CH1/templates/8_NumPy_-SciPy_-Matplotlib-intro.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#Первое знакомство с NumPy, SciPy и Matplotlib"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Numpy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x = [2, 3, 4, 6]\n",
    "y = np.array(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<type 'list'> [2, 3, 4, 6]\n",
      "<type 'numpy.ndarray'> [2 3 4 6]\n"
     ]
    }
   ],
   "source": [
    "print type(x), x\n",
    "print type(y), y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[3, 4]\n"
     ]
    }
   ],
   "source": [
    "print x[1:3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[3 4]\n"
     ]
    }
   ],
   "source": [
    "print y[1:3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "TypeError",
     "evalue": "list indices must be integers, not list",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-7-1703eef47ef6>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0;32mprint\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m2\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mTypeError\u001b[0m: list indices must be integers, not list"
     ]
    }
   ],
   "source": [
    "print x[[0, 2]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2 4]\n"
     ]
    }
   ],
   "source": [
    "print y[[0, 2]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4 6]\n"
     ]
    }
   ],
   "source": [
    "print y[y>3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2, 3, 4, 6, 2, 3, 4, 6, 2, 3, 4, 6, 2, 3, 4, 6, 2, 3, 4, 6]\n"
     ]
    }
   ],
   "source": [
    "print x * 5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[10 15 20 30]\n"
     ]
    }
   ],
   "source": [
    "print y * 5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "TypeError",
     "evalue": "unsupported operand type(s) for ** or pow(): 'list' and 'int'",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-12-8f3433247060>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0;32mprint\u001b[0m \u001b[0mx\u001b[0m \u001b[0;34m**\u001b[0m \u001b[0;36m2\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mTypeError\u001b[0m: unsupported operand type(s) for ** or pow(): 'list' and 'int'"
     ]
    }
   ],
   "source": [
    "print x ** 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 4  9 16 36]\n"
     ]
    }
   ],
   "source": [
    "print y ** 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "matrix = [[1, 2, 4], [3, 1, 0]]\n",
    "nd_array = np.array(matrix)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0\n"
     ]
    }
   ],
   "source": [
    "print matrix[1][2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0\n"
     ]
    }
   ],
   "source": [
    "print nd_array[1, 2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.438842696211\n"
     ]
    }
   ],
   "source": [
    "print np.random.rand()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-0.511813938677\n"
     ]
    }
   ],
   "source": [
    "print np.random.randn()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-1.42291178  0.67413655  1.34859743 -1.36775309]\n"
     ]
    }
   ],
   "source": [
    "print np.random.randn(4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-0.82076944 -0.57758927  0.35274212 -0.90060401  0.3356505 ]\n",
      " [-0.06885306 -0.55435176  0.44261636 -0.67454043 -0.98557812]\n",
      " [ 1.63089984  0.52053926 -1.39521558  0.64451813  0.30286612]\n",
      " [-0.25467814  0.67001453  0.2518447  -0.11396418 -0.59441236]]\n"
     ]
    }
   ],
   "source": [
    "print np.random.randn(4, 5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.   0.1  0.2  0.3  0.4  0.5  0.6  0.7  0.8  0.9  1.   1.1  1.2  1.3  1.4\n",
      "  1.5  1.6  1.7  1.8  1.9  2.   2.1  2.2  2.3  2.4  2.5  2.6  2.7  2.8  2.9\n",
      "  3.   3.1  3.2  3.3  3.4  3.5  3.6  3.7  3.8  3.9  4.   4.1  4.2  4.3  4.4\n",
      "  4.5  4.6  4.7  4.8  4.9  5.   5.1  5.2  5.3  5.4  5.5  5.6  5.7  5.8  5.9\n",
      "  6.   6.1  6.2  6.3  6.4  6.5  6.6  6.7  6.8  6.9  7.   7.1  7.2  7.3  7.4\n",
      "  7.5  7.6  7.7  7.8  7.9]\n"
     ]
    }
   ],
   "source": [
    "print np.arange(0, 8, 0.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "TypeError",
     "evalue": "range() integer step argument expected, got float.",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-27-8fe6ca95c7b3>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0;32mprint\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m8\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m0.1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mTypeError\u001b[0m: range() integer step argument expected, got float."
     ]
    }
   ],
   "source": [
    "print range(0, 8, 0.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The slowest run took 17.63 times longer than the fastest. This could mean that an intermediate result is being cached \n",
      "100000 loops, best of 3: 5.51 µs per loop\n",
      "10000 loops, best of 3: 98.9 µs per loop\n"
     ]
    }
   ],
   "source": [
    "%timeit np.arange(0, 10000)\n",
    "%timeit range(0, 10000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##SciPy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from scipy import optimize"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.0\n"
     ]
    }
   ],
   "source": [
    "def f(x):\n",
    "    return (x[0] - 3.2) ** 2 + (x[1] - 0.1) ** 2 + 3\n",
    "\n",
    "print f([3.2, 0.1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   status: 0\n",
      "  success: True\n",
      "     njev: 3\n",
      "     nfev: 12\n",
      " hess_inv: array([[1, 0],\n",
      "       [0, 1]])\n",
      "      fun: 3.0000000000000058\n",
      "        x: array([ 3.19999993,  0.10000002])\n",
      "  message: 'Optimization terminated successfully.'\n",
      "      jac: array([ -1.49011612e-07,   5.96046448e-08])\n"
     ]
    }
   ],
   "source": [
    "x_min = optimize.minimize(f, [5, 5])\n",
    "print x_min"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 3.19999993  0.10000002]\n"
     ]
    }
   ],
   "source": [
    "print x_min.x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from scipy import linalg"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 2. -2.  9.]\n"
     ]
    }
   ],
   "source": [
    "a = np.array([[3, 2, 0], [1, -1, 0], [0, 5, 1]])\n",
    "b = np.array([2, 4, -1])\n",
    "\n",
    "x = linalg.solve(a, b)\n",
    "print x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 2.  4. -1.]\n"
     ]
    }
   ],
   "source": [
    "print np.dot(a, x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(4, 4) (3,) (3, 3)\n",
      "<type 'numpy.ndarray'> <type 'numpy.ndarray'> <type 'numpy.ndarray'>\n"
     ]
    }
   ],
   "source": [
    "X = np.random.randn(4, 3)\n",
    "U, D, V = linalg.svd(X)\n",
    "print U.shape, D.shape, V.shape\n",
    "print type(U), type(D), type(V)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Matplotlib"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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vzM7cNIqkspj4zjwzDwGH2sc/iYgDwLOAA0WvOWnd0ijbtplGkVQ9I+lmiYg1wAuBPaO4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\nSaoBg7kk1YDBXJJqwGAuSTVgMJekGvhf3kAwE/Ra4D0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1061f6990>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib import pylab as plt\n",
    "\n",
    "plt.plot([1, 2, 3, 4], [1, 4, 9, 16])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x107123190>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.arange(-10, 10, 0.1)\n",
    "y = x ** 3\n",
    "plt.plot(x, y)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Все вместе"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy import interpolate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 2 4 6 8]\n",
      "[ 1.04770822  0.56934814  0.24696548  0.1199503   0.19566904]\n"
     ]
    }
   ],
   "source": [
    "x = np.arange(0, 10, 2)\n",
    "y = np.exp(-x/3.0) + np.random.randn(len(x)) * 0.05\n",
    "\n",
    "print x[:5]\n",
    "print y[:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "f = interpolate.interp1d(x, y, kind='quadratic')\n",
    "xnew = np.arange(0, 8, 0.1)\n",
    "ynew = f(xnew)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ghyM/sOfIHtIOpRETFUODKg1oWLUhTas3pWn1psRVjyOuRhxx1ePC8mQrFbmI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\nFxEJcypyEZEwpyIXEQlz/x9ZNtZw0bOXigAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x107cd61d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, y, 'o', xnew, ynew, '-')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}