi(x) for fi in llsq['f']])\n",
"nbi.plot_fit(llsq['x'],llsq['y'],llsq['ey'],g,p,cov);"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"### NLSQ \n",
"\n",
"Next, we re-do the non-linear least squared fit done earlier (see [above](#lsq_fit)). Here, we have a regular function in `nlsq['f']` and we also give values for $x$, $y$ and $\\delta_y$. "
]
},
{
"cell_type": "code",
"execution_count": 84,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:26:56.355455Z",
"iopub.status.busy": "2021-11-16T10:26:56.338151Z",
"iopub.status.idle": "2021-11-16T10:27:00.447266Z",
"shell.execute_reply": "2021-11-16T10:27:00.446617Z"
}
},
"outputs": [
{
"data": {
"application/pdf": 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\n",
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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"p, cov = nbi.fit(nlsq['f'],nlsq['x'],nlsq['y'],nlsq['p0'],nlsq['ey'])\n",
"\n",
"nbi.plot_fit(nlsq['x'],nlsq['y'],nlsq['ey'],nlsq['f'],p,cov,\n",
" data=dict(xerr=nlsq['ex'],fmt='.'));"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"### MLE \n",
"\n",
"Finally, we re-do the maximum likelihood fit (see [above](#mle_fit)). Our function is reqular function stored in `mle['f']` and we have the list of observations in `mle['t']`. "
]
},
{
"cell_type": "code",
"execution_count": 85,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:27:00.482707Z",
"iopub.status.busy": "2021-11-16T10:27:00.476019Z",
"iopub.status.idle": "2021-11-16T10:27:02.745772Z",
"shell.execute_reply": "2021-11-16T10:27:02.744561Z"
}
},
"outputs": [
{
"data": {
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\n",
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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"p, cov = nbi.fit(mle['f'],mle['t'],mle['p0'])\n",
"\n",
"nbi.plot_fit(mle['x'],mle['y'],mle['ey'],mle['f'],p,cov,\n",
" data=dict(xerr=mle['ex'],fmt='.'));"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The above illustrates the utility of `fit` - we simply pass it the appropriate variables and then the function takes care to do the right kind of fitting for the inputs. "
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"## Binned MLE"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The package `nbi_stat` also provides a mechanism for performing binned maximum likelihood estimates (or fits). Let generate as sample with a normal signal peak over an exponential background. "
]
},
{
"cell_type": "code",
"execution_count": 86,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:27:02.841230Z",
"iopub.status.busy": "2021-11-16T10:27:02.823798Z",
"iopub.status.idle": "2021-11-16T10:27:04.583649Z",
"shell.execute_reply": "2021-11-16T10:27:04.584636Z"
},
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"data": {
"application/pdf": 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\n",
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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"from scipy.stats import expon, norm\n",
"from numpy import linspace, concatenate, diff, sqrt\n",
"from numpy.random import poisson, seed \n",
"from matplotlib.pyplot import legend,xlabel,ylabel\n",
"import nbi_stat as nbi \n",
"\n",
"seed(1234)\n",
"\n",
"nobs = 1000\n",
"bins = linspace(0,10,21) \n",
"x = (bins[1:]+bins[:-1])/2\n",
"w = diff(bins)\n",
"background = poisson(nobs * expon.pdf(x,scale=4))\n",
"signal = poisson(nobs/2 * norm .pdf(x,loc=4,scale=.7))\n",
"data = background+signal\n",
"hist_bg = background,x,w,sqrt(background)\n",
"hist_sg = signal, x,w,sqrt(signal)\n",
"hist = data, x,w,sqrt(data)\n",
"nbi.plot_hist(*hist, label='Data',fmt='o')\n",
"nbi.plot_hist(*hist_sg,background,label='Signal', as_bar=True,alpha=.3,color='C1',ecolor='C1')\n",
"nbi.plot_hist(*hist_bg, label='Background',as_bar=True,alpha=.3,color='C2',ecolor='C2')\n",
"legend();"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"The PDF we want to fit to the data is given by "
]
},
{
"cell_type": "code",
"execution_count": 87,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:27:04.609181Z",
"iopub.status.busy": "2021-11-16T10:27:04.604274Z",
"iopub.status.idle": "2021-11-16T10:27:04.713854Z",
"shell.execute_reply": "2021-11-16T10:27:04.714788Z"
}
},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle f{\\left(x,\\tau,x_{0},W,a,b \\right)} = \\frac{a e^{- \\frac{x}{\\tau}}}{\\tau} + \\frac{\\sqrt{2} b e^{- \\frac{\\left(x - x_{0}\\right)^{2}}{2 W^{2}}}}{2 \\sqrt{\\pi} W}$"
],
"text/plain": [
"Eq(f(x, tau, x0, W, a, b), a*exp(-x/tau)/tau + sqrt(2)*b*exp(-(x - x0)**2/(2*W**2))/(2*sqrt(pi)*W))"
]
},
"execution_count": 87,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"from sympy import pi as sypi, Lambda, sqrt as sysqrt, S\n",
"x,tau,x0,W,a,b = symbols('x tau x0 W a b',real=True,positive=True)\n",
"f = a/tau*syexp(-x/tau)+b/(sysqrt(2*sypi)*W)*syexp(-S.Half*((x-x0)/W)**2)\n",
"nf = Function('f')(x,tau,x0,W,a,b)\n",
"Eq(nf,f)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"This is _not_ normalised over the range $x\\in[0,10]$, so let us calculate the integral "
]
},
{
"cell_type": "code",
"execution_count": 88,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:27:04.731060Z",
"iopub.status.busy": "2021-11-16T10:27:04.729786Z",
"iopub.status.idle": "2021-11-16T10:27:09.839149Z",
"shell.execute_reply": "2021-11-16T10:27:09.838583Z"
}
},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\int\\limits_{l}^{u} f{\\left(x,\\tau,x_{0},W,a,b \\right)}\\, dx = a \\left(- e^{- \\frac{u}{\\tau}} + e^{- \\frac{l}{\\tau}}\\right) + b \\left(- \\frac{\\operatorname{erf}{\\left(\\frac{\\sqrt{2} \\left(l - x_{0}\\right)}{2 W} \\right)}}{2} + \\frac{\\operatorname{erf}{\\left(\\frac{\\sqrt{2} \\left(u - x_{0}\\right)}{2 W} \\right)}}{2}\\right)$"
],
"text/plain": [
"Eq(Integral(f(x, tau, x0, W, a, b), (x, l, u)), a*(-exp(-u/tau) + exp(-l/tau)) + b*(-erf(sqrt(2)*(l - x0)/(2*W))/2 + erf(sqrt(2)*(u - x0)/(2*W))/2))"
]
},
"execution_count": 88,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"from sympy import Integral\n",
"l,u = symbols('l u',real=True)\n",
"intf = f.integrate((x,l,u)).collect((a,b))\n",
"Eq(Integral(nf,(x,l,u)),intf)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"With \n",
"\n",
"\\begin{align*}\n",
" F_n(x;x_0,W) &= \\frac12\\left[1+\\mathrm{erf}\\left(\\frac{x-x_0}{\\sqrt{2}W}\\right)\\right]\\\\\n",
" F_e(x;\\tau) &= 1-e^{-x/\\tau}\\quad,\n",
"\\end{align*}\n",
"\n",
"being the CDFs for the normal and exponential distributions, respectively, we find "
]
},
{
"cell_type": "code",
"execution_count": 89,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:27:09.881561Z",
"iopub.status.busy": "2021-11-16T10:27:09.874688Z",
"iopub.status.idle": "2021-11-16T10:27:09.987805Z",
"shell.execute_reply": "2021-11-16T10:27:09.996278Z"
}
},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\int\\limits_{l}^{u} f{\\left(x,\\tau,x_{0},W,a,b \\right)}\\, dx = a \\left(- \\operatorname{F_{e}}{\\left(l,\\tau \\right)} + \\operatorname{F_{e}}{\\left(u,\\tau \\right)}\\right) + b \\left(- \\operatorname{F_{n}}{\\left(l,x_{0},W \\right)} + \\operatorname{F_{n}}{\\left(u,x_{0},W \\right)}\\right)$"
],
"text/plain": [
"Eq(Integral(f(x, tau, x0, W, a, b), (x, l, u)), a*(-F_e(l, tau) + F_e(u, tau)) + b*(-F_n(l, x0, W) + F_n(u, x0, W)))"
]
},
"execution_count": 89,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"from sympy import Wild, erf as syerf, evaluate, UnevaluatedExpr\n",
"\n",
"Fn = Function('F_n')\n",
"Fe = Function('F_e')\n",
"wn = Wild('wn')\n",
"we = Wild('we')\n",
"intfe = intf.replace(syexp(-we/tau),-Fe(we,tau)+1)\\\n",
" .replace(syerf(sysqrt(2)*(wn-x0)/(2*W))/2,Fn(wn,x0,W)-S.Half)\\\n",
" .replace(-syerf(sysqrt(2)*(wn-x0)/(2*W))/2,-Fn(wn,x0,W)+S.Half)\n",
"Eq(Integral(nf,(x,l,u)),intfe)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"such that the normalisation is given by the appropriate sum of the CDFs evaluated at the end points of the interval. "
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"With $l=0$ and in the limit $u\\rightarrow\\infty$, it is easy to see that this becomes $a+b$"
]
},
{
"cell_type": "code",
"execution_count": 90,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:27:10.027152Z",
"iopub.status.busy": "2021-11-16T10:27:10.025865Z",
"iopub.status.idle": "2021-11-16T10:27:13.232867Z",
"shell.execute_reply": "2021-11-16T10:27:13.232173Z"
}
},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\lim_{u \\to \\infty} \\int\\limits_{0}^{u} f{\\left(x,\\tau,x_{0},W,a,b \\right)}\\, dx = a + \\frac{b \\left(\\operatorname{erf}{\\left(\\frac{\\sqrt{2} x_{0}}{2 W} \\right)} - 1\\right)}{2} + b$"
],
"text/plain": [
"Eq(Limit(Integral(f(x, tau, x0, W, a, b), (x, 0, u)), u, oo, dir='-'), a + b*(erf(sqrt(2)*x0/(2*W)) - 1)/2 + b)"
]
},
"execution_count": 90,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"from sympy import Limit, limit, oo \n",
"lintf = limit(intf.subs(l,S.Zero),u,oo).simplify()\n",
"Eq(Limit(Integral(nf,(x,0,u)),u,oo),lintf)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"as long as $x_0 > 2\\sqrt{2}W$, as the error function rapidly approaches 1 for arguments larger than 2. What this means, is as long as our peak distribution is sufficiently (e.g., $3\\sigma$ or so) far away from 0, the approximation to the integral by $a+b$ is close. "
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"Let us define our normalised PDF, which we will fit to our binned data. "
]
},
{
"cell_type": "code",
"execution_count": 91,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:27:13.242185Z",
"iopub.status.busy": "2021-11-16T10:27:13.241449Z",
"iopub.status.idle": "2021-11-16T10:27:13.246367Z",
"shell.execute_reply": "2021-11-16T10:27:13.245679Z"
}
},
"outputs": [],
"source": [
"def pdf(x,tau,x0,W,b,a=1,l=bins[0],u=bins[-1]):\n",
" from scipy.stats import expon, norm \n",
" from numpy import log, isnan, any\n",
" \n",
" ef = expon(scale=tau) \n",
" nf = norm(loc=x0,scale=W) \n",
" f = a*ef.pdf(x) + b*nf.pdf(x)\n",
" n = a*ef.cdf(u) + b*(nf.cdf(u)-nf.cdf(l))\n",
" \n",
" return f / n"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"We can now fit our normalized PDF to the binned data "
]
},
{
"cell_type": "code",
"execution_count": 92,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:27:13.297156Z",
"iopub.status.busy": "2021-11-16T10:27:13.261382Z",
"iopub.status.idle": "2021-11-16T10:27:18.765566Z",
"shell.execute_reply": "2021-11-16T10:27:18.767251Z"
}
},
"outputs": [
{
"data": {
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\n",
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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"p, cov, opt = nbi.mle_fit(pdf,(bins,hist[0]),(4,4,1,1,1),\n",
" normalized=True,density=False,full_output=True)\n",
"\n",
"def viz_pdf(x,*p,w=w,a=hist[0].sum()):\n",
" return a * w[0] * pdf(x,*p) \n",
"\n",
"nbi.plot_hist(*hist_sg,background,label='Signal', as_bar=True,alpha=.3,color='C1',ecolor='C1')\n",
"nbi.plot_hist(*hist_bg, label='Background',as_bar=True,alpha=.3,color='C2',ecolor='C2')\n",
"nbi.plot_fit(hist[1],hist[0],hist[3],viz_pdf,p,cov,\n",
" parameters=[r'\\tau','x_0','W','b','a'],\n",
" data={'fmt':'o'},chi2=False,pvalue=False)\n",
"xlabel(r'$x$')\n",
"ylabel(r'$\\mathrm{d}N/\\mathrm{d}x$')\n",
"title('Binned MLE');"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"Alternatively, we can specify a logarithmic PDF"
]
},
{
"cell_type": "code",
"execution_count": 93,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:27:18.775075Z",
"iopub.status.busy": "2021-11-16T10:27:18.772749Z",
"iopub.status.idle": "2021-11-16T10:27:18.790380Z",
"shell.execute_reply": "2021-11-16T10:27:18.792631Z"
}
},
"outputs": [],
"source": [
"def logpdf(x,tau,x0,W,b,a=1,l=bins[0],u=bins[-1]):\n",
" from scipy.stats import expon, norm \n",
" from numpy import log\n",
" \n",
" ef = expon(scale=tau)\n",
" nf = norm(loc=x0,scale=W) \n",
" f = a*ef.pdf(x) + b*nf.pdf(x)\n",
" n = a*ef.cdf(u) + b*(nf.cdf(u)-nf.cdf(l))\n",
" \n",
" return log(f) - log(n)"
]
},
{
"cell_type": "code",
"execution_count": 94,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:27:18.804004Z",
"iopub.status.busy": "2021-11-16T10:27:18.798951Z",
"iopub.status.idle": "2021-11-16T10:27:23.998819Z",
"shell.execute_reply": "2021-11-16T10:27:24.000085Z"
},
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"data": {
"application/pdf": 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\n",
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o0j5//nxOOeWUBm1JSUk8/fTTzJkzh5ycHEaPHs20adMIBoMNYmtunQMHDvDGG29w4MABKisrKSgoYObMmZ32evWYm/2MGzfOaFXW3uum508nGHTzqxl3kZf3FUI3YlNKtUZE1hljxjX3mBbeUz2CIYCIcPjwW1RVfdT2BkqpVmlyUN1eMOgB4wcsOBx5FBU9i9er5VSU6ghNDqrbW7T1D2yyWFhvgdlrl7G8tJQDB54hGPTFOzSlui1NDqpbW1y4mIfWLcAnAiKUelw8u7OQt/Z+SFnZ3+MdnlLdls5WUt3H802v/nxc9uORhjNDPMEAf/t8F1/ZeDsB52+wWlNCD8xaHIsoVTusXr2aG2+8keeff56zzjqLhx56iC9/+csMHjy4U58nGAxy6aWXcuaZZ+L1etmxYwd/+MMfmkyTfeyxx9i/fz/Jycl4PB4eeughRKTZukud5XhrK0V6TMdLk4PqPlyHmjQVJzWdMghwUMDmDeL37sTiyEPEGu3o1HGYMGECjz32GD/4wQ+46qqruPLKK8nLy+MnP/kJAwYMIC8vj2uuuabJdsdTW2nixIncfffdAFx22WW8/vrrfOUrXzn6+IYNG/jjH/94tLbSVVddxd///neuuOKKZusutSXatZWmTp3a5jF1hCYH1X1Ma/ofVe7aezjo9zRpz7E5OHLGZPz+IzjseWRnX6F9qF3U9OnTmTt3Lk6nk2HDhvGnP/2J8ePHc80113D55Zc3mxzaW1vJYrEc/RD1+/3s27ePYcOGNVhn+/btFBQUHF0eMmQIS5Ys4Yorrmi27lJn6GhtpbaOqSP070V1W4Ggl6+lJONoNO7s8Bq+VpUOgM2aicezl6oqvQamq/q///s/7rnnHp588kl8Ph979+6l7v4sLper2W0uv/xyLrjggiZf7733XqvP9d///pdLLrmESy65hHHjGk7vHz9+PFu2bMHtdmOMYe3atVRWVrb7eKZNm8aUKVOYO3cuL7zwAlOmTGHKlCls2tS0xEtHayu1dUwdoWcOqtvyePZxbqkF978D/OELFmrskGtzMHNNkAmrSwnclY01LwGbLZvKyvex124jKanz/rNSHfeb3/yG888/nzFjxvD2229z8803M23aNOru7NhS/3l7aivVd/HFF3PxxRfzta99jaeeeupoqQqAQYMGsWDBAn72s5+Rk5PDqFGjyMjIaPdzxLK2UlvH1BF65qC6LVftVvzrXUz+DEZ7A5zhD/LygFF84QsnI1ah+qnPMe4AYrFitaayf/9v8Psrmuxn1puzjlZ1VbH13e9+lzFjxgDwwgsv8OKLL3LNNdewZs0afvOb33Ra//nmzZtZvPjYhITBgwdTWFgIhGoY1cnKyuLnP/85c+fOpby8vEPPP2rUKK699tpW16lfNwlg5cqVR8tu18XV0jqtHVNn0DMH1S0Fgl5qa7bjX1+LfVQ6XmcFhlApGGsfJ8nfHEL1459R88ddJM8egsWaRCDg5sCB5ygouK3hALVWdO1SkpKS+NWvftWp+3Q6nTz33HN89NFH+Hw+tmzZwhNPPNGkhtGcOXOYPHkyTqeTyy+/nBEjRgA0W3eppbOaWNVW2rFjR7PH1Fm0tpLqPrb95+iPta5CSj74G675B0n+xmDuydgJGH4x5GSsttB4g/vNIlyv7yfx6v4kXJRPbf8heDw7yc29nj59ph/d16wXQv20z9+k7x/Vu2htJdXj1NZsxv+RG+wW7KMzABCxYjAEA7UAOC/Oxz42E9dr+/BtrUREcDj6U1LyZ1yuHXGMXqmuT5OD6nYCQQ+umh3419dgH52OOENdRIKVnOzLCARqMEEfIkLyTYOw5CdQs6AQU1KDxeLAak1n//7f4vc3f7tIpVSUk4OIWERksYjcKyIPishCEUkMP/aBiCwNfy2pt80FIvKUiMwTkaYT21Wv5/HsJbDdhany4xiXRTDowp+SDpmDcTpPICvrInz+Q2CCSIKVlFtOxPgN3gdXYrwB7PZM/P5KiotfwJhgvA9HqS4pFgPSq4wxDwKIyD+AK4GXgTeNMfPqrygiScAzwChjjEdEXhORacaYJY13qnqv2prN+Nd7wGnBfmo6/sAhnjnxMlJTxwCQlDQcn/8IVZUfYLfnY81PIPnrg6h5agf+367DNnc8DscJVFauJilpVHwPRqkuKqrJwYT+LatLDDagP7At/PCpInI7kAisMcYsBiYCu40xdZe8rgRmAM0mBxGZDcwGGDBgQLQOQ3UhgaAbV81O/BuqcZyWgdgt4DMkJB6rxSMipKedRcBfjsu1HZs9B8eYTNwzRxJYuBkZloXtiyfidJ7Aa5sfYyMevMBFr17EbWNvY8aQpjWcVOfbvn07X/7yl8nLy+OXv/wlo0ePZu7cuSQmJvLQQw9RVFTEzJkzmT59OnfccUeHniuS+kXbtm1j4cKFJCYmsmzZMubNm8eECRN45JFH2LVrF9nZ2Wzfvp3nnnuu0+oXRRpbj62tJCIXA98H3jDG1E0JedgYs1pCcwqXi0gVkAtU1du0MtzWLGPMAmABhGYrRSV41aV43Hvxb63F1ASwj88iGKzB7sjDHp6hVEfEQkbmBfj8Ffj9h7HZMrF9ZRRm+2H8T3+EZXAGy7NqeXbnbrzhm8YV1RQx7/15AJogYuCkk07iggsuIDk5mdGjR3Pw4EGWLFly9Crf7OxsJk2a1GxiaE9tpUjqFwUCAX7wgx/wr3/9C4vFwte+9jVsNhvFxcU89NBDlJWVYbFY2lW/SGsrRcAY81/gvyLyoojcaox5yhizOvxYQETeA6YCK4DUepumASVN96h6q5razQTWe5BEK/aRafgDh0hLP7vZda0WB9l9LqWkZCEBfzV9336NwBmGou2GwD1LeOU7VjzWhrcTdQfcPL78LmYse6rhzrSia1Tk5+ezfft2AJ599ll+8pOfHL1/9EsvvcQNN9zQ7Hbtqa0USf2iNWvWYIzhySefpLa2lj59+vDNb36TqqoqHA4HlZWVZGRkUF1dzahRndcV2ZVrK0U1OYjISGBwuMsIYCcwRESGA5OMMc+F208CXgdWAQNFxBnuWpoEPNV4v6p3CgRcuKt24v+4BvvpGYhNwAcJzoEtbmOzpZCdfTklJX/B4q7BKhbyLxT2/93OwRamYxQTaLYCrOp8eXl5rFixgpKSEhwOB8OHD+fgwYP4/X527NjB17/+9Wa3u/zyy5s9c7jvvvuYPHlyg7ZI6hft3r2bVatWsXDhQtLT0/nqV7+Kw+Hgpptu4pFHHuG6666jb9++9O/fnxNPPLHVY5o2bRqBQIDy8nLKy8uPFux78sknOfXUU9sdWyS1lR577LFuV1vJA9wsIqcDdmAEMIfQLKlLRKQfobODvcBCY0xQRG4BnhCRUmCjDkarOm73XvybXRhXAMe4LAKBGpzOE7DZUlrdzuHIIavPDEpO9WGz9UEsNhLTD9Gncg9l6U3Xz3dmwMQ7o3MQqoG8vDwOHjzIs88+y3e+8x2qq6spLi7mlVdeabV7pD21lSKpX5SWlsbw4cNJTw+9Ic455xyWLl3KmDFjeOSRR1i/fj02m40f/vCHPPDAA61ewa21lSJgjNlhjLnSGPOgMeY+Y8y1xphiY8wBY8wVxpifGWN+bIyZGx68xhjztjHmW8aYu40x90czPtW91NaGLnyTZBu24akY4yI5+ZS2NwSSEgeTkTEFv78MTBDnmX34WmkKDm/DoaoEi53bCqa3sBfV2eq6laxWK1lZWeTl5VFaWsq2bdsYOXJkpzxHJPWLzjzzTA4dOnS07MXu3bs5+eST2b9/P1lZWdhsof+j+/bti9vtjuh5u3ttJS2foboFv7+KorevovqO/TgmZJH81YH4fGX06zcbqzWy2RnGGMrL36W6+mPs9jxMIMi/X93Mn4b7KEuDXJud7w+6iktyzmi68bAvdPIRKYCysjIGDx7Mrl276NOnDxAqfrd8+fImdYg64u233+bVV18lJycHu91+dLbPkCFDjtYvWrRoEf/73//Iyclhz549PPnkkzgcDubMmUNCQgIZGRl88sknzJ8/n759+7b4XO2prRRpbM2ts2PHDn784x8zduzYBrWV8vPzI35dWiufoclBdQsVFR9weMGPcT9XRsoPTsZyIjgc+eTkXN6u/QSDfg4d+hcez15s9myClT72zfsYjxMGPzCQ/Pybm++m0uSgeiCtraS6vYqK9/CvdyNpNmwnp2KMh+Tk9s8asVhsZGVNx2rNIOCvwJJm58PxkH0Igkf8+PxlUYheqe5Hk4Pq8vz+SmoOfYL/kxocZ2QhYgDBmXB8Fz5arYlk53wJgGCglv0nhNoDhV68nqJOilqp7k2Tg+ryamo+hdWHwWdwjMvEH6gkIWEoVovzuPdpt2WQnX0ZwWANB3PAa4PgzgBuz55OjFyp7kuTg+ryysuXw8oKJMOOdWgKGB/JKR2fyeJ09iMz8yI8aYkc6G8lUOjG5z1IMOjvhKiV6t70TnCqS/P7K6gt/QTWH8IxJQcIglhxOvp3yv6Tk0dgtaWzr38Zg96vxXgC+PyHcDryOmX/qn2CwSCzZ8/m0KFDLFq0qNP225HaSo899hj79+8nOTkZj8fDQw89hIg08yzRi62ldc466ywSEhIAsFqtR6+x6AyaHFSXVl39CXx4BPxBHOMzCQQrSUw8GYvF3mnP8eKpP2JfyQKqV3xGYLcXX16JJoc4sVgsjB07lsrKylbXi1VtpQ0bNvDHP/6RDRs2AHDVVVfx97//nSuuuKLNY4l2baVp06Yxffr0VvffEZocVJdWUbEcVpYj+clYByUT8JeRnDS8U59DxELqyFOo5jMCO/24R+8lJeXUtjdUUbF69Wpyc3N59NFHeeONN7j33nuZOnVqg3ViVVtp6dKlFBQUHF1vyJAhLFmyJKLk0FmxtbbOpk2bePjhh3G5XIwfP/7oBXSdQZOD6rJ8vnJqiz+Fjw9juXIYmACIHYejX6c/V0LWQCz5doI7fXg8ezDGdGrXgYrcmjVreOWVVzjttNMYPHgwv/rVr5okh1jVVpoyZQo//elPcbvdOJ1O1q5d2yBZNCeWtZVuv/12JkyYQCAQ4NxzzyU1NZVzzz231fgipclBdVk1NZvgg8MQMFjPHUAg+DnJSSOxWDr/bWu3Z2MZ7CCwsYZgwI0/UIXdltbpz6NaV1VVhcVi4bTTTgNCV1BnZGQ0WS9WtZVuuukmFixYwM9+9jNycnIYNWpUs/HUF8vaShMmTABC4w2TJ0/m3Xff7bTkoLOVVJdVUbEc3q9ATkhFhmaACZCU1HklieuzWhOxn5iFqQkQLPHj8+nFcPGwbt06MjMzjy6//PLLLVZmjVRHaitBqJzHz3/+c+bOnUt5eXnE90uIdm2lrVu38txzzx3d1/bt29usGNseeuaguiSf7zC1BzbDpiNYrhuBMR5EnDgcLde06ajkUSfhYi+BQi+eE/eTlDgkas+lmrdmzRqGDBnCvffey44dO7j++uu58MILO7TPpKQknn76aebMmUNOTg6jR49m2rRpBINBpkyZcrR+0cMPP8zcuXPJycmhtLSUe++9F4A5c+YwefJknE4nl19+OSNGjGj1+dpTWynS2Jpb58CBA7zxxhscOHCAyspKCgoKmDlzZodeq/q0tpLqksrLl1P0h4dgwS4cz0zHl19FXkUumRmT2974ONXUbmfPzc9iH5NGyo1DyM//6rEHtbaS6oG0tpLqdsrLl4UufBuYhmVgOhAgKemkqD6nw5GDdYiTQKEbv/8QgaA3qs+nVFemyUF1OT7fIVz7t8LmI6GB6EAtVms6DnuLtxPvFDZrOrYhyQSL3ZjqAH6f3g1O9V6aHFSXU129EVYeAgOWcwfg9x8iI+M8RKL7dhUREoaHivn5Cz14vQej+nxKdWWaHFSXE6qlVI4MzcDSPxVjgqSmNnMDnihIGX4KWCC4S4vwqd5Nk4PqUrzeMtx7tsK2inCXUg12ezZOZ+sXHnUWZ2pfLAWO0Iwlzz7Cd69VPVRxcTHf+MY3GD9+fKvruVwuRo8ezY9+9KMYRRbyzjvvcOuttzJv3jzuv7/5uyZHegztFdWprBLqB/gX8CHgAIYCXzfGuETkAuBKoAQwdfeLbqld9Q41NRth5WEALOcW4PMfIifn6phdrWy39cE6xIlvRTXG78Xvr8Buz2x7Q9VpDh8+zKOPPkpaWhp//etfee655xgzZkyDddpTW6k1K1as4LLLLjtaO6kld999N6effnrE+4XILoJrTSR1lyDyY2ivWFznsMoY8yCAiPwDuFJEFgHPAKOMMR4ReU1EpgGrmms3xnReqUHVpYVmKZUjw7KQvGSMp4yUlPb9UXaExWLDeXI+vne3E9znxZdTpskhhmpra7nmmmv4/e9/z+DBg1m0aBHDhzetpdWe2kqtufrqq4+Wt2jJSy+9xKRJk9i4cWOzCSlaIqm7BJEdw/GIanIwoXPyusRgA/oD24CJwG5jjCe86kqgrmJUc+3NJgcRmQ3MBhgw4PjuCqa6Dq+3FHfhNthRiXX2GAKBKpzOE3A4Ir9hemdIGTmCarYTKPThGbk/6lNo1TELFy7krLPOYvDgwbhcLoCjJanra09tpY7YvHkzW7Zs4Re/+AUbN26MaJv21FZqTSR1l6IpJldIi8jFwPeBN4wxa0VkJlBVb5VKIDf81Vx7s4wxC4AFELoIrrPjVrFVW7slNEsJsJ5TgMdfSp8+X4x5AbzE/CFIppXgTj9utw5Kx9J7773H5ZdfDsBrr712tMZSY+2prdQRixYtIiEhgV/+8pesWLECr9fL/PnzmTt3bovbtKe2UmsiqbsUTTFJDsaY/wL/FZEXReRWQmcPqfVWSSM0xlDSQrvqBW5d9gCzlxSTPyobshPBAykpzX84RJPdHroYzr+jFp/vMIGgG2vMo+idrr/+eh555BG2bNnC2rVrcblcVFVVNfgPOhZ27drFoEGDuOuuu462ud1uqqurW00M9Y0aNapDH+b1ayo5nU5WrlzJrbfe2iC+aIr2gPRIYLAxZnG4aScwBHgBGCgiznAX0iTgKUJjDs21qx4uEKgl60AVeQcDWK8aQCBQQULCIByOnJjHEirCl4F/3QEoD+DLLdPkECMXXXQRF110Ucyeb9myZbz00ksUFRXx4IMP8sMf/hCn09mgrhGEzmKWL1+O1+tl4cKFrdYwak9tpdZEWnepuWNITExs92vRWFRrK4nIUOARYD1gB0YAc4wxxSJyIXA1UAr46s1Wara9LVpbqXurrt7En793LRM/gMSXL8ObdJC8vBvJzJxybKVt/4lZPCUfLeLQvPdImJVNn2kXkzbu7pg9t1Kx0lptpWgPSO8gNC21ucfeBt6OtF31bJWV6xm+FfYUwLAMJyZOXUp1kk8cySHHCoI7A3jcu+MWh1LxohfBqbgzJkjV5nfpcwS2DhP8/iMkJQ2L6xRSR2Ie1kGhInwe7wGMadpNoFRPpslBxZ3Hs5fgh0UAfH6iEAxWkZFxXlxjslnTsQ5NIrDPhXH58HqL4xqPUrGmyUHFXU3NZt4rKuVb37OyPF245aONLCvZH9eYRISEYQUQBP9uL2733rjGo1SsaXJQcffPj1/h2TFejqQIiFDm9fKzDx9mceHitjeOotSRIwEI7vRRW7s5rrEoFWt6m1AVW8/PaLAYNH7+5N+H19nw/xR3wM3jy+9ixrJ6M5nP/m4sIjzKmTkAS187wUIfNTWfxvS5lYo3TQ4qtlwNb6BjAi5KU5u/ArqYQJP1Y6muCJ//o1qMpwy/vwKbLT1u8SgVS5ocVGxNu6/B4uHif9Fn43LK0pqumu/MgIl3xiauZlgsNhwn5eJbWQgHPHgG7dPkoHoNHXNQcRMM+qn5dAsz3w3iNA3PHhIsdm4rmB6nyI5JHhGuCLqlCperML7BKBVDmhxU3Ph8B/FvrGHydpibeQJ2Y8BAX0cG8wZfxYycsfEOkaSBJyEpFmSbO3SvCaV6Ce1WUnFT6yrEv8mFfUQa56cl8k5pELHYeX5s/LqSGnM4crAMdhLcWonLtZNg0IfFYo93WEpFnZ45qLgwxlC9YxPmkB/76AwCgVqQrlfezmpNwn5iGmZ/NabSg9d7IN4hKRUTmhxUXPj95Xg3lAFgPyU0yCvE9r4NkUocPiT0w5ZKvRhO9RqaHFRceDz78H/iwjogCTIMNlsaZA6GjEHxDq2JlOGjwCawzU1trV7voHoHTQ4qLqoPfkJwpwf76HSCgSqSkkbEO6QWOZP7wpBkZFsNNTWbiWaZe6W6Ch2QVjEXCLpxbSgEA/bTMoBaEhIH8fyos+IdWrNstnQYnoF58wB+Vzl+/xHs9qx4h6VUVOmZg4o5r7cI3yYXkmHH0t8B4sBhj929cdtLxELCmBHgDcKuWjweHXdQPZ8mBxVztZXbCWxxYT81nWCwiqTEkxHp2m/F1HHhEuJbq6mt/Ty+wSgVA137L1L1OMYEqdq4EdwG+2kZGBMgMWlovMNqU3LBGMh1Itvc1NZ+Eu9wlIq6qI45hO8h/SChe0j3Bw4ZYx4IP/YB4A6vGjDGTAu3X0Do1qIlgIn0HtKqe/D6SvFvrAK7YB+WQkDKcTj6xTusNjmd/WF4KubTclyu3QSDHiwWZ7zDUipqoj0gnQX82RjzDwAR2Swii40x64A3jTHz6q8sIknAM8AoY4xHRF4TkWnGmCVRjlPFiNu1G/8ntdhHpBG01uJ0DsJqccQ7rDZZLE7spw7Et3wdlLjxDNpPYuKQeIelVNREtVvJGLOmLjHUe76a8M+nisjtIjJPROqK/E8EdhtjPOHllUDDGwDUIyKzRWStiKwtLS3t9PhV56ve8THmUAD76AyM8ZCUOCzeIUUs+YyJoR+2VuF2745vMEpFWczGHETkCuC/xpit4aaHjTEPAz8D7hSRc4FcoKreZpXhtmYZYxYYY8YZY8bl5OREK3TVSXy+w7g3hO4VbT81HWPC3TXdRMrISZBQV4RPxx1UzxaT5CAiU4GpwPfr2owxq8PfA8B74cdLgNR6m6aF21QPUFv7Gf5NtVgHJkGaH7sjB5stOd5hRSwxZTCcnALbqqit3aoXw6keLerJIdxldDFwG5AvIhNFZLiI3FxvtZOAz4FVwEARqRvpmwTE90bCqtNU7F1GcKcX++gMgsEakpJGxjukdrHZ0rGMysXsrCBQXY3PVxbvkJSKmmjPVjoD+AuwFngXSAZ+C7wFXCIi/QidHewFFhpjgiJyC/CEiJQCG3UwumcIBr3ULF8Zuip6dDrG1JKYMCDeYbVb4pjTqVn4OWyvwnPSXhwO7c5UPVNUk0N4VlJKCw9f0cI2bwNvRy0oFRcuVyGsOYRk2JH+ViySgs2WGe+w2i1t3BRq5G+wtYbaKZ+Rmhr/GxIpFQ16EZyKiarD6+Cj8tBAdLCapKQRiHTNEt2tScweDgWJyGcuamo2xTscpaJGk4OKOmMMlaveBHcwXGjPkJgwKM5RHR+HIx9GZGC2luNx7w/dpEipHkiTQysmvjKRiS+fSVWV3ju4I7zeIgIf7AWnFdvJySB27Pa8eId1XEQsOE87GWp8sNeNx7Mv3iEpFRWaHNpgjJ89ex6kouL9eIfSbdXUbIG15VjG5BG01ZCYOBSLpevdEjRSKUeL8FXicunFcKpn0uTQigFFfu77vRs5CPv3P83hw0t0bvtxqNj0JpR4sJzZDxP0kZR0crxD6pDkoeMg3YZsdVNbq+MOqmeKODmIyMBGy/bOD6drsQUguyKI3LUV+4E0iov/yKFDizVBtIPfX437vVC3nGVCPiJ0i0J7rUlIKAgV4dtWSW3tNowJxjskpTpde84cZorISQAiYgV+F52Quo7C/jYeujERLIL/9vewb0+ktPQvlJa+qh8IEXK5tsOaw8hJmQTS3DidA7B282qmVmsCtlMGwIEagkdq8XoPxjskpTpdxMnBGPNLQheu3Qp8CvToT8fFhYup8dWwPdPHrbdaWXG6Df89K7F95ODQoX9y8OBLhCp/qNZU7n0PPqvGemY/AoEqEpOGxzukTpE0dkLoh62Vemc41SO1p1tpAnA18D3gfmPM16MWVZwtLlzMvPfnYQh1H5X5fTx7boAV5yTif3AVtmVw+PASDhz4PcGgL87Rdl3GBKha+j8wIBP6AUJCNyq015q0MeeCTWBbbWjAXakepj1XSL8AzDXGvCUi3xeR0caYHjHHc9YL4xosb8SDt9H1WR4T5JnxLk4oNAyev5alHwkfnLmWn1/o5oQTvq03fmmG270bs7oU+iQSHGTFaTsBmy+17Q27gYS0oTA0GdlWQ23t5niHo1Sna8+Yw43GmLcAjDGPAZOjE1Ls+YP+Bl/eFtbzCiy8Ej4dDlOXGaa8a6iu+oh9++Y3ezHUxFcmMvGVidENvgurPvIxbCgPdylVkJ4+Kd4hdRqbLQPLyBx8nx3hnnXL8Pur2t5IqW6kzTOH8H0WmvwMjIlGQPFw84XzGyzfu/JejniONFkvMyGDL4wYiOcUL2ULDzHx7SIsTx2k5tvCnsAjFBR8H5stLUZRd30V7y8GdxDLmf0Iip/k5FOgrGfcB0FESDjtVIKLdjLgswo8nr3YbN2ryqxSrYnkzOExYBZwD/Bz4Obw954xstiMS4deit3ScKau3WLn0qGXkZt7HVZ7GrtnZlB85QCC7+zC8qs9uCt3s2fPw/h8TZNKbzLrzVnMenMWPt8hfO9/Dk4r5pQ0rNZUnM4T4h1ep0qdcD4ABfvQcQfV40SSHOYYY2YRuovbZGPMjcaYyfTgyqnj88czc/jMo8uZzkxmDp/J+Pzx2Gxp5ORcjcPZj32XJGL7zliCaw4gD2zHe6SI3bt/gder9yeqrt4Ka45gOT2PgLWctLSJiPSsay6TTziFIxlwwgGoqvpQr39RPUqbf63GmJXhHwc3eqhnTDtpwfj88SRYE0iwJvDApAcYnz/+6GNWayLZ2ZeRlDQM/wVWbHechdl2GO7aTKD0MLt3/xyPZ38co4+/ik1vQqkXy4R+GBMgJWVMvEPqdG/vW89PbrRyz5VWvrF6Cf/c/pd4h6RUp2nPv3J+EVksIvNF5N+AJ1pBdQcWi52srIvJzJyOf4If27yzMQdrMHd8THB/FS+tvY0aXw3VvmouevUiFhf2khvaFW+C4o24lq0GQMbnYLHYSUwcEufAOtfiwsXcv+oBKpIERCjzevnZ6kd6z+9Z9XiRDEifboz5yBhzm4h8ERgFvG2M6fV/BSIW8vJmYrdncdC8gu0XZxO470OW/24tz14kR6+TKKopYt778wCYMWRGRPuum+W06vpVUYk9mgxBWFt3VbSLlJSxWCyOeIfVMc83/L09LvtxS8OLID0BL48vv4sZy55quO2sXv+norqhSK5zuFlETiV0m8+Fxph/RzmmbuXrfwx1NxnjJ2i8ZF0LHzkteGl4oYQ74Obe5Xfw6vL7jrY9f9PamMYabYsLF4euEQFunebjq/5MJhk3aWkT4h1ax7kONVgsTmr+6vhiAk3WVao7ajM5GGO+K6GRxGnAT0RkMPAm8BdjTI+uV/zIeY+0uY4/6K+3ZKM008fhFqpRe5us33PUXVVed/FgWbrwtBwkUJrA10/s3lVYAZh2X4PF/PW/oMhb3mS1PEcqTLwnRkEpFT0RXSFtQlXm3gbeDldj/QLwkIi8Y4z5Q0vbichQ4EFgPaEB7EPGmAfCj10AXAmUhJ7C3N9ae1fV+BoJr7eU+z94iEp/07Ia6Y4EZk36GRZLQoyii5Lnm3aNNdvNYoL87fOdzP78umONZ3832tHFxG0F05m38zXc9cqnOA3MzumxM7xVL9PmgLSI3FV/2RjjM8b80xhzfWuJISwL+LMx5hFjzG3Al0XkDBFJAp4Bvm+MmQeMFpFpLbUfx3HFjcORw6VDL8PWaNqmww/nJady8OBf27wWoq7oX5cdzHYdavJVTPPdLAel0fo9xIycscwbfBUOAxhDdoXh1u0JTHa44x2aUp0ikjOHy0SkL1ABrAPWGGMiKkNpjFnTqMkC1AATgd3GmLoZTyuBun9Hm2tf0tz+RWQ2MBtgwIABkYQUE2edcB4iNv609c8AZAasfOU/Ps48eITCOSmUBBfSp8+Xmt22cdG/4xnMjrpGXSzQcjdLvjMNJt4dg6Bib0bOWF797K9gDD9dZsOU+PCffxi/vxqbLSXe4SnVIZEkh3uNMW+KSAowFrhaRL4CFBljLo30iUTkCkIX0m0VkdOB+sVoKoHc8Fdz7c0yxiwAFgCMGzeuS12BdGa/Sby6/e8Y4+ebJxWQlujA8sR2hj24g93fHETp2Fe5acWvEWn4K2iu6F93GMz+Xv8LuH/na3jqXQjmFGFOwRfiGFWMiGA7JQnPXw4RLPHhzSrCZjsp3lEp1SGRXAT3Zvh7NaFxgC8CacBvI30SEZkKTAW+H24qAeqX50wLt7XU3m2J2MjMvIiqQQG23DcM14BkBv+mkP6LqvH7PfgC7siK/tGwQGBXc469mu+lp5NVacAYcq1W7ug7nktyzoh3aDGRfHooGfg/9eJyfR7naJTquIgGpEUkFbgf+Drwa+BXxpiWPscabzuDUAXX24C+4duNrgIGiogz3IU0CXiqlfZuLSXlFByOHMos/2Tbj/sz8JUj5P9rP987LZMd38zCnjWErKwvYLUmtlL0L5ObJz0Qh+jb5nLvorp6A+cfzGTCb8t440uJfPmiXHLzekzh3pZlDAIgZcBpHMlbS2CzB9f5OwkGA1gsLUxbU6obiGRA+ibgM2AIcJox5sF2JIYzgL8AZxG6TuIfwDBjTC1wC/CEiDwIbDTGLGmp/TiOq8txOPLIy7seR0p/dn4tjb2zhpL6STkjHzyAZddOSkr+jM93uJWifxH34MVUIFDLkcP/RaqSqPn9Lg5nWdg80obF4sRhz4l3eFH3/Khv8/yob+N09sM2KhH/Z9UYjwefvzTeoSnVIZGcOTwLfEhoFtHRmxbUXTnd2obGmHVAsyNzxpi3aaZ4X0vt3VHj6ySs1mT69LmMqqrVHJy8Cne/4Qz6zecMe2Anu2b7KRn7CqdkXcLM4TN5cfOLQKjo36VDL21Q26mrMMZQXr6UgMeN63dlGE+Av301CY8zSFLSsB5XaK81NlsqzlNz8f2vCv82N57svTgd+fEOS6njFkly+D6h//jHAd8Tkbp3/MnAlCjF1WNZLFbS0yficORx2PJvtt43lKFP7mPoE7souqIf+2e8zvCsqSRYQ9dCPNBFu5IAXK7t1NRuxfe6m0BhDcnfGsIdY7LweUtJTBwa7/BiLu20M6h2FBLc7Kd27HbS0rpeQlcqUpFcIV3X57+fUJIAQER+Ha2geoPExCHk5l7PIetittxhGPzSEfouOkDS7kx23LwEY/xNZjJ1JX5/FYePvEPwA4N3eRkJ0/NxnJEFJoiIBYejb7xDjLmE1EFYhyXg/7QGr6eEQKAGqzU53mEpdVzadSe4RjI7OZZex27PIjf3Oo4c+R+FszZTOyiJE17Zxcifu8m7zM/BLIPfX47NlhHvUBswJsiRI+8Q2FmL689F2EamkXB56EY+/kAVCQmDsTQaN+kNHPZcbKNS8GwqxZT48eQUk9QLz6BUzxDJv6aPARsJlb9IAAoJDU6rTmCxOMjKuhiHI5/i85fi6n8yg39TyP1/8PO7S6H4xD+RmTmVpKQRXaYPv6bmU2pLPsf1uzIsGXaSvzkEsQjBoAcT9JKaOjbeIcaFiIWUM0bg+XNpaNbSkB2aHFS3pXeC6wJEhNTUMeTmXkv1iCS23jcY6ZvC3Ff9DHm2mMpd/+bQoTfw+2viHSoeTzFHyt7F84dKTE2A5FtOxJJswwR9BPzl9OkzA6ezX7zDjJuUglOx5NsJfOrB5dpBqCyZUt2P3gmuC3E6+5Gb+xVMvwK23NmXoqsGkL7mMKfcs4fEZZs4WPwCtbU74nY7ymDQT1HR7/C8foTA5zUk3zgQW0ESJujH5z9EVtZ0kpJOjEtsXYXT0Q/rqET8n9cQdLnx+criHZJSx0XvBNfF2GwpZGdfQXLGGeyfkcC2B0bgzUlgyDP7GPrkPip3vM6RI2/j91fHPLYjR/6La/EqfMsqcF6Yh2NCH0wwgM9fRmbGNJKTR8Q8pq7Gak0k4bR+4DcEtrlxe/bFOySljkvEySFcVfW3hGYt/dYY872oRdXLWSw2MjLOJTv7SjwFSWz+aT/2f3kgqZsqGXX3bhLf+oDCwjupqdkSs5jc7t2UrHoBntmNbXgqiVf2BxPE5y8lI30yKSmjYxZLV5c6+gxwCsEtflyu7fEOR6nj0q65kuG7wOmd4GJAREhMHIjTeQNVVesovng15WNOZODzxQx6rojgRz72fGsemcMuIyfnSqzW6N0jIhj0sO/TJ+CX2yEzITwAbfD5SkhLO5PU1HGISNs76iUSkwcendLqcRdplVbVLXWN6S+qRRaLg/T0ieTmfoVgwQls/XEe+742ELO5HOZu5sjCl9hZeC8uV2HUYigtfh3fQ+9BpR/HPZOwpNjw+UpJSRlLetpETQyN2O1ZOE5JJ3jYS7DYh9u9I94hKdVumhy6CYcjm5ycq8nKnk7J+Wnw+GnI8D7w7C58d7zHrlV3Ulr6D4LBpneg64ja2s84/Niz8EkV9jnjkKGZ+HwlJCWPIiPj3C4zvbYrCU1pPRWA4GYvVVWtVplRqkvSv+xuRMRCcvJI8vNvJP2kKZh7BiDfGwW7auD7n1D23G/ZVfgAN/77ema9OavDzxcI1LLv5XvgXwexXnYSlvMH4vHsJjHxJDIzpmliaEVy/5FY+toJbPZQVbVOp7Sqbqfr1mdQLbJak+nX7xukp59D8fTn8Y5xIM8WYV7Yi+f9CiqnuijKdeLxHMBuz8ZicbT7OYwxHFj5JIEnP0FOycF682l4PHtJTj6FLIZpOeo2OBx9sZ2SiPd/VVBVgcdzgIQEnf2tug9NDt1YcvJwBg/+GYfT/0vpTxchKzIwvyvk/t/7WHZ6gMLKb8HAROxDCkhIGUhCwhCczn7Y7dnY7TlYrYlN9ll3xvHYqK9TfdcrkObEcefZeIMHSEwcygknfAfL50tjfKTdj9XiIOG0gXjf3gSbKnAN2abJQXUrmhy6OYvFQXb2paSmjudg8otUj0pg7aMbOXdDENaG7kjms36Cr38yVYMSYHASDEqGgYnYsrNxOgtITByC03kCdnsOxgSQQJCiH90O5X4cj5yLN+kQTmd/+ve/rdmEopqXNnoclQmfIOtrqJy6mszMafEOSamIaXLoIZzOfAoKfsSrlU8y/0ufYLCQbXXwVd8JTN5lwxSWE/ykHJYdu2LXn+HEPziFmoFOGJgIg1PwVO9i2ltu+NiD7fvj8Q/2YbdlU1DwA52O2U4JyQVYhyUSWHeY2trPCARqsVqT4h2WUhHR5NCD/Hvnf/jVhj9RV1yjLODlKdtughcO5Jw+AxE5CWutE9nlxeyqwOwsJ1hYjnmjGPyhAdM7rWALgHXGUMzUFKyWRAYM+BE2W3r8DqybslnTcYzOxPXxfthdi6tgBykpp8Y7LKUiosmhu3p+RpOmx2U/bgk0aPMGg/zt893M2nqEYMBFIFiLCXrY88UpQAIiA7GaZORAgGW7C3nOu5MqJ2Q7i/lqWRI3jHsSu71PbI6phxERUs8Yg+ul/bC+kuoxGzU5qG5Dk0M3Ncs0rdlTJM1PlywiyDctleGJy3bAztOD7sXjOUBt7TZqa7fxP8enPGPbjTc8O7XM6+GZwkLy89cyY0jTRKQik9JvOCWD3kXWV1F1zRry8q7XiwZVtxD15BC+reiDwGnGmPH12j8A3OHFgDFmWrj9AuBKoAQwxpj7ox1jd1Tep+ktNWwVu/Abf9N2i43yzEEN2hIW3koCUNdZdIvsx9soubgDHh5ffhczlj3VoJ2zv9uByHsXuz0PzsjCLNqPv/IQXm8xTmfvu0ue6n5iceZwDqHbi45p1P6mMWZe/QYRSQKeAUYZYzwi8pqITDPGLGluxyIyG5gNMGDAgM6Ou0u7bextTdrWFK9h4daF+OpdJW232Jk5fCbj8xvdz/hfdzRYLE5q2B11tJ0AuA51POBeymKxkXjOeFyv7YOPK6gd8pkmB9UtRD05GGNeFZEpzTx0qojcDiQCa4wxi4GJwG5jTF058JXADKDZ5GCMWQAsABg3blx8bnLQhdQlgBc3vwhApjOTS4de2jQxAEy7r8Fi/vpfUOQtb7JavjMDJt7Z2aH2KplnXoor6Z/I+hqqLlhNZuZ58Q5JqTbFs/7Bw8aYh4GfAXeG71WdC1TVW6cy3KYiND5/PAnWBBKsCTww6YHmE0MzbiuYTkKj+z4nWOzcVjA9GmH2Kkmpw2FMOmb9YWpqthAIuNveSKk4i1tyMMasDn8PAO8BUwmNM6TWWy0t3KaibEbOWOYNvoq6odK+jgzmDb6KGTm9837Qncluz8Q2YTAcdsPOGtzu6FXQVaqzxCU5iMhwEbm5XtNJwOfAKmCgiDjD7ZOAxbGOr7eakTOWZGsCKdYE3hp753ElhlmfPsOsT5+JQnTdW9qU8Iyv9RVUV2+KbzBKRSAWs5XOA24A+orI3cCjhLqLLhGRfoTODvYCC40xQRG5BXhCREqBjS0NRquWPXLeI/EOQTWSNvAsDg9JDk1prVpNbu61OqVVdWmxGJBeBixr1OwCrmhh/beBt6MdV2/X1n/3rT3+/Khvd3Y4PV5CwgA4Ixvz2h58R0rw+UpxOHQ4TXVdehFcL1Vubb5H0d/G4+r4iFhJmXw21X/bHZrSetJ2TQ6qS9Pk0Es1d50EwOPrH2/1cQBqXdEIqcdLH/9FqlP+inxUTdXFq8nImBTvkJRqkSYH1W6tdTltrT3Q6jq9uUsqNKU1A7PuMNVVnxAMeo/rRkxKxYImB9VurXU5abdUy2y2FBxnDcO74n0orMI9aCdJScPiHZZSzdLkoNqttS6nNrulenmXVPqUSyj99fuwvpyaMz/V5KC6LP33TqkYSi2YACcmIx9VU1n5Acb0+qovqovSMwfVQKsD0arDHI5+yLg8zF8L8ZYdwD/gsN4vQ3VJeuagVAyJCCmTz4UgoSmttZ/FOySlmqXJQakYyxj/BUi1wfpqqqrWxTscpZql3UqqU2m3VNsSk0+G0zPgo8NUV20kGPRhaVQRV6l40zMHpWLMak3AOfFUqPBiPi/H7d4d75CUakKTg+oyelNF14ypl4IA68qprv4o3uEo1YQmB6XiIKXfGXBSaErr4cP/weM5EO+QlGpAk4NScWC352AdfwLmsyNIlVBc/EeMCcY7LKWO0uSgVByICCnnTQMDb72ykdraLVRWrop3WEodpbOVVExp0b5j0s+4mA9H/J4pb1djuySZYsufSE4+BZstPd6hKaVnDiq2yq2WFr/8hAr3tfR4a7rjYHZi4hDeOt+HxwGB/9tA0OuhpORv8Q5LKUDPHFSMadG+Y/6z6y0+TLWxYo4hu7KKr/x3D5Nm+ElPP4fk5OHxDk/1crG4h3Q+8CBwmjFmfL32C4ArgRLAGGPub61dqWipO+OIZbfV4sLFzHt/Hj4BEMrS4WlfMXyaiN3+HEOGPIjF4oxZPEo1Foszh3OAfwBj6hpEJAl4BhhljPGIyGsiMg1Y1Vy7MWZJDOJUKjqen9Gk6XHZj1sCDdq8duGV4p1c98Zm/EnLcdizYdbiWEWpVANRTw7GmFdFZEqj5onAbmOMJ7y8Eqj7C2quvdnkICKzgdkAAwYM6MSoVVfUkcFsiOOAtutQk6bipEAzK0JZClT+y0L2OQcI2gM6KKjiJl5jDrlAVb3lynBbS+3NMsYsABYAjBs3Tgvj93Dd9g500+5r0pS//hcUecubtGd7LVR+asN//skkjh5Ijgki0gWPSfV48UoOJUBqveW0cFtL7aoXaKtoX4cGs4FZax5rtj0eZx23FUxn3s7XcAd9R9sSxMqN2clY8mtxvVSK3ClUVLxPRsY5ze5j1puzQrFNf75TY1MK4pccVgEDRcQZ7kKaBDzVSrtSHdbSWUU8zjpm5IwF4N7CV/EaP30dGcwpuJiJ1kNU3bAB16MH8b5aw8FhoWsf7PaMmMWmFMRmttJ5wA1AXxG5G3jUGFMrIrcAT4hIKbCxbtC5pXalOqqls4pIzjqiMY12Rs5YXi1ZDRw7MwkEvfhOPEjwiz48bxyCFcWUpv6Vvn2/iYgc3XZx4WI2lm7EG/Ry0asXcdvY25gxpOnAt1LHKxYD0suAZc20vw28HWm7Uj1R4+4qq8VBnz4z8F30Mv5NtQSe3UnF8HdJT59McvII4Ng0WG/QC0BRTRHz3p8HoAlCdRq9CE71CD3pJkN2exZ9ci6m5Ia/436omISffYRcegUmaTCCpdlpsO6Am8eX38WMZfV6YXUarOoAnQahVBeUmHgS6SdOIPNMN65dQvUGD4Gq3eA6RDHNT4MtJhCaNlv3pVQH6JmD6vW64lmHiJCefg4lNxZhPfQJh1ZbcF+QT99Rs8jf9Gyz02DznRkw8c6Yx6p6Jj1zUKqLslhs9Mn+Igk35IIF3C8e5vChd5hTcDEJje45nWCxc1vB9DhFqnoiTQ5KdUC0q8HabenknHQZzmsyCOxwU/2frUxJSmDe4Kuom7vU15HBvMFXHZ0eq1Rn0OSgVBeXmDCIrGnnYz0tEe8blRz69C0uzhxGsjWBFGsCb429UxOD6nSaHJTqBtLSziT9plORRAvuFw5SXraU4Un9GJ7UL96hqR5KB6SVikBLXUfRLr1Rf7/GBBh0iZ3rFrpZ9NIytp7nALG0fOe8YV847udVSpODUhGIV+mNhvu18NHovgzatpezV/r531D4vCChaxYbVN2eJgelIhCv0hvN7be64AN8c1/m1n8FmP/dZL4z5jtYLPqnrDqX/suhVDeTnDuBA7eMI+uI4ZYFpbjfmE9t9WcYE4x3aKoH0eSgVDcjYsE56VpeviYRhxcGP7mD/Ft/i+fVx3BV7dAkoTqFJgeluiGrNZEpN97B3l+fwo5v9QWrlYELPqfv7Pn4X/k/3JU7MUbvf6WOn/SUN9C4cePM2rVrj2vbpXuXdmosStU3pQNjDkuTElt9PBj04nLtoLLiQ5LX7aPv4iOk7KjFm24l+Zox5N/4E5KzT21Q7lupOiKyzhgzrrnHdBRLqW7MYnGQnDyCpKRheC7cz+6z1mH7aDN9Fx/G8ft17P3z9divOI2+3/gpyXmnxDtc1Y1oclAqjuquUejobUhFLCQkFJCQUIBv6nkUTdhE2s7N8OoefC+tZ8/frsPxpTHkz/4pyf01Sai26ZiDUj2M3Z5JRsa5nDzjOfLmP4j1N+dgxmfgeXU9e75wLTt+8mVqCj+Od5iqi9MzB6V6KKs1mays88mcdh41Z31K6aaFuBeu4J3Cjfz5ja9Qlga5pHDrgJlcee53EFv0Pw4mvjIRgFXXr4r6c6mO0eSgVJS1VlqjrfIbN47/foefX8RKSspoks86lb9nvcjvPpyPx4Su7S6hhl/s+B2HFvyeqfaBJI8bR8qE80gZezYWp7PDz13f4sLF1PhqMBi973U3ENfkICIfAO7wYsAYMy3cfgFwJVACGGPM/XEKUakOa628RTTLb8x6oekklI148DaauOR1CH+cYhj2p8/JXbODiqf/gt8KCSP7k3DG6aROOJeU8edhS0097ljq7nttCM2O1Pted31xncoqIvOMMfMatSUBG4FRxhiPiLwGPGWMWdLM9rOB2QADBgw4Y/fu3ccVh05lVfESUfmN4/Tc23ObtG2wBKC5Wa0GTgtCQm2A/vsNA/bBmUccyE4vEgAsYBmaS+LY0aRMOIfUCVOx5+S2+NyNE1NzSQnAYWA0Dc9Qnr/p+Kakq/brylNZTxWR24FEYI0xZjEwEdhtjPGE11kJzACaJAdjzAJgAYSuc4hNyEp1DzdfOL9J270r7+WI50iT9syETL4x6QEAjAni91dQkN2P6rKPqFq/ksDHe/FvLqd60RJq/vIOB5mH9EnCPmwgCSOGkzjydJJPnYCjYAAigj/ob7B/bwsnRl5osm5rdMwiduKdHB42xqwWESuwXESqgFygqt46leE2pVQHXTr0UhZuXYgv6DvaZrfYuXTopUeXRSzY7ZmkpZ1JWtqZmMHfwn/ZYdzuPfxz6195dOMb+KyGbI+PL6/dzuTnt1AZXBTaONmO7aQT+G7BKPwnDSZw0skEB53AvR/e32JSujmclNqiYxaxFdfkYIxZHf4eEJH3gKnACqB+52YaobEHpXqcaHQntWZ8/ngAXtz8IgCZzkwuHXrp0fbmiAh2ex/e2vsB87e9g88GIJQlGH53np2kmy/grCM1+D7bg9lRgXfnAZLf3IX1X+sBCNqF6yYl8YcJgtd67AS/cVJqjY5ZxF7cxhxEZDgwyRjzXHj5NeB1YBERjjnUp+UzlOpcf1zyowbLbY8bGMBgTJDLT78c2V2IrXA/ibuqSdzjZkOCn79OFA6lQZ9KuHaNhQm+PHwD8wkOHkBg4CCCg/vzwgf3NHmOSMcsdLyifbrqmEMlcImI9CN0drAXWGiMCYrILcATIlIKbGwrMSilOl9Hxg0y+kyBPlMwpwcJBCop9x3hBG8ptxXvwPr5HpwHK0mwuggeLCbl031Yfcc+1L+dCqXZQlkfCX3PtuDtH/lzN2dx4WJ++t5PMRj6JvfVLqkIaOE99MxBqUi0OJjtzOSBCMcNAIwxBINuAoEK/P4KvK4SOLAL2+4DOPdVkbDfReJ+L4nFfizhoZFbb7VSlt701CHTnh56bksoc00pmNJknbouKXfAfbQtwZrAvLPn9foE0dqZgyYHNDkoFYk1xWuaHcyeOXxmq2MWkTqWNCrx+yvwuUvhwC6su/bxSUUZf8t147UeW9/hNXzrP0EmbRd8fdPxn5DNRnZyJNPC4SwLR7IsuBJho3h1Gm0Lumq3klKqG6lLAP/a8S+OeI5ENJjdHiKC1ZqI1ZqIw5EHSSdD1iQ4BSYEPZgDK/j3riWUe6tItzq5yJFBwTg/Jf1dOA+6SNhZyIQSP9bgsUzgSoAb51pp7uKO9k6j7W00OSilIjY+f3ynJYP2sFicTOw/jYn9pzVoNyZIIFBDVaCKI/4q/J4y5MAeLHv3Yz9QibPYTZbLxeGkpvvMrjL88I1kAnmZBPrmEOibR9X//oejoAB7//5YEkP30lhcuJjH1z9OcU0x+cn5vWa8QpODUqrbErFgs6Vis6XidALJw46ebQSDAfzBai4u+oBXd7yJr95Zgj0IXyhzUJtRi3N/JUkfF2L1GPbxj2P7zkph5fhknj7tCB5r6NarRTVFzFt5H0Gvl0uHXxHrw40pTQ5KqR7JYrFisaRzdsHF2O1ZDbrDLhlyCWOnjKQ6WENFoBq/r5LgoQOsWv5vMsqDpFdARnk1L5zswmNt2CXlDnr4v7fuod/MO6lMEyrThKo04eIp38FxwkAc/fph69sXW3Y2YrW2EF3Xp8lBKdXjtdwdlgLkhQr4pJ3O/s/fZn+/uscM5ZZgs/srS4MtJ0NaZZCMIzBgt1C27omGK1ktWHIzsOXnYs/Px56Xjz2/AHteX+x5edhy87Dl5mBxOFqMO55TcDU5KKVUWON6VC3Xosoi/5c/Jhh0URuooTpYyxmOdDz7t+Pe9znBg+WY0loCpW4CZXvxrNsBR/yIr+nsUElPxpqThS03G1tuLva8fjjy+/O/lH08fOQvcbsqXJODUkq1oLVaVDZbKvUr/eQXTIEhx7YNBj34/aFpuYFAJT5fOZ6yPXiKd+At2kWwrAJzyEXwkJttO/aSWriXlI2QXAMWA7+91Yq70bUd7oCbe5ffwavL7zvaFq3pt5oclFKqBR2ZvmuxOHE4cnA4co41ZgEnH1usm2310IvnQPgcQYJBkmsMZWnN7zdWU3A1OSilVCs6Mn23rWmwdbOtbr7w8Sbbbm6lvHqklWw7ovNvP6WUUupo2Y6imiIM5uiYweLCxRFtf+nQS7Fb7A3a2lPJtqP0zEEppTpBJHe/a27MAODGab9usr9oX5HeFk0OSinVCaJx97t4XZEOmhyUUqpTRD4NNjZjBh2lYw5KKRUF8R4z6Cg9c1BKqSiI95hBR2lyUEqpKInnmEFHabeSUkqpJrrkmYOIXABcCZQAxhhzf5xDUkqpXqXLJQcRSQKeAUYZYzwi8pqITDPGLIl3bEop1Vt0ueQATAR2G2M84eWVwAygSXIQkdnA7PBitYhsO87nzAbKjnPb7kqPuefrbccLesztNbClB7picsgFquotV4bbmjDGLAAWdPQJRWRtSzfZ7qn0mHu+3na8oMfcmbrigHQJ9evgQlq4TSmlVIx0xeSwChgoIs7w8iQgskpVSimlOkWX61YyxtSKyC3AEyJSCmyMwWB0h7umuiE95p6vtx0v6DF3GjGm6W3rlFJK9W5dsVtJKaVUnGlyUEop1YQmB6WUUk1oclBKKdVEl5utFEu9rYaTiAwFHgTWA/2BQ8aYrn/XkU4gIonAh8BbxpgfxTueaBORYcBMwAWcB8wzxqyOb1TRIyI/BgYRulL4JOBmY4wrrkFFgYjkE/obPs0YM75ee6d/lvXa2UrhGk4bqVfDCXiqJ9dwEpHxQD9jzD/Cy5uBG4wx6+IbWfSJyKOEygyU9vTkICJW4J/ApcaYoIj0BfzGmNI4hxYV4Q/MzUB2+Hj/AfzVGPNynEPrdCJyNeAB7qu7Kjpan2W9uVuppRpOPZYxZk1dYgizADXxiidWROQGQr/fnfGOJUbGAwJ8T0R+ClxKz643VEvo1sxp4eUU4NP4hRM9xphXaVheCKL0Wdabu5UiruHUE4nIFcB/jTFb4x1LNInISGCEMeZOERkd73hiZCChD4yZxpgKEfkToQ/PF+IaVZQYYyrD3Up/EZEiYB/weZzDiqWofJb15jOHXlvDSUSmAlOB78c7lhi4AnCLyB3AOcAEEZkb35CirhLYaoypCC+vAKbEL5zoEpExwI+BGcaYmwidJd0bz5hiLCqfZb35zOFoDafw6dgk4Kk4xxR1IjIDmAzcBvQVkYHGmFVxDitqjDE/r/tZRBKAFGPM/PhFFBMfAn1ExGqMCRA6k/gszjFF0wnAYWOMP7xcBAyIYzyxFpXPsl47IA0gIhcCVwOlgK8XzFY6A1gGrA03JQO/Nca8ELegYkRErgK+AzgIHfPCOIcUVeFuw/MJvbcHAN/ribN34OgA/BOAGygHTgHmGmOK4hlXNIjIecDXgOnA08CjxhhXND7LenVyUEop1bzePOaglFKqBZoclFJKNaHJQSmlVBOaHJRSSjWhyUEppVQTmhyUUko1oclBKaVUE5oclIoCEZkgIltE5Kzw8k9FZHC841IqUnoRnFJRIiLTCdX4eQ14wxizLc4hKRUxPXNQKkqMMW8CWYBHE4PqbvTMQakoEZEfAAcJnT2cYozxxTkkpSKmZw5KRYGIfBf4X/huZKuA50TEGeewlIqYnjkopZRqQs8clFJKNaHJQSmlVBOaHJRSSjWhyUEppVQTmhyUUko1oclBKaVUE5oclFJKNfH/889MKF4zSF4AAAAASUVORK5CYII=\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"p, cov, opt = nbi.mle_fit(logpdf,(bins,hist[0]),(4,4,1,1,1),logpdf=True,\n",
" normalized=True,density=False,full_output=True)\n",
"\n",
"nbi.plot_hist(*hist_sg,background,label='Signal', as_bar=True,alpha=.3,color='C1',ecolor='C1')\n",
"nbi.plot_hist(*hist_bg, label='Background',as_bar=True,alpha=.3,color='C2',ecolor='C2')\n",
"nbi.plot_fit(hist[1],hist[0],hist[3],viz_pdf,p,cov,\n",
" parameters=[r'\\tau','x_0','W','b','a'],\n",
" data={'fmt':'o'},chi2=False,pvalue=False)\n",
"xlabel(r'$x$')\n",
"ylabel(r'$\\mathrm{d}N/\\mathrm{d}x$')\n",
"title('Binned MLE (using logarithmic PDF)');"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"## Extended MLE"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can also perform an extended MLE fit. This allows us to estimate the number of events from the data with Poissonian uncertainties. Let us fit a sample as above (normal signal over exponential background). Note, we need to regenerate the sample as the samples above where binned. "
]
},
{
"cell_type": "code",
"execution_count": 95,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:27:24.014326Z",
"iopub.status.busy": "2021-11-16T10:27:24.007403Z",
"iopub.status.idle": "2021-11-16T10:27:24.024431Z",
"shell.execute_reply": "2021-11-16T10:27:24.023408Z"
},
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [],
"source": [
"background = exponential(4, size=nobs)\n",
"signal = normal (4,.7,size=nobs)\n",
"data = concatenate((background,signal))\n",
"hist_bg = nbi.histogram(background, bins)\n",
"hist_sg = nbi.histogram(signal, bins)\n",
"hist = nbi.histogram(data, bins)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"Next, we define an unnormalized PDF. If the data range is large enough (in our case it is), then the normalisation is approximately given by $a+b$. We will use that to visualize the fit. "
]
},
{
"cell_type": "code",
"execution_count": 96,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:27:24.043334Z",
"iopub.status.busy": "2021-11-16T10:27:24.035550Z",
"iopub.status.idle": "2021-11-16T10:27:24.051363Z",
"shell.execute_reply": "2021-11-16T10:27:24.053562Z"
}
},
"outputs": [],
"source": [
"def pdf(x,tau,x0,W,b,a):\n",
" from scipy.stats import expon, norm \n",
" from numpy import log, isnan, any\n",
" \n",
" ef = expon(scale=tau) \n",
" nf = norm(loc=x0,scale=W) \n",
" f = a*ef.pdf(x) + b*nf.pdf(x)\n",
" \n",
" return f\n",
"\n",
"def viz_pdf(x,*p):\n",
" return p[0] * pdf(x,*p[1:]) / (p[-2] + p[-1])"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"We are now ready to do our extended MLE (E-MLE) fit. Note, when performing an E-MLE fit, we have _one_ additional parameter $\\nu$ - the integral of the sample. This will be the first returned parameter from `mle_fit` and we must give a starting value for it (typically 1 or the number of observations). We perform the fit (note, this may take a little time as we evaluate the integral of the PDF on every evaluation of the logarithmic likelihood function). "
]
},
{
"cell_type": "code",
"execution_count": 97,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:27:24.062828Z",
"iopub.status.busy": "2021-11-16T10:27:24.060350Z",
"iopub.status.idle": "2021-11-16T10:30:07.956900Z",
"shell.execute_reply": "2021-11-16T10:30:07.957399Z"
}
},
"outputs": [],
"source": [
"p0 = (len(data),4,4,1,1,1)\n",
"p,cov, opt = nbi.mle_fit(pdf,data,p0,normalized=False,extended=True,full_output=True,tol=1-3)"
]
},
{
"cell_type": "code",
"execution_count": 98,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:30:07.979562Z",
"iopub.status.busy": "2021-11-16T10:30:07.974627Z",
"iopub.status.idle": "2021-11-16T10:30:10.769824Z",
"shell.execute_reply": "2021-11-16T10:30:10.768794Z"
},
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"data": {
"application/pdf": 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\n",
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"nbi.plot_hist(*hist_sg,hist_bg[0],label='Signal', as_bar=True,alpha=.3,color='C1',ecolor='C1')\n",
"nbi.plot_hist(*hist_bg, label='Background',as_bar=True,alpha=.3,color='C2',ecolor='C2')\n",
"nbi.plot_fit(hist[1],hist[0],hist[3],viz_pdf,p,cov,\n",
" parameters=[r'\\nu',r'\\tau','x_0','W','b','a'],\n",
" data={'fmt':'o'},chi2=False,pvalue=False);"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"We can use our approximation of the normalization of $a+b$ to fit the same data, but with a normalized PDF. "
]
},
{
"cell_type": "code",
"execution_count": 99,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:30:10.782495Z",
"iopub.status.busy": "2021-11-16T10:30:10.781110Z",
"iopub.status.idle": "2021-11-16T10:30:10.783877Z",
"shell.execute_reply": "2021-11-16T10:30:10.784886Z"
}
},
"outputs": [],
"source": [
"def pdf(x,tau,x0,W,b,a):\n",
" from scipy.stats import expon, norm \n",
" from numpy import log, isnan, any\n",
" \n",
" ef = expon(scale=tau) \n",
" nf = norm(loc=x0,scale=W) \n",
" f = a*ef.pdf(x) + b*nf.pdf(x)\n",
" \n",
" return f / (a + b)\n",
"\n",
"\n",
"def viz_pdf(x,*p):\n",
" return p[0] * pdf(x,*p[1:])"
]
},
{
"cell_type": "code",
"execution_count": 100,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:30:10.801036Z",
"iopub.status.busy": "2021-11-16T10:30:10.799895Z",
"iopub.status.idle": "2021-11-16T10:30:14.187411Z",
"shell.execute_reply": "2021-11-16T10:30:14.189007Z"
},
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"data": {
"application/pdf": 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\n",
"image/png": 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\n",
"text/plain": [
""
]
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"source": [
"p0 = (len(data),4,4,1,1,1)\n",
"p,cov, opt = nbi.mle_fit(pdf,data,p0,normalized=True,extended=True,full_output=True,tol=1e-5)\n",
"\n",
"nbi.plot_hist(*hist_sg,hist_bg[0],label='Signal', as_bar=True,alpha=.3,color='C1',ecolor='C1')\n",
"nbi.plot_hist(*hist_bg, label='Background',as_bar=True,alpha=.3,color='C2',ecolor='C2')\n",
"nbi.plot_fit(hist[1],hist[0],hist[3],viz_pdf,p,cov,\n",
" parameters=[r'\\nu',r'\\tau','x_0','W','b','a'],\n",
" data={'fmt':'o'},chi2=False,pvalue=False);"
]
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"source": [
"It is also possible to do extended _and_ binned MLE fits (EB-MLE). We will leave that as an exercise to the user. For more, see also the book on statistics this note accompanies. "
]
},
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"source": [
"# More information\n",
"\n",
"- More information on the methods used here can be found in the longer text \n",
" [Statistics Overview - With Python](https://cholmcc.gitlab.io/nbi-python/statistics/#Statistik) (available in English and Danish).\n",
" \n",
"- Application Programming Interface (API) documentation of `nbi_stat` is also [available](https://cholmcc.gitlab.io/nbi-python/statistics/nbi_stat).\n",
"\n",
"- Many other notes on Python can be found at [the **NBI Python** site](https://cholmcc.gitlab.io/nbi-python). \n",
"\n",
"- Other documentation \n",
" - [NumPy](https://numpy.org)\n",
" - [SciPy](https://scipy.org)\n",
" - [SymPy](https://sympy.org)\n",
" - [Matplotlib](https://matplotlib.org)\n",
" "
]
}
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