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  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Featured Recipe #2: Simulating a Physical System by Minimizing an Energy"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "> This is a featured recipe from the [**IPython Cookbook**](http://ipython-books.github.io/), the definitive guide to **high-performance scientific computing** and **data science** in Python."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Mathematical optimization is a wide area of applied mathematics. It consists in finding a best solution to a given problem. Many real-world problems can be expressed in an optimization framework."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In this recipe, we show how to find the equilibrium configuration of a physical system by minimizing its potential energy. More specifically, we consider a structure made of masses and springs, attached to a vertical wall and subject to gravity. Starting from an initial position, we want to find the equilibrium configuration where the gravity and elastic forces compensate."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## How to do it..."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "1. Let's import NumPy, SciPy and matplotlib."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "import scipy.optimize as opt\n",
      "import matplotlib.pyplot as plt\n",
      "%matplotlib inline"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "2. We define a few constants in the International System of Units."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "g = 9.81  # gravity of Earth\n",
      "m = .1  # mass, in kg\n",
      "n = 20  # number of masses\n",
      "e = .1  # initial distance between the masses\n",
      "l = e  # relaxed length of the springs\n",
      "k = 10000  # spring stiffness"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "3. We define the initial positions of the masses. They are arranged on a two-dimensional grid with two lines and $n/2$ columns."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "P0 = np.zeros((n, 2))\n",
      "P0[:,0] = np.repeat(e*np.arange(n//2), 2)\n",
      "P0[:,1] = np.tile((0,-e), n//2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "4. Now, let's define the connectivity matrix between the masses. Coefficient $i,j$ is $1$ if masses $i$ and $j$ are connected by a spring."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "A = np.eye(n, n, 1) + np.eye(n, n, 2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "5. We also specify the spring stiffness of each spring. It is $l$, except for *diagonal* springs where it is $l \\times \\sqrt{2}$."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "L = l * (np.eye(n, n, 1) + np.eye(n, n, 2))\n",
      "for i in range(n//2-1):\n",
      "    L[2*i+1,2*i+2] *= np.sqrt(2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "6. We also need the indices of the spring connections."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "I, J = np.nonzero(A)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "7. The `dist` function computes the distance matrix (distance between any pair of masses)."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "dist = lambda P: np.sqrt((P[:,0]-P[:,0][:, np.newaxis])**2 + \n",
      "                         (P[:,1]-P[:,1][:, np.newaxis])**2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "8. We define a function that displays the system. The springs are colored according to their tension."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def show_bar(P):\n",
      "    plt.figure(figsize=(5,4));\n",
      "    # Wall.\n",
      "    plt.axvline(0, color='k', lw=3);\n",
      "    # Distance matrix.\n",
      "    D = dist(P)\n",
      "    # We plot the springs.\n",
      "    for i, j in zip(I, J):\n",
      "        # The color depends on the spring tension, which\n",
      "        # is proportional to the spring elongation.\n",
      "        c = D[i,j] - L[i,j]\n",
      "        plt.plot(P[[i,j],0], P[[i,j],1], \n",
      "                 lw=2, color=plt.cm.copper(c*150));\n",
      "    # We plot the masses.\n",
      "    plt.plot(P[[I,J],0], P[[I,J],1], 'ok',);\n",
      "    # We configure the axes.\n",
      "    plt.axis('equal');\n",
      "    plt.xlim(P[:,0].min()-e/2, P[:,0].max()+e/2);\n",
      "    plt.ylim(P[:,1].min()-e/2, P[:,1].max()+e/2);\n",
      "    plt.xticks([]); plt.yticks([]);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "9. Here is the system in its initial configuration."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "show_bar(P0);\n",
      "plt.title(\"Initial configuration\");"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
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Wt73tbTnjjDOmvp93vvOdU99HFWtmubMtW7YcmuTa3bdt3Lgx++yz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\n1+NAX4sdWosdWosdWo8dWosdSmXC2Dr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       "text": [
        "<matplotlib.figure.Figure at 0x776d5f8>"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "10. To find the equilibrium state, we need to minimize the total potential energy of the system. The following function computes the energy of the system, given the positions of the masses. This function is explained in *How it works...*."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def energy(P):\n",
      "    # The argument P is a vector (flattened matrix).\n",
      "    # We convert it to a matrix here.\n",
      "    P = P.reshape((-1, 2))\n",
      "    # We compute the distance matrix.\n",
      "    D = dist(P)\n",
      "    # The potential energy is the sum of the\n",
      "    # gravitational and elastic potential energies.\n",
      "    return (g * m * P[:,1].sum() + \n",
      "            .5 * (k * A * (D - L)**2).sum())"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 10
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "11. Let's compute the potential energy of the initial configuration."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "energy(P0.ravel())"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 11,
       "text": [
        "-0.98099999999999998"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "12. Now, let's minimize the potential energy with a function minimization method. We need a **constrained optimization algorithm**, because we make the assumption that the two first masses are fixed to the wall. Therefore, their positions cannot change. The [**L-BFGS-B**](http://en.wikipedia.org/wiki/Limited-memory_BFGS#L-BFGS-B) algorithm, a variant of the BFGS algorithm, accepts bound constraints. Here, we force the first two points to stay at their initial positions, whereas there are no constraints on the other points. The `minimize` function accepts a `bounds` list containing, for each dimension, a pair of `[min, max]` values."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "bounds = np.c_[P0[:2,:].ravel(), P0[:2,:].ravel()].tolist() + \\\n",
      "         [[None, None]] * (2*(n-2))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 12
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "P1 = opt.minimize(energy, P0.ravel(),\n",
      "                  method='L-BFGS-B',\n",
      "                  bounds=bounds).x.reshape((-1, 2))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 13
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "13. Let's display the stable configuration."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "show_bar(P1);\n",
      "plt.title(\"Equilibrium configuration\");"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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6V9R3Ca9tvcHYQNtujLlvTv8tTonGBmMQzhf3E6bVqHQIoQfkRsLfbiUhzN+z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GJTKnWo8/ruWfrtT7i5eoeo0aTp1x5sxpDXy9n1q3DNHuXbtcnBDuRjEGAAAAAH/g5+enoUOH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\n+fj43PNZPj4+SkxM1Ec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       "text": [
        "<matplotlib.figure.Figure at 0x7764780>"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This configuration looks realistic. The tension appears to be maximal on the top springs near the wall."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## How it works..."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This example is conceptually simple. The state of the system is only described by the positions of the masses. If we can write a Python function that returns the total energy of the system, finding the equilibrium is just a matter of minimizing this function. This is the **principle of minimum total potential energy**, due to the second law of thermodynamics."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here, we give an expression of the total energy of the system. Since we are only interested in the *equilibrium*, we omit any kinetic aspect and we only consider potential energy due to gravity (**gravitational force**) and spring forces (**elastic potential energy**)."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Let $U$ be the total potential energy of the system. It is the sum of the gravitational potential energies of the masses, and the elastic potential energies of the springs. Therefore:"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "$$U = \\sum_{i=1}^n mgy_i + \\frac{1}{2} \\sum_{i,j=1}^n k a_{ij} \\left( ||\\mathbf{p}_i - \\mathbf{p}_j|| - l_{ij} \\right)^2$$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "where:\n",
      "\n",
      "* $m$ is the mass,\n",
      "* $g$ is the gravity of Earth,\n",
      "* $k$ is the stiffness of the springs,\n",
      "* $\\mathbf{p}_i = (x_i, y_i)$ is the position of mass $i$,\n",
      "* $a_{ij}$ is 1 if masses $i$ and $j$ are attached by a spring, $0$ otherwise,\n",
      "* $l_{ij}$ is the relaxed length of spring $(i,j)$, or $0$ if masses $i$ and $j$ are not attached."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The `energy` function implements this formula using vectorized computations on NumPy arrays."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## There's more..."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The following references contain details about the physics behind this formula:\n",
      "\n",
      "* [Potential energy](http://en.wikipedia.org/wiki/Potential_energy).\n",
      "* [Elastic potential energy](http://en.wikipedia.org/wiki/Elastic_potential_energy).\n",
      "* [Hooke's law, which is the linear approximation of the spring's response](http://en.wikipedia.org/wiki/Hooke%27s_law).\n",
      "* [Principle of minimum energy](http://en.wikipedia.org/wiki/Minimum_total_potential_energy_principle)."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "You will find related recipes on the [book's repository](https://github.com/ipython-books/cookbook-code)."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "> This was a featured recipe from the [IPython Cookbook](http://ipython-books.github.io/), by [Cyrille Rossant](http://cyrille.rossant.net), Packt Publishing, 2014."
     ]
    }
   ],
   "metadata": {}
  }
 ]
}