{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
   ],
   "source": [
    "import numpy as np\n",
    "import plotly.graph_objects\n",
    "from IPython.display import display, YouTubeVideo, HTML\n",
    "#from ipywidgets import interactive_output, VBox, HBox, IntSlider, SelectionSlider\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
   ],
   "source": [
    "mydefault = plotly.graph_objects.layout.Template()\n",
    "mydefault.layout.xaxis.showgrid = False\n",
    "mydefault.layout.yaxis.showgrid = False\n",
    "mydefault.layout.xaxis.showline = True\n",
    "mydefault.layout.yaxis.showline = True\n",
    "mydefault.layout.yaxis.linewidth = 2\n",
    "mydefault.layout.xaxis.ticks = \"outside\"\n",
    "mydefault.layout.yaxis.ticks = \"outside\"\n",
    "mydefault.layout.hovermode = False\n",
    "mydefault.layout.dragmode = \"pan\"\n",
    "mydefault.layout.scene.hovermode = False\n",
    "mydefault.layout.xaxis.showspikes = False\n",
    "mydefault.layout.yaxis.showspikes = False\n",
    "mydefault.layout.scene.xaxis.showspikes = False\n",
    "mydefault.layout.scene.yaxis.showspikes = False\n",
    "mydefault.layout.scene.zaxis.showspikes = False\n",
    "plotly.io.templates[\"mydefault\"] = mydefault\n",
    "plotly.io.templates.default = \"mydefault\"\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<!-- To disable the modebar IN ALL PLOT.LY PLOTS -->\n",
       "<style>\n",
       ".modebar {\n",
       "    display: none !important;\n",
       "}\n",
       "</style>\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 3,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%%html\n",
    "<!-- To disable the modebar IN ALL PLOT.LY PLOTS -->\n",
    "<style>\n",
    ".modebar {\n",
    "    display: none !important;\n",
    "}\n",
    "</style>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
   ],
   "source": [
    "def transformation_matrix(M):\n",
    "    columns = []\n",
    "    for evalue, evecs, mult in M.eigenvectors_right():\n",
    "        if evalue.imag() < 0:\n",
    "            continue\n",
    "        if evalue.imag():\n",
    "            for evec in evecs:\n",
    "                u = vector(RDF, [a.real() for a in evec])\n",
    "                v = vector(RDF, [a.imag() for a in evec])\n",
    "                columns.append(u)\n",
    "                columns.append(v)\n",
    "        else:\n",
    "            for v in evecs:\n",
    "                columns.append(vector(RDF, v))\n",
    "    return column_matrix(columns)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
   ],
   "source": [
    "def make_block_diagonal(M):\n",
    "    dim = M.dimensions()[0]\n",
    "    blocks = []\n",
    "    i = 0\n",
    "    while i < dim:\n",
    "        size = 2 if (i+1 < dim and M[i,i+1] != 0) else 1\n",
    "        blocks.append(M[i:i+size,i:i+size])\n",
    "        i += size\n",
    "    return block_diagonal_matrix(*blocks)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
   ],
   "source": [
    "def round_complex(z, digits):\n",
    "    if z.imag_part():\n",
    "        return round(z.real_part(), digits) + round(z.imag_part(), digits) * I\n",
    "    return round(z, digits)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
   ],
   "source": [
    "def latex_vector(v, round=None):\n",
    "    if round is None:\n",
    "        result = column_matrix(v)\n",
    "    else:\n",
    "        result = column_matrix(RDF, v).round(round)\n",
    "    result = latex(result).replace(\"left(\", \"left[\").replace(\"right)\", \"right]\")\n",
    "    return LatexExpr(result)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
   ],
   "source": [
    "life_stages = LatexExpr(r\"\"\"\\left[ \\begin{array}{c}\n",
    "    \\text{Eggs/hatchlings} \\\\\n",
    "    \\text{Small juveniles} \\\\\n",
    "    \\text{Large juveniles} \\\\\n",
    "    \\text{Subadults} \\\\\n",
    "    \\text{Novice breeders} \\\\\n",
    "    \\text{1st-year remigrants} \\\\\n",
    "    \\text{Mature breeders}\n",
    "\\end{array} \\right] = \"\"\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
   ],
   "source": [
    "def discrete_linear_interactive(M, initial_state, **options):\n",
    "    max_t = options.get(\"max_t\", 100)\n",
    "    pre_text = options.get(\"pre_text\", \"\")\n",
    "    post_text = options.get(\"post_text\", \"\")\n",
    "    show_distribution = options.get(\"show_distribution\", False)\n",
    "    font_size = options.get(\"font_size\", 18)\n",
    "    fig_height = options.get(\"fig_height\", 250)\n",
    "    solution = [vector(initial_state)]\n",
    "    for t in range(max_t):\n",
    "        solution.append(M * solution[-1])\n",
    "\n",
    "    fig = plotly.graph_objects.FigureWidget()\n",
    "    fig.layout.xaxis.visible = False\n",
    "    fig.layout.yaxis.visible = False\n",
    "    fig.layout.height = fig_height\n",
    "    fig.layout.margin = dict(b=10, t=10, l=10, r=10)\n",
    "    text = \"${}$\".format(pre_text + latex_vector(solution[0], round=2))\n",
    "    fig.add_annotation(showarrow=False, font_size=font_size, x=0, y=1, \n",
    "                       xref=\"paper\", yref=\"paper\", xanchor=\"left\", yanchor=\"top\")\n",
    "    annotation = fig.layout.annotations[-1]\n",
    "\n",
    "    @interact(t=slider(0, max_t, 1, label=\"$t$\"))\n",
    "    def update(t):\n",
    "        text = pre_text + latex_vector(solution[t], round=2)\n",
    "        if show_distribution:\n",
    "            percentages = 100 * solution[t].normalized(1)\n",
    "            text += r\" \\hspace{6em} \\text{Percentages: } \"\n",
    "            text += latex_vector(percentages, 1)\n",
    "        annotation.text = \"${}$\".format(text + post_text)\n",
    "\n",
    "    return fig\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "**A model of the worldwide population of loggerhead sea turtles**\n",
    "\n",
    "From the paper “A stage-based population model for loggerhead sea turtles and implications for conservation”, by Deborah Crouse, Larry Crowder, and Hal Caswell, published in the journal *Ecology*, 1987. \n",
    "\n",
    "Seven life stages: \n",
    "\n",
    "1. Hatchlings (less than 1 year old)\n",
    "1. Small juveniles (age 1–7 years)\n",
    "1. Large juveniles (age 8–15 years)\n",
    "1. Subadults (age 16–21 years)\n",
    "1. Novice breeders (age 22 years)\n",
    "1. First-year remigrants (age 23 years)\n",
    "1. Mature breeders (age 24–54 years)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}C = \\left(\\begin{array}{rrrrrrr}\n",
       "0.0 & 0.0 & 0.0 & 0.0 & 127.0 & 4.0 & 80.0 \\\\\n",
       "0.6747 & 0.737 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
       "0.0 & 0.0486 & 0.661 & 0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
       "0.0 & 0.0 & 0.0147 & 0.6907 & 0.0 & 0.0 & 0.0 \\\\\n",
       "0.0 & 0.0 & 0.0 & 0.0518 & 0.0 & 0.0 & 0.0 \\\\\n",
       "0.0 & 0.0 & 0.0 & 0.0 & 0.8091 & 0.0 & 0.0 \\\\\n",
       "0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.8091 & 0.8089\n",
       "\\end{array}\\right)</script></html>"
      ],
      "text/latex": [
       "\\begin{math}\n",
       "\\newcommand{\\Bold}[1]{\\mathbf{#1}}C = \\left(\\begin{array}{rrrrrrr}\n",
       "0.0 & 0.0 & 0.0 & 0.0 & 127.0 & 4.0 & 80.0 \\\\\n",
       "0.6747 & 0.737 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
       "0.0 & 0.0486 & 0.661 & 0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
       "0.0 & 0.0 & 0.0147 & 0.6907 & 0.0 & 0.0 & 0.0 \\\\\n",
       "0.0 & 0.0 & 0.0 & 0.0518 & 0.0 & 0.0 & 0.0 \\\\\n",
       "0.0 & 0.0 & 0.0 & 0.0 & 0.8091 & 0.0 & 0.0 \\\\\n",
       "0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.8091 & 0.8089\n",
       "\\end{array}\\right)\n",
       "\\end{math}"
      ],
      "text/plain": [
       "C = \\left(\\begin{array}{rrrrrrr}\n",
       "0.0 & 0.0 & 0.0 & 0.0 & 127.0 & 4.0 & 80.0 \\\\\n",
       "0.6747 & 0.737 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
       "0.0 & 0.0486 & 0.661 & 0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
       "0.0 & 0.0 & 0.0147 & 0.6907 & 0.0 & 0.0 & 0.0 \\\\\n",
       "0.0 & 0.0 & 0.0 & 0.0518 & 0.0 & 0.0 & 0.0 \\\\\n",
       "0.0 & 0.0 & 0.0 & 0.0 & 0.8091 & 0.0 & 0.0 \\\\\n",
       "0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.8091 & 0.8089\n",
       "\\end{array}\\right)"
      ]
     },
     "execution_count": 10,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "C = matrix(RDF, [\n",
    "    [0,      0,      0,      0,      127,      4,      80     ],\n",
    "    [0.6747, 0.7370, 0,      0,        0,      0,       0     ],\n",
    "    [0,      0.0486, 0.6610, 0,        0,      0,       0     ],\n",
    "    [0,      0,      0.0147, 0.6907,   0,      0,       0     ],\n",
    "    [0,      0,      0,      0.0518,   0,      0,       0     ],\n",
    "    [0,      0,      0,      0,        0.8091, 0,       0     ],\n",
    "    [0,      0,      0,      0,        0,      0.8091,  0.8089],\n",
    "])\n",
    "show(r\"C = \" + latex(C))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\text{Eigenvalues of $C$:}</script></html>"
      ],
      "text/latex": [
       "\\begin{math}\n",
       "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\text{Eigenvalues of $C$:}\n",
       "\\end{math}"
      ],
      "text/plain": [
       "\\text{Eigenvalues of $C$:}"
      ]
     },
     "execution_count": 11,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}-0.0884 + 0.1196i</script></html>"
      ],
      "text/latex": [
       "\\begin{math}\n",
       "\\newcommand{\\Bold}[1]{\\mathbf{#1}}-0.0884 + 0.1196i\n",
       "\\end{math}"
      ],
      "text/plain": [
       "-0.0884 + 0.1196*I"
      ]
     },
     "execution_count": 11,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}-0.0884 - 0.1196i</script></html>"
      ],
      "text/latex": [
       "\\begin{math}\n",
       "\\newcommand{\\Bold}[1]{\\mathbf{#1}}-0.0884 - 0.1196i\n",
       "\\end{math}"
      ],
      "text/plain": [
       "-0.0884 - 0.1196*I"
      ]
     },
     "execution_count": 11,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}0.2655</script></html>"
      ],
      "text/latex": [
       "\\begin{math}\n",
       "\\newcommand{\\Bold}[1]{\\mathbf{#1}}0.2655\n",
       "\\end{math}"
      ],
      "text/plain": [
       "0.2655"
      ]
     },
     "execution_count": 11,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}0.3717</script></html>"
      ],
      "text/latex": [
       "\\begin{math}\n",
       "\\newcommand{\\Bold}[1]{\\mathbf{#1}}0.3717\n",
       "\\end{math}"
      ],
      "text/plain": [
       "0.3717"
      ]
     },
     "execution_count": 11,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}0.7462 + 0.2131i</script></html>"
      ],
      "text/latex": [
       "\\begin{math}\n",
       "\\newcommand{\\Bold}[1]{\\mathbf{#1}}0.7462 + 0.2131i\n",
       "\\end{math}"
      ],
      "text/plain": [
       "0.7462 + 0.2131*I"
      ]
     },
     "execution_count": 11,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}0.7462 - 0.2131i</script></html>"
      ],
      "text/latex": [
       "\\begin{math}\n",
       "\\newcommand{\\Bold}[1]{\\mathbf{#1}}0.7462 - 0.2131i\n",
       "\\end{math}"
      ],
      "text/plain": [
       "0.7462 - 0.2131*I"
      ]
     },
     "execution_count": 11,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}0.945</script></html>"
      ],
      "text/latex": [
       "\\begin{math}\n",
       "\\newcommand{\\Bold}[1]{\\mathbf{#1}}0.945\n",
       "\\end{math}"
      ],
      "text/plain": [
       "0.945"
      ]
     },
     "execution_count": 11,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "show(LatexExpr(r\"\\text{Eigenvalues of $C$:}\"))\n",
    "for evalue in C.eigenvalues():\n",
    "    show(round_complex(evalue, 4))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}T = \\left(\\begin{array}{rrrrrrr}\n",
       "-0.7768 & 0.0 & -0.57 & -0.471 & -0.0127 & -0.2951 & 0.2908 \\\\\n",
       "0.6219 & 0.0901 & 0.8155 & 0.8699 & -0.9345 & 0.0 & 0.943 \\\\\n",
       "-0.0384 & -0.012 & -0.1002 & -0.1461 & -0.0735 & 0.1838 & 0.1614 \\\\\n",
       "0.0007 & 0.0003 & 0.0035 & 0.0067 & 0.0106 & 0.0078 & 0.0093 \\\\\n",
       "-0.0 & -0.0003 & 0.0007 & 0.0009 & 0.0008 & 0.0003 & 0.0005 \\\\\n",
       "-0.001 & 0.001 & 0.0021 & 0.002 & 0.0009 & 0.0001 & 0.0004 \\\\\n",
       "0.001 & -0.0008 & -0.0031 & -0.0038 & -0.0007 & -0.0033 & 0.0026\n",
       "\\end{array}\\right)</script></html>"
      ],
      "text/latex": [
       "\\begin{math}\n",
       "\\newcommand{\\Bold}[1]{\\mathbf{#1}}T = \\left(\\begin{array}{rrrrrrr}\n",
       "-0.7768 & 0.0 & -0.57 & -0.471 & -0.0127 & -0.2951 & 0.2908 \\\\\n",
       "0.6219 & 0.0901 & 0.8155 & 0.8699 & -0.9345 & 0.0 & 0.943 \\\\\n",
       "-0.0384 & -0.012 & -0.1002 & -0.1461 & -0.0735 & 0.1838 & 0.1614 \\\\\n",
       "0.0007 & 0.0003 & 0.0035 & 0.0067 & 0.0106 & 0.0078 & 0.0093 \\\\\n",
       "-0.0 & -0.0003 & 0.0007 & 0.0009 & 0.0008 & 0.0003 & 0.0005 \\\\\n",
       "-0.001 & 0.001 & 0.0021 & 0.002 & 0.0009 & 0.0001 & 0.0004 \\\\\n",
       "0.001 & -0.0008 & -0.0031 & -0.0038 & -0.0007 & -0.0033 & 0.0026\n",
       "\\end{array}\\right)\n",
       "\\end{math}"
      ],
      "text/plain": [
       "T = \\left(\\begin{array}{rrrrrrr}\n",
       "-0.7768 & 0.0 & -0.57 & -0.471 & -0.0127 & -0.2951 & 0.2908 \\\\\n",
       "0.6219 & 0.0901 & 0.8155 & 0.8699 & -0.9345 & 0.0 & 0.943 \\\\\n",
       "-0.0384 & -0.012 & -0.1002 & -0.1461 & -0.0735 & 0.1838 & 0.1614 \\\\\n",
       "0.0007 & 0.0003 & 0.0035 & 0.0067 & 0.0106 & 0.0078 & 0.0093 \\\\\n",
       "-0.0 & -0.0003 & 0.0007 & 0.0009 & 0.0008 & 0.0003 & 0.0005 \\\\\n",
       "-0.001 & 0.001 & 0.0021 & 0.002 & 0.0009 & 0.0001 & 0.0004 \\\\\n",
       "0.001 & -0.0008 & -0.0031 & -0.0038 & -0.0007 & -0.0033 & 0.0026\n",
       "\\end{array}\\right)"
      ]
     },
     "execution_count": 12,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "T = transformation_matrix(C)\n",
    "show(r\"T = \" + latex(T.round(4)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\tilde{D} = \\left(\\begin{array}{rrrrrrr}\n",
       "-0.0884 & 0.1196 & -0.0 & 0.0 & 0.0 & -0.0 & 0.0 \\\\\n",
       "-0.1196 & -0.0884 & -0.0 & -0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
       "0.0 & 0.0 & 0.2655 & -0.0 & -0.0 & 0.0 & 0.0 \\\\\n",
       "-0.0 & -0.0 & 0.0 & 0.3717 & 0.0 & -0.0 & -0.0 \\\\\n",
       "0.0 & 0.0 & 0.0 & 0.0 & 0.7462 & 0.2131 & 0.0 \\\\\n",
       "0.0 & -0.0 & 0.0 & -0.0 & -0.2131 & 0.7462 & -0.0 \\\\\n",
       "-0.0 & 0.0 & -0.0 & 0.0 & 0.0 & -0.0 & 0.945\n",
       "\\end{array}\\right)</script></html>"
      ],
      "text/latex": [
       "\\begin{math}\n",
       "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\tilde{D} = \\left(\\begin{array}{rrrrrrr}\n",
       "-0.0884 & 0.1196 & -0.0 & 0.0 & 0.0 & -0.0 & 0.0 \\\\\n",
       "-0.1196 & -0.0884 & -0.0 & -0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
       "0.0 & 0.0 & 0.2655 & -0.0 & -0.0 & 0.0 & 0.0 \\\\\n",
       "-0.0 & -0.0 & 0.0 & 0.3717 & 0.0 & -0.0 & -0.0 \\\\\n",
       "0.0 & 0.0 & 0.0 & 0.0 & 0.7462 & 0.2131 & 0.0 \\\\\n",
       "0.0 & -0.0 & 0.0 & -0.0 & -0.2131 & 0.7462 & -0.0 \\\\\n",
       "-0.0 & 0.0 & -0.0 & 0.0 & 0.0 & -0.0 & 0.945\n",
       "\\end{array}\\right)\n",
       "\\end{math}"
      ],
      "text/plain": [
       "\\tilde{D} = \\left(\\begin{array}{rrrrrrr}\n",
       "-0.0884 & 0.1196 & -0.0 & 0.0 & 0.0 & -0.0 & 0.0 \\\\\n",
       "-0.1196 & -0.0884 & -0.0 & -0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
       "0.0 & 0.0 & 0.2655 & -0.0 & -0.0 & 0.0 & 0.0 \\\\\n",
       "-0.0 & -0.0 & 0.0 & 0.3717 & 0.0 & -0.0 & -0.0 \\\\\n",
       "0.0 & 0.0 & 0.0 & 0.0 & 0.7462 & 0.2131 & 0.0 \\\\\n",
       "0.0 & -0.0 & 0.0 & -0.0 & -0.2131 & 0.7462 & -0.0 \\\\\n",
       "-0.0 & 0.0 & -0.0 & 0.0 & 0.0 & -0.0 & 0.945\n",
       "\\end{array}\\right)"
      ]
     },
     "execution_count": 13,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "D = T.inverse()*C*T\n",
    "show(r\"\\tilde{D} = \" + latex(D.round(4)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\tilde{D} = \\left(\\begin{array}{rr|r|r|rr|r}\n",
       "-0.0884 & 0.1196 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
       "-0.1196 & -0.0884 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
       "\\hline\n",
       " 0.0 & 0.0 & 0.2655 & 0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
       "\\hline\n",
       " 0.0 & 0.0 & 0.0 & 0.3717 & 0.0 & 0.0 & 0.0 \\\\\n",
       "\\hline\n",
       " 0.0 & 0.0 & 0.0 & 0.0 & 0.7462 & 0.2131 & 0.0 \\\\\n",
       "0.0 & 0.0 & 0.0 & 0.0 & -0.2131 & 0.7462 & 0.0 \\\\\n",
       "\\hline\n",
       " 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.945\n",
       "\\end{array}\\right)</script></html>"
      ],
      "text/latex": [
       "\\begin{math}\n",
       "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\tilde{D} = \\left(\\begin{array}{rr|r|r|rr|r}\n",
       "-0.0884 & 0.1196 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
       "-0.1196 & -0.0884 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
       "\\hline\n",
       " 0.0 & 0.0 & 0.2655 & 0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
       "\\hline\n",
       " 0.0 & 0.0 & 0.0 & 0.3717 & 0.0 & 0.0 & 0.0 \\\\\n",
       "\\hline\n",
       " 0.0 & 0.0 & 0.0 & 0.0 & 0.7462 & 0.2131 & 0.0 \\\\\n",
       "0.0 & 0.0 & 0.0 & 0.0 & -0.2131 & 0.7462 & 0.0 \\\\\n",
       "\\hline\n",
       " 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.945\n",
       "\\end{array}\\right)\n",
       "\\end{math}"
      ],
      "text/plain": [
       "\\tilde{D} = \\left(\\begin{array}{rr|r|r|rr|r}\n",
       "-0.0884 & 0.1196 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
       "-0.1196 & -0.0884 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
       "\\hline\n",
       " 0.0 & 0.0 & 0.2655 & 0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
       "\\hline\n",
       " 0.0 & 0.0 & 0.0 & 0.3717 & 0.0 & 0.0 & 0.0 \\\\\n",
       "\\hline\n",
       " 0.0 & 0.0 & 0.0 & 0.0 & 0.7462 & 0.2131 & 0.0 \\\\\n",
       "0.0 & 0.0 & 0.0 & 0.0 & -0.2131 & 0.7462 & 0.0 \\\\\n",
       "\\hline\n",
       " 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.945\n",
       "\\end{array}\\right)"
      ]
     },
     "execution_count": 14,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "show(r\"\\tilde{D} = \" + latex(make_block_diagonal(D.round(4))))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\text{The absolute values of the eigenvalues:}</script></html>"
      ],
      "text/latex": [
       "\\begin{math}\n",
       "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\text{The absolute values of the eigenvalues:}\n",
       "\\end{math}"
      ],
      "text/plain": [
       "\\text{The absolute values of the eigenvalues:}"
      ]
     },
     "execution_count": 15,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}| -0.0884 + 0.1196i | = 0.1488</script></html>"
      ],
      "text/latex": [
       "\\begin{math}\n",
       "\\newcommand{\\Bold}[1]{\\mathbf{#1}}| -0.0884 + 0.1196i | = 0.1488\n",
       "\\end{math}"
      ],
      "text/plain": [
       "| -0.0884 + 0.1196i | = 0.1488"
      ]
     },
     "execution_count": 15,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}| -0.0884 - 0.1196i | = 0.1488</script></html>"
      ],
      "text/latex": [
       "\\begin{math}\n",
       "\\newcommand{\\Bold}[1]{\\mathbf{#1}}| -0.0884 - 0.1196i | = 0.1488\n",
       "\\end{math}"
      ],
      "text/plain": [
       "| -0.0884 - 0.1196i | = 0.1488"
      ]
     },
     "execution_count": 15,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}0.2655</script></html>"
      ],
      "text/latex": [
       "\\begin{math}\n",
       "\\newcommand{\\Bold}[1]{\\mathbf{#1}}0.2655\n",
       "\\end{math}"
      ],
      "text/plain": [
       "0.2655"
      ]
     },
     "execution_count": 15,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}0.3717</script></html>"
      ],
      "text/latex": [
       "\\begin{math}\n",
       "\\newcommand{\\Bold}[1]{\\mathbf{#1}}0.3717\n",
       "\\end{math}"
      ],
      "text/plain": [
       "0.3717"
      ]
     },
     "execution_count": 15,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}| 0.7462 + 0.2131i | = 0.776</script></html>"
      ],
      "text/latex": [
       "\\begin{math}\n",
       "\\newcommand{\\Bold}[1]{\\mathbf{#1}}| 0.7462 + 0.2131i | = 0.776\n",
       "\\end{math}"
      ],
      "text/plain": [
       "| 0.7462 + 0.2131i | = 0.776"
      ]
     },
     "execution_count": 15,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}| 0.7462 - 0.2131i | = 0.776</script></html>"
      ],
      "text/latex": [
       "\\begin{math}\n",
       "\\newcommand{\\Bold}[1]{\\mathbf{#1}}| 0.7462 - 0.2131i | = 0.776\n",
       "\\end{math}"
      ],
      "text/plain": [
       "| 0.7462 - 0.2131i | = 0.776"
      ]
     },
     "execution_count": 15,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}0.945</script></html>"
      ],
      "text/latex": [
       "\\begin{math}\n",
       "\\newcommand{\\Bold}[1]{\\mathbf{#1}}0.945\n",
       "\\end{math}"
      ],
      "text/plain": [
       "0.945"
      ]
     },
     "execution_count": 15,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "show(LatexExpr(r\"\\text{The absolute values of the eigenvalues:}\"))\n",
    "for evalue in C.eigenvalues():\n",
    "    if evalue.imag() or evalue < 0:\n",
    "        show(r\"|\" + latex(round_complex(evalue, 4)) + r\"| = \" + latex(round(abs(evalue), 4)))\n",
    "    else:\n",
    "        show(round(abs(evalue), 4))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "5010982595fe43efb678f81e642df50e",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Interactive function <function discrete_linear_interactive.<locals>.update at 0x7f208e921040> with 1 widget\n",
       "  …"
      ]
     },
     "execution_count": 16,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "713c0708960d4899b13fad8314e60e79",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "FigureWidget({\n",
       "    'data': [],\n",
       "    'layout': {'annotations': [{'font': {'size': 18},\n",
       "                         …"
      ]
     },
     "execution_count": 16,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "state = vector([100.0] * 7)\n",
    "discrete_linear_interactive(C, state, pre_text=life_stages)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "85713cba591548d799f935037bc278a7",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Interactive function <function discrete_linear_interactive.<locals>.update at 0x7f208e921dc0> with 1 widget\n",
       "  …"
      ]
     },
     "execution_count": 17,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "7889e1b04c384ab8a1b8a7b735075a56",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "FigureWidget({\n",
       "    'data': [],\n",
       "    'layout': {'annotations': [{'font': {'size': 18},\n",
       "                         …"
      ]
     },
     "execution_count": 17,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "state = vector([100.0] * 7)\n",
    "discrete_linear_interactive(C, state, pre_text=life_stages, show_distribution=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "**Protecting eggs, nests, and baby sea turtles**\n",
    "\n",
    "<center>\n",
    "<img src=\"images/IMAG1835.jpg\" alt=\"A loggerhead nest, protected by a plastic cage\" width=\"1050\" />\n",
    "<br><span style=\"font-size: 50%\">Bald Head Island, NC<br>August, 2016</span>\n",
    "</center>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "**Protecting eggs, nests, and baby sea turtles**\n",
    "\n",
    "<center>\n",
    "<img src=\"images/IMAG1836.jpg\" alt=\"Guide rails leading from the nest to the ocean\" width=\"360\" />\n",
    "<br><span style=\"font-size: 50%\">Bald Head Island, NC<br>August, 2016</span>\n",
    "</center>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "**Protecting eggs, nests, and baby sea turtles**\n",
    "\n",
    "<center>\n",
    "<img src=\"images/IMAG1933.jpg\" alt=\"Excavating a loggerhead sea turtle nest\" width=\"1050\" />\n",
    "<br><span style=\"font-size: 50%\">Bald Head Island, NC<br>August, 2016</span>\n",
    "</center>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "**Protecting eggs, nests, and baby sea turtles**\n",
    "\n",
    "<center>\n",
    "<img src=\"images/IMAG1934.jpg\" alt=\"Unhatched eggs found while excavating a nest\" width=\"1050\" />\n",
    "<br><span style=\"font-size: 50%\">Bald Head Island, NC<br>August, 2016</span>\n",
    "</center>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "**Protecting eggs, nests, and baby sea turtles**\n",
    "\n",
    "<center>\n",
    "<img src=\"images/IMAG1927.jpg\" alt=\"A live straggler found while excavating a nest!\" width=\"1050\" />\n",
    "<br><span style=\"font-size: 50%\">Bald Head Island, NC<br>August, 2016</span>\n",
    "</center>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "**Protecting eggs, nests, and baby sea turtles**\n",
    "\n",
    "<center>\n",
    "<img src=\"images/IMAG1929.jpg\" alt=\"A live straggler found while excavating a nest!\" width=\"1050\" />\n",
    "<br><span style=\"font-size: 50%\">Bald Head Island, NC<br>August, 2016</span>\n",
    "</center>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "**What if we do everything we can to protect eggs, nests, and baby sea turtles?**\n",
    "\n",
    "(And what if that's all we do?) \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}C_2 = \\left(\\begin{array}{rrrrrrr}\n",
       "0.0 & 0.0 & 0.0 & 0.0 & 150.0 & 6.0 & 100.0 \\\\\n",
       "0.6747 & 0.737 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
       "0.0 & 0.0486 & 0.661 & 0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
       "0.0 & 0.0 & 0.0147 & 0.6907 & 0.0 & 0.0 & 0.0 \\\\\n",
       "0.0 & 0.0 & 0.0 & 0.0518 & 0.0 & 0.0 & 0.0 \\\\\n",
       "0.0 & 0.0 & 0.0 & 0.0 & 0.8091 & 0.0 & 0.0 \\\\\n",
       "0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.8091 & 0.8089\n",
       "\\end{array}\\right)</script></html>"
      ],
      "text/latex": [
       "\\begin{math}\n",
       "\\newcommand{\\Bold}[1]{\\mathbf{#1}}C_2 = \\left(\\begin{array}{rrrrrrr}\n",
       "0.0 & 0.0 & 0.0 & 0.0 & 150.0 & 6.0 & 100.0 \\\\\n",
       "0.6747 & 0.737 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
       "0.0 & 0.0486 & 0.661 & 0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
       "0.0 & 0.0 & 0.0147 & 0.6907 & 0.0 & 0.0 & 0.0 \\\\\n",
       "0.0 & 0.0 & 0.0 & 0.0518 & 0.0 & 0.0 & 0.0 \\\\\n",
       "0.0 & 0.0 & 0.0 & 0.0 & 0.8091 & 0.0 & 0.0 \\\\\n",
       "0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.8091 & 0.8089\n",
       "\\end{array}\\right)\n",
       "\\end{math}"
      ],
      "text/plain": [
       "C_2 = \\left(\\begin{array}{rrrrrrr}\n",
       "0.0 & 0.0 & 0.0 & 0.0 & 150.0 & 6.0 & 100.0 \\\\\n",
       "0.6747 & 0.737 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
       "0.0 & 0.0486 & 0.661 & 0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
       "0.0 & 0.0 & 0.0147 & 0.6907 & 0.0 & 0.0 & 0.0 \\\\\n",
       "0.0 & 0.0 & 0.0 & 0.0518 & 0.0 & 0.0 & 0.0 \\\\\n",
       "0.0 & 0.0 & 0.0 & 0.0 & 0.8091 & 0.0 & 0.0 \\\\\n",
       "0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.8091 & 0.8089\n",
       "\\end{array}\\right)"
      ]
     },
     "execution_count": 18,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "C2 = matrix(RDF, [\n",
    "    [0,      0,      0,      0,      150,      6,     100     ],\n",
    "    [0.6747, 0.7370, 0,      0,        0,      0,       0     ],\n",
    "    [0,      0.0486, 0.6610, 0,        0,      0,       0     ],\n",
    "    [0,      0,      0.0147, 0.6907,   0,      0,       0     ],\n",
    "    [0,      0,      0,      0.0518,   0,      0,       0     ],\n",
    "    [0,      0,      0,      0,        0.8091, 0,       0     ],\n",
    "    [0,      0,      0,      0,        0,      0.8091,  0.8089],\n",
    "])\n",
    "show(r\"C_2 = \" + latex(C2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "**The difference between this matrix, $C_2$, and the original one, $C$:**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}C_2 - C = \\left(\\begin{array}{rrrrrrr}\n",
       "0.0 & 0.0 & 0.0 & 0.0 & 23.0 & 2.0 & 20.0 \\\\\n",
       "0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
       "0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
       "0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
       "0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
       "0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
       "0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\n",
       "\\end{array}\\right)</script></html>"
      ],
      "text/latex": [
       "\\begin{math}\n",
       "\\newcommand{\\Bold}[1]{\\mathbf{#1}}C_2 - C = \\left(\\begin{array}{rrrrrrr}\n",
       "0.0 & 0.0 & 0.0 & 0.0 & 23.0 & 2.0 & 20.0 \\\\\n",
       "0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
       "0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
       "0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
       "0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
       "0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
       "0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\n",
       "\\end{array}\\right)\n",
       "\\end{math}"
      ],
      "text/plain": [
       "C_2 - C = \\left(\\begin{array}{rrrrrrr}\n",
       "0.0 & 0.0 & 0.0 & 0.0 & 23.0 & 2.0 & 20.0 \\\\\n",
       "0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
       "0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
       "0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
       "0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
       "0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
       "0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\n",
       "\\end{array}\\right)"
      ]
     },
     "execution_count": 19,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "show(r\"C_2 - C = \" + latex(C2 - C))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\text{Eigenvalues of $C_2$:}</script></html>"
      ],
      "text/latex": [
       "\\begin{math}\n",
       "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\text{Eigenvalues of $C_2$:}\n",
       "\\end{math}"
      ],
      "text/plain": [
       "\\text{Eigenvalues of $C_2$:}"
      ]
     },
     "execution_count": 20,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}-0.09492 + 0.12621i</script></html>"
      ],
      "text/latex": [
       "\\begin{math}\n",
       "\\newcommand{\\Bold}[1]{\\mathbf{#1}}-0.09492 + 0.12621i\n",
       "\\end{math}"
      ],
      "text/plain": [
       "-0.09492 + 0.12621*I"
      ]
     },
     "execution_count": 20,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}-0.09492 - 0.12621i</script></html>"
      ],
      "text/latex": [
       "\\begin{math}\n",
       "\\newcommand{\\Bold}[1]{\\mathbf{#1}}-0.09492 - 0.12621i\n",
       "\\end{math}"
      ],
      "text/plain": [
       "-0.09492 - 0.12621*I"
      ]
     },
     "execution_count": 20,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}0.3165 + 0.07173i</script></html>"
      ],
      "text/latex": [
       "\\begin{math}\n",
       "\\newcommand{\\Bold}[1]{\\mathbf{#1}}0.3165 + 0.07173i\n",
       "\\end{math}"
      ],
      "text/plain": [
       "0.3165 + 0.07173*I"
      ]
     },
     "execution_count": 20,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}0.3165 - 0.07173i</script></html>"
      ],
      "text/latex": [
       "\\begin{math}\n",
       "\\newcommand{\\Bold}[1]{\\mathbf{#1}}0.3165 - 0.07173i\n",
       "\\end{math}"
      ],
      "text/plain": [
       "0.3165 - 0.07173*I"
      ]
     },
     "execution_count": 20,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}0.7495 + 0.22485i</script></html>"
      ],
      "text/latex": [
       "\\begin{math}\n",
       "\\newcommand{\\Bold}[1]{\\mathbf{#1}}0.7495 + 0.22485i\n",
       "\\end{math}"
      ],
      "text/plain": [
       "0.7495 + 0.22485*I"
      ]
     },
     "execution_count": 20,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}0.7495 - 0.22485i</script></html>"
      ],
      "text/latex": [
       "\\begin{math}\n",
       "\\newcommand{\\Bold}[1]{\\mathbf{#1}}0.7495 - 0.22485i\n",
       "\\end{math}"
      ],
      "text/plain": [
       "0.7495 - 0.22485*I"
      ]
     },
     "execution_count": 20,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}0.95545</script></html>"
      ],
      "text/latex": [
       "\\begin{math}\n",
       "\\newcommand{\\Bold}[1]{\\mathbf{#1}}0.95545\n",
       "\\end{math}"
      ],
      "text/plain": [
       "0.95545"
      ]
     },
     "execution_count": 20,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "show(LatexExpr(r\"\\text{Eigenvalues of $C_2$:}\"))\n",
    "for evalue in C2.eigenvalues():\n",
    "    show(round_complex(evalue, 5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\tilde{D}_2 = \\left(\\begin{array}{rr|rr|rr|r}\n",
       "-0.09492 & 0.12621 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
       "-0.12621 & -0.09492 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
       "\\hline\n",
       " 0.0 & 0.0 & 0.3165 & 0.07173 & 0.0 & 0.0 & 0.0 \\\\\n",
       "0.0 & 0.0 & -0.07173 & 0.3165 & 0.0 & 0.0 & 0.0 \\\\\n",
       "\\hline\n",
       " 0.0 & 0.0 & 0.0 & 0.0 & 0.7495 & 0.22485 & 0.0 \\\\\n",
       "0.0 & 0.0 & 0.0 & 0.0 & -0.22485 & 0.7495 & 0.0 \\\\\n",
       "\\hline\n",
       " 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.95545\n",
       "\\end{array}\\right)</script></html>"
      ],
      "text/latex": [
       "\\begin{math}\n",
       "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\tilde{D}_2 = \\left(\\begin{array}{rr|rr|rr|r}\n",
       "-0.09492 & 0.12621 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
       "-0.12621 & -0.09492 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
       "\\hline\n",
       " 0.0 & 0.0 & 0.3165 & 0.07173 & 0.0 & 0.0 & 0.0 \\\\\n",
       "0.0 & 0.0 & -0.07173 & 0.3165 & 0.0 & 0.0 & 0.0 \\\\\n",
       "\\hline\n",
       " 0.0 & 0.0 & 0.0 & 0.0 & 0.7495 & 0.22485 & 0.0 \\\\\n",
       "0.0 & 0.0 & 0.0 & 0.0 & -0.22485 & 0.7495 & 0.0 \\\\\n",
       "\\hline\n",
       " 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.95545\n",
       "\\end{array}\\right)\n",
       "\\end{math}"
      ],
      "text/plain": [
       "\\tilde{D}_2 = \\left(\\begin{array}{rr|rr|rr|r}\n",
       "-0.09492 & 0.12621 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
       "-0.12621 & -0.09492 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
       "\\hline\n",
       " 0.0 & 0.0 & 0.3165 & 0.07173 & 0.0 & 0.0 & 0.0 \\\\\n",
       "0.0 & 0.0 & -0.07173 & 0.3165 & 0.0 & 0.0 & 0.0 \\\\\n",
       "\\hline\n",
       " 0.0 & 0.0 & 0.0 & 0.0 & 0.7495 & 0.22485 & 0.0 \\\\\n",
       "0.0 & 0.0 & 0.0 & 0.0 & -0.22485 & 0.7495 & 0.0 \\\\\n",
       "\\hline\n",
       " 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.95545\n",
       "\\end{array}\\right)"
      ]
     },
     "execution_count": 21,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "T2 = transformation_matrix(C2)\n",
    "D2 = T2.inverse()*C2*T2\n",
    "show(r\"\\tilde{D}_2 = \" + latex(make_block_diagonal(D2.round(5))))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\text{The absolute values of the eigenvalues:}</script></html>"
      ],
      "text/latex": [
       "\\begin{math}\n",
       "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\text{The absolute values of the eigenvalues:}\n",
       "\\end{math}"
      ],
      "text/plain": [
       "\\text{The absolute values of the eigenvalues:}"
      ]
     },
     "execution_count": 22,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}| -0.0949 + 0.1262i | = 0.1579</script></html>"
      ],
      "text/latex": [
       "\\begin{math}\n",
       "\\newcommand{\\Bold}[1]{\\mathbf{#1}}| -0.0949 + 0.1262i | = 0.1579\n",
       "\\end{math}"
      ],
      "text/plain": [
       "| -0.0949 + 0.1262i | = 0.1579"
      ]
     },
     "execution_count": 22,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}| -0.0949 - 0.1262i | = 0.1579</script></html>"
      ],
      "text/latex": [
       "\\begin{math}\n",
       "\\newcommand{\\Bold}[1]{\\mathbf{#1}}| -0.0949 - 0.1262i | = 0.1579\n",
       "\\end{math}"
      ],
      "text/plain": [
       "| -0.0949 - 0.1262i | = 0.1579"
      ]
     },
     "execution_count": 22,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}| 0.3165 + 0.0717i | = 0.3245</script></html>"
      ],
      "text/latex": [
       "\\begin{math}\n",
       "\\newcommand{\\Bold}[1]{\\mathbf{#1}}| 0.3165 + 0.0717i | = 0.3245\n",
       "\\end{math}"
      ],
      "text/plain": [
       "| 0.3165 + 0.0717i | = 0.3245"
      ]
     },
     "execution_count": 22,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}| 0.3165 - 0.0717i | = 0.3245</script></html>"
      ],
      "text/latex": [
       "\\begin{math}\n",
       "\\newcommand{\\Bold}[1]{\\mathbf{#1}}| 0.3165 - 0.0717i | = 0.3245\n",
       "\\end{math}"
      ],
      "text/plain": [
       "| 0.3165 - 0.0717i | = 0.3245"
      ]
     },
     "execution_count": 22,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}| 0.7495 + 0.2249i | = 0.7825</script></html>"
      ],
      "text/latex": [
       "\\begin{math}\n",
       "\\newcommand{\\Bold}[1]{\\mathbf{#1}}| 0.7495 + 0.2249i | = 0.7825\n",
       "\\end{math}"
      ],
      "text/plain": [
       "| 0.7495 + 0.2249i | = 0.7825"
      ]
     },
     "execution_count": 22,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}| 0.7495 - 0.2249i | = 0.7825</script></html>"
      ],
      "text/latex": [
       "\\begin{math}\n",
       "\\newcommand{\\Bold}[1]{\\mathbf{#1}}| 0.7495 - 0.2249i | = 0.7825\n",
       "\\end{math}"
      ],
      "text/plain": [
       "| 0.7495 - 0.2249i | = 0.7825"
      ]
     },
     "execution_count": 22,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}0.9554</script></html>"
      ],
      "text/latex": [
       "\\begin{math}\n",
       "\\newcommand{\\Bold}[1]{\\mathbf{#1}}0.9554\n",
       "\\end{math}"
      ],
      "text/plain": [
       "0.9554"
      ]
     },
     "execution_count": 22,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "show(LatexExpr(r\"\\text{The absolute values of the eigenvalues:}\"))\n",
    "for evalue in C2.eigenvalues():\n",
    "    if evalue.imag() or evalue < 0:\n",
    "        show(r\"|\" + latex(round_complex(evalue, 4)) + r\"| = \" + latex(round(abs(evalue), 4)))\n",
    "    else:\n",
    "        show(round(abs(evalue), 4))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "5a1d8ee394da4ec5aa079e97c1ce9de7",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Interactive function <function discrete_linear_interactive.<locals>.update at 0x7f2091aaca60> with 1 widget\n",
       "  …"
      ]
     },
     "execution_count": 23,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "d024671e55824ae1a49de318bc115a90",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "FigureWidget({\n",
       "    'data': [],\n",
       "    'layout': {'annotations': [{'font': {'size': 18},\n",
       "                         …"
      ]
     },
     "execution_count": 23,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "state = vector([100.0] * 7)\n",
    "discrete_linear_interactive(C2, state, pre_text=life_stages)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "38bcf6f50a464ece8d78950b8111b06c",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Interactive function <function discrete_linear_interactive.<locals>.update at 0x7f208e90cf70> with 1 widget\n",
       "  …"
      ]
     },
     "execution_count": 24,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "c451177b2bb54d8dbb0aed7f88b6c57e",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "FigureWidget({\n",
       "    'data': [],\n",
       "    'layout': {'annotations': [{'font': {'size': 18},\n",
       "                         …"
      ]
     },
     "execution_count": 24,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "state = vector([100.0] * 7)\n",
    "discrete_linear_interactive(C2, state, pre_text=life_stages, show_distribution=True)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# That didn't work. ☹\n",
    "\n",
    "<br>\n",
    "<br>\n",
    "\n",
    "**Conclusion, so far:** Protecting eggs, nests, hatchlings ***isn't enough*** by itself. \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "**What if, instead, we protect the juvenile turtles, and especially the older juveniles?**\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}C_3 = \\left(\\begin{array}{rrrrrrr}\n",
       "0.0 & 0.0 & 0.0 & 0.0 & 127.0 & 4.0 & 80.0 \\\\\n",
       "0.6747 & 0.747 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
       "0.0 & 0.0531 & 0.7597 & 0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
       "0.0 & 0.0 & 0.0403 & 0.7289 & 0.0 & 0.0 & 0.0 \\\\\n",
       "0.0 & 0.0 & 0.0 & 0.071 & 0.0 & 0.0 & 0.0 \\\\\n",
       "0.0 & 0.0 & 0.0 & 0.0 & 0.8091 & 0.0 & 0.0 \\\\\n",
       "0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.8091 & 0.8089\n",
       "\\end{array}\\right)</script></html>"
      ],
      "text/latex": [
       "\\begin{math}\n",
       "\\newcommand{\\Bold}[1]{\\mathbf{#1}}C_3 = \\left(\\begin{array}{rrrrrrr}\n",
       "0.0 & 0.0 & 0.0 & 0.0 & 127.0 & 4.0 & 80.0 \\\\\n",
       "0.6747 & 0.747 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
       "0.0 & 0.0531 & 0.7597 & 0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
       "0.0 & 0.0 & 0.0403 & 0.7289 & 0.0 & 0.0 & 0.0 \\\\\n",
       "0.0 & 0.0 & 0.0 & 0.071 & 0.0 & 0.0 & 0.0 \\\\\n",
       "0.0 & 0.0 & 0.0 & 0.0 & 0.8091 & 0.0 & 0.0 \\\\\n",
       "0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.8091 & 0.8089\n",
       "\\end{array}\\right)\n",
       "\\end{math}"
      ],
      "text/plain": [
       "C_3 = \\left(\\begin{array}{rrrrrrr}\n",
       "0.0 & 0.0 & 0.0 & 0.0 & 127.0 & 4.0 & 80.0 \\\\\n",
       "0.6747 & 0.747 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
       "0.0 & 0.0531 & 0.7597 & 0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
       "0.0 & 0.0 & 0.0403 & 0.7289 & 0.0 & 0.0 & 0.0 \\\\\n",
       "0.0 & 0.0 & 0.0 & 0.071 & 0.0 & 0.0 & 0.0 \\\\\n",
       "0.0 & 0.0 & 0.0 & 0.0 & 0.8091 & 0.0 & 0.0 \\\\\n",
       "0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.8091 & 0.8089\n",
       "\\end{array}\\right)"
      ]
     },
     "execution_count": 25,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "C3 = matrix(RDF, [\n",
    "    [0,      0,      0,      0,      127,      4,      80     ],\n",
    "    [0.6747, 0.7470, 0,      0,        0,      0,       0     ],\n",
    "    [0,      0.0531, 0.7597, 0,        0,      0,       0     ],\n",
    "    [0,      0,      0.0403, 0.7289,   0,      0,       0     ],\n",
    "    [0,      0,      0,      0.0710,   0,      0,       0     ],\n",
    "    [0,      0,      0,      0,        0.8091, 0,       0     ],\n",
    "    [0,      0,      0,      0,        0,      0.8091,  0.8089],\n",
    "])\n",
    "show(r\"C_3 = \" + latex(C3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "**The difference between this third matrix, $C_3$, and the original one, $C$:**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}C_3 - C = \\left(\\begin{array}{rrrrrrr}\n",
       "0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
       "0.0 & 0.01 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
       "0.0 & 0.0045 & 0.0987 & 0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
       "0.0 & 0.0 & 0.0256 & 0.0382 & 0.0 & 0.0 & 0.0 \\\\\n",
       "0.0 & 0.0 & 0.0 & 0.0192 & 0.0 & 0.0 & 0.0 \\\\\n",
       "0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
       "0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\n",
       "\\end{array}\\right)</script></html>"
      ],
      "text/latex": [
       "\\begin{math}\n",
       "\\newcommand{\\Bold}[1]{\\mathbf{#1}}C_3 - C = \\left(\\begin{array}{rrrrrrr}\n",
       "0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
       "0.0 & 0.01 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
       "0.0 & 0.0045 & 0.0987 & 0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
       "0.0 & 0.0 & 0.0256 & 0.0382 & 0.0 & 0.0 & 0.0 \\\\\n",
       "0.0 & 0.0 & 0.0 & 0.0192 & 0.0 & 0.0 & 0.0 \\\\\n",
       "0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
       "0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\n",
       "\\end{array}\\right)\n",
       "\\end{math}"
      ],
      "text/plain": [
       "C_3 - C = \\left(\\begin{array}{rrrrrrr}\n",
       "0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
       "0.0 & 0.01 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
       "0.0 & 0.0045 & 0.0987 & 0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
       "0.0 & 0.0 & 0.0256 & 0.0382 & 0.0 & 0.0 & 0.0 \\\\\n",
       "0.0 & 0.0 & 0.0 & 0.0192 & 0.0 & 0.0 & 0.0 \\\\\n",
       "0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
       "0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\n",
       "\\end{array}\\right)"
      ]
     },
     "execution_count": 26,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "show(r\"C_3 - C = \" + latex((C3 - C).round(5)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\text{Eigenvalues of $C_3$:}</script></html>"
      ],
      "text/latex": [
       "\\begin{math}\n",
       "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\text{Eigenvalues of $C_3$:}\n",
       "\\end{math}"
      ],
      "text/plain": [
       "\\text{Eigenvalues of $C_3$:}"
      ]
     },
     "execution_count": 27,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}-0.13101 + 0.16979i</script></html>"
      ],
      "text/latex": [
       "\\begin{math}\n",
       "\\newcommand{\\Bold}[1]{\\mathbf{#1}}-0.13101 + 0.16979i\n",
       "\\end{math}"
      ],
      "text/plain": [
       "-0.13101 + 0.16979*I"
      ]
     },
     "execution_count": 27,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}-0.13101 - 0.16979i</script></html>"
      ],
      "text/latex": [
       "\\begin{math}\n",
       "\\newcommand{\\Bold}[1]{\\mathbf{#1}}-0.13101 - 0.16979i\n",
       "\\end{math}"
      ],
      "text/plain": [
       "-0.13101 - 0.16979*I"
      ]
     },
     "execution_count": 27,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}1.05704</script></html>"
      ],
      "text/latex": [
       "\\begin{math}\n",
       "\\newcommand{\\Bold}[1]{\\mathbf{#1}}1.05704\n",
       "\\end{math}"
      ],
      "text/plain": [
       "1.05704"
      ]
     },
     "execution_count": 27,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}0.79315 + 0.2994i</script></html>"
      ],
      "text/latex": [
       "\\begin{math}\n",
       "\\newcommand{\\Bold}[1]{\\mathbf{#1}}0.79315 + 0.2994i\n",
       "\\end{math}"
      ],
      "text/plain": [
       "0.79315 + 0.2994*I"
      ]
     },
     "execution_count": 27,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}0.79315 - 0.2994i</script></html>"
      ],
      "text/latex": [
       "\\begin{math}\n",
       "\\newcommand{\\Bold}[1]{\\mathbf{#1}}0.79315 - 0.2994i\n",
       "\\end{math}"
      ],
      "text/plain": [
       "0.79315 - 0.2994*I"
      ]
     },
     "execution_count": 27,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}0.33159 + 0.18977i</script></html>"
      ],
      "text/latex": [
       "\\begin{math}\n",
       "\\newcommand{\\Bold}[1]{\\mathbf{#1}}0.33159 + 0.18977i\n",
       "\\end{math}"
      ],
      "text/plain": [
       "0.33159 + 0.18977*I"
      ]
     },
     "execution_count": 27,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}0.33159 - 0.18977i</script></html>"
      ],
      "text/latex": [
       "\\begin{math}\n",
       "\\newcommand{\\Bold}[1]{\\mathbf{#1}}0.33159 - 0.18977i\n",
       "\\end{math}"
      ],
      "text/plain": [
       "0.33159 - 0.18977*I"
      ]
     },
     "execution_count": 27,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "show(LatexExpr(r\"\\text{Eigenvalues of $C_3$:}\"))\n",
    "for evalue in C3.eigenvalues():\n",
    "    show(round_complex(evalue, 5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\tilde{D}_3 = \\left(\\begin{array}{rr|r|rr|rr}\n",
       "-0.13101 & 0.16979 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
       "-0.16979 & -0.13101 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
       "\\hline\n",
       " 0.0 & 0.0 & 1.05704 & 0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
       "\\hline\n",
       " 0.0 & 0.0 & 0.0 & 0.79315 & 0.2994 & 0.0 & 0.0 \\\\\n",
       "0.0 & 0.0 & 0.0 & -0.2994 & 0.79315 & 0.0 & 0.0 \\\\\n",
       "\\hline\n",
       " 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.33159 & 0.18977 \\\\\n",
       "0.0 & 0.0 & 0.0 & 0.0 & 0.0 & -0.18977 & 0.33159\n",
       "\\end{array}\\right)</script></html>"
      ],
      "text/latex": [
       "\\begin{math}\n",
       "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\tilde{D}_3 = \\left(\\begin{array}{rr|r|rr|rr}\n",
       "-0.13101 & 0.16979 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
       "-0.16979 & -0.13101 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
       "\\hline\n",
       " 0.0 & 0.0 & 1.05704 & 0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
       "\\hline\n",
       " 0.0 & 0.0 & 0.0 & 0.79315 & 0.2994 & 0.0 & 0.0 \\\\\n",
       "0.0 & 0.0 & 0.0 & -0.2994 & 0.79315 & 0.0 & 0.0 \\\\\n",
       "\\hline\n",
       " 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.33159 & 0.18977 \\\\\n",
       "0.0 & 0.0 & 0.0 & 0.0 & 0.0 & -0.18977 & 0.33159\n",
       "\\end{array}\\right)\n",
       "\\end{math}"
      ],
      "text/plain": [
       "\\tilde{D}_3 = \\left(\\begin{array}{rr|r|rr|rr}\n",
       "-0.13101 & 0.16979 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
       "-0.16979 & -0.13101 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
       "\\hline\n",
       " 0.0 & 0.0 & 1.05704 & 0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
       "\\hline\n",
       " 0.0 & 0.0 & 0.0 & 0.79315 & 0.2994 & 0.0 & 0.0 \\\\\n",
       "0.0 & 0.0 & 0.0 & -0.2994 & 0.79315 & 0.0 & 0.0 \\\\\n",
       "\\hline\n",
       " 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.33159 & 0.18977 \\\\\n",
       "0.0 & 0.0 & 0.0 & 0.0 & 0.0 & -0.18977 & 0.33159\n",
       "\\end{array}\\right)"
      ]
     },
     "execution_count": 28,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "T3 = transformation_matrix(C3)\n",
    "D3 = T3.inverse()*C3*T3\n",
    "show(r\"\\tilde{D}_3 = \" + latex(make_block_diagonal(D3.round(5))))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\text{The absolute values of the eigenvalues:}</script></html>"
      ],
      "text/latex": [
       "\\begin{math}\n",
       "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\text{The absolute values of the eigenvalues:}\n",
       "\\end{math}"
      ],
      "text/plain": [
       "\\text{The absolute values of the eigenvalues:}"
      ]
     },
     "execution_count": 29,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}| -0.131 + 0.1698i | = 0.2145</script></html>"
      ],
      "text/latex": [
       "\\begin{math}\n",
       "\\newcommand{\\Bold}[1]{\\mathbf{#1}}| -0.131 + 0.1698i | = 0.2145\n",
       "\\end{math}"
      ],
      "text/plain": [
       "| -0.131 + 0.1698i | = 0.2145"
      ]
     },
     "execution_count": 29,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}| -0.131 - 0.1698i | = 0.2145</script></html>"
      ],
      "text/latex": [
       "\\begin{math}\n",
       "\\newcommand{\\Bold}[1]{\\mathbf{#1}}| -0.131 - 0.1698i | = 0.2145\n",
       "\\end{math}"
      ],
      "text/plain": [
       "| -0.131 - 0.1698i | = 0.2145"
      ]
     },
     "execution_count": 29,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}1.057</script></html>"
      ],
      "text/latex": [
       "\\begin{math}\n",
       "\\newcommand{\\Bold}[1]{\\mathbf{#1}}1.057\n",
       "\\end{math}"
      ],
      "text/plain": [
       "1.057"
      ]
     },
     "execution_count": 29,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}| 0.7931 + 0.2994i | = 0.8478</script></html>"
      ],
      "text/latex": [
       "\\begin{math}\n",
       "\\newcommand{\\Bold}[1]{\\mathbf{#1}}| 0.7931 + 0.2994i | = 0.8478\n",
       "\\end{math}"
      ],
      "text/plain": [
       "| 0.7931 + 0.2994i | = 0.8478"
      ]
     },
     "execution_count": 29,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}| 0.7931 - 0.2994i | = 0.8478</script></html>"
      ],
      "text/latex": [
       "\\begin{math}\n",
       "\\newcommand{\\Bold}[1]{\\mathbf{#1}}| 0.7931 - 0.2994i | = 0.8478\n",
       "\\end{math}"
      ],
      "text/plain": [
       "| 0.7931 - 0.2994i | = 0.8478"
      ]
     },
     "execution_count": 29,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}| 0.3316 + 0.1898i | = 0.3821</script></html>"
      ],
      "text/latex": [
       "\\begin{math}\n",
       "\\newcommand{\\Bold}[1]{\\mathbf{#1}}| 0.3316 + 0.1898i | = 0.3821\n",
       "\\end{math}"
      ],
      "text/plain": [
       "| 0.3316 + 0.1898i | = 0.3821"
      ]
     },
     "execution_count": 29,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}| 0.3316 - 0.1898i | = 0.3821</script></html>"
      ],
      "text/latex": [
       "\\begin{math}\n",
       "\\newcommand{\\Bold}[1]{\\mathbf{#1}}| 0.3316 - 0.1898i | = 0.3821\n",
       "\\end{math}"
      ],
      "text/plain": [
       "| 0.3316 - 0.1898i | = 0.3821"
      ]
     },
     "execution_count": 29,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "show(LatexExpr(r\"\\text{The absolute values of the eigenvalues:}\"))\n",
    "for evalue in C3.eigenvalues():\n",
    "    if evalue.imag() or evalue < 0:\n",
    "        show(r\"|\" + latex(round_complex(evalue, 4)) + r\"| = \" + latex(round(abs(evalue), 4)))\n",
    "    else:\n",
    "        show(round(abs(evalue), 4))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "14b5a079cdc24c719212aa270cb87fd6",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Interactive function <function discrete_linear_interactive.<locals>.update at 0x7f208e8890d0> with 1 widget\n",
       "  …"
      ]
     },
     "execution_count": 30,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "70d3a9bb9af2483790bd5aa239809351",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "FigureWidget({\n",
       "    'data': [],\n",
       "    'layout': {'annotations': [{'font': {'size': 18},\n",
       "                         …"
      ]
     },
     "execution_count": 30,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "state = vector([100.0] * 7)\n",
    "discrete_linear_interactive(C3, state, pre_text=life_stages)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "8026b59a5fd94beaa17af5f3a1915ba7",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Interactive function <function discrete_linear_interactive.<locals>.update at 0x7f208e889430> with 1 widget\n",
       "  …"
      ]
     },
     "execution_count": 31,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "6a3a694f0b6b4658b2cc71ea86e60872",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "FigureWidget({\n",
       "    'data': [],\n",
       "    'layout': {'annotations': [{'font': {'size': 18},\n",
       "                         …"
      ]
     },
     "execution_count": 31,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "state = vector([100.0] * 7)\n",
    "discrete_linear_interactive(C3, state, pre_text=life_stages, show_distribution=True)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Success! ☺\n",
    "\n",
    "<br>\n",
    "<br>\n",
    "\n",
    "**New conclusion:** We must protect juveniles, and especially larger juveniles. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/jpeg": "9fa9a3d0c9d017fe160a0bd94d13345a878180e9",
      "text/html": [
       "\n",
       "        <iframe\n",
       "            width=\"400\"\n",
       "            height=\"300\"\n",
       "            src=\"https://www.youtube.com/embed/hIJvSymWsCc?start=62\"\n",
       "            frameborder=\"0\"\n",
       "            allowfullscreen\n",
       "        ></iframe>\n",
       "        "
      ],
      "text/plain": [
       "<IPython.lib.display.YouTubeVideo object at 0x7f208e8dfdc0>"
      ]
     },
     "execution_count": 32,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "display(YouTubeVideo(\"hIJvSymWsCc\", start=62))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/jpeg": "5424fa0b6f7e9fc778e1d8a2fff21ceed93c0c9a",
      "text/html": [
       "\n",
       "        <iframe\n",
       "            width=\"400\"\n",
       "            height=\"300\"\n",
       "            src=\"https://www.youtube.com/embed/y71cgxmyMO4?start=246\"\n",
       "            frameborder=\"0\"\n",
       "            allowfullscreen\n",
       "        ></iframe>\n",
       "        "
      ],
      "text/plain": [
       "<IPython.lib.display.YouTubeVideo object at 0x7f208e91d070>"
      ]
     },
     "execution_count": 33,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "display(YouTubeVideo(\"y71cgxmyMO4\", start=246))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "**The happy ending to this story:**\n",
    "\n",
    "This paper was published in 1987. That same year, the U.S. Congress passed a law requiring all shrimp trawling boats in the U.S. to use nets equipped with a *turtle excluder device* (TED). \n",
    "\n",
    "A few years later, an international treaty was signed, requiring shrimp fishers from most other developed nations to use TEDs on their nets. The U.S. also passed, with support from the World Trade Organization, a trade embargo that prohibits the import of shrimp from countries that do not require TEDs. \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "While loggerhead sea turtles are still considered a threatened species, the populations in the southeastern U.S. have recovered significantly since the 1980s. \n",
    "\n",
    "***In short:*** **This math paper has helped to save the loggerhead sea turtles!** "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
   ],
   "source": [
   ]
  }
 ],
 "metadata": {
  "celltoolbar": "Slideshow",
  "hide_input": false,
  "kernelspec": {
   "display_name": "SageMath 9.2",
   "language": "sagemath",
   "metadata": {
    "cocalc": {
     "description": "Open-source mathematical software system",
     "priority": 1,
     "url": "https://www.sagemath.org/"
    }
   },
   "name": "sage-9.2",
   "resource_dir": "/ext/jupyter/kernels/sage-9.2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}