{ "cells": [ { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "view-in-github" }, "source": [ "\"Open" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "vO7m8G_uBsEz" }, "source": [ "# Statistics " ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "hbK6vM09BsE7" }, "source": [ "Considering the amount of data produced nowadays in many fields, the computer manipulation of this information is not only important but also has become a very active field of study. Despite of the fact of increasing computational facilities, the effort necessary to make statistical analysis has become more complicated, at least in the computational aspect. This is why \n", "becomes fundamental to some aspects, leastwise in a raw way. " ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "xzHB-SSKBsE_" }, "source": [ "- - -\n", "```{contents}\n", ":depth: 2\n", "```\n", "- - -" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 34 }, "colab_type": "code", "id": "l6ZbjjUlBsFG", "outputId": "8107ac68-9f7a-435a-e429-42627cc01ce0" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "%pylab is deprecated, use %matplotlib inline and import the required libraries.\n", "Populating the interactive namespace from numpy and matplotlib\n" ] } ], "source": [ "%pylab inline" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "colab": {}, "colab_type": "code", "id": "Dy4OMR4xBsFY" }, "outputs": [], "source": [ "import numpy as np\n", "from matplotlib import animation" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "WnxpZdlpBsFh" }, "source": [ "https://drive.google.com/file/d/12cwfl5i2SVlNF60oUF9-ep3q7NHB4AcH/view?usp=sharing### Data Adjust\n", "See also: \n", "* https://www.mathsisfun.com/data/least-squares-regression.html\n", "* http://blog.mmast.net/least-squares-fitting-numpy-scipy\n", "* https://stackoverflow.com/a/43623588/2268280" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "5S6xRqjVBsFj" }, "source": [ "Given a data set, the first approach to find a function that passes through the points would be using a\n", "interpolation polynomial. But we should take special attention to the way data set is gathered, i.e., usually\n", "is a sample obtained experimentally or in a way that has associated an intrinsic error. \n", "Then, forcing that the approximate function passes through all the points would actually incur in incrementing the error. This is why it is necessary to build a different procedure to build the function that fits the data.\n", "\n", "The fitting functions, though, are build using a Lagrange polynomial and the order of this polynomial constitutes\n", "the approximation that is going to be used. But the fitting function is not going to take the exact value in\n", "the known points, they are going to desagree in certain tolerance value. \n", "\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "CIOTmaQ0BsFm" }, "source": [ "## Linear least squares" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "xwBHVZ4NBsFp" }, "source": [ "Approximating a data set to a linear Langrange polynomial would be just to use\n", "$$\n", "y_i= f(x_i) = a_1x_i + a_0\\,.\n", "$$\n", "However, with experimental data, the problem is that the values $y_i$ are not precise, then it is proposed to find the best approximation.\n", "For the best _linear approximation_, we need to find for _all_ points the value of $a_0$ and $a_1$ that _minimize_ the error\n", "$$\n", "E = E(a_0,a_1) = \\sum_{i=1}^{m}[y_i - (a_1 x_i + a_0)]^2 \n", "$$\n", "where the square is more well suited for the minimization procedure since avoids the fluctions for changes of sign.\n", "\n", "To minimize the function of 2 variables, $E(a_0,a_1)$ with respect to $a_0$ and $a_1$, it is necessary to set its partial derivatives to zero and simultaneously \n", "solve to the resulting equations. \n", "\n", "\n", "To establish the minimzation equations, it is necesary to take the partial derivatives with respect to $a_0$ and $a_1$ and and equal them to zero\n", "$$\n", "\\frac{\\partial E}{\\partial a_0} = 0\\,, \\hspace{1cm} \n", "\\frac{\\partial E}{\\partial a_1} = 0\\,.\n", "$$\n", "\n", "Afterwards, \n", "\n", "\\begin{align}\n", "&0= 2\\sum_{i=1}^{m}(y_i -a_1x_i-a_0)(-1)\\,, && \n", "&0 =& 2\\sum_{i=1}^{m}(y_i -a_1x_i-a_0)(-x_i) \\\\\n", "&a_0 m + a_1\\sum_{i=1}^{m}x_i = \\sum_{i=1}^{m} y_i\\,,&& &a_0\\sum_{i=1}^{m}x_i + a_1\\sum_{i=1}^{m}x_i^2 = \\sum_{i=1}^{m} x_iy_i \n", "\\end{align}\n", "\n", "\\begin{align}\n", "a_0= &\\frac{ \\sum_{i=1}^{m} y_i-a_1\\sum_{i=1}^{m}x_i }{m} \n", "\\end{align}\n", "\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "FrnkrXDUEHjG" }, "source": [ "Replacing back in the second equation\n", "\\begin{align}\n", " \\left( \\frac{ \\sum_{i=1}^{m} y_i-a_1\\sum_{i=1}^{m}x_i }{m} \\right)\\sum_{i=1}^{m}x_i + a_1\\sum_{i=1}^{m}x_i^2 = \\sum_{i=1}^{m} x_iy_i \n", "\\end{align}\n", "\\begin{align}\n", " \\frac{1}{m}\\sum_{i=1}^{m} y_i \\sum_{i=1}^{m}x_i -a_1\\frac{1}{m} \\sum_{i=1}^{m}x_i \\sum_{i=1}^{m}x_i + a_1\\sum_{i=1}^{m}x_i^2 = \\sum_{i=1}^{m} x_iy_i \n", "\\end{align}\n", "\\begin{align}\n", " a_1\\left[ \\sum_{i=1}^{m}x_i^2 -\\frac{1}{m}\\left( \\sum_{i=1}^{m}x_i \\right)^2 \\right] = \\sum_{i=1}^{m} x_iy_i - \\frac{1}{m}\\sum_{i=1}^{m} y_i \\sum_{i=1}^{m}x_i\n", "\\end{align}\n", "\\begin{align}\n", " a_1\\left[ m\\sum_{i=1}^{m}x_i^2 -\\left( \\sum_{i=1}^{m}x_i \\right)^2 \\right] = m\\sum_{i=1}^{m} x_iy_i -\\sum_{i=1}^{m} y_i \\sum_{i=1}^{m}x_i\n", "\\end{align}\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "JYA6CoCYIxvX" }, "source": [ "Therefore\n", "\\begin{align}\n", "a_1 = \\frac{m\\sum_{i=1}^{m} x_iy_i - \\sum_{i=1}^{m} x_i \\sum_{i=1}^{m} y_i }\n", "{m\\sum_{i=1}^{m} x_i^2 - \\left(\\sum_{i=1}^{m} x_i\\right)^2} \n", "\\end{align}\n" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "Rd7JYsebJlOa" }, "source": [ "Replacing back in $a_0$\n", "\\begin{align}\n", "ma_0= &\\sum_{i=1}^{m} y_i-a_1\\sum_{i=1}^{m}x_i \\\\\n", " = &\\sum_{i=1}^{m} y_i-\\left[\\frac{m\\sum_{i=1}^{m} x_iy_i - \\sum_{i=1}^{m} x_i \\sum_{i=1}^{m} y_i }\n", "{m\\sum_{i=1}^{m} x_i^2 - \\left(\\sum_{i=1}^{m} x_i\\right)^2} \\right]\\sum_{i=1}^{m}x_i \\\\\n", "= &\\sum_{i=1}^{m} y_i-\\frac{m\\sum_{i=1}^{m}x_i\\sum_{i=1}^{m} x_iy_i - \\left( \\sum_{i=1}^{m} x_i\\right)^2 \\sum_{i=1}^{m} y_i }\n", "{m\\sum_{i=1}^{m} x_i^2 - \\left(\\sum_{i=1}^{m} x_i\\right)^2} \\\\\n", "= &\\frac{m\\sum_{i=1}^{m} x_i^2\\sum_{i=1}^{m} y_i-m\\sum_{i=1}^{m}x_i\\sum_{i=1}^{m} x_iy_i }\n", "{m\\sum_{i=1}^{m} x_i^2 - \\left(\\sum_{i=1}^{m} x_i\\right)^2} \\\\\n", "\\end{align}" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "P6BS40QyLqe-" }, "source": [ "\\begin{align}\n", "a_0= &\\frac{\\sum_{i=1}^{m} x_i^2\\sum_{i=1}^{m} y_i-\\sum_{i=1}^{m}x_i\\sum_{i=1}^{m} x_iy_i }\n", "{m\\sum_{i=1}^{m} x_i^2 - \\left(\\sum_{i=1}^{m} x_i\\right)^2} \\\\\n", "\\end{align}" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "c73y29bGL_2v" }, "source": [ "where the coefficients $a_0$ and $a_1$ can be easily obtained\n", "\n", "$$\n", "a_0 = \\frac{\\sum_{i=1}^{m} x_i^2\\sum_{i=1}^{m}y_i - \\sum_{i=1}^{m} x_iy_i \\sum_{i=1}^{m} x_i }\n", "{m\\sum_{i=1}^{m} x_i^2 - \\left(\\sum_{i=1}^{m} x_i\\right)^2}\\,, \\hspace{1.5cm}\n", "a_1 = \\frac{m\\sum_{i=1}^{m} x_iy_i - \\sum_{i=1}^{m} x_i \\sum_{i=1}^{m} y_i }\n", "{m\\sum_{i=1}^{m} x_i^2 - \\left(\\sum_{i=1}^{m} x_i\\right)^2} \n", "$$\n", "\n", "Now, using the error definition one can find the error associated to the approximation made,\n", "\n", "since the coefficients $a_0$ and $a_1$ are already known. " ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "T7TZF-WeBsFt" }, "source": [ "From [Least square method in python](https://stackoverflow.com/a/43623588/2268280):\n", "\n", "> There are many [curve fitting](https://python4mpia.github.io/fitting_data/fitting_data.html) functions in scipy and numpy and each is used differently, e.g. [scipy.optimize.leastsq](https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.leastsq.html) and [scipy.optimize.least_squares](https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.least_squares.html). For simplicity, we will use [scipy.optimize.curve_fit](https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.curve_fit.html), but it is difficult to find an optimized regression curve without selecting reasonable starting parameters. A simple technique will later be demonstrated on selecting starting parameters.\n", "\n", "In our first example the starting parameters will be just zeros" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "fBRt-ri7BsFw" }, "source": [ "### Example 1" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "ofp7NY8fBsF0" }, "source": [ "A body is moving under the influence of an external force, the variation of the position measured for different \n", "times are compiled in table 1 \n", "\n", "| t(s) | x(m) | v(m/s) \n", "| :------: |:-------------: | :-------:|\n", "|0| 2.76 | 33.10\n", "| 1.11| 29.66 | 21.33\n", "| 2.22|46.83 | 16.57\n", "|3.33 | 44.08 |-5.04\n", "| 4.44| 37.26| -11.74\n", "| 5.55| 12.03| -27.32| \n" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "%pylab is deprecated, use %matplotlib inline and import the required libraries.\n", "Populating the interactive namespace from numpy and matplotlib\n" ] } ], "source": [ "%pylab inline" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "colab": {}, "colab_type": "code", "id": "Vf0fRX69BsF2" }, "outputs": [], "source": [ "import pandas as pd" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 225 }, "colab_type": "code", "id": "YGJ5sVVuBsGA", "outputId": "60508d74-e84a-47a2-89f1-5c9e24a12fb2" }, "outputs": [ { "data": { "text/html": [ "
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" ], "text/plain": [ " t v\n", "0 0.00 33.10\n", "1 1.11 21.33\n", "2 2.22 16.57\n", "3 3.33 -5.04\n", "4 4.44 -11.74\n", "5 5.55 -27.32" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "#'x': [2.76, 29.66,46.83,44.08,37.26,12.03],\n", "df=pd.DataFrame( {'t': [ 0., 1.11, 2.22, 3.33, 4.44, 5.55],#'x': [2.76, 29.66,46.83,44.08,37.26,12.03],\n", " 'v': [33.10, 21.33, 16.57, -5.04, -11.74, -27.32]} )\n", "df[['t','v']]" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 282 }, "colab_type": "code", "id": "QkN3TR5NBsGJ", "outputId": "153342da-67a7-4c2e-889d-8c9003fc3791" }, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(df.t,df.v,'ro')\n", "plt.xlabel('$t$ [s]',size=15 )\n", "plt.ylabel('$v$ [m/s]',size=15 )\n", "plt.grid()" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "colab": {}, "colab_type": "code", "id": "IcEnlISIBsGU" }, "outputs": [], "source": [ "import scipy.optimize as optimize" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "colab": {}, "colab_type": "code", "id": "YnwJIU_vBsGb" }, "outputs": [], "source": [ "def func(t,a1,a0):\n", " return a1*t+a0" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The starting point is optional" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "colab": {}, "colab_type": "code", "id": "UFQC5b6AVWx0" }, "outputs": [], "source": [ "starting_parameters=[0,0]" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "colab": {}, "colab_type": "code", "id": "IE1rQ4_kBsGh" }, "outputs": [], "source": [ "a,Δa=optimize.curve_fit(func,df.t,df.v,p0=starting_parameters)" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([-10.88597169, 34.69190478])" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "a" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The correlation matrix,$\\Delta a$ , give as the error in the determination of the parameters" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[ 0.68398817, -1.89806718],\n", " [-1.89806718, 7.72513347]])" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Δa" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([0.68398817, 7.72513347])" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.diag(Δa)" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 52 }, "colab_type": "code", "id": "2I36ufAgBsGm", "outputId": "731c2082-8382-4b93-8eb7-92248b1881b4" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[-10.88597169 34.69190478]\n", "--------------------\n", "[[ 0.68398817 -1.89806718]\n", " [-1.89806718 7.72513347]]\n", "--------------------\n", "a1=-10.89±0.83, a0=34.7±2.8\n" ] } ], "source": [ "print(a)\n", "print('-'*20)\n", "print(Δa)\n", "σ = np.sqrt(np.diag(Δa))\n", "print('-'*20)\n", "print('a1={:.2f}±{:.2f}, a0={:.1f}±{:.1f}'.format(a[0],σ[0],a[1],σ[1]) )" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "colab": {}, "colab_type": "code", "id": "HO_aUb_CBsGu" }, "outputs": [], "source": [ "t_lin=np.linspace(0,5.55)\n", "v_model=func(t_lin,*a) #func(t_lin,a[0],a[1])\n", "df['v_fitted']=func(df.t,*a)" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 225 }, "colab_type": "code", "id": "Rawx3qY4BsG0", "outputId": "e01a1121-4684-49c4-fa3e-3d8dfc7b086b" }, "outputs": [ { "data": { "text/html": [ "
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" ], "text/plain": [ " t v v_fitted\n", "0 0.00 33.10 34.691905\n", "1 1.11 21.33 22.608476\n", "2 2.22 16.57 10.525048\n", "3 3.33 -5.04 -1.558381\n", "4 4.44 -11.74 -13.641810\n", "5 5.55 -27.32 -25.725238" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 305 }, "colab_type": "code", "id": "gLiwTDi4BsG6", "outputId": "f677f02c-89d2-4895-cacd-17b915a5a65a" }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(df.t,df.v,'b.',label='exp. data')\n", "plt.plot(df.t,a[0]*df.t+a[1],'g-',lw=2,label=\"Linear adjust\")\n", "for i in range(df.t.size):\n", " plt.plot(np.array([df.t[i],df.t[i]]), np.array([df.v[i],df.v_fitted[i] ]),\"c-\")\n", " \n", "plt.xlabel( \"$t$ [s]\", fontsize = 18 )\n", "plt.ylabel( \"$v$ [m/s]\", fontsize = 18 )\n", "plt.title(\"Linear data adjust\")\n", "plt.legend()\n", "plt.grid() " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "__Activity__: plot the error bands. Use https://beta.deepnote.com/project/4b6ea05f-f155-4eae-959c-cd064deaa7b6" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "__Activity__: Solve the problem with `fmin_powell` for the fit only (not the error correlation matrix)\n", "$$\n", "E = E(a_0,a_1) = \\sum_{i=1}^{m}[y_i - (a_1 x_i + a_0)]^2 \n", "$$\n", "\n", "__Solution__:\n", "Let a=[a_0,a_1]" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [], "source": [ "def E(a,x=df.t.values,y=df.v.values):\n", " return ((y-(a[1]*x+a[0]))**2).sum()" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "2686.9554000000003" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "E([1,0])" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "3105.6670999999997" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "E([2,1])" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "79.44340000000005" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "E([33,-10])" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [], "source": [ "def Ea0(x,a1=-10):\n", " EE=[]\n", " for a0 in x:\n", " EE.append( E([a0,a1]))\n", " return np.array(EE)" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([5560.2434, 5203.4434])" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Ea0([2,3])" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "a0=np.linspace(10,50)\n", "plt.plot(a0,Ea0(a0,-10))" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Optimization terminated successfully.\n", " Current function value: 58.991928\n", " Iterations: 5\n", " Function evaluations: 169\n" ] }, { "data": { "text/plain": [ "(array([ 34.69190471, -10.88597167]),\n", " 58.99192761904762,\n", " array([[ 9.58580558, -2.62474386],\n", " [ 0.03589244, 0.0271459 ]]),\n", " 5,\n", " 169,\n", " 0)" ] }, "execution_count": 30, "metadata": {}, "output_type": "execute_result" } ], "source": [ "optimize.fmin_powell(E,[0,0],full_output=True)" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "cOlJ375RBsHF" }, "source": [ "### How does this work:\n", "From [Least sqaure method in python](https://stackoverflow.com/a/43623588/2268280):\n", "\n", "> [curve_fit]() is one of many optimization functions offered by scipy. Given an initial value, the resulting estimated parameters are iteratively refined so that the resulting curve minimizes the residual error, or difference between the fitted line and sampling data. A better guess reduces the number of iterations and speeds up the result. With these estimated parameters for the fitted curve, one can now calculate the specific coefficients for a particular equation (a final exercise left to the OP)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example: Least Action\n", "[Least_action_minimization.ipynb](./Least_action_minimization.ipynb)" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "ov-qmQoQBsHa" }, "source": [ "## Non-linear least square" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "2VCre7UHBsHc" }, "source": [ "In general, it can be used any polynomial order to adjust a data set, since it is satisfied that $n **Activity** " ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "RWu5luLmBsHf" }, "source": [ " \n", "Adjust the position column data in the table 1 to a second order polynomial. What is the acceleration suffered\n", "by the body?\n", "\n" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "from scipy import optimize" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "colab": {}, "colab_type": "code", "id": "No7rs6J7Xtkv" }, "outputs": [], "source": [ "def func(t,a2,a1,a0):\n", " return a2*t**2+a1*t+a0\n", "a,kk=optimize.curve_fit(func,df.t,df.v)\n", "t_lin=np.linspace(0,5.55)\n", "v2_model=func(t_lin,*a)\n", "df['v2_fitted']=func(df.t,*a)" ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 225 }, "colab_type": "code", "id": "LF1w9PnMYT-u", "outputId": "93803f85-586a-4b26-aea9-91e94e46a9c4" }, "outputs": [ { "data": { "text/html": [ "
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tvv_fittedv2_fitted
00.0033.1034.69190533.096072
11.1121.3322.60847622.927643
22.2216.5710.52504811.801714
33.33-5.04-1.558381-0.281715
44.44-11.74-13.641810-13.322643
55.55-27.32-25.725238-27.321071
\n", "
" ], "text/plain": [ " t v v_fitted v2_fitted\n", "0 0.00 33.10 34.691905 33.096072\n", "1 1.11 21.33 22.608476 22.927643\n", "2 2.22 16.57 10.525048 11.801714\n", "3 3.33 -5.04 -1.558381 -0.281715\n", "4 4.44 -11.74 -13.641810 -13.322643\n", "5 5.55 -27.32 -25.725238 -27.321071" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df" ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 305 }, "colab_type": "code", "id": "EOey_XZoYomW", "outputId": "be6116ee-790b-4e53-a821-cc55a621bd63" }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(df.t,df.v,'b.',label='exp. data')\n", "plt.plot(t_lin,v_model,'g-',lw=2,label=\"Linear adjust\")\n", "plt.plot(t_lin,v2_model,'r--',lw=2,label=\"quadratic adjust\")\n", "for i in range(df.t.size):\n", " plt.plot(np.array([df.t[i],df.t[i]]), np.array([df.v[i],df.v_fitted[i] ]),\"c-\")\n", " \n", "plt.xlabel( \"$t$ [s]\", fontsize = 18 )\n", "plt.ylabel( \"$v$ [m/s]\", fontsize = 18 )\n", "plt.title(\"Linear data adjust\")\n", "plt.legend()\n", "plt.grid(1) " ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "Unu1o3YMBsHh" }, "source": [ "### **Activity** \n" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "d5xD53YiBsHj" }, "source": [ " \n", "The air drag for a sphere that is moving at high speeds can be expresed in the following form \n", "$$\n", "f_{drag} = -\\frac{1}{2} C \\rho A v^2\n", "$$\n", "\n", "where C is the drag coefficient(0.5 for a sphere), $\\rho$ is the air density (1.29kg/$m^3$) \n", "and A is the cross-sectional area. \n", "Generate points that have a bias of the value obtanied with\n", "$f_{drag}$ using np.random.random. \n", "\n", "\n", "Afterwards, use a second order polynomial to fit the data \n", "generated and find the error associated to the approximation. \n", "" ] }, { "cell_type": "code", "execution_count": 44, "metadata": {}, "outputs": [], "source": [ "import scipy.optimize as optimize" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Fit to a non-linear function\n", "$$\n", "f(x)=A \\operatorname{e}^{cx} + d\\,.\n", "$$\n", "Determinar: $A,c,d$" ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "colab": {}, "colab_type": "code", "id": "1f8iqq0cBsHl" }, "outputs": [], "source": [ "import pandas as pd\n", "T_values = np.array([222, 284, 308.5, 333, 358, 411, 477, 518, 880, 1080, 1259])\n", "C_values = np.array([0.1282, 0.2308, 0.2650, 0.3120 , 0.3547, 0.4530, 0.5556, 0.6154, 0.8932, 0.9103, 0.9316])\n", "\n", "x_samp = T_values\n", "y_samp = C_values" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 31, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(x_samp,y_samp,'ro')" ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "colab": {}, "colab_type": "code", "id": "W0UI1CatBsHq" }, "outputs": [], "source": [ "def func(x, A, c, d):\n", " return A*np.exp(c*x) + d" ] }, { "cell_type": "code", "execution_count": 52, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "E]stimated Parameters [-1.66301124 -0.0026884 1.0099538 ]\n" ] } ], "source": [ "## REGRESSION ------------------------------------------------------------------\n", "p0 = [0, -3e-2, 1] ## guessed params\n", "w, _ = optimize.curve_fit(func, x_samp, y_samp, p0=p0) \n", "print(\"E]stimated Parameters\", w) \n", "\n", "## Model\n", "x_lin=np.linspace(200,1350)\n", "y_model = func(x_lin, *w)" ] }, { "cell_type": "code", "execution_count": 53, "metadata": { "colab": {}, "colab_type": "code", "id": "KiKVC2i2BsH5", "outputId": "cad54ee3-6f4f-4ac0-e7e0-9adbdec5064d" }, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'f(x)')" ] }, "execution_count": 53, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x_lin = np.linspace(0, x_samp.max(), 50) ## 50 evenly spaced digits between 0 and max\n", "## PLOT ------------------------------------------------------------------------\n", "## Visualize data and fitted curves\n", "plt.plot(x_samp, y_samp, \"ko\", label=\"Data\")\n", "plt.plot(x_lin, y_model, \"k--\", label=\"Fit\")\n", "plt.title(\"Least squares regression\")\n", "plt.legend(loc=\"upper left\")\n", "plt.xlabel('x')\n", "plt.ylabel('f(x)')" ] }, { "cell_type": "code", "execution_count": 61, "metadata": { "colab": {}, "colab_type": "code", "id": "3pk7TUB5BsH-", "outputId": "ae7234c5-9fae-4efd-d08a-bfebb65d4310" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "90\r" ] } ], "source": [ "import time\n", "for i in range(100):\n", " time.sleep(0.1)\n", " if i%10==0:\n", " print(i,end='\\r')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Example: exponential fit" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Guess the number of pages of a book\n", "https://docs.google.com/forms/d/e/1FAIpQLSeZJ0QII5JcST-M9_JgGYNzX3GahULVVFc31DQnWjJ4SdUQwg/viewform?fbclid=IwAR0wEadM0ZH-HXmp3lkAM3emCDPxs_6F509BS3EkOvldp-NFzbCOkZVSjR4" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\n", "f(x)=a\\exp\\left[ -\\frac{(x-\\mu)^2}{2\\sigma^2} \\right]\n", "$$\n", "where $a$ is the height of the gaussian, $\\mu$ is the mean (expected value), and $\\sigma$ es la varianze" ] }, { "cell_type": "code", "execution_count": 54, "metadata": {}, "outputs": [], "source": [ "import pandas as pd" ] }, { "cell_type": "code", "execution_count": 55, "metadata": {}, "outputs": [ { "ename": "HTTPError", "evalue": "HTTP Error 404: Not Found", "output_type": "error", "traceback": [ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[0;31mHTTPError\u001b[0m Traceback (most recent call last)", "Cell \u001b[0;32mIn [55], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m df\u001b[38;5;241m=\u001b[39mpd\u001b[38;5;241m.\u001b[39mread_csv(\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mhttps://docs.google.com/spreadsheets/d/e/2PACX-1vTu_XE2dAiTcjHTfbaVKt7xEl_GnNeF_VYFsIBi5uM-gqBlBRfNHso-X1z3lxV7IW2f9UYKmZkSOYv-/pub?output=csv\u001b[39m\u001b[38;5;124m'\u001b[39m)\n", "File \u001b[0;32m/usr/local/lib/python3.9/dist-packages/pandas/util/_decorators.py:211\u001b[0m, in \u001b[0;36mdeprecate_kwarg.._deprecate_kwarg..wrapper\u001b[0;34m(*args, **kwargs)\u001b[0m\n\u001b[1;32m 209\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[1;32m 210\u001b[0m kwargs[new_arg_name] \u001b[38;5;241m=\u001b[39m new_arg_value\n\u001b[0;32m--> 211\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mfunc\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43margs\u001b[49m\u001b[43m,\u001b[49m\u001b[43m 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\u001b[43mfunc\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43margs\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mkwargs\u001b[49m\u001b[43m)\u001b[49m\n", "File \u001b[0;32m/usr/local/lib/python3.9/dist-packages/pandas/io/parsers/readers.py:950\u001b[0m, in \u001b[0;36mread_csv\u001b[0;34m(filepath_or_buffer, sep, delimiter, header, names, index_col, usecols, squeeze, prefix, mangle_dupe_cols, dtype, engine, converters, true_values, false_values, skipinitialspace, skiprows, skipfooter, nrows, na_values, keep_default_na, na_filter, verbose, skip_blank_lines, parse_dates, infer_datetime_format, keep_date_col, date_parser, dayfirst, cache_dates, iterator, chunksize, compression, thousands, decimal, lineterminator, quotechar, quoting, doublequote, escapechar, comment, encoding, encoding_errors, dialect, error_bad_lines, warn_bad_lines, on_bad_lines, delim_whitespace, low_memory, memory_map, float_precision, storage_options)\u001b[0m\n\u001b[1;32m 935\u001b[0m kwds_defaults \u001b[38;5;241m=\u001b[39m _refine_defaults_read(\n\u001b[1;32m 936\u001b[0m dialect,\n\u001b[1;32m 937\u001b[0m delimiter,\n\u001b[0;32m (...)\u001b[0m\n\u001b[1;32m 946\u001b[0m defaults\u001b[38;5;241m=\u001b[39m{\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mdelimiter\u001b[39m\u001b[38;5;124m\"\u001b[39m: \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124m,\u001b[39m\u001b[38;5;124m\"\u001b[39m},\n\u001b[1;32m 947\u001b[0m )\n\u001b[1;32m 948\u001b[0m kwds\u001b[38;5;241m.\u001b[39mupdate(kwds_defaults)\n\u001b[0;32m--> 950\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43m_read\u001b[49m\u001b[43m(\u001b[49m\u001b[43mfilepath_or_buffer\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mkwds\u001b[49m\u001b[43m)\u001b[49m\n", "File \u001b[0;32m/usr/local/lib/python3.9/dist-packages/pandas/io/parsers/readers.py:605\u001b[0m, in \u001b[0;36m_read\u001b[0;34m(filepath_or_buffer, kwds)\u001b[0m\n\u001b[1;32m 602\u001b[0m _validate_names(kwds\u001b[38;5;241m.\u001b[39mget(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mnames\u001b[39m\u001b[38;5;124m\"\u001b[39m, \u001b[38;5;28;01mNone\u001b[39;00m))\n\u001b[1;32m 604\u001b[0m \u001b[38;5;66;03m## Create the parser.\u001b[39;00m\n\u001b[0;32m--> 605\u001b[0m parser \u001b[38;5;241m=\u001b[39m \u001b[43mTextFileReader\u001b[49m\u001b[43m(\u001b[49m\u001b[43mfilepath_or_buffer\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mkwds\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m 607\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m chunksize \u001b[38;5;129;01mor\u001b[39;00m iterator:\n\u001b[1;32m 608\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m parser\n", "File \u001b[0;32m/usr/local/lib/python3.9/dist-packages/pandas/io/parsers/readers.py:1442\u001b[0m, in \u001b[0;36mTextFileReader.__init__\u001b[0;34m(self, f, engine, 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\u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mopener\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mopen\u001b[49m\u001b[43m(\u001b[49m\u001b[43murl\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mdata\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mtimeout\u001b[49m\u001b[43m)\u001b[49m\n", "File \u001b[0;32m/usr/lib/python3.9/urllib/request.py:523\u001b[0m, in \u001b[0;36mOpenerDirector.open\u001b[0;34m(self, fullurl, data, timeout)\u001b[0m\n\u001b[1;32m 521\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m processor \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mprocess_response\u001b[38;5;241m.\u001b[39mget(protocol, []):\n\u001b[1;32m 522\u001b[0m meth \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mgetattr\u001b[39m(processor, meth_name)\n\u001b[0;32m--> 523\u001b[0m response \u001b[38;5;241m=\u001b[39m \u001b[43mmeth\u001b[49m\u001b[43m(\u001b[49m\u001b[43mreq\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mresponse\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m 525\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m response\n", "File \u001b[0;32m/usr/lib/python3.9/urllib/request.py:632\u001b[0m, in \u001b[0;36mHTTPErrorProcessor.http_response\u001b[0;34m(self, request, response)\u001b[0m\n\u001b[1;32m 629\u001b[0m \u001b[38;5;66;03m## According to RFC 2616, \"2xx\" code indicates that the client's\u001b[39;00m\n\u001b[1;32m 630\u001b[0m \u001b[38;5;66;03m# request was successfully received, understood, and accepted.\u001b[39;00m\n\u001b[1;32m 631\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m (\u001b[38;5;241m200\u001b[39m \u001b[38;5;241m<\u001b[39m\u001b[38;5;241m=\u001b[39m code \u001b[38;5;241m<\u001b[39m \u001b[38;5;241m300\u001b[39m):\n\u001b[0;32m--> 632\u001b[0m response \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mparent\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43merror\u001b[49m\u001b[43m(\u001b[49m\n\u001b[1;32m 633\u001b[0m \u001b[43m \u001b[49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[38;5;124;43mhttp\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mrequest\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mresponse\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mcode\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mmsg\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mhdrs\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m 635\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m response\n", "File \u001b[0;32m/usr/lib/python3.9/urllib/request.py:555\u001b[0m, in \u001b[0;36mOpenerDirector.error\u001b[0;34m(self, proto, *args)\u001b[0m\n\u001b[1;32m 553\u001b[0m http_err \u001b[38;5;241m=\u001b[39m \u001b[38;5;241m0\u001b[39m\n\u001b[1;32m 554\u001b[0m args \u001b[38;5;241m=\u001b[39m (\u001b[38;5;28mdict\u001b[39m, proto, meth_name) \u001b[38;5;241m+\u001b[39m args\n\u001b[0;32m--> 555\u001b[0m result \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43m_call_chain\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43margs\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m 556\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m result:\n\u001b[1;32m 557\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m result\n", "File \u001b[0;32m/usr/lib/python3.9/urllib/request.py:494\u001b[0m, in \u001b[0;36mOpenerDirector._call_chain\u001b[0;34m(self, chain, kind, meth_name, *args)\u001b[0m\n\u001b[1;32m 492\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m handler \u001b[38;5;129;01min\u001b[39;00m handlers:\n\u001b[1;32m 493\u001b[0m func \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mgetattr\u001b[39m(handler, meth_name)\n\u001b[0;32m--> 494\u001b[0m result \u001b[38;5;241m=\u001b[39m \u001b[43mfunc\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43margs\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m 495\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m result \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m:\n\u001b[1;32m 496\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m result\n", "File \u001b[0;32m/usr/lib/python3.9/urllib/request.py:747\u001b[0m, in \u001b[0;36mHTTPRedirectHandler.http_error_302\u001b[0;34m(self, req, fp, code, msg, headers)\u001b[0m\n\u001b[1;32m 744\u001b[0m fp\u001b[38;5;241m.\u001b[39mread()\n\u001b[1;32m 745\u001b[0m fp\u001b[38;5;241m.\u001b[39mclose()\n\u001b[0;32m--> 747\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mparent\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mopen\u001b[49m\u001b[43m(\u001b[49m\u001b[43mnew\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mtimeout\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43mreq\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mtimeout\u001b[49m\u001b[43m)\u001b[49m\n", "File \u001b[0;32m/usr/lib/python3.9/urllib/request.py:523\u001b[0m, in \u001b[0;36mOpenerDirector.open\u001b[0;34m(self, fullurl, data, timeout)\u001b[0m\n\u001b[1;32m 521\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m processor \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mprocess_response\u001b[38;5;241m.\u001b[39mget(protocol, []):\n\u001b[1;32m 522\u001b[0m meth \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mgetattr\u001b[39m(processor, meth_name)\n\u001b[0;32m--> 523\u001b[0m response \u001b[38;5;241m=\u001b[39m \u001b[43mmeth\u001b[49m\u001b[43m(\u001b[49m\u001b[43mreq\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mresponse\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m 525\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m response\n", "File \u001b[0;32m/usr/lib/python3.9/urllib/request.py:632\u001b[0m, in \u001b[0;36mHTTPErrorProcessor.http_response\u001b[0;34m(self, request, response)\u001b[0m\n\u001b[1;32m 629\u001b[0m \u001b[38;5;66;03m## According to RFC 2616, \"2xx\" code indicates that the client's\u001b[39;00m\n\u001b[1;32m 630\u001b[0m \u001b[38;5;66;03m# request was successfully received, understood, and accepted.\u001b[39;00m\n\u001b[1;32m 631\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m (\u001b[38;5;241m200\u001b[39m \u001b[38;5;241m<\u001b[39m\u001b[38;5;241m=\u001b[39m code \u001b[38;5;241m<\u001b[39m \u001b[38;5;241m300\u001b[39m):\n\u001b[0;32m--> 632\u001b[0m response \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mparent\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43merror\u001b[49m\u001b[43m(\u001b[49m\n\u001b[1;32m 633\u001b[0m \u001b[43m \u001b[49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[38;5;124;43mhttp\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mrequest\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mresponse\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mcode\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mmsg\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mhdrs\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m 635\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m response\n", "File \u001b[0;32m/usr/lib/python3.9/urllib/request.py:561\u001b[0m, in \u001b[0;36mOpenerDirector.error\u001b[0;34m(self, proto, *args)\u001b[0m\n\u001b[1;32m 559\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m http_err:\n\u001b[1;32m 560\u001b[0m args \u001b[38;5;241m=\u001b[39m (\u001b[38;5;28mdict\u001b[39m, \u001b[38;5;124m'\u001b[39m\u001b[38;5;124mdefault\u001b[39m\u001b[38;5;124m'\u001b[39m, \u001b[38;5;124m'\u001b[39m\u001b[38;5;124mhttp_error_default\u001b[39m\u001b[38;5;124m'\u001b[39m) \u001b[38;5;241m+\u001b[39m orig_args\n\u001b[0;32m--> 561\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43m_call_chain\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43margs\u001b[49m\u001b[43m)\u001b[49m\n", "File \u001b[0;32m/usr/lib/python3.9/urllib/request.py:494\u001b[0m, in \u001b[0;36mOpenerDirector._call_chain\u001b[0;34m(self, chain, kind, meth_name, *args)\u001b[0m\n\u001b[1;32m 492\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m handler \u001b[38;5;129;01min\u001b[39;00m handlers:\n\u001b[1;32m 493\u001b[0m func \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mgetattr\u001b[39m(handler, meth_name)\n\u001b[0;32m--> 494\u001b[0m result \u001b[38;5;241m=\u001b[39m \u001b[43mfunc\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43margs\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m 495\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m result \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m:\n\u001b[1;32m 496\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m result\n", "File \u001b[0;32m/usr/lib/python3.9/urllib/request.py:641\u001b[0m, in \u001b[0;36mHTTPDefaultErrorHandler.http_error_default\u001b[0;34m(self, req, fp, code, msg, hdrs)\u001b[0m\n\u001b[1;32m 640\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mhttp_error_default\u001b[39m(\u001b[38;5;28mself\u001b[39m, req, fp, code, msg, hdrs):\n\u001b[0;32m--> 641\u001b[0m \u001b[38;5;28;01mraise\u001b[39;00m HTTPError(req\u001b[38;5;241m.\u001b[39mfull_url, code, msg, hdrs, fp)\n", "\u001b[0;31mHTTPError\u001b[0m: HTTP Error 404: Not Found" ] } ], "source": [ "df=pd.read_csv('https://docs.google.com/spreadsheets/d/e/2PACX-1vTu_XE2dAiTcjHTfbaVKt7xEl_GnNeF_VYFsIBi5uM-gqBlBRfNHso-X1z3lxV7IW2f9UYKmZkSOYv-/pub?output=csv')" ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [], "source": [ "df['Guess']=df.Guess.str.replace(',','').astype(int)" ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [], "source": [ "bins=range(0,1500,100)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "See solution: [gaussian_fit.ipynb](./gaussian_fit.ipynb)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "See fit exponential: https://github.com/restrepo/COVID-19" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [], "source": [ "import pandas as pd" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [], "source": [ "DataSource='https://raw.githubusercontent.com/CSSEGISandData/COVID-19/'\n", "DataFile='master/csse_covid_19_data/csse_covid_19_time_series/time_series_covid19_confirmed_global.csv'\n", "cva=pd.read_csv('{}{}'.format(DataSource,DataFile))\n", "cva=cva.reset_index(drop=True)\n", "#Special cases\n", "c='Hong Kong'\n", "try:\n", " cva.loc[cva[cva['Province/State']==c].index[0],'Country/Region']=c\n", "except IndexError:\n", " pass " ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [], "source": [ "def index_field(df,column,filter=None):\n", " '''\n", " WARNING: Nonumerical columns are dropped\n", " \n", " Parameters:\n", " ----------\n", " filter: list, default None\n", " Select only the columns in this list\n", " '''\n", " dff=df.copy()\n", " if filter:\n", " dff=df[[column]+list(filter)]\n", " return dff.groupby(column).sum()\n", "\n", "d=[ c for c in cva.columns if re.search(r'^[0-9]{1,2}\\/[0-9]{1,2}\\/[1920]{2}',c)]\n", "cv=index_field(cva,\"Country/Region\",filter=d)" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "PadKA9WIBsIC" }, "source": [ "## Random Numbers " ] }, { "cell_type": "code", "execution_count": 56, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "%pylab is deprecated, use %matplotlib inline and import the required libraries.\n", "Populating the interactive namespace from numpy and matplotlib\n" ] } ], "source": [ "%pylab inline" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "KGMlj58KBsIE" }, "source": [ "In nature it is not uncommon finding phenomena that are random intrinsic, this is why it becomes a necessity to produce random numbers in order to model such events. But, let us think about the operations that a computer can do, they are done following certain stablished rules, how then can be generated random numbers? \n", "\n", "This is achieved until certain point, it is only possible produce pseudo numbers, i.e, numbers obtained following some basic rules. At sequence of numbers apparently random but that are going to repeat after some period. \n", "\n", "Now, the most basic way to understand the generation of a pseudo-random number consists in following the next recurrence rule that produces integer random numbers\n", "\n", "$$\n", "r_{i+1} = (ar_i+b)\\%N \n", "$$\n", "\n", "$r_i$ is the seed, $a$ and $b$ and $N$ are coefficients chose. Notice that $\\%$ represents the module, then the numbers obtained are going to be smaller than N. \n", "\n", "Now, consider the case when $ a= 3 $, $b = 2$ and $N = 10$ and the initial seed $r_0 = 3$. The new seed is the number obtaine\n", "in the last step. " ] }, { "cell_type": "code", "execution_count": 57, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 34 }, "colab_type": "code", "id": "a6qr3z1FbG2p", "outputId": "c11035d2-0b9d-4caf-e420-75cb1f38f7d5" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "%pylab is deprecated, use %matplotlib inline and import the required libraries.\n", "Populating the interactive namespace from numpy and matplotlib\n" ] } ], "source": [ "%pylab inline" ] }, { "cell_type": "code", "execution_count": 66, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 70 }, "colab_type": "code", "id": "v3q8vZjWBsIF", "outputId": "f5a45bde-b239-466c-e55d-582d21fad69d" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0\n", "1\n", "2\n", "3\n", "4\n", "5\n", "6\n", "7\n", "8\n", "9\n", "10\n", "11\n", "12\n", "13\n", "14\n", "Random numbers produced using a = 3, b = 2 and N = 10\n", "\n", "[4. 4. 4. 4. 4. 4. 4. 4. 4. 4. 4. 4. 4. 4. 4.]\n" ] } ], "source": [ "import numpy as np\n", "## Randon number function \n", "def random_number(seed,a=4,b=1,N=9):\n", " return (a*seed + b)%N\n", "\n", "#Constant values \n", "a = 3\n", "b = 2\n", "N = 10\n", "#Amount of random numbers \n", "N_iter = 15\n", "rnumber = np.zeros(N_iter+1)\n", "#Initial seed\n", "rnumber[0] = 4\n", "#rnumber[0] = 10\n", "\n", "for i in range(N_iter): \n", " print(i)\n", " rnumber[i+1] = random_number(seed=rnumber[i],a=3,b=2,N=10)\n", "\n", "print (\"Random numbers produced using a = %d, b = %d and N = %d\\n\" % ( a,b,N )) \n", "print (rnumber[1:]) " ] }, { "cell_type": "code", "execution_count": 67, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([4., 4., 4., 4., 4., 4., 4., 4., 4., 4., 4., 4., 4., 4., 4., 4.])" ] }, "execution_count": 67, "metadata": {}, "output_type": "execute_result" } ], "source": [ "rnumber" ] }, { "cell_type": "code", "execution_count": 68, "metadata": {}, "outputs": [], "source": [ "x=[]\n", "x.append( random_number(seed=2,a=3,b=2,N=10) )" ] }, { "cell_type": "code", "execution_count": 69, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[8]" ] }, "execution_count": 69, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x" ] }, { "cell_type": "code", "execution_count": 70, "metadata": {}, "outputs": [], "source": [ "x.append( random_number(seed=x[0],a=3,b=2,N=10) )" ] }, { "cell_type": "code", "execution_count": 71, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[8, 6]" ] }, "execution_count": 71, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x" ] }, { "cell_type": "code", "execution_count": 72, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[8, 6, 0]" ] }, "execution_count": 72, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x.append( random_number(seed=x[1],a=3,b=2,N=10) )\n", "x" ] }, { "cell_type": "code", "execution_count": 73, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[8, 6, 0, 2]" ] }, "execution_count": 73, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x.append( random_number(seed=x[2],a=3,b=2,N=10) )\n", "x" ] }, { "cell_type": "code", "execution_count": 74, "metadata": { "colab": {}, "colab_type": "code", "id": "i2s6dGgYBsIO" }, "outputs": [], "source": [ "import random\n", "import numpy as np\n", "import time" ] }, { "cell_type": "code", "execution_count": 84, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 52 }, "colab_type": "code", "id": "wWjZspQ6ciEw", "outputId": "be3ef638-8b07-4308-a1ce-c8e3999437f2" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1666895594.8727255\n", "1666895596.8751295\n" ] } ], "source": [ "print( time.time() )\n", "time.sleep(2)\n", "print( time.time() )" ] }, { "cell_type": "code", "execution_count": 87, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "52.85691862843985" ] }, "execution_count": 87, "metadata": {}, "output_type": "execute_result" } ], "source": [ "t=time.time()\n", "t/3600/24/365 #s → h → dias → años" ] }, { "cell_type": "code", "execution_count": 82, "metadata": {}, "outputs": [], "source": [ "random.seed(666)" ] }, { "cell_type": "code", "execution_count": 88, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 34 }, "colab_type": "code", "id": "Vbi8kO6jBsIR", "outputId": "3338b846-2bb8-4aa9-c0f1-0d1b57a0c677" }, "outputs": [ { "data": { "text/plain": [ "0.9033231539802643" ] }, "execution_count": 88, "metadata": {}, "output_type": "execute_result" } ], "source": [ "random.random() #seed is unix time" ] }, { "cell_type": "code", "execution_count": 90, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 34 }, "colab_type": "code", "id": "_uiVBakGBsIa", "outputId": "feaee75d-b5b7-4d81-d249-ce68554d3869" }, "outputs": [ { "data": { "text/plain": [ "(0.6771981606438447, 0.7282646242796362, 0.12733022922307846)" ] }, "execution_count": 90, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x=random.seed(4890098)\n", "(random.random(),\n", "random.random(),\n", "random.random())" ] }, { "cell_type": "code", "execution_count": 93, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 34 }, "colab_type": "code", "id": "SZ_ZYW57BsIf", "outputId": "3bc40de6-b79b-4cb4-a4a6-af225ba9a772" }, "outputs": [ { "data": { "text/plain": [ "array([0.24322603, 0.97041503, 0.65472299, 0.94004507, 0.3412584 ])" ] }, "execution_count": 93, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.random.random(5)" ] }, { "cell_type": "code", "execution_count": 95, "metadata": { "colab": {}, "colab_type": "code", "id": "Iv-MXauLBsIh", "outputId": "61dbcf2a-f348-467b-c1ee-385fe147a856" }, "outputs": [ { "data": { "text/plain": [ "array([0.4359949 , 0.02592623, 0.54966248, 0.43532239, 0.4203678 ])" ] }, "execution_count": 95, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.random.seed(2)\n", "np.random.random(5)" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "n3n2naF6BsIm" }, "source": [ "Notice that after N random numbers produced the apparently random sequence starts repeating again, i.e., N is the period of the sequence. Then, it is necessary to take N as big as possible but without incuring in an overflow. What happens when the initial seed is changed? \n", "\n", "\n", "\n", "To generate random numbers can be used numpy library, specifically the set functions random. There is also another library\n", "used random, but it contains few functions comparing with numpy. \n", "To generate a random number between 0 and 1 initiallizing the seed with the actual time.\n", "\n" ] }, { "cell_type": "code", "execution_count": 96, "metadata": { "colab": {}, "colab_type": "code", "id": "flQIkBvaBsIn", "outputId": "7edc6414-c7e7-4391-fd9c-6a017a1a5a49" }, "outputs": [ { "data": { "text/plain": [ "0.09840819900262943" ] }, "execution_count": 96, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.random.seed()\n", "np.random.random()" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "PN1FfXYJBsIu" }, "source": [ "To generate a number between and a number A" ] }, { "cell_type": "code", "execution_count": 98, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 105 }, "colab_type": "code", "id": "YL8gnAbaBsIw", "outputId": "d9b70d59-4e35-4439-8525-fb74203c90d7" }, "outputs": [ { "data": { "text/plain": [ "array([[29.44100242, 80.18303874, 41.54074954, 47.428621 , 59.96446129],\n", " [88.96894761, 63.74695651, 3.30716668, 58.30336497, 52.97612528],\n", " [33.46185039, 98.57715046, 89.81785063, 71.37166278, 22.40593102],\n", " [44.35460793, 5.25429925, 47.19143365, 6.66930382, 82.06947756],\n", " [37.72730204, 90.61374564, 86.0463719 , 38.98453034, 44.1387734 ]])" ] }, "execution_count": 98, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A = 100.\n", "A*np.random.random((5,5))" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "AU0sykGKBsI0" }, "source": [ "To generate a random number between a range -B to B " ] }, { "cell_type": "code", "execution_count": 55, "metadata": { "colab": {}, "colab_type": "code", "id": "SDx8K9S3BsI1", "outputId": "7a46512e-70c8-4b0e-ac84-e038748797cc" }, "outputs": [ { "data": { "text/plain": [ "2.385238175287217" ] }, "execution_count": 55, "metadata": {}, "output_type": "execute_result" } ], "source": [ "B = 15\n", "B - 2*B*np.random.random()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The implementation in numpy is with:" ] }, { "cell_type": "code", "execution_count": 100, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 52 }, "colab_type": "code", "id": "AUL_MB2ABsI4", "outputId": "5d80f9be-df2a-4ebd-ff12-db5ac565669f" }, "outputs": [ { "data": { "text/plain": [ "array([[13.3778732 , 8.04570564],\n", " [-1.98608587, -3.11302379]])" ] }, "execution_count": 100, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.random.uniform(-15,15,(2,2))" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "HQQ3Srq-BsI7" }, "source": [ "### Example 2" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "Jnee7IWbBsI8" }, "source": [ "#### Random walk\n", "\n", "Start at the origin and take a 2D random walk. It is chosen values for $\\Delta x'$ and $\\Delta y'$ in the range [-1,1].\n", "They are normalized so each step is of unit length. " ] }, { "cell_type": "code", "execution_count": 101, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "-0.5980004387516238" ] }, "execution_count": 101, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.random.uniform(1,-1)" ] }, { "cell_type": "code", "execution_count": 107, "metadata": {}, "outputs": [], "source": [ "#Initial positions\n", "x0 = 0.\n", "y0 = 0.\n", "pos = [x0,y0]\n", "#Number of random steps\n", "N_steps = 1000\n", "#Number of random walks\n", "N_walks = 3\n", "\n", "\n", "def Random_walk(N, x0=0,y0=0):\n", " pos=[x0,y0]\n", " \n", " x = [x0] \n", " y = [y0] \n", "\n", " #Generating random positions\n", " for i in range(1,N):\n", " x.append( np.random.uniform(1,-1) + x[i-1] )\n", " y.append( np.random.uniform(1,-1) + y[i-1] )\n", " \n", " return x, y\n", " " ] }, { "cell_type": "code", "execution_count": 108, "metadata": {}, "outputs": [], "source": [ "x,y=Random_walk(500)" ] }, { "cell_type": "code", "execution_count": 109, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(x,y)\n", "plt.grid()" ] }, { "cell_type": "code", "execution_count": 111, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 111, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "colors = ('b', 'g', 'c', 'r', 'm', 'y', 'k')\n", "axisNum = 0\n", "plt.figure( figsize = (8,6) )\n", "\n", "N_walks=3\n", "#Plotting random walks\n", "for j,c in zip( range(N_walks),colors):\n", " \n", " axisNum += 1\n", " x,y= Random_walk( N_steps )\n", " #If N_walks > repeat the colors\n", " color = colors[axisNum % len(colors)] \n", " plt.plot(x,y,\"v-\", color = color, lw= 0.5, label = \"walk %d\"%(j+1))\n", " \n", "\n", "plt.title(\"Random walks\")\n", "plt.legend()" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "pq9z8GhHBsI_" }, "source": [ "### \n", "**Activity** \n" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "dbKRljv9BsI_" }, "source": [ " \n", "Radioactive decay: Spontaneous decay is a natural process in which a particle, with no external stimulation, decays into other\n", "particles. Then, the total amount of particles in a sample decreases with time, so will the number of decays. \n", "The probability decay is constant per particle and is given by \n", "\n", "$$\n", "P = -\\lambda \n", "$$\n", "\n", "Determin when radioactive decay looks like exponential decay and when it looks stochastic depending on the initial number of particles $N(t)$ .For this, suposse that the decay rate is 0.3$\\times 10^6 s^{-1}$ . Make a logarithmic plot to show the results. \n", "" ] }, { "cell_type": "code", "execution_count": 112, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 52 }, "colab_type": "code", "id": "rOWjJAmxehpS", "outputId": "34dc65ee-2f35-4bbf-a019-eb1ced1f9f4b" }, "outputs": [ { "data": { "text/plain": [ "array([[-11.81307268, -4.22920799],\n", " [ -4.73925943, 7.47052026]])" ] }, "execution_count": 112, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.random.uniform(-15,15,(2,2))" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "G-JVOfJoesR0" }, "source": [ "Espacio de parámetros aleatorios\n", "\n" ] }, { "cell_type": "code", "execution_count": 113, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 282 }, "colab_type": "code", "id": "ORIfK11NeiLs", "outputId": "d7ab9eaa-a6c5-4f91-aea6-9d3d98bede18" }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 113, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "N=10000\n", "plt.plot(np.random.random(N),np.random.random(N),'r.')" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "ER30yxPffEgT" }, "source": [ "Hasta dos ordenes de magnitud" ] }, { "cell_type": "code", "execution_count": 114, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 282 }, "colab_type": "code", "id": "8E2TZBbsfdaa", "outputId": "635f6983-41ec-46bf-c918-e033e7d467df" }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 114, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "N=10000\n", "plt.plot(np.random.uniform(1,100,N),np.random.uniform(1,100,N),'r.')" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "NmXuewclfqua" }, "source": [ "Varios ordenes de magnitud: $10^{-4}$ a $10^2$" ] }, { "cell_type": "code", "execution_count": 115, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 286 }, "colab_type": "code", "id": "H_UorYO2gBaB", "outputId": "c5d87a9c-66c7-42d1-df0e-f087242d7e3e" }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 115, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "N=10000\n", "plt.loglog(np.random.uniform(1E-4,1E2,N),np.random.uniform(1E-4,1E2,N),'r.')" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "N6a3V-o4ga_Y" }, "source": [ "$x=10^{\\log_{10}(x)}$" ] }, { "cell_type": "code", "execution_count": 116, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 34 }, "colab_type": "code", "id": "5iPEDPrigq3w", "outputId": "24fa32a9-8a52-4b2d-b754-31ab89821fef" }, "outputs": [ { "data": { "text/plain": [ "24.455999999999996" ] }, "execution_count": 116, "metadata": {}, "output_type": "execute_result" } ], "source": [ "10**np.log10(24.456)" ] }, { "cell_type": "code", "execution_count": 117, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 293 }, "colab_type": "code", "id": "fr5yrb0Hh_0e", "outputId": "852ee5cd-d002-44f1-fba8-cdd849592c3e" }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 117, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "N=10000\n", "xmin=3E-4;xmax=5E2\n", "ymin=xmin;ymax=xmax\n", "plt.loglog( 10**np.random.uniform(np.log10(xmin),np.log10(xmax),N),\n", " 10**np.random.uniform(np.log10(ymin),np.log10(ymax),N),'r.')" ] }, { "cell_type": "code", "execution_count": 158, "metadata": { "colab": {}, "colab_type": "code", "id": "2Ac2bisUg6oB" }, "outputs": [ { "data": { "text/plain": [ "27" ] }, "execution_count": 158, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.random.randint(1,100)" ] }, { "cell_type": "markdown", "metadata": { "colab": {}, "colab_type": "code", "id": "ZuBJozy-h4GW" }, "source": [ "## Appendix" ] }, { "cell_type": "code", "execution_count": 40, "metadata": { "colab": {}, "colab_type": "code", "id": "EO96JCsnBsHG" }, "outputs": [], "source": [ "## Finding adjusting parameters \n", "def Linear_least_square( x,y ):\n", " \n", " #Finding coefficients \n", " length = len(x)\n", " square_x = np.sum([x[i]**2 for i in xrange(length)])\n", " sum_xy = np.sum([x[i]*y[i] for i in xrange(length)])\n", " sum_x = np.sum(x)\n", " sum_y = np.sum(y)\n", " a0 = ( square_x*sum_y - sum_xy*sum_x ) / ( length*square_x - sum_x**2 )\n", " a1 = ( length*sum_xy - sum_x*sum_y ) / ( length*square_x - sum_x**2 )\n", " \n", " #Returning a_0 and a_1 coefficients\n", " return np.array([a0,a1])\n", "\n", "#Line function adjusting the data set\n", "def Line(a0,a1,x):\n", " return a0+a1*x\n" ] }, { "cell_type": "code", "execution_count": 42, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 359 }, "colab_type": "code", "id": "UcmtrbajBsHP", "outputId": "8fcab155-0de2-4a4e-dd29-8817a9eb935d" }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "xrange=range\n", "#========================================================\n", "## Adjusting to a first order polynomy the data set v \n", "#========================================================\n", "#Setting figure\n", "plt.figure( figsize = (8,5) )\n", "\n", "#Time\n", "t = np.array([ 0., 1.11, 2.22, 3.33, 4.44, 5.55])\n", "\n", "#Velocities measured for every time t[i]\n", "v = np.array([33.10, 21.33, 16.57, -5.04, -11.74, -27.32])\n", "\n", "#Making data adjust\n", "a0, a1 = Linear_least_square( t,v )\n", "\n", "#Finding error associated to linear approximation\n", "E = np.sum([ ( v[i] - Line(a0,a1,t[i]) )**2 for i in xrange(len(t))])\n", "\n", "#Plotting solution\n", "plt.plot( t, Line(a0,a1,t), \".-\", lw = 3.,color = \"green\",label=\"Lineal adjust\" )\n", "plt.plot( t, v, \".\",color = \"blue\", label = \"Data set\" )\n", "for i in xrange(len(t)):\n", " plt.plot(np.array([t[i],t[i]]), np.array([v[i],Line(a0,a1,t[i])]),\"c-\")\n", " \n", "#Format of figure\n", "plt.xlabel( \"$t(s)$\", fontsize = 18 )\n", "plt.ylabel( \"$v(m/s)$\", fontsize = 18 )\n", "plt.xlim( (t[0], t[-1]) )\n", "plt.ylim( (v[-1], v[0]) )\n", "plt.title(\"Linear data adjust with error %f\"%E)\n", "plt.legend()\n", "plt.grid(1)" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "6xROQHWYBsHV" }, "source": [ "### **Activity** \n", "http://scipy-cookbook.readthedocs.io/items/robust_regression.html" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "A8KY6k_lBsHa" }, "source": [ " \n", "Using the next data set of a spring mass system, find the lineal adjust. \n", "\n", "\n", "" ] } ], "metadata": { "colab": { "include_colab_link": true, "name": "statistics.ipynb", "provenance": [], "version": "0.3.2" }, "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": "3.9.2" } }, "nbformat": 4, "nbformat_minor": 4 }