{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Оптимизация\n", "\n", "Подмодуль [scipy.optimize](https://docs.scipy.org/doc/scipy/reference/optimize.html#module-scipy.optimize) содержит в себе множество методов для решения задач оптимизации (минимизация, максимизация)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Минимизация скалярной функции одного аргумента\n", "\n", "Функция [scipy.optimize.minimize_scalar](https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.minimize_scalar.html#scipy.optimize.minimize_scalar) позволяет минимизировать функцию $f: \\mathbb{R} \\to \\mathbb{R}$:\n", "\n", "$$\n", "\\min_{x \\in D} f(x).\n", "$$" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " fun: -9.914949590828147\n", " nfev: 15\n", " nit: 11\n", " success: True\n", " x: 1.2807764040333458\n" ] }, { "data": { "text/plain": [ "" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "from scipy import optimize\n", "from matplotlib import pyplot as plt\n", "\n", "\n", "def f(x):\n", " return (x - 2) * x * (x + 2)**2\n", "\n", "\n", "sol = optimize.minimize_scalar(f)\n", "print(sol)\n", "\n", "\n", "x = np.linspace(-4, 3, 100)\n", "plt.plot(x, f(x))\n", "plt.scatter(sol.x, f(sol.x), color=\"r\")\n", "plt.xlabel(\"x\")\n", "plt.ylabel(\"y = f(x)\")\n", "plt.legend([\"Минимизируемая функция\", \"Найденный минимум\"])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "У функции $f(x) = (x - 1)x(x + 2)^2$ два локальных минимума и функция `minimize_scalar` вернула из них глобальный. Можно сузить поиск область поиска минимума используя метод `bounded`." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "a, b = -3, 1\n", "sol = optimize.minimize_scalar(f, bounds=(a, b), method=\"bounded\")\n", "\n", "plt.plot(x, f(x))\n", "plt.scatter(sol.x, f(sol.x), color=\"r\")\n", "plt.xticks([a, b])\n", "upper = np.array([100, 100])\n", "lower = np.array([-30, -30])\n", "plt.fill_between([a, b], lower, upper, where=upper>0, facecolor='blue', alpha=0.10)\n", "plt.xlabel(\"x\")\n", "plt.ylabel(\"y = f(x)\")\n", "plt.legend([\"Минимизируемая функция\", \"Найденный минимум\"])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Минимизация функции многих переменных\n", "\n", "Функция [scipy.optimize.minimize](https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.minimize.html) предназначена для минимизации функции многих переменных. Рассмотрим её на примере [функции Розенброка](https://ru.wikipedia.org/wiki/%D0%A4%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%8F_%D0%A0%D0%BE%D0%B7%D0%B5%D0%BD%D0%B1%D1%80%D0%BE%D0%BA%D0%B0)\n", "\n", "$$\n", "f(x_1, x_2) = (1 - x_1)^2 + 100(1-x_2)^2.\n", "$$\n", "\n", "Её минимум равен 0 при $x_1 = 1$ и $x_2 = 1$. Эта функция часто применяется для тестирования алгоритмов оптимизации и поэтому присутствует в `SciPy` под именем [scipy.optimize.rosen](https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.rosen.html#scipy.optimize.rosen).\n" ] }, { "cell_type": "code", "execution_count": 62, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "from scipy import optimize\n", "from matplotlib import pyplot as plt\n", "from mpl_toolkits.mplot3d import Axes3D\n", "\n", "f = optimize.rosen\n", "jac = optimize.rosen_der\n", "hess = optimize.rosen_hess\n", "\n", "\n", "x = np.linspace(0, 2, 200)\n", "X, Y = np.meshgrid(x, x)\n", "fig, ax = plt.subplots(subplot_kw={\"projection\": \"3d\"})\n", "fig.set_size_inches((10, 9))\n", "ax.plot_surface(X, Y, f([X, Y]), cmap=\"coolwarm\")\n", "plt.show()\n", " " ] }, { "cell_type": "code", "execution_count": 63, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " fun: 1.8932820837847567e-11\n", " hess_inv: array([[0.51676073, 1.03186646],\n", " [1.03186646, 2.06557555]])\n", " jac: array([ 5.27409301e-06, -2.50588723e-06])\n", " message: 'Optimization terminated successfully.'\n", " nfev: 105\n", " nit: 30\n", " njev: 35\n", " status: 0\n", " success: True\n", " x: array([0.99999565, 0.99999129])\n" ] }, { "data": { "image/png": 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yP5Okqs5M8vIk353kgiQvr6oDe91ZgN363k8cyk++65fywNv/Lt+Ulgfe/nf5yXf9klAGa6KuXMxCgay19p4kx0+yySVJXtc23JDkAVV1dpJnJrm+tXa8tfaFJNfn5MEOYKme8+e/kXvf9ZW7Lbv3XV/Jc/78NzraI9iaunLaljWH7Jwkt87dPzpbtt3ye6iqK6rqcFUdvvOOk2U/gMWddftnd7UcGL++zR9LejSpv7V2dWvtYGvt4On3ObPr3QFG4nNnnL2r5cDyqCsXt6xAdizJeXP3z50t2245wFr83pNfkq+ceu+7LfvKqffO7z35JR3tEdyTupJlBbJDSX5s9mnLJyX5Ymvts0nenuQZVXVgNpn/GbNlAGvx3kdcnFc+/Vdy2xkPytdTue2MB+WVT/+VvPcRF3e9a0AH+lhXJsmpi2xUVdcmuTDJWVV1NBufnDwtSVprr0pyXZJnJTmS5MtJfny27nhVvSLJjbOnurK1ZoIYsFbvfcTFAhismbpydxYKZK21y3ZY35K8aJt11yS5Zve7BgDjp64k6dGkfgCAVeprXZkIZADQmbGOjqkrd08gAwDomEAGANAxgQwAOqCuXK8+zx9LBDIAgM4JZAAAHRPIAGDNxlpX9lXf68pEIAMAlqSv88eGQCADAOiYQAYAa6SuXK8h1JWJQAYALIG6cn8EMgCAjglkALAm6kq2I5ABAPvS17pyKPPHEoEMANbC6BgnI5ABAHRMIAMA9kxduRwCGQCsmLqSnQhkAAAdE8gAgD1RVy6PQAYAK6SuZBECGQBAxwQyAGDX+lpXDpVABgAroq5cvyHOH0sEMgCAzglkALACYx4dU1cun0AGAIzCUOvKRCADAOicQAYAS6auZLcEMgBg8IZcVyYCGQBA5wQyAFgidSV7IZABAOzR2bf+xVKeRyADAAZt6PPHEoEMAJZGXTktyxodSwQyAIDOCWQAsARjHh3rszHUlYlABgDsQF25egIZAMAuLXP+WCKQAcC+qSu7MZa6MhHIAAA6J5ABANsyf+yell1XJgIZAOyLupJlEMgAgMEZ0/yxRCADgD0b++iYunJ9BDIAgAWtYv5YIpABAAMztroyEcgAYE/UlSyTQAYAsIBV1ZWJQAYADMgY68pEIAOAXVNXsmwLBbKquqiqPl5VR6rqpVus/82qumn284mq+oe5dV+bW3doifsOADAKp+60QVWdkuSqJN+f5GiSG6vqUGvt5hPbtNb+89z2P5Xk8XNPcUdr7XFL22MAgDVb5fyxZLERsguSHGmt3dJa+2qS1ye55CTbX5bk2mXsHAD0jbqyO2OdP5YsFsjOSXLr3P2js2X3UFUPSXJ+knfOLb53VR2uqhuq6tnb/ZKqumK23eE77zi+wG4BAIzDjpXlLl2a5A2tta/NLXtIa+1YVT0syTur6sOttU9tfmBr7eokVyfJgQc+pi15vwBg38Y+OsbWVl1XJouNkB1Lct7c/XNny7ZyaTbVla21Y7N/b0ny7tx9fhkA0BPqyu4sEshuTPLwqjq/qu6VjdB1j09LVtV3JjmQ5M/nlh2oqtNnt89K8pQkN29+LADAlO1YWbbW7qqqFyd5e5JTklzTWvtoVV2Z5HBr7UQ4uzTJ61tr83XjI5O8uqq+no3w92vzn84EgKFQV7JKC80ha61dl+S6Tctetun+L2/xuPclecw+9g8AWAN15dbWMX8scaV+AIDOCWQAsAN1JasmkAHAxKkrt7auujIRyADgpIyOsQ4CGQBAxwQyAJiwPteVXVpnXZkIZACwLXVlt8Z+df55AhkAQMcEMgCYKHVlfwhkALAFdWW3pnK5ixMEMgCAjglkALDJFEbH1JX9IpABAL0ytboyEcgAADonkAHAHHUlXRDIAIDemNLFYOcJZAAwM4XRMbbX1fyxRCADgElRV/aTQAYA0DGBDACiruyDKV7u4gSBDAAmQl3ZXwIZAEDHBDIAJk9d2b2pXu7iBIEMACZAXbm9ruePJQIZABNndIw+EMgAgE5Nva5MBDIAGD115fb6UFcmAhkAE6aupC8EMgCgM+rKDQIZAJM0ldExdeX2+lJXJgIZAEDnBDIAgI4JZABMjrqyH8wf+waBDACYnD7NH0sEMgCAzglkAEyKurIf1JV3J5ABAJPSt7oyEcgAmJCpjI4xPAIZAIyMunJ4BDIAgI4JZABMgrqSpJ/zxxKBDABGRV05TAIZAKNndIy+E8gAYCT6PjrWtb7WlYlABgCsibpyewIZAKOmrmQIBDIAGAF15cn1ua5MBDIARszoWH+oK09OIAMA6JhABgADp64cPoEMgFFSV3JC3+ePJQIZALBi5o/tbKFAVlUXVdXHq+pIVb10i/XPq6q/r6qbZj8vmFt3eVV9cvZz+TJ3HgCmTl05DqfutEFVnZLkqiTfn+Rokhur6lBr7eZNm/5ha+3Fmx57ZpKXJzmYpCX5wOyxX1jK3gPAFtSVnDCEujJZbITsgiRHWmu3tNa+muT1SS5Z8PmfmeT61trxWQi7PslFe9tVAGBo1JWLWSSQnZPk1rn7R2fLNvvhqvpQVb2hqs7b5WNTVVdU1eGqOnznHccX2C0AuKcpjY6pK8djWZP6/yTJQ1tr35WNUbDX7vYJWmtXt9YOttYOnn6fM5e0WwDAVA2lrkwWC2THkpw3d//c2bJ/1lr7fGvtztnd30nyxEUfCwCMk7pycYsEshuTPLyqzq+qeyW5NMmh+Q2q6uy5uxcn+djs9tuTPKOqDlTVgSTPmC0DgKVTVzJUO37KsrV2V1W9OBtB6pQk17TWPlpVVyY53Fo7lOSnq+riJHclOZ7kebPHHq+qV2Qj1CXJla01E8QAAOZUa63rfbiHAw98TLvwP7yp690AYECmNDqW9H+ErOu6cp3zx+779P/0gdbawf08hyv1A8DA9D2MsXsCGQBAxwQyAAZvanVl302prlwWgQwABkRd2S9fvfF9S3kegQyAQTM6RleWFcYSgQwAWKKu68qhEsgAYCDUlTsb4vyxRCADYMDUlYyFQAYAsEvLnD+WCGQADNTURseGUFd2PX9sqHVlIpABAHROIAOAnhvC6Bj7I5ABMDhTqyuHYEp15bLnjyUCGQBA5wQyAAZlaqNj6sppEMgAgH3puq5cp1XUlYlABgAM3JAvd3GCQAbAYKgrGSuBDADYM3XlcghkAAzC1EbHWMwY6spEIAOAXlJXTotABgDsyZTqylUTyADoPXUlWxn61fnnCWQA0DPqyukRyADoNaNj/aSuXC6BDAAYnDHVlYlABgC9oq6cJoEMgN5SV/aTunL5BDIA6AmjY9MlkAHQS0bH2M7Y5o8lAhkAsAvqytUQyADonSmOjqkrp00gAwAGY4x1ZSKQAQALUleujkAGQK+oK5kigQwAGIR11pXrJpAB0BtTHB0biqnVleucP5YIZADQKXUliUAGANA5gQyAXlBX9lcf6sqxXu7iBIEMADqiruQEgQyAzhkdY+oEMgCg18Z8uYsTBDIAOjXV0bGh1JV9mD+2Tl3MH0sEMgCAzglkALBmQxkd64Mp1JWJQAZAh6ZaVw6FunJ9BDIAgI4JZAB0YqqjY+rKxU2lrkwEMgBgC1OrK7smkAEAk9fl/LFEIAOgA+pKuLuFAllVXVRVH6+qI1X10i3Wv6Sqbq6qD1XVn1bVQ+bWfa2qbpr9HFrmzgMAy9eHunJK88eS5NSdNqiqU5JcleT7kxxNcmNVHWqt3Ty32V8mOdha+3JVvTDJf03yH2fr7mitPW65uw3AUE11dIz+6rquTBYbIbsgyZHW2i2tta8meX2SS+Y3aK29q7X25dndG5Kcu9zdBIBhU1dyMosEsnOS3Dp3/+hs2Xaen+Stc/fvXVWHq+qGqnr27ncRgLEwOtZ/6spu7FhZ7kZVPSfJwSRPm1v8kNbasap6WJJ3VtWHW2uf2uKxVyS5Iknuc8aDlrlbANApo2P91Ye6MllshOxYkvPm7p87W3Y3VfV9SX4xycWttTtPLG+tHZv9e0uSdyd5/Fa/pLV2dWvtYGvt4On3OXPhFwAAMHSLBLIbkzy8qs6vqnsluTTJ3T4tWVWPT/LqbISx2+aWH6iq02e3z0rylCTzHwYAYCLUlf2nruzOjpVla+2uqnpxkrcnOSXJNa21j1bVlUkOt9YOJfn1JGck+eOqSpK/ba1dnOSRSV5dVV/PRvj7tU2fzgSAUVNXsoiF5pC11q5Lct2mZS+bu/192zzufUkes58dBGD4jI7RR32ZP5a4Uj8AEHVl1wQyAFgRdSWLEsgAWCl1JX3Up7oyEcgAYPL6UFdOnUAGwMpMeXRMXbk7U54/lghkAACdE8gAWAmjY8Mwxbqyb/PHEoEMAOjY1OvKRCADAOicQAbA0qkrh0Fd2R8CGQDQGXXlBoEMgKWa8ugY7JVABgBLoq7st77WlYlABsASGR1jN9SV3yCQAQB0TCADgCVQV7IfAhkAS6GuZDfWXVf2ef5YIpABwL4NaXSMfhLIANg3o2PDoa7sJ4EMABi1vteViUAGwD5NfXRMXbl7LndxTwIZAEyEurK/BDIA9mzqo2P03xDqykQgA4A9U1funrpyawIZAEyAunI1PvW2v1zK8whkAOzJ1OtKo2Msk0AGAKzF2K7Ov6zRsUQgA2APpj46NjTqyv4TyABgl9SVLJtABsCuGB1jL8ZWVy6bQAYAI6auXI1lzh9LBDIA2BV1JasgkAGwMHUle+FisDsTyABgQUMbHZtqXTmky12cIJABsBCjY7A6AhkAsDLqysUIZADsyOiYunIohna5ixMEMgCABa1i/lgikAGwA6NjsHoCGQDsQF25N67OvziBDABgAauqKxOBDICTUFcaHWM9BDIAYOlc7mJ3BDIAtmR0jCEZ8vyxRCADgG2pKzlhlfPHEoEMgC0YHWM/1JW7J5ABAIM29LoyEcgA2MTo2AZ1JSesuq5MBDIAYInUlXsjkAHAJkMbHZuyMdSViUAGwBx15TCpK1dnHXVlIpABAEuirty7hQJZVV1UVR+vqiNV9dIt1p9eVX84W//+qnro3Lqfny3/eFU9c4n7DsASGR3boK4cjrHUlckCgayqTklyVZIfSPKoJJdV1aM2bfb8JF9orf2LJL+Z5L/MHvuoJJcmeXSSi5K8cvZ8AMASqCvHYZERsguSHGmt3dJa+2qS1ye5ZNM2lyR57ez2G5L8m6qq2fLXt9bubK19OsmR2fMB0CNGx9ivMdaV65o/liwWyM5Jcuvc/aOzZVtu01q7K8kXk3zLgo8FgF5QV9KVU7vegROq6ookV8zu3vmWqx7xkS73p4fOSvK5rneihxyXrTkuW3Nc7umsJJ97y1Vd70bvOFe25rhs7Tv2+wSLBLJjSc6bu3/ubNlW2xytqlOTfHOSzy/42CRJa+3qJFcnSVUdbq0dXOQFTIVjsjXHZWuOy9Ycl3tyTLbmuGzNcdlaVR3e73MsUlnemOThVXV+Vd0rG5P0D23a5lCSy2e3fyTJO1trbbb80tmnMM9P8vAk4yuZAQD2YccRstbaXVX14iRvT3JKkmtaax+tqiuTHG6tHUryu0n+V1UdSXI8G6Ets+3+KMnNSe5K8qLW2tdW9FoAAAZpoTlkrbXrkly3adnL5m5/Jcm/3+axv5rkV3e5X1fvcvspcEy25rhszXHZmuNyT47J1hyXrTkuW9v3camNZhEAgK746iQAgI6tNZD5CqatLXBcXlJVN1fVh6rqT6vqIXPrvlZVN81+Nn/YYtAWOC7Pq6q/n3v9L5hbd3lVfXL2c/nmxw7VAsfkN+eOxyeq6h/m1o35XLmmqm6rqi0vl1Mbfmt23D5UVU+YWzfWc2WnY/Kjs2Px4ap6X1U9dm7dZ2bLb1rGp8f6ZIHjcmFVfXHub+Vlc+tO+vc3ZAscl5+bOyYfmb2fnDlbN8rzparOq6p3zf77+9Gq+pkttlnee0trbS0/2fhAwKeSPCzJvZL8VZJHbdrmJ5O8anb70iR/OLv9qNn2pyc5f/Y8p6xr33twXJ6e5L6z2y88cVxm92/v+jV0eFyel+S3t3jsmUlumf17YHb7QNevaR3HZNP2P5WND+GM+lyZvbZ/leQJST6yzfpnJXlrkkrypCTvH/O5suAx+Z4TrzUbX433/rl1n0lyVtevoaPjcmGS/7PF8l39/Q3tZ6fjsmnbH8zG1RRGfb4kOTvJE2a375/kE1v8d2hp7y3rHCHzFUxb2/G4tNbe1Vr78uzuDdm4ntvYLXK+bOeZSa5vrR1vrX0hyfXZ+C7VodvtMbksybVr2bOOtdbek41PeG/nkiSvaxtuSPKAqjo74z1XdjwmrbX3zV5zMp33lUXOle3s5z2p93Z5XCbx3tJa+2xr7YOz2/+Y5GO557cNLe29ZZ2BzFcwbW23r+352UjjJ9y7qg5X1Q1V9ewV7F9XFj0uPzwbJn5DVZ24CPFYz5eFX9es1j4/yTvnFo/1XFnEdsdurOfKbm1+X2lJ3lFVH6iNb1GZmidX1V9V1Vur6tGzZc6VJFV132wEizfOLR79+VIbU6gen+T9m1Yt7b2lN1+dxM6q6jlJDiZ52tzih7TWjlXVw5K8s6o+3Fr7VDd7uHZ/kuTa1tqdVfUT2Rhd/dcd71NfXJrkDe3u1/2b8rnCNqrq6dkIZE+dW/zU2bnywCTXV9Vfz0ZQpuCD2fhbub2qnpXkLdm4qDkbfjDJn7XW5kfTRn2+VNUZ2QigP9ta+9Kqfs86R8h28xVMqT1+BdMALfTaqur7kvxikotba3eeWN5aOzb795Yk785Ggh+DHY9La+3zc8fid5I8cdHHDtRuXtel2VQpjPhcWcR2x26s58pCquq7svG3c0lr7fMnls+dK7cleXPGM0VkR621L7XWbp/dvi7JaVV1ViZ+rsw52XvL6M6XqjotG2Hs91trb9pik+W9t6xxctyp2ZjUdn6+MSHy0Zu2eVHuPqn/j2a3H527T+q/JeOZ1L/IcXl8NiaTPnzT8gNJTp/dPivJJzOSSaYLHpez527/UJIbZrfPTPLp2fE5MLt9ZtevaR3HZLbdd2Zjkm1N4VyZe40PzfYTtf9t7j7x9i/GfK4seEwenI35uN+zafn9ktx/7vb7klzU9WtZ43H59hN/O9kIFn87O28W+vsb8s/Jjsts/TdnY57Z/aZwvsz+d39dkv92km2W9t6ytsqy+QqmLS14XH49yRlJ/njjMw7529baxUkemeTVVfX1bIx2/lpr7eZOXsiSLXhcfrqqLs7GOXE8G5+6TGvteFW9Ihvfw5okV7a7D68P0oLHJNn4u3l9m70rzIz2XEmSqro2G5+OO6uqjiZ5eZLTkqS19qpsfNPIs7IRQL6c5Mdn60Z5riQLHZOXZWOO7itn7yt3tY0vjf62JG+eLTs1yR+01t629hewIgsclx9J8sKquivJHUkunf0tbfn318FLWIkFjkuy8X9839Fa+6e5h475fHlKkucm+XBV3TRb9gvZ+D8zS39vcaV+AICOuVI/AEDHBDIAgI4JZAAAHRPIAAA6JpABAHRMIAMA6JhABgDQMYEMAKBj/x+yyfLV06OoIQAAAABJRU5ErkJggg==", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "res = optimize.minimize(f, [2, 2])\n", "print(res)\n", "\n", "fig, ax = plt.subplots()\n", "fig.set_size_inches((10, 9))\n", "ax.contourf(X, Y, f([X, Y]), cmap=\"coolwarm\")\n", "ax.scatter(res.x[0], res.x[1], color=\"r\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Как видно из сообщения, метод успешно сошелся и алгоритму потребовалось 30 итераций и 105 вызовов функции `f`, чтобы сойтись. Передадим этому методу функцию, вычисляющую матрицу градиент искомой функции." ] }, { "cell_type": "code", "execution_count": 64, "metadata": {}, "outputs": [ { "data": { "text/plain": [ " fun: 3.271435067604758e-14\n", " hess_inv: array([[0.51671918, 1.03179112],\n", " [1.03179112, 2.06544014]])\n", " jac: array([ 5.26067293e-06, -2.49959031e-06])\n", " message: 'Optimization terminated successfully.'\n", " nfev: 35\n", " nit: 30\n", " njev: 35\n", " status: 0\n", " success: True\n", " x: array([1.00000013, 1.00000025])" ] }, "execution_count": 64, "metadata": {}, "output_type": "execute_result" } ], "source": [ "res = optimize.minimize(f, [2, 2], jac=jac)\n", "res\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Количество вызовов функции снизилось до 35, но количество итераций осталось прежним. Это достигается за счет того, что метод минимизации вычисляет производную, вызывая переданную функцию `jac`, а до этого он её оценивал численно, что требовало дополнительных вызовов `f`. \n", "\n", "Передадим ещё информацию о второй производной функции `f`, т.е. матрицу Гессе. Метод минимизации по умолчанию (`BFGS`) --- метод первого порядка, чтобы задействовать матрицу Гессе, необходимо использовать метод второго порядка, например, `dogleg`" ] }, { "cell_type": "code", "execution_count": 65, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " fun: 7.335116582097013e-13\n", " hess: array([[ 802.00135535, -400.00033735],\n", " [-400.00033735, 200. ]])\n", " jac: array([ 7.65326055e-06, -2.98326426e-06])\n", " message: 'Optimization terminated successfully.'\n", " nfev: 16\n", " nhev: 13\n", " nit: 15\n", " njev: 14\n", " status: 0\n", " success: True\n", " x: array([1.00000084, 1.00000167])\n" ] } ], "source": [ "res = optimize.minimize(f, [2, 2], jac=optimize.rosen_der, hess=optimize.rosen_hess, method=\"dogleg\")\n", "print(res)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Методу второго порядка потребовалось всего 15 итераций и 16 вызовов функции `f`, чтобы сойтись." ] } ], "metadata": { "interpreter": { "hash": "8617202e12f254480e1fae3258716b685f1a56bcbf234a446366b4fd3345ed22" }, "kernelspec": { "display_name": "Python 3.8.10 64-bit", "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": "3.8.10" } }, "nbformat": 4, "nbformat_minor": 2 }