3.1. NumPy, SciPy, Matplotlib intro. Linsolve, UDV, plots.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": false
   },
   "outputs": [],
   "source": [
    "x = [2, 3, 4, 6]\n",
    "y = np.array(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "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": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[3, 4]\n"
     ]
    }
   ],
   "source": [
    "print x[1:3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[3 4]\n"
     ]
    }
   ],
   "source": [
    "print y[1:3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "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-6-1703eef47ef6>\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": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2 4]\n"
     ]
    }
   ],
   "source": [
    "print y[[0, 2]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4 6]\n"
     ]
    }
   ],
   "source": [
    "print y[y>3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "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": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[10 15 20 30]\n"
     ]
    }
   ],
   "source": [
    "print y * 5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "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-13-8f3433247060>\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": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 4  9 16 36]\n"
     ]
    }
   ],
   "source": [
    "print y ** 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "matrix = [[1, 2, 4], [3, 1, 0]]\n",
    "nd_array = np.array(matrix)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0\n"
     ]
    }
   ],
   "source": [
    "print matrix[1][2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0\n"
     ]
    }
   ],
   "source": [
    "print nd_array[1, 2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.203653866743\n"
     ]
    }
   ],
   "source": [
    "print np.random.rand()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-1.16155079438\n"
     ]
    }
   ],
   "source": [
    "print np.random.randn()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-0.11146086 -0.68278119 -0.4282472   0.10307349]\n"
     ]
    }
   ],
   "source": [
    "print np.random.randn(4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.45545958  1.21281263 -1.72321375 -0.78670898  0.37050079]\n",
      " [ 0.6243632   4.37438047  1.56668947 -0.04340312 -0.08764298]\n",
      " [-1.01685001 -0.50566773 -0.04752706  1.55562379 -0.74174894]\n",
      " [-1.45885117  1.04960839 -0.27236579 -0.10655772 -0.5562488 ]]\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 13.45 times longer than the fastest. This could mean that an intermediate result is being cached \n",
      "100000 loops, best of 3: 5.87 µs per loop\n",
      "10000 loops, best of 3: 81.4 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": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "      fun: 3.0000000000000058\n",
      " hess_inv: array([[1, 0],\n",
      "       [0, 1]])\n",
      "      jac: array([ -1.49011612e-07,   5.96046448e-08])\n",
      "  message: 'Optimization terminated successfully.'\n",
      "     nfev: 12\n",
      "      nit: 1\n",
      "     njev: 3\n",
      "   status: 0\n",
      "  success: True\n",
      "        x: array([ 3.19999993,  0.10000002])\n"
     ]
    }
   ],
   "source": [
    "x_min = optimize.minimize(f, [5, 5])\n",
    "print x_min"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "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": 36,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from scipy import linalg"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "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": 39,
   "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": 41,
   "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": 44,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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F0iRYfpkyyyuSJsnyyxQ89BBce20vK//hDy2vSKoeM/UB9pZXNm2C+XnLK5KmY+rll4hY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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10fca0d10>"
      ]
     },
     "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": 46,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10fca05d0>"
      ]
     },
     "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": 61,
   "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": 78,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 2 4 6 8]\n",
      "[ 1.05198782  0.56109437  0.22947433  0.21192873  0.02633492]\n"
     ]
    }
   ],
   "source": [
    "x = np.arange(0, 10, 2)\n",
    "y = np.exp(-x/3.) + np.random.randn(len(x)) * 0.05\n",
    "\n",
    "print x[:5]\n",
    "print y[:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "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": 80,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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LRugiIgGy69guhswbQnxMPNP7Tad62eoBeV+N0EVEgqxOQh3eH/E+LRNbcvVL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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110364090>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, y, 'o', xnew, ynew, '-')\n",
    "plt.show()"
   ]
  }
 ],
 "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": "2.7.11"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}