session2_numpy_scipy.ipynb

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   "source": [
    "from IPython.core.display import HTML\n",
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div><img src=\"https://raw.githubusercontent.com/ACM-SIAM-KAUST-chapter/python_tutorial_2017/gh-pages/images/acmchapterlogo.png\" width=\"260px\" style=\"float: left; margin-right: 3em\">\n",
    "<img src=\"https://raw.githubusercontent.com/ACM-SIAM-KAUST-chapter/python_tutorial_2017/gh-pages/images/siamchapterlogo.png\" width=\"260px\" style=\"float: right;\"></div>\n",
    "<h1 align=\"center\">Introduction to</h1>\n",
    "<h1 align=\"center\">NumPy &amp; Scipy:</h1>\n",
    "<h1 align=\"center\">the core numerical scientific packages</h1>\n",
    "\n",
    "<p><br style=\"clear: both;\"/></p><p><br style=\"clear: both;\"/></p><p><br style=\"clear: both;\"/></p>"
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   "source": [
    "<div style=\"color:#5f5c48\">\n",
    "This tutorial is prepared by ACM/SIAM Student Chapter of King Abdullah University of Science and Technology (KAUST).\n",
    "<br/>\n",
    "What we'll study here has been adapted from the following tutorials:\n",
    "<ul>\n",
    "<li>David Ketcheson's [Introduction to NumPy and Matplotlib](http://nbviewer.ipython.org/github/ketch/AMCS252/blob/master/2_Introduction_to_Numpy%20and_Matplotlib.ipynb)</li>\n",
    "<li>Software Carpentry's [Numerical analysis with NumPy](http://nbviewer.ipython.org/github/geocarpentry/2014-01-30-mit/blob/gh-pages/lessons/vignettes/Numerical%20analysis%20with%20NumPy.ipynb)</li>\n",
    "<li>J.R. Johansson's [Numpy - multidimensional data arrays](http://nbviewer.ipython.org/github/jrjohansson/scientific-python-lectures/blob/master/Lecture-2-Numpy.ipynb) and [SciPy - Library of scientific algorithms for Python](http://nbviewer.ipython.org/github/jrjohansson/scientific-python-lectures/blob/master/Lecture-3-Scipy.ipynb#SciPy---Library-of-scientific-algorithms-for-Python)</li>\n",
    "<li>Official [Tentative NumPy tutorial](http://www.scipy.org/Tentative_NumPy_Tutorial)</li>\n",
    "</ul>\n",
    "<br/>\n",
    "\n",
    "Current version is adapted from [KAUST Python Tutorials 2015](http://alshedivat.github.io/ACM-Python-Tutorials-KAUST-2015/) by Dmitry Kabanov.\n",
    "<br/><br/>\n",
    "\n",
    "Presented on 26 February, 2017.\n",
    "<br/><br/>\n",
    "\n",
    "**Prerequisites:** Introduction to Python, basic knowledge of numerical methods\n",
    "</div>"
   ]
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## NumPy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Python includes a package for numerical computation called numpy, which is an essential tool for scientific computing. \n",
    "It is based on multidimensional arrays (vectors and matrices) and provides a large library of functions and operators that work efficiently on these objects.\n",
    "In this way, any numerical algorithm is expressed as operations on arrays and in many cases runs almost as quickly as the equivalent C code.\n",
    "\n",
    "`Numpy` serves as a foundation library that makes Python a competitor to MATLAB for scientific computing.\n",
    "\n",
    "`NumPy` is used in: \n",
    "Numerical Analysis, Linear algebra, Solution of differential equations, Statistical analysis and many more...\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Why to use NumPy?\n",
    "\n",
    "Consider the following list and suppose we want to perform some simple algebraic operations:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
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   "outputs": [],
   "source": [
    "price = [5.99, 10.25, 2.0, 40.99, 5.60, 63.49]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
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    {
     "data": {
      "text/plain": [
       "[5.99, 10.25, 2.0, 40.99, 5.6, 63.49, 5.99, 10.25, 2.0, 40.99, 5.6, 63.49]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "price*2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "TypeError",
     "evalue": "can only concatenate list (not \"float\") to 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-4-ba6ebb983a2c>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mprice\u001b[0m\u001b[0;34m+\u001b[0m\u001b[0;36m0.5\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mTypeError\u001b[0m: can only concatenate list (not \"float\") to list"
     ]
    }
   ],
   "source": [
    "price+0.5"
   ]
  },
  {
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   "source": [
    "Clearly, if we wanted to double the value of each element and add half, this cannot be done easily. Instead, we would have to use a loop:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[12.48, 21.0, 4.5, 82.48, 11.7, 127.48]\n"
     ]
    }
   ],
   "source": [
    "for i in range(len(price)):\n",
    "    price[i] = price[i]*2\n",
    "    price[i] = price[i]+0.5\n",
    "print(price)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "However, it is slow (first) and requires too much code (second). It can be done more efficient using `NumPy`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Getting started\n",
    "\n",
    "We start, by importing the NumPy module. Import statements like this are the typical way of getting access to functions in Python. The most general way to import a module is the following:"
   ]
  },
  {
   "cell_type": "code",
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   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First example: compute $\\sin (3\\pi/2)$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "-1.0"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sin(3*np.pi/2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Second example: compute $e + \\pi$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.8598744820488378"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.exp(1) + np.pi"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Arrays"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In above examples we compute scalars.\n",
    "What makes NumPy brilliant is that it allows you make computations on multidimensional quantities (such as vectors and matrices) using thing called `ndarray` ($N$-dimensional array).\n",
    "Computer scientists call such a thing a *data structure*.\n",
    "We will consider only one-dimensional (vectors) and two-dimensional (matrices) arrays in this tutorial."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's create a 1D array $p$ as we did before and compute $2p + 0.5$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "numpy.ndarray"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "price = np.array([1, 2, 3, 4, 5])\n",
    "type(price)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  2.5,   4.5,   6.5,   8.5,  10.5])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "price = price*2+0.5\n",
    "price"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are other ways to create one-dimensional arrays:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Function `linspace` has three arguments: the value of the left point, the value of the right point and the number of points in total:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.  ,  0.25,  0.5 ,  0.75,  1.  ])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.linspace(0, 1, num=5)\n",
    "x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Another function, `arange` is very similar but it takes a step between points as the third argument:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.  ,  0.25,  0.5 ,  0.75])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y = np.arange(0, 1, 0.25)\n",
    "y"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice, that `arange` does not include the right point in the result!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Other functions that can be used to create an array:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.  0.  0.  0.  0.] \n",
      " [ 1.  1.  1.]\n"
     ]
    }
   ],
   "source": [
    "x = np.zeros(5)\n",
    "y = np.ones(3)\n",
    "print(x, '\\n', y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's compute $\\sin 2\\pi x$ and see its graph:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1108d5470>]"
      ]
     },
     "execution_count": 14,
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     "output_type": "execute_result"
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    {
     "data": {
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9ZJ8s4jeTEv1uNLsVBmN81JTkjvSMbcFTi3ZSWl7pdBxzEfIKS3lx6W6u7hnD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\nGGPMWawwGGOMOYsVBmOMMWf5/5ha1YBxnwKWAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10fa820b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(0, 1, num=21)\n",
    "y = np.sin(2*np.pi*x)\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "plt.figure()\n",
    "plt.plot(x, y, '-')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "### Exercise 1\n",
    "\n",
    "Change the inputs of the *linspace* and *arange* function until you understand exactly what they do. Using both ways, create a vector of starting from -1.5 to 4.5 inclusive with a step of 0.5. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# type your solution here"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Solution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# %load solutions/session2/1D_array.py\n",
    "x = np.linspace(-1.5,4.5,13)\n",
    "y = np.arange(-1.5,5,0.5)\n",
    "print (x)\n",
    "print (y)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can always find out what a function does by typing its name, followed by a question mark:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "np.arange?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Resize the help window (to get it out of your way) by dragging the divider. Double click on the divider to close it."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Multidimensional arrays\n",
    "\n",
    "We can create multidimensional arrays, like the following:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "A = \n",
      " [[  1.    2.4 -13. ]\n",
      " [  4.1   5.    0. ]\n",
      " [  7.2   8.    9. ]]\n",
      "(3, 3)\n"
     ]
    }
   ],
   "source": [
    "A = np.array([\n",
    "    [1, 2.4, -13],\n",
    "    [4.1, 5, 0],\n",
    "    [7.2, 8, 9]\n",
    "])\n",
    "print(\"A = \\n\", A)\n",
    "print(A.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To see all different attributes of the array object type its name followed by a fullstop and press *tap*. Note that some attributes are basically functions and require parentheses (with or without arguments), e.g. *transpose* and others don't, e.g. *ndim*:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[  1.    4.1   7.2]\n",
      " [  2.4   5.    8. ]\n",
      " [-13.    0.    9. ]]\n",
      "2\n"
     ]
    }
   ],
   "source": [
    "print(A.transpose())\n",
    "print(A.ndim)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also define the shape of the array:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.83140826,  0.57806063,  0.02359354,  0.8937764 ,  0.59164341],\n",
       "       [ 0.13891259,  0.31376313,  0.82242634,  0.80782011,  0.25030733],\n",
       "       [ 0.65847677,  0.95811486,  0.1987836 ,  0.7035087 ,  0.28968929],\n",
       "       [ 0.15904085,  0.97726721,  0.41033834,  0.49373835,  0.79527837],\n",
       "       [ 0.27062751,  0.15695301,  0.70117262,  0.25383595,  0.03348545]])"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.uniform(0, 1, size=(5,5)) # 5 x 5 matrix with elements from a uniform distribution"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Other ways to create matrices\n",
    "\n",
    "We can use functions `zeros` and `ones` (that we used before) to create matrices.\n",
    "Also we can use function `eye` to create an identity matrix and function `diag` to create a diagonal matrix:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.]]\n",
      "\n",
      "\n",
      "[[ 1.  1.  1.]\n",
      " [ 1.  1.  1.]]\n",
      "\n",
      "\n",
      "[[ 1.  0.  0.]\n",
      " [ 0.  1.  0.]\n",
      " [ 0.  0.  1.]]\n",
      "\n",
      "\n",
      "[[1 0 0]\n",
      " [0 2 0]\n",
      " [0 0 3]]\n"
     ]
    }
   ],
   "source": [
    "print(np.zeros((3,4)))\n",
    "print('\\n')\n",
    "print(np.ones((2,3)))\n",
    "print('\\n')\n",
    "print(np.eye(3))\n",
    "print('\\n')\n",
    "print(np.diag([1, 2, 3]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice how many parentheses we should use: to construct zero matrix of size $2\\times3$, we should pass the size as a *tuple*: `(2,`&nbsp;`3)`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Indexing and Slicing\n",
    "\n",
    "To index an element in an array, we use brackets `[]`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.array([1, 1, 2, 3, 5, 8, 13])\n",
    "x[4]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And with matrices we put comma between the index of a row and a column:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1 2 3]\n",
      " [4 5 6]\n",
      " [7 8 9]]\n",
      "1\n",
      "8\n"
     ]
    }
   ],
   "source": [
    "A = np.array([\n",
    "    [1, 2, 3],\n",
    "    [4, 5, 6],\n",
    "    [7, 8, 9]\n",
    "])\n",
    "print(A)\n",
    "print(A[0, 0])\n",
    "print(A[-1, 1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice, how the negative indices are used to index from the end instead of the beginning."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can index several elements simultaneously: this is called *slicing*."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1 2 3]\n",
      " [4 5 6]\n",
      " [7 8 9]]\n"
     ]
    }
   ],
   "source": [
    "print(A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 2])"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A[0, 0:2]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that the fundamental difference from MATLAB is that the indexing starts from zero and is exclusive of the second index. Hence, in the above example 1:3 refers to the second and third row and 0:2 to the first and second column."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can index in some clever ways too:  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1 2 3]\n",
      "[3 6 9]\n"
     ]
    }
   ],
   "source": [
    "print(A[0, :]) # row selection\n",
    "print(A[:, 2]) # column selection"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[2 3]\n",
      " [5 6]\n",
      " [8 9]]\n",
      "[7 8 9]\n"
     ]
    }
   ],
   "source": [
    "print(A[:, 1:]) # all rows, from 2nd column until the end\n",
    "print(A[-1, :]) # last row, all columns"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can change array's elements:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1 2 3]\n",
      " [4 5 6]\n",
      " [7 8 9]]\n",
      "\n",
      "[[ 1  2 23]\n",
      " [ 4  5 26]\n",
      " [ 7  8 29]]\n"
     ]
    }
   ],
   "source": [
    "print(A)\n",
    "print()\n",
    "A[:, 2] = [23, 26, 29]\n",
    "print(A)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There is an easy way to reverse a vector:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 1 2 3 4 5 6 7 8 9]\n",
      "[9 8 7 6 5 4 3 2 1 0]\n"
     ]
    }
   ],
   "source": [
    "a = np.arange(0, 10)\n",
    "print(a)\n",
    "print(a[: :-1]) # reverse a"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also index an array using boolean arrays:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[False False False False False False  True  True  True  True]\n",
      "[0 1 2 3 4 5 0 0 0 0]\n"
     ]
    }
   ],
   "source": [
    "b = a > 5\n",
    "print(b)\n",
    "a[b] = 0  # All elements of 'a' higher than 5 become 0\n",
    "print(a)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Follow-the-instructor example: computing derivatives numerically"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we will use the knowledge we obtained to compute a first derivative to $\\sin 2\\pi x$ numerically."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will use the finite-difference formula of the second order of accuracy:\n",
    "\n",
    "$$ y'(x_i) \\approx \\frac{y_{i+1} - y_{i-1}}{2\\Delta x} $$\n",
    "\n",
    "with formulas of the first order of accuracy at endpoints:\n",
    "\n",
    "$$ y'(x_0) \\approx \\frac{y_1 - y_0}{\\Delta x}, \\quad\n",
    "y'(x_N) \\approx \\frac{y_N - y_{N-1}}{\\Delta x} $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#follow the instructor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Other basic operations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can use array functions `min` or `max` to find minimum or maximum element in the array:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "x = np.array([np.pi, 1, 27, 34.0, 5, 44, 15])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.0\n",
      "44.0\n"
     ]
    }
   ],
   "source": [
    "print(x.min())\n",
    "print(x.max())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[12 15 78]\n",
      "[1 4 7]\n",
      "[[ 1  3 26]\n",
      " [ 4  9 35]\n",
      " [ 7 15 44]]\n"
     ]
    }
   ],
   "source": [
    "print(A.sum(axis=0))     # sum of each column\n",
    "print(A.min(axis=1))     # min of each row\n",
    "print(A.cumsum(axis=1))  # cumulative sum along each row"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In Python *axis* refers to the dimensions of arrays; *axis=0* refers to the colums and *axis=1* to the rows."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "### Exercise 2\n",
    "\n",
    "1. Create a vector with values ranging from 10 to 99\n",
    "2. Find indices of non-zero elements from [1,2,0,0,4,0]. Hint: use <em>np.nonzero</em>\n",
    "3. Declare a 8x8 zero matrix and set all the elements in the first column to value 3.\n",
    "4. Create a 4x4 array with numbers from a normal distribution with mean = 3 and standard deviation = 1.5. Hint: use <em>np.random.normal</em>. Sum the values of each row and store the result in a new array."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# type your solution here"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Solution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Part 1:\n",
      "[10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34\n",
      " 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59\n",
      " 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84\n",
      " 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99]\n",
      "\n",
      "Part 2:\n",
      "[0 1 4]\n",
      "\n",
      "Part 3:\n",
      "[[ 0.  1.  0.  1.  0.  1.  0.  1.]\n",
      " [ 1.  0.  1.  0.  1.  0.  1.  0.]\n",
      " [ 0.  1.  0.  1.  0.  1.  0.  1.]\n",
      " [ 1.  0.  1.  0.  1.  0.  1.  0.]\n",
      " [ 0.  1.  0.  1.  0.  1.  0.  1.]\n",
      " [ 1.  0.  1.  0.  1.  0.  1.  0.]\n",
      " [ 0.  1.  0.  1.  0.  1.  0.  1.]\n",
      " [ 1.  0.  1.  0.  1.  0.  1.  0.]]\n",
      "\n",
      "Part 4:\n",
      "[[ 1  4  9]\n",
      " [ 2  8 18]\n",
      " [ 3 12 27]\n",
      " [ 4 16 36]\n",
      " [ 5 20 45]]\n",
      "\n",
      "Part 5:\n",
      "[[ 0.96015636  2.55634018  4.17590916  2.91010113]\n",
      " [ 5.64964804  3.27467046  4.3661072   0.84234394]\n",
      " [ 0.36539678  4.7330197   3.91428631  1.39736621]\n",
      " [ 5.38352132  0.61407006  4.02491362  1.86491946]]\n",
      "[ 10.60250683  14.13276963  10.41006901  11.88742445]\n"
     ]
    }
   ],
   "source": [
    "# %load solutions/session2/array_operations.py\n",
    "print('Part 1:')\n",
    "print(10+np.arange(90))\n",
    "\n",
    "print('\\nPart 2:')\n",
    "print(np.nonzero([1,2,0,0,4,0])[0])\n",
    "\n",
    "print('\\nPart 3:')\n",
    "chess = np.zeros((8,8))\n",
    "chess[1::2,::2] = 1\n",
    "chess[::2,1::2] = 1\n",
    "print(chess)\n",
    "\n",
    "print('\\nPart 4:')\n",
    "print(np.fromfunction(lambda i, j: (i +1)* (j+1)**2, (5, 3), dtype=int))\n",
    "\n",
    "print('\\nPart 5:')\n",
    "normal_dist = np.random.normal(3, 1.5, (4,4))\n",
    "print(normal_dist)\n",
    "print(normal_dist.sum(axis=1))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's work with some real data. Ensure that the <em>stockholm_temp.txt</em> in the same directory with this notebook. \n",
    "This file contains the [daily average temperatures](http://bolin.su.se/data/stockholm/homogenized_daily_mean_temperatures.php)\n",
    "according to observations of Stockholm for the years 1756 - 2012.\n",
    "The following code checks if the file exists, opens it, prints the first lines and stores the data in an array."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[  1.75600000e+03   1.00000000e+00   1.00000000e+00  -8.70000000e+00]\n",
      " [  1.75600000e+03   1.00000000e+00   2.00000000e+00  -9.20000000e+00]\n",
      " [  1.75600000e+03   1.00000000e+00   3.00000000e+00  -8.60000000e+00]]\n"
     ]
    }
   ],
   "source": [
    "filename = 'data/session2/stockholm_temp.txt'\n",
    "data = np.loadtxt(filename) # alternative we can use getfromtxt command\n",
    "    \n",
    "# Print first three lines of data.\n",
    "print(data[0:3, :])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since the data are in the form\n",
    "\n",
    "- Year\n",
    "- Month\n",
    "- Day\n",
    "- Temperature\n",
    "\n",
    "we would like to express them in a better way. We define a `dtype`, that is the data type for each column: int, int, int, float:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([(1756, 1,  1, -8.7), (1756, 1,  2, -9.2), (1756, 1,  3, -8.6),\n",
       "       (1756, 1,  4, -7.7), (1756, 1,  5, -7.2), (1756, 1,  6, -1.6),\n",
       "       (1756, 1,  7,  0.7), (1756, 1,  8,  1.3), (1756, 1,  9,  2.4),\n",
       "       (1756, 1, 10,  0.8)], \n",
       "      dtype=[('Year', '<i2'), ('Month', 'i1'), ('Day', 'i1'), ('Temp', '<f8')])"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dt = np.dtype([('Year', 'int16'), ('Month', 'int8'), ('Day', 'int8'), ('Temp', 'float64')])\n",
    "data = np.loadtxt(filename, dtype=dt)\n",
    "data[:10] # first 10 entries of our data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can now look for the example only on the temperatures:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-8.7, -9.2, -8.6, ...,  0.2,  2.6,  2.2])"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data['Temp']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and plot temperature in July 2012:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([(2012, 7,  1,  17.7), (2012, 7,  2,  16.3), (2012, 7,  3,  17.7),\n",
       "       (2012, 7,  4,  17.4), (2012, 7,  5,  16.4), (2012, 7,  6,  17.2),\n",
       "       (2012, 7,  7,  19.7), (2012, 7,  8,  17.9), (2012, 7,  9,  19.3),\n",
       "       (2012, 7, 10,  17.2), (2012, 7, 11,  16.5), (2012, 7, 12,  16.9),\n",
       "       (2012, 7, 13,  14.9), (2012, 7, 14,  15.2), (2012, 7, 15,  15. ),\n",
       "       (2012, 7, 16,  16.1), (2012, 7, 17,  14. ), (2012, 7, 18,  14.6),\n",
       "       (2012, 7, 19,  14.9), (2012, 7, 20,  15.5), (2012, 7, 21,  13.6),\n",
       "       (2012, 7, 22,  16.3), (2012, 7, 23,  15.9), (2012, 7, 24,  20.3),\n",
       "       (2012, 7, 25,  20.6), (2012, 7, 26,  17.9), (2012, 7, 27,  16.4),\n",
       "       (2012, 7, 28,  19.2), (2012, 7, 29,  18.6), (2012, 7, 30,  17. ),\n",
       "       (2012, 7, 31,  13.9)], \n",
       "      dtype=[('Year', '<i2'), ('Month', 'i1'), ('Day', 'i1'), ('Temp', '<f8')])"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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DePDVs2ovhWmA2xtUrcJFUmTQYdOK8rh59L5x5cbmxiNdCiM1C2pBxgGdiAwA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\nCA7ojDFWIDigM8ZYgfj/AdbSXcAoKs/VAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110877908>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "years = data['Year']\n",
    "temp = data['Temp']\n",
    "\n",
    "\n",
    "plot_data = data[(data['Year'] == 2012) & (data['Month'] == 7)]\n",
    "\n",
    "plt.figure()\n",
    "plt.plot(plot_data['Day'], plot_data['Temp'], '-')\n",
    "plot_data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "### Exercise 3\n",
    "\n",
    "Make an array with the temperatures of the 5th day of every month in 2000."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# type your solution here"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Solution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3084\n",
      "[-7.2 -1.2 -1.  ...,  8.5  3.9 -4.2]\n"
     ]
    }
   ],
   "source": [
    "# %load solutions/session2/temperatures.py\n",
    "day = 5\n",
    "indices = np.where(data['Day'] == day) # find indices of 5th day for every month (over all data)\n",
    "temp = data['Temp'][indices] # find corresponding temperatures\n",
    "print(temp.size)\n",
    "print(temp)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Linear algebra\n",
    "\n",
    "Handling *ndarrays* is really powerful. Of the many things one can do with NumPy's arrays is linear algebra:  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.51551471  0.13270754  0.55979456  0.24638503  0.86521711  0.27927764\n",
      "  0.49640099  0.81195922  0.71634199  0.21532327]\n"
     ]
    }
   ],
   "source": [
    "x = np.random.random(10)\n",
    "print(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can find $L_\\infty$-norm of this vector:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.86521710548285347"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.norm(x, np.inf) # maximum norm of a vector"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can use this module to solve a linear system of equations\n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "x + 2y &= 12, \\\\\n",
    "3x + 4y &= 29\n",
    "\\end{align}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1 2]\n",
      " [3 4]]\n",
      "[12 29]\n"
     ]
    }
   ],
   "source": [
    "A = np.array([[1, 2],[3, 4]])\n",
    "b = np.array([12, 29])\n",
    "print(A)\n",
    "print(b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "14.9330343737\n",
      "[ 5.   3.5]\n"
     ]
    }
   ],
   "source": [
    "print(np.linalg.cond(A))\n",
    "x = np.linalg.solve(A,b)\n",
    "print(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To check that the solution is correct (that is, that $x$ that we computed satisfies $Ax = b$), we do matrix-vector multiplication. For that, function `dot` should be used:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 12.,  29.])"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.dot(A, x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and inner products of two vectors are computed with the same function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "11"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.array([1, 2])\n",
    "y = np.array([3, 4])\n",
    "np.dot(x, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also solve eigenvalue problems using function `linalg.eig`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-0.37228132  5.37228132]\n",
      "[[-0.82456484 -0.41597356]\n",
      " [ 0.56576746 -0.90937671]]\n"
     ]
    }
   ],
   "source": [
    "lamda, V = np.linalg.eig(A)\n",
    "print(lamda)\n",
    "print(V)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "### Exercise 4\n",
    "\n",
    "Create a diagonal matrix using the *lamda* variable and then multiply from the left with V and from the right with the inverse of V (use *np.linalg.inv()*). What do you find?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# type your solution here"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Solution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# %load solutions/session2/linear_algebra.py\n",
    "print(np.dot(np.dot(V,np.diag(lamda)),np.linalg.inv(V)))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p></br></p>\n",
    "<p></br></p>\n",
    "<p></br></p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## SciPy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`NumPy` is complemented by `SciPy`; a library that adds more MATLAB-like features to Python.\n",
    "\n",
    "`SciPy` consists of several subpackages that can be used for linear algebra, image and signal processing, statistics, numerical integration of differential equations and more.\n",
    "\n",
    "Here we'll study only a couple of subpackages to get the idea of how useful `SciPy` is."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Getting started\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is customary to import subpackages of `SciPy` in the following manner:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Integration\n",
    "\n",
    "Subpackage `scipy.integrate` contains functions to compute quadratures and to solve ordinary differential equations.\n",
    "\n",
    "The numerical evaluation of the definite integral of a function is called numerical quadrature, or simply quadature. \n",
    "SciPy provides a series of functions for different kind of quadrature, for example the quad, dblquad and tplquad for single, double and triple integrals, respectively.\n",
    "\n",
    "Let's compute the Gauss integral numerically:\n",
    "\n",
    "$$ \\int_{-\\infty}^{+\\infty} \\exp(-x^2) \\, dx = \\sqrt \\pi $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from scipy import integrate, special"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "integral value = 1.7724538509055159 , absolute error = 7.768296244985151e-09 analytic value =  1.77245385091\n"
     ]
    }
   ],
   "source": [
    "xl = -1000  # the lower limit of x\n",
    "xu = +1000  # the upper limit of x\n",
    "\n",
    "def f(x):\n",
    "    return np.exp(-x**2)\n",
    "\n",
    "val, abserr = integrate.quad(f, xl, xu)\n",
    "\n",
    "print(\"integral value =\", val, \", absolute error =\", abserr, 'analytic value = ', np.sqrt(np.pi))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can pass extra arguments to integrand function, by using the `args` keyword argument.\n",
    "For example we can use `args=(3,)` for the third order Bessel function."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "### Exercise 5\n",
    "\n",
    "Compute the integral\n",
    "\n",
    "$$ \\int_{-1}^{1} x \\, dx $$\n",
    "\n",
    "and compare with the analytic value."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# type your solution here"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Solution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# %load solutions/session2/bessel_integral.py\n",
    "def integrand(x, n):\n",
    "    \"\"\"\n",
    "    Bessel function of first kind and order n. \n",
    "    \"\"\"\n",
    "    return special.jv(n, x)\n",
    "\n",
    "xl = 0  # the lower limit of x\n",
    "xu = 10 # the upper limit of x\n",
    "\n",
    "val, abserr = integrate.quad(integrand, xl, xu, args=(0,))\n",
    "\n",
    "print(val, abserr)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "### Example of integration of system of ordinary differential equations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will have a look at the Lotka-Volterra model, also known as the predator-prey equations,\n",
    "which is a pair of first order, non-linear, differential equations frequently used to describe\n",
    "the dynamics of biological systems in which two species interact, one a predator and the other its prey.\n",
    "The model was proposed independently by Alfred J. Lotka in 1925 and Vito Volterra in 1926,\n",
    "and can be described by\n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "\\frac{du}{dt} &= \\phantom{-}au - \\phantom{d}buv, \\\\\n",
    "\\frac{dv}{dt} &= -cv + dbuv, \\\\\n",
    "\\end{align}\n",
    "$$\n",
    "where\n",
    "*  $u(t)$: number of preys (for example, rabbits)\n",
    "\n",
    "*  $v(t)$: number of predators (for example, foxes)\n",
    "\n",
    "*  $a$, $b$, $c$, $d$ are constant parameters defining the behavior of the population:\n",
    "\n",
    "  + $a$ is the natural growing rate of rabbits, when there's no fox\n",
    "\n",
    "  + $b$ is the natural dying rate of rabbits, due to predation\n",
    "\n",
    "  + $c$ is the natural dying rate of fox, when there's no rabbit\n",
    "\n",
    "  + $d$ is the factor describing how many caught rabbits let create a new fox"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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E2Nf5tcjycp2HfSerKahqYkkvE9PNxeS4EKoa2zhWfnb4wdKoUXi9Y8u/my8ztI16S1+b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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110c67b00>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a = 1.0\n",
    "b = 0.1\n",
    "c = 1.5\n",
    "d = 0.75\n",
    "\n",
    "def dy_dt(t, y):\n",
    "    \"\"\"Compute right-hand side of Lotka--Volterra system.\"\"\"\n",
    "    u, v = y[0], y[1]\n",
    "    return np.array([\n",
    "         a*u -   b*u*v,\n",
    "        -c*v + d*b*u*v\n",
    "    ])\n",
    "\n",
    "# Initial value.\n",
    "y0 = [10, 5]\n",
    "t0 = 0.0\n",
    "dt = 0.1\n",
    "tfinal = 10\n",
    "\n",
    "# Two lists that will hold the solution.\n",
    "times = np.linspace(0, tfinal, num=101)\n",
    "u = [y0[0]]\n",
    "v = [y0[1]]\n",
    "\n",
    "s = integrate.ode(dy_dt)\n",
    "s.set_integrator('dopri5')\n",
    "s.set_initial_value(y0, t0)\n",
    "\n",
    "for t in times[1:]:\n",
    "    s.integrate(t)\n",
    "    u.append(s.y[0])\n",
    "    v.append(s.y[1])\n",
    "    \n",
    "plt.figure()\n",
    "plt.plot(times, u, '-', label='Rabbits')\n",
    "plt.plot(times, v, '--', label='Foxes')\n",
    "plt.legend(loc='best');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Interpolation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `interpolate.interp1d` function accepts array of points $(X, Y)$ and returns a new function that can find interpolated values from this array.\n",
    "You can use an options for interpoland kinds such as linear, quadratic and cubic spline interpolation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from scipy import interpolate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "x = np.linspace(0, 1, num=11)\n",
    "y = np.sin(2 * np.pi * x)\n",
    "\n",
    "f1 = interpolate.interp1d(x, y) # linear interpolation\n",
    "f3 = interpolate.interp1d(x, y, kind='cubic')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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zitOpREQkh9HiL3lccswuxs7sQLczsfg8NBNKN3A6kkjuFLOHC5Pv4wXfNFZ6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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x111eab588>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# new points where we want to evaluate the interpoland\n",
    "xnew = np.linspace(0, 1, num=101)\n",
    "\n",
    "plt.figure(figsize=(12,4))\n",
    "plt.plot(x, y,'o', label='Given')\n",
    "plt.plot(xnew, f1(xnew), '-', label='linear')\n",
    "plt.plot(xnew, f3(xnew), '--', label='cubic')\n",
    "plt.legend(loc='best');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fast Fourier Transform"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When you need to study the spectrum of a signal (function of time), you can use Fourier Transform for this.\n",
    "The implementation of the Fourier transform, known as Fast Fourier Transform, can be used with the help of subpackage `scipy.fftpack`.\n",
    "\n",
    "Let's apply Fast Fourier Transform to the signal:\n",
    "\n",
    "$$ y(t) = \\sin 2\\pi f t + \\text{normal noise},$$\n",
    "\n",
    "where $f = 4$.\n",
    "\n",
    "Suppose, that the signal is sampled with sampling rate 50 times per unit time (time step is 0.02).\n",
    "Hence, we can compute the spectrum with upper bound of frequency being 25."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from scipy import fftpack"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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cPRnXvOkIAFFaWWSvAPdZqrzfJA9xf28JrZ7Rm7GDc4heam+xHMlg7ZRKWZpk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\nqCiKoiiACkRFURRFAeD/ASkvgkMg5FoXAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11156b7b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "f0 = 4\n",
    "timestep = 0.02\n",
    "tfinal = 10.0\n",
    "\n",
    "# Create the oscillator\n",
    "time = np.arange(0, tfinal, timestep)\n",
    "y = np.sin(2*np.pi*f0 * time)\n",
    "y = y + np.random.normal(size=len(y))\n",
    "\n",
    "# Use an FFT to calculate its spectrum\n",
    "yhat = fftpack.rfft(y)\n",
    "\n",
    "# Find the positive frequencies\n",
    "frequency = fftpack.rfftfreq(y.size, d=timestep)\n",
    "spectrum = 2*timestep*np.abs(yhat)\n",
    "\n",
    "# Create a figure\n",
    "fig, (ax1, ax2) = plt.subplots(2, 1)\n",
    "\n",
    "# Create x-y plots of the amplitude and transform with labeled axes\n",
    "\n",
    "ax1.set_xlabel('Time')\n",
    "ax1.set_ylabel('Signal')\n",
    "ax1.plot(time, y)\n",
    "\n",
    "ax2.set_xlabel('Frequency')\n",
    "ax2.set_ylabel('Power spectrum')\n",
    "ax2.plot(frequency, spectrum, '-')\n",
    "\n",
    "fig.tight_layout(pad=0.1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Sparse matrices\n",
    "\n",
    "Sparse matrices are often useful in numerical analysis dealing with large systems.\n",
    "Whenever the problem involves vectors or matrices with mostly zero values then one should take advantage of the sparsity.\n",
    "SciPy has an extensive library for sparse matrices, with basic linear algebra operations (such as equation solving, eigenvalue calculations, etc)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To create a sparse matrix we have to choose the format that will be stored in:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from scipy import sparse"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  10. ,    0. ,    0. ,    0. ],\n",
       "       [   0. ,    0.3,    0. ,    0. ],\n",
       "       [   0. ,    2. ,    1.5,    0. ],\n",
       "       [  -3. ,    0. ,    0. ,  100. ]])"
      ]
     },
     "execution_count": 98,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# dense matrix\n",
    "M = np.array([[10,0,0,0], [0,.3,0,0], [0,2,1.5,0], [-3,0,0,100]])\n",
    "M"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<4x4 sparse matrix of type '<class 'numpy.float64'>'\n",
       "\twith 6 stored elements in Compressed Sparse Row format>"
      ]
     },
     "execution_count": 99,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# convert from dense to sparse\n",
    "M_sparse = sparse.csr_matrix(M); # or csc_matrix(M)\n",
    "M_sparse "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can go back to the dense form:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  (0, 0)\t10.0\n",
      "  (1, 1)\t0.3\n",
      "  (2, 1)\t2.0\n",
      "  (2, 2)\t1.5\n",
      "  (3, 0)\t-3.0\n",
      "  (3, 3)\t100.0\n",
      "[[  10.     0.     0.     0. ]\n",
      " [   0.     0.3    0.     0. ]\n",
      " [   0.     2.     1.5    0. ]\n",
      " [  -3.     0.     0.   100. ]]\n"
     ]
    }
   ],
   "source": [
    "print(M_sparse)\n",
    "print(M_sparse.todense())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The easiest way to create a sparse matrix is to use the `lil_matrix` function.\n",
    "It creates an empty matrix and then we allocating non-zero entries by using matrix indexing.\n",
    "This way we avoid creating large dense matrices."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<4x4 sparse matrix of type '<class 'numpy.float64'>'\n",
       "\twith 6 stored elements in LInked List format>"
      ]
     },
     "execution_count": 101,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = sparse.lil_matrix((4,4)) # empty 4x4 sparse matrix\n",
    "A[0,0] = 1\n",
    "A[1,1] = 3\n",
    "A[2,2] = A[2,1] = 1\n",
    "A[3,3] = A[3,0] = 1\n",
    "A"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also change the format based on the sparsity:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<4x4 sparse matrix of type '<class 'numpy.float64'>'\n",
       "\twith 6 stored elements in Compressed Sparse Row format>"
      ]
     },
     "execution_count": 102,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = sparse.csr_matrix(A); A # if the rows are sparse"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<4x4 sparse matrix of type '<class 'numpy.float64'>'\n",
       "\twith 6 stored elements in Compressed Sparse Column format>"
      ]
     },
     "execution_count": 103,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = sparse.csc_matrix(A); A # if the columns are sparse"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "### Exercise 6\n",
    "\n",
    "Construct a $10000 \\times 10000$ `lil_matrix` $A$ and add values to it by setting all rows and columns $2000$ to $3000$ into random values. Also set random diagonal entries (you can do this without a loop!). Then use the `spy` function from `matplotlib.pyplot` to \"spy\" the matrix.\n",
    "\n",
    "Using a vector $b$ with $10000$ random values solve the system $A x = b$. \n",
    "To do so use the direcet solver `linsolve` from `scipy.sparse.linalg.dsolve`.\n",
    "Change to different sparse formats (CSR and CSC) and measure the time needed to solve the system. You can use the `time` package."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# type your solution here"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Solution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    },
    {
     "data": {
      "image/png": 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PWTg8meumSyZmYrz4/OK841MWDo9VluNTXg6PVdr2dSu4afnlo9Ycn85zeKzydqy/1vEp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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1121042e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "residual: 1.48698589756e-12\n",
      "0.010876178741455078\n"
     ]
    }
   ],
   "source": [
    "# %load solutions/session2/sparse_matrices.py\n",
    "\"\"\"\n",
    "Construct a 1000x1000 lil_matrix and add some values to it, convert it\n",
    "to CSC format and solve A x = b for x with a direct solver.\n",
    "\"\"\"\n",
    "%pylab inline --no-import-all\n",
    "from matplotlib import pyplot as plt\n",
    "import numpy as np\n",
    "import scipy.sparse as sps\n",
    "from scipy.sparse.linalg.dsolve import linsolve\n",
    "import time\n",
    "\n",
    "rand = np.random.rand\n",
    "\n",
    "A = sps.lil_matrix((10000, 10000), dtype=np.float64)\n",
    "A[0::100, 2000:3000] = rand(1000)\n",
    "A.setdiag(rand(10000))\n",
    "\n",
    "A = A.tocsc() # Compressed Sparse Column format\n",
    "\n",
    "# Spy matrix\n",
    "plt.spy(A, marker='.', markersize=2)\n",
    "plt.show()\n",
    "\n",
    "b = rand(10000) # random rhs\n",
    "\n",
    "t1 = time.time() # initial time\n",
    "x = linsolve.spsolve(A, b) # solve system\n",
    "t2 = time.time() # final time\n",
    "print('residual:', np.linalg.norm(A * x - b))\n",
    "print(t2-t1)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## References:\n",
    "\n",
    "#### NumPy:\n",
    "\n",
    "- [NumPy tutorial](http://www.scipy.org/Tentative_NumPy_Tutorial) \n",
    "- [NumPy tutorial video](http://showmedo.com/videotutorials/series?name=i9KuJuNcG) \n",
    "- [NumPy: lock 'n load](http://mentat.za.net/numpy/intro/intro.html)\n",
    "- [NumPy for Matlab users](http://www.scipy.org/NumPy_for_Matlab_Users)\n",
    "\n",
    "\n",
    "#### SciPy\n",
    "- [SciPy getting started](http://www.scipy.org/getting-started.html)\n",
    "- [SciPy tutorial](https://docs.scipy.org/doc/scipy-0.14.0/reference/tutorial/index.html)\n",
    "\n",
    "#### More general\n",
    "\n",
    "- [General Python tutorial](http://docs.python.org/tutorial/)\n",
    "- [Dive Into Python](http://diveintopython.org/)\n",
    "- [Hans Petter Langtangen book 1 (short)](https://link.springer.com/book/10.1007/978-3-319-32428-9)\n",
    "- [Hans Petter Langtangen book 2 (long)](http://link.springer.com/book/10.1007/978-3-662-49887-3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Other packages\n",
    "Besides NumPy and Scipy, there are many other useful Python packages for scientific computing. Here is a short list:  \n",
    "\n",
    "- [matplotlib](http://www.matplotlib.org/) - plotting and visualization\n",
    "- [sympy](http://sympy.org/) - symbolic computation\n",
    "- [mpi4py](http://mpi4py.scipy.org/) - parallel computing\n",
    "- [petsc4py](http://code.google.com/p/petsc4py/), [pytrilinos](http://trilinos.sandia.gov/packages/pytrilinos/) - Python bindings for the \"big 2\" parallel scientific libraries\n",
    "- [pyCUDA](http://mathema.tician.de/software/pycuda), [pyOpenCL](http://mathema.tician.de/software/pyopencl) - GPGPU computing\n",
    "- [FENiCS](http://fenicsproject.org/), [FiPy](http://www.ctcms.nist.gov/fipy/), [PyClaw](http://numerics.kaust.edu.sa/pyclaw/) - solve complicated PDEs with very sophisticated numerical methods\n",
    "- [networkX](http://networkx.github.com/), [pygraphviz](http://networkx.lanl.gov/pygraphviz/) - graphs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Copyright 2017, ACM/SIAM Student Chapter of King Abdullah University of Science and Technology*"
   ]
  }
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