{ "cells": [ { "cell_type": "markdown", "id": "c0c42e8b", "metadata": {}, "source": [ "#### Linear Regression\n", "\n", "#### Fitting Polynomial Functions to Data" ] }, { "cell_type": "markdown", "id": "3871e5c3", "metadata": {}, "source": [ "When looking at the results of experiments, it is critically important to be able to fit curves to scattered data points. We will demonstrate that doing so in python is relatively simple, but the theory behind how it works is a bit more involved.\n", "\n", "There are different ways of fitting curves to scattered points. One of the most frequently used is known as Linear Least Squares, a subset of Bayesian generalized fitting. Note, we can fit any order polynomial, not just straight lines, using this method. The “linear” part refers to how the distance between the data point and the line is measured, as we describe momentarily. The method of LLS fits a line to your data that minimizes the squared distances between all the points and the line. The reason for choosing the squared distances is that some points will lie below your line, but distances are positive. By squaring we allow for points below the line to also be a “positive” distance away from the line. The formula for generating a LLS fit outputs the constants of the equation ($a_0+a_1x+a_2x^2 +$...) for as many orders as you require based on the degree/order of your fit. For the linear case, then, LLS outputs a slope and a y-intercept. The formula requires linear algebra and looks like this:" ] }, { "cell_type": "markdown", "id": "2e10ef14", "metadata": {}, "source": [ "\\begin{equation} \\quad \\begin{pmatrix}N & \\sum x_i & \\sum x_{i}^2 & \\cdots & \\sum x_{i}^m\\\\ \\sum x_{i} & \\sum x_{i}^2 & \\sum x_{i}^3 & \\cdots & x_{i}^{m+1}\\\\ \\vdots & \\vdots & \\vdots & \\ddots & \\vdots\\\\ \\sum x_{i}^m & \\sum x_{i}^{m+1} & \\sum x_{i}^{m+2} & \\cdots & \\sum x_{i}^{2m} \\end{pmatrix} \\begin{pmatrix} c_1 \\\\ c_2 \\\\ c_3 \\\\ \\vdots \\\\ c_n \\end{pmatrix}=\\begin{pmatrix} \\sum y_i \\\\ \\sum x_i y_i \\\\ \\vdots \\\\ \\sum x^{n-1}y_i \\end{pmatrix}\\end{equation}" ] }, { "cell_type": "markdown", "id": "15378056", "metadata": {}, "source": [ "This may look complex, it's not hard to implement. $N$ is the number of data points you are trying to fit to. To enter the $x$ sums, simply take your x array (such as an array of centroids), and run `np.sum` on them (squared, cubed, etc as required). The $y_i$ are the\n", "$y$ values of the data points, which can be multiplied by the $x$ arrays within the `np.sum` function." ] }, { "cell_type": "markdown", "id": "f4fadcb0", "metadata": {}, "source": [ "### Fitting a Straight Line to Data\n", "\n", "The equation above shows us how to fit any order polynomial to a set of data (based on how large you make the array). Let us begin by fitting an order 1 polynomial (a straight line) to some data. In this case, the LLS formula simplifies to:" ] }, { "cell_type": "markdown", "id": "023dacfc", "metadata": {}, "source": [ "\\begin{equation}\n", "\\quad\n", "\\begin{pmatrix} \n", "N & \\sum x_i \\\\\n", "\\sum x_i & \\sum x_{i}^2\n", "\\end{pmatrix}\n", "\\begin{pmatrix}\n", "c_1 \\\\\n", "c_2 \\\\\n", "\\end{pmatrix}=\n", "\\begin{pmatrix}\n", "\\sum y_i \\\\\n", "\\sum x_i y_i\n", "\\end{pmatrix}\n", "\\end{equation}" ] }, { "cell_type": "markdown", "id": "11f5592c", "metadata": {}, "source": [ "where we are solving for $c_1$ and $c_2$, the slope and intercept of our best fit. We know N (it's just the number of data points), we know the $x_i$ and $y_i$, so now it's just a matter of figuring out how to do matrix multiplication in python. If we remember our linear algebra, to get the $c_1, c_2$ on it's own, we need to multiply both sides *on the left* by the *inverse* of the (N...) array. So we arrive at:" ] }, { "cell_type": "markdown", "id": "e46748c6", "metadata": {}, "source": [ "\\begin{equation}\n", "\\quad\n", "\\begin{pmatrix}\n", "c_1 \\\\\n", "c_2 \\\\\n", "\\end{pmatrix}=\n", "\\begin{pmatrix} \n", "N & \\sum x_i \\\\\n", "\\sum x_i & \\sum x_{i}^2\n", "\\end{pmatrix}^{-1}\n", "\\begin{pmatrix}\n", "\\sum y_i \\\\\n", "\\sum x_i y_i\n", "\\end{pmatrix}\n", "\\end{equation}" ] }, { "cell_type": "markdown", "id": "2fed23fd", "metadata": {}, "source": [ "where the inverse of the (N...) matrix is now being dotted into the ($\\sum y_i$...) array. The functions you'll find useful when setting this up:\n", "- `np.linalg.inv(arr)`\n", "- `np.dot(arr1, arr2)`\n", "\n", "Remember that to set up multidimensional arrays, the format is `np.array( [ [a,b,c,...] , [d,e,f,g,...],...])`\n", "that is, lists nested inside a list nested inside the function call. " ] }, { "cell_type": "markdown", "id": "c4c22aa0", "metadata": {}, "source": [ "#### Loading the Data \n", "There is a file called data.txt in our data area, which contains the data we are going to be fitting. You can load it into python using the `np.loadtxt` function. You'll want to end up with an array of $x$ values and an array of $y$ values. Once you've done that, you can use the given code to generate a plot to see what data we are fitting." ] }, { "cell_type": "code", "execution_count": 1, "id": "dd0f9938", "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "from scipy.optimize import curve_fit\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "code", "execution_count": 2, "id": "c75d2336", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x,y = np.loadtxt('data/data.txt', unpack=True)\n", "plt.plot(x,y,'bo',label='data')\n", "plt.xlabel('x values')\n", "plt.ylabel('y values');" ] }, { "cell_type": "markdown", "id": "fb958210", "metadata": {}, "source": [ "Let's define a function called `linear_fit` that implements the equations given above and returns two values: the slope $m$ and the y-intercept. " ] }, { "cell_type": "code", "execution_count": 26, "id": "059dd632", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(array([2.57251848]), array([47.7249833]))" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "def linear_fit(x_data, y_data):\n", " N = len(x_data)\n", " array_1 = np.array([[N, np.sum(x_data)],[np.sum(x_data),np.sum(x_data**2)]])\n", " array_2 = np.array([[np.sum(y_data)],[np.sum(y_data*x_data)]])\n", " array_1_inv = np.linalg.inv(array_1)\n", " out_arr = np.dot(array_1_inv,array_2)\n", " intercept, slope = out_arr[0], out_arr[1]\n", " return slope, intercept\n", "\n", "linear_fit(x,y)" ] }, { "cell_type": "markdown", "id": "58cd3ba4", "metadata": {}, "source": [ "Now we have the y-intercept and slope of our \"best fit\" to the data. From a scientific perspective, we are basically done - it's almost always the values of the slope and intercept that are of interest to us when fitting. But just to see what we've accomplished, let's plot the best fit line over our data:" ] }, { "cell_type": "code", "execution_count": 27, "id": "9de185a0", "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def plot_fit(x,y):\n", " slope, intercept = linear_fit(x,y)\n", " fit_line = slope*x + intercept\n", " plt.plot(x,fit_line,'r',label='Linear Fit')\n", " plt.plot(x,y,'bo',label='data')\n", " plt.legend()\n", " plt.xlabel('x values')\n", " plt.ylabel('y values')\n", " plt.title('Best fit to our data');\n", " \n", "plot_fit(x,y)" ] }, { "cell_type": "markdown", "id": "ebf0ec26", "metadata": {}, "source": [ "#### Evaluating the Fit\n", "So we have a fit to our data. But is it a good fit? Visually, it seems so. But we can be a little bit more quantitative. \n", "\n", "To do so, we are going to evaluate the **residuals,** that is, the *difference* between the prediction of our fit and our data itself. Given that our data has no uncertainty (at least, none that has been specified), this is easy to calculate. Fill in the residual function below to simply return the difference between the fit and the data, along with a single quantity that is the sum of those residuals. As an arbitrary convention, subtract the fit from the data, instead of the converse." ] }, { "cell_type": "code", "execution_count": 5, "id": "27313fa5", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "6.700417998217745e-12\n" ] } ], "source": [ "def return_residuals(x,y):\n", " slope, intercept = linear_fit(x,y)\n", " fit_line = slope*x + intercept\n", " residuals = y - fit_line\n", " return residuals, np.sum(residuals)\n", "\n", "residuals, sum_residuals = return_residuals(x,y)\n", "print(sum_residuals)" ] }, { "cell_type": "markdown", "id": "9fe2e784", "metadata": {}, "source": [ "If we take a look at the sum of the residuals, we notice it's an absurdly small value. This means that though the spread in residuals might be large, on average, the fit overpredicts the data and underpredicts the data in equal amounts, which is a sign of a good fit.\n", "\n", "The actual spread is large, as shown by the histogram of the residuals. Note: stats.gaussian_kde does at kernel density estimation on the residuals, turns each residual into a little gaussian bell curve then adds them up. This is a clever way to display a histogram where the choice of the bins does not distort the distribution of the points." ] }, { "cell_type": "code", "execution_count": 6, "id": "d0734fb0", "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from scipy import stats\n", "\n", "bins = np.arange(-40,40,5)\n", "plt.hist(residuals, density=True, bins=bins, alpha=0.5)\n", "kde = stats.gaussian_kde(residuals)\n", "xx = np.linspace(min(residuals), max(residuals), 100)\n", "plt.plot(xx, kde(xx));" ] }, { "cell_type": "markdown", "id": "5430f361", "metadata": {}, "source": [ "#### Higher Order Polynomial Fits\n", "\n", "We have successfully fit a straight line (polynomial order 1) to our data. But what if the data were better described by a quadratic? It may look linear when we plot it, but it might be that the \"section\" of the data we have access to represents a small one, and we can't see the overall curvature well. \n", "\n", "We can fit any order of polynomial to our data (being careful to avoid over-fitting - remember, a high enough order polynomial can fit *any* set of data with 0 residual). But, instead of going through the pain of constructing a 3x3 array in the way we did above, let's go ahead and utilize the handy function created for the purpose in the Numpy module - since we now know how it works. " ] }, { "cell_type": "code", "execution_count": 7, "id": "715c5b81", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "-0.001795051067732664 2.7502285323029043 44.82238572194903\n" ] }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def quadratic_fit(x,y):\n", " fit_coefficients = np.polyfit(x,y,2)\n", " a0, a1, a2 = fit_coefficients[0], fit_coefficients[1], fit_coefficients[2]\n", " return a0, a1, a2\n", "\n", "def plot_quadratic_fit(x,y):\n", " a0, a1, a2 = quadratic_fit(x,y)\n", " print(a0,a1,a2)\n", " fit_line = x*a0**2 + x*a1 + a2\n", " plt.plot(x,y,'bo',label='data')\n", " plt.plot(x,fit_line,'r',label='quadratic fit')\n", " plt.legend()\n", " plt.show()\n", " \n", "plot_quadratic_fit(x,y)" ] }, { "cell_type": "markdown", "id": "3ce48e7b", "metadata": {}, "source": [ "This looks like it could be a decent fit as well, though it doesn't look as good as the linear fit. In fact, if you print them out, you'll see that `polyfit` is telling us that it thinks that *if* this data is quadratic, the quadratic coefficient is very small; the remaining linear and constant coefficients are very similar to those in our linear fits. Looking at the residuals will be helpful:" ] }, { "cell_type": "code", "execution_count": 8, "id": "bd1d155b", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "-589.4209680212757\n" ] } ], "source": [ "def quadratic_residuals(x,y):\n", " a0,a1,a2 = quadratic_fit(x,y)\n", " fit_line = x*a0**2 + x*a1 + a2\n", " residuals = y - fit_line\n", " return residuals, np.sum(residuals)\n", "\n", "q_residuals, q_residual_sum = quadratic_residuals(x,y)\n", "print(q_residual_sum)" ] }, { "cell_type": "markdown", "id": "614edd96", "metadata": {}, "source": [ "The net sum of the residuals is much larger for the quadratic case. So it would appear that the linear fit is better here, e.g., the data most likely *are* linear in nature. The residuals look a little lopsided." ] }, { "cell_type": "code", "execution_count": 9, "id": "be0464c7", "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "bins = np.arange(-40,40,5)\n", "plt.hist(q_residuals, density=True, bins=bins, alpha=0.5)\n", "kde = stats.gaussian_kde(q_residuals)\n", "xx = np.linspace(min(q_residuals), max(q_residuals), 100)\n", "plt.plot(xx, kde(xx));" ] }, { "cell_type": "markdown", "id": "c38740a7", "metadata": {}, "source": [ "As a note though, that means situations like this, where one order of fit is better than another, rarely actually happens. Even when *nature* chooses a truly, fundamentally linear relation between two measurable variables, we can almost never obtain measurements of that relation so perfectly distributed around the true values so as to find that the linear (or any other order) fit is the best. In reality, we tend to simply try to use the lowest order fit that adequately describes our data. \n", "\n", "This isn't too difficult - if you, for example, plot the residuals for each data point for both the linear and quadratic fits, you'll find they look similar in form. Typically, if the data truly were quadratic, the linear residuals would have a strong functional form to them (an under, then over, then under fit)." ] }, { "cell_type": "markdown", "id": "2382ea12", "metadata": {}, "source": [ "#### Least Square Method\n", "\n", "The least-squares method is a crucial statistical method that is practised to find a regression line or a best-fit line for the given pattern. This method is described by an equation with specific parameters. The method of least squares is generously used in evaluation and regression. In regression analysis, this method is said to be a standard approach for the approximation of sets of equations having more equations than the number of unknowns.\n", "\n", "The method of least squares actually defines the solution for the minimization of the sum of squares of deviations or the errors in the result of each equation. Find the formula for sum of squares of errors, which help to find the variation in observed data.\n", "\n", "The least-squares method is often applied in data fitting. The best fit result is assumed to reduce the sum of squared errors or residuals which are stated to be the differences between the observed or experimental value and corresponding fitted value given in the model.\n", "\n", "There are two basic categories of least-squares problems:\n", "\n", "1) Ordinary or linear least squares\n", "2) Nonlinear least squares\n", "\n", "These depend upon linearity or nonlinearity of the residuals. The linear problems are often seen in regression analysis in statistics. On the other hand, the non-linear problems are generally used in the iterative method of refinement in which the model is approximated to the linear one with each iteration." ] }, { "cell_type": "code", "execution_count": 10, "id": "8cfbacb4", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(array([5.10939915, 2.87266832]), 1)\n", "[5.10939915 2.87266832]\n" ] }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAhMAAAGkCAYAAACLhKd0AAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjguMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/SrBM8AAAACXBIWXMAAAxOAAAMTgF/d4wjAAA09klEQVR4nO3deXxU5aH/8U+GbGASkohRNGgrtCyKgNXWVlBAqwi4FtRWjVZF7bVq7aKtiLet5Xr7U6nXtu61alGKC1qQiLaiUm21FmWpJOKKCwKJkoSQZZLM/P4YTBvZErKcWT7v1ysvnDMnZ744wHzzPOc8Jy0ajUaRJEnaRaGgA0iSpMRmmZAkSZ1imZAkSZ1imZAkSZ1imZAkSZ1imZAkSZ2S3pMvFolEWLt2Lbm5uaSlpfXkS0uSpF0UjUbZtGkTe++9N6HQ1uMQPVom1q5dy4ABA3ryJSVJUhd5//33KS4u3mp7j5aJ3Nzc1jB5eXk9+dKSJGkX1dTUMGDAgNbP8c/q0TLx6dRGXl6eZUKSpASzvVMUPAFTkiR1SofKxJIlS0hLS2v9uv766wGoq6tj2rRpXHrppZx55pmsWbOmW8JKkqT406FpjnvuuYdf/epXrY/PPvtsAEpKSjjhhBMoKSlh5cqVHH/88SxdupSMjIyuTStJkuJOu8tEWVkZxcXFfO9732uzfenSpSxcuJD7778fgOHDh5OWlsacOXMoKSnp0rCSJCn+tHua44YbbuB//ud/OOKIIygtLW3dPn/+fAYNGkRWVlbrthEjRrBgwYKuTSpJkuJSu8vElClTuOGGG2hsbGTSpElcd911AKxatYp+/fq12begoIDVq1dv91hDhw6luLiY4uJiZs2atYvRJUlSPGj3NMdxxx3Hcccdx2WXXcaMGTO45pprOPnkk6murqawsLDNvllZWdTV1W33WGVlZV4aKklSkujwpaFpaWlce+21HHjggTzzzDMUFhbS2NjYZp/6+noKCgq6LKQkSYpfu7TORFpaGuPHj6exsZGBAwdSWVnZ5vmKigoGDx7cJQElSVJ82+VFqz766CMmTJjAlClTWLFiRZvRiVWrVjFp0qQuCShJkuJbu8rEe++9xyWXXMJ7770HwNy5cznggAMYMmQIo0aNYvTo0SxatAiAZcuWEQqFmDp1avelliRJcaNdZSI9PZ3nnnuOYcOGceSRR9Lc3Mz06dNbn3/ggQd4+OGHueKKK7j55pspLS2lV69e3RZakiTFj7RoNBrtqRerqamhb9++VFdXezWHJEkJYmef397oS5KkZFD5JjTWBvLSlglJkhLda48SvWMs1csXEG6O9PjLd+hGX5IkKb5EF02n8eV7+EXGpTz5VD9ylixh/JAipk8cSiiU1iMZLBOSJCWiSAuEejF/XT6/afwFb2wuAsJU1IaZ/eIaAGZMHtYjUZzmkCQp0bz9LPz2K4SrN3BT5aG80VzU5unG5giLy9f32JSHZUKSpEQRicCS62HOt+Dwy6hKy6O2oWmbu9Y2tlBVH+6RWE5zSJKUKP75O3h1Npy7CPofRH5zhJzsDCpqty4NOVnp5PfO7JFYjkxIkhTv1i6D+o0w6iy44DnofxAAmekhxg8pIiu97cd51pbtmek98zHvyIQkSfEqGoWlv4cnp8PJt8OwEyAju80u0ycOBWBx+XpqG1vIyUpvvZqjp7gCpiRJ8ShcB49fDm8thil3w+fH7Hj35ghV9WHye2d2+YjEzj6/HZmQJCkeNTdAtAUu+ivk7rXT3TPTQxTlZu90v+7gOROSJMWT1x6DP18DfQrhG3e1q0gEzTIhSVI8aGmCRVfB/Eug+NCg03SI0xySJMWDuWdC9QdwwbOw+8Cg03SIZUKSpCDVrIW8veHIK2GPIZDZJ+hEHeY0hyRJQYhEYMkN8NuvwOZK2OfghCwS4MiEJEk9r34jPHoRbCiDsxfAbv2CTtQplglJknpa2eNAGlz4HPQuCDpNp1kmJEnqCdEovHIf7HsYjDoTRp4BoeQ42yA5fheSJMWzcB089h1YfG1siiMtLWmKBDgyIUlS99q0Hv5wMmTlwoVLYlduJBnLhCRJ3aWlCfrsDl86Bw75NvTKCDpRt0ieMRZJknZBuDnChpoGws2RrjtoS1PsTp8Png290uErFyRtkQBHJiRJKSoSiTKztIzF5RuobWgiJzuj9dbdoVDarh+45iN4+FxoqIZT7+u6wHHMMiFJSkkzS8uY/eIaGreMSFTUhpn94hoAZkwetusHfuR8KNgPJs1K2EWoOsppDklSygk3R1hcvqG1SHyqsTnC4vL1HZ/yiETg9Sdil3+ePhtOujVligQ4MiFJSkFVdWFqG5q2+VxtYwtV9WGKcrPbd7D6jfDYf8H6f8Xu9pngq1nuCkcmJEkpJ79PJjnZ2z4hMicrnfzeme070EfL4fYjIdICFzyXkkUCLBOSpBSUmR5i/JAistLbfgxmbdmemd7Oj8f6jXBwCXzzj9CnsBuSJganOSRJKWn6xKEALC5fT21jCzlZ6a1Xc+xQuA6e+BEMOwm+8HXYf2y3Z413lglJUkoKhdKYMXkYV04YQlV9mPzemTsfkfj4LXiwBDJ3gz0P6JmgCcBpDklSSstMD1GUm73zIlH9IdwxDj5/JJyzMCmXxd5VjkxIkrQjLc2w6SPIHwBn/wn2HhV0orjjyIQkSduzaR3cdwI8cUXssUVimywTkiRty7vPw+1HQN8B8I27gk4T15zmkCRpW166Hcb+GL70bUjrxL06UoAjE5Ikfaq+Cv7yU2gOx27Sdci5Fol2sExIkgTw0Qq4Yyys+xc011siOsAyIUlS2eNw97Ew8gz41oOQ3TfoRAnFcyYkSamrqQHSs6BoKJx+PwwcH3SihOTIhCQpNX3yNvzuaFj+R9h9oEWiEywTkqTUU74Qbh8L+42GA78RdJqE5zSHJCm1VH8If/ouHH8THHhK0GmSgmVCkpQaNq2HirLYXT6/twKycoNOlDSc5pAkJb93X4Dbx8Brj8UeWyS6lCMTkqTk9sLN8Ox1cMy1cMh5QadJSpYJSVJyizTD2Y9D8ZeCTpK0nOaQJCWfdSvh95Ng88cw5vsWiW5mmZAkJZdX74ffHQv7Hwm9C4JOkxKc5pAkJY+l98Bffgan/QEGHRV0mpRhmZAkJb6Na2C3PeCAU2DQ0dC3OOhEKcVpDklSYnv9idhln+ULITvPIhEARyYkSYmppRme+QX8467YapbDpwSdKGVZJiRJiamuEt5/GaY9DXsMDjpNSrNMSJISy5q/w9pX4av/Bd9eGHQa4TkTkqREEY3C334Ns0+BXhlBp9F/cGRCkpQYHr0wdo+NsxdA8SFBp9F/sExIkuJbYy1k5cBBp8Kx18FuuwedSJ/hNIckKX4tmwP/dxBsroytH2GRiEuOTEiS4k9TAyy6ElbNh2/cCbv1CzqRdsAyIUmKP8tmx27WdeESyB8QdBrthGVCkhQ/Vj8Few6DL30bRp0F6VlBJ1I7eM6EJCl4kRZ4+ufw8LdhQzmEelkkEkiHy0RpaSmf//znWx/X1dUxbdo0Lr30Us4880zWrFnTpQElSUmu7hP4w0lQtgDOfxq+cHTQidRBHZrm2LhxI5deeinRaLR1W0lJCSeccAIlJSWsXLmS448/nqVLl5KR4YIikqSdiEYhPRv2+RKM+QFk5QadSLugQyMTV199NSUlJa2Ply5dysKFCznttNMAGD58OGlpacyZM6drU0qSkks0Cn//bWwhqsw+cPRPLRIJrN1l4rHHHuPQQw9l3333bd02f/58Bg0aRFbWv+e1RowYwYIFC7o2pSQpeTTUwENnx8rEodOCTqMu0K4yUVlZycKFCznnnHPabF+1ahX9+rW99regoIDVq1d3WUBJUpKZe0asUFy4BAYcGnQadYF2lYkZM2Zw7bXXbrW9urqawsLCNtuysrKoq6vb4fGGDh1KcXExxcXFzJo1qwNxJUkJa+2rsV9P+A2c+YgLUSWRnZ6AOXfuXMaOHctee+211XOFhYXU1ta22VZfX09BQcEOj1lWVkZeXl4Ho0qSElJTAyz6Max6DL77TyjYL+hE6mI7LRO33XYbzz77LKeffnqb7WlpaXzta1+jpaWlzfaKigoGDx7ctSklSYlp4xp4sATSQrFpDUcjktJOy8Sdd97ZZvRh/vz53HbbbZSWlrJp0yaOPfZYGhsbW0/CXLVqFVdddVX3JZYkJY6PlsUu+5xwnYtQJbGdlolBgwa1ebxs2TIyMzMZOXIkAKNHj2bRokWceOKJLFu2jFAoxNSpU7slrCQpAURa4Nn/jd3lc9iJsS8ltU7fm+OBBx7g8ssv54UXXqCyspLS0lJ69erVFdkkSYlmcyU8ch5UfwgHnhJ0GvWQtOh/LmfZzWpqaujbty/V1dWegClJyaZmLdx5FOz7FTjh1y5ClUR29vntXUMlSZ0TjUJDFeT2h8mz4IsTIC0t6FTqQd41VJK06xo3wUPnwLwLYgVi8HEWiRRkmZAk7ZoNZXDHOKjfCCfeEnQaBchpDknSrln0EzjgJBj7Ewh54n0qs0xIktqvuRFeuQ8OORfOeAh6ZQSdSHHAMiFJap+q9+DBs4EoHPgN6FO4029RavCcCUnSzr39HNx+BOw9Es590iKhNhyZkCRtXyQCoRD0LoAJv4QRpwWdSHHIkQlJ0rZt/hhmnwL/egT6H7RVkQg3R9hQ00C4ORJQQMULRyYkSVt7/2V46GwoPgQGfb3NU5FIlJmlZSwu30BtQxM52RmMH1LE9IlDCYVcYyIVWSYkSW1Vfwh/OAnGTYfDvrPVIlQzS8uY/eIaGreMSFTUhpn94hoAZkwe1tNpFQec5pAkxTRugo+WQ9994OJ/wFf/a6siEW6OsLh8Q2uRaP3W5giLy9c75ZGiLBOSpNhqlneOh+dvij3uu882d6uqC1Pb0LTN52obW6iqD3dTQMUzy4QkpboVD8FdR8PQ4+Ebd+1w1/w+meRkb3uhqpysdPJ7Z3ZHQsU5y4QkpboP/wnf+B0cdc1Ol8XOTA8xfkgRWeltPz6ytmzPTPdjJRV5AqYkpaKq9+Hpn8GkWXDcLzv0rdMnDgVgcfl6ahtbyMlKb72aQ6nJMiFJqebNv8Aj02DYidCr49MSoVAaMyYP48oJQ6iqD5PfO9MRiRRnmZCkVLJ8Ljx+OUy6EUZ+s1OHykwPUZSb3UXBlMgsE5KUCuo+gaxcGDgOznsK9jow6ERKIo5LSVKy++CfcNsYWPEg5BRZJNTlLBOSlKyiUXjpDrj3eDjsIhj5raATKUk5zSFJyapmLfzjdjjzEdjva0GnURKzTEhSsql4HT5aAQdNjS2LvZO1I6TOcppDkpLJyodjy2J//EbssUVCPcCRCUlKFouugmWzY0tiDz4u6DRKIZYJSUp0Lc3QKx36j4AvT4PCzwedSCnGaQ5JSmRvPg2/PRQ2V8KI0ywSCoRlQpISUSQCz/4S5p4FY34Iu/ULOpFSmNMcktTDws0RqurC5PfpxD0t/vk7WPFHOO9J2Gt41waUOsgyIUk9JBKJMrO0jMXlG6htaCInO6P1bpuhUFr7DvLhK1DwOTi4BA46FbL7dmtmqT2c5pCkHjKztIzZL67hncrNVNSGeadyM7NfXMPM0rKdf3M0Cv+4E+6ZBO8+D+lZFgnFDcuEJPWAcHOExeUbaGyOtNne2Bxhcfl6wp/Z3vabN8O8abDkejjjYRh2QjenlTrGaQ5J6gFVdWFqG5q2+VxtYwtV9eHt3867JQxpveDCv0Lunt2YUto1jkxIUg/I75NJTnbGNp/LyUonv3fm1k+89ig8OR16F8Apt1skFLcsE5LUAzLTQ4wfUkTWZ67eyNqyvc1VHc1heOLHMP8y2O/wHk4qdZzTHJLUQ6ZPHArA4vL11Da2kJOV3no1RxsPngU1H8KFz0Lh/j0fVOqgtGg0Gu2pF6upqaFv375UV1eTl5fXUy8rSXEl3Byhqj5Mfu/PrDNR9T7kD4CPlkO/L0JG7+BCSv9hZ5/fTnNIUg/LTA9RlJv97yIRicBz18OtX4Paitg9NiwSSiBOc0hSkOo+gUcvhMrVcM5CyNkj6ERSh1kmJClIrz8BoXS44DnonR90GmmXWCYkqadFo7D097DvV2Hkt2Jfae1cTluKQ54zIUk9Kbw5Nq3xzHXQUBMrERYJJThHJiSpp2xaD/edCH0K4aK/Qu5eQSeSuoRlQpJ6QnMY+uwOX54GB58NvfznV8nDaQ5J6k4tTbDoJ/BgSaxAHHqeRUJJxz/RktRdatbCQ+fEzpM49b6g00jdxjIhSd1l3gWw+yCYeANk9gk6jdRtLBOS1JUiEXh9IQyZDKfNdu0IpQTLhCR1lbpP4NGLoKIcBhzmapZKGZ6AKUldYe0yuONICPWCC5+zSCilODIhSV0hXAtf+jYc/j0I+XOaUotlQpJ2VbgOFv4Ahp0IgyfA50YHnUgKhGVCknbFx2/B3LMgOy92y3AphTkWJ0kdVbMW7hgHA8fB2Qsgr3/QiaRAOTIhSe3V0gQ1H0LB5+Ccx6H/QUEnkuKCIxOS1B41H8G9x8MTP449tkhIrSwTkrQz7yyB28dA4f4w5e6g00hxx2kOSdqZf/4exs+Ag0sgLS3oNFLccWRCkralfiM8NQOaG2OjEV862yIhbYdlQpI+a+0yuP1IqFwNzQ2WCGknLBOS9J/KHoffT4yNRJw+B7L7Bp1IinueMyFJAE310CsL9joQvjkH9j8y6ERSwnBkQpI+fgvuOhpW/DG2hoRFQuoQy4Sk1Fa2ILaa5f5jYfjUoNNICandZaKiooLJkyeTm5vLIYccwvLly1ufq6urY9q0aVx66aWceeaZrFmzplvCSlKXqlkLC74HJ/4ajp0JvTKCTiQlpLRoNBptz46XX345xx13HBkZGVx88cX06tWLlStXAjBlyhROOOEESkpKWLlyJWeccQZLly4lI6PtX8yamhr69u1LdXU1eXl5Xf+7kaT22LQO1r8Gg46C8GbI3C3oRFJc29nnd7tGJhoaGvjBD37AMcccw7hx4/jZz37G+++/D8DSpUtZuHAhp512GgDDhw8nLS2NOXPmdOFvQ5K6yDt/hdvGQPnjsccWCanT2lUmsrOzKS4ubn3c1NTEd77zHQDmz5/PoEGDyMrKan1+xIgRLFiwoIujSlInvfB/8MCpMO4nMGlW0GmkpNHhEzA/+OADZs+ezfTp0wFYtWoV/fr1a7NPQUEBq1ev3u4xhg4dSnFxMcXFxcya5V9oSd3s09nctBCcsxAOOdeFqKQu1KF1JpYtW8bVV1/NE088wbhx43j++eeprq6msLCwzX5ZWVnU1dVt9zhlZWWeMyGpZ3y0HEqvgNMfgK9dEnQaKSl1aGRi5MiRPP7448ybN4+lS5fyyCOPUFhYSGNjY5v96uvrKSgo6NKgktRhr9wHd0+ALxwNvf03Seouu7TOxMknn8yRRx7J2rVrGThwIJWVlW2er6ioYPDgwV0SUJJ2ydJ74C8/i41IHPEjCLmsjtRddvlvV35+PgcddBBTpkxhxYoVbUYnVq1axaRJk7okoCR1yCfvxC73PPAbcOESGDgu6ERS0mtXmaipqeHee++lpqYGgBUrVhAOhznmmGMYNWoUo0ePZtGiRUDsvIpQKMTUqa4kJ6mHlT0eu9tneSlk5ULffYJOJKWEdi1a9cYbb3DMMcewefNmxo4dy8CBA7nqqqvIzc0FoLKykssvv5z+/ftTWVnJL37xC/bee++tjuOiVZK6RUszLP45vHx3bDXLA04OOpGUVHb2+d3uFTB7Iowk7ZLaDfDIeTDxRtjji0GnkZLOzj6/vQW5pMT17vPw4VI4/DI424XypKB4erOkxBONwvM3wf1TITMn6DRSynNkQlLimTcN3nsRznkc9vlS0GmklGeZkJQ4GmogOw9GngHH/T/oU7jz75HU7ZzmkJQYXp0N/zcCaitia0dYJKS44ciEpPjWVA+lP4LXS2HK3ZCzR9CJJH2GZUJSfFs+ByrKY6tZ9i0OOo2kbbBMSIpPry+CPYfBwefAyDMhPTPoRJK2w3MmJMWXlmb4y0/hkfOhcnXsBl0WCSmuOTIhKX7UfQIPlsDmCpi22NUspQRhmZAUH6JRyOgN+x4Gh38PsrZejCrcHKGqLkx+n0wy0x1YleKFZUJSsKJR+Nuv4aPlMOV3MP7qrXaJRKLMLC1jcfkGahuayMnOYPyQIqZPHEoolBZAaEn/yTIhKTgN1fCni+HDV+HUe7e728zSMma/uIbG5ggAFbVhZr+4BoAZk4f1SFRJ2+c4oaTgzD0TwnWxyz6LD9nmLuHmCIvLN7QWiU81NkdYXL6e8Ge2S+p5jkxI6nkfLIXiL8GJt0DePrErNrajqi5MbUPTNp+rbWyhqj5MUW52dyWV1A6OTEjqOU0NsOAyuH9KbFns/AE7LBIA+X0yycnO2OZzOVnp5Pf2slEpaJYJST1j47tw9zGw7l9w0V/bvSx2ZnqI8UOKyPrM1RtZW7Z7VYcUPKc5JPWM9a/BgK/AMTM7vAjV9IlDAVhcvp7axhZystJbr+aQFLy0aDQa7akXq6mpoW/fvlRXV5OXl9dTLyspKC3N8Oz/wKCjYb+vdfpw4eYIVfVh8nu7zoTUk3b2+e3fRkndo7YCZp8MZY9D7665XXhmeoii3GyLhBRn/BspqevVrIXbx8Bue8SWxS4aEnQiSd3IcyYkdZ1oFOo3Qm5/OP5m+MLXIc0VKqVk58iEpK7RUBO7Sde8C2IF4ovHWCSkFGGZkNR561+DO8ZCuBZOvj3oNJJ6mNMckjrvqRkwfCoceQWEegWdRlIPs0xI2jVNDfDPu+ErF8K3HoRe/nMipSqnOSR13MY1cPexsPKh2J0/LRJSSrNMSOqYt56B24+Afb4E5y6CPl2zhoSkxOWPE5LaJxKJXZ2x2x4w8QY4aGrQiSTFCUcmJO1cbQX84SRY+TDsdaBFQlIblglJO/beS7FpjT67w+AJQaeRFIec5pC0fTVrYfYpcNQ18OULXIRK0jZZJiRtrXETfPwm7D0KLlkKuXsFnUhSHHOaQ1JbG8rgjnHwws2xxxYJSTthmZD0b8vnwl1HwwEnwTfuCjqNpAThNIeUAsLNEarqwuT3ySQzfQc/Q6xbAVPvid3tU5LayTIhJbFIJMrM0jIWl2+gtqGJnOwMxg8pYvrEoYRCW06mrHoP/nwNHP9/cOzMYANLSkhOc0hJbGZpGbNfXMM7lZupqA3zTuVmZr+4hpmlZbEdVj/178s+07ODDSspYTkyISWpcHOExeUbaGyOtNne2Bxhcfl6frLPctKf+CFMvslFqCR1imVCSlJVdWFqG5q22l5ADQ0NITbuPYY9zv8LFA0NIJ2kZOI0h5Sk8vtkkpOd0WbbqLQ3WJh1FSf1eoG+u+9tkZDUJSwTUpLKTA8xfkgRWekhIMo5vRZxf+b/cE9kMuEDv7njqzokqQOc5pCS2PSJsZGHFatWUVK3mCt6/4w9DziydbskdQXLhJTEQpXlzCheTnjCaVTVTWRWn2xHJCR1Of9VkZLViodiq1lufJfM9BBFeX0sEpK6hSMTUjJa9BNY9gBMuRu+eGzQaSQlOcuElExamqFXOuzzJfjKRVCwX9CJJKUAxzylZPHGX+DXB0NtBQyfYpGQ1GMcmZASXaQFnvsl/O03MHkW5OwRdCJJKcYyISW6pb+HlQ/D+X+GPQ8IOo2kFGSZkBLVB/+Egs/BqBIYfipk5wWdSFKK8pwJKdFEo/DS7XDv8bDmb5CeaZGQFChHJqRE0lgL8y+B9/4OZ86D/b4adCJJskxICSXaAhl94MIlkFMUdBpJApzmkBLDyofhiSshuy+c9FuLhKS4YpmQ4llzGEp/BAu/D/uPCzqNJG2T0xxSPJt7JtSugwueg8LPB51GkrbJMiHFo41rYitYHnUN7D4IMrKDTiRJ2+U0hxRPIi3wzHVw6+GxZbH3OtAiISnuOTIhxYvNH8O882Hju3DuIpfFlpQwLBNSvHjzz7HLPi94NnbVhiQlCMuEFKRoFF6+C/b9Khx0WuwrLS3oVJLUIZ4zIQWlsRbmTYMlN0BTXaxEWCQkJaB2lYk1a9Zw7LHHkpuby6hRo3jmmWdan6urq2PatGlceumlnHnmmaxZs6bbwkpJY9N6uOso2LQutprlgC8HnUiSdtlOy0Q0GmXatGkcffTR3HLLLUSjUSZPnsxbb70FQElJCWPGjOHmm2/myiuv5Pjjj6epqanbg0sJq7kRdusHh/0XnPUY5O4ZdCJJ6pS0aDQa3dEOK1euZMOGDRx11FEAbNiwgf3335+ZM2cyevRoRo8eTVVVFVlZWQCMGDGCH/zgB5SUlGx1rJqaGvr27Ut1dTV5ed7lUCmmOQx/ngGfvANnPBh0Gklqt519fu90ZGLw4MGtRQKgqKiIYcOGkZWVxfz58xk0aFBrkYBYmViwYEEXxZeSRPWHcM+k2C3Dj/tl0GkkqUvttExkZmZutW3jxo1MnjyZVatW0a9fvzbPFRQUsHr16q5LKCWDxy6CPQbDeU+5LLakpNPhqzmWLFnCKaecQnFxMdXV1RQWFrZ5Pisri7q6uh0eY+jQoRQXF1NcXMysWbM6GkFKDJEIvPZo7PLP0+6HE38DGb2DTiVJXa5D60w0NTUxZ84cbrrpJgAKCwupra1ts099fT0FBQU7PE5ZWZnnTCi51X0C8y6Aj9+E/Ua7mqWkpNahkYkbb7yRq666qvUciYEDB1JZWdlmn4qKCgYPHtx1CaVE8+ErcPsRkJ4VW83SIiEpybW7TNx1111MmDCBAQMGANDY2Mgpp5zCihUraGxsbN1v1apVTJo0qeuTSomiuRG+PA1Omw2984NOI0ndrl1l4pZbbuHtt99m3bp1LFq0iHnz5nH++eczatQoRo8ezaJFiwBYtmwZoVCIqVOndmtoKe6EN8O8C6F8Iez3VTj8MlezlJQydnrOxN13383FF18MwHXXXde6/ZJLLiEUCvHAAw9w+eWX88ILL1BZWUlpaSm9evXqvsRSvKl8A+aeBX12h30OCTqNJPW4nS5a1ZVctEpJp+Yj+O2X4ZBzYfwM6OW98yQln519fvsvn7QrmsNQ8wEU7g/nLoI9Dwg6kSQFxruGSh1VsxbunQyLfhJ7bJGQlOIsE1JHvPUM3DYG+n0Bpt4TdBpJigtOc0gdsewBOPq/4eCtb2QnSanKkQlpZ+o+gUVXQVM9nHKHRUKSPsMyIe3Ih6/AHUfCxnegpcm1IyRpGywT0vaULYjdNvyQ8+D0ByDby5klaVs8Z0L6rHAdpGdD/xHwrQfh82OCTiRJcc2RCek/Vb4Jdx0Fyx+A/H0tEpLUDpYJ6VOvPQZ3joNBR8NBpwedRpIShtMcEsSWxS79EZx0Cww9Pug0kpRQLBNKbTVrYf1r8IWvw2XLIbNP0IkkKeE4zaHU9fZzcPsRsHpR7LFFQpJ2iSMTSk1/nQVLrocJ/7vDRajCzRGq6sLk98kkM93uLUnbYplQaolGYwtPZfSGbz8Be4/c5m6RSJSZpWUsLt9AbUMTOdkZjB9SxPSJQwmFXLhKkv6TZUKpY+2rsZMsv/lHOOw7O9x1ZmkZs19cQ2NzBICK2jCzX1wDwIzJw7o9qiQlEsdtlfyiUVh6D/x+Igw+DnoX7nD3cHOExeUbWovEpxqbIywuX0/4M9slKdU5MqHk98p9sPgX8K258Pkjdrp7VV2Y2oambT5X29hCVX2Yotzsrk4pSQnLMqHk9fFbkFMEw6fAF46BvP7t+rb8PpnkZGdQURve6rmcrHTye2d2dVJJSmhOcyg5rZoPd4yF15+AzN3aXSQAMtNDjB9SRNZnrt7I2rLdqzokqS1HJpRcWprgLz+NTW2c+BsYduIuHWb6xKEALC5fT21jCzlZ6a1Xc0iS2rJMKLnUV8GGVTDtGeg3aJcPEwqlMWPyMK6cMISq+jD5vV1nQpK2xzKh5PDOX+GDl2HM9+GsR7vssJnpIU+2lKSd8EctJbZIJLaa5QOnQu+CoNNIUkpyZEKJ7dEL4P2X4NulsPeooNNIUkpyZEKJqb4q9uvBJXDBcxYJSQqQZUKJJRqFpffC/42A2g2xRaj67HhFS0lS93KaQ4kjXAelP4TVT8Kp98YWpJIkBc4yocSx8kH4+E246K+Qt3fQaSRJW1gmFP/KF8KeB8CoEhh5BvTKCDqRJOk/eM6E4ldLMzx1Ncy7MDYiEQpZJCQpDjkyofi0+WN48Cyo+wQueAb6fSHoRJKk7bBMKP5Eo7Gbc31uDBx+aey/JUlxy2kOxY9oFJ7/FTx0DmRkw7ifWCQkKQE4MqH4UF8Fj/0XrFsZu+xTkpQwLBOKDw+WQK9MuPA5F6GSpARjmVCw3nsJ9v0KnHQr5PaPXbEhSUoo/sutYDTVw58uhj9+K7Ysdt99LBKSlKAcmVDP++Tt2LRGRh+4cInLYktSgrNMqOdVrI5d9vn1n7sIlSQlAcuEekZLMzzzCxh4FAyeEPuSJCUFJ6nV/Tath/tOhNefgJw9g04jSepilgl1r5qP4PYxkNcfzn8a9vhi0IkkSV3MaQ51j2gU6j6G3L1il30OHA9paUGnkiR1A0cm1PUaqmHumfDohbECMegoi4QkJTHLhLrWupVwx1hoboBT7gw6jSSpBzjNoa719M9hxDdhzA9dhEqSUoRlQp3X1AAv3wlf+Q58848Q6hV0IklSD/JHR3XOJ+/A774Orz0WO1diS5EIN0fYUNNAuDkSbD5JUrdzZEK77q1n4KGz4aDT4ZhfQHomkUiUmaVlLC7fQG1DEznZGYwfUsT0iUMJhTwJU5KSkWVCHRdpgbRQ7LLPSbNg+JTWp2aWljH7xTU0bhmRqKgNM/vFNQDMmDwskLiSpO7lNIc65tPVLFc8CEVD2xSJcHOExeUbWovEpxqbIywuX++UhyQlKcuE2m/N3+D2I2JLYg+ZtNXTVXVhahuatvmttY0tVNWHuzuhJCkAlgm1T81HcP+pcMQP4Rt3QVbOVrvk98kkJ3vbdwHNyUonv3dmd6eUJAXAMqEda6iBD5bG7q1x6Svw5WnbXc0yMz3E+CFFZKW3/WOVtWV7Zrp/3CQpGXkCprZv/Wsw9yzYeyRMuRtyinb6LdMnDgVgcfl6ahtbyMlKb72aQ5KUnNKi0Wi0p16spqaGvn37Ul1dTV5eXk+9rHbFsjmw8Adw+KVwxI86vBBVuDlCVX2Y/N6ZjkhIUoLb2ee3IxPatopyOO0+GHT0Ln17ZnqIotzsLg4lSYpH/siof9v4buxun/Ub4es/2+UiIUlKLZYJxby+aMtln3tBRp+g00iSEojTHILlf4ydHzH5JjhoatBpJEkJxjKRyjZXQlYufOEYOP9pKBoSdCJJUgJymiNVvfci3DYaVj4EfQotEpKkXWaZSDXRKPz9t/CHk2H092HkGUEnkiQluA5Nc1RWVvLLX/6SzZs3c8stt7Rur6ur47LLLqN379588sknzJw5k/3226/Lwya7cHOEqrow+X26cW2G2vXw6mwomQ8DDu2e15AkpZR2l4mmpiaef/55/vSnP/G1r32tzXMlJSWccMIJlJSUsHLlSo4//niWLl1KRsa279OgtiKRKDNLy1hcvoHahiZysjNaV40Mhba9dHWHrV8Fa1+BUWfCRS9AyEEpSVLXaPcnSkZGBieddBKHHtr2p9mlS5eycOFCTjvtNACGDx9OWloac+bM6dqkSWxmaRmzX1zDO5WbqagN807lZma/uIaZpWVd8wLL58Lvvg41a2OPLRKSpC7U4U+Vz442zJ8/n0GDBpGVldW6bcSIESxYsKDz6VJAuDnC4vINNDZH2mxvbI6wuHw94c9s77AnroRFV8LUe+HIKzp3LEmStqHTP6KuWrWKfv36tdlWUFDA6tWrt/s9Q4cOpbi4mOLiYmbNmtXZCAmtqi5MbUPTNp+rbWyhqj68awdu2XLMfQ+DC5fAF1zNUpLUPTq9zkR1dTWFhYVttmVlZVFXV7fd7ykrK/NGX1vk98kkJzuDitqtS0NOVjr5vTM7ftDVT8YWoZq2GA44uQtSSpK0fZ0emSgsLKSxsbHNtvr6egoKCjp76JSQmR5i/JAisj5z9UbWlu0duqoj0gJPXwsPnwtHXdOuW4ZLktRZnR6ZGDhwIE8//XSbbRUVFQwePLizh04Z0ycOBWBx+XpqG1vIyUpvvZqjQ5beA6v+BOf/BYo6+L2SJO2iTpeJKVOm8Ktf/YrGxsbWkzBXrVrFVVdd1elwqSIUSmPG5GFcOWEIVfVh8nt3cJ2J91+Ggv3g4BI46NTYEtmSJPWQDk9ztLS0EIn8+wqDUaNGMXr0aBYtWgTAsmXLCIVCTJ3qDaM6KjM9RFFudvuLRDQKL94K950A778EvTIsEpKkHtehkYm5c+eyZMkSQqEQDz30UGtheOCBB7j88st54YUXqKyspLS0lF69enVLYG3RuAnmXwLvvQQlf4IBXw46kSQpRaVFo9FoT71YTU0Nffv2pbq62qs5OquhBp6aDkf9N+zWb+f7S5K0i3b2+e1SiIlmxYPw+PchOw9O+LVFQpIUOMtEomhujJWI0h/BF48NOo0kSa06fTWHesjcs2J3/LxwSezKDUmS4oRlIt598jYU7g9H/zT2a0Z20IkkSWrDaY54FWmBxTPhtiOgdgPsOcwiIUmKS45MxKPNlfDI+VD9Ppz3lMtiS5LimmUiHr31TOxqjVO3/CpJUhyzTMSLaBT+cUfsluEHTYXhUyAtLehUkiTtlOdMxIPGTbE7fT7/K2jecityi4QkKUE4MhG0Tevh3smQuxdc+FfI2SPoRJIkdYhlIkhN9bDbHnD4ZTDimxDyfiaSpMTjNEcQmhth4Q9iC1GFQjDqTIuEJClhOTLR06reh4fOhkgznHpf0GkkSeo0y0RP+9PFsNdBMOF/XYRKkpQULBM9IRKB1+bBgd+A0x+ArJygE0mS1GUsE91t88cwbxpsfBc+f6RXa0iSko4nYHanD5fC7UdAZh+44BmLhCQpKTky0Z0iLXDYd+CrF7sIlSQpaVkmulpjLTz+PRh6Agw7AQZ8OehEkiR1K6c5ulLF63DneNi0LnaPDUmSUoBloqvUfAR3HgVDJsFZj3nbcElSynCao7Oaw1D9Puw+EM7/CxQNCTqRJEk9ypGJzqj+AH5/HDw5PfbYIiFJSkGWiV315tNw2xjY8wCYek/QaSRJCozTHLtq5cNwzC9g1BlBJ5EkKVCOTHRE3SdQegWE6+DkWy0SkiRhmWi/D7asZlnzYeyOn5IkCbBMtM+q+XDvZPjyBXDabMjOCzqRJElxw3MmdiS8GdKzYZ+D4YyH4XOHB51IkqS448jE9lSsjq1muex+6FtskZAkaTssE9vyr3mxIvHFCTDiW0GnkSQprjnN8Vk1H8Gin8Apd8CQiUGnkSQp7lkmPlX9IaxbCYMnwGXLISM76ESSJCUEpzkA3noGbh8Db/4l9tgiIUlSuzkyseQG+OuNcNz/g4PPCjqNJEkJJ3XLRDQKaWmQlQfnPgn9Dwo6kSRJCSk1pzk+fAXuHAe1FfCVCywSkiR1QmqViWgUXv4d3DMJDjgZdusXdCJJkhJeak1zvHIfPPdLV7OUJKkLpUaZqHwTcvaA4VNjC1Hl7hl0IkmSkkbyT3O89ijcMRZWPwmZfSwSkiR1seQdmWhpgj9fA6/eDyffBkMnB51IkqSklLxloqEaPn4TLngGdh8YdBpJkpJW8pWJt5+D91+CI6+AMx4KOo0kSUkvKc6ZCDdH2FBdR/Oz18Ocb0Ju/6AjSZKUMhJ6ZCISiTKztIzF5Ru4cvP1DOdNSof+lvNGnpQcLUmSpASQ0GViZmkZs19cQ2NzhLvTxlEePZvGFdms61PGjMnDgo4nSVJKSNgf4MPNERaXb6CxOQLAP6JDqWE3GpsjLC5fT3jLdkmS1L0StkxU1YWpbWja5nO1jS1U1Yd7OJEkSakpYctEfp9McrIztvlcTlY6+b0zeziRJEmpKWHLRGZ6iPFDishKb/tbyNqyPTM9YX9rkiQllIQ+AXP6xKEALC5fT21jCzlZ6YwfUtS6XZIkdb+0aDQa7akXq6mpoW/fvlRXV5OXl9dlxw03R6iqD5PfO9MRCUmSutjOPr8TemTiU5npIYpys4OOIUlSSvLHeEmS1CmWCUmS1CmWCUmS1CmWCUmS1CmWCUmS1CmWCUmS1CmWCUmS1CmWCUmS1ClJUyZmzZoVdAR9hu9JfPH9iC++H/HF96NzkmI5bYDi4mI++OCDLj2mOsf3JL74fsQX34/44vuxYzv7/E6akQlJkhSMHr03x6eDIDU1Nd1y7O44rnad70l88f2IL74f8cX3Y8c+/X+zvcmMHp3m+OCDDxgwYEBPvZwkSepC77//PsXFxVtt79EyEYlEWLt2Lbm5uaSlpfXUy0qSpE6IRqNs2rSJvffem1Bo6zMkerRMSJKk5OMJmJIkqVMsE5IkqVN69GqO7nLdddfx9ttvU1dXx3nnncf48eODjpSy1qxZwwUXXMDf/vY3Bg0axKxZsxg3blzQsQSUlpZy8cUX88477wQdRUB1dTX33nsvhYWF7LPPPv49CUBtbS1XXnkleXl5NDc309jYyPXXX09WVlbQ0RJOwp8z8Zvf/IZXXnmFu+++m4aGBkaOHMnChQsZOHBg0NFSTjQa5dhjj+XrX/86e+21FzfeeCNvvPEGK1as8P0I2MaNGzn00ENpbm7m3XffDTpOynvrrbe4+uqr+c1vfsPuu+8edJyUdfHFFzNw4EC+//3vA/Dd736XgoICrr322oCTJZ6EnuYIh8P89Kc/5eyzzwYgOzubY489lpkzZwacLDX961//4sorr+RHP/oRZ511Fk899RRpaWk8/vjjQUdLeVdffTUlJSVBxxCxYldSUsJNN91kkQjYs88+y3777df6ePjw4axYsSLARIkrocvECy+8wMcff8yBBx7Yum3EiBF+eAVk8ODBHHXUUa2Pi4qKGDZsmEOGAXvsscc49NBD2XfffYOOIuC///u/2X///bnuuus47LDDuOKKK2hubg46Vko66KCDuOWWW4hEIgD885//5KKLLgo4VWJK6DKxatUqQqEQBQUFrdsKCgqoqKhg48aNASZLTZmZmVtt27hxI5MnTw4gjQAqKytZuHAh55xzTtBRBNTV1XHXXXdx8MEH86tf/Yp77rmHW2+9lSuvvDLoaClp1qxZvP3225SUlPC3v/2Nk046ieOOOy7oWAkpoctEdXU1+fn5bRbQ+PSn4Lq6uqBiaYslS5ZwyimnbHO1NPWMGTNmOP8bR1566SXq6+s544wzSEtLY8iQIZx22mnceuutrT8dq+f079+fuXPn0rdvXyZOnOh70AkJXSYKCwtpbGxss62+vh6gzWiFel5TUxNz5szh5z//edBRUtbcuXMZO3Yse+21V9BRtMW6desA2G233Vq3jR07lvr6ej788MOgYqWssrIy/v73v/Pb3/6WG264gVNOOYUnn3wy6FgJKaHLxMCBA9m8eTMNDQ2t2yoqKiguLqZPnz4BJtONN97IVVdd5fkSAbrttts4/fTTSUtLIy0tjW9/+9usWbOGtLQ0nn322aDjpaTc3FyANtOwRUVFgD8ABeH8889nzJgxrf/93e9+lx/+8IcBp0pMCV0mxo4dS79+/Xj55Zdbt61atYpJkyYFmEp33XUXEyZMaL2pW2NjIy0tLQGnSj133nknr776auvXz372M/r378+rr77KIYccEnS8lPTVr36VjIwM/vGPf7Ru++STTxg1ahQ5OTkBJktNy5cvb3Ou13nnncf7778fYKLEldBlIiMjg8svv5x58+YBsHnzZv785z/z4x//OOBkqeuWW27h7bffZt26dSxatIh58+Zx/vnne2O3AAwaNIiRI0e2fu27775kZmYycuRIP7gCsvvuu3PZZZdx6623tm579NFHmT59eoCpUtdxxx3HE0880fr49ddf94TxXZTwi1a1tLTw4x//mHA4THV1NdOmTePwww8POlZKuvvuuznvvPO22n7JJZdw8803B5BI/+mee+7hpz/9qYtWBay5uZkrrriCuro68vLy2G+//bj44ouDjpWSqqur+eEPf8jee+9NTk4O69at45prrqFv375BR0s4CV8mJElSsBJ6mkOSJAXPMiFJkjrFMiFJkjrFMiFJkjrFMiFJkjrFMiFJkjrFMiFJkjrFMiFJkjrFMiFJkjrFMiFJkjrFMiFJkjrl/wOms+uLs7Nh9wAAAABJRU5ErkJggg==\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from scipy.optimize import leastsq\n", "\n", "def residuals(parameters, data_x, data_y, model):\n", " '''\n", " Returns the residuals of a model vs data.\n", " '''\n", " return data_y - model(data_x, *parameters)\n", "\n", "def linear(x,*params):\n", " a, b = params\n", " return a*x + b \n", "\n", "# Test using scipy.optimize.leastsq on a dummy fitting case.\n", "data_x = np.array(range(10))\n", "\n", "#Our data will be the function y = 5*x + 3, and we will add some random noise to it.\n", "data_y = 5 * data_x + 3 + np.random.normal(0, 1, size=len(data_x))\n", "\n", "model = linear\n", "# inputs are residual function, initial guess (x0), data\n", "coeff, _ = leastsq(residuals,[0.1, 1], args=(data_x, data_y, model))\n", "# coeff, _ is python way of dumping useless 2nd term\n", "print(leastsq(residuals,[0.1, 1], args=(data_x, data_y, model)))\n", "\n", "plt.figure(figsize=[8,6])\n", "plt.plot(data_x,data_y, 'o')\n", "fit_x = np.linspace(data_x[0], data_x[-1])\n", "plt.plot(fit_x, model(fit_x, *coeff), '--');\n", "# *coeff is python way of list of parameters of unknown length (see linear)\n", "\n", "print(coeff)" ] }, { "cell_type": "markdown", "id": "de8ad985", "metadata": {}, "source": [ "Now consider a non-linear function, like a polynomical fit" ] }, { "cell_type": "code", "execution_count": 11, "id": "306093f7", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 5.0000000e+00 -2.0000000e+00 1.0000000e+00 4.7461911e-24]\n", "4.74619110259308e-24\n" ] }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAiQAAAGkCAYAAAABqz41AAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjguMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/SrBM8AAAACXBIWXMAAAxOAAAMTgF/d4wjAABBAklEQVR4nO3deXhU5d3G8e8M2YEkE8IWwppAQJaAiFtAwA0RC28RUAERq0hdMCwWKAV3BBcoVVAsFBRprUVQQRa1yKIRIWxhSWTf1ySECcnMZJvz/pGamgqCZJKTmdyf68rV5jyT5M7o5dz5neecsRiGYSAiIiJiIqvZAURERERUSERERMR0KiQiIiJiOhUSERERMZ0KiYiIiJhOhURERERM52d2gF/D7XZz8uRJatasicViMTuOiIiIXAHDMLhw4QJRUVFYrRefhXhVITl58iQNGzY0O4aIiIhchWPHjhEdHX3RNa8qJDVr1gSKf6HQ0FCT04iIiMiVyM7OpmHDhiWv4xfjVYXkx9M0oaGhKiQiIiJe5pe2W2hTq4iIiJhOhURERERMp0IiIiIiplMhEREREdN5fFOr3W7n/fffJyIiggYNGtC9e3ccDgeJiYkEBwdz7tw5Jk+eTOPGjUu+ZuPGjcyYMQObzUZ4eDiTJ0/WfUZERESqEIthGIanvtmBAweYOHEiM2fOpFatWiXH+/XrR+/evRkyZAg7d+5k0KBBbNmyBX9/f06cOEGXLl3YsmULNpuNZ555hsjISMaPH/+z75+dnU1YWBh2u11X2YiIiHiJK3n99tgpm6ysLIYMGcKMGTNKlZEtW7awfPly7rvvPgDatm2LxWLhww8/BGDq1Kl07doVm80GwKBBg5g8eTK5ubmeiiYiIiKVnMcKyXPPPUezZs2YMmUKN954I2PHjqWwsJClS5cSGxtLYGBgyWPj4+NZtmwZAEuXLqVNmzYla23btsXhcLB27VpPRRMREZFKziN7SBwOB3PnzmXy5MmMHDmSPXv20KlTJ4qKijh69CiRkZGlHm+z2UhJSSE3N/dn635+ftSoUYO9e/fSq1evi/68Vq1alewxGT16NKNHj/bEryEiIiIm8Ugh2bhxI06nk0GDBmGxWGjZsiX33Xcf77zzDp07dyYiIqLU4wMDA3E4HNjtdoBLrl9KWlqa9pCIiIj4EI+csjl9+jQA1atXLznWrVs3nE4nRUVF5OXllXq80+nEZrOVFJFLrYuIiEjFMAyD89+e59R7pzj/7Xk8eM3LFfHIhOTHN8vJysoqKSV16tQBoH379iQlJZV6fHp6OnFxcQQFBREVFUVGRkbJmtPpJCcnh7i4OE9EExERkctwHXGR0iMF1yEXlgALRr5BUNMg4r+IJ6hxUIVk8MiE5KabbsLf359NmzaVHDt37hwdOnRg8ODB7Nixo9QUJDU1tWR/SL9+/UhOTi5ZS0tLIywsjISEBE9EExERkV9gGAYpPVJwHnBi5Bu4c9wY+QbOA0523LWjwiYlHikktWrVIjExkXfeeafk2CeffMKf/vQnOnToQOfOnVm1ahUA27dvx2q10r9/fwBGjBjBmjVrcLlcAHzwwQdMnDiRoKCKaWQiIiJVmT3JjuuwCwphKVmcI7t4oRCcB53Yk+wVksNjN0YrLCxk7NixOBwOQkNDady4MU8++SQAGRkZjBo1ivr165ORkcHLL79MVFRUydeuWrWKhQsXEhERQZ06dZg4ceJFf4ZujCYiIuJZp947xb4R+ziSk87vuYt/sZ7qBANgrWGl+VvNqT+0fpl+xpW8fnv0Tq3lTYVERETEs85/e56U21KYnu8mEgcP8t8LVCwBFuJXxxPeObxMP6NC79QqIiIi3icsIYzzdRx8wU30oui/C34Q3CyYsISwCsnh8TfXExEREe9hsVj4PDCE3v5J1LKElVxlE9wsmHZftKuwN7tVIREREanCTm0/w8ID17Np8TEa1qmDc7+T4NjiyUhFlRFQIREREanS/vL7NG6vE0LbvtcDlHm/yNVSIREREami7EftvLOxA8tnHTE7igqJiIhIVTV7+Dba1oyg8xPtzI6iq2xERESqItd5FzO+bMW4RJfZUQAVEhERkSppwVObqOWfTa/nrjM7CqBCIiIiUuUUOAqY+lETxj98Fqtf5agClSOFiIiIVJh/JG7EisH9f77B7CglVEhERESqkKL8Il55vwETBh/FL6jyXNuiQiIiIlKFLHpmIy63Pw/OutHsKKWokIiIiFQR7kI3L/+1NuP7H8Q/xN/sOKWokIiIiFQRn/1pE1kFNXj4nevNjvIzKiQiIiJVgOE2eOmtMMb22UtQeJDZcX6m8uxmERERkXKz8qXNnHA1YdhfG5sd5aI0IREREfFxhtvgpTeCGHPXbkIiQ8yOc1GakIiIiPi4L6dsYV9uUx6f28TsKJekCYmIiIgPM9wGz04JYuxdO6kZVdPsOJekCYmIiIgPW/HiZg47mvDke03NjvKLNCERERHxUYbb4NnXajC+926q16ludpxfpAmJiIiIj/rsT5s4mdeE389rYnaUy9KERERExAe5C908NyOcCb/9geCIYLPjXJYmJCIiIj5oybiNZOY3Ydjcynnfkf+lCYmIiIiPKcov4rlZtfnTgH2V8q6sF6NCIiIi4mP+NWYjOYVBPDKncr2j7y9RIREREfEhBY4Cnnu3PpMGHSKgRoDZca6YComIiIgPmTdsA1aLwdB3bzI7yq+iQiIiIuIjHBkOXvhnCyY/fQa/IO+6bkWFRERExEe89eAmGgSdo++r3rN35EfeVZ9ERETkorIOnWfqF+35+NWDWKwWs+P8aiokIiIiPuC1gdu5zlaT2/7Q0ewoV0WFRERExMud3HqaN7/vxNr3jpgd5aqpkIiIiHi5lx7cy90N/On0kHddWfNTKiQiIiJebO8Xh5ifej3bl580O0qZ6CobERERLzb+4TMMbbWJlnc3MztKmWhCIiIi4qW+mZnCV6das/9Ll9lRykwTEhERES/kLnQzZrwf42/fQt02tc2OU2aakIiIiHihj0Z9z0lnU0Z92NTsKB6hCYmIiIiXcZ138cd3GjH5dwcIiQwxO45HqJCIiIh4mbcGfY8tIIcH37nZ7Cgeo1M2IiIiXiRjTyaTV3RgyRsHsfr5zlxBhURERMSLvDhgF53rBHPrmOvNjuJR5VJIVqxYwZNPPsmhQ4cAcDgcJCYmEhwczLlz55g8eTKNGzcuefzGjRuZMWMGNpuN8PBwJk+ejMXifW8MJCIiUp52fbKPOTuuZ9vyU2ZH8TiLYRiGJ79hVlYWnTp1orCwkMOHDwPQr18/evfuzZAhQ9i5cyeDBg1iy5Yt+Pv7c+LECbp06cKWLVuw2Ww888wzREZGMn78+J997+zsbMLCwrDb7YSGhnoytoiISKVmuA3uiNxGu6bZTN/Szew4v8qVvH57/OTTxIkTGTJkSMnnW7ZsYfny5dx3330AtG3bFovFwocffgjA1KlT6dq1KzabDYBBgwYxefJkcnNzPR1NRETEa336x43sON+QZ5d0MDtKufBoIfn000/p1KkTjRo1Kjm2dOlSYmNjCQwMLDkWHx/PsmXLStbbtGlTsta2bVscDgdr1671ZDQRERGv5TrvYsz0KKYM+YHwxmFmxykXHiskGRkZLF++nKFDh5Y6npqaSmRkZKljNpuNvXv3kpuby9GjR0ut+/n5UaNGDfbu3eupaCIiIl5tWv/viQjI4eG5CWZHKTceKySTJk3ipZde+tlxu91OREREqWOBgYE4HA7sdjvAJdcvpVWrVkRHRxMdHc306dM9kF5ERKRyOp58iin/vo43pxf51GW+/8sjV9l89NFHdOvWjXr16v1sLSIigpycnFLHnE4nNputpIjk5eVddP1S0tLStKlVRESqhHH9D/J/TeDm4b47HQEPFZLZs2ezdu1a7r///lLHLRYLN998M0VFRaWOp6enExcXR1BQEFFRUWRkZJSsOZ1OcnJyiIuL80Q0ERERr/XNzBQ+OxLPnuQLZkcpdx6Z/cyZM4dt27aVfLzwwgvUr1+fbdu2MXXqVHbs2FFqCpKamkqvXr2A4kuCk5OTS9bS0tIICwsjIcG3m6CIiMgvKXAU8MQzITzbczMNrqtvdpxy55EJSWxsbKnPt2/fTkBAAO3btwegc+fOrFq1ij59+rB9+3asViv9+/cHYMSIEdx55524XC6CgoL44IMPmDhxIkFBQZ6IJiIi4pXevC8JN9GM+rhq/IFeIbeO/8c//sGoUaNISkoiIyODFStWUK1aNaC4zLz99ts8+uijREREUKdOHZ555pmKiCUiIlIpHdt4kuc/78jyNw/iH+JvdpwK4fE7tZYn3alVRESqgn7RG6geWMT7BzqbHcUjruT1W2+uJyIiUomsfDGZ1Sdb8cOOArOjVCjfvaBZRETEyzjPOXnqpTq8ct8O6rapbXacCqVCIiIiUklM/e1GIgJyeez9qrGR9ad0ykZERKQSSF26n9fXX883HxyhWkA1s+NUOE1IRERETOYudDNssIMnOm6i4+BWZscxhSYkIiIiJps9+BtOOZvywooYs6OYRhMSEREREx3beJLxH3Xg3ZfSqV6nutlxTKMJiYiIiEkMt8ETvY/TNyafO8b7xj1HrpYKiYiIiEkWjdnAxvTmpH1b9Tax/i+dshERETHBuQNZjPhLc958ah+1mkeYHcd0mpCIiIiYIPGO3VxfO4D7ZtxkdpRKQYVERESkgn36x40sP9yaXZvzsFgtZsepFHTKRkREpAJl7Mlk+KvNeOv3qURdW8/sOJWGJiQiIiIV6Kk79nBzPSsDZ95sdpRKRYVERESkgiwavYF/H49j9w63TtX8D52yERERqQBndqXz+IwWvJ24p8q9k++V0IRERESknBlug8fvPMBt0W4G/Fmnai5GhURERKScvffot2w404KdqXrZvRSdshERESlH+1cf4en57Zn/wjEi42qZHafSUlUTEREpJwWOAgb3ucDv4g9z18SuZsep1DQhERERKScv90wipzCQqV9fb3aUSk8TEhERkXKQ9M4O3ljfiQ2LThAcEWx2nEpPExIREREPyz6ezeCnbbzcJ5l2/VqYHccraEIiIiLiQYbb4PHOO2keGkTix7eYHcdrqJCIiIh40N8e/pbVx+JISbFg9dOJiCulZ0pERMRDdny8l5ELOvD3qcd1N9ZfSYVERETEA3JO5zBgkB9jbtnMbX+41uw4XkenbERERMrIcBs8kbCd+iHVefarLmbH8UoqJCIiImX03qPfsupQS7ZvLqJaQDWz43glnbIREREpgx0f72XE/A4snHyUqGvrmR3Ha6mQiIiIXKWsQ+f57QOBjO2+mTv/2NHsOF5Np2xERESugrvQzeAb9nFNhMHEL3W/kbJSIREREbkKL96+nr3nm5C8z6b7jXiAComIiMiv9Pmzm5i2riPffXyK8MZhZsfxCap0IiIiv8L+1Ud48OUWzBmxk7b36n1qPEWFRERE5AplH8+mT68CHu6wnfvfvNnsOD5Fp2xERESuQFF+EQ9cu4eGNSy8ltTZ7Dg+R4VERETkCoy9+RsO2hvy/b5I/IL08ulpekZFREQu429Dv+G9re3Y+NUFwhppE2t50B4SERGRX7D+rRSefv9aPn7jCLG3NTY7js9SIREREbmEA18f4d7EBkwfuIXuozuYHcenqZCIiIhcRMaeTHre5ebBDrsY/nfdibW8aQ+JiIjI/3BkOPjNdSdpXzeHNzaqjFQETUhERER+oii/iEHtduBndbNgZwfdFr6CeOxZPnLkCD169KBmzZp06NCBNWvWlKw5HA6GDRvG008/zeDBgzly5Eipr924cSMPPPAATzzxBBMmTMAwDE/FEhERuWKG22Dkdd+SllmHz7Y2Iig8yOxIVYZHColhGAwbNozbb7+dt99+G8MwuOeeezhw4AAAQ4YMoUuXLrz55puMGzeO3/zmNxQUFABw4sQJHnjgAd5++23efvtt8vPzefXVVz0RS0RE5Fd54zfrWLS7FSu/8icixmZ2nCrFYnhgHLFz507Onj3LbbfdBsDZs2dp1qwZkydPpnPnznTu3Jnz588TGBgIQHx8PGPGjGHIkCGMGDGCnJwc5s+fD8C2bdu45ZZbOH36NNWrVy/1c7KzswkLC8NutxMaGlrW2CIiIiX+NvQbRr/fjq8/OEnHwa3MjuNTruT12yMTkri4uJIyAlCnTh2uueYaAgMDWbp0KbGxsSVlBIoLybJlywBYunQpbdq0KVlr27YtDoeDtWvXeiKaiIjIZX08ZgOJ73dg6YxDKiMm8UghCQgI+NmxrKws7rnnHlJTU4mMjCy1ZrPZ2Lt3L7m5uRw9erTUup+fHzVq1GDv3r2X/HmtWrUiOjqa6Ohopk+f7olfQUREqqgvp2zhoent+OekVLomtjc7TpVVLpf9rl+/nr59+xIdHY3dbiciIqLUemBgIA6HA7vdDnDJ9UtJS0vTKRsRESmz797dyb0TWjDnie3c82KC2XGqNI8XkoKCAj788ENmzJgBFJeNnJycUo9xOp3YbLaSIpKXl3fRdRERkfKy/aM99Hq8Ia/dv42Bs3SvEbN5/OLqadOmMWHChJI9IzExMWRkZJR6THp6OnFxcQQFBREVFVVq3el0kpOTQ1xcnKejiYiIAJDyrz3c9kBtJvTczuMfqoxUBh4tJHPnzuWuu+6iYcOGQPHko2/fvuzYsaPUFCQ1NZVevXoB0K9fP5KTk0vW0tLSCAsLIyFBozMREfG8HR/v5bb7IxnbYwd/WN7N7DjyHx4rJG+//TYHDx7k9OnTrFq1iiVLlvDoo4/SoUMHOnfuzKpVqwDYvn07VquV/v37AzBixAjWrFmDy+UC4IMPPmDixIkEBelmNCIi4lk7F+/ltgERjL59J+NWdjM7jvyER+5DMm/ePB555JGfHR8xYgRvvvkmGRkZjBo1ivr165ORkcHLL79MVFRUyeNWrVrFwoULiYiIoE6dOkycOPGiP0f3IRERkau165N9dL/XRuKtu5j4725mx6lSruT12yOFpKKokIiIyNXY9uEP9BhUi6e67ebZr7uZHafKqbAbo4mIiFRWG/66k1sH1eOZu1RGKjMVEhER8VmrX9/KncOb8Mp9Oxi7opvZceQXqJCIiIhPWjZpE33GtmDWsBRd2usFVEhERMTn/P2JJO5/uTXvP7OTIX/tbHYcuQLlcut4ERERMxhug9fvWcfLK6/lk1d+4M4/3mR2JLlCKiQiIuITivKLGNXpWxbtasW6f5ykwwMdzY4kv4IKiYiIeD3XeReD22xj59lGfLcmn6a3tDQ7kvxKKiQiIuLV0tMy6HvjCYrcNUjaGUpkXC2zI8lV0KZWERHxWrs+2cf17ZzUD3Xw70MxKiNeTIVERES80vLnk0noW4eHEg7wz0M3EBIZYnYkKQOdshEREa9iuA2m9V7H88uv429P7+C+v3QzO5J4gAqJiIh4DUeGg9/fsJV/H27JmveO0umhm82OJB6iQiIiIl5h/+oj3HuPi5r+oWxOhqhrrzE7kniQ9pCIiEilt/RPG7nu9nBubXWaNadbEXVtPbMjiYdpQiIiIpVWoauQ5277lje/68jcp3dy31+6mh1JyokKiYiIVEpHko4zsOc5svIasvGzM1zTW/tFfJlO2YiISKWzaPQG2nepQZsG59l8oj7X9I41O5KUM01IRESk0nBkOBjZZTMf72nL3575gb6v3WJ2JKkgKiQiIlIpfPfuToaOqEG94DC2JzlodNONZkeSCqRTNiIiYirXeRdjr1/LHb9vxmN3HmFNehsa3dTA7FhSwTQhERER0yS/n8pDjwVSw782yZ+d4pre3cyOJCbRhERERCpczukcnrluLV2HNmFw12N8lxGnjatVnAqJiIhUqGWTNnFNtJ2N+2xs/uwkE77shl+QBvZVnf4NEBGRCnFi8yme7nOENafieH3ILh6em4DVT38XSzH9myAiIuXKdd7FK3euJa5TTYIDivhhZyGPvNdFZURK0YRERETKzDAM7El2nPudBMcGE5YQBgYsGfc9z8yIJsK/LqtmHaTzEwlmR5VKSoVERETKxHXERUqPFFyHXFgCLBj5BqcjspntaEBaTgyvDNnD0Dk6PSO/TIVERESummEYpPRIwXnACYVwNj+LhYTx79O38nDQGj49HENYwy5mxxQvoLoqIiJXzZ5kx3XYhb0wh7m4GEIPQnHxD76mv7smxhHD7IjiJVRIRETkqh384gjzC3K5n9u4QCAL+IJHCCaMmlgCLDj3O82OKF5Cp2xERORXO7j2KFN+f5gP9lxPD84xj1XUxwaElzzGyDcIjg02LaN4F01IRETkim1ekMqgJklc070OeQVWtn1+gglxIdT3s5V+oB8EN/vP1TYiV0CFREREflFRfhGfTdhI1/DtdHuoEbXCCtm9+gwLDnSmVa8Y4r+IJzgmGEuABWsNK5YACyGxIbT7oh0Wi8Xs+OIldMpGREQuKmNPJu+N2cnsL5ridDfi6Tv38Onbhdiadi31uKDGQVyfdv3P7kOiMiK/hgqJiIiUMNwGSbN3Mvv1C3x8uCM3hYfx8uMn6PvKdQTU6HbJr7NYLIR3Die8c3iFZRXfokIiIiIc23iShc/uZcHahpwuaMRD8SlsW3aCVvd0MDuaVBEqJCIiVZT9qJ1PX9rJB4tDWJfVltsjT/Dc8DP0eT6K4Iiul/8GIh6kQiIiUoXYj9pZ+spOFn3qzxdn2tMqqDaDbzvFBy+fo377TmbHkypMhURExMcd3XCC5W8eYNnqYFant+Oa4Ej6dz7NG2NO0qJHHBBndkQRFRIREV+Tn5PP9/PT+PKjLD7fUp/drmYkhKXzmy7n+cvTp2h+R0ugpdkxRUpRIRER8XJF+UXs/GQ/X//jFP/eUJ116ddQ01qf2xvlMH5YJj1G1cXWtL3ZMUV+kQqJiIiXyT2by5aP9vPN0iy+3V6d7zJa4CaKLrWzuePmXF576CSt+8RisdYxO6rIFVMhERGpxJznnOz+/BCbV2WQvNlC8rG67HbFUNdal85RDnre4uCVfqdo+9tY/IK0KVW8V6UqJFOmTOHgwYM4HA4eeeQRbr31VrMjiYhUiPycfA6sPcYP36STutXFjj0BpJypx778xoRZ6tPR5qRT3AVe+O05OvWrSYOO9bBY65kdW8RjKk0hmTlzJvv27WPevHm4XC7at2/P8uXLiYmJMTuaiJQzwzCqxG3Hc07ncGTjaQ5tOcfB3U4OHoQDJ4PZm1WbAwUNCaA+ccEFtKqTybWt8xn6aCbt7g4m6tp6WKwdzY4vUq4shmEYZofIz88nKiqKxYsX07Vr8c14EhMTuXDhAvPmzSt5XHZ2NmFhYdjtdkJDQ82KKyIe5DriIqVHCq5DLiwBFox8g6CmQcR/EU9Q4yCz412Wu9CN/Vg2GfvPk37wAqcP5HLmWD6nT7o5fdbK8cxgjl0I41heHc4b4YSQS7PAkzSznaNZfRfNmkFcxxq07FaP6E71sfrpPU/F91zJ63elmJAkJSWRmZlJmzZtSo7Fx8czfvx4E1OJSHkzDIOUHik4DzihEIz84r+PnAec7LhrB51SO5VpUmK4DdyFbgocBRS6CinMK6LAUUBeTgH5uf/5X0chrgsFOC8U4swuwJlThONCEbnZReRku8nJgZwcyM6xcj7XD7sjgPOuIM4XhJBZEMo5w4abcPwJobY1k3qBftSrkUO9cBd1I4uIj3fQsLlBwzYG0e2LqNU8Aou1uaeeQhGfUSkKSWpqKlarFZvNVnLMZrORnp5OVlZWqeMiUr4Mt4HznJPskzlkn8ol+4yT7PQ8LmTmk2svxJHjJveCm9wcA5eL4o88C848C3kFVvILrOQXWikospJfZKXQ/d+PIreVQsOK27BQZFhxF1koKIjAwIKBBTdW3FhwF1oxfrCA3wkMS/GaYVhw/+dxBhbcxk+/pvh7urFSRLWffPgB1f7zUZofBQSSR4ClgCBLHsHWPIKr5RNcrYBgvwJqBuZTI6iA6kFFVA9yU7uWm9hm+YTZCgmvnU9YpItaDV1ENnNRq1kYNerVwGKtD9Sv6H9kIj6hUhQSu91OeHg4Vut/R5WBgYEAOByOnxWSVq1alfzVNHr0aEaPHl1xYUW8UF52Hie3n+XErixO7svh7PECzp4xOJNu5aw9gIzcYLLyQjhXUJNz7nDyCAFCCMJJqCWHUL9cavi5qO6XT/WAfKoHFBISWERIUBFBAQaBAQZhoQaBgW4CAiAg0EJAIPgHWPAPsOLnbyn5qOZX/GGtZsGxM5dzyzOhwMACWAArFsDAGmClzoDa2G4Ox2K1YLGAtZql+P//5HOrn7X4f//zUc3fSrWAalTzLz7uH+yHX2A1/EP88Qushl+QH4GhgVj9/AF/U/+5iMh/VYpCEhERQV5eXqljTqcT4KLTkbS0NO0hEfmJvOw8Dqw9xv6NmRz+wcXhwwaHTwVx+HwYx1y1yTAiqUZ96lerRlSQlXo1c6kTlkedWm6uaZVHrbpF1KqfT0SDPGzRTmyNahLWMJSAGsFAMFC7XHKf//Y8KStSMPj5VjYLFuKHt9Pb2YtUEZWikMTExJCbm4vL5SIoqHgTW3p6OtHR0YSEhJicTqTysB+1s3vlUXYnZbFrh8EPx6uzz16HI4UNCCSK2CA3TcOzaFLXxS035PFgCzuN2kKDdm5qt6xFtYAoIMrsX6NEWEIYQU2DSvaQlPCD4GbFV9uISNVQKQpJt27diIyMJDk5mS5dugDF+0p69eplcjIRcxhug1Pbz7Dlk6Ns/dbB1h+C2ZYezbGiBtSz1qFNeD6tG+XQt4eDFh0zad7Fn6gOdbH6tTA7+q9isViI/yL+Z1fZBDcLpt0X7Xzy0l8RubhKUUj8/f0ZNWoUS5YsoUuXLuTm5vLVV1+xcuVKs6OJVAjXeRdbP9rHd8sy2bAtiO9ON+WMuw4tA3Lp2CCf7je6GNU1nTY9g4iMqwvUNTuyxwQ1DuL6tOurxH1IROTSKsV9SACKiooYP348+fn52O12hg0bRkJCQqnH6D4k4itc511smJfGmk/trEmxsSm7JWGWbG6qe5Cb2zu56W4b1/aPoUa9GmZHFREpsyt5/a40heRKqJCItzLcBqnLDrDir8dZtSGUpKxriLCep3vDA3Tv6qbr4IbE3tYYi1VTARHxPV5zYzQRX+Q672L1jJ0s+5eTFXtjyCiK4tY65+h7+wXefvgkLXo01XuRiIj8hwqJiAflnM5h5Ws7WbLYYPnRNtTyq0fv1geZ88Ipuj5Zi6Dw682OKCJSKamQiJRRXnYeq6Zu5+8fuFl2vD3NAmvTt9Nx1k09Sfv74rBYG5odUUSk0lMhEbkKhtsgafZOPnjrPIv2tCW8Wn0G3nCQLbNOcE3vWCDW7IgiIl5FhUTkV0hPy2DB2F3M/bIhZwoa8kDrLD5/5zg3DWuDxdrI7HgiIl5LhUTkMgy3wfq3Upj1hpPPjl/LzeFhTHr0NH0nNyAovKvZ8UREfIIKicgluM67+MeoZN78Zx2O5jXm0etS2DXvFM3v6GB2NBERn6NCIvI/0tMyePOxXcxOakPdgHo83e8Ug2c0JCSym9nRRER8ltXsACKVxdENJ0hsv44m1wSTnFaDD6ceZacjlscW3kJIpN7kUUSkPKmQSJW3f/URHm7+DS1ursWpzAC+WXiUVRnXcfvYa3XnVBGRCqJCIlXW0Q0nGNZyPW1uL36jupQVJ/nXsZu4dlArk5OJiFQ9KiRS5ZzafoYR7dYRd3MEzrxq7PzyNPP3dSGuZzOzo4mIVFkqJFJl5JzO4bmua2neoTqnzgWw+dMTLDyUQPM7mpgdTUSkytNVNuLzivKLeH/4d0xc0JwmIbX495zD3PjoTWbHEhGRn1AhEZ+27i/bSRwfjL2wCTOePkj/aTdpo6qISCWkQiJezzAM7El2nPudBMcGE5YQxtndGfyhzx4+ORjPxLu2kPjhjQSF603uREQqKxUS8WquIy5SeqTgOuTCEmCh0FXIt0F2pufcyh0NqpG2KYfoTt3MjikiIpehQiJeyzAMUnqk4DzghEI4np/JNFqQndOUNyLX8MixPlgsOj0jIuINdJWNeC17kh3XYRcFhQUs4TzDuIsEDvAOB2iebcOeZDc7ooiIXCFNSMRrOfc7OUImU2hDIAXMYRUNiADAEmDBud9JeOdwc0OKiMgVUSERr5Sfk8/013czK+8unmAVPQmj2n/KCICRbxAcG2xiQhER+TVUSMTr/LDiIIP65VFkNGRh1BoizkZA4U8e4AfBzYqvthEREe+gPSTiNQy3wdv3r+O6XnW4rc0ZNp5pwt3f3UZwTDCWAAvWGlYsARZCYkNo90U7bWgVEfEimpCIV8jYk8nDtxxge2Zzlk3bR/fR3YoXQuH6tOt/dh8SlREREe+iQiKV3nfv7uS+J2txfV03O/aFYGvaodS6xWIhvHO4NrCKiHgxnbKRSstwG0zvs5Y7ft+MZ3rv4+NjN2BrGm52LBERKQeakEildP6InYdvSmPL2easnnOIGx/tanYkEREpRyokUumkLt1Pn35+tAivxra0YGo1b2B2JBERKWc6ZSOVyrJJm7ipT20euPEwy052pFbziMt/kYiIeD1NSKRSMNwGr/RYx9R/d2TeqF30n97N7EgiIlKBVEjEdI4MBw9fu52NJ2P59qOTxA+4yexIIiJSwVRIxFRndqXT+8YzBFarTvLOIGq3ijY7koiImEB7SMQ0P6w4yE0dnMRG2vnqWEtqt4o0O5KIiJhEhURMse4v27n5HhsDbzjIwoM3ExgaaHYkERExkQqJVLh/PJnE3SOb89qDu3j5225YrLrNu4hIVac9JFKh3rx3HX9aci1LXk6jx5+6mB1HREQqCRUSqRCG2+CFW9fx1vp2/HvuEW545DqzI4mISCWiQiLlzl3oZmTHb1i8K471n5yjdZ82ZkcSEZFKRoVEylWBo4DftdnI98cbk7SuiCadY82OJCIilZAKiZSb/Jx8Hojbyv5ztfl2a3XqtqltdiQREamkVEikXOTn5DOg+TaO2sNYs6sOETE2syOJiEglpkIiHpeXnUf/Fts5daEmq3fXx9Y03OxIIiJSyamQiEe5zru4t8VOMhzV+Sq1AeGNw8yOJCIiXkCFRDwmLzuPvi12kuUM4svUhoQ1UhkREZEr45E7ta5Zs4Z27doRGhpKz549OXz4cKn1ffv2MXDgQJ566imeeuop8vLySq3Pnz+fhx56iKFDh/Lhhx96IpJUsAJHAfe33EaGI4Qv0hqrjIiIyK9S5gnJyZMnmTBhAiNHjiQ3N5cXXniBXr16kZKSgp+fH7m5udx9992sXLmS2NhYZs6cSWJiIrNnzwZg2bJlLFy4kNWrV+N2u0lISKBRo0YkJCSU+ZeTilGUX8TQazZxIKs2a3fVJjQ61OxIIiLiZcpcSL7++muWLVtGZGTxO7XGxMTQq1cvdu/eTXx8PLNnzyY6OprY2OL7TwwcOJDatWszfvx4mjRpwoQJE3jmmWcAsFqtDBgwgEmTJvH111+XNZpUAMNt8Hh8EptPNmT91hq6mkZERK5KmU/ZDBgwoKSMAHTr1g2AwMDid29dunQpbdr8986cERERNGjQgOXLl3Po0CF27dpVaj0+Pp61a9dy4cKFskaTcma4DUZ1XM9X+5uyOilI9xkREZGrVuZCEhAQUOrz06dP07p1a1q2bAlAampqqcICYLPZ2Lt3L6mpqQCl1m02G4ZhsH///kv+zFatWhEdHU10dDTTp08v668gV+nF29axaEcL/v2Fm+hO9c2OIyIiXuyyp2zGjBlDSkrKJddHjhzJPffcU/L5woULef3110s+t9vtRERElPqawMBAHA4HdrsdoNT6j5MVh8NxyZ+ZlpZGaKj2KZjpr4PXM2Nde779JIOYW3U7eBERKZvLFpJp06Zd8Tc7evQoeXl59OzZs+RYRETEz66qcTqd2Gy2kiKSl5dHzZo1S9ageFIildOnf9zI6L9fy8q3DtC6T7zZcURExAd45LJfKC4S77zzDs8//3yp4zExMWRkZJQ6lp6eTlxcHDExMQCl1tPT0wkICKBJkyaeiiYe9O3bOxg8tTULx++my1MqIyIi4hkeKSRFRUVMnTqV8ePH4+/vD0Bubi4A/fr1Izk5ueSxmZmZZGZm0qNHD5o3b067du1KraemptK9e3dCQkI8EU08aPdn++n9VEOmDdzK/025wew4IiLiQ8pcSIqKinjsscdo0qQJGzZsYNWqVSxYsIDJkycDMHToUPbv38+ZM2eA4j0mw4cPJzo6GoBx48axZMmSku+1aNGin01ZxHyntp+h573BPH1LCsP/fovZcURExMdYDMMwyvINHnroIRYsWPCz44sXL6Zv374AbN68mWnTphEVFYXFYmHKlCklkxSAV199lcOHD5Ofn0/v3r3p06fPRX9WdnY2YWFh2O12bWqtQI4MB10bH6Z1/XPM35uAxWoxO5KIiHiRK3n9LnMhqUgqJBXPXeimf+NNZOQG8dXxawioEXD5LxIREfmJK3n91pvryS+a0Hk9O9Kb8P3uUJUREREpNyokcknzf/cNf90Uz4blWdRqHnH5LxAREblKHrvsV3zL2hnbeWr+tSx+4zBxPZuZHUdERHycCon8zJGk4/QfHc2MB7fQfXQHs+OIiEgVoFM2Uoojw8Fv77hA/2sOMmyBLu8VEZGKoQmJlDDcBsOu20Z1/3xmfH+j2XFERKQK0YRESkzvs451x+LYkuKnK2pERKRCaUIiAHw1dQvPft6JT+ZlUbdNbbPjiIhIFaNCIhxJOs79E5oy65FtdHroGrPjiIhIFaRTNlVcfk4+/XvYGdDqIEPnahOriIiYQxOSKu6ZhA0Uua38Oel6s6OIiEgVpglJFbZo9AYW7GjP1jV2gsKDzI4jIiJVmCYkVdTeLw7xyJ9b8974H2jWrZHZcUREpIpTIamCnOec9P+/fB7ruJX/m3KD2XFERERUSKqixIRkavjnMWV9gtlRREREAO0hqXI+HrOBRXvakZKUi3+Iv9lxREREAE1IqpSjG04w7M+tmDsmjUY3NTA7joiISAlNSKqIQlchg+7KoH/cAe59XfcbERGRykUTkipics9vyXDV4M/rOpodRURE5Gc0IakCkt7ZwWtrO/HdR8epXqe62XFERER+RhMSH3f+iJ1BIyJ45bebiR8QZ3YcERGRi9KExMcl3rqTluFBPP2x9o2IiEjlpULiwz4Z9z3LDrVm5yYXFqvF7DgiIiKXpFM2Purs7nSGvx7DrCfTaHBdfbPjiIiI/CJNSHyQ4TZ47PaDdGvg5v6/3GR2HBERkctSIfFBC4YnsfFsc3am+ulUjYiIeAWdsvExR5KO8/TctsyddJTIuFpmxxEREbkimpD4EMNt8MhvztK/xSF6Pd/F7DgiIiJXTIXEh/zt4W/Zkx3Dkh01zI4iIiLyq+iUjY84sfkUzyxox7uTThAaHWp2HBERkV9FExIfYLgNHr/nKL2bFXD3c53NjiMiIvKrqZD4gH8mbmDj2eak7qlmdhQREZGrolM2Xi49LYOnZ7Vg1qj91GoeYXYcERGRq6IJiZd7+q693FLfSr9pugGaiIh4LxUSL/b5s5v44lgrUrcXmB1FRESkTHTKxkvlns3lyVeieO3BXdRrV8fsOCIiImWiQuKlXrgnmYYh5/jd3xLMjiIiIlJmOmXjhXZ8vJeZydeT/OlJrH7qlCIi4v30auZl3IVuhj+cR+KNm2jdJ9bsOCIiIh6hCYmXmfPQt5xxNWHSshizo4iIiHiMJiRe5MyudMZ/2I5Zk84QEhlidhwRERGP0YTEi4z5zV7uaGCl57O654iIiPgWFRIvsf6tFD473I4fknPMjiIiIuJxHi8kY8eO5ezZs7z33nslx/bt28dzzz1HRETxrc2nTZtGYGBgyfr8+fNZu3YtFouFHj168MADD3g6llcrdBXy1Nhgnr17Cw2u62Z2HBEREY/zaCH57rvveOedd7j33ntLjuXm5nL33XezcuVKYmNjmTlzJomJicyePRuAZcuWsXDhQlavXo3b7SYhIYFGjRqRkKD7a/zoncFJ5LsbkvjRzWZHERERKRce29TqcDiYNWsWffr0KXV89uzZREdHExtbfInqwIEDmTNnDocPHwZgwoQJDBkypDiM1cqAAQOYNGmSp2J5vbO705m0uD1vPp9FQI0As+OIiIiUC48VkhdffJGJEyfi51d66LJ06VLatGlT8nlERAQNGjRg+fLlHDp0iF27dpVaj4+PZ+3atVy4cMFT0bzahL4/0L1+Gnf+saPZUURERMqNRwrJunXrqFu3Lq1atfrZWmpqKpGRkaWO2Ww29u7dS2pqKkCpdZvNhmEY7N+/3xPRvNqm+bv5cO+1TP9nA7OjiIiIlKvL7iEZM2YMKSkpl1wfOXIkixYtYv78+Rddt9vtJZtZfxQYGIjD4cButwOUWv9xs6vD4bjkz2zVqhUWiwWA0aNHM3r06Mv9Gl7HXejmqREwtlsyTW/pZnYcERGRcnXZQjJt2rRfXP/DH/7Ac889h9V68WFLREQEeXl5pY45nU5sNltJEcnLy6NmzZola1A8KbmUtLQ0QkNDLxfdq703LIn0vCaMXdzM7CgiIiLlrsynbN544w1iYmKwWCxYLBbef/993n///ZIJRkxMDBkZGaW+Jj09nbi4OGJiim9//tP19PR0AgICaNKkSVmjea0LJy/wpwUteP3p4wRHBJsdR0REpNyV+bLfbdu2lfr82WefBYo3uQL069ePzz//vGQ9MzOTzMxMevToQXR0NO3atSM5OZmWLVsCxXtOunfvTkhI1b01+qsDthBbw8a9r99odhQREZEKUeYJSfv27Ut9REREEBERQfv27QEYOnQo+/fv58yZMwAsXLiQ4cOHEx0dDcC4ceNYsmQJAEVFRSxatIjnn3++rLG81tENJ/hzUiemv+mPxWoxO46IiEiFKPdbx9tsNhYvXszIkSOJiorCYrHw5z//uWR94MCBHDt2jMcff5z8/HzGjx/PjTdW3cnAHx84zL3NDDo91NnsKCIiIhXGYhiGYXaIK5WdnU1YWBh2u90nN7Vu/Nsubn20KXs2ZRPdqb7ZcURERDziSl6/PXZjNCkbw20waqTBM7ckq4yIiEiVo3f7rST+NWoDhx3NGLtIl/mKiEjVowlJJZCXnce4WY145eH9VK9T3ew4IiIiFU6FpBJ4e8gGwv1zGTJb7+YrIiJVk07ZmMx+1M7LS9vx9xcPYvVTPxQRkapJhcRkr96/jfiwMHpM0Lv5iohI1aVCYqITm0/xlw2dWPveEd0ETUREqjQVEhO98OA+7mnoR6eHtHdERESqNhUSk/yw4iAf/NCJHV+eMTuKiIiI6bSL0iR/fPQsv2uzieZ3NDE7ioiIiOk0ITHBd+/u5N+nWrP/S5fZUURERCoFTUgqmOE2mDCuiFFdtlC3TW2z44iIiFQKmpBUsNVvbGNHdlM+W9jU7CgiIiKVhiYkFchwG0x8MYCxd6YQ1ijM7DgiIiKVhiYkFWj588kccjRlxAJNR0RERH5KE5IK4i50M/H1MP7YJ1VvoCciIvI/NCGpIIvHbiQjvwm/n9/Y7CgiIiKVjiYkFaAov4hnZ9Vh0v37CAoPMjuOiIhIpaNCUgH+8fQG8tz+PPzujWZHERERqZRUSMpZgaOA5//WkOeGHiWgRoDZcURERColFZJy9sGT31PN4mbQW5qOiIiIXIoKSTkqdBUyeWEjJg49gV+Q9g+LiIhcigpJOfr7iO+xWgwGvqnpiIiIyC9RISknha5CJr/fgD8NOa7piIiIyGWokJSTf47aSKFRjUFv3mB2FBERkUpPhaQcFOUX8fK8+vxp0BH8Q/zNjiMiIlLpqZCUg3+N2YirKIAHZ2o6IiIiciVUSDysKL+Il/5alwn3H9R9R0RERK6QComHLR63kZyiIIbO1pU1IiIiV0qFxIMMt8Hk2bUY32+/piMiIiK/gq5H9aAVL27mTH5jfjdb7+grIiLya2hC4iGG2+CV6YGMujNV7+grIiLyK2lC4iHfzNrB7gtNWDmnidlRREREvI4mJB4y5cV8nkrYRmh0qNlRREREvI4mJB6w9e9prMtozYL1DrOjiIiIeCVNSDxg6vjzDItPpnarSLOjiIiIeCVNSMpo7xeHWHq8A3v/lWl2FBEREa+lCUkZvTriOA/EJtPopgZmRxEREfFampCUwfHkU/x9Xye2Lz9pdhQRERGvpkJSBm8+uYee9YNoebduEy8iIlIWKiRXKft4Nu8md2Dl7KNmRxEREfF6KiRXac7jW2ldoxY3D29rdhQRERGvp02tV6HAUcCMlS34wxO5ZkcRERHxCR6dkOzfv5/PPvuMxo0b06JFC9q1awfAvn37eO6554iIiABg2rRpBAYGlnzd/PnzWbt2LRaLhR49evDAAw94MpbHfTRmE0HWBvR+qZPZUURERHyCxwrJihUr+Oqrr3j99dfx8/vvt83NzeXuu+9m5cqVxMbGMnPmTBITE5k9ezYAy5YtY+HChaxevRq3201CQgKNGjUiISHBU9E8ynAbvPFeJKPvPUq1gCZmxxEREfEJHjlls2nTJmbNmsUbb7xRqowAzJ49m+joaGJjYwEYOHAgc+bM4fDhwwBMmDCBIUOGFIexWhkwYACTJk3yRKxysfqNbZzIq8VDb11ndhQRERGfUeZC4na7eeyxx+jYsSPDhg3jxhtvZN68eSXrS5cupU2bNiWfR0RE0KBBA5YvX86hQ4fYtWtXqfX4+HjWrl3LhQsXyhqtXLz+mpsnb9lFSGSI2VFERER8RpkLyfr169m7dy933HEH8+bN46mnnuKRRx5h2bJlAKSmphIZWfo9Xmw2G3v37iU1NRWg1LrNZsMwDPbv31/WaB634+O9rM9szROzWpsdRURExKdcdg/JmDFjSElJueR6VlYWTZo0oUuXLgAMHjyYF154gZkzZ/Kb3/wGu91espn1R4GBgTgcDux2O0Cp9R83uzocl37n3FatWmGxWAAYPXo0o0ePvtyv4RHTxp3loVanqdP6lgr5eSIiIlXFZQvJtGnTfnF9+PDhbN26tdSxrl27smbNGqC4bOTl5ZVadzqd2Gy2kiKSl5dHzZo1S9ageFJyKWlpaYSGhl4uuked3nGWjw5eR8oK3SZeRETE08p8yqZmzZpkZWWVOlanTp2SQhETE0NGRkap9fT0dOLi4oiJiQEotZ6enk5AQABNmjQpazSPemdEKrfW3klcz2ZmRxEREfE5ZS4kXbt25eDBg6VKxblz57jlluLTGv369SM5OblkLTMzk8zMTHr06EHz5s1p165dqfXU1FS6d+9OSEjl2TTqOu/inW9aM3KU7iMnIiJSHsr8CturVy86derEu+++CxSfflm/fj2JiYkADB06lP3793PmzBkAFi5cyPDhw4mOjgZg3LhxLFmyBICioiIWLVrE888/X9ZYHvXPZzYT6Z/NHeOuNTuKiIiIT7IYhmGU9ZucOXOGJ598kri4ODIzM3nggQfo2rVryfrmzZuZNm0aUVFRWCwWpkyZgr+/f8n6q6++yuHDh8nPz6d379706dPnoj8nOzubsLAw7HZ7he0hMdwGHarv5fG+Zxj+d21mFRER+bWu5PXbI4WkophRSNbO2E7f0Y05fjZQ9x4RERG5Clfy+q1NEZfxl9dcDL8hRWVERESkHHn0zfV8zcG1R1lxqgNvfpJpdhQRERGfpgnJL5g55iC/bbiFhjdEmR1FRETEp2lCcgnZx7OZu/Vavpxz1OwoIiIiPk+F5BIWjNpGy+qR3Phom8s/WERERMpEp2wuwnAbzFoazVMDsy7/YBERESkzTUgu4utp28goaMSA1xqYHUVERKRK0ITkImb9OZ9Hb9hFUHiQ2VFERESqBE1I/sfRDSdYfqoDf16UbnYUERGRKkMTkv/x7jP7uKvedhonRJsdRUREpMpQIfmJvOw85mxozVOJGhyJiIhUJBUSwDAMzn97nvf/bz22ahe4dUx7syOJiIhUKVV+FOA64iKlRwquQy7m5temv2Urm9umE/9FPEGNtalVRESkIlTpCYlhGKT0SMF5wMmx/Ax205wEowbOA0523LUDL3ojZBEREa9WpQuJPcmO67ALCmE5NejLeoIJgkJwHnRiT7KbHVFERKRKqNKFxLnficXfAkAIhdyNq2TNEmDBud9pVjQREZEqpUrvIQmODcbILz4t8yDVgeola0a+QXBssEnJREREqpYqPSEJSwgjqGnQz2uZHwQ3CyYsIcyUXCIiIlVNlS4kFouF+C/iCY4JxhJgwVrDiiXAQkhsCO2+aIfFYjE7ooiISJVQpU/ZAAQ1DuL6tOuxJ9lx7ncSHFs8GVEZERERqThVvpBA8aQkvHM44Z3DzY4iIiJSJVXpUzYiIiJSOaiQiIiIiOlUSERERMR0KiQiIiJiOhUSERERMZ0KiYiIiJhOhURERERMp0IiIiIiplMh8XLTp083O0KVoOe5Yuh5rhh6niuOnusrZzEMwzA7xJXKzs4mLCwMu91OaGio2XEqhejoaI4fP252DJ+n57li6HmuGHqeK46e62JX8vqtCYmIiIiYzqvey+bHYU52drbJSSoPwzD0fFQAPc8VQ89zxdDzXHH0XBf78Tn4pZMyXnXK5vjx4zRs2NDsGCIiInIVjh07RnR09EXXvKqQuN1uTp48Sc2aNbFYLGbHERERkStgGAYXLlwgKioKq/Xiu0W8qpCIiIiIb9KmVhERETGdComIiIiYToXEx4wdO5ahQ4eaHcMnrVmzhnbt2hEaGkrPnj05fPiw2ZF8ypQpUxg2bBiDBg3i66+/NjuOTzpy5Ag9evSgZs2adOjQgTVr1pgdyeetWLGCpk2bmh3DK2gPiQ/57rvv6NGjB/feey/vvfee2XF8ysmTJ7n33nsZNmwYubm5vPDCC9StW5eUlBT8/Lzq6vlKaebMmWzdupV58+bhcrlo3749y5cvJyYmxuxoPsMwDHr06MEdd9xBvXr1mDZtGvv27WPHjh16nstJVlYWnTp1orCwUH/AXAEVEh/hcDgYNmwYFosFPz8/FRIPW7hwIXfddReRkZFA8V89vXr1Yvv27cTHx5uczrvl5+cTFRXF4sWL6dq1KwCJiYlcuHCBefPmmZzOd+zcuZOzZ89y2223AXD27FmaNWvG5MmTSUxMNDmdb3ryySepW7cu8+bNUyG5Ajpl4yNefPFFJk6cqL/Wy8mAAQNKyghAt27dAAgMDDQpke9ISkoiMzOTNm3alByLj4/n888/NzGV74mLiyspIwB16tThmmuu0b/D5eTTTz+lU6dONGrUyOwoXkOFxAesW7eOunXr0qpVK7Oj+KyAgIBSn58+fZrWrVvTsmVLkxL5jtTUVKxWKzabreSYzWYjPT2drKwsE5P5lv/9dxiKTyncc889JqTxbRkZGSxfvlz7+X4l/TldyY0ZM4aUlJRLro8cOZJFixYxf/78Ckzle67kef7pf7gXLlzI66+/XhHRfJ7dbic8PLzUzZJ+/Kvd4XCUKiriOevXr6dv376XvGumXL1Jkybx0ksvmR3D66iQVHLTpk37xfU//OEPPPfcc5e8851cmcs9zz919OhR8vLy6NmzZzkmqjoiIiLIy8srdczpdAKojJSTgoICPvzwQ2bMmGF2FJ/z0Ucf0a1bN+rVq2d2FK+jTa1e7pduoa9/tJ7ndDp58cUXefHFF/H39zc7jk/46quvuPPOO3E6nQQFBQEwe/ZsJk+ezLFjx0xO55umTp3KoEGD9N5g5aB79+6sXbv2omtr1qwp2X8mP6cJiZfbtm1bqc+fffZZoHiTq3hWUVERU6dOZfz48SVlJDc3l+rVq5uczLt169aNyMhIkpOT6dKlC1C8r6RXr14mJ/NNc+fO5a677iopI3l5efj5+VGtWjWTk/mGOXPmkJOTU/L50qVLmT17NitWrCA2NtbEZJWfComXa9++fanPIyIiLnpcyqaoqIjHHnuMzp07s2HDBqD4sskffviBV155xeR03s3f359Ro0axZMkSunTpQm5uLl999RUrV640O5rPefvttzl+/DjR0dGsWrUKh8PBJ598wvvvv292NJ/xv6Vj+/btBAQE6L/JV0CFROQK/O53v2PBggU/uy/G4sWLTUrkW8aNG8f48eNJTEzEbrczd+5cmjRpYnYsnzJv3jyefPJJoPiuuD8aMWKE9qBJpaA9JCIiImI61WIRERExnQqJiIiImE6FREREREynQiIiIiKmUyERERER06mQiIiIiOlUSERERMR0KiQiIiJiOhUSERERMZ0KiYiIiJhOhURERERM9/9ZC94yDckw/gAAAABJRU5ErkJggg==\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# curve fitting, a non-linear least squares routine\n", "from scipy.optimize import curve_fit\n", "\n", "def func(x, a, b, c, d):\n", " \"\"\"A polynomial function.\"\"\"\n", " return a*x**3 + b*x**2 + c*x + d\n", "\n", "xs = np.linspace(-5, 5, 5)\n", "ys = func(xs, 5, -2, 1, 0)\n", "\n", "# feed it some data points that are *exactly* the right numbers\n", "\n", "popt, pcov = curve_fit(func, xs, ys)\n", "print(popt)\n", "print(func(0, *popt))\n", "\n", "x=np.linspace(-5,5,100)\n", "y=func(x,*popt)\n", "plt.scatter(xs,func(xs,*popt),color='m')\n", "plt.plot(x,func(x,5, -2, 1, 0),color='r')\n", "plt.plot(x,y,color='b');\n", "\n", "# you can't tell the fit from the actual polynomial (10^-24 is effectively zero)" ] }, { "cell_type": "code", "execution_count": 15, "id": "aececa2a", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[-5. -2.5 0. 2.5 5. ]\n", "[ 77.2199776 -272.54442983 -113.55093182 -160.47467963 257.42200382]\n", "[-602.7800224 -365.66942983 -113.55093182 -92.34967963 837.42200382]\n", "[ 5.89953022 10.30456272 -7.37762702 -163.70683125]\n", "-163.70683125041236\n" ] }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# now add some noise\n", "\n", "np.random.seed(43) # fix random seed\n", "errs = np.random.normal(loc=0, scale=300, size=len(ys))\n", "ys_err = func(xs, 5, -2, 1, 0) + errs\n", "print(xs)\n", "print(errs)\n", "print(ys_err)\n", "popt, pcov = curve_fit(func, xs, ys_err, sigma=errs, absolute_sigma=True)\n", "print(popt)\n", "print(func(0, *popt))\n", "\n", "x=np.linspace(-5,5,100)\n", "plt.scatter(xs,func(xs, 5, -2, 1, 0),color='m')\n", "plt.plot(x,func(x, 5, -2, 1, 0),color='r')\n", "\n", "plt.scatter(xs, ys_err,color='k')\n", "plt.errorbar(xs, ys_err, yerr=abs(errs), fmt='o')\n", "\n", "x=np.linspace(-5,5,100)\n", "y=func(x,*popt)\n", "plt.plot(x,y,color='b');\n", "\n", "# not bad, but least-squared is very limited when the \n", "# data display complex behavior, better to use chi^2" ] }, { "cell_type": "markdown", "id": "d5440c1d", "metadata": {}, "source": [ "#### Residuals and Averaging, A Spectral Centroiding Example" ] }, { "cell_type": "markdown", "id": "b0528f22", "metadata": {}, "source": [ "If we take a look at a typical a neon emission spectrum, (or any gas for that matter) we would see sharp emission peaks at very distinct wavelengths. This occurs because when atoms are energized (in the case of a neon lamp, by an electric current) they release photons, but they can only do so at several quantized energies (wavelengths). \n", "\n", "However, when we view spectra like the one we will plot below, we notice that the sharp peaks do in fact have a certain width, despite the description above indicating they should be perfect vertical lines at some defined wavelengths. There are numerous reasons for the widening: spectrometers introduce some widening (instrumental effects), fast moving gas has doppler shifts associated with some photons, and, at a theoretical level, we know from quantum physics that there is always imprecision in either the electron's position or momentum (though this would be a tiny effect in this situation). \n", "\n", "In any case, if we are to perform any sort of scientific analysis on a spectrum, we need to know for each of those peaks what our best guess for the single \"right\" wavelength for that line should be. One typical method of determining this is centroiding." ] }, { "cell_type": "markdown", "id": "23d00c7a", "metadata": {}, "source": [ "Centroiding amounts to finding the \"center of mass\" of a given peak. The formula for determining the centroid of a range of values (such as intensity/signal) is\n", "\\begin{equation}\n", "x_{cm} = \\frac{\\sum x_iI_i}{\\sum I_i}.\n", "\\end{equation}\n", "where $x_i$ will end up being our wavelength (or pixel number) array, and \"I\" represents intensity (or Brightness, or # of photons/unit time) at each pixel value. It basically represents a \"weighted average\" of the peak. Note: we can't simply choose the x value where the peak hits its maximum because the limitations of the spectrometer result in the true \"peak value\" not lining up with the real wavelength we are looking for. This weighted average of the whole peak provides a better guess. Think about it, just because one extra photon happens to pile into pixel x, doesn't mean pixel x is representitive of that spectral line." ] }, { "cell_type": "code", "execution_count": 6, "id": "319c6492", "metadata": {}, "outputs": [], "source": [ "# https://prappleizer.github.io/Tutorials/Centroiding/centroiding_tutorial.html\n", "\n", "import numpy as np \n", "import matplotlib.pyplot as plt\n", "%matplotlib inline\n", "plt.rcParams['figure.figsize'] = (20.0, 10.0)\n", "#Load up neon spectrum \n", "pixels = np.loadtxt('data/neon.txt',usecols=(0,)) #take zeroth column\n", "signal = np.loadtxt('data/neon.txt',usecols=(1,)) #take first column" ] }, { "cell_type": "markdown", "id": "41d4baed", "metadata": {}, "source": [ "So now we have a pixel and signal array. Our goal is to find the centroid of all the peaks in the plot. Speaking of, let's plot pixels vs signal just to get an idea of what were are looking at:" ] }, { "cell_type": "code", "execution_count": 7, "id": "9c1d6049", "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(pixels,signal)\n", "plt.xlabel('Pixel Value')\n", "plt.ylabel('Signal');" ] }, { "cell_type": "markdown", "id": "1fd77873", "metadata": {}, "source": [ "Notice there are quite a few jitters there. We are only interested in the major features, so when we are performing the following analysis, it would probably be smart to implement some sort of threshold (say, 20,000?) to catch only the major peaks. \n", "\n", "In order to find the centroid of each peak, we need to first determine, roughly, where the peaks are in the first place. We need a peak-finding algorithm. \n", "\n", "1. Iterate over a range that's the length of the pixel array (or signal, they're the same length by construction) checking whether each value of signal is higher or lower than the value of signal one to the left and one to the right.\n", "2. If you want to be extra robust, check whether it is in fact higher than its two left and right neighbors. \n", "3. If it is, call it a peak and append that index where the peak occurs out into a separate array." ] }, { "cell_type": "code", "execution_count": 8, "id": "b8aaf9bb", "metadata": {}, "outputs": [], "source": [ "#Find the peaks \n", "\n", "threshhold = 30000 # You can just pick slightly lower than the lowest peak you want to centroid\n", "peaks = [] # x positions of the peaks, or rather, their index\n", "for i in range(len(signal)-1):\n", " if (signal[i] > signal[i+1]) and (signal[i]>signal[i-1]) and (signal[i]>threshhold):\n", " if (signal[i] > signal[i-2]) and (signal[i] > signal[i+2]):\n", " peaks.append(i)" ] }, { "cell_type": "markdown", "id": "3dc49cc2", "metadata": {}, "source": [ "We should now have the positions (in pixel space) where the peaks occur. We now want to calculate the centroid in a region around each peak. This raises a bit of an issue, for example, how wide do we make that region? Too narrow and we don't include the whole peak, too wide and we are biased or influenced by things not actually a part of the peak. \n", "\n", "Most astronomers' solution to this issue is to use a standardized region known as the Full Width (at) Half Maximum (or FWHM). What this means is we want to use a region that is as wide as where the peak has dropped to half its maximum value. This works well, because the width will automatically be adjusted to handle larger and smaller peaks, and the same \"amount\" of each peak is being used in our calculation. \n", "\n", "In the space below, iterate over the peaks we just found, and determine the FWHM (in this case it will be very narrow because our spectrometer did not have very high resolution). I suggest defining an xmin and xmax, and using the \"np.where\" function to search out where the signal array drops below the half max value (easily calculated by taking signal indexed at \"i\" and dividing by 2). Using that FWHM, caculate the center of mass of each peak, and append the final pixel positions of the centers of mass to a new array/list. Remember that you can sum arrays (and arrays times arrays) without iterating!" ] }, { "cell_type": "code", "execution_count": 9, "id": "d995fce6", "metadata": {}, "outputs": [], "source": [ "centroids = [] # Values for all the centroids\n", "for i in peaks:\n", " # Calculate how far backward and forward to go:\n", " half_max = signal[i] / 2.\n", " xmin = (np.where(signal[i::-1] < half_max)[0])[0]\n", " xmax = (np.where(signal[i:] < half_max)[0])[0]\n", " x_range = pixels[i-xmin:i+xmax]\n", " I_range = signal[i-xmin:i+xmax]\n", " x_range = np.array(x_range)\n", " I_range = np.array(I_range)\n", " xcm = np.sum((x_range*I_range)) / np.sum(I_range)\n", " centroids.append(xcm) " ] }, { "cell_type": "markdown", "id": "a937a607", "metadata": {}, "source": [ "Now we have our centroids. Lets go ahead and plot the centroids as vertical, dashed lines over our data. While this seems a somewhat trivial step, visual inspection is important." ] }, { "cell_type": "code", "execution_count": 10, "id": "7ef4032c", "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def plot_vert(x): \n", " '''\n", " Just plots vertical lines, in blue dashes\n", " '''\n", " plt.axvline(x, color='blue', ls='-.')\n", " \n", "for i in centroids[1:]: # call the plotting function on every centroid except the first\n", " plot_vert(i)\n", " \n", "plt.axvline(centroids[0],color='blue',ls='-.',label='Centroid') #Reserve the first so I don't have a million \"centroid\" labels\n", "plt.plot(pixels, signal, 'r', label='Spectrum') #Plot the actual spectrum\n", "plt.xlabel('Pixel Value')\n", "plt.ylabel('Signal')\n", "plt.legend(loc=2);" ] }, { "cell_type": "markdown", "id": "99f50bcc", "metadata": {}, "source": [ "The vertical lines line up with the peaks of the spectrum, roughly (they shouldn't be at the exact peak, if we calculated our centers of mass correctly. In fact, let's plot this just to show ourselves that we did in fact get something different. We still have our \"peaks\" array, which contains the pixel positions of the peak values. Let's plot a \"residual\" (not exactly a residual in a scientific context, but close enough)- plot the difference between the peaks array and the centroids array against a new x-array that is just a range the length of the peaks/centroids array, to get a feel for whether the centroids were actually any different than the peaks:" ] }, { "cell_type": "code", "execution_count": 11, "id": "07e14f4f", "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "residual = np.array(peaks) - np.array(centroids)\n", "plt.plot(np.arange(len(residual)),residual,'bo')\n", "plt.xlabel('Peak number (of those found)')\n", "plt.ylabel('Residual [peak value - centroid value]')\n", "plt.axhline(0,ls='-.');" ] }, { "cell_type": "markdown", "id": "6534bbd6", "metadata": {}, "source": [ "We can see in the plot above several things, the first being that there is definitely a difference between the peak value and the centroid value, sometimes by as much as 3 pixels (this is of course specific to this spectrum taken with this spectrometer- values will differ). Secondly, we can see that they seem to be randomly distributed, but perhaps slightly weighted to being above zero rather than below. Assuming no systematics (of which there are likely several here), we would expect roughly half the points to be negative (roughly have the centroids be to the left of the peak and half to the right). \n", "\n", "We would want to, as scientists, explore further why this bias might exist. Is there bias in how we are calculating our FWHM (perhaps accidentally weighting to the right? Perhaps the spectrograph itself has a slight systematic bias towards shuffling incoming photons into slightly higher wavelength bins than they should be? Perhaps, in some inherent sense, the shape of neon spectral peaks is not symmetric but is in fact slightly asymmetric? " ] }, { "cell_type": "markdown", "id": "3af07d85-53d9-4a1a-8bf9-81b060be5acd", "metadata": {}, "source": [ "\n", "---\n", "\n", "

To illustrate the use of curve_fit in weighted and unweighted least squares fitting, the following program fits the Lorentzian line shape function centered at $x_0$ with halfwidth at half-maximum (HWHM), $\\gamma$, amplitude, $A$:\n", "$$\n", "f(x) = \\frac{A \\gamma^2}{\\gamma^2 + (x-x_0)^2},\n", "$$\n", "to some artificial noisy data. The fit parameters are $A$, $\\gamma$ and $x_0$. The noise is such that a region of the data close to the line centre is much noisier than the rest.

\n" ] }, { "cell_type": "code", "execution_count": 30, "id": "bf3f278a-871d-4b3b-bf6b-627bf6533440", "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# https://scipython.com/book2/chapter-8-scipy/examples/weighted-and-non-weighted-least-squares-fitting/\n", "\n", "x0, A, gamma = 12, 3, 5\n", "\n", "n = 200\n", "x = np.linspace(1, 20, n)\n", "yexact = A * gamma**2 / (gamma**2 + (x-x0)**2)\n", "\n", "# Add some noise with a sigma of 0.5 apart from a particularly noisy region\n", "# near x0 where sigma is 3\n", "sigma = np.ones(n)*0.5\n", "sigma[np.abs(x-x0+1)<1] = 3\n", "np.random.seed(39)\n", "noise = np.random.randn(n) * sigma\n", "y = yexact + noise\n", "plt.plot(x, yexact, label='Exact')\n", "plt.plot(x, y, 'o', label='Noisy data')\n", "plt.ylim(-1,4)\n", "plt.ylabel('f(x)')\n", "plt.xlabel('x')\n", "plt.legend(loc='lower center');" ] }, { "cell_type": "code", "execution_count": 32, "id": "de9d9b37", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Unweighted fit parameters: [12.2673854 2.64551234 5.79411823]\n", "Covariance matrix:\n", "[[ 0.11381664 -0.00237058 0.02055555]\n", " [-0.00237058 0.02378964 -0.06510259]\n", " [ 0.02055555 -0.06510259 0.34715297]]\n", "rms error in fit: 2.3995624658913606\n", "\n", "Weighted fit parameters: [12.00694929 2.91791538 5.21572298]\n", "Covariance matrix:\n", "[[ 0.02229751 -0.00336162 0.00801772]\n", " [-0.00336162 0.01088023 -0.02246182]\n", " [ 0.00801772 -0.02246182 0.07384679]]\n", "rms error in fit: 0.5331058594136591\n" ] }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def f(x, x0, A, gamma):\n", " \"\"\" The Lorentzian entered at x0 with amplitude A and HWHM gamma. \"\"\"\n", " return A *gamma**2 / (gamma**2 + (x-x0)**2)\n", "\n", "def rms(y, yfit):\n", " return np.sqrt(np.sum((y-yfit)**2))\n", "\n", "# Unweighted fit\n", "p0 = 10, 4, 2\n", "popt, pcov = curve_fit(f, x, y, p0)\n", "yfit = f(x, *popt)\n", "print('Unweighted fit parameters:', popt)\n", "print('Covariance matrix:'); print(pcov)\n", "print('rms error in fit:', rms(yexact, yfit))\n", "print()\n", "\n", "# Weighted fit\n", "popt2, pcov2 = curve_fit(f, x, y, p0, sigma=sigma, absolute_sigma=True)\n", "yfit2 = f(x, *popt2)\n", "print('Weighted fit parameters:', popt2)\n", "print('Covariance matrix:'); print(pcov2)\n", "print('rms error in fit:', rms(yexact, yfit2))\n", "\n", "plt.plot(x, yexact, label='Exact')\n", "plt.plot(x, y, 'o', label='Noisy data')\n", "plt.plot(x, yfit, label='Unweighted fit')\n", "plt.plot(x, yfit2, label='Weighted fit')\n", "plt.ylim(-1,4)\n", "plt.ylabel('f(x)')\n", "plt.xlabel('x')\n", "plt.legend(loc='lower center');" ] }, { "cell_type": "markdown", "id": "87a5c28b-a9ed-402f-8b25-a61da2b63895", "metadata": {}, "source": [ "\n", "---\n", "\n", "

The NASA Cosmic Background Explorer (COBE) satellite carried an instrument, FIRAS (Far-Infrared Absolute Spectrophotometer) to measure the cosmic microwave background (CMB) radiation, which was confirmed to be distributed according to a black-body curve in accordance with the big bang theory:

\n", "

\\begin{align*}\n", "I(\\tilde{\\nu}, T) = \\frac{2h\\tilde{\\nu}^3c^2}{\\exp\\left(\\frac{hc\\tilde{\\nu}}{k_\\mathrm{B}T}\\right) - 1}\n", "\\end{align*}\n", "where the radiation frequency is expressed in wavenumbers, $\\mathrm{cm^{-1}}$, and the speed of light, $c$, is taken to be in $\\mathrm{cm\\,s^{-1}}$.

\n", "

The data file cmb-data.txt contains measurements of $I(\\tilde{\\nu})$ based on the FIRAS observations. Note that the units of $I$ in this file are $\\mathrm{erg\\,s^{-1}\\,cm^{-2}\\,sr^{-1}\\,cm}$ and that $1\\;\\mathrm{J}\\equiv 10^7\\;\\mathrm{erg}$. Use scipy.optimize.curve_fit to determine the temperature of the CMB and take the estimated $1\\sigma$ error in the measurement to be $2 \\times 10^{-6}\\;\\mathrm{erg\\,s^{-1}\\,cm^{-2}\\,sr^{-1}\\,cm}$.

\n", "\n", "\n" ] }, { "cell_type": "code", "execution_count": 23, "id": "f7e0a4d4-fa78-40c2-a312-9bec7e537687", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Tcmb = 2.715 ± 0.004 K\n" ] }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# https://scipython.com/book2/chapter-8-scipy/additional-problems/fitting-the-cosmic-microwave-background/\n", "\n", "from scipy.constants import h, c, k\n", "c = 100 * c\n", "from scipy.optimize import curve_fit\n", "\n", "nu, cmb = np.loadtxt('data/cmb-data.txt', unpack=True)\n", "\n", "def B(nu, T):\n", " return 2 * h * nu**3 * c**2 / (np.exp(h*c*nu/k/T)-1) * 1.e7\n", "\n", "sig = np.array(len(nu)*[2.e-6])\n", "\n", "T0 = 1\n", "popt, pcov = curve_fit(B, nu, cmb, p0=(T0,), sigma=sig, absolute_sigma=True)\n", "Tfit = popt[0]\n", "Bfit = B(nu, Tfit)\n", "\n", "perr = np.sqrt(np.diag(pcov))[0]\n", "print('Tcmb = {:.3f} ± {:.3f} K'.format(Tfit, perr))\n", "\n", "plt.plot(nu, cmb * 1.e4, '+r', markersize=12, label='exp')\n", "plt.plot(nu, Bfit * 1.e4, label='fit')\n", "plt.ylabel(r'$B(\\tilde{\\nu})\\,/10^4\\mathrm{erg\\,s^{-1}\\,cm^{-2}\\,sr^{-1}\\,cm}$')\n", "plt.xlabel(r'$\\tilde{\\nu}\\,/cm^{-1}$')\n", "plt.legend();" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.12.3" } }, "nbformat": 4, "nbformat_minor": 5 }