Astro585_Lab2_Robert_M.ipynb

{
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  "language": "Julia",
  "name": ""
 },
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  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "#Robert Morehead\n",
      "# Astro 585 Lab/Homework #2 (Assertions, Benchmarking, Plotting)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<b>Benchmarking.</b>  Julia provides several tools for measuring code performance.  Perhaps the simplest way is using the @time or @elapsed macro which can be placed prior to a command, like \u201c@time randn(1000)\u201d.  The @time macro prints the time, but returns the value of the following expression.  The @elapsed macro discards the following expression\u2019s return value and returns the elapsed time evaluating the expression.  For finer control, you can investigate the tic(), toc() and toq() functions (see here in the Julia manual for details).\n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Q1:  For several common mathematical functions, calculate how many million evaluations your computer performs per second.  Try at least three arithmatic operations, two trig functions, and a logarithm.   For example, \n",
      "<code>\n",
      "N = 1000000;\n",
      "println(\"rand:  \", 1./(@elapsed x = rand(N)));\n",
      "println(\u201c.+:    \u201c,1./(@elapsed x.+x));\n",
      "</code>"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "N = 1000000\n",
      "x = rand(N)\n",
      "println(\".+ \",1./(@elapsed 1.+x))\n",
      "println(\"+ \",1./(@elapsed x+x))\n",
      "println(\".* \",1./(@elapsed x.*x))\n",
      "println(\"sin \",1./(@elapsed sin(x)))\n",
      "println(\"tan \",1./(@elapsed tan(x)))\n",
      "println(\"log \",1./(@elapsed log(x)))\n",
      "println(\"sin(tan(log(x+x))) \",1./(@elapsed sin(tan(log(x+x)))))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        ".+ 87"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        ".82926202253049\n",
        "+ 60.48602700193023\n",
        ".* "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "1.975328943479492\n",
        "sin 31.21724627987978\n",
        "tan 23.402748381325505\n",
        "log "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "25.063268461741398\n",
        "sin(tan(log(x+x))) "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "7.8100949788774425\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Q2:  For the text below, we\u2019ll consider the log_likelihood function and synthetic data from Lab/HW \\#1, which was probably very similar to the following.\n",
      "<code>"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "srand(42);\n",
      "Nobs = 100;\n",
      "z = zeros(Nobs);\n",
      "sigma = 2. * ones(Nobs);\n",
      "y = z + sigma .* randn(Nobs);\n",
      "\n",
      "normal_pdf(z, y, sigma) = exp(-0.5*((y-z)/sigma)^2)/(sqrt(2*pi)*sigma);\n",
      "\n",
      "function log_likelihood(y::Array, sigma::Array, z::Array)\n",
      "   n = length(y);\n",
      "   sum = zero(y[1]);\n",
      "   for i in 1:n\n",
      "    sum = sum + log(normal_pdf(y[i],z[i],sigma[i]));\n",
      "   end;\n",
      "   return sum;\n",
      "end\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 3,
       "text": [
        "log_likelihood (generic function with 1 method)"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "2a)  Write a function, calc_time_log_likelihood(Nobs::Int, M::Int = 1), that takes one required argument (the number of observations) and one optional argument (the number of times to repeat the calculation), initializes the y, sigma and z arrays with the same values each call (with the same Nobs), and returns the time required to evaluate the log_likelihood function M times.  \n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "function calc_time_log_likelihood(Nobs::Int, M::Int=1)\n",
      "    #Let's steal Eric's code to iniatialize the dummy arrays\n",
      "    srand(42);\n",
      "    z = zeros(Nobs);\n",
      "    sigma = 2. * ones(Nobs);\n",
      "    y = z + sigma .* randn(Nobs)\n",
      "\n",
      "  return @elapsed  [log_likelihood(y,sigma,z) for i in 0:M ] #I still love list comprehensions so, so much!\n",
      "    \n",
      "  \n",
      "  \n",
      "end"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 4,
       "text": [
        "calc_time_log_likelihood (generic function with 2 methods)"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "2b) Time how long it takes to run log_likelihood using Nobs=100 and M = 1.  Time it again.  Compare the two.  Why was there such a big difference?  \n",
      "\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "println(calc_time_log_likelihood(100,1))\n",
      "println(calc_time_log_likelihood(100,1))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "3"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        ".2314e-5\n",
        "1.5795e-5\n"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "__It was a pretty big difference the very first time I ran it. Then I ran the cell again and Julia is to smart (I even restarted the kernal), so it doesn't look like there was a big difference. But the first time the function was called it had to compile incresing the overhead, for the subsecant calls it was already compiled in memory and is just evauluated.__ "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "2c)  If you were only calling this function a few times, then speed wouldn\u2019t matter.  But if you were calling it with a very large number of observations or many times, then the performance could be important.  Plot the run time versus the size of the array.  The following example demonstrates how to use the PyPlot module, \u201ccomprehensions\u201d to construct arrays easily, and the map function to apply a function to an array of values.  "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "using PyPlot\n",
      "n_list = [ 2^i for i=1:10 ]\n",
      "elapsed_list = map(calc_time_log_likelihood,n_list)\n",
      "plot(log10(n_list), log10(elapsed_list), color=\"orange\", linewidth=2, marker=\"^\", markersize=12);\n",
      "xlabel(\"log N\"); ylabel(\"log (Time/s)\");"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "Figure(PyObject <matplotlib.figure.Figure object at 0x10f78e910>)"
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      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": [
        "Warning: Possible conflict in library symbol dtrtri_\n",
        "Warning: Possible conflict in library symbol dgetri_\n",
        "Warning: Possible conflict in library symbol dgetrf_\n"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "2d) Does the run time increase linearly with the number of observations?  If not, try to explain the origin of the non-linearity.  What does this imply for how you will go about future timing.\n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "__No, it is nonlinear until N ~ 15, then it becomes linear. I am not sure why.__ "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<b>Assertions:</b>  Sometimes a programmer calls a function with arguments that either don\u2019t make sense or represent a case that the function was not originally designed to handle properly.  The worst possible function behavior in such a case is returning an incorrect result without any warning that something bad has happened.  Returning an error at the end is better, but can make it difficult to figure out the problem.  Generally, the earlier the problem is spotted, the easier it will be to fix the problem.  Therefore, good developers often include assertions to verify that the function arguments are acceptable.   "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "2e) Time your current function with Nobs = 100 & M = 100.  Then add @assert statements to check that the length of the y, z and sigma arrays match.  Retime with the same parameters and compare.  What does this imply for your future decisions about how often to insert assert statements in your codes?\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "Nobs = 100\n",
      "M = 100\n",
      "println(\"Original: \",calc_time_log_likelihood(Nobs,M))\n",
      "\n",
      "\n",
      "\n",
      "\n",
      "\n",
      "function asserted_log_likelihood(y::Array, sigma::Array, z::Array)\n",
      "   n = length(y);\n",
      "   sum = zero(y[1]);\n",
      "   @assert y == sigma & sigma == z\n",
      "   for i in 1:n\n",
      "    sum = sum + log(normal_pdf(y[i],z[i],sigma[i]));\n",
      "   end;\n",
      "   return sum;\n",
      "end\n",
      "\n",
      "\n",
      "function asserted_calc_time_log_likelihood(Nobs::Int, M::Int=1)\n",
      "    #Let's steal Eric's code to iniatialize the dummy arrays\n",
      "    srand(42);\n",
      "    z = zeros(Nobs);\n",
      "    sigma = 2. * ones(Nobs);\n",
      "    y = z + sigma .* randn(Nobs)\n",
      "  \n",
      "  @assert y == sigma & sigma == z\n",
      "\n",
      "  return @elapsed  [asserted_log_likelihood(y,sigma,z) for i in 0:M ] #I still love list comprehensions so, so much!\n",
      "      \n",
      "end\n",
      "\n",
      "println(\"Asserted: \",calc_time_log_likelihood(Nobs,M))\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Original: 0."
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "000852596\n",
        "Asserted: 0.000696991\n"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "__The assertions seem to speed the code up a bit, why? Does the assertion stop julia from doing something additionally under ther hood?__"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "2f) Write a version of the log_likelihood and calc_time_likelihood functions that take a function as an argument, so that you could use them for distributions other than the normal distribution.  Retime and compare.  What does this imply for your future decisions about whether to write generic functions that take another function as an argument?"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "2g) Write a version of the log_likelihood function that makes use of your knowledge about the normal distribution, so as to avoid calling the exp() function.  Retime and compare.  How could this influence your future decisions about whether generic or specific functions?"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "2h)  Optional (important for IDL & Python gurus):  Rewrite the above function without using any for loops.  Retime and compare.  What does this imply for choosing whether to write loops or vectorized code?"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "2i)  Optional (potenetially useful for IDL & Python gurus):  Try to improve the performance using either the Devectorize and/or NumericExpressions modules.  Retime and compare.  Does this change your conclusions from part 2h?  If so, how?"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<hr>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "__Running low on the time I set aside for homework, so I am going to start on this problem which looks more fun__\n",
      "\n",
      "\n",
      "Q3:  Consider integrating the equations of motion for a test particle orbiting a star fixed at the origin.  In 2D, there are two 2nd order ODEs:  \n",
      "$$\\frac{d^2 r_x}{dt^2} = a_x = -GM r_x/r^3$$\n",
      "$$\\frac{d^2 r_y}{dt^2} = a_y = -GM r_y/r^3,$$\n",
      "where $r = \\sqrt(r_x^2+r_y^2)$ and $a_x$ and $a_y$ are the accelerations in the x and y directions.  \n",
      "Numerically, it is generally easier to integrate 1st order ODEs, so we transform these into:\n",
      "\t\\begin{eqnarray}\n",
      "    d v_x/dt & = a_x & = -GM r_x/r^3  \\\\\n",
      "\td v_y/dt & = a_y & = -GM r_y/r^3 \\\\\n",
      "\td r_x/dt & = v_x & \\\\\n",
      "\td r_y/dt & = v_y & \\\\\n",
      "    \\end{eqnarray}\n",
      "Euler\u2019s method is a simplistic algorithm for integrating a set of 1st order ODEs with state stored in a vector x:\n",
      "$$\n",
      "r(t_n+1) = r(t_n) + dt * \\frac{dr}{dt}|_{t_n} \\\\\n",
      "v(t_n+1) = v(t_n) + dt * \\frac{dv}{dt}|_{t_n}\n",
      "$$\n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "3a) Write a function integrate_euler!(state,dt, duration) that integrates a system (described by state) using Euler\u2019s method and steps of size dt for an interval of time given by duration.  It would probably be wise to write at least two additional functions.  Have your function return a two dimensional array containing a list of the states of the system during your integration\n",
      "\n",
      "__Shouldn't the ! be dropped, since it takes a vector as input but returns a 2 dimensonal list of vectors instead of the modified version of the oringinal vector?__\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "function derrivatives(state::Array,GM)\n",
      "    \n",
      "    r = sqrt(state[1]^2+state[2]^2)\n",
      "    dvx = -GM*state[1]/r^3\n",
      "    dvy = -GM*state[2]/r^3\n",
      "    drx = state[3]\n",
      "    dry = state[4]\n",
      "  \n",
      "  return [drx,dry,dvx,dvy]\n",
      "end\n",
      "\n",
      "function update_state(state::Array,ds::Array,dt)\n",
      "\n",
      "  newstate = [state[1]+dt*ds[1],state[2]+dt*ds[2],state[3]+dt*ds[3],state[4]+dt*ds[4]]\n",
      "  #print(newstate)\n",
      "  #state[1] = newstate[1] Tried to make the a mutable function (!), but this kept giving an inexact error???\n",
      "  #state[2] = newstate[2]\n",
      "  #state[3] = newstate[3]\n",
      "  #state[4] = newstate[4]\n",
      "  return newstate\n",
      "  \n",
      "end\n",
      "\n",
      "function integrate_euler(state::Array,dt,duration,GM=1) \n",
      "    #state vector = (r_x, r_y, v_x, v_y) \n",
      "  \n",
      "  #I like dictionaries, but apparently julia can't do a dictionary of arrays or at least I couldn't get it to work\n",
      "  r_x,r_y,v_x,v_y = [],[],[],[]\n",
      "  N = duration/dt \n",
      "  for i in 0:N\n",
      "    \n",
      "    ds = derrivatives(state,GM)\n",
      "    state = update_state(state,ds,dt)\n",
      "    \n",
      "    #print(state)\n",
      "    \n",
      "    r_x = vcat(r_x,[state[1]])\n",
      "    r_y = vcat(r_y,[state[2]])\n",
      "    v_x = vcat(v_x,[state[3]])\n",
      "    v_y = vcat(v_y,[state[4]])\n",
      "    \n",
      "    \n",
      "  end\n",
      "  \n",
      "  out = (r_x,r_y,v_x,v_y)\n",
      "  return out\n",
      "  \n",
      "end\n",
      "  \n",
      "  \n",
      "  \n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 145,
       "text": [
        "integrate_euler (generic function with 4 methods)"
       ]
      }
     ],
     "prompt_number": 145
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "3b) Use the above code to integrate a system with an initial state of (r_x, r_y, v_x, v_y) = (1, 0, 0, 1) for roughly 3 orbits (i.e., 3*2pi time units if you set GM=1) using approximately 200 time steps per orbit.  Inspect the final state and comment on the accuracy of the integration."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "orbit = integrate_euler([1,0,0,1],2pi/200,6pi);\n",
      "println(\"X:\",orbit[1][end],\" Y:\",orbit[2][end],\" Vx:\",orbit[3][end],\" Vy:\",orbit[4][end])\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "X:1"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        ".316248682241439 Y:-1.103037563364932 Vx:0.46002097632970257 Vy:0.5900726317705094\n"
       ]
      }
     ],
     "prompt_number": 156
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "__That looks pretty far from three orbits around back to (1,0,0,1)__"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "3c)  Plot the trajectory of the test particle (e.g., x vs y).  Is the calculated behavior accurate?  "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "using PyPlot\n",
      "plot(orbit[1],orbit[2])\n",
      "xlabel(\"X\")\n",
      "ylabel(\"Y\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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     "source": [
      "__Clearly there is an unseen companion perturbing the orbit! Either that or the accuracy of the intergration is not great.__"
     ]
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      "3d) Write a new function integrate_leapfrog!(state,dt, duration) that is analogous to integrate_euler, but uses the \u201cleapfrog\u201d or modified Euler\u2019s integration method:\n",
      "$$\n",
      "r(t_n+1/2) = r(t_n) + dt/2 * \\frac{dr}{dt}|_{t_n} \\\\\n",
      "v(t_n+1) = v(t_n) + dt * \\frac{dv}{dt}|_{t_n+1/2} \\\\\n",
      "r(t_n+1) = r(t_n+1/2) + dt/2 * \\frac{dr}{dt}|_{t_n+1/2}\n",
      "$$"
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     "input": [
      "\n",
      "function leapfrog(state::Array,dt)  \n",
      "  \n",
      "  Rx = state[1] + .5*dt*state[3]\n",
      "  Ry = state[2] + .5*dt*state[4]  \n",
      "    \n",
      "\n",
      "  newstate = [Rx,Ry,state[3],state[4]]\n",
      "    \n",
      "  return newstate\n",
      "end\n",
      "\n",
      "function update_state_leapfrog(state::Array,ds,dt)\n",
      "      \n",
      "  \n",
      "  newstate = [state[1]+.5*dt*ds[1],state[2]+.5*dt*ds[2],state[3]+dt*ds[3],state[4]+dt*ds[4]]\n",
      "  #print(newstate)\n",
      "  #state[1] = newstate[1] Tried to make the a mutable function (!), but this kept giving an inexact error???\n",
      "  #state[2] = newstate[2]\n",
      "  #state[3] = newstate[3]\n",
      "  #state[4] = newstate[4]\n",
      "  return newstate\n",
      "  \n",
      "end\n",
      "\n",
      "\n",
      "function integrate_leapfrog(state::Array,dt,duration,GM=1) \n",
      "    #state vector = (r_x, r_y, v_x, v_y) \n",
      "  \n",
      "  #I like dictionaries, but apparently julia can't do a dictionary of arrays or at least I couldn't get it to work\n",
      "  r_x,r_y,v_x,v_y = [],[],[],[]\n",
      "  N = duration/dt \n",
      "  for i in 0:N\n",
      "    \n",
      "    state = leapfrog(state,dt)\n",
      "    ds = derrivatives(state,GM)\n",
      "    state = update_state_leapfrog(state,ds,dt)\n",
      "    \n",
      "    #print(state)\n",
      "    \n",
      "    r_x = vcat(r_x,[state[1]])\n",
      "    r_y = vcat(r_y,[state[2]])\n",
      "    v_x = vcat(v_x,[state[3]])\n",
      "    v_y = vcat(v_y,[state[4]])\n",
      "    \n",
      "    \n",
      "  end\n",
      "  \n",
      "  out = (r_x,r_y,v_x,v_y)\n",
      "  return out\n",
      "end"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
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       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 148,
       "text": [
        "integrate_leapfrog (generic function with 2 methods)"
       ]
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     "prompt_number": 148
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     "metadata": {},
     "source": [
      "3e) Repeat the integration from part 3b, but using the integrate_leapfrog code.  Inspect the final end state and make a similar plot.  Describe the main difference in the results and explain on what basis you would choose one over the other.  "
     ]
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     "input": [
      "orbitL = integrate_leapfrog([1,0,0,1],2pi/200,6pi);\n",
      "println(\"X:\",orbitL[1][end],\" Y:\",orbitL[2][end],\" Vx:\",orbitL[3][end],\" Vy:\",orbitL[4][end])\n",
      "using PyPlot\n",
      "plot(orbitL[1],orbitL[2])\n",
      "xlabel(\"X\")\n",
      "ylabel(\"Y\")\n",
      "figure()\n",
      "plot(orbit[1],orbit[2],label=\"Eular\")\n",
      "plot(orbitL[1],orbitL[2],label=\"Leapfrog\")\n",
      "xlabel(\"X\")\n",
      "ylabel(\"Y\")\n",
      "legend(loc=\"lower left\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "X:-"
       ]
      },
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       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "0.034124103380557214 Y:1.3785656635520707 Vx:-0.8599773397674502 Vy:-0.012178307773462533\n"
       ]
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    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "__They both look bad, I don't think a case can be made one way or another.__"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "3f) Time how long your code for a similar integration of 100 orbits.  How long would it take to integrate for 4.5*10^9 orbits (e.g., age of Earth)?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "Time_eular = @elapsed integrate_euler([1,0,0,1],2pi/200,200pi)\n",
      "Time_Leap_frog = @elapsed integrate_leapfrog([1,0,0,1],2pi/200,200pi)\n",
      "\n",
      "time_age_eular = Time_eular * 4.5e7\n",
      "time_age_leap_frog = Time_Leap_frog * 4.5e7\n",
      "\n",
      "println(\"Eular: \",Time_eular,\" sec; Time for 4.5e9: \", time_age_eular/86400.,\" days\")\n",
      "println(\"Leap Frog: \",Time_Leap_frog,\" sec; Time for 4.5e9: \", time_age_leap_frog/86400.,\" days\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Eular: 7"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        ".301136525 sec; Time for 4.5e9: 3802.6752734375 days\n",
        "Leap Frog: 7.237521332 sec; Time for 4.5e9: 3769.5423604166667 days\n"
       ]
      }
     ],
     "prompt_number": 164
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "#No more time left to work on this, julia and I were fighting a lot this time. "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "3g) Repeat the integration from part 3e, but using a larger dt.  Inspect the final end state.  How much less accurate is the integration that used a larger dt?  "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "3h) Make a log-log plot of the accuracy of the integration versus the integration duration for durations spanning at least a few orders of magnitude.  Estimate the slope (by eye is fine).  What are the implications for the accuracy of a long-term integration?  "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "3i) List a few ideas for how you could accelerate the integrations.  Comment on how likely each of your ideas is to make a significant difference.  (If you try it out, report the new time for 100 orbits, so we can compare.)  Discuss any drawbacks of each idea to accelerate the integrations.  "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<hr>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Q4:  Consider a modern laptop CPU with 4 GB ($=4*2^{30}$) of usable memory and capable performing 20 Gflops/second. Assume it uses 8 bytes of memory to store each floating point number (\u201cdouble precision\u201d).   [Based on Oliveira & Stewart\u2019s Writing Scientific Software, Chapter 5, Problem #6.]\n",
      "\n",
      "4a) What is the largest matrix that the above computer could fit into its available memory at one time?  \n",
      "<br>\n",
      "<br>\n",
      "4b) If we use LU factorization to solve a linear system, estimate how long would it take to solve the maximum size linear system that would fit into memory at once.  You may assume the computation is maximally efficient, the computer reaches peak performance and the LU decomposition requires $\\sim \\frac{2}{3} n^3$ flops.  \n",
      "<br>\n",
      "<br>\n",
      "\n",
      "4c) For a modern laptop, does memory or compute time limit the size of system that can be practically solved with LU decomposition? \n",
      "<br>\n",
      "<br>\n",
      "\n",
      "4d) For real life problems, what other considerations are likely to limit performance?  \n",
      "<br>\n",
      "<br>\n",
      "\n",
      "4e) How could one practically solve even larger systems?  "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "10^1.2"
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     "language": "python",
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