SBT_03 Optimization.ipynb

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     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from scipy import optimize\n",
      "\n",
      "def f(x):   # The rosenbrock function\n",
      "     return .5*(1 - x[0])**2 + (x[1] - x[0]**2)**2\n",
      "    \n",
      "f([1, 1])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 1,
       "text": [
        "0.0"
       ]
      }
     ],
     "prompt_number": 1
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     "cell_type": "markdown",
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     "source": [
      "\u0414\u043b\u044f \u043d\u0430\u0447\u0430\u043b\u0430 \u043f\u043e\u0441\u043c\u043e\u0442\u0440\u0438\u043c, \u0447\u0442\u043e \u0434\u0430\u0435\u0442 \u043f\u0440\u043e\u0441\u0442\u043e\u0439 \u043f\u0435\u0440\u0435\u0431\u043e\u0440 \u0438\u0437 \u0442\u043e\u0439 \u0436\u0435 \u0431\u0438\u0431\u043b\u0438\u043e\u0442\u0435\u043a\u0438:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "optimize.brute(f, ((-1, 2), (-1, 2)))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 19,
       "text": [
        "array([ 1.00001462,  1.00001547])"
       ]
      }
     ],
     "prompt_number": 19
    },
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     "source": [
      "\u0415\u0441\u043b\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u043e\u0447\u0435\u043d\u044c \u0437\u0430\u0448\u0443\u043c\u043b\u0435\u043d\u043d\u0430\u044f \u0438 \u043d\u0438 \u043e \u043a\u0430\u043a\u043e\u0439 \u0433\u043b\u0430\u0434\u043a\u043e\u0441\u0442\u0438 \u043d\u0435\u0442 \u0438 \u0440\u0435\u0447\u0438, \u043c\u043e\u0436\u0435\u0442 \u0431\u044b\u0442\u044c \u043f\u043e\u043b\u0435\u0437\u0435\u043d \u043c\u0435\u0442\u043e\u0434 \u0438\u043c\u043c\u0438\u0442\u0430\u0446\u0438\u0438 \u043e\u0442\u0436\u0438\u0433\u0430 (anneal simulation). \u041e\u0434\u043d\u0430\u043a\u043e \u0434\u043b\u044f \u0433\u043b\u0430\u0434\u043a\u0438\u0445 \u0444\u0443\u043d\u043a\u0446\u0438\u0439 \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442 \u043f\u0440\u0438\u043c\u0435\u043d\u0435\u043d\u0438\u044f \u043e\u0442\u0436\u0438\u0433\u0430 \u043e\u0431\u044b\u0447\u043d\u043e \u043d\u0435 \u0432\u043f\u0435\u0447\u0430\u0442\u043b\u044f\u0435\u0442:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from scipy import optimize\n",
      "\n",
      "optimize.anneal(f, [2, 2])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Warning: Cooled to 4785.003119 at [   58.8369672   3405.99941162] but this is not the smallest point found.\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 20,
       "text": [
        "(array([ -16.00743456,  248.851836  ]), 5)"
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     "prompt_number": 20
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    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "\n",
      "def fprime(x):\n",
      "        return np.array((-2*.5*(1 - x[0]) - 4*x[0]*(x[1] - x[0]**2), 2*(x[1] - x[0]**2)))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
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    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\u0420\u0430\u0437\u0440\u0430\u0431\u043e\u0442\u0447\u0438\u043a\u0438 SciPy \u043f\u043e\u0437\u0430\u0431\u043e\u0442\u0438\u043b\u0438\u0441\u044c \u043e \u0442\u043e\u043c, \u0447\u0442\u043e\u0431\u044b \u043c\u044b \u043d\u0435 \u043f\u044b\u0442\u0430\u043b\u0438\u0441\u044c \u0447\u0442\u043e-\u0442\u043e \u0440\u0435\u0448\u0430\u0442\u044c \u0441 \u043d\u0435\u043f\u0440\u0430\u0432\u0438\u043b\u044c\u043d\u043e \u043f\u043e\u0441\u0447\u0438\u0442\u0430\u043d\u043d\u044b\u043c \u0433\u0440\u0430\u0434\u0438\u0435\u043d\u0442\u043e\u043c \u0438 \u043f\u0440\u0435\u0434\u0443\u0441\u043c\u043e\u0442\u0440\u0435\u043b\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u044e \u043f\u0440\u043e\u0432\u0435\u0440\u043a\u0438 \u0433\u0440\u0430\u0434\u0438\u0435\u043d\u0442\u0430. \u041e\u043d\u0430 \u0432\u043e\u0437\u0432\u0440\u0430\u0449\u0430\u0435\u0442 \u043d\u043e\u0440\u043c\u0443 \u0440\u0430\u0437\u043d\u043e\u0441\u0442\u0438 \u043d\u0430\u0448\u0435\u0433\u043e \u0433\u0440\u0430\u0434\u0438\u0435\u043d\u0442\u0430 \u0438 \u043e\u0446\u0435\u043d\u0435\u043d\u043d\u043e\u0433\u043e \u0447\u0438\u0441\u043b\u0435\u043d\u043d\u043e (\u0432 \u0437\u0430\u0434\u0430\u043d\u043d\u043e\u0439 \u0442\u043e\u0447\u043a\u0435, \u0432 \u0434\u0430\u043d\u043d\u043e\u043c \u0441\u043b\u0443\u0447\u0430\u0435 - [2 2])."
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     "cell_type": "code",
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     "input": [
      "optimize.check_grad(f, fprime, [2, 2])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 8,
       "text": [
        "2.384185791015625e-07"
       ]
      }
     ],
     "prompt_number": 8
    },
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     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\u0415\u0441\u043b\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0443 \u0432\u0430\u0441 \u0433\u043b\u0430\u0434\u043a\u0430\u044f, \u0434\u0430\u0436\u0435 \u0435\u0441\u043b\u0438 \u043d\u0435\u0442 \u043f\u043e\u0441\u0447\u0438\u0442\u0430\u043d\u043d\u043e\u0433\u043e \u0433\u0440\u0430\u0434\u0438\u0435\u043d\u0442\u0430 (\u0432 \u043d\u0430\u0448\u0435\u043c \u0441\u043b\u0443\u0447\u0430\u0435 \u0432\u044b \u043c\u043e\u0436\u0435\u0442\u0435 \u043f\u0435\u0440\u0435\u0434\u0430\u0442\u044c \u0433\u0440\u0430\u0434\u0438\u0435\u043d\u0442 \u043a\u0430\u043a \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 fmin_bfgs), \u043f\u043e\u043b\u044c\u0437\u0443\u0439\u0442\u0435\u0441\u044c \u043f\u043e \u0443\u043c\u043e\u043b\u0447\u0430\u043d\u0438\u044e bfgs \u0438\u043b\u0438 \u0435\u0433\u043e \u0432\u0430\u0440\u0438\u0430\u0446\u0438\u044f\u043c\u0438:"
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    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "optimize.fmin_bfgs(f, [2, 2])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Optimization terminated successfully.\n",
        "         Current function value: 0.000000\n",
        "         Iterations: 16\n",
        "         Function evaluations: 96\n",
        "         Gradient evaluations: 24\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 6,
       "text": [
        "array([ 1.00000007,  1.00000005])"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\u0411\u043b\u0430\u0433\u043e\u0434\u0430\u0440\u044f \u0440\u0430\u0437\u0440\u0430\u0431\u043e\u0442\u0447\u0438\u043a\u0430\u043c SciPy, \u044d\u0442\u0430 \u0440\u0435\u043a\u043e\u043c\u0435\u043d\u0434\u0430\u0446\u0438\u044f \u043d\u0430\u0445\u043e\u0434\u0438\u0442 \u0441\u0432\u043e\u0435 \u043e\u0442\u0440\u0430\u0436\u0435\u043d\u0438\u0435 \u0432 \u0442\u043e\u043c, \u043a\u0430\u043a\u043e\u0439 \u043c\u0435\u0442\u043e\u0434 \u043f\u043e \u0443\u043c\u043e\u043b\u0447\u0430\u043d\u0438\u044e \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u0442 \u0444\u0443\u043d\u043a\u0446\u0438\u044f minimize:"
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    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "optimize.minimize(f, [2, 2])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 21,
       "text": [
        "   status: 0\n",
        "  success: True\n",
        "     njev: 24\n",
        "     nfev: 96\n",
        " hess_inv: array([[ 0.98632001,  1.97824278],\n",
        "       [ 1.97824278,  4.46512261]])\n",
        "      fun: 9.538460152507302e-15\n",
        "        x: array([ 1.00000007,  1.00000005])\n",
        "  message: 'Optimization terminated successfully.'\n",
        "      jac: array([  4.74186475e-07,  -1.53939058e-07])"
       ]
      }
     ],
     "prompt_number": 21
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     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "(\u043f\u043e\u043f\u0440\u043e\u0431\u0443\u0439\u0442\u0435 \u0437\u0430\u043f\u0443\u0441\u0442\u0438\u0442\u044c \u043e\u0442\u0434\u0435\u043b\u044c\u043d\u043e \u043e\u0442 ipython notebook)"
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     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "import matplotlib.pyplot as plt\n",
      "import matplotlib.animation as animation\n",
      "import scipy.optimize as si\n",
      "import scipy.optimize as so\n",
      "\n",
      "fig = plt.figure()\n",
      "ax = plt.axes(xlim=(-0.5, 3.5), ylim=(-10, 100))\n",
      "line, = ax.plot([], [], 'o')\n",
      "\n",
      "def F(x):\n",
      "        return (x**3-x**2-9.)**2\n",
      "\n",
      "#get the optimize progress\n",
      "res_x = []\n",
      "so.fmin(F, -9, callback=res_x.append)\n",
      "res_x = np.array(res_x).ravel()\n",
      "res_y = F(res_x)\n",
      "\n",
      "def init():\n",
      "    line.set_data([], [])\n",
      "    return line,\n",
      "\n",
      "# animation function.  This is called sequentially\n",
      "def animate(i):\n",
      "    line.set_data(res_x[i], res_y[i])\n",
      "    return line,\n",
      "\n",
      "#print type(animate(0))\n",
      "\n",
      "ax.plot(np.linspace(0,10,100), F(np.linspace(0,10,100)), 'g')\n",
      "#frames is the length of res_x\n",
      "anim = animation.FuncAnimation(fig, animate, init_func=init,\n",
      "                               frames=len(res_x), interval=200, blit=True)\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Optimization terminated successfully.\n",
        "         Current function value: 0.000000\n",
        "         Iterations: 22\n",
        "         Function evaluations: 44\n",
        "<class 'matplotlib.lines.Line2D'>\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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p3KZethEkmq4RkYgxM/4+6O98XPgxV79zdcT36J/48glGTxvNpCGTVPD1TCUv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\ngg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x14ffb2b0>"
       ]
      }
     ],
     "prompt_number": 30
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}