{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# IMinuit\n", "\n", "Minuit - программа численной минимизации функций многих переменных, широко применяемая в физике элементарных частиц. Есть два питонских интерфейса, PyMinuit и IMinuit (он особенно удобен в ipython)." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Populating the interactive namespace from numpy and matplotlib\n" ] } ], "source": [ "from iminuit import Minuit\n", "%pylab inline" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Простой пример\n", "\n", "Определим квадратичную функцию от двух параметров." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def f(a,b):\n", " return 10*a**2+10*b**2-16*a*b+12*a-24*b" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Создадим объект класса `Minuit`. `a` и `b` - грубые догадки, около чего надо искать минимум; `error_a` и `error_b` - оценки точности этих догадок (в начале минимизации программа будет делать шаги порядка этих величин, потом они будут уменьшаться). Пределы изменения задавать не обязательно. Валичина `errordef` показывает, насколько функция должна быть выше своего минимума, чтобы это считалось отклонением на одну сигму; поскольку минимизируемая функция - это, как правило, $\\chi^2$, значение 1 по умолчанию вполне годится." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/usr/lib64/python3.4/site-packages/ipykernel/__main__.py:2: InitialParamWarning: errordef is not given. Default to 1.\n", " from ipykernel import kernelapp as app\n" ] } ], "source": [ "m=Minuit(f,a=0,error_a=1,limit_a=(-10,10),\n", " b=0,error_b=1,limit_b=(-10,10))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Наиболее популярный метод минимизации - `migrad`." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "
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FCN = -17.999997281186666TOTAL NCALL = 36NCALLS = 36
EDM = 2.7187527367825896e-06GOAL EDM = 1e-05\n", " UP = 1.0
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ValidValid ParamAccurate CovarPosDefMade PosDef
TrueTrueTrueTrueFalse
Hesse FailHasCovAbove EDMReach calllim
FalseTrueFalseFalse
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+NameValueParab ErrorMinos Error-Minos Error+Limit-Limit+FIXED
1a0.9998230.52678800-10.010.0
2b1.999350.52677600-10.010.0
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" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "({'fval': -17.999997281186666, 'up': 1.0, 'is_above_max_edm': False, 'has_valid_parameters': True, 'edm': 2.7187527367825896e-06, 'has_made_posdef_covar': False, 'has_covariance': True, 'has_posdef_covar': True, 'nfcn': 36, 'has_accurate_covar': True, 'hesse_failed': False, 'is_valid': True, 'has_reached_call_limit': False},\n", " [{'is_const': False, 'number': 0, 'upper_limit': 10.0, 'lower_limit': -10.0, 'name': 'a', 'is_fixed': False, 'error': 0.5267876810263843, 'value': 0.9998227792225478, 'has_upper_limit': True, 'has_limits': True, 'has_lower_limit': True},\n", " {'is_const': False, 'number': 1, 'upper_limit': 10.0, 'lower_limit': -10.0, 'name': 'b', 'is_fixed': False, 'error': 0.5267762744877214, 'value': 1.9993477581584944, 'has_upper_limit': True, 'has_limits': True, 'has_lower_limit': True}])" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "m.migrad()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Значения параметров." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "{'a': 0.9998227792225478, 'b': 1.9993477581584944}" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "m.values" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Значение функции в точке минимума." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "-17.999997281186666" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "m.fval" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Ошибки параметров." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "{'a': 0.5267876810263843, 'b': 0.5267762744877214}" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "m.errors" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Если, скажем, `a` - наш окончательный физический результат, то мы напишем в статье $a=1\\pm0.5$. На самом деле у нас есть больше информации, поскольку ошибки `a` и `b` сильно скоррелированы. Матрица корреляции ошибок:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "((0.27776493841711364, 0.22220727646667665),\n", " (0.22220727646667665, 0.27776101882046583))" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "m.matrix()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Минимизация квадратичной формы сводится к решению системы линейных уравнений, а матрица корреляции ошибок - обратная матрица этой системы. В таком простом случае не имеет смысла использовать инструмент минимизации произвольных функций, такой, как Minuit." ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([[ 0.27777778, 0.22222222],\n", " [ 0.22222222, 0.27777778]])" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "M=array([[10.,-8.],[-8.,10.]])\n", "M=inv(M)\n", "M" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([[ 1.],\n", " [ 2.]])" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "M.dot(array([[-6],[12]]))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Нарисуем контуры, соответствующие отклонению на 1, 2 и 3 сигмы от оптимальной точки." ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "(array([-1.03835166, -0.997266 , -0.95618035, -0.9150947 , -0.87400905,\n", " -0.8329234 , -0.79183775, -0.7507521 , -0.70966645, -0.6685808 ,\n", " -0.62749514, -0.58640949, -0.54532384, -0.50423819, -0.46315254,\n", " -0.42206689, -0.38098124, -0.33989559, -0.29880994, -0.25772428,\n", " -0.21663863, -0.17555298, -0.13446733, -0.09338168, -0.05229603,\n", " -0.01121038, 0.02987527, 0.07096092, 0.11204657, 0.15313223,\n", " 0.19421788, 0.23530353, 0.27638918, 0.31747483, 0.35856048,\n", " 0.39964613, 0.44073178, 0.48181743, 0.52290309, 0.56398874,\n", " 0.60507439, 0.64616004, 0.68724569, 0.72833134, 0.76941699,\n", " 0.81050264, 0.85158829, 0.89267395, 0.9337596 , 0.97484525,\n", " 1.0159309 , 1.05701655, 1.0981022 , 1.13918785, 1.1802735 ,\n", " 1.22135915, 1.26244481, 1.30353046, 1.34461611, 1.38570176,\n", " 1.42678741, 1.46787306, 1.50895871, 1.55004436, 1.59113001,\n", " 1.63221567, 1.67330132, 1.71438697, 1.75547262, 1.79655827,\n", " 1.83764392, 1.87872957, 1.91981522, 1.96090087, 2.00198652,\n", " 2.04307218, 2.08415783, 2.12524348, 2.16632913, 2.20741478,\n", " 2.24850043, 2.28958608, 2.33067173, 2.37175738, 2.41284304,\n", " 2.45392869, 2.49501434, 2.53609999, 2.57718564, 2.61827129,\n", " 2.65935694, 2.70044259, 2.74152824, 2.7826139 , 2.82369955,\n", " 2.8647852 , 2.90587085, 2.9469565 , 2.98804215, 3.0291278 ]),\n", " array([ -3.83516801e-02, 2.73397445e-03, 4.38196290e-02,\n", " 8.49052835e-02, 1.25990938e-01, 1.67076592e-01,\n", " 2.08162247e-01, 2.49247901e-01, 2.90333556e-01,\n", " 3.31419210e-01, 3.72504865e-01, 4.13590519e-01,\n", " 4.54676174e-01, 4.95761828e-01, 5.36847483e-01,\n", " 5.77933138e-01, 6.19018792e-01, 6.60104447e-01,\n", " 7.01190101e-01, 7.42275756e-01, 7.83361410e-01,\n", " 8.24447065e-01, 8.65532719e-01, 9.06618374e-01,\n", " 9.47704028e-01, 9.88789683e-01, 1.02987534e+00,\n", " 1.07096099e+00, 1.11204665e+00, 1.15313230e+00,\n", " 1.19421796e+00, 1.23530361e+00, 1.27638926e+00,\n", " 1.31747492e+00, 1.35856057e+00, 1.39964623e+00,\n", " 1.44073188e+00, 1.48181754e+00, 1.52290319e+00,\n", " 1.56398885e+00, 1.60507450e+00, 1.64616015e+00,\n", " 1.68724581e+00, 1.72833146e+00, 1.76941712e+00,\n", " 1.81050277e+00, 1.85158843e+00, 1.89267408e+00,\n", " 1.93375974e+00, 1.97484539e+00, 2.01593105e+00,\n", " 2.05701670e+00, 2.09810235e+00, 2.13918801e+00,\n", " 2.18027366e+00, 2.22135932e+00, 2.26244497e+00,\n", " 2.30353063e+00, 2.34461628e+00, 2.38570194e+00,\n", " 2.42678759e+00, 2.46787324e+00, 2.50895890e+00,\n", " 2.55004455e+00, 2.59113021e+00, 2.63221586e+00,\n", " 2.67330152e+00, 2.71438717e+00, 2.75547283e+00,\n", " 2.79655848e+00, 2.83764414e+00, 2.87872979e+00,\n", " 2.91981544e+00, 2.96090110e+00, 3.00198675e+00,\n", " 3.04307241e+00, 3.08415806e+00, 3.12524372e+00,\n", " 3.16632937e+00, 3.20741503e+00, 3.24850068e+00,\n", " 3.28958633e+00, 3.33067199e+00, 3.37175764e+00,\n", " 3.41284330e+00, 3.45392895e+00, 3.49501461e+00,\n", " 3.53610026e+00, 3.57718592e+00, 3.61827157e+00,\n", " 3.65935723e+00, 3.70044288e+00, 3.74152853e+00,\n", " 3.78261419e+00, 3.82369984e+00, 3.86478550e+00,\n", " 3.90587115e+00, 3.94695681e+00, 3.98804246e+00,\n", " 4.02912812e+00]),\n", " masked_array(data =\n", " [[-- -- -- ..., -- -- --]\n", " [-- -- -- ..., -- -- --]\n", " [-- -- -- ..., -- -- --]\n", " ..., \n", " [-- -- -- ..., -- -- --]\n", " [-- -- -- ..., -- -- --]\n", " [-- -- -- ..., -- -- --]],\n", " mask =\n", " [[ True True True ..., True True True]\n", " [ True True True ..., True True True]\n", " [ True True True ..., True True True]\n", " ..., \n", " [ True True True ..., True True True]\n", " [ True True True ..., True True True]\n", " [ True True True ..., True True True]],\n", " fill_value = 1e+20),\n", " )" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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Bhw4jRs4RTj7y4Ug9k07FXL58lyFDNlGxYjHCwiZQpkzuPUFwxYrTrFx5hqCg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\nzdrevSlcpgy9fv1V1UsOMsn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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "m.draw_mncontour('a','b',nsigma=3)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "То же в виде цветов." ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "a,b,g,r=m.mncontour_grid('a','b',nsigma=3)\n", "pcolormesh(a,b,g)\n", "colorbar()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Дайте мне 3 параметра, и я профитирую слона. С 4 параметрами он будет махать хоботом.\n", "\n", "Пусть у нас есть экспериментальные данные, и мы хотим профитировать их прямой." ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def fit(a,b,x):\n", " return a*x+b" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Данные не настоящие, а сгенерированные. Все имеют ошибки 0.1." ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": true }, "outputs": [], "source": [ "x=linspace(0,1,11)\n", "dy=0.1*ones(11)\n", "y=x+dy*normal(size=11)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Функция $\\chi^2$." ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def chi2(a,b):\n", " global x,y,dy\n", " return (((y-fit(a,b,x))/dy)**2).sum()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Минимизируем." ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/usr/lib64/python3.4/site-packages/ipykernel/__main__.py:1: InitialParamWarning: errordef is not given. Default to 1.\n", " if __name__ == '__main__':\n" ] } ], "source": [ "m=Minuit(chi2,a=0,b=0,error_a=1,error_b=1)" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "
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FCN = 7.341081582910074TOTAL NCALL = 32NCALLS = 32
EDM = 6.20027421166483e-24GOAL EDM = 1e-05\n", " UP = 1.0
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"m.migrad()" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "{'a': 0.9529192501482413, 'b': -0.0578365609047049}" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "m.values" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "7.341081582910074" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "m.fval" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "((0.009090909052849335, -0.004545454524510073),\n", " (-0.004545454524510073, 0.003181818170392941))" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "m.matrix()" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "(array([ 0.58416759, 0.59160027, 0.59903294, 0.60646562, 0.61389829,\n", " 0.62133097, 0.62876364, 0.63619631, 0.64362899, 0.65106166,\n", " 0.65849434, 0.66592701, 0.67335969, 0.68079236, 0.68822503,\n", " 0.69565771, 0.70309038, 0.71052306, 0.71795573, 0.7253884 ,\n", " 0.73282108, 0.74025375, 0.74768643, 0.7551191 , 0.76255178,\n", " 0.76998445, 0.77741712, 0.7848498 , 0.79228247, 0.79971515,\n", " 0.80714782, 0.8145805 , 0.82201317, 0.82944584, 0.83687852,\n", " 0.84431119, 0.85174387, 0.85917654, 0.86660922, 0.87404189,\n", " 0.88147456, 0.88890724, 0.89633991, 0.90377259, 0.91120526,\n", " 0.91863794, 0.92607061, 0.93350328, 0.94093596, 0.94836863,\n", " 0.95580131, 0.96323398, 0.97066666, 0.97809933, 0.985532 ,\n", " 0.99296468, 1.00039735, 1.00783003, 1.0152627 , 1.02269538,\n", " 1.03012805, 1.03756072, 1.0449934 , 1.05242607, 1.05985875,\n", " 1.06729142, 1.0747241 , 1.08215677, 1.08958944, 1.09702212,\n", " 1.10445479, 1.11188747, 1.11932014, 1.12675282, 1.13418549,\n", " 1.14161816, 1.14905084, 1.15648351, 1.16391619, 1.17134886,\n", " 1.17878154, 1.18621421, 1.19364688, 1.20107956, 1.20851223,\n", " 1.21594491, 1.22337758, 1.23081026, 1.23824293, 1.2456756 ,\n", " 1.25310828, 1.26054095, 1.26797363, 1.2754063 , 1.28283898,\n", " 1.29027165, 1.29770432, 1.305137 , 1.31256967, 1.32000235]),\n", " array([-0.27599298, -0.27159575, -0.26719852, -0.26280129, -0.25840407,\n", " -0.25400684, -0.24960961, -0.24521238, -0.24081515, -0.23641792,\n", " -0.23202069, -0.22762346, -0.22322623, -0.218829 , -0.21443177,\n", " -0.21003454, -0.20563731, -0.20124008, -0.19684285, -0.19244562,\n", " -0.18804839, -0.18365117, -0.17925394, -0.17485671, -0.17045948,\n", " -0.16606225, -0.16166502, -0.15726779, -0.15287056, -0.14847333,\n", " -0.1440761 , -0.13967887, -0.13528164, -0.13088441, -0.12648718,\n", " -0.12208995, -0.11769272, -0.11329549, -0.10889827, -0.10450104,\n", " -0.10010381, -0.09570658, -0.09130935, -0.08691212, -0.08251489,\n", " -0.07811766, -0.07372043, -0.0693232 , -0.06492597, -0.06052874,\n", " -0.05613151, -0.05173428, -0.04733705, -0.04293982, -0.0385426 ,\n", " -0.03414537, -0.02974814, -0.02535091, -0.02095368, -0.01655645,\n", " -0.01215922, -0.00776199, -0.00336476, 0.00103247, 0.0054297 ,\n", " 0.00982693, 0.01422416, 0.01862139, 0.02301862, 0.02741585,\n", " 0.03181308, 0.0362103 , 0.04060753, 0.04500476, 0.04940199,\n", " 0.05379922, 0.05819645, 0.06259368, 0.06699091, 0.07138814,\n", " 0.07578537, 0.0801826 , 0.08457983, 0.08897706, 0.09337429,\n", " 0.09777152, 0.10216875, 0.10656598, 0.1109632 , 0.11536043,\n", " 0.11975766, 0.12415489, 0.12855212, 0.13294935, 0.13734658,\n", " 0.14174381, 0.14614104, 0.15053827, 0.1549355 , 0.15933273]),\n", " masked_array(data =\n", " [[-- -- -- ..., -- -- --]\n", " [-- -- -- ..., -- -- --]\n", " [-- -- -- ..., -- -- --]\n", " ..., \n", " [-- -- -- ..., -- -- --]\n", " [-- -- -- ..., -- -- --]\n", " [-- -- -- ..., -- -- --]],\n", " mask =\n", " [[ True True True ..., True True True]\n", " [ True True True ..., True True True]\n", " [ True True True ..., True True True]\n", " ..., \n", " [ True True True ..., True True True]\n", " [ True True True ..., True True True]\n", " [ True True True ..., True True True]],\n", " fill_value = 1e+20),\n", " )" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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IT8/7mLu+ODvbsGvXYPz83GndejH//e9hNJpXn0R+HgccSCCBDDLYwTYe8IAq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\n5JdfGHXiBObFC9e8jiwQklQIZD14QMi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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "m.draw_mncontour('a','b',nsigma=3)" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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IrqCel+c2rSLEtFCcP3QTK+ZERR8YdRe4+wmHfS/Z2PER72sPcwTIyXnemMng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\nYRjGYuJ90cjLvC/ArsA8ZsP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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "a,b,g,r=m.mncontour_grid('a','b',nsigma=3)\n", "pcolormesh(a,b,g)\n", "colorbar()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Нарисуем на одном графике экспериментальные точки, наш фит (сплошная линия) и истинную теоретическую кривую (пунктир)." ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "errorbar(x,y,dy,fmt='ro')\n", "xt=linspace(0,1,101)\n", "plot(xt,fit(m.values['a'],m.values['b'],xt),'b-')\n", "plot(xt,fit(1,0,xt),'g--')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Когда фитирующая функция есть линейная комбинация каких-то фиксированных функций с неизвестными коэффициентами, минимизация $\\chi^2$ сводится к решению системы линейных уравнений. Нет надобности использовать Minuit.\n", "\n", "## Резонанс без фона\n", "\n", "Пусть теперь наша фитирующая функция - Брейт-Вигнеровский резонанс (без фона), с двумя параметрами - положением и шириной (лучше бы ввести третий - высоту, но я не стал этого делать для простоты). Теперь $\\chi^2$ - сложная нелинейная функция параметров." ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def fit(x0,Gamma,x):\n", " return 1/((x-x0)**2+Gamma**2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Вот наши экспериментальные данные (с ошибками 0.1)." ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "collapsed": true }, "outputs": [], "source": [ "x=linspace(-3,3,21)\n", "dy=0.1*ones(21)\n", "y=fit(0,1,x)+dy*normal(size=21)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Минимизируем $\\chi^2$." ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def chi2(x0,Gamma):\n", " global x,y,dy\n", " return (((y-fit(x0,Gamma,x))/dy)**2).sum()" ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "collapsed": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/usr/lib64/python3.4/site-packages/ipykernel/__main__.py:1: InitialParamWarning: errordef is not given. Default to 1.\n", " if __name__ == '__main__':\n" ] } ], "source": [ "m=Minuit(chi2,x0=0,error_x0=1,Gamma=1,error_Gamma=1)" ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "
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FCN = 18.097376960150946TOTAL NCALL = 33NCALLS = 33
EDM = 1.7129910452155893e-07GOAL EDM = 1e-05\n", " UP = 1.0
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Hesse FailHasCovAbove EDMReach calllim
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1.16103064, 1.16341748, 1.16580432]),\n", " masked_array(data =\n", " [[-- -- -- ..., -- -- --]\n", " [-- -- -- ..., -- -- --]\n", " [-- -- -- ..., -- -- --]\n", " ..., \n", " [-- -- -- ..., -- -- --]\n", " [-- -- -- ..., -- -- --]\n", " [-- -- -- ..., -- -- --]],\n", " mask =\n", " [[ True True True ..., True True True]\n", " [ True True True ..., True True True]\n", " [ True True True ..., True True True]\n", " ..., \n", " [ True True True ..., True True True]\n", " [ True True True ..., True True True]\n", " [ True True True ..., True True True]],\n", " fill_value = 1e+20),\n", " )" ] }, "execution_count": 34, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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rNwgO9uWFF/rQv7+HLlui91JMMUv4nBH40YveWse5L/veew9DaqrJb6pXq5vo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\nXno6m+bOJfPSJYK+/ZaWPXtqHUkTlQf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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "m.draw_mncontour('x0','Gamma',nsigma=3)" ] }, { "cell_type": "code", "execution_count": 35, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 35, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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mnF7PJhDE9XpjOd06Xiust5RNbIhZBoMos47jFQzT5kT0kOMO6sfM+cg8hZQp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\nEadKu0OIUc7HgnJ2ZTwGBvS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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x0,Gamma,g,r=m.mncontour_grid('x0','Gamma',nsigma=3)\n", "pcolormesh(x0,Gamma,g)\n", "colorbar()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Теперь контуры постоянной высоты $\\chi^2$ - уже не симметричные эллипсы с центром в оптимальной точке, а какие-то сложные кривые. Ошибки положения и ширины резонанса довольно-таки независимы.\n", "\n", "Нарисуем на одном графике экспериментальные точки, наш фит (сплошная линия) и истинную теоретическую кривую (пунктир)." ] }, { "cell_type": "code", "execution_count": 36, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 36, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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6emBp4tq/HzpWT+fqUefxfw8doFqlagGI1PhcER/yR444pZ369eG6Bz/hlg8H\ns2TAEr8tqWx8wyZehYjc2nei+3IoKM1w0YMH4eqr4RK+YMyoCpbsw5A3c0IqVoT33oONG+GzKd14\nuvMzdHmrC9/99l1ggzV+YT38QAmRUQulObdw5Aj06AE1asCMt6KI0vI5gaw8yy0vJuWWF+PjGTJt\nWqHlxV9+cc619+kDJ3Z+iUmrJ/HFoC+oXaV2gCM33rCSTqgJkYRf0uGihw9Dr+uV6ArC7NkQUzE0\n/g7jvdIOINi92znXOnAg/NV2FOk/pjO/7/wARW1Kwko6pswOH4akgUv5Kq4bs2YpMT5cW8sEjrfr\nIRVUd3MKS656gRkv/Ez04PpM39zUGV5bio03TGiwcfgRJiEhgRlxcXQv0NtbGhdHj3xf7w8dgo6D\nUkhvcj3zb5pJxYq2onXESUritKQkltwHnU67iBxuZdQo58uqCU/Ww48wUVFRDJk2jeT4eObFxjIP\nGNGyJUOmTcv7ar9/P7Tu9wkZTa7nw5tn0SWuc3CDNmVS3HpIxalbF5bQkfffh+RkKKdrAEYEq+EH\nSojU8HMVNixz92644La3+DnxXhbd8gEXnXHhsXcMsb/DeKfMc0JE2P+rcs01zpDN6dMhJkb56c+f\nqHNiHf8GH2hhOIHMTtqGmlBNlPni2rTJGYN9+oCRvDqkPy3qNC+yvQkvZZoT4n7eDx1y9sU9fBhG\nTVpPz/cvY37f+bSp18Z/gQdTmLzeLeGHGn+9cMraG3HHtWiRs8TxuHHOqAyfHsOEltK8FvPd5+hR\nGDECli6F5Ekf8vCqwbx25Wv0OqeXH4INMkv4/mMJPwjHEOG1ScqYMTB7NrRv75/QTAgpY8LPNXEi\n/OMf8PT0dB7bdA13JN7ByEtGIuXprG45S/g2SieCHToEd8vrrJzo7EPbuHGwIzLhZNgw5zUzcEAC\nIx5dxfubr+VwzmGe6PhEsEMzhbAefqCEWA9/+3boNHQuB2o/yraXNlL1JBuwFTF81MPPtXWrs2Vi\n8/hDPDHuFxrXqeeDIENEOevhW8L3p0DXvr18cc6ae5hBbz9M5YT3WTh5O612laP/uSmejxM+OGst\n3XEHrFnjbGTv9UYqoX5+yBK+/5S7hB9oXrwpB923mQ+i+9K22Rm8P3AaNWJPCYsXtPEhPyR8cG6e\nMQPuv9+ZkHvXXSWcpBWKyTUUY/IgoAlfRLoCE3Amcv1TVZ8tcPs9wK1ANrAXGKyq33t4nNBN+KHe\nE4EiX5zNlSCvAAAQfUlEQVSrVkG/u7ezs1trnunyFCMuut05uRYmL2jjQ35K+Lm2bIG+faFOHZgy\nRRmfeR99WvShdb3Wvo/L30IxJg8ClvBFJArIAjoDu4BUoI+qfp2vTQdglar+JSJ3AEmq2sfDY4Vu\nws8vVF8EHuL66y8YNcrpeb38MlzcbRennXRakfcx5VwJnvPSjt0/csQZwTNpEvQaPYt5B4czOH4w\no5JGUSm6UpnjKpGydNbC5P0RyITfFhilqt3c1x8CtGAvP1/7eGCiql7i4TZL+GVRIK4lS+DOO516\n6qRJUNvTyrah+rcY//HyOS/pksqepKc78zpOabCHij3u4ruDm3jjmjc876LlTVw+mnfitTB5f3ib\n8FHVMv0A1wGv57t+I/ByEe0nAiMLuU3DQqjG6Y5rzx7V3gN/0vr1VT/4wLv7mAjixXOek5Ojw+Lj\nNcdJd6qgOeD8LienRIc7ckT1mWdUa5zi0j5PztLTnj9N39v4XqniKlP7QB0jCNy5s9h87Ytx+J4+\nVTx+JIrIjUAi0KGwBxs9enTe5aSkJJJCpT4eBo4Qw7Mv7OMfK0YT02I+29Z+Ta3qlYMdlglDxS2p\nXHDfhKLExMCDD8INNwjDhvWm0jddyGlcEW0auitv5pWygASXK2R2q8uVkpJCSimWqfZVSWe0qnZ1\nX/dY0hGRS4GXgPaquq+Qx9KyxhMQIfY1TxXe+88R7nx2NL91foNezXrzco8xnBJ7iuc7hMMJaOM/\nXrx+S7pRTkksWAD33OMswvb883Deed7HdQw/nXz2RSkr0AJZw68AbMY5absb+Aroq6qb8rVJAOYA\nXVR1WxGPZQm/hJYvh7ueXs6mpgNovOd35rywhBZ1vB0EbSJGCT/kS7tLlreys2HyZBg7Fi67DJ54\nAn5IEqqsTOP8uud79yB+SPj+/rv9JRjDMl/i72GZz4jIGCBVVT8SkUVAC5wPBAF2qGp3D48T2Qm/\nBG/KlSthzBhYt/YwZ1a/j845b9By819h0Rsx4aHMSyp74cABePFFZwTZ+XVvY93NH9PhzIsZ1WEU\nzWt7WK01Pz8kfH9+s/Enm3jlT0FaJkEVvvjC6RV9/TU8+KCLzCltmbguNax6IyZ8lGlJ5RL4+Wd4\nodbTTKk9nCb9X+WbOi/S/syLeKz9Y8SfGu/5Tpbw89ietuVITg68O/cQZ/Wewk33radXL2dyywUX\npNN5a2aJ9yo1xltRUVEkJiaS6L7sLzVrwtOMZMvGKlwW+wA6YRvbllzMwNnDcGngttgq6+5goc4S\nfgjbvx9GPb+Tmtc/zs1rGnLKhR8x/z/CbbdBxYrBjs4Y33C5XKSlpZEGVK/u4qmnYPuWKgxqeg+/\nvvAF7S+JYtYsp+7vb95sARrWvBm7GagfwmTMqz/H5rpcqqmpqn2qjdWYfr214mPVtde0u3XjTxuP\na+vLsdLGFMlPr/kNa9bosPh4nRcbq/Pcr90Na9bk3Z6drTp3rmr79qqnnab6+OOqO3aopnyboltq\n+G8cfk5Ojq5evVpXQ1i8l/ByHL7V8EvAn/XMffvg3Xdh2jSnZ993zwgqf9CY4e0HUPWEqoXeLxAn\n1ozxx3mrko6IWbcOpk6Fd96B2t1fYNcpj5DQrB1DWt1G96bdqRzjxZyTCJ9pawnfS/4Ym/vXX/De\nR38y590TWPJZNFdc4UxDv/RSiKrg//VOjPGaHxJfaU+QHjwIc+bA9FsWkNbqd6p3+if7q6RyfYue\nTLryVU6IPuG4+5T6PVLOEr5lBi+4XC6mDB7MhIwMeh48SE9gQkYGUwYPxuUq2Qmlw4fh/Y8O0enu\n96k6uA8D1tajeae17Njh9FwuvxxKmq8DdWLNmFBQqZKLFi3SeCGnG2vf6cXtsQs59f31fDDxQh5/\n5ARSU4/N0Znp6SQnJrKjfXt2AMmJiWRG6qAGb+o+gfohRGv4q1ev1nmxsXl18tyfubGxunr16mLv\n//vvqnPmqF52a4rG9O+lFR6pqo2f7KjPLJqse//c6/lOgVgnxBhv+eG1VZpzUIXV/F0u1bVrVR9+\nWDUuTvWMM1RHjFBdvDhHb7qwhS5uiB6JKsV5rjB5T2E1fN8pzVfPLVvgk0/gv/+FFSugXTto3HUh\nZ7Xcyc0XXEPN2JpFH9TPa5YbUyJ+em2V5ByUtzV/VcjMhPfeg5kz/+TbQ4uJveweDtfYyeVb4bqs\nIxzeVZmWC78oflx9mLynrIbvQ9680H79FeYv2sfbK5aQ8fVvRK+7hW7doFs3p0xTtfDzrp5Zwjeh\nxI+vLW/r66XpeKWlpbHm4hvQvzrx3kkXsDTuDyo1eY8/Gn5Fv9qP8/pdD3PC8SX/v4XJe8oSvo8V\n7IksaH4xzW+dQsrurXy5O4WfqywlquZWmpxwCb3P7cGoa24p20qAlvBNKAnS7PL8SpPwC3bWjhDD\nctpxf90bkIY38vW6k7jgAujYETp0gNat4YeDW6lftb5z8jdM3lOW8H1IFbZtg//9z8WHH+4jY96P\n7DmxBYkX/snOi3rRsVF7+l7YgYsbtiGmQkyZjlWmETdh8uI0YSgEEn5pFzYrqmy0f7+zAOGSJbBs\nGWzaBCcM6MGBWotocuL5XLpgNZe+Oou2p7elVpVavv+bfcQSfhns3g2frdrDfzNSSd2Zyo6jq6m1\n9F0ubl2VCy+Ei+5pTfyRVGLKltuPU+ahn5bwjb+EQMKH0s878bYj9ccf8OWXkLLiAAs3rmTD3k+R\nJmvJqZPKqJO/5eJW1UhIKEWJ1s8s4XshJ8fpua9bBxkZzs+SKkM4dMZHVDjhEKdXSCTx1NZc0bIN\nfVt3+XtiRwhMQvHIEr7xpUDvm+Dl6zeQ34JdEsWWr12sXOVidWoUq1c7+aJePUhIgBbxh1hy0m20\na9SSS5q0JP7UltQ5sY738fiIJfx8XC7YvsPFsowfWL55I+t2b+TQ2qv5JrUJtWs7GzDExzs/nL6S\n+Man0rBaA6SwInwITULxd1zGBEyIbIBSXPujR53Sz9q1kJpxkEW7Z7H90FqyT1kLddYSUyGa5pUv\n4/kL36ZZM6hVy/87e3mb8H2xxWHI2rULWg9/kd2134IaWcS4qlInqjlN6p9D8pVHuaqtp69mbYMR\nqjEmTERHw7nnOj833hgLDAJgzx5Yu1b5MnMXGVt3M/JD54NBBJo2hbPPhmqNv+a0Rvu474aLghJ7\nue7hZ2fDzKVrOP2Mo5x/xtmcXOlk3zywlXSM8b1Q6eH7sJSlCnv3Ook/KwvSt/yI4uK1caeV6HGK\nYyUdfwqBSSiBjMuYgAiVhB+GLOH7UwhMQsljG5Kb8sISfqlZwvenEBmiZky5Ygm/1Gy1TGOMMcew\nhG+MMRHCSjqlYSUdY3yjLOegrKSTx2r4/mQJ35jgs4SfJ6AJX0S6AhNwSkT/VNVnC9xeEXgTSAR+\nBm5Q1e88PE7oJvwQnWZuTMSyhJ8nYAlfRKKALKAzsAtIBfqo6tf52twJnKuqd4nIDUAPVe3j4bFC\nN+EHWjl9YRpTJqXpeEXA0OVAJvy2wChV7ea+/hDOdlvP5muzwN1mlYhUAH5U1ePWGrWEn48lfGOM\nlwI5LLMe8H2+6z+4f+exjar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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "errorbar(x,y,dy,fmt='ro')\n", "xt=linspace(-3.5,3.5,101)\n", "plot(xt,fit(m.values['x0'],m.values['Gamma'],xt),'b-')\n", "plot(xt,fit(0,1,xt),'g--')" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "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": "3.4.3" } }, "nbformat": 4, "nbformat_minor": 0 }