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Forked from anonymous/Resistances.ipynb
Created January 15, 2016 15:24
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Example of correlated and uncorrelated systematics error, computed with pseudo-experiments (toys) or with analytical formula using numpy and sympy
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{
"cells": [
{
"metadata": {
"trusted": true,
"collapsed": false
},
"cell_type": "code",
"source": "import numpy as np\nfrom scipy import stats\nfrom IPython.html.widgets import interact\n%matplotlib inline\nfrom matplotlib import pyplot as plt",
"execution_count": 113,
"outputs": []
},
{
"metadata": {
"trusted": true,
"collapsed": true
},
"cell_type": "code",
"source": "def sum_series(x):\n return np.sum(x, axis=1)\n\ndef sum_parallel(x):\n return 1. / np.sum(1. / x, axis=1)",
"execution_count": 2,
"outputs": []
},
{
"metadata": {
"trusted": true,
"collapsed": false
},
"cell_type": "code",
"source": "def run_toy(NTOYS=100000, correlated=True, mean=(10., 20., 30.), rel_stat=(0., 0., 0.), rel_sys=(0.05, 0.05, 0.01)):\n R_EXP = R1_EXP, R2_EXP, R3_EXP = np.array(mean)\n R_SYS = R1_SYS, R2_SYS, R3_SYS = rel_sys * R_EXP\n R_STAT = R1_STAT, R2_STAT, R3_STAT = rel_stat * R_EXP\n R_ERR = R1_ERR, R2_ERR, R3_ERR = np.hypot(R_SYS, R_STAT)\n\n print \"expected R = \", R_EXP\n print \"sys = \", R_SYS\n print \"stat = \", R_STAT\n \n print \"computing...\",\n\n if correlated:\n pull_sys = stats.norm(0, 1).rvs(NTOYS) # generate all the values for all the toys\n else:\n pull_sys = stats.norm(0, 1).rvs((3, NTOYS))\n bias_sys = np.array(R_SYS)[:, np.newaxis] * pull_sys\n pull_stat = stats.norm(0, 1).rvs((3, NTOYS))\n bias_stat = np.array(R_STAT)[:, np.newaxis] * pull_stat\n R = R_EXP + bias_sys.T + bias_stat.T\n Requiv = sum_parallel(R)\n print \"done\"\n\n fig, axs = plt.subplots(2, 2, figsize=(10, 7))\n\n lineObjects = axs[0][0].plot(R, label=['R1', 'R2', 'R3'])\n lineEquiv = axs[0][0].plot(Requiv)\n axs[0][0].legend(lineObjects + lineEquiv, ['R1', 'R2', 'R2', 'Requiv'])\n axs[0][0].set_xlabel('#toy (first 100)')\n axs[0][0].set_xlim(0, 100)\n axs[0][1].hist(Requiv, bins=100, histtype='stepfilled')\n axs[0][1].set_xlabel('Requiv')\n\n axs[1][0].hist2d(R[:,0], R[:,1], bins=(np.linspace(R1_EXP * 0.7, R1_EXP * 1.3, 100),\n np.linspace(R2_EXP * 0.7 , R2_EXP * 1.3, 100)))\n axs[1][1].hist2d(R[:,1], R[:,2], bins=(np.linspace(R2_EXP * 0.7 , R2_EXP * 1.3, 100),\n np.linspace(R3_EXP * 0.7 , R3_EXP * 1.3, 100)))\n axs[1][0].set_xlabel('R1'); axs[1][0].set_ylabel('R2');\n axs[1][1].set_xlabel('R2'); axs[1][1].set_ylabel('R3');\n plt.plot()\n print \"<Requiv> = %.3f std(Requiv) = %.3f\" % (np.mean(Requiv), np.std(Requiv))\n print \"correlation matrix = \\n\", np.corrcoef(R.T)\n print \"covariance matrix = \\n\", np.cov(R.T)",
"execution_count": 136,
"outputs": []
},
{
"metadata": {},
"cell_type": "markdown",
"source": "## Only statistical error"
},
{
"metadata": {
"trusted": true,
"collapsed": false
},
"cell_type": "code",
"source": "run_toy(correlated=False, rel_stat=(0.01, 0.01, 0.01), rel_sys=(0.00, 0.00, 0.00))",
"execution_count": 137,
"outputs": [
{
"output_type": "stream",
"text": "expected R = [ 10. 20. 30.]\nsys = [ 0. 0. 0.]\nstat = [ 0.1 0.2 0.3]\ncomputing... done\n<Requiv> = 5.454 std(Requiv) = 0.035\ncorrelation matrix = \n[[ 1.00000000e+00 4.83160504e-04 2.28157571e-03]\n [ 4.83160504e-04 1.00000000e+00 -4.78593152e-03]\n [ 2.28157571e-03 -4.78593152e-03 1.00000000e+00]]\ncovariance matrix = \n[[ 9.97737447e-03 9.65634452e-06 6.82687340e-05]\n [ 9.65634452e-06 4.00337599e-02 -2.86852407e-04]\n [ 6.82687340e-05 -2.86852407e-04 8.97341301e-02]]\n",
"name": "stdout"
},
{
"output_type": "display_data",
"data": {
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GjBjBgAEDSmM3z5kxJhCbkE0SkfxfIRw2xtRyza8NJLrKDwCFf+lQD9tCdsA1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\nmZmZmVkJ/H/P0b0DHrE/ZgAAAABJRU5ErkJggg==\n",
"text/plain": "<matplotlib.figure.Figure at 0x7141590>"
},
"metadata": {}
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "## No statistical error, fully correlated"
},
{
"metadata": {
"trusted": true,
"collapsed": false
},
"cell_type": "code",
"source": "run_toy(correlated=True, rel_stat=(0., 0., 0.), rel_sys=(0.05, 0.05, 0.01))",
"execution_count": 138,
"outputs": [
{
"output_type": "stream",
"text": "expected R = [ 10. 20. 30.]\nsys = [ 0.5 1. 0.3]\nstat = [ 0. 0. 0.]\ncomputing... done\n<Requiv> = 5.454 std(Requiv) = 0.233\ncorrelation matrix = \n[[ 1. 1. 1.]\n [ 1. 1. 1.]\n [ 1. 1. 1.]]\ncovariance matrix = \n[[ 0.25024736 0.50049471 0.15014841]\n [ 0.50049471 1.00098943 0.30029683]\n [ 0.15014841 0.30029683 0.09008905]]\n",
"name": "stdout"
},
{
"output_type": "display_data",
"data": {
"image/png": 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EeToKEektIo1EpLGIdBGRY07bfCgitUWknogsdCrfKCINHcte9s4RKaXyA48l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\nYWYLovm7ndMjIiIi0tZlcoiKWuBqd58VjbMy3cxeJjG+yunAIe5eG50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yo9sNQVOIiIhI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\nRK5CYII=\n",
"text/plain": "<matplotlib.figure.Figure at 0x5fd1910>"
},
"metadata": {}
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "## No statistical error, fully uncorrelated"
},
{
"metadata": {
"trusted": true,
"collapsed": false
},
"cell_type": "code",
"source": "run_toy(correlated=False, rel_stat=(0., 0., 0.), rel_sys=(0.05, 0.05, 0.01))",
"execution_count": 139,
"outputs": [
{
"output_type": "stream",
"text": "expected R = [ 10. 20. 30.]\nsys = [ 0.5 1. 0.3]\nstat = [ 0. 0. 0.]\ncomputing... done\n<Requiv> = 5.448 std(Requiv) = 0.167\ncorrelation matrix = \n[[ 1. 0.00212718 -0.00101359]\n [ 0.00212718 1. -0.0057157 ]\n [-0.00101359 -0.0057157 1. ]]\ncovariance matrix = \n[[ 2.49078104e-01 1.05849509e-03 -1.52143015e-04]\n [ 1.05849509e-03 9.94109366e-01 -1.71398845e-03]\n [ -1.52143015e-04 -1.71398845e-03 9.04571845e-02]]\n",
"name": "stdout"
},
{
"output_type": "display_data",
"data": {
"image/png": 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OLEm3jogwd/dc3uv4HkfOHyHySvb/SJ+6dOraldKx4a8Nqdb/YssXjFk75gaj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\nzCwTN2JmZmZmmbgRMzMzM8vkbyqY1jGOdoM0AAAAAElFTkSuQmCC\n",
"text/plain": "<matplotlib.figure.Figure at 0x60a9d10>"
},
"metadata": {}
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "## Statistical error, fully correlated"
},
{
"metadata": {
"trusted": true,
"collapsed": false
},
"cell_type": "code",
"source": "run_toy(correlated=True, rel_stat=(0.01, 0.01, 0.01), rel_sys=(0.05, 0.05, 0.01))",
"execution_count": 140,
"outputs": [
{
"output_type": "stream",
"text": "expected R = [ 10. 20. 30.]\nsys = [ 0.5 1. 0.3]\nstat = [ 0.1 0.2 0.3]\ncomputing... done\n<Requiv> = 5.454 std(Requiv) = 0.236\ncorrelation matrix = \n[[ 1. 0.96160301 0.69409841]\n [ 0.96160301 1. 0.69376689]\n [ 0.69409841 0.69376689 1. ]]\ncovariance matrix = \n[[ 0.25988967 0.4992609 0.14975802]\n [ 0.4992609 1.03722854 0.29903727]\n [ 0.14975802 0.29903727 0.17912204]]\n",
"name": "stdout"
},
{
"output_type": "display_data",
"data": {
"image/png": 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US5LbkjAROSIim1J+jwZ2AFWBjsDklMUmA50vtK2GwZkH54cdDcO/hD9Tt0wl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\n",
"text/plain": "<matplotlib.figure.Figure at 0x4336650>"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true,
"collapsed": false
},
"cell_type": "code",
"source": "import sympy\nsympy.init_printing(use_latex=True, use_unicode=True)",
"execution_count": 141,
"outputs": []
},
{
"metadata": {
"trusted": true,
"collapsed": false
},
"cell_type": "code",
"source": "# define the variables\nR1 = sympy.var('R1')\nR2 = sympy.var('R2')\nR3 = sympy.var('R3')\n\n# compute the jacobian of R_equiv(R1, R2, R3) analytically\n\nR = sympy.Matrix((R1, R2, R3))\nf = 1 / (1 / R1 + 1 / R2 + 1 / R3)\nF = sympy.Matrix([f])\nJ = sympy.simplify(F.jacobian(R))",
"execution_count": 142,
"outputs": []
},
{
"metadata": {
"trusted": true,
"collapsed": false
},
"cell_type": "code",
"source": "sympy.pprint(J)",
"execution_count": 143,
"outputs": [
{
"output_type": "stream",
"text": "⎡ 2 2 2 2 2 2 ⎤\n⎢ R₂ ⋅R₃ R₁ ⋅R₃ R₁ ⋅R₂ ⎥\n⎢──────────────────────── ──────────────────────── ────────────────────────⎥\n⎢ 2 2 2⎥\n⎣(R₁⋅R₂ + R₁⋅R₃ + R₂⋅R₃) (R₁⋅R₂ + R₁⋅R₃ + R₂⋅R₃) (R₁⋅R₂ + R₁⋅R₃ + R₂⋅R₃) ⎦\n",
"name": "stdout"
}
]
},
{
"metadata": {
"trusted": true,
"collapsed": false
},
"cell_type": "code",
"source": "R1_exp, R2_exp, R3_exp = np.array(run_toy.func_defaults[2]) # take the value from the function\n\n# substitute numerical values\nJ = J.subs({'R1': R1_exp, 'R2': R2_exp, 'R3': R3_exp})\nJ = np.matrix((J[0], J[1], J[2]), dtype=float)\nprint J",
"execution_count": 144,
"outputs": [
{
"output_type": "stream",
"text": "[[ 0.29752066 0.07438017 0.03305785]]\n",
"name": "stdout"
}
]
},
{
"metadata": {
"trusted": true,
"collapsed": false
},
"cell_type": "code",
"source": "rel_stat = np.array((0.01, 0.01, 0.01))\nrel_sys = np.array((0.05, 0.05, 0.01))\nerr_stat = rel_stat * (R1_exp, R2_exp, R3_exp)\nerr_sys = rel_sys * (R1_exp, R2_exp, R3_exp)\n\n# define correlation for the systematics part for the fully correlated case\ncorr_sys = np.array([[1,1,1],[1,1,1],[1,1,1]])\n# compute the covariance as cov(i,j) = outer(error, error)(i, j) * corr(i, j) = (error(i) * error(j)) * corr(i, j)\ncov_sys = np.outer(err_sys, err_sys) * corr_sys\n# define covariance for the statistical part\ncov_stat = np.diag(err_stat ** 2)\n# define the full covariance matrix\ncov = np.matrix(cov_stat + cov_sys)\ncorr = cov / np.outer(np.sqrt(np.diag(cov)), np.sqrt(np.diag(cov)))",
"execution_count": 145,
"outputs": []
},
{
"metadata": {
"trusted": true,
"collapsed": false
},
"cell_type": "code",
"source": "# print full covariance and correlation matrix\nprint cov\nprint\nprint corr",
"execution_count": 146,
"outputs": [
{
"output_type": "stream",
"text": "[[ 0.26 0.5 0.15]\n [ 0.5 1.04 0.3 ]\n [ 0.15 0.3 0.18]]\n\n[[ 1. 0.96153846 0.69337525]\n [ 0.96153846 1. 0.69337525]\n [ 0.69337525 0.69337525 1. ]]\n",
"name": "stdout"
}
]
},
{
"metadata": {
"hide_input": false,
"trusted": true,
"collapsed": false
},
"cell_type": "code",
"source": "error = float(np.sqrt(J * cov * J.T))\nerror_stat = float(np.sqrt(J * cov_stat * J.T))\nerror_sys = float(np.sqrt(J * cov_sys * J.T))\nprint \"error = %.2f\" % error\nprint \"stat-error = %.2f\" % error_stat\nprint \"sys-error = %.2f\" % error_sys",
"execution_count": 147,
"outputs": [
{
"output_type": "stream",
"text": "error = 0.24\nstat-error = 0.03\nsys-error = 0.23\n",
"name": "stdout"
}
]
}
],
"metadata": {
"kernelspec": {
"name": "python2",
"display_name": "Python 2",
"language": "python"
},
"hide_input": false,
"latex_envs": {
"eqNumInitial": 0,
"eqLabelWithNumbers": true,
"current_citInitial": 1,
"cite_by": "apalike",
"bibliofile": "biblio.bib"
},
"language_info": {
"mimetype": "text/x-python",
"nbconvert_exporter": "python",
"name": "python",
"pygments_lexer": "ipython2",
"version": "2.7.5",
"file_extension": ".py",
"codemirror_mode": {
"version": 2,
"name": "ipython"
}
},
"gist": {
"id": "",
"data": {
"description": "Example of correlated and uncorrelated systematics error, computed with pseudo-experiments (toys) or with analytical formula using numpy and sympy",
"public": true
}
}
},
"nbformat": 4,
"nbformat_minor": 0
}
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