\n",
+ "\n",
+ "\n",
+ " \n",
+ "
\n",
+ "
"
+ ],
+ "text/plain": [
+ "olin 10\n",
+ "wellesley 2\n",
+ "dtype: int64"
+ ]
+ },
+ "execution_count": 43,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
"source": [
"bikeshare"
]
@@ -353,24 +556,128 @@
},
{
"cell_type": "code",
- "execution_count": 13,
+ "execution_count": 44,
"metadata": {},
- "outputs": [],
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "10"
+ ]
+ },
+ "execution_count": 44,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
"source": [
"bikeshare.olin"
]
},
{
"cell_type": "code",
- "execution_count": 14,
+ "execution_count": 47,
"metadata": {
"scrolled": true
},
- "outputs": [],
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "2"
+ ]
+ },
+ "execution_count": 47,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
"source": [
"bikeshare.wellesley"
]
},
+ {
+ "cell_type": "code",
+ "execution_count": 51,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "| \n", + " | value | \n", + "
|---|---|
| olin | \n", + "10 | \n", + "
| wellesley | \n", + "2 | \n", + "
\n",
+ "\n",
+ "\n",
+ " \n",
+ "
\n",
+ "
"
+ ],
+ "text/plain": [
+ "olin 10\n",
+ "wellesley 2\n",
+ "babson 0\n",
+ "dtype: int64"
+ ]
+ },
+ "execution_count": 51,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "bikeshare"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 52,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "0"
+ ]
+ },
+ "execution_count": 52,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "bikeshare.babson"
+ ]
+ },
{
"cell_type": "markdown",
"metadata": {},
@@ -400,8 +707,10 @@
},
{
"cell_type": "code",
- "execution_count": 15,
- "metadata": {},
+ "execution_count": 63,
+ "metadata": {
+ "collapsed": true
+ },
"outputs": [],
"source": [
"newfig()\n",
@@ -418,9 +727,62 @@
},
{
"cell_type": "code",
- "execution_count": 16,
- "metadata": {},
- "outputs": [],
+ "execution_count": 76,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "| \n", + " | value | \n", + "
|---|---|
| olin | \n", + "10 | \n", + "
| wellesley | \n", + "2 | \n", + "
| babson | \n", + "0 | \n", + "
\n",
+ "\n",
+ "\n",
+ " \n",
+ "
\n",
+ "
"
+ ],
+ "text/plain": [
+ "olin 3\n",
+ "wellesley 9\n",
+ "babson 0\n",
+ "dtype: int64"
+ ]
+ },
+ "execution_count": 76,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
"source": [
"bikeshare.olin -= 1\n",
"bikeshare.wellesley += 1\n",
@@ -436,7 +798,7 @@
},
{
"cell_type": "code",
- "execution_count": 17,
+ "execution_count": 66,
"metadata": {
"collapsed": true
},
@@ -455,11 +817,12 @@
},
{
"cell_type": "code",
- "execution_count": 18,
+ "execution_count": 81,
"metadata": {},
"outputs": [],
"source": [
- "# Solution goes here"
+ "plot(bikeshare.olin, 'rs-')\n",
+ "plot(bikeshare.wellesley, 'bo-')"
]
},
{
@@ -473,7 +836,7 @@
},
{
"cell_type": "code",
- "execution_count": 19,
+ "execution_count": 82,
"metadata": {
"collapsed": true
},
@@ -493,7 +856,7 @@
},
{
"cell_type": "code",
- "execution_count": 20,
+ "execution_count": 83,
"metadata": {
"collapsed": true
},
@@ -513,9 +876,64 @@
},
{
"cell_type": "code",
- "execution_count": 21,
- "metadata": {},
- "outputs": [],
+ "execution_count": 86,
+ "metadata": {
+ "scrolled": true
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "| \n", + " | value | \n", + "
|---|---|
| olin | \n", + "3 | \n", + "
| wellesley | \n", + "9 | \n", + "
| babson | \n", + "0 | \n", + "
\n",
+ "\n",
+ "\n",
+ " \n",
+ "
\n",
+ "
"
+ ],
+ "text/plain": [
+ "olin -1\n",
+ "wellesley 13\n",
+ "babson 0\n",
+ "dtype: int64"
+ ]
+ },
+ "execution_count": 86,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
"source": [
"bike_to_wellesley()\n",
"plot_state()\n",
@@ -533,9 +951,20 @@
},
{
"cell_type": "code",
- "execution_count": 22,
+ "execution_count": 87,
"metadata": {},
- "outputs": [],
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "| \n", + " | value | \n", + "
|---|---|
| olin | \n", + "-1 | \n", + "
| wellesley | \n", + "13 | \n", + "
| babson | \n", + "0 | \n", + "
\n",
+ "\n",
+ "\n",
+ " \n",
+ "
\n",
+ "
"
+ ],
+ "text/plain": [
+ "olin 10\n",
+ "wellesley 2\n",
+ "babson 0\n",
+ "dtype: int64"
+ ]
+ },
+ "execution_count": 105,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
"source": [
- "# Solution goes here"
+ "def bike_to_olin():\n",
+ " bikeshare.olin += 1\n",
+ " bikeshare.wellesley -= 1\n",
+ " \n",
+ "bike_to_olin()\n",
+ "bikeshare"
]
},
{
@@ -579,8 +1066,10 @@
},
{
"cell_type": "code",
- "execution_count": 24,
- "metadata": {},
+ "execution_count": 123,
+ "metadata": {
+ "collapsed": true
+ },
"outputs": [],
"source": [
"bikeshare = System(olin=10, wellesley=2)\n",
@@ -597,7 +1086,7 @@
},
{
"cell_type": "code",
- "execution_count": 25,
+ "execution_count": 124,
"metadata": {
"collapsed": true
},
@@ -617,7 +1106,7 @@
},
{
"cell_type": "code",
- "execution_count": 26,
+ "execution_count": 125,
"metadata": {
"collapsed": true
},
@@ -641,9 +1130,57 @@
},
{
"cell_type": "code",
- "execution_count": 27,
- "metadata": {},
- "outputs": [],
+ "execution_count": 126,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "| \n", + " | value | \n", + "
|---|---|
| olin | \n", + "10 | \n", + "
| wellesley | \n", + "2 | \n", + "
| babson | \n", + "0 | \n", + "
\n",
+ "\n",
+ "\n",
+ " \n",
+ "
\n",
+ "
"
+ ],
+ "text/plain": [
+ "olin 9\n",
+ "wellesley 3\n",
+ "dtype: int64"
+ ]
+ },
+ "execution_count": 126,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
"source": [
"bike_to_wellesley()\n",
"plot_state()\n",
@@ -659,9 +1196,57 @@
},
{
"cell_type": "code",
- "execution_count": 28,
- "metadata": {},
- "outputs": [],
+ "execution_count": 127,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "| \n", + " | value | \n", + "
|---|---|
| olin | \n", + "9 | \n", + "
| wellesley | \n", + "3 | \n", + "
\n",
+ "\n",
+ "\n",
+ " \n",
+ "
\n",
+ "
"
+ ],
+ "text/plain": [
+ "olin 10\n",
+ "wellesley 2\n",
+ "dtype: int64"
+ ]
+ },
+ "execution_count": 127,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
"source": [
"bike_to_olin()\n",
"plot_state()\n",
@@ -677,7 +1262,7 @@
},
{
"cell_type": "code",
- "execution_count": 29,
+ "execution_count": 128,
"metadata": {
"collapsed": true
},
@@ -697,22 +1282,20 @@
"cell_type": "markdown",
"metadata": {},
"source": [
- "Whenever you make a figure, you should put labels on the axes to explain what they mean and what units they are measured in.\n",
- "\n",
- "We can use `decorate`, which is defined in the `modsim` library, to label the axes and add a title."
+ "Whenever you make a figure, you should put labels on the axes to explain what they mean and what units they are measured in. Here's how:"
]
},
{
"cell_type": "code",
- "execution_count": 30,
+ "execution_count": 129,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
- "decorate(title='Olin-Wellesley Bikeshare',\n",
- " xlabel='Time step (min)', \n",
- " ylabel='Number of bikes')"
+ "label_axes(title='Olin-Wellesley Bikeshare',\n",
+ " xlabel='Time step (min)', \n",
+ " ylabel='Number of bikes')"
]
},
{
@@ -726,9 +1309,17 @@
},
{
"cell_type": "code",
- "execution_count": 31,
+ "execution_count": 115,
"metadata": {},
- "outputs": [],
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Saving figure to file chap01_fig01.pdf\n"
+ ]
+ }
+ ],
"source": [
"savefig('chap01_fig01.pdf')"
]
@@ -744,20 +1335,33 @@
},
{
"cell_type": "code",
- "execution_count": 32,
- "metadata": {
- "collapsed": true
- },
- "outputs": [],
+ "execution_count": 171,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "olin 10\n",
+ "wellesley 2\n",
+ "dtype: int64\n",
+ "| \n", + " | value | \n", + "
|---|---|
| olin | \n", + "10 | \n", + "
| wellesley | \n", + "2 | \n", + "
\n",
+ "\n",
+ "\n",
+ " \n",
+ "
\n",
+ "
"
+ ],
+ "text/plain": [
+ "olin 8\n",
+ "wellesley 4\n",
+ "dtype: int64"
+ ]
+ },
+ "execution_count": 193,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
"source": [
"if flip(0.7):\n",
" bike_to_wellesley()\n",
@@ -902,9 +1615,64 @@
},
{
"cell_type": "code",
- "execution_count": 41,
- "metadata": {},
- "outputs": [],
+ "execution_count": 195,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Moving a bike to Olin\n"
+ ]
+ },
+ {
+ "data": {
+ "text/html": [
+ "| \n", + " | value | \n", + "
|---|---|
| olin | \n", + "8 | \n", + "
| wellesley | \n", + "4 | \n", + "
\n",
+ "\n",
+ "\n",
+ " \n",
+ "
\n",
+ "
"
+ ],
+ "text/plain": [
+ "olin 9\n",
+ "wellesley 3\n",
+ "dtype: int64"
+ ]
+ },
+ "execution_count": 195,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
"source": [
"if flip(0.6):\n",
" bike_to_olin()\n",
@@ -923,7 +1691,7 @@
},
{
"cell_type": "code",
- "execution_count": 42,
+ "execution_count": 199,
"metadata": {
"collapsed": true
},
@@ -948,9 +1716,64 @@
},
{
"cell_type": "code",
- "execution_count": 43,
- "metadata": {},
- "outputs": [],
+ "execution_count": 204,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Moving a bike to Wellesley\n"
+ ]
+ },
+ {
+ "data": {
+ "text/html": [
+ "| \n", + " | value | \n", + "
|---|---|
| olin | \n", + "9 | \n", + "
| wellesley | \n", + "3 | \n", + "
\n",
+ "\n",
+ "\n",
+ " \n",
+ "
\n",
+ "
"
+ ],
+ "text/plain": [
+ "olin 9\n",
+ "wellesley 3\n",
+ "dtype: int64"
+ ]
+ },
+ "execution_count": 204,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
"source": [
"step()\n",
"plot_state()\n",
@@ -961,39 +1784,61 @@
"cell_type": "markdown",
"metadata": {},
"source": [
- "Finally, we should label the axes and add a title. This time, I'll wrap `decorate` in a function, so we don't have to write the same code over and over."
+ "The following function labels the axes and adds a legend to the figure."
]
},
{
"cell_type": "code",
- "execution_count": 44,
- "metadata": {
- "collapsed": true
- },
- "outputs": [],
+ "execution_count": 206,
+ "metadata": {},
+ "outputs": [
+ {
+ "ename": "SyntaxError",
+ "evalue": "invalid syntax (| \n", + " | value | \n", + "
|---|---|
| olin | \n", + "9 | \n", + "
| wellesley | \n", + "3 | \n", + "
\n",
+ "\n",
+ "\n",
+ " \n",
+ "
\n",
+ "
"
+ ],
+ "text/plain": [
+ "olin 10\n",
+ "wellesley 2\n",
+ "dtype: int64"
+ ]
+ },
+ "execution_count": 287,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "bikeshare1 = System(olin=10, wellesley=2)\n",
+ "bikeshare1"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 288,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "| \n", + " | value | \n", + "
|---|---|
| olin | \n", + "10 | \n", + "
| wellesley | \n", + "2 | \n", + "
\n",
+ "\n",
+ "\n",
+ " \n",
+ "
\n",
+ "
"
+ ],
+ "text/plain": [
+ "olin 10\n",
+ "wellesley 2\n",
+ "dtype: int64"
+ ]
+ },
+ "execution_count": 288,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "bikeshare2 = System(olin=10, wellesley=2)\n",
+ "bikeshare2"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "And whenever we call a function, we indicate which `System` object to work with:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 289,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "bike_to_olin(bikeshare1)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 290,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "bike_to_wellesley(bikeshare2)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "And you can confirm that the different systems are getting updated independently:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 291,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "| \n", + " | value | \n", + "
|---|---|
| olin | \n", + "10 | \n", + "
| wellesley | \n", + "2 | \n", + "
\n",
+ "\n",
+ "\n",
+ " \n",
+ "
\n",
+ "
"
+ ],
+ "text/plain": [
+ "olin 11\n",
+ "wellesley 1\n",
+ "dtype: int64"
+ ]
+ },
+ "execution_count": 291,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "bikeshare1"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 292,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "| \n", + " | value | \n", + "
|---|---|
| olin | \n", + "11 | \n", + "
| wellesley | \n", + "1 | \n", + "
\n",
+ "\n",
+ "\n",
+ " \n",
+ "
\n",
+ "
"
+ ],
+ "text/plain": [
+ "olin 9\n",
+ "wellesley 3\n",
+ "dtype: int64"
+ ]
+ },
+ "execution_count": 292,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "bikeshare2"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Negative bikes"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "In the code we have so far, the number of bikes at one of the locations can go negative, and the number of bikes at the other location can exceed the actual number of bikes in the system.\n",
+ "\n",
+ "If you run this simulation a few times, it happens quite often."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 293,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "bikeshare = System(olin=10, wellesley=2)\n",
+ "newfig()\n",
+ "plot_system(bikeshare)\n",
+ "decorate()\n",
+ "run_steps(bikeshare, 60, 0.4, 0.2)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "But this is relatively easy to fix, using the `return` statement to exit the function early if the update would cause negative bikes.\n",
+ "\n",
+ "If the second `if` statement seems confusing, remember that `n` can be negative."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 294,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "def move_bike(system, n):\n",
+ " # make sure the number of bikes won't go negative\n",
+ " olin_temp = system.olin - n\n",
+ " if olin_temp < 0:\n",
+ " return\n",
+ " \n",
+ " wellesley_temp = system.wellesley + n\n",
+ " if wellesley_temp < 0:\n",
+ " return\n",
+ " \n",
+ " # update the system\n",
+ " system.olin = olin_temp\n",
+ " system.wellesley = wellesley_temp"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Now if you run the simulation again, it should behave."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 295,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "bikeshare = System(olin=10, wellesley=2)\n",
+ "newfig()\n",
+ "plot_system(bikeshare)\n",
+ "decorate()\n",
+ "run_steps(bikeshare, 60, 0.4, 0.2)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "The variables `olin` and `wellesley` are created inside `move_bike`, so they are local. When the function ends, they go away.\n",
+ "\n",
+ "If you try to access a local variable from outside its function, you get an error:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 296,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "# If you remove the # from the last line in this cell and run it, you'll get\n",
+ "# NameError: name 'olin' is not defined\n",
+ "\n",
+ "#olin"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "**Exercise:** Add print statements in `move_bike` so it prints a message each time a customer arrives and doesn't find a bike. Run the simulation again to confirm that it works as you expect. Then you might want to remove the print statements before you go on."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Comparison operators"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "The `if` statements in the previous section used the comparison operator `<`. The other comparison operators are listed in the book.\n",
+ "\n",
+ "It is easy to confuse the comparison operator `==` with the assignment operator `=`.\n",
+ "\n",
+ "Remember that `=` creates a variable or gives an existing variable a new value."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 297,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "6\n"
+ ]
+ }
+ ],
+ "source": [
+ "x = 6\n",
+ "print(x)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Whereas `==` compared two values and returns `True` if they are equal."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 298,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "False"
+ ]
+ },
+ "execution_count": 298,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "x == 5"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "You can use `==` in an `if` statement."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 299,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "yikes\n"
+ ]
+ }
+ ],
+ "source": [
+ "if x == 5:\n",
+ " print('yes, x is 5')\n",
+ "else:\n",
+ " print('yikes')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "But if you use `=` in an `if` statement, you get an error."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 300,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "# If you remove the # from the if statement and run it, you'll get\n",
+ "# SyntaxError: invalid syntax\n",
+ "\n",
+ "#if x = 5:\n",
+ "# print('yes, x is 5')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "**Exercise:** Add an `else` clause to the `if` statement above, and print an appropriate message.\n",
+ "\n",
+ "Replace the `==` operator with one or two of the other comparison operators, and confirm they do what you expect."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Metrics"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Now that we have a working simulation, we'll use it to evaluate alternative designs and see how good or bad they are. The metric we'll use is the number of customers who arrive and find no bikes available, which might indicate a design problem."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "First we'll make a new `System` object that creates and initializes the system variables that will keep track of the metrics."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 301,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "bikeshare = System(olin=10, wellesley=2, \n",
+ " olin_empty=0, wellesley_empty=0)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Next we need a version of `move_bike` that updates the metrics."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 302,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "def move_bike(system, n):\n",
+ " olin_temp = system.olin - n\n",
+ " if olin_temp < 0:\n",
+ " system.olin_empty += 1\n",
+ " return\n",
+ " \n",
+ " wellesley_temp = system.wellesley + n\n",
+ " if wellesley_temp < 0:\n",
+ " system.wellesley_empty += 1\n",
+ " return\n",
+ " \n",
+ " system.olin = olin_temp\n",
+ " system.wellesley = wellesley_temp"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Now when we run a simulation, it keeps track of unhappy customers."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 303,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "newfig()\n",
+ "plot_system(bikeshare)\n",
+ "decorate()\n",
+ "run_steps(bikeshare, 60, 0.4, 0.2)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "After the simulation, we can print the number of unhappy customers at each location."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 304,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "5"
+ ]
+ },
+ "execution_count": 304,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "bikeshare.olin_empty"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 305,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "0"
+ ]
+ },
+ "execution_count": 305,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "bikeshare.wellesley_empty"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "**Exercise:** Let's add a \"clock\" to keep track of how many time steps have elapsed:\n",
+ "\n",
+ "1. Add a new system variable named `clock` to `bikeshare`, initialized to 0, and \n",
+ "\n",
+ "2. Modify `step` so it increments (adds one to) `clock` each time it is invoked.\n",
+ "\n",
+ "Test your code by adding a print statement that prints the value of `clock` at the beginning of each time step."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 306,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "bikeshare = System(olin=10, wellesley=2, \n",
+ " olin_empty=0, wellesley_empty=0,clock=0)\n",
+ "\n",
+ "def step(system, p1=0.5, p2=0.5):\n",
+ " \"\"\"Simulate one minute of time.\n",
+ " \n",
+ " system: bikeshare System object\n",
+ " p1: probability of an Olin->Wellesley customer arrival\n",
+ " p2: probability of a Wellesley->Olin customer arrival\n",
+ " \"\"\"\n",
+ " system.clock += 1\n",
+ " \n",
+ " if flip(p1):\n",
+ " bike_to_wellesley(system)\n",
+ " \n",
+ " if flip(p2):\n",
+ " bike_to_olin(system)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 307,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "step(bikeshare)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 308,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "# Solution goes here"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "After the simulation, check the final value of `clock`."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 309,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "1\n"
+ ]
+ }
+ ],
+ "source": [
+ "print (bikeshare.clock)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "**Exercise:** Now suppose we'd like to know how long it takes to run out of bikes at either location. Modify `move_bike` so the first time a student arrives at Olin and doesn't find a bike, it records the value of `clock` in a system variable.\n",
+ "\n",
+ "Hint: create a system variable named `t_first_empty` and initialize it to `None`, which is a special value (like `True` and `False`) that can be used to indicate a \"special case\".\n",
+ "\n",
+ "Test your code by running a simulation for 60 minutes and checking the metrics."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 310,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Yup, example is None.\n"
+ ]
+ }
+ ],
+ "source": [
+ "example = None\n",
+ "\n",
+ "if example == None:\n",
+ " print('Yup, example is None.')"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 311,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "bikeshare = System(olin=10, wellesley=2, \n",
+ " olin_empty=0, wellesley_empty=0,clock=0, t_first_empty=None)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 312,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "def move_bike(system, n):\n",
+ " olin_temp = system.olin - n\n",
+ " if olin_temp < 0:\n",
+ " system.t_first_empty +=1\n",
+ " system.olin_empty += 1\n",
+ " return\n",
+ " \n",
+ " wellesley_temp = system.wellesley + n\n",
+ " if wellesley_temp < 0:\n",
+ " system.wellesley_empty += 1\n",
+ " return\n",
+ " \n",
+ " system.olin = olin_temp\n",
+ " system.wellesley = wellesley_temp"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 313,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "# Solution goes here"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "After the simulation, check the final value of `t_first_empty`."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 314,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "nan\n"
+ ]
+ }
+ ],
+ "source": [
+ "print(bikeshare.t_first_empty)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Before we go on, let's put `step` and `move_bike` back the way we found them, so they don't break the examples below."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 315,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "def step(system, p1=0.5, p2=0.5):\n",
+ " if flip(p1):\n",
+ " bike_to_wellesley(system)\n",
+ " \n",
+ " if flip(p2):\n",
+ " bike_to_olin(system)\n",
+ "\n",
+ "def move_bike(system, n):\n",
+ " olin_temp = system.olin - n\n",
+ " if olin_temp < 0:\n",
+ " system.olin_empty += 1\n",
+ " return\n",
+ " \n",
+ " wellesley_temp = system.wellesley + n\n",
+ " if wellesley_temp < 0:\n",
+ " system.wellesley_empty += 1\n",
+ " return\n",
+ " \n",
+ " system.olin = olin_temp\n",
+ " system.wellesley = wellesley_temp"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Returning values"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Here's a simple function that returns a value:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 316,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "def add_five(x):\n",
+ " return x + 5"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "And here's how we call it."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 317,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "8"
+ ]
+ },
+ "execution_count": 317,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "y = add_five(3)\n",
+ "y"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "If you run a function on the last line of a cell, Jupyter displays the result:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 318,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "10"
+ ]
+ },
+ "execution_count": 318,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "add_five(5)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "collapsed": true
+ },
+ "source": [
+ "But that can be a bad habit, because usually if you call a function and don't assign the result in a variable, the result gets discarded.\n",
+ "\n",
+ "In the following example, Jupyter shows the second result, but the first result just disappears."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 319,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "10"
+ ]
+ },
+ "execution_count": 319,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "add_five(3)\n",
+ "add_five(5)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "collapsed": true
+ },
+ "source": [
+ "When you call a function that returns a variable, it is generally a good idea to assign the result to a variable."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 320,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "8 10\n"
+ ]
+ }
+ ],
+ "source": [
+ "y1 = add_five(3)\n",
+ "y2 = add_five(5)\n",
+ "\n",
+ "print(y1, y2)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "**Exercise:** Write a function called `init_system` that creates a `System` object with the system variables `olin=10` and `wellesley=2`, and then returns the new `System` object.\n",
+ "\n",
+ "Write a line of code that calls `init_system` and assigns the result to a variable."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 321,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "\n",
+ "\n",
+ "def init_system():\n",
+ " exercise=System(olin=10,wellesley=2)\n",
+ " return exercise"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 322,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "| \n", + " | value | \n", + "
|---|---|
| olin | \n", + "9 | \n", + "
| wellesley | \n", + "3 | \n", + "
\n",
+ "\n",
+ "\n",
+ " \n",
+ "
\n",
+ "
"
+ ],
+ "text/plain": [
+ "olin 10\n",
+ "wellesley 2\n",
+ "dtype: int64"
+ ]
+ },
+ "execution_count": 322,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "init_system()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Running simulations"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Before we go on, I want to update `run_steps` so it doesn't always plot the results. The new version takes an additional parameter, `plot_flag`, to indicate whether we want to plot.\n",
+ "\n",
+ "\"flag\" is a conventional name for a boolean variable that indicates whether or not a condition is true.\n",
+ "\n",
+ "This version of `run_steps` works even if `num_steps` is not an integer. It uses the `int` function to round down. See https://docs.python.org/3/library/functions.html#int"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 323,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "def run_steps(system, num_steps=1, p1=0.5, p2=0.5, plot_flag=True):\n",
+ " \"\"\"Simulate the given number of time steps.\n",
+ " \n",
+ " `num_steps` should be an integer; if not, it gets rounded down.\n",
+ " \n",
+ " system: bikeshare System object\n",
+ " num_steps: number of time steps\n",
+ " p1: probability of an Olin->Wellesley customer arrival\n",
+ " p2: probability of a Wellesley->Olin customer arrival\n",
+ " plot_flag: boolean, whether to plot\n",
+ " \"\"\"\n",
+ " for i in range(int(num_steps)):\n",
+ " step(system, p1, p2)\n",
+ " if plot_flag:\n",
+ " plot_system(system)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Now when we run a simulation, we can choose not to plot the results:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 324,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "bikeshare = System(olin=10, wellesley=2, \n",
+ " olin_empty=0, wellesley_empty=0)\n",
+ "run_steps(bikeshare, 60, 0.4, 0.2, plot_flag=False)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "But after the simulation, we can still read the metrics."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 325,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "2"
+ ]
+ },
+ "execution_count": 325,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "bikeshare.olin_empty"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Let's wrap all that in a function."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 326,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "def run_simulation():\n",
+ " system = System(olin=10, wellesley=2, \n",
+ " olin_empty=0, wellesley_empty=0)\n",
+ " run_steps(system, 60, 0.4, 0.2, plot_flag=False)\n",
+ " return system"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "And test it."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 327,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "system = run_simulation()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 328,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "0 0\n"
+ ]
+ }
+ ],
+ "source": [
+ "print(system.olin_empty, system.wellesley_empty)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "If we generalize `run_simulation` to take `p1` and `p2`, we can use it to run simulations with a range of values for the parameters."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 329,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "def run_simulation(p1=0.4, p2=0.2):\n",
+ " bikeshare = System(olin=10, wellesley=2, \n",
+ " olin_empty=0, wellesley_empty=0)\n",
+ " run_steps(bikeshare, 60, p1, p2, plot_flag=False)\n",
+ " return bikeshare"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "When `p1` is small, we probably don't run out of bikes at Olin."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 330,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "0"
+ ]
+ },
+ "execution_count": 330,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "system = run_simulation(p1=0.2)\n",
+ "system.olin_empty"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "When `p1` is large, we probably do."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 331,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "12"
+ ]
+ },
+ "execution_count": 331,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "system = run_simulation(p1=0.6)\n",
+ "system.olin_empty"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "collapsed": true
+ },
+ "source": [
+ "**Exercise:** Write a version of `run_simulation` that takes all five model parameters as function parameters."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 332,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "def run_simulation(p1=0.4, p2=0.2,olin=10,wellesley=2,num_steps=60):\n",
+ " bikeshare = System(olin=olin, wellesley=wellesley, \n",
+ " olin_empty=0, wellesley_empty=0)\n",
+ " run_steps(bikeshare,num_steps, p1, p2, plot_flag=False)\n",
+ " return bikeshare"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 333,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "6"
+ ]
+ },
+ "execution_count": 333,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "system=run_simulation(p1=.5,p2=.3,olin=4,wellesley=30,num_steps=20)\n",
+ "system.olin"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "collapsed": true
+ },
+ "source": [
+ "## More for loops"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "`linspace` creates a NumPy array of equally spaced numbers."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 334,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "array([ 0. , 0.25, 0.5 , 0.75, 1. ])"
+ ]
+ },
+ "execution_count": 334,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "p1_array = linspace(start=0, stop=1, num=5)\n",
+ "p1_array"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "We can use an array in a `for` loop, like this:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 335,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "0.0\n",
+ "0.25\n",
+ "0.5\n",
+ "0.75\n",
+ "1.0\n"
+ ]
+ }
+ ],
+ "source": [
+ "for p1 in p1_array:\n",
+ " print(p1)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "This will come in handy in the next section."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "**Exercise:** The function `linspace` is part of NumPy. [You can read the documentation here](https://docs.scipy.org/doc/numpy/reference/generated/numpy.linspace.html).\n",
+ "\n",
+ "Use `linspace` to make an array of 10 equally spaced numbers from 1 to 10 (including both)."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 336,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "array([ 0. , 1.11111111, 2.22222222, 3.33333333,\n",
+ " 4.44444444, 5.55555556, 6.66666667, 7.77777778,\n",
+ " 8.88888889, 10. ])"
+ ]
+ },
+ "execution_count": 336,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "p3_array = linspace(0,10,10)\n",
+ "p3_array"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "**Exercise:** The `modsim` library provides a related function called `linrange`. You can view the documentation by running the following cell:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 337,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Help on function linrange in module modsim:\n",
+ "\n",
+ "linrange(start=0, stop=None, step=1, **kwargs)\n",
+ " Returns an array of evenly-spaced values in the interval [start, stop].\n",
+ " \n",
+ " This function works best if the space between start and stop\n",
+ " is divisible by step; otherwise the results might be surprising.\n",
+ " \n",
+ " By default, the last value in the array is `stop` (at least approximately).\n",
+ " If you provide the keyword argument `endpoint=False`, the last value\n",
+ " in the array is `stop-step`. \n",
+ " \n",
+ " start: first value\n",
+ " stop: last value\n",
+ " step: space between values\n",
+ " \n",
+ " Also accepts the same keyword arguments as np.linspace. See\n",
+ " https://docs.scipy.org/doc/numpy/reference/generated/numpy.linspace.html\n",
+ " \n",
+ " returns: array or Quantity\n",
+ "\n"
+ ]
+ }
+ ],
+ "source": [
+ "help(linrange)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Use `linrange` to make an array of numbers from 1 to 10 with a step size of 2."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 338,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "array([ 1. , 3.25, 5.5 , 7.75, 10. ])"
+ ]
+ },
+ "execution_count": 338,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "linrange(1,10,2)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "collapsed": true
+ },
+ "source": [
+ "## Sweeping parameters"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "The following example runs simulations with a range of values for `p1`; after each simulation, it prints the number of unhappy customers at the Olin station:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 339,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "array([ 0. , 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1. ])"
+ ]
+ },
+ "execution_count": 339,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "p1_array = linspace(0, 1, 11)\n",
+ "p1_array"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 340,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "0.0 0\n",
+ "0.1 0\n",
+ "0.2 0\n",
+ "0.3 0\n",
+ "0.4 0\n",
+ "0.5 13\n",
+ "0.6 21\n",
+ "0.7 17\n",
+ "0.8 22\n",
+ "0.9 23\n",
+ "1.0 41\n"
+ ]
+ }
+ ],
+ "source": [
+ "for p1 in p1_array:\n",
+ " system = run_simulation(p1=p1)\n",
+ " print(p1, system.olin_empty)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Now we can do the same thing, but plotting the results instead of printing them.\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 341,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "newfig()\n",
+ "for p1 in p1_array:\n",
+ " system = run_simulation(p1=p1)\n",
+ " plot(p1, system.olin_empty, 'rs', label='olin')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "As always, we should decorate the figure. This version of `decorate` takes `xlabel` as a parameter, for reasons you will see soon."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 342,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "def decorate(xlabel):\n",
+ " legend(loc='best')\n",
+ " label_axes(title='Olin-Wellesley Bikeshare',\n",
+ " xlabel=xlabel, \n",
+ " ylabel='Number of unhappy customers')"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 343,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "decorate(xlabel='Arrival rate at Olin (p1 in customers/min)')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "**Exercise:** Wrap this code in a function named `parameter_sweep` that takes an array called `p1_array` as a parameter. It should create a new figure, run a simulation for each value of `p1` in `p1_array`, and plot the results.\n",
+ "\n",
+ "Once you have the function working, modify it so it also plots the number of unhappy customers at Wellesley. Looking at the plot, can you estimate a range of values for `p1` that minimizes the total number of unhappy customers?"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 344,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "def parameter_sweep(p1_array):\n",
+ " newfig()\n",
+ " for p1 in p1_array:\n",
+ " system = run_simulation(p1=p1)\n",
+ " plot(p1, system.olin_empty, 'rs', label='olin')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "collapsed": true
+ },
+ "source": [
+ "**Exercise:** Write a function called `parameter_sweep2` that runs simulations with `p1=0.2` and a range of values for `p2`.\n",
+ "\n",
+ "Note: If you run `parameter_sweep2` a few times without calling `newfig`, you can plot multiple runs on the same axes, which will give you a sense of how much random variation there is from one run to the next. "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 345,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "p2_array = linspace(0, 1, 11)\n",
+ "\n",
+ "def parameter_sweep2(p2_array):\n",
+ " \n",
+ " for p in p2_array:\n",
+ " system = run_simulation(p1=0.2, p2=p)\n",
+ " plot(p, system.olin_empty, 'rs', label='olin')\n",
+ "parameter_sweep2(p2_array)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 346,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "newfig()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 347,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "# Solution goes here"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "**Exercise:** Hold `p1=0.4` and `p2=0.2`, and sweep a range of values for `num_steps`.\n",
+ "\n",
+ "Hint: You will need a version of `run_simulation` that takes `num_steps` as a parameter.\n",
+ "\n",
+ "Hint: Because `num_steps` is supposed to be an integer use `range` rather than `linrange`."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 348,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "def run_simulation(p1=0.4, p2=0.2,olin=10,wellesley=2,num_steps=60):\n",
+ " bikeshare = System(olin=olin, wellesley=wellesley, \n",
+ " olin_empty=0, wellesley_empty=0)\n",
+ " run_steps(bikeshare,num_steps, p1, p2, plot_flag=False)\n",
+ " return bikeshare\n",
+ "\n",
+ "sweep_array = range(0,5)\n",
+ "\n",
+ "def sweep(steps_array):\n",
+ " for i in steps_array:\n",
+ " system = run_simulation(num_steps=i)\n",
+ "\n",
+ " plot(i, system.olin_empty, 'rs', label='olin')\n",
+ "sweep(sweep_array)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 349,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "# Solution goes here"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 350,
+ "metadata": {
+ "collapsed": true,
+ "scrolled": false
+ },
+ "outputs": [],
+ "source": [
+ "# Solution goes here"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "collapsed": true
+ },
+ "source": [
+ "**Exercise:** The code below runs a simulation with the same parameters 10 times and computes the average number of unhappy customers.\n",
+ "\n",
+ "1. Wrap this code in a function called `run_simulations` that takes `num_runs` as a parameter.\n",
+ "\n",
+ "2. Test `run_simulations`, and increase `num_runs` until the results are reasonably consistent from one run to the next.\n",
+ "\n",
+ "3. Generalize `run_simulations` so it also takes the initial value of `olin` as a parameter.\n",
+ "\n",
+ "4. Run the generalized version with `olin=12`. How much do the two extra bikes decrease the average number of unhappy customers.\n",
+ "\n",
+ "5. Make a plot that shows the average number of unhappy customers as a function of the initial number of bikes at Olin."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 361,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "4.0"
+ ]
+ },
+ "execution_count": 361,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "num_runs = 10\n",
+ "total = 0\n",
+ "for i in range(num_runs):\n",
+ " system = run_simulation(p1=0.4, p2=0.2, olin=10, wellesley=2, num_steps=60)\n",
+ " total += system.olin_empty + system.wellesley_empty\n",
+ "total / num_runs"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 366,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "\n",
+ "def run_simulations (num_runs,olin):\n",
+ " total=0\n",
+ " for i in range(num_runs):\n",
+ " system=run_simulation(p1=0.4, p2=0.2, olin=olin, wellesley=2, num_steps=60)\n",
+ " total += system.olin_empty + system.wellesley_empty\n",
+ " return total / num_runs"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 369,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "2.1000000000000001"
+ ]
+ },
+ "execution_count": 369,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "run_simulations(10,10)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 371,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "1.3999999999999999"
+ ]
+ },
+ "execution_count": 371,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "run_simulations(10,12)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 375,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "0 olin 0\n",
+ "wellesley 2\n",
+ "olin_empty 9\n",
+ "wellesley_empty 0\n",
+ "dtype: int64\n",
+ "10 olin 0\n",
+ "wellesley 12\n",
+ "olin_empty 6\n",
+ "wellesley_empty 0\n",
+ "dtype: int64\n"
+ ]
+ }
+ ],
+ "source": [
+ "for olin in range (0,12,10):\n",
+ " avg=run_simulation(olin=olin)\n",
+ " print (olin,avg)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 380,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "newfig()\n",
+ "for p1 in p1_array:\n",
+ " system = run_simulation(p1=p1)\n",
+ " plot(p1, system.olin_empty, 'rs', label='olin')\n",
+ "xlabel('Initial bikes at Olin')\n",
+ "ylabel('Avg # of unhappy customers')\n",
+ "ylim([0, 12]);"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 354,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "# Solution goes here"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.6.1"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 1
+}
diff --git a/code/chap03mine.ipynb b/code/chap03mine.ipynb
new file mode 100644
index 00000000..c7bfe360
--- /dev/null
+++ b/code/chap03mine.ipynb
@@ -0,0 +1,4597 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Modeling and Simulation in Python\n",
+ "\n",
+ "Chapter 3: Explain\n",
+ "\n",
+ "Copyright 2017 Allen Downey\n",
+ "\n",
+ "License: [Creative Commons Attribution 4.0 International](https://creativecommons.org/licenses/by/4.0)\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 400,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "# If you want the figures to appear in the notebook, \n",
+ "# and you want to interact with them, use\n",
+ "# %matplotlib notebook\n",
+ "\n",
+ "# If you want the figures to appear in the notebook, \n",
+ "# and you don't want to interact with them, use\n",
+ "# %matplotlib inline\n",
+ "\n",
+ "# If you want the figures to appear in separate windows, use\n",
+ "# %matplotlib qt5\n",
+ "\n",
+ "# To switch from one to another, you have to select Kernel->Restart\n",
+ "\n",
+ "%matplotlib inline\n",
+ "\n",
+ "from modsim import *"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Pandas is a module that provides tools for reading and processing data. The `read_html` reads a web page from a file or the Internet and creates one DataFrame for each table on the page."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 401,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "from pandas import read_html"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "The data directory contains a downloaded copy of https://en.wikipedia.org/wiki/World_population_estimates"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 402,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "filename = 'data/World_population_estimates.html'\n",
+ "tables = read_html(filename, header=0, index_col=0, decimal='M')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "`tables` is a sequence of DataFrame objects. We can select the DataFrame we want using the bracket operator. The tables are numbered from 0, so `table2` is actually the third table on the page.\n",
+ "\n",
+ "`head` selects the header and the first five rows."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 403,
+ "metadata": {
+ "scrolled": true
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "| \n", + " | value | \n", + "
|---|---|
| olin | \n", + "10 | \n", + "
| wellesley | \n", + "2 | \n", + "
\n",
+ "\n",
+ "\n",
+ " \n",
+ "
\n",
+ "
"
+ ],
+ "text/plain": [
+ " United States Census Bureau (2015)[18] \\\n",
+ "Year \n",
+ "1950 2557628654 \n",
+ "1951 2594939877 \n",
+ "1952 2636772306 \n",
+ "1953 2682053389 \n",
+ "1954 2730228104 \n",
+ "\n",
+ " Population Reference Bureau (1973–2015)[6] \\\n",
+ "Year \n",
+ "1950 2.516000e+09 \n",
+ "1951 NaN \n",
+ "1952 NaN \n",
+ "1953 NaN \n",
+ "1954 NaN \n",
+ "\n",
+ " United Nations Department of Economic and Social Affairs (2015)[7] \\\n",
+ "Year \n",
+ "1950 2525149000 \n",
+ "1951 2572850917 \n",
+ "1952 2619292068 \n",
+ "1953 2665865392 \n",
+ "1954 2713172027 \n",
+ "\n",
+ " Maddison (2008)[8] HYDE (2007)[15] Tanton (1994)[9] \\\n",
+ "Year \n",
+ "1950 2.544000e+09 2.527960e+09 2.400000e+09 \n",
+ "1951 2.571663e+09 NaN NaN \n",
+ "1952 2.617949e+09 NaN NaN \n",
+ "1953 2.665959e+09 NaN NaN \n",
+ "1954 2.716927e+09 NaN NaN \n",
+ "\n",
+ " Biraben (1980)[10] McEvedy & Jones (1978)[11] Thomlinson (1975)[12] \\\n",
+ "Year \n",
+ "1950 2.527000e+09 2.500000e+09 2.400000e+09 \n",
+ "1951 NaN NaN NaN \n",
+ "1952 NaN NaN NaN \n",
+ "1953 NaN NaN NaN \n",
+ "1954 NaN NaN NaN \n",
+ "\n",
+ " Durand (1974)[13] Clark (1967)[14] \n",
+ "Year \n",
+ "1950 NaN 2.486000e+09 \n",
+ "1951 NaN NaN \n",
+ "1952 NaN NaN \n",
+ "1953 NaN NaN \n",
+ "1954 NaN NaN "
+ ]
+ },
+ "execution_count": 403,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "table2 = tables[2]\n",
+ "table2.head()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "`tail` selects the last five rows."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 404,
+ "metadata": {
+ "scrolled": true
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "| \n", + " | United States Census Bureau (2015)[18] | \n", + "Population Reference Bureau (1973–2015)[6] | \n", + "United Nations Department of Economic and Social Affairs (2015)[7] | \n", + "Maddison (2008)[8] | \n", + "HYDE (2007)[15] | \n", + "Tanton (1994)[9] | \n", + "Biraben (1980)[10] | \n", + "McEvedy & Jones (1978)[11] | \n", + "Thomlinson (1975)[12] | \n", + "Durand (1974)[13] | \n", + "Clark (1967)[14] | \n", + "
|---|---|---|---|---|---|---|---|---|---|---|---|
| Year | \n", + "\n", + " | \n", + " | \n", + " | \n", + " | \n", + " | \n", + " | \n", + " | \n", + " | \n", + " | \n", + " | \n", + " |
| 1950 | \n", + "2557628654 | \n", + "2.516000e+09 | \n", + "2525149000 | \n", + "2.544000e+09 | \n", + "2.527960e+09 | \n", + "2.400000e+09 | \n", + "2.527000e+09 | \n", + "2.500000e+09 | \n", + "2.400000e+09 | \n", + "NaN | \n", + "2.486000e+09 | \n", + "
| 1951 | \n", + "2594939877 | \n", + "NaN | \n", + "2572850917 | \n", + "2.571663e+09 | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "
| 1952 | \n", + "2636772306 | \n", + "NaN | \n", + "2619292068 | \n", + "2.617949e+09 | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "
| 1953 | \n", + "2682053389 | \n", + "NaN | \n", + "2665865392 | \n", + "2.665959e+09 | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "
| 1954 | \n", + "2730228104 | \n", + "NaN | \n", + "2713172027 | \n", + "2.716927e+09 | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "
\n",
+ "\n",
+ "\n",
+ " \n",
+ "
\n",
+ "
"
+ ],
+ "text/plain": [
+ " United States Census Bureau (2015)[18] \\\n",
+ "Year \n",
+ "2011 6944055583 \n",
+ "2012 7022349283 \n",
+ "2013 7101027895 \n",
+ "2014 7178722893 \n",
+ "2015 7256490011 \n",
+ "\n",
+ " Population Reference Bureau (1973–2015)[6] \\\n",
+ "Year \n",
+ "2011 6.986951e+09 \n",
+ "2012 7.057075e+09 \n",
+ "2013 7.136796e+09 \n",
+ "2014 7.238184e+09 \n",
+ "2015 7.336435e+09 \n",
+ "\n",
+ " United Nations Department of Economic and Social Affairs (2015)[7] \\\n",
+ "Year \n",
+ "2011 6997998760 \n",
+ "2012 7080072417 \n",
+ "2013 7162119434 \n",
+ "2014 7243784000 \n",
+ "2015 7349472000 \n",
+ "\n",
+ " Maddison (2008)[8] HYDE (2007)[15] Tanton (1994)[9] \\\n",
+ "Year \n",
+ "2011 NaN NaN NaN \n",
+ "2012 NaN NaN NaN \n",
+ "2013 NaN NaN NaN \n",
+ "2014 NaN NaN NaN \n",
+ "2015 NaN NaN NaN \n",
+ "\n",
+ " Biraben (1980)[10] McEvedy & Jones (1978)[11] Thomlinson (1975)[12] \\\n",
+ "Year \n",
+ "2011 NaN NaN NaN \n",
+ "2012 NaN NaN NaN \n",
+ "2013 NaN NaN NaN \n",
+ "2014 NaN NaN NaN \n",
+ "2015 NaN NaN NaN \n",
+ "\n",
+ " Durand (1974)[13] Clark (1967)[14] \n",
+ "Year \n",
+ "2011 NaN NaN \n",
+ "2012 NaN NaN \n",
+ "2013 NaN NaN \n",
+ "2014 NaN NaN \n",
+ "2015 NaN NaN "
+ ]
+ },
+ "execution_count": 404,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "table2.tail()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Long column names are awkard to work with, but we can replace them with abbreviated names."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 405,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "table2.columns = ['census', 'prb', 'un', 'maddison', \n",
+ " 'hyde', 'tanton', 'biraben', 'mj', \n",
+ " 'thomlinson', 'durand', 'clark']"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Here's what the DataFrame looks like now. \n",
+ "\n",
+ "Some of the values use scientific notation; for example, `2.544000e+09` is shorthand for $2.544 \\cdot 10^9$ or 2.544 billion.\n",
+ "\n",
+ "`NaN` is a special value that indicates missing data."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 406,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "| \n", + " | United States Census Bureau (2015)[18] | \n", + "Population Reference Bureau (1973–2015)[6] | \n", + "United Nations Department of Economic and Social Affairs (2015)[7] | \n", + "Maddison (2008)[8] | \n", + "HYDE (2007)[15] | \n", + "Tanton (1994)[9] | \n", + "Biraben (1980)[10] | \n", + "McEvedy & Jones (1978)[11] | \n", + "Thomlinson (1975)[12] | \n", + "Durand (1974)[13] | \n", + "Clark (1967)[14] | \n", + "
|---|---|---|---|---|---|---|---|---|---|---|---|
| Year | \n", + "\n", + " | \n", + " | \n", + " | \n", + " | \n", + " | \n", + " | \n", + " | \n", + " | \n", + " | \n", + " | \n", + " |
| 2011 | \n", + "6944055583 | \n", + "6.986951e+09 | \n", + "6997998760 | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "
| 2012 | \n", + "7022349283 | \n", + "7.057075e+09 | \n", + "7080072417 | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "
| 2013 | \n", + "7101027895 | \n", + "7.136796e+09 | \n", + "7162119434 | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "
| 2014 | \n", + "7178722893 | \n", + "7.238184e+09 | \n", + "7243784000 | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "
| 2015 | \n", + "7256490011 | \n", + "7.336435e+09 | \n", + "7349472000 | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "
\n",
+ "\n",
+ "\n",
+ " \n",
+ "
\n",
+ "
"
+ ],
+ "text/plain": [
+ " census prb un maddison hyde \\\n",
+ "Year \n",
+ "1950 2557628654 2.516000e+09 2525149000 2.544000e+09 2.527960e+09 \n",
+ "1951 2594939877 NaN 2572850917 2.571663e+09 NaN \n",
+ "1952 2636772306 NaN 2619292068 2.617949e+09 NaN \n",
+ "1953 2682053389 NaN 2665865392 2.665959e+09 NaN \n",
+ "1954 2730228104 NaN 2713172027 2.716927e+09 NaN \n",
+ "1955 2782098943 NaN 2761650981 2.769074e+09 NaN \n",
+ "1956 2835299673 NaN 2811572031 2.822502e+09 NaN \n",
+ "1957 2891349717 NaN 2863042795 2.879934e+09 NaN \n",
+ "1958 2948137248 NaN 2916030167 2.939254e+09 NaN \n",
+ "1959 3000716593 NaN 2970395814 2.995909e+09 NaN \n",
+ "1960 3043001508 NaN 3026002942 3.041507e+09 3.042000e+09 \n",
+ "1961 3083966929 NaN 3082830266 3.082161e+09 NaN \n",
+ "1962 3140093217 NaN 3141071531 3.135787e+09 NaN \n",
+ "1963 3209827882 NaN 3201178277 3.201354e+09 NaN \n",
+ "1964 3281201306 NaN 3263738832 3.266477e+09 NaN \n",
+ "1965 3350425793 NaN 3329122479 3.333138e+09 NaN \n",
+ "1966 3420677923 NaN 3397475247 3.402224e+09 NaN \n",
+ "1967 3490333715 NaN 3468521724 3.471464e+09 NaN \n",
+ "1968 3562313822 NaN 3541674891 3.543086e+09 NaN \n",
+ "1969 3637159050 NaN 3616108749 3.615743e+09 NaN \n",
+ "1970 3712697742 NaN 3691172616 3.691157e+09 3.710000e+09 \n",
+ "1971 3790326948 NaN 3766754345 3.769818e+09 NaN \n",
+ "1972 3866568653 NaN 3842873611 3.846499e+09 NaN \n",
+ "1973 3942096442 NaN 3919182332 3.922793e+09 3.923000e+09 \n",
+ "1974 4016608813 NaN 3995304922 3.997677e+09 NaN \n",
+ "1975 4089083233 NaN 4071020434 4.070671e+09 NaN \n",
+ "1976 4160185010 NaN 4146135850 4.141445e+09 NaN \n",
+ "1977 4232084578 NaN 4220816737 4.213539e+09 NaN \n",
+ "1978 4304105753 NaN 4295664825 4.286317e+09 NaN \n",
+ "1979 4379013942 NaN 4371527871 4.363144e+09 NaN \n",
+ "... ... ... ... ... ... \n",
+ "1986 4940571232 NaN 4953376710 4.920968e+09 NaN \n",
+ "1987 5027200492 NaN 5045315871 5.006672e+09 NaN \n",
+ "1988 5114557167 NaN 5138214688 5.093306e+09 NaN \n",
+ "1989 5201440110 NaN 5230000000 5.180540e+09 NaN \n",
+ "1990 5288955934 NaN 5320816667 5.269029e+09 5.308000e+09 \n",
+ "1991 5371585922 NaN 5408908724 5.351922e+09 NaN \n",
+ "1992 5456136278 NaN 5494899570 5.435722e+09 NaN \n",
+ "1993 5538268316 NaN 5578865109 5.518127e+09 NaN \n",
+ "1994 5618682132 NaN 5661086346 5.599396e+09 NaN \n",
+ "1995 5699202985 5.760000e+09 5741822412 5.681575e+09 NaN \n",
+ "1996 5779440593 NaN 5821016750 5.762212e+09 NaN \n",
+ "1997 5857972543 5.840000e+09 5898688337 5.842122e+09 NaN \n",
+ "1998 5935213248 NaN 5975303657 5.921366e+09 NaN \n",
+ "1999 6012074922 NaN 6051478010 5.999622e+09 NaN \n",
+ "2000 6088571383 6.067000e+09 6127700428 6.076558e+09 6.145000e+09 \n",
+ "2001 6165219247 6.137000e+09 6204147026 6.154791e+09 NaN \n",
+ "2002 6242016348 6.215000e+09 6280853817 6.231704e+09 NaN \n",
+ "2003 6318590956 6.314000e+09 6357991749 6.308364e+09 NaN \n",
+ "2004 6395699509 6.396000e+09 6435705595 6.374056e+09 NaN \n",
+ "2005 6473044732 6.477000e+09 6514094605 6.462987e+09 NaN \n",
+ "2006 6551263534 6.555000e+09 6593227977 6.540214e+09 NaN \n",
+ "2007 6629913759 6.625000e+09 6673105937 6.616689e+09 NaN \n",
+ "2008 6709049780 6.705000e+09 6753649228 6.694832e+09 NaN \n",
+ "2009 6788214394 6.809972e+09 6834721933 6.764086e+09 NaN \n",
+ "2010 6866332358 6.892319e+09 6916183482 NaN NaN \n",
+ "2011 6944055583 6.986951e+09 6997998760 NaN NaN \n",
+ "2012 7022349283 7.057075e+09 7080072417 NaN NaN \n",
+ "2013 7101027895 7.136796e+09 7162119434 NaN NaN \n",
+ "2014 7178722893 7.238184e+09 7243784000 NaN NaN \n",
+ "2015 7256490011 7.336435e+09 7349472000 NaN NaN \n",
+ "\n",
+ " tanton biraben mj thomlinson \\\n",
+ "Year \n",
+ "1950 2.400000e+09 2.527000e+09 2.500000e+09 2.400000e+09 \n",
+ "1951 NaN NaN NaN NaN \n",
+ "1952 NaN NaN NaN NaN \n",
+ "1953 NaN NaN NaN NaN \n",
+ "1954 NaN NaN NaN NaN \n",
+ "1955 NaN NaN NaN NaN \n",
+ "1956 NaN NaN NaN NaN \n",
+ "1957 NaN NaN NaN NaN \n",
+ "1958 NaN NaN NaN NaN \n",
+ "1959 NaN NaN NaN NaN \n",
+ "1960 NaN NaN NaN NaN \n",
+ "1961 NaN NaN NaN NaN \n",
+ "1962 NaN NaN NaN NaN \n",
+ "1963 NaN NaN NaN NaN \n",
+ "1964 NaN NaN NaN NaN \n",
+ "1965 NaN NaN NaN NaN \n",
+ "1966 NaN NaN NaN NaN \n",
+ "1967 NaN NaN NaN NaN \n",
+ "1968 NaN NaN NaN NaN \n",
+ "1969 NaN NaN NaN NaN \n",
+ "1970 NaN 3.637000e+09 NaN 3.600000e+09 \n",
+ "1971 NaN NaN NaN NaN \n",
+ "1972 NaN NaN NaN NaN \n",
+ "1973 NaN NaN NaN NaN \n",
+ "1974 NaN NaN NaN NaN \n",
+ "1975 NaN NaN 3.900000e+09 4.000000e+09 \n",
+ "1976 NaN NaN NaN NaN \n",
+ "1977 NaN NaN NaN NaN \n",
+ "1978 NaN NaN NaN NaN \n",
+ "1979 NaN NaN NaN NaN \n",
+ "... ... ... ... ... \n",
+ "1986 NaN NaN NaN NaN \n",
+ "1987 NaN NaN NaN NaN \n",
+ "1988 NaN NaN NaN NaN \n",
+ "1989 NaN NaN NaN NaN \n",
+ "1990 NaN NaN NaN NaN \n",
+ "1991 NaN NaN NaN NaN \n",
+ "1992 NaN NaN NaN NaN \n",
+ "1993 NaN NaN NaN NaN \n",
+ "1994 NaN NaN NaN NaN \n",
+ "1995 NaN NaN NaN NaN \n",
+ "1996 NaN NaN NaN NaN \n",
+ "1997 NaN NaN NaN NaN \n",
+ "1998 NaN NaN NaN NaN \n",
+ "1999 NaN NaN NaN NaN \n",
+ "2000 NaN NaN 5.750000e+09 NaN \n",
+ "2001 NaN NaN NaN NaN \n",
+ "2002 NaN NaN NaN NaN \n",
+ "2003 NaN NaN NaN NaN \n",
+ "2004 NaN NaN NaN NaN \n",
+ "2005 NaN NaN NaN NaN \n",
+ "2006 NaN NaN NaN NaN \n",
+ "2007 NaN NaN NaN NaN \n",
+ "2008 NaN NaN NaN NaN \n",
+ "2009 NaN NaN NaN NaN \n",
+ "2010 NaN NaN NaN NaN \n",
+ "2011 NaN NaN NaN NaN \n",
+ "2012 NaN NaN NaN NaN \n",
+ "2013 NaN NaN NaN NaN \n",
+ "2014 NaN NaN NaN NaN \n",
+ "2015 NaN NaN NaN NaN \n",
+ "\n",
+ " durand clark \n",
+ "Year \n",
+ "1950 NaN 2.486000e+09 \n",
+ "1951 NaN NaN \n",
+ "1952 NaN NaN \n",
+ "1953 NaN NaN \n",
+ "1954 NaN NaN \n",
+ "1955 NaN NaN \n",
+ "1956 NaN NaN \n",
+ "1957 NaN NaN \n",
+ "1958 NaN NaN \n",
+ "1959 NaN NaN \n",
+ "1960 NaN NaN \n",
+ "1961 NaN NaN \n",
+ "1962 NaN 3.036000e+09 \n",
+ "1963 NaN NaN \n",
+ "1964 NaN NaN \n",
+ "1965 NaN NaN \n",
+ "1966 NaN 3.288000e+09 \n",
+ "1967 NaN NaN \n",
+ "1968 NaN NaN \n",
+ "1969 NaN NaN \n",
+ "1970 3,600,000,000– 3,700,000,000 3.632000e+09 \n",
+ "1971 NaN NaN \n",
+ "1972 NaN NaN \n",
+ "1973 NaN 3.860000e+09 \n",
+ "1974 NaN NaN \n",
+ "1975 NaN NaN \n",
+ "1976 NaN NaN \n",
+ "1977 NaN NaN \n",
+ "1978 NaN NaN \n",
+ "1979 NaN NaN \n",
+ "... ... ... \n",
+ "1986 NaN NaN \n",
+ "1987 NaN NaN \n",
+ "1988 NaN NaN \n",
+ "1989 NaN NaN \n",
+ "1990 NaN NaN \n",
+ "1991 NaN NaN \n",
+ "1992 NaN NaN \n",
+ "1993 NaN NaN \n",
+ "1994 NaN NaN \n",
+ "1995 NaN NaN \n",
+ "1996 NaN NaN \n",
+ "1997 NaN NaN \n",
+ "1998 NaN NaN \n",
+ "1999 NaN NaN \n",
+ "2000 NaN NaN \n",
+ "2001 NaN NaN \n",
+ "2002 NaN NaN \n",
+ "2003 NaN NaN \n",
+ "2004 NaN NaN \n",
+ "2005 NaN NaN \n",
+ "2006 NaN NaN \n",
+ "2007 NaN NaN \n",
+ "2008 NaN NaN \n",
+ "2009 NaN NaN \n",
+ "2010 NaN NaN \n",
+ "2011 NaN NaN \n",
+ "2012 NaN NaN \n",
+ "2013 NaN NaN \n",
+ "2014 NaN NaN \n",
+ "2015 NaN NaN \n",
+ "\n",
+ "[66 rows x 11 columns]"
+ ]
+ },
+ "execution_count": 406,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "table2"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "We can use dot notatio to select a column from a DataFrame. The result is a Series."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 407,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "Year\n",
+ "1950 2557628654\n",
+ "1951 2594939877\n",
+ "1952 2636772306\n",
+ "1953 2682053389\n",
+ "1954 2730228104\n",
+ "1955 2782098943\n",
+ "1956 2835299673\n",
+ "1957 2891349717\n",
+ "1958 2948137248\n",
+ "1959 3000716593\n",
+ "1960 3043001508\n",
+ "1961 3083966929\n",
+ "1962 3140093217\n",
+ "1963 3209827882\n",
+ "1964 3281201306\n",
+ "1965 3350425793\n",
+ "1966 3420677923\n",
+ "1967 3490333715\n",
+ "1968 3562313822\n",
+ "1969 3637159050\n",
+ "1970 3712697742\n",
+ "1971 3790326948\n",
+ "1972 3866568653\n",
+ "1973 3942096442\n",
+ "1974 4016608813\n",
+ "1975 4089083233\n",
+ "1976 4160185010\n",
+ "1977 4232084578\n",
+ "1978 4304105753\n",
+ "1979 4379013942\n",
+ " ... \n",
+ "1986 4940571232\n",
+ "1987 5027200492\n",
+ "1988 5114557167\n",
+ "1989 5201440110\n",
+ "1990 5288955934\n",
+ "1991 5371585922\n",
+ "1992 5456136278\n",
+ "1993 5538268316\n",
+ "1994 5618682132\n",
+ "1995 5699202985\n",
+ "1996 5779440593\n",
+ "1997 5857972543\n",
+ "1998 5935213248\n",
+ "1999 6012074922\n",
+ "2000 6088571383\n",
+ "2001 6165219247\n",
+ "2002 6242016348\n",
+ "2003 6318590956\n",
+ "2004 6395699509\n",
+ "2005 6473044732\n",
+ "2006 6551263534\n",
+ "2007 6629913759\n",
+ "2008 6709049780\n",
+ "2009 6788214394\n",
+ "2010 6866332358\n",
+ "2011 6944055583\n",
+ "2012 7022349283\n",
+ "2013 7101027895\n",
+ "2014 7178722893\n",
+ "2015 7256490011\n",
+ "Name: census, Length: 66, dtype: int64"
+ ]
+ },
+ "execution_count": 407,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "census = table2.census\n",
+ "census"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "A Series object has two parts, `values` and `index`.\n",
+ "\n",
+ "The `values` part is an array."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 408,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "array([2557628654, 2594939877, 2636772306, 2682053389, 2730228104,\n",
+ " 2782098943, 2835299673, 2891349717, 2948137248, 3000716593,\n",
+ " 3043001508, 3083966929, 3140093217, 3209827882, 3281201306,\n",
+ " 3350425793, 3420677923, 3490333715, 3562313822, 3637159050,\n",
+ " 3712697742, 3790326948, 3866568653, 3942096442, 4016608813,\n",
+ " 4089083233, 4160185010, 4232084578, 4304105753, 4379013942,\n",
+ " 4451362735, 4534410125, 4614566561, 4695736743, 4774569391,\n",
+ " 4856462699, 4940571232, 5027200492, 5114557167, 5201440110,\n",
+ " 5288955934, 5371585922, 5456136278, 5538268316, 5618682132,\n",
+ " 5699202985, 5779440593, 5857972543, 5935213248, 6012074922,\n",
+ " 6088571383, 6165219247, 6242016348, 6318590956, 6395699509,\n",
+ " 6473044732, 6551263534, 6629913759, 6709049780, 6788214394,\n",
+ " 6866332358, 6944055583, 7022349283, 7101027895, 7178722893,\n",
+ " 7256490011], dtype=int64)"
+ ]
+ },
+ "execution_count": 408,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "census.values"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "The `index` part is yet another kind of object, an `Int64Index`."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 409,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "Int64Index([1950, 1951, 1952, 1953, 1954, 1955, 1956, 1957, 1958, 1959, 1960,\n",
+ " 1961, 1962, 1963, 1964, 1965, 1966, 1967, 1968, 1969, 1970, 1971,\n",
+ " 1972, 1973, 1974, 1975, 1976, 1977, 1978, 1979, 1980, 1981, 1982,\n",
+ " 1983, 1984, 1985, 1986, 1987, 1988, 1989, 1990, 1991, 1992, 1993,\n",
+ " 1994, 1995, 1996, 1997, 1998, 1999, 2000, 2001, 2002, 2003, 2004,\n",
+ " 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014, 2015],\n",
+ " dtype='int64', name='Year')"
+ ]
+ },
+ "execution_count": 409,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "census.index"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "If you ever wonder what kind of object a variable refers to, you can use the `type` function.\n",
+ "\n",
+ "The result indicates what type the object is, and the module where that type is defined.\n",
+ "\n",
+ "DataFrame, Series, and Int64Index are defined by Pandas.\n",
+ "\n",
+ "array is defined by NumPy."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 410,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "pandas.core.frame.DataFrame"
+ ]
+ },
+ "execution_count": 410,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "type(table2)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 411,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "pandas.core.series.Series"
+ ]
+ },
+ "execution_count": 411,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "type(census)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 412,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "pandas.core.indexes.numeric.Int64Index"
+ ]
+ },
+ "execution_count": 412,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "type(census.index)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 413,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "numpy.ndarray"
+ ]
+ },
+ "execution_count": 413,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "type(census.values)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "This function plots the estimates generated by the US Censis and UN DESA, and labels the axes.\n",
+ "\n",
+ "`1e9` is scientific notation for $1 \\cdot 10^9$ or 1 billion."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 414,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "def plot_estimates(table):\n",
+ " \"\"\"Plot world population estimates.\n",
+ " \n",
+ " table: DataFrame with columns 'un' and 'census'\n",
+ " \"\"\"\n",
+ " un = table.un / 1e9\n",
+ " census = table.census / 1e9\n",
+ " \n",
+ " plot(census, ':', color='darkblue', label='US Census')\n",
+ " plot(un, '--', color='green', label='UN DESA')\n",
+ " \n",
+ " decorate(xlabel='Year',\n",
+ " ylabel='World population (billion)')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Now we can plot the estimates."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 415,
+ "metadata": {
+ "scrolled": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Saving figure to file chap03-fig01.pdf\n"
+ ]
+ },
+ {
+ "data": {
+ "image/png": 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P8y2LiYlBKcUzzzyT4745rZB13fVjs/5r1qwZ9957L3PmzMnWU+G///3vLftm/ffzzz9n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\n",
+ "text/plain": [
+ "| \n", + " | census | \n", + "prb | \n", + "un | \n", + "maddison | \n", + "hyde | \n", + "tanton | \n", + "biraben | \n", + "mj | \n", + "thomlinson | \n", + "durand | \n", + "clark | \n", + "
|---|---|---|---|---|---|---|---|---|---|---|---|
| Year | \n", + "\n", + " | \n", + " | \n", + " | \n", + " | \n", + " | \n", + " | \n", + " | \n", + " | \n", + " | \n", + " | \n", + " |
| 1950 | \n", + "2557628654 | \n", + "2.516000e+09 | \n", + "2525149000 | \n", + "2.544000e+09 | \n", + "2.527960e+09 | \n", + "2.400000e+09 | \n", + "2.527000e+09 | \n", + "2.500000e+09 | \n", + "2.400000e+09 | \n", + "NaN | \n", + "2.486000e+09 | \n", + "
| 1951 | \n", + "2594939877 | \n", + "NaN | \n", + "2572850917 | \n", + "2.571663e+09 | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "
| 1952 | \n", + "2636772306 | \n", + "NaN | \n", + "2619292068 | \n", + "2.617949e+09 | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "
| 1953 | \n", + "2682053389 | \n", + "NaN | \n", + "2665865392 | \n", + "2.665959e+09 | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "
| 1954 | \n", + "2730228104 | \n", + "NaN | \n", + "2713172027 | \n", + "2.716927e+09 | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "
| 1955 | \n", + "2782098943 | \n", + "NaN | \n", + "2761650981 | \n", + "2.769074e+09 | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "
| 1956 | \n", + "2835299673 | \n", + "NaN | \n", + "2811572031 | \n", + "2.822502e+09 | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "
| 1957 | \n", + "2891349717 | \n", + "NaN | \n", + "2863042795 | \n", + "2.879934e+09 | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "
| 1958 | \n", + "2948137248 | \n", + "NaN | \n", + "2916030167 | \n", + "2.939254e+09 | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "
| 1959 | \n", + "3000716593 | \n", + "NaN | \n", + "2970395814 | \n", + "2.995909e+09 | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "
| 1960 | \n", + "3043001508 | \n", + "NaN | \n", + "3026002942 | \n", + "3.041507e+09 | \n", + "3.042000e+09 | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "
| 1961 | \n", + "3083966929 | \n", + "NaN | \n", + "3082830266 | \n", + "3.082161e+09 | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "
| 1962 | \n", + "3140093217 | \n", + "NaN | \n", + "3141071531 | \n", + "3.135787e+09 | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "3.036000e+09 | \n", + "
| 1963 | \n", + "3209827882 | \n", + "NaN | \n", + "3201178277 | \n", + "3.201354e+09 | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "
| 1964 | \n", + "3281201306 | \n", + "NaN | \n", + "3263738832 | \n", + "3.266477e+09 | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "
| 1965 | \n", + "3350425793 | \n", + "NaN | \n", + "3329122479 | \n", + "3.333138e+09 | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "
| 1966 | \n", + "3420677923 | \n", + "NaN | \n", + "3397475247 | \n", + "3.402224e+09 | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "3.288000e+09 | \n", + "
| 1967 | \n", + "3490333715 | \n", + "NaN | \n", + "3468521724 | \n", + "3.471464e+09 | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "
| 1968 | \n", + "3562313822 | \n", + "NaN | \n", + "3541674891 | \n", + "3.543086e+09 | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "
| 1969 | \n", + "3637159050 | \n", + "NaN | \n", + "3616108749 | \n", + "3.615743e+09 | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "
| 1970 | \n", + "3712697742 | \n", + "NaN | \n", + "3691172616 | \n", + "3.691157e+09 | \n", + "3.710000e+09 | \n", + "NaN | \n", + "3.637000e+09 | \n", + "NaN | \n", + "3.600000e+09 | \n", + "3,600,000,000– 3,700,000,000 | \n", + "3.632000e+09 | \n", + "
| 1971 | \n", + "3790326948 | \n", + "NaN | \n", + "3766754345 | \n", + "3.769818e+09 | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "
| 1972 | \n", + "3866568653 | \n", + "NaN | \n", + "3842873611 | \n", + "3.846499e+09 | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "
| 1973 | \n", + "3942096442 | \n", + "NaN | \n", + "3919182332 | \n", + "3.922793e+09 | \n", + "3.923000e+09 | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "3.860000e+09 | \n", + "
| 1974 | \n", + "4016608813 | \n", + "NaN | \n", + "3995304922 | \n", + "3.997677e+09 | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "
| 1975 | \n", + "4089083233 | \n", + "NaN | \n", + "4071020434 | \n", + "4.070671e+09 | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "3.900000e+09 | \n", + "4.000000e+09 | \n", + "NaN | \n", + "NaN | \n", + "
| 1976 | \n", + "4160185010 | \n", + "NaN | \n", + "4146135850 | \n", + "4.141445e+09 | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "
| 1977 | \n", + "4232084578 | \n", + "NaN | \n", + "4220816737 | \n", + "4.213539e+09 | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "
| 1978 | \n", + "4304105753 | \n", + "NaN | \n", + "4295664825 | \n", + "4.286317e+09 | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "
| 1979 | \n", + "4379013942 | \n", + "NaN | \n", + "4371527871 | \n", + "4.363144e+09 | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "
| ... | \n", + "... | \n", + "... | \n", + "... | \n", + "... | \n", + "... | \n", + "... | \n", + "... | \n", + "... | \n", + "... | \n", + "... | \n", + "... | \n", + "
| 1986 | \n", + "4940571232 | \n", + "NaN | \n", + "4953376710 | \n", + "4.920968e+09 | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "
| 1987 | \n", + "5027200492 | \n", + "NaN | \n", + "5045315871 | \n", + "5.006672e+09 | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "
| 1988 | \n", + "5114557167 | \n", + "NaN | \n", + "5138214688 | \n", + "5.093306e+09 | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "
| 1989 | \n", + "5201440110 | \n", + "NaN | \n", + "5230000000 | \n", + "5.180540e+09 | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "
| 1990 | \n", + "5288955934 | \n", + "NaN | \n", + "5320816667 | \n", + "5.269029e+09 | \n", + "5.308000e+09 | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "
| 1991 | \n", + "5371585922 | \n", + "NaN | \n", + "5408908724 | \n", + "5.351922e+09 | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "
| 1992 | \n", + "5456136278 | \n", + "NaN | \n", + "5494899570 | \n", + "5.435722e+09 | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "
| 1993 | \n", + "5538268316 | \n", + "NaN | \n", + "5578865109 | \n", + "5.518127e+09 | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "
| 1994 | \n", + "5618682132 | \n", + "NaN | \n", + "5661086346 | \n", + "5.599396e+09 | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "
| 1995 | \n", + "5699202985 | \n", + "5.760000e+09 | \n", + "5741822412 | \n", + "5.681575e+09 | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "
| 1996 | \n", + "5779440593 | \n", + "NaN | \n", + "5821016750 | \n", + "5.762212e+09 | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "
| 1997 | \n", + "5857972543 | \n", + "5.840000e+09 | \n", + "5898688337 | \n", + "5.842122e+09 | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "
| 1998 | \n", + "5935213248 | \n", + "NaN | \n", + "5975303657 | \n", + "5.921366e+09 | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "
| 1999 | \n", + "6012074922 | \n", + "NaN | \n", + "6051478010 | \n", + "5.999622e+09 | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "
| 2000 | \n", + "6088571383 | \n", + "6.067000e+09 | \n", + "6127700428 | \n", + "6.076558e+09 | \n", + "6.145000e+09 | \n", + "NaN | \n", + "NaN | \n", + "5.750000e+09 | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "
| 2001 | \n", + "6165219247 | \n", + "6.137000e+09 | \n", + "6204147026 | \n", + "6.154791e+09 | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "
| 2002 | \n", + "6242016348 | \n", + "6.215000e+09 | \n", + "6280853817 | \n", + "6.231704e+09 | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "
| 2003 | \n", + "6318590956 | \n", + "6.314000e+09 | \n", + "6357991749 | \n", + "6.308364e+09 | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "
| 2004 | \n", + "6395699509 | \n", + "6.396000e+09 | \n", + "6435705595 | \n", + "6.374056e+09 | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "
| 2005 | \n", + "6473044732 | \n", + "6.477000e+09 | \n", + "6514094605 | \n", + "6.462987e+09 | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "
| 2006 | \n", + "6551263534 | \n", + "6.555000e+09 | \n", + "6593227977 | \n", + "6.540214e+09 | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "
| 2007 | \n", + "6629913759 | \n", + "6.625000e+09 | \n", + "6673105937 | \n", + "6.616689e+09 | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "
| 2008 | \n", + "6709049780 | \n", + "6.705000e+09 | \n", + "6753649228 | \n", + "6.694832e+09 | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "
| 2009 | \n", + "6788214394 | \n", + "6.809972e+09 | \n", + "6834721933 | \n", + "6.764086e+09 | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "
| 2010 | \n", + "6866332358 | \n", + "6.892319e+09 | \n", + "6916183482 | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "
| 2011 | \n", + "6944055583 | \n", + "6.986951e+09 | \n", + "6997998760 | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "
| 2012 | \n", + "7022349283 | \n", + "7.057075e+09 | \n", + "7080072417 | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "
| 2013 | \n", + "7101027895 | \n", + "7.136796e+09 | \n", + "7162119434 | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "
| 2014 | \n", + "7178722893 | \n", + "7.238184e+09 | \n", + "7243784000 | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "
| 2015 | \n", + "7256490011 | \n", + "7.336435e+09 | \n", + "7349472000 | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "
66 rows × 11 columns
\n", + "\n",
+ "\n",
+ "\n",
+ " \n",
+ "
\n",
+ "
"
+ ],
+ "text/plain": [
+ "1950 2.557629\n",
+ "dtype: float64"
+ ]
+ },
+ "execution_count": 428,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "results[1950] = census[1950]\n",
+ "results"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "After that, the population in the model grows by a constant amount each year."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 429,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "for t in linrange(1950, 2015):\n",
+ " results[t+1] = results[t] + annual_growth"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Here's what the results looks like, compared to the actual data."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 430,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Saving figure to file chap03-fig02.pdf\n"
+ ]
+ },
+ {
+ "data": {
+ "image/png": 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X17O2NQylc3R0RKfTcWaVtoZC1mAusA7w9ttvExYWZnXc6b8MFMUWer2eoqIi\nNDSOFh/laPlRKv0qqXOvAx1cO3g4BUX9KK3Rc+ut0QQEuJ2/UaVVNXXn74z1xK7t9V+dgIbb0X31\nX22t+vUbUAHEA3vAMgKoH/C9jW0omLt5fv/9d6tte/futewrKSmxFFH38fEBYP/+/ZZjw8LCcHJy\nIjc3l1GjRlm2//vf/8ZoNPLwww9fhHehdBQODg4ERwbzv2//x0nHk1QGV6FzBBdHF6b0m8KVPa8k\nL6ISvV5Hly7qjv9S0NQkrzEtfTEpZaUQ4nVgvhAiF/MngDlAJOaRQ4qN7r33Xm655RYWLlzIlClT\nyM7O5rnnnmP06NFERkYSFBTEokWL+Pvf/86jjz5Kbm4ub731luV8Nzc3Zs2axWuvvYaHhwcxMTFs\n2bKFRYsWMX/+/DZ8Z8qlTtM0cnNzCQoKsnwy3ZW1i4/2f0SVZx3J6QV4ljpxbfxlzBw4k0B3czdi\nUJBHU80qF1mjn++FECOa06AQYuR5DpkLvAq8gTn5Xw5cLaWUzbleZxUdHc27777L7t27ufHGG3nq\nqaeYMGECb775JgCenp6sXLkSg8HAlClTeP7557n33nut2vjrX//KHXfcwSuvvMJ1113Hf/7zH55/\n/nn+8Ic/tMVbUtqBsrIyduzYwa+//kpOTo5le4hnCOWVNfyaeJzSEgPOhwdxvf8sS+JXLj26M/uF\nGwghEoBk4EUp5f5zHmR9fDzmh79RUsoW7SgXQoQDR2xdlkBRlJZlMplITU3l8OHDmEwmAFxcXBgz\nZozl+dEGuYH31n+N75EReGiBTJkSzfjxYU01q7SirKwsxo8fD9DrXKsnNNXnPxSYB+ypX9XzU2A3\ncARzv70v5r7/K4HrME/gehuY1nLhK4rS1k6ePEliYiJlZeZ1Hg0mA5WGSuJFvNUghYnRE7ni3nEs\nXZLElCmCiAjftgpZsUFTff51mJdvWAw8AtyLucvm9I8KOuAo8D/gBill9lkNKYrSLp05WQuguLqY\nlPIUyv0qCDwRR3T0qZ5jvU6Pv587f/+7mrDVHpx3nH99Qn8MeEwI0QeIwLywWwGQKaW0bQqtoijt\nRm5uLklJSZblQkyaiczSTFL1qRS5VpC8r5DdpW/h5zqPyy6zHuynEn/7YFclLyllCuZZuYqidFAZ\nGRkkJVmm4lBZV0lKVQo5HjlojhrZqeUYKpyIqBnCmjUp9OkTgLe3Wna5vVFlHBVFsRISEoKUktra\nWnKrc0meTfKYAAAgAElEQVQyJVHtVW3u5AVuGn4lWRsFNdWOTJ4cjZeXc9sGrDSLSv6KolhxcXEh\nPCqcL3//ksNOh9EczP39Tg5OTO0/lZE9R3IstAwXFwc1dr8dU8lfUTopTdM4cuQINTU19O3b17I9\nOT+Z5YeXU+xYQvqRYtzcnBjWpw+zB88mxCsEgJ49VT3d9k4lf0XphEpLS0lISKC4uBidTkdQUBD+\n/uY6uTXGGvJLT5K0v4DKSgM9DYO5a+JDhHj5tXHUSktSK3gpSidiMplISUnhp59+ori4GDB/AkhP\nT7ccMzB4IFdFjcNN78mAipsIrxjJnt35bRWy0kpsLePoCjyFuYavB2f/0tCklBdWyURRlFZ18uRJ\nEhISKC8vt2zT6/X06NWDAX0GWB1724CpDPMbx7tvpnDzzVFceWX3M5tT2jlbu33exFx05UdgP2Bq\nrYAURWlZBoOB5ORkMjIyrLb7+PqQ5pzG9uPbud/nb4R372LZ5+TgRFTPEF56qQsuLqp3uCOy9V/1\nVuBpKeXC1gxGUZSWlZubS2JiItXV1ZZtjo6OdA3ryobcDWSdzObIkRJ2bHqRZQ88S3S0v9X5KvF3\nXLb2+TtjXtdHUZR2QtM00tLSrBJ/UFAQHlEefJDxAcfLj5OWXkz28XJ0mp5ly/dRWVnXRItKR2Jr\n8v8W8+JtiqK0EzqdjtjYWPR6PS4uLsTExXDQ6SCrk1dTazSXA40M9ydGuxpReS29wvzPqv6mdFy2\nfqZbBSwVQgQCO4HKMw9oqMmrKErbqKysxM3NzWptHU9PT4YOHUqtcy3LE5ZzvOxUxdVgz2DuG3If\nhZHOFBdXM3JkqFqXpxOxNfl/Wv91Vv2fM2mASv6K0gYaJmulpKQghCAyMtJq/1HDUT767SMKikox\nGDT8/FwZHjqcaTHTcHF0ofvFK1OtXEJsTf4tXlxdUZQLd/pkLQApJcHBwXh4mJddSM5PZulvSzme\nXU76kRKcHZxYMH0m1/Uf15ZhK5cAm5K/lDKz4bUQwgPwAgrr1/xXFOUiMxqNlspap/fTe3h4YDQa\nLd/3CexDX78B7P7le1yNvvQtnciRrX7Qvy2iVi4lNo/jEkKMARYCQ6hf308IsRt4Rkr5Q6tEpyjK\nWQoLC0lMTDxrslZ0dDSRkZHo9afGceh0Ou4fNhuq3Tn4aTARPbswdaqaj6nYPsN3FOYRPymYq3nl\nAt2AqcBXQojxUsptrRaloijU1dWRnJxMZmam1faAgABiY2Px8PDgl+xfiO8Wj4PewbLf3cmdR66a\nTXL3QqKi/HB0VKu6KLbf+b8AfA9cL6W0fMYUQrwIbMRc63d8i0enKAoAZWVl7Nq166zJWv369aNn\nz55UG6p5d8+7/HpsL8uPbeP52+YQHGy93HLfvgEXO2zlEmbrLcBQYNHpiR+g/vtFQHxLB6Yoyinu\n7u44OJy6mw8KCmLMmDGEhYVxovwEC7YvYOuhX9j7Wx7bsn9k/pLPqaszNtGi0tnZmvyLAM9G9nkB\n6n+ZorQiBwcH4uLicHFxYciQIcTHx+Pm5kbCiQRe3v4yueW5ODroMRhMdK8ZSHW2PwcOFLZ12Mol\nzNbkvxmYJ4SwqtRc//08zF1CiqK0gIqKCqSUZ822DQgIYPz48XTrZv4x3HhoI4t/XUy1wdwV5Oft\nwZ+vuJ+BThP461/iGTiw60WPXWk/bO3zfwrYA6QKIbYDJ4Bg4EqgFHiidcJTlM6jYV19KSVGoxEv\nLy9Lom/g4OBAtaGaD/Z9wG85v6GrL6wb4B7AnPg5dPfqTuX4Ojw8VF1dpWk23flLKbOBQcBiwAe4\nHPDF3N8/SEqZ3sTpiqKcR0lJCdu3b+fgwYOWcfoHDhzAZLJePb2gsoCXt7/Mxt+28ftveRiNJvoE\n9uHpkU8T6m1enkElfsUWNo/zl1KeAB5vxVgUpdMxGo0cOnSItLQ0q24eb29v4uLirMbsA3yw7wN+\n+v0gOTkVAOgyovjLjX+xGtqpKLZoNPkLIZ4GVkgpc+pfN0WTUi5o2dAUpWMrLCwkISGBiooKy7bG\nJms1mBk3k72HDpGbU01U5TjCyodRU23C3V0lf8U+Td35v4j5QW5O/eumaIBK/opig/NN1vL0bGxg\nHXTx6MKzN/yNb/TH8NVCmDatL05OKvEr9ms0+Usp9ed6rSjKhUlJSbFK/KdP1jp9SeXSmlKOnMxA\n+PXD1fXUj2qfwD5EzxDo9Wr5ZaX5bErqQoi5Zw7zPG1fmBDirZYNS1E6rujoaJydzQ9lg4ODGTt2\nLGFhYVaJ/1jJMZ79/gX+tPwFFry76axhnyrxKxfK1ge+zwJfAcfPse9y4D7gLy0VlKJ0FJqmoWma\nVf+9i4sLsbHmRfSDg4PPKqCy9/helu55n593Z1Fba2R90SqGbBTceINakE1pOU098N2OObGDeRXP\nXUI0+p/vV1svKIToBxw4x66RUsrttrajKJe6iooKEhMT8fT0JCYmxmpfSEjIWcdrmsaGQxvYcGgD\n6CAoyJ2cozVEV0/A2VEN31RaVlN3/rOByZgT//PAEiDrjGOMQDHwuR3XjAEK6r+eTs1FVzqEhsLp\nhw4dwmg0UlBQQPfu3fH392/0nBpDjWXiVoPL+vXGx3EsN4wZqBZlU1pcUw98U4D5AEIIB2BZ/WSv\nCzUAOFg/b0BROpSSkhISEhIoKSmxbNPpdBQXFzea/AsrC3n1xzc4acy1zNjt26Uv9w6+F4/xHuc8\nR1EulK2VvJ4DEEIEAM7UF3PB/MDYA3OXzTIbrzkASLYzTkW5pDU2WcvHx4e4uDh8fHzOeV5qYSrP\nbniNxOQsunX3pFe4D2N7jWVq/6nodWqQndJ6bC3mEgOspvHibxpgT/J3FULsAsKB/cDTUsrdNp6v\nKJeUgoICEhMTrSZrOTg4EB0dTURExDkna4F5KOfcTS+z74D5Q3D2sQqm9Z/B7QNuuChxK52brbcW\nrwIBwGPAj8A3wEPAJsyJf4wtjQgh3IAIzOsDPQ7ciHkE0VYhRF874laUNmc0GklISODnn3+2SvwB\nAQGMHj2a3r17N5r4AbxdvJk9Yhr+/q44a26MdZ3B1X3GXITIFcX2oZ6XA49IKZcLISqA6VLKd4B3\nhBD/wzzM87wjdaSUVUIIP6BGSlkDIISYhbku8Bzgz814D4rSJvR6vVXSd3Jyol+/fvTo0eOs4ZuN\nGddrHKXXV1CY2JUZk4daTeZSlNZk6/80FyC1/vUhIO60fSuAd229oJSy9IzvTUKIA0APW9tQlEuB\nTqcjNjaWrVu3EhQUxIABA3B1dW30eJmfSlaqgfFX9LVq45aYG88e+6YorczWbp+jQK/614cAbyFE\nWP331UDjY9hOI4QYIoQoFUIMOW2bAzCQc4/9V5RLgqZpHD9+/Kwllj09PRkzZgxDhw5tMvF/kfgt\nM999kqc+fYWffzna2uEqynnZmvzXAS8LIW6RUh4HUoAX6vvpHwHSbGwnAcgA3hNCDBNC9Mf8ySEQ\neNOuyBXlIqmoqODnn39m7969pKefXbrCw6Px4Zh1xjo+TPiQN75fRklZNWUOeTy3dgknT1a1ZsiK\ncl62Jv/ngF3AvfXfPwLcinmkztWYSzmel5TSAFwHSOBLYDfmimCjpJR5NketKBeByWTi8OHD/Pjj\njxQWmucgSimt+vmbUlBZwMIdC9lxdAcRET64uTniZerCfeNvxc+v8U8JinIx2DrOvxL4gxDCpf77\nb+qHfw4GfpNS2nrn31AVbHpzglWUi6W4uJjExMSzJmtFREQ02b3TIDE3kRW/r6CyrhIABwc900Zf\nw6SetyJ6q9q6Stuza2hBwwid+tdp2N7doyjtgtFoREpJenq6XZO1LOebjCz4bAW7T24hJMS8Lr+j\n3pHbBtzGyJ4jbR4FpCitramF3VIxj+G3hSalVEsOKu1aY5O1hBBEREScN3GfKCrkwfdf4mBeCnq9\nDi9vZ3oEBvHA0AcI9w1v5egVxT5N3fnvwPbkryjtWk5ODnv27LHaFhgYSGxsbJMPdE+368R2jlWZ\nPwybTBp1xwN55g/P4OnceGUuRWkrTS3sNusixqEobapr1654enpSXl7erMlaAJPEDeyJT2T91t1c\nFzmRF+6ajYuzUytGrSjNZ+vaPlec7xgp5c4LD0dR2oaDgwOxsbEcOXLkvJO1GpSU1ODj43KqDb0D\nj45+iBvFUS7rFdfEmYrS9mx94Lud83cBqSrSyiVP0zSOHj1KYWEhgwYNsrqzDwgIICDg/Ovma5rG\nsvXf859t37D43qfo0+fUOX5uflzWy69VYleUlmRr8h97jm2ewEjgTsxFXxTlklZeXk5iYqJlzH5Q\nUBDdu3e3qw2jycg/PnqXLw5sQnOAuStXsOKZv+DhoSptKe2LreP8tzaya6MQohx4BlDr0CqXJJPJ\nZKmsdfryDBkZGXTr1s3mfv3CykKW/baMXM9UHJ301NWZyPNIpLyqWiV/pd1piSUEtwFPtkA7itLi\niouLSUhIoLT01HqCOp2O3r17ExUVZXPi33N8D6sSV1FVV4WzswPR0X741vXk1WmP4efu3VrhK0qr\naYnkPwkoPe9RinIRGQwGDh06dNZkLV9fX+Li4vD2ti1hpx7J45ODH3PUtN+yTa/Tc++I6VwdebWa\ntKW0W7aO9vn2HJsdMC/DHAksbMmgFOVC5Ofnk5iYSGVlpWWbg4MDffr0oVevXjYlbE3TWLVhB2/8\ntJhapzKGDO6Ki4sjge6B3DP4HiL8IlrzLShKq7P1zt+Zs0f7aMBB4BVgeUsGpSgXIisryyrxBwYG\nEhcXh7u7u81t/JaVwOu//pMqXR0YIPVwMfdccz3TYqbh6qgWZVPaP1sf+I5p5TgUpcX079+f/Px8\nTCYT/fv3JzQ01O7umf4hfbgiLorNvxzE18uTZyb+ietix7ROwIrSBuzq8xdCXId5eKcfkAtsllL+\n1BqBKYotqqqqcHR0xMnp1ExaZ2dnhgwZgqenJy4uLk2c3ThXR1ceG/8g7g4reXT8nwjyUitxKh2L\nrX3+AcBXwFCgBsgHugL/V/884BYpZXWrRakoZ9A0jczMTJKTk+nevTuxsbFW+22ZrNUgK7eQlz/6\nH/+YPt2yEidAuG84C2+aqx7qKh2SrcVc3sZcxnGSlNJNStlTSukK3IL5F8LLrRWgopypvLycn3/+\nmaSkJAwGA5mZmZaJW/b6fPsObn79QX7I+4Jnl3xMXZ3Rar9K/EpHZWvyvw54TEq58fSNUsovgKeA\nO1o6MEU5k8lkIjU1la1bt1ole09PT/R6W/8rm9Uaa/nv/v/yWc5yqigHYFfFRhIOZrdozIpyqbK1\nz98AFDeyLwfzaCBFaTXnm6zl4GD70lJHio6wYt8KcstzcXN1JDzMm5MnTDw9aQ5D43q2RviKcsmx\nNfkvBl4SQvxaX8AdACGEN+bZvW+3RnCKYjAYkFJy5MiRC5qsBXAk8yRfpW0iqXIHJu3UMg/XDb6C\nO/pPJ8BTLcimdB62Jv9u9X/ShBDbgeNAADAC8AJqTpsIpkkpr2nxSJVOp6qqip07d17QZC0Ag8HE\nh+t38O7Py6h1LWLIkCAcHfW4OLpwW//buKLHFapvX+l0bE3+vYF9p53T8Nm4YZsDaklnpYW5urri\n5uZmSf5dunQhNjbWrslaAL9k7uGt3/5Jjd4AtXAko4SJwy5j1sBZBLoHtkboinLJs3WS17mWdFaU\nVqXT6YiLi2Pnzp306dOnWZO1AGJD+zKgTwh7k47h7+POnNF3MXnQ9epuX+nU7J3k1Q8YDfhgHuu/\nXUopWyMwpXOpqqoiPT2dvn37Wo3c8fDwYPz48XaN5iktrcHb+9TkLi8XL/521X185LaOJ655kGCv\n4BaNXVHaI1sneemB94A/AqffLmlCiI+Au6WUqti7YjdN08jIyCAlJQWDwYCzszNRUVFWx9ia+Kuq\n6lj68XY2J/3K+0//mYAAN8u+wSGDGTR5kLrbV5R6tt5OPQncVf81FHDC3O//FHA78HirRKd0aGVl\nZezcuZP9+/djMBgASE1Npba21u62jCYjf120mPcO/gvpsJU3PvraanQQqAlbinI6W7t97gHmSylf\nPW1bFvCKEMK1fv8rLR2c0jGZTCYOHz5MamqqVWUtLy8vYmNjcXa2b9pIVmkWK/etpLRbKlqeub3f\n6r6mtnYSLi4tUbJCUToeW38yQoAdjezbifkTgKKcV1FREQkJCZSVlVm26fV6y2Qte/r2jSYjXx/+\nmo2pGzGajHh7udAzzJvegRE8fd2DKvErShNs/elIBy4HfjjHvssxz/JVlEY1NlnLz8+PuLg4vLy8\nbG7rxIkKFn20hcroXZTr8y3bHfWOPHLNLCZETkCvs2+5B0XpbGxN/suABUKICuC/mJdzDsK8ps/T\nwEutE57SUWRkZJCenm753tHRkT59+hAeHm5XX/zPvxzjxf+u5IjTLtwrHRk8qCs6nY4IvwhmDpxJ\nsKcayaMotrA1+b8NDAJeA/552nYdsAqY38JxKR1MREQEx44do7y8nK5duxITE2P3ZC2AfYZvyXTZ\nhWbSqKyso7LcxMxhtzE+Yry621cUO9g6ycsIzBRCvIK5mIs/UAT8JKU80IrxKe2QpmkYjUYcHU/9\n99Lr9cTFxVFZWUn37t2bPfJm8sBJfJW0ldz8Mq4aMpi/jLqPIM+glgpdUToNe5+IHcPc/18E5NW/\nbjYhxHBgO3CVlPLHC2lLuTRUVlaSlJQEwGWXXWaV5P39/fH397e5rd9/z8XJSc+AAV0s27p6dOWv\nV9+NwWTgqkh1t68ozWXPJK9XgIcwj/Fv+ImuEELMl1LaXcxFCOEBfIRaE6hDOHOyFkB2djahoaF2\nt1VWVsuq1Qf44uBGvN3dWTH3z7i7nyrTOC5CrTaiKBfK1tumecDDmPv+R2Be6G0EsBR4XggxpxnX\n/hfmuQJKO1dWVsaOHTusJmvpdDoqKiqa1V5eVQ5rji4iw/Vn9pt+ZNXnu1oyXEVRsG+S1/NSyhdO\n25YO/CyEKAMewbzmv02EEBOB6zFXCEu09Tzl0tJQWevw4cPnnKxlTxcPgEkz8V3ad3whv6BrVC0F\nydA12BXH6HTMj5oURWkptiZ/H2B3I/u2A4/ZekEhRCDwPnA35mcHSjt08uRJEhMTL3iylqZpnDhR\ngd6rghX7VnCk6AgAgYFuXDa0G9MG38qEyAmt8h4UpTOzNflvAB4AvjnHvtuBTXZc8z3gCynl10II\n+zuElTalaRoHDhwgIyPjgidrFRZWsXLlfrZl/UjAlWk4OJ1qL8w3jLvH3E2IV0iLxq8oipmtyf8n\nYL4QIhHzJK8czJW8bgCuBP4lhHi6/lhNSrngXI0IIWZini8Qe0FRK21Gp9NRV1dnSfzNnaylaRr/\nencrPxR+SonjcfykCwMGBOKod+SG6Bu4tve1aiSPorQiW5P/v+u/+gAvnmP/6d0+GnDO5A/Mwrwq\n6AkhBJwaNfSVEGKllPIBG+NR2lD//v3Jz8/Hx8en2ZO1AKr6b6d053F0gKenM929Qrln8B8J9VYf\nCBWltdk6yaulbsFmAG6nfR8MbANmA9+10DWUFqJpGsePH6dr1644OZ0aauns7MzIkSNxdXVt9mQt\nnU7Hg6Pu5nBeBt5eLkwdfBMToybiqFeLsSnKxXBRf9KklNmnfy+EqK5/mS2lzLuYsShNa5islZeX\nR1hYGLGx1j11bm5ujZx5tqKialatOsCkSZGEh/tatkf6R/LIhHuI8IsgzDesxWJXFOX81G2WYkXT\nNI4cOUJKSgpGoxGAzMxMunfvTkBAgN3tHThQwL+X/kyS7luSVg5k8T/uxtHx1AfJsb3UhC1FaQtt\nmvyllFlYl4VU2lBpaSkJCQkUFxdbtul0OsLDw/Hx8bG7PU3TyNIO8rPrSmpMVewqz+bXpDFcPiiy\nJcNWFKUZ1J2/YpmslZqaajV808vLi7i4OPz8/Oxus6ymjDVJa/gt5zd69HIhO7uOaOGNwf84oJK/\norQ1lfw7uZMnT5KQkEB5ebllm16vJyoqit69e9tVWauyso7CwioKndJZlbiKshrzBLCQbh70CQ/l\nniF30yewT4u/B0VR7Ndo8hdCdLOnISnl8QsPR7mYioqK2LHDujqnv78/sbGxdk3WAkhOLmTJB7+S\n4rCFbvEnrfr1R/YcyZT+U3B1dG2RuBVFuXBN3flnYR6zbyu1Omc74+vrS2BgIAUFBTg6OtK3b1/C\nwsLsHr5ZU2Pg5RWfs0/7mlqtksrDbvTpE4Cvqy93xt3JgK4DWukdKIrSXE0l/z9yKvn7Ay9jruH7\nCadm+N6IeZbv31oxRqWFaJpmldh1Oh2xsbEkJyfTv39/u4ZvWnEwosXupTaxEicnPYFd3BkeOpzb\nBtyGu1PzJoApitK6Gk3+UsoPGl4LIdYBH0op7z3jsDVCiDeBqcCSVolQuWCappGVlcWxY8cYPny4\nVT++h4cHQ4cOtbu903+JuDi68Nfxs3m28jV6dQtidvwsYoPUCh6Kcimz9YHv1cDNjezbAJz5S0G5\nRFRWVpKYmEh+fj4AaWlpREVFNbu99PRiVv9nP3MeGEJAwKlPCoNDBvPo1fcS3y0eD2ePC45bUZTW\nZetQjgLgskb2jQGyG9mntBFN00hPT+fHH3+0JH6ArKwsq7X37bFly1Ge/NcnfFr0Nv9csclqWCjA\nmPAxKvErSjth653/UmCuEMIN+ALIB4KAKcBfgL+2TnhKczQ2WatXr14IIewavtmgsq6SPYYN7Hff\niAZ8n/8Z92ePITzU/lm/iqK0PVuT/3zAF3gceOq07dXA/0kpF7V0YIr9jEajpbJWS03WAkg4kcDq\npNWUVJcQ2sOLsrJaBvfvgt6rAvNzf0VR2htbV/XUgMeEEC8AlwN+mLuCdkopm1eoVWlRjU3Wio6O\nJjIy0u67/bS0Ygy6KrYXb2J39qkibuFh3sR3j+eOmDvwdPZssfgVRbm47JrhK6UsAb5upViUC5Cf\nn2+V+P39/YmLi8PT074EXV1t4LPPUvl052Zyuuyg/yBP9PUje7xdvJkeO52BwQNbNHZFUS6+pmb4\npmL7JC9NSilaJiSlOaKiosjJyaGqqqrZk7UAThQXsvT39zjhngoVcOyYRlhPb4aFDuO2/repB7qK\n0kE0dee/A/tm+CoXSU1NDSaTyWpSll6vZ/DgwTg5OTV/shbg6e2Ab1QxJw5DQIAr0T1DmH2ZGrev\nKB1NU5O8ZjW8FkLcDvwgpcxv7Hil9TVM1jpw4AC+vr4MGzbM6u7e29vbrvZMJo28vEqCg0/dzQe6\nBzJn/AyWuH7IjXETmNxvspqlqygdkD1DPWcBn7ZeKEpTKisrSUhIoKCgADD38WdnZxMa2rx6t5mZ\nJXy06gDpRem8/dxUPDycLfvGR4wj0j+CCL+IFoldUZRLj63JPxtQt39toGGylpTSUlkLwN3dHVfX\n5q2SaTJpvLLkG3ZXb6LCoYD3P+nOX+4+VVFLr9OrxK8oHZytyf8d4E0hxHAgASg/8wAp5ZqWDEw5\n/2QtR0f7yzFUG6r5Qn5BXvRGyg8UoNfr2Gf6GpNpdLMmfymK0j7Zmj1er//6p0b2a4BK/i2kscla\n3t7exMXF4evr28TZZ6utNeLkpGfP8T2sPbiWkuoS/P1dCQ/3pluQN1PjxqlimorSydia/Hu1ahSK\nhcFgYNu2bS0yWctoNLF581HWfr2H0GvTyK5Ot9p/7eDhTI+dTqB7YIvFryhK+2DrDN/MhtdCCA/A\nCyiUUta1VmCdlaOjI35+fpbkHxAQQGxsrN2TtQCWf7iPtfvWk+3yG96/OhETE4gOHT6uPkzpN4Wh\n3YY2ay6Aoijtn82dxkKIMcBCYAj1nQRCiN3AM1LKH1oluk6qX79+nDx5ksjISHr27NnsBJ0fupWs\n5D1oQF2dCaNB45roq7hR3KhKKipKJ2dT8hdCjAK+BVKAuUAu0A1zEZevhBDjpZTbWi3KDqqmpgYp\nJX379sXJycmy3dnZmbFjx17wXfn0+D+wVe7GwUHHqAFxzIibTqh384aGKorSsdh65/8C8D1wff0i\nbwAIIV4ENgLzgPEtHl0HpWkax44d4+DBg9TV1aFpGnFxcVbH2JP48/IqeH/1r9xyfX/6RHexbA/z\nDeNPV91GkEcQw0OHqy4eRVEsbH16OBRYdHriB8tqn4uA+JYOrKOqqKhg165dJCQkUFdnfmRy9OhR\nqwe89ti1J5NZL7/Gqpx/8dKaNRgM1oVabu5zM5f3uFwlfkVRrNh6518ENPbE0QswNrJPqdfUZK3m\nrL5p0kzsOLqDT3I+46hLKiajxr6KrSQcvIUhsT1bOnxFUToYW5P/ZmCeEGKblPJ4w0YhRDfMXT7f\nt0JsHUZJSQkJCQmUlJRYtul0OiIiIhBC4ODgYHNbmqax78Q+1sv15JTlANAr3IcTuRWMHtiP7hHO\n52lBURTF9uT/FLAHSBVCbAdOAMHAlUAp8ETrhNe+GY1GDh06RFpa2gVP1tI0jU9/3MFP+V9T42a9\nvl7fXt156rpbuLyH6tdXFMU2to7zzxZCDAIeBUZinvRVhLm//19SyhOtF2L7deLECQ4fPmz5Xq/X\nI4QgIiLCrslah06k8+TKd0guPIizk54hQ4NwcnTA1dGVa3pfw1URV+HsoO74FUWxXVPFXEZjLtNY\nB1Cf4B+/WIF1BN26dePo0aMUFBQQEBBAXFwcHh72F0NJL0sls/IQALV1JrKPVTF7/M1cF3WdKqWo\nKEqzNHXnvwWoEEL8hHmM//dSygMXJ6z2qa6uzmq8vk6nIy4ujvz8fLsma2maZnXsuIix9I34nN8O\nHGN05JX839Q/0s2va4vHryhK59FU8r8Fc5/+SOBVwEEIcQLzw93vMP8ysLu7RwgRinmhuPGYh5p+\nDfzt9AfJ7U11dTX79++nvLycUaNGWXXpuLu7ExYWdt42amoMbP45hY92fUp80Ageufsqyz5nB2ee\nuCyMn20AABLhSURBVOZBaoY7M1REt8p7UBSlc2mqktd6YD2AEMIduBzzL4NR/H97Zx5eVXUt8N/N\nzQAJGAMJyBAZElgIGLC1IihosKCoSGutny3Pp++1pa2ftWpfpd9rrVVbqq991qG+j34dbG1f1U7y\n7IBCVapYh2o1QIYFYQpCgBAMGAKR5N73xz43OYQMF5Lcgbt+33e/JGfvs89aOfuuvc86e68Fy4GB\nIlKOGwhWq2qPid1FJIDbFFYHRALIPwz8ERc2IqnouFkLoLq6mokTT8xA7z+8n6feXsEjf/kDYcLs\nqNvH9ftmkZ/fnkLh7DOmulfshmEYfUC0L3ybgOe9DyKSDlwELAFuBm4FolmvOByoBL6mqtu8th4A\nVohInqq+d6IKxItDhw5RVlZGfX39Mcebm5t7PLe2tpH8/IE0thxkZfVK1taspTXUSm5uJg0HmqkP\nbmHNm+Vcc5ntnTMMo384kcBuA4CLgY/iZu0luDj+b+DeCfSI5ya6ztfmaODzwD+SxfCHw2E2b97M\nxo0bj9mslZOTQ0lJCfn5XYdHfu21Xbz44g6qtu+geMEeatPLaQ21tzFq9CDOHjWJJRd9inPHnd2v\nehiGkdp0a/xFZCpwqfe5EBgAbMYZ+3uAF1X14MlcWERWAItwS0ZLe6ieEHS1WauoqIiJEyf2uFmr\ncnsNq/b8gT2nVVBdkcXUqe0DRdGQIm49fyGT8ifZWn3DMPqd7pZ6vguMwBnnNTjXzqqIu6YPuBNY\nBnwDWC0i56jqzj5qu8+pqqo6LrNWbm4u06ZNIzc397j6LS0h0tOPXctff8br7M0qJxAIEEwPECZM\n8ZBirpx4JWfln2VG3zCMmNHdzH8ksA/4Ke6l7st9mbxFVdcDiMh1wA7gBtxgkJCkpaW1Gf5gMNiW\nWaujwX7vvSOsXLmVDRv2cffds8jIaH8auLpkIW/U/JNBgzKYPHwSV068EhkqZvQNw4g53Rn/j+Lc\nPQuAO4Am35r/VapaeaIXE5HhQKmqPhk5pqpNIrIZGHWi7cWS4uJidu3aRWZmZpebtUKhMPff/wbb\nD26lNnMda/8+mtKL2jNgjs8bz3XnLmLqsKlMHGpLNg3DiB/dLfV8ARfQbalntC8F5uHi/PzAcwut\nxg0Gq1V1fxTXGwM8ISLVqvomgIjkAgL8olea9BHhcJjdu3eTm5tLdnb7Usu0tDRmzpxJZmZmpzP1\ncDhM5b4K6ic9yzsVZQCsLH+B0os+c0y9q8+6un8VMAzDiIJol3ruAR73PojIdNxAMAf4uddORlfn\n+3gTeBn4iYgsAY4C9+HW/cfd+B85coT169eze/duCgoKmDFjxjGGPisrq+33hoYj7NjxPlOmDuWt\nXW/x3Obn2HFgB+G8MEOHDmDkiEEER1YTCodIC0Qfx8cwDCMWRL3UE0BETsdt9poFzMAleUkH3orm\nfFUNicjVwPeBP+FWDz0HXKSqJ5fNpA8Ih8PU1NRQUVFBS0sLAHV1dezcuZPRo49Ne9jc3MLTT1ez\n5uUt7B1QSdG8vRw82tBWHkwLcPaUYZw/+nzmF803w28YRkLS01LPCThDf4H3cxIuJEMFbsPXD4E1\nJ7LcU1X3ATeepLx9TmNjI+vWrTtus9aYMWMYPnz4cfVDaUdZUbWC8uw3aAk0c6h6MGPHuNU+GcEM\nZp85m3lF8xgycEhM5DcMwzgZulvqWQcMAQJADc7YLwNeOBVCOIdCobbNWqFQe+rDnJwcpk2bxtCh\nQwFobQ0RDLbP3oNpQYLjt9KyoZnBgzPJzc0iJzOH0rGllI4rtSibhmEkBT1F9fwr8Lyqbo6RPDGh\noaGBsrIyDh5sf2AJBAIUFxczYcIE0tLSqKqq57nntpGR3cpNnzuvrV5mMJNrz7uClsDvKRo5ivlF\n85lVOMvi6RuGkVR0t9rn2lgKEiuamppYu3btMZu1Tj/9dEpKSto2a217t56vPvozdmWVkR3K45N1\nUykoaF/5M3dcKaNPG8U5I84xn75hGEnJCb3wPRXIzs6msLCQmpoagsFgW2atQCDAvqZ9vLj1RV7Z\n8Qr1I2toeq+Zw2kNvLpuI1ddMr2tjcFZg/nwyKQLQmoYhtHGKW/8OyZGAZg8eTKtra3k5RXy6qt1\nlNWupTZzHev3rm97IigsPI2BA5soOjOf0ZNDnTVtGIaRtJyyxj8cDlNbW8umTZvaNmdFyMjIoOHQ\naXzzsZ+xK2sdWVsPU1JScMz5MupMvnBBKTMLZzIgfUCsxTcMw+hXTknjf/jwYTZs2MDu3W5RUkVF\nBdOnTz+mTnngebZkv0Q4DIcPQFPTUbKzM5gybApzx81lSsEUi7ljGMYpyyll/MPhMNu3b6eyspKW\nlhbCYaivP0xVVTnFxcKgQQPb6i6YfAm/e3U1raE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+ "text/plain": [
+ "| \n", + " | value | \n", + "
|---|---|
| 1950 | \n", + "2.557629 | \n", + "
\n",
+ "\n",
+ "\n",
+ " \n",
+ "
\n",
+ "
"
+ ],
+ "text/plain": [
+ " Population Reference Bureau (1973–2015)[6] \\\n",
+ "Year \n",
+ "-10000 NaN \n",
+ "-9000 NaN \n",
+ "-8000 5.0 \n",
+ "-7000 NaN \n",
+ "-6000 NaN \n",
+ "\n",
+ " United Nations Department of Economic and Social Affairs (2015)[7] \\\n",
+ "Year \n",
+ "-10000 NaN \n",
+ "-9000 NaN \n",
+ "-8000 NaN \n",
+ "-7000 NaN \n",
+ "-6000 NaN \n",
+ "\n",
+ " Maddison (2008)[8] HYDE (2010)[citation needed] Tanton (1994)[9] \\\n",
+ "Year \n",
+ "-10000 NaN 2M[15] NaN \n",
+ "-9000 NaN 4. NaN \n",
+ "-8000 NaN 5. NaN \n",
+ "-7000 NaN 8. NaN \n",
+ "-6000 NaN 11. NaN \n",
+ "\n",
+ " Biraben (1980)[10] McEvedy & Jones (1978)[11] Thomlinson (1975)[12] \\\n",
+ "Year \n",
+ "-10000 NaN 4.0 1–10M \n",
+ "-9000 NaN NaN NaN \n",
+ "-8000 NaN NaN NaN \n",
+ "-7000 NaN NaN NaN \n",
+ "-6000 NaN NaN NaN \n",
+ "\n",
+ " Durand (1974)[13] Clark (1967)[14] \n",
+ "Year \n",
+ "-10000 NaN NaN \n",
+ "-9000 NaN NaN \n",
+ "-8000 5–10M NaN \n",
+ "-7000 NaN NaN \n",
+ "-6000 NaN NaN "
+ ]
+ },
+ "execution_count": 487,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "table1 = tables[1]\n",
+ "table1.head()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Not all agencies and researchers provided estimates for the same dates. Again `NaN` is the special value that indicates missing data."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 488,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "| \n", + " | Population Reference Bureau (1973–2015)[6] | \n", + "United Nations Department of Economic and Social Affairs (2015)[7] | \n", + "Maddison (2008)[8] | \n", + "HYDE (2010)[citation needed] | \n", + "Tanton (1994)[9] | \n", + "Biraben (1980)[10] | \n", + "McEvedy & Jones (1978)[11] | \n", + "Thomlinson (1975)[12] | \n", + "Durand (1974)[13] | \n", + "Clark (1967)[14] | \n", + "
|---|---|---|---|---|---|---|---|---|---|---|
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| -9000 | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "4. | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "
| -8000 | \n", + "5.0 | \n", + "NaN | \n", + "NaN | \n", + "5. | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "5–10M | \n", + "NaN | \n", + "
| -7000 | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "8. | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "
| -6000 | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "11. | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "
\n",
+ "\n",
+ "\n",
+ " \n",
+ "
\n",
+ "
"
+ ],
+ "text/plain": [
+ " Population Reference Bureau (1973–2015)[6] \\\n",
+ "Year \n",
+ "1913 NaN \n",
+ "1920 NaN \n",
+ "1925 NaN \n",
+ "1930 NaN \n",
+ "1940 NaN \n",
+ "\n",
+ " United Nations Department of Economic and Social Affairs (2015)[7] \\\n",
+ "Year \n",
+ "1913 NaN \n",
+ "1920 1860.0 \n",
+ "1925 NaN \n",
+ "1930 2070.0 \n",
+ "1940 2300.0 \n",
+ "\n",
+ " Maddison (2008)[8] HYDE (2010)[citation needed] Tanton (1994)[9] \\\n",
+ "Year \n",
+ "1913 1793. NaN NaN \n",
+ "1920 1863. 1912. NaN \n",
+ "1925 NaN NaN NaN \n",
+ "1930 NaN 2092. NaN \n",
+ "1940 2299. 2307. NaN \n",
+ "\n",
+ " Biraben (1980)[10] McEvedy & Jones (1978)[11] Thomlinson (1975)[12] \\\n",
+ "Year \n",
+ "1913 NaN NaN NaN \n",
+ "1920 NaN NaN NaN \n",
+ "1925 NaN 2000.0 NaN \n",
+ "1930 NaN NaN NaN \n",
+ "1940 NaN NaN NaN \n",
+ "\n",
+ " Durand (1974)[13] Clark (1967)[14] \n",
+ "Year \n",
+ "1913 NaN NaN \n",
+ "1920 NaN 1968. \n",
+ "1925 NaN NaN \n",
+ "1930 NaN 2145. \n",
+ "1940 NaN 2340. "
+ ]
+ },
+ "execution_count": 488,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "table1.tail()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Some of the estimates are in a form we can't read as numbers. We could clean them up by hand, but for simplicity I'll replace any value that has an `M` in it with `NaN`."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 489,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "table1.replace('M', np.nan, regex=True, inplace=True)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Again, we'll replace the long column names with more convenient abbreviations."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 490,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "table1.columns = ['prb', 'un', 'maddison', 'hyde', 'tanton', \n",
+ " 'biraben', 'mj', 'thomlinson', 'durand', 'clark']"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "This function plots selected estimates."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 491,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "def plot_prehistory(table):\n",
+ " \"\"\"Plots population estimates.\n",
+ " \n",
+ " table: DataFrame\n",
+ " \"\"\"\n",
+ " plot(table.prb, 'ro', label='PRB')\n",
+ " plot(table.un, 'co', label='UN')\n",
+ " plot(table.hyde, 'yo', label='HYDE')\n",
+ " plot(table.tanton, 'go', label='Tanton')\n",
+ " plot(table.biraben, 'bo', label='Biraben')\n",
+ " plot(table.mj, 'mo', label='McEvedy & Jones')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Here are the results. Notice that we are working in millions now, not billions."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 492,
+ "metadata": {
+ "scrolled": false
+ },
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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Qhg4dCkBoaCihoaEaxxUKRa4DUkhICJMmTaJ169aMGTMGyAokaWlpavlUKhXG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\ngg==\n",
+ "text/plain": [
+ "| \n", + " | Population Reference Bureau (1973–2015)[6] | \n", + "United Nations Department of Economic and Social Affairs (2015)[7] | \n", + "Maddison (2008)[8] | \n", + "HYDE (2010)[citation needed] | \n", + "Tanton (1994)[9] | \n", + "Biraben (1980)[10] | \n", + "McEvedy & Jones (1978)[11] | \n", + "Thomlinson (1975)[12] | \n", + "Durand (1974)[13] | \n", + "Clark (1967)[14] | \n", + "
|---|---|---|---|---|---|---|---|---|---|---|
| Year | \n", + "\n", + " | \n", + " | \n", + " | \n", + " | \n", + " | \n", + " | \n", + " | \n", + " | \n", + " | \n", + " |
| 1913 | \n", + "NaN | \n", + "NaN | \n", + "1793. | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "
| 1920 | \n", + "NaN | \n", + "1860.0 | \n", + "1863. | \n", + "1912. | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "1968. | \n", + "
| 1925 | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "2000.0 | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "
| 1930 | \n", + "NaN | \n", + "2070.0 | \n", + "NaN | \n", + "2092. | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "2145. | \n", + "
| 1940 | \n", + "NaN | \n", + "2300.0 | \n", + "2299. | \n", + "2307. | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "NaN | \n", + "2340. | \n", + "
\n",
+ "\n",
+ "\n",
+ " \n",
+ "
\n",
+ "
"
+ ],
+ "text/plain": [
+ "t0 1950.000000\n",
+ "t_end 2015.000000\n",
+ "p0 2.557629\n",
+ "alpha 0.025000\n",
+ "beta -0.001800\n",
+ "dtype: float64"
+ ]
+ },
+ "execution_count": 160,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "system = System(t0=t0, \n",
+ " t_end=t_end,\n",
+ " p0=p0,\n",
+ " alpha=0.025,\n",
+ " beta=-0.0018)\n",
+ "\n",
+ "system"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Run the model and plot results."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 161,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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39WN8/GomHuFWZs7sfVYmfmjgAu6uIgu4CyGcVVxSzIc/fIjer+kc0I0+3Xoz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\nhVaeXVPMlUvPbTsmKz2La86+JhbVNsaYEyIpk38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+ "text/plain": [
+ "| \n", + " | value | \n", + "
|---|---|
| t0 | \n", + "1950.000000 | \n", + "
| t_end | \n", + "2015.000000 | \n", + "
| p0 | \n", + "2.557629 | \n", + "
| alpha | \n", + "0.025000 | \n", + "
| beta | \n", + "-0.001800 | \n", + "
\n",
+ "\n",
+ "\n",
+ " \n",
+ "
\n",
+ "
"
+ ],
+ "text/plain": [
+ " United States Census Bureau (2015)[18] \\\n",
+ "Year \n",
+ "2016 7.334772e+09 \n",
+ "2017 7.412779e+09 \n",
+ "2018 7.490428e+09 \n",
+ "2019 7.567403e+09 \n",
+ "2020 7.643402e+09 \n",
+ "\n",
+ " Population Reference Bureau (1973-2015)[6] \\\n",
+ "Year \n",
+ "2016 NaN \n",
+ "2017 NaN \n",
+ "2018 NaN \n",
+ "2019 NaN \n",
+ "2020 NaN \n",
+ "\n",
+ " United Nations Department of Economic and Social Affairs (2015)[7] \n",
+ "Year \n",
+ "2016 7.432663e+09 \n",
+ "2017 NaN \n",
+ "2018 NaN \n",
+ "2019 NaN \n",
+ "2020 7.758157e+09 "
+ ]
+ },
+ "execution_count": 166,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "table3 = tables[3]\n",
+ "table3.head()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "`NaN` is a special value that represents missing data, in this case because some agencies did not publish projections for some years."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 167,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "table3.columns = ['census', 'prb', 'un']"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "This function plots projections from the UN DESA and U.S. Census. It uses `dropna` to remove the `NaN` values from each series before plotting it."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 168,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "def plot_projections(table):\n",
+ " \"\"\"Plot world population projections.\n",
+ " \n",
+ " table: DataFrame with columns 'un' and 'census'\n",
+ " \"\"\"\n",
+ " census = table.census / 1e9\n",
+ " un = table.un / 1e9\n",
+ " \n",
+ " plot(census.dropna(), ':', color='darkblue', label='US Census')\n",
+ " plot(un.dropna(), '--', color='green', label='UN DESA')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Run the model until 2100, which is as far as the other projections go."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 169,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "system.p0 = census[t0]\n",
+ "system.t_end = 2100\n",
+ "run_simulation(system, update_func2)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Plot the results."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 170,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Saving figure to file chap04-fig02.pdf\n"
+ ]
+ },
+ {
+ "data": {
+ "image/png": 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hWI3Jw8vJiwj/iCpPDDqdjnGh44jwj8DXxbfZJA+w/AkkHhgCVFdRNwRItVpE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\nSfRNjT+LSE+gN1CuqjbqXhKVlZXxrwUvU1i5lrp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+ "text/plain": [
+ "| \n", + " | United States Census Bureau (2015)[18] | \n", + "Population Reference Bureau (1973-2015)[6] | \n", + "United Nations Department of Economic and Social Affairs (2015)[7] | \n", + "
|---|---|---|---|
| Year | \n", + "\n", + " | \n", + " | \n", + " |
| 2016 | \n", + "7.334772e+09 | \n", + "NaN | \n", + "7.432663e+09 | \n", + "
| 2017 | \n", + "7.412779e+09 | \n", + "NaN | \n", + "NaN | \n", + "
| 2018 | \n", + "7.490428e+09 | \n", + "NaN | \n", + "NaN | \n", + "
| 2019 | \n", + "7.567403e+09 | \n", + "NaN | \n", + "NaN | \n", + "
| 2020 | \n", + "7.643402e+09 | \n", + "NaN | \n", + "7.758157e+09 | \n", + "
\n",
+ "\n",
+ "\n",
+ " \n",
+ "
\n",
+ "
"
+ ],
+ "text/plain": [
+ "S 89\n",
+ "I 1\n",
+ "R 0\n",
+ "dtype: int64"
+ ]
+ },
+ "execution_count": 65,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "init = State(S=89, I=1, R=0)\n",
+ "init"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "To convert from number of people to fractions, we divide through by the total."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 66,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "| \n", + " | value | \n", + "
|---|---|
| S | \n", + "89 | \n", + "
| I | \n", + "1 | \n", + "
| R | \n", + "0 | \n", + "
\n",
+ "\n",
+ "\n",
+ " \n",
+ "
\n",
+ "
"
+ ],
+ "text/plain": [
+ "S 0.988889\n",
+ "I 0.011111\n",
+ "R 0.000000\n",
+ "dtype: float64"
+ ]
+ },
+ "execution_count": 66,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "init /= sum(init)\n",
+ "init"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "`make_system` creates a `System` object with the given parameters."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 67,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "def make_system(beta, gamma):\n",
+ " \"\"\"Make a system object for the SIR model.\n",
+ " \n",
+ " beta: contact rate in days\n",
+ " gamma: recovery rate in days\n",
+ " \n",
+ " returns: System object\n",
+ " \"\"\"\n",
+ " init = State(S=89, I=1, R=0)\n",
+ " init /= sum(init)\n",
+ "\n",
+ " t0 = 0\n",
+ " t_end = 7 * 14\n",
+ "\n",
+ " return System(init=init, t0=t0, t_end=t_end,\n",
+ " beta=beta, gamma=gamma)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Here's an example with hypothetical values for `beta` and `gamma`."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 68,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "| \n", + " | value | \n", + "
|---|---|
| S | \n", + "0.988889 | \n", + "
| I | \n", + "0.011111 | \n", + "
| R | \n", + "0.000000 | \n", + "
\n",
+ "\n",
+ "\n",
+ " \n",
+ "
\n",
+ "
"
+ ],
+ "text/plain": [
+ "init S 0.988889\n",
+ "I 0.011111\n",
+ "R 0.000000\n",
+ "dtyp...\n",
+ "t0 0\n",
+ "t_end 98\n",
+ "beta 0.333333\n",
+ "gamma 0.25\n",
+ "dtype: object"
+ ]
+ },
+ "execution_count": 68,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "tc = 3 # time between contacts in days \n",
+ "tr = 4 # recovery time in days\n",
+ "\n",
+ "beta = 1 / tc # contact rate in per day\n",
+ "gamma = 1 / tr # recovery rate in per day\n",
+ "\n",
+ "system = make_system(beta, gamma)\n",
+ "system"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "The update function takes the state during the current time step and returns the state during the next time step."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 69,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "def update1(state, system):\n",
+ " \"\"\"Update the SIR model.\n",
+ " \n",
+ " state: State with variables S, I, R\n",
+ " system: System with beta and gamma\n",
+ " \n",
+ " returns: State object\n",
+ " \"\"\"\n",
+ " s, i, r = state\n",
+ "\n",
+ " infected = system.beta * i * s \n",
+ " recovered = system.gamma * i\n",
+ " \n",
+ " s -= infected\n",
+ " i += infected - recovered\n",
+ " r += recovered\n",
+ " \n",
+ " return State(S=s, I=i, R=r)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "To run a single time step, we call it like this:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 70,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "| \n", + " | value | \n", + "
|---|---|
| init | \n", + "S 0.988889\n", + "I 0.011111\n", + "R 0.000000\n", + "dtyp... | \n", + "
| t0 | \n", + "0 | \n", + "
| t_end | \n", + "98 | \n", + "
| beta | \n", + "0.333333 | \n", + "
| gamma | \n", + "0.25 | \n", + "
\n",
+ "\n",
+ "\n",
+ " \n",
+ "
\n",
+ "
"
+ ],
+ "text/plain": [
+ "S 0.985226\n",
+ "I 0.011996\n",
+ "R 0.002778\n",
+ "dtype: float64"
+ ]
+ },
+ "execution_count": 70,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "state = update1(init, system)\n",
+ "state"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Now we can run a simulation by calling the update function for each time step."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 71,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "def run_simulation(system, update_func):\n",
+ " \"\"\"Runs a simulation of the system.\n",
+ " \n",
+ " system: System object\n",
+ " update_func: function that updates state\n",
+ " \n",
+ " returns: State object for final state\n",
+ " \"\"\"\n",
+ " state = system.init\n",
+ " for t in linrange(system.t0, system.t_end):\n",
+ " state = update_func(state, system)\n",
+ " return state"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "The result is the state of the system at `t_end`"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 72,
+ "metadata": {
+ "scrolled": true
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "| \n", + " | value | \n", + "
|---|---|
| S | \n", + "0.985226 | \n", + "
| I | \n", + "0.011996 | \n", + "
| R | \n", + "0.002778 | \n", + "
\n",
+ "\n",
+ "\n",
+ " \n",
+ "
\n",
+ "
"
+ ],
+ "text/plain": [
+ "S 0.520453\n",
+ "I 0.000615\n",
+ "R 0.478933\n",
+ "dtype: float64"
+ ]
+ },
+ "execution_count": 72,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "run_simulation(system, update1)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "**Exercise** Suppose the time between contacts is 4 days and the recovery time is 5 days. After 14 weeks, how many students, total, have been infected?\n",
+ "\n",
+ "Hint: what is the change in `S` between the beginning and the end of the simulation?"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 73,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "0.37943042989926101"
+ ]
+ },
+ "execution_count": 73,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "tc = 4 # time between contacts in days \n",
+ "tr = 5 # recovery time in days\n",
+ "\n",
+ "beta = 1 / tc # contact rate in per day\n",
+ "gamma = 1 / tr # recovery rate in per day\n",
+ "\n",
+ "system = make_system(beta, gamma)\n",
+ "\n",
+ "s0=system.init.S\n",
+ "\n",
+ "final=run_simulation(system, update1)\n",
+ "\n",
+ "sf=final.S\n",
+ "\n",
+ "Change_S=s0-sf\n",
+ "\n",
+ "Change_S"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Using Series objects"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "If we want to store the state of the system at each time step, we can use one `TimeSeries` object for each state variable."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 74,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "def run_simulation(system, update_func):\n",
+ " \"\"\"Runs a simulation of the system.\n",
+ " \n",
+ " Add three Series objects to the System: S, I, R\n",
+ " \n",
+ " system: System object\n",
+ " update_func: function that updates state\n",
+ " \"\"\"\n",
+ " S = TimeSeries()\n",
+ " I = TimeSeries()\n",
+ " R = TimeSeries()\n",
+ "\n",
+ " state = system.init\n",
+ " t0 = system.t0\n",
+ " S[t0], I[t0], R[t0] = state\n",
+ " \n",
+ " for t in linrange(system.t0, system.t_end):\n",
+ " state = update_func(state, system)\n",
+ " S[t+1], I[t+1], R[t+1] = state\n",
+ " \n",
+ " system.S = S\n",
+ " system.I = I\n",
+ " system.R = R"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Here's how we call it."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 75,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "tc = 3 # time between contacts in days \n",
+ "tr = 4 # recovery time in days\n",
+ "\n",
+ "beta = 1 / tc # contact rate in per day\n",
+ "gamma = 1 / tr # recovery rate in per day\n",
+ "\n",
+ "system = make_system(beta, gamma)\n",
+ "run_simulation(system, update1)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "And then we can plot the results."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 76,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "def plot_results(S, I, R):\n",
+ " \"\"\"Plot the results of a SIR model.\n",
+ " \n",
+ " S: TimeSeries\n",
+ " I: TimeSeries\n",
+ " R: TimeSeries\n",
+ " \"\"\"\n",
+ " plot(S, '--', color='blue', label='Susceptible')\n",
+ " plot(I, '-', color='red', label='Infected')\n",
+ " plot(R, ':', color='green', label='Recovered')\n",
+ " decorate(xlabel='Time (days)',\n",
+ " ylabel='Fraction of population')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Here's what they look like."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 77,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Saving figure to file chap05-fig01.pdf\n"
+ ]
+ },
+ {
+ "data": {
+ "image/png": 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FhYU8/fTTDBo0iB49enDVVVfx008/sXfvXsY5Ox+HDRvGs88+a+l+R44c4d5776VXr14M\nHDiQZcuW1cifjb9ZqqlorUu2T1NKRQJRwCGtdeFJfOZM4HrgOuAQsBBTExrofaFSKgn4GHgMuAro\nCbwMHAP+dRKfLSoweDC0bQuLF8PBg+bYDz/Azp1w000ySqzeWbkSPvrIP8sshIaaLSeHDz/pW/zz\nn/9k+vTpzJgxg08++YQnnniCs88+mwsuuICYmBhuv/123n77bdq1a8eBAwcYP348l156KTNmzCAr\nK4t58+bx17/+lSVLlgCmD2b16tXMnDmTDh068NJLLzFx4kQ++eQTFi5cWHK/xMRES/e76667yMzM\n5PnnnycwMJBZs2ZR7L6Naz1leUa9UmqwUmo9cBTYB+Qppb5VSg2rxD1CgLsww5NXaq03YpLFAKVU\n/zLeMgLI1VrP1lrv0lq/AywHzrf6maJy2rY1O0qmpJQeO3wYnnwSPvjAc2tjUcetXOm/dXvy883n\nn4IhQ4Zw5ZVX0qpVK26++Waio6P56aefCAsLIyYmBjA7RkZFRfHaa6/RsmVLpkyZQvv27enRowdP\nP/0069ev58cffyQnJ4d3332Xe+65h3PPPZc2bdowY8YMxo4dS1ZWlsf9IiMjT3i/nTt38t133/HQ\nQw+RnJxMt27dePzx02NGhtUZ9edgRoClAg8CB4AE4Argf0qpYVrrryzcqgemlrPGdUBrnaaUSgNS\nMIMA3P0JxCmlrgbeBDoB52BqN6KahIaafcc7d4ZXXjE7TDocZu+W1FRTa5FO/Hpg+HD/1lROoZYC\n0LZtW4/XUVFRFBaW3XiydetWtm7dSnJyss+5nTt3EhQURGFhId26dSs5HhQUxJQpUwDIzMys1P0i\nIyMB6Ny5c8nxpKSkkuP1mdWO+oeBVcCFWuuSHiul1BxMzWEmYKXG4uox896geT/Qqozr3wUWA68C\nrwCBwFvAHItxi1OQnAzt2pm+Fdd6Ybt2wcsvw733+jc2UQWGDz/lL3Z/cu097668DvXg4GAGDBjA\n/fff73MuLi6u3D3jy3Oi+61bt67MeIJPgz0orDZ/9Qb+5Z5QAJyv/wX0sXifCMBeRl9MPhBWxvUN\ngbbAPOdnXA8MBx6y+HniFDVsCHfdBZdcAgEBEBJiajFC1CVJSUns3LmThIQE2rRpQ5s2bQgICODR\nRx8lPT2d1q1bExQUxJYtW0reY7fbOf/881m+fDk2ryGQJ7pfx44dAfjxxx9L3rN3716OHDlSMz+w\nH1lNKoeBBuWciwKstrTnAgFKKe8aUiim893b40CR1nqq1vpHrfUSYDIwTSkVb/EzxSkKCIARI2DK\nFLNWWNNyx+oJUTtde+21ZGVlMXXqVLTWbN68mXvuuYe0tDTatm1LREQE11xzDU8//TRr164lLS2N\n2bNnc/ToUfr27VvSbLV161ays7NPeL+2bdsybNgwZs2axffff8/WrVuZMmUKAQH1f2F4qz/h58BM\npVSC+0Hn65mYpjErfnc+Nvc6noBvkxjA2cAPXsfWA8FAa4ufKapI27bQq5fv8S+/NH2uMpRf1FaN\nGzfmxRdfJCMjgyuuuIKJEyfSvHlzXnzxxZJmtL///e+MHDmS6dOnc/HFF7Nz504WL15Mo0aNSEpK\n4vzzz2fSpEk888wzlu73xBNP0LdvX+644w5uuOEGhgwZQuPGjf35x1AjbFYm9SilWmC+3KOBr4E/\ngGaYYcBZwACt9S4L9wnFdL7frrVe6jzWFvgN6Ke1/s7r+k+BfK31RW7HrsRMtIzVWmdRBtc9V69e\nXSUTn0T59u6FuXPN8i6dO5uaTHS0v6MSQpyMvXv3MmzYMIB2Wuu0k7mHpZqK1nofkIwZdRUD9MP0\nd/wLSLaSUJz3yXfe4wml1AilVE/gDWCt1vo7pVSIUqqZc+gxmCX3Ryml7ldKtVdKjQKeAhaWl1BE\nzVq50iQUMEvpP/ww/Pqrf2MSQviP5T3qtdZ/AH+vgs+8H9N8tdT5+Alwh/Ncf+ALYAiwRmu9Qil1\nqfM9UzE1pOeAR6sgDlEFxo83qx9/+ql5nZUF//wnnHcejBkDQZb/hQkh6oNym7+UUtOBF7XW6c7n\nFXForedWeXQnSZq/at7WrfDCCyapuLRpY7Y1btLEf3EJIayriuavin6PnIPpgE/nxPNCHECtSSqi\n5p15Jjz4ILz0ErhGZe7eDXPmwFVXQb9+sjClEKeDcpOK1jqgrOdClCcqCv76V/j8c3j3XbOkS36+\nmSy5bx+MHevvCIUQ1c1SslBKPeg9nNjtXBul1DNVG5aoq2w2GDYMpk0rnc9is5nZ+UKI+s9qDeQh\noEU55/oBf6macER90aoVzJgBAwfChRdCUpK/IxJC1IRym7+UUl9jEgaADfhOKVXe5RuqOC5RD4SG\nmtFhZY0FSU2F+Hg4DeaCCXFaqaijfiJwGSahzMYM5d3rdU0xcAR4v1qiE/WCdwf9kSPw3HNmfsuV\nV0L//tKJL0R9UVFHfSrwCJjdGoHnnZMghTglS5aY5fRdzzdvNotUNihvdTkhMLs9eq8mHBYWRkJC\nAldeeSU33HCDfwLzk+HDh3PRRRfxt7/9zd+heLC68+MsAOcijiGY2guYPplIIEVr/Xy1RCjqnTFj\nICMDDhwwr3/80ewued110LWrf2MTtdvNN9/M9ddfX/L6yJEjvPHGG8ydO5cmTZpwwQUX+DE6AdZH\nf3VVSv0MHMQ0gf3uLLuBX4FF1RahqHfatDG7Sw4eXHosKwsWLIClS/23GaGo/SIiImjcuHFJ6dCh\nAw888ACtW7dmxYoV/g5PYH3013wgHrPs/BrgU+CvwArMxMfB1RCbqMdCQuDqq+Fvf/NcgPKrr2D2\nbNi+3X+xibonODiYwMBAANLT07nzzjvp2bMn/fv3Z9KkSRxwVYsxG2e99NJLnHfeeXTv3p0xY8aw\ndu3akvPbtm3j5ptvpk+fPpx11lncd999JTs/Tp06lfHjx3t89s8//4xSirS0NABWrVrFRRddRNeu\nXRkxYgSLFy/GbrcDZsa6UopFixbRr18/Ro4cSUFBwQljzs/PZ/bs2fTt25ezzjqL5557rlr+HKuC\n1aTSD3hAa/00ZlvfSK31v7XWozGd9HdWV4CifuvSBR56CHr2LD2WkQFPPmm2LxaiIrm5uTz//PPs\n3LmTiy66iOPHjzN+/HhCQ0N54403WLx4MYWFhVx//fUUFBQA8N///pdnnnmG22+/nY8++ogRI0Zw\nxx13sH37dvbu3cvVV19NTEwMr776KgsXLiQ1NZUbb7yR4uJiLr74Yn744QePL/yPPvqI5ORk2rZt\ny9q1a5k8eTLXXXcdy5cv5+9//ztLlixh4ULPHdCXL1/O0qVLeeKJJygqKjphzLNmzWL16tU89dRT\nvPLKK3z//ffs2bOn5v6gK8Hqcn+hgOt3x21Ad7dzLyLNX+IUNGgAf/kLrF8Pb7wBublmGHKL8mZG\niSrzkf6Ij7d9DMCoM0YxWo32OP/2L2+zapfZLunyTpczPNFz++GlPy/lq91fAXBtt2tJaZPicf75\njc+zYZ+ZcXBTz5s4q8VZpxTvwoUL+e9//wuYGkd+fj5KKZ566imGDRvG22+/TW5uLo899lhJzeWp\np56ib9++fPbZZ1x44YUsWbKECRMmcPHFFwNw2223UVRUxPHjx1m2bBnR0dHMnTu3ZOvfp59+mgsu\nuICvvvqKQYMG0bx5c1asWMGECRMoLi5mxYoVJZ3lixYt4uqrr+byyy8HoHXr1hw7dowHHniA22+/\nveTnGDduHImJiebP+AQxDx48mA8//JA5c+YwYMAAAObPn89g9/bjWsRqUtkDtAO+wiSVaKVUG631\nbiAPiKum+MRpwmaDs88GpeCVV8ySL927n/h94vQybtw4rrnmGoqLi1m9ejULFy7k0ksv5cILLwTg\n119/JTMzk969e3u8Lzc3l507d3L48GH+/PNPunXr5nHelRQWLFhA165dPfaST0xMJDY2lm3btjF4\n8GAuuugiPv74YyZMmMC3335LVlZWyQCBrVu3snnzZt54442S99vtdvLy8ti3b1/JtsStWrUqOX+i\nmFu3bk1hYSFdunQpORcbG0vr1rVzn0KrSWUZ8JhSKltrvUwplQo8rJSaC0wCdlZbhOK0Ehtr+llc\ne7S427bNPJ5xRs3GJGqPmJgY2rRpA0D79u0JCAjgkUceIS4ujlGjRhEcHExSUhILFizweW9UVJRH\nsihLWFhYmcftdnvJey+++GL+/e9/k5aWxscff8zQoUOJdnYMBgcHM3HiREaPHu1zj6ZNm3Lw4EEA\nQkNDS46fKGbXMGrvFeVP9LP4i9WkMgvoANyMSTCTnI/jMBMgr6qW6MRpyWYD7/8veXlmaf3DhyEl\nBS67DMLD/RNffTJajfZp8nI3tvNYxnYufyXQa7tdy7Xdri33/MSeE5nYc+IpxViRCRMmsHr1ambN\nmkXfvn3p0KEDb7/9Ng0bNiQmJgaAnJwcJk+ezA033MDZZ59N48aN2bx5M4MGDSq5z/jx4xk0aBCJ\niYl88MEHFBYWlnxp79ixg6NHj5Y0V7Vt25bk5GSWL1/OqlWrmD9/fsl9kpKSSEtLK0l8ACtXrmT5\n8uXMmzevzJ/hRDF37dqVkJAQfvzxRzp06FBy3jUwoLaxuvPjca31pcAlztefAl0xyeRMrfV71Rei\nEPDhhyahgBkhNnOmmd9iYTdsUY8FBATw8MMPk5eXx5w5cxg9ejSxsbHcfffdbN68mW3btnHvvfey\nadOmki/kiRMn8tJLL7F8+XL27NnDwoUL2bRpE4MGDeLaa68lOzubadOmsX37dn744QcmT55Mx44d\n6devX8nnXnLJJSxevJiQkBBSUkr7kW677TaWL1/Oc889R1paGmvWrOHBBx8kLCysZO96byeKOTIy\nkquuuop//OMffP755+zYsYPp06eTl5dXvX+4J6lS+/I5twN2Pd+JNHuJGnLeeWZU2KZN5vWRI7Bo\nEXTrZvZriY/3b3zCfxITE7nlllt49tlnGTNmDC+++CKPPfYY119/PTabjR49evDyyy8T7/xHct11\n15GXl8f8+fPJzMykQ4cOLFq0qCTpvPDCC8yfP5/LLruM8PBwhg4dyt///neP5qaRI0fyyCOPMGrU\nKILctjc955xzmDdvHs899xzPPPMMcXFxXHzxxUyaNKnc+MPCwk4Y85QpUwgLC2PGjBnk5+czduxY\nn36h2qKinR+3Y+agWOHQWpe72mRNk50f6yeHw9ROXn/dc4fJkBAYPdosue8cPCOEOAnVvfPjOqwn\nFSGqnc1m5rN07AjLlsGXX5rjBQVmU7BvvoFrrpGOfCH8qaIFJW+owTiEsCwiAsaNM0OQly6F/fvN\n8fR0+Pe/Ye5cKGcQjxCimlnqU1FK9T/RNVrrb049HCGsS0w0a4h9/jl89JFZM+ziiyWhCOFPVjvq\nv+bETWHSmi1qXGAgDB8OffrAmjVmuLG3nTuhfXvZs0WImmA1qQwp41gDIAUYj9nMSwi/adjQ1FK8\n7doF8+aZpHL55aZ2I4SoPlb3U1lbzqnlSqkc4H5gVJVFJUQVcDjgnXfMc1dySU42yadZM//GJkR9\nZXWV4op8hSx9L2qh4mJTM3GbRsCPP5qJk0uWlE6mFEJUnUpNfizHaCDrhFcJUcOCgsxyLoMGmSHI\nP/xgjjscsG6dWRU5JQVGjgTn6hhCiFNkdfTXZ2UcDgRaAYnA41UZlBBVqVEjuPlmMyt/2TLYutUc\nLyqCL76Ar7+GIUPg0kulM1+IU2W1phKC7+gvB2Yr4XnAC1UZlBDVoU0buPtuSE2F99+H334zxwsL\n4dAhSShCVAWrHfWDqzkOIWpMx44wZQr88otZqHL3bnBuh+Hh+HEz0VIIYV2l+lSUUiMxw4hjgQPA\n51rrL6sjMCGqk81mtjLu3NnUWLyXiMvLgxkzICnJNJslJUlNRggrrPapxAP/A3oD+cCfQBPgAWd/\nyyVa69q5DrMQFbDZzBwWb199ZWoqP/9sSqtWcO650Lu352gyIYQnq/89nsVsJzxaa73cdVApdRGw\nGHgMuNvKjZRSgcAc4AYgCvgEuENrfaCc61sC/wDOB3KBd4DJWuvjFmMXotKcG/SV+P13ePFFM+8l\nJcWUONlEjyzSAAAgAElEQVREWwgfVuepjMR8kS93P6i1/hCYBlxdic+cCVwPXAecA7QE3i3rQqVU\nKLASiAMGAFdiJlmWvYWaEFVk3DgznyUlxXMXyuxsWLECpk+HhQth82aw2/0WphC1jtWkUgQcKedc\nOmZ02AkppUKAu4DpWuuVWuuNmN0jB5SzaOU1QHPgMq31z1rrL4CHgLMsxi3ESWveHK69Fh57zMzC\nb9iw9JzDYTYMW7DAJBYhhGE1qSwEHlVKJbgfVEpFA1MxzWNW9MA0ea1xHXBuBJOGGQDg7Xxgpdb6\nsNv1L2qtJamIGtOggZkgOXcu3HqrGT3mEh1tOvzdFRWZ/hghTkdW+1QSnGWnUuprYD8Qj2mSigLy\n3SZIOrTW55dzH9cYm31ex/djJlJ6OwP4XCn1MHAtZm7Me8D9MjBA1LSAALN2WHIyHDhgJk02aOC7\n2+SmTfDCC9C1K5x1lnl0b0IToj6zmlSSgJ/c3tPa+dx1LBBrS99HAHatdaHX8XygrF0wooGbMCPP\nxgItgAWYkWfXWYxdiCrXtKlZAqYs335rais//mhKaKhJLD17mlpNaGjNxipETbI6+bGspe9PRi4Q\noJQK0loXuR0PBY6VcX0hkAmM11oXAz8opYKBt5VSk7TWh6ooLiGqRHGx6cx3l59v1h374QdTYznz\nTOjRA7p1g6go/8QpRHWp7OTHTsAgIAYzV+VrrbWuxC1+dz42d3sOpmnNu0kM57E8Z0Jx+dX52BaQ\npCJqlcBAmDbNNI99/z1s2GCeuxQWls59sdngnnvgjDP8F68QVc3q5McA4D/AjYD7vGKHUuoVYILW\n+kQ7QwJsArIxiWmp895tMQmirJn5XwE3K6WC3ZrMugDFmM59IWqlpk1h9GgYNQrS0+H//g82boT9\n+0uvCQw065G5c9VqzjxT5sGIuslqTWUqpg9jKvAqZomW5pghv7MpXViyQlrrfKXUQuAJpVQGcBAz\nsmyt1vo755DjOCBTa10ALAL+BixRSs3CdPTPB5ZI05eoC2w2SEgwZfRo+PNP05H/008QFubbv6K1\n2esFzOrKSpmaTIcOJsnIUjGitrOaVG4CHtFaz3c7theYp5QKc563OiHxfiAYU1MJxjmj3nmuP/AF\nZvviNVrrA0qpc4CngY1AjvN90yx+lhC1SuPGZrmXc88te9Kka1l+gIwMU9atM69jY80aZImJZmmZ\nli19R54J4W9Wk0pzYF05576hEl/yzg76e53F+9waPJvX0Fr/ipmvIkS9ElDGLLHWraFTJ9ixAwoK\nPM8dPmz6aDZsMK9TUszkTCFqE6tJZRfQD1hdxrl+mFn1QohT1K+fKUVFkJZmmsO2b4ddu0x/i7t2\n7Xzfv2gRZGWZBTBbtoQWLUyRYcyiplhNKs8Dc5VSx4A3MH0qTTFrfk0HHq2e8IQ4PQUFmaaupCTz\n2m43i1ru3GkSzK5dvqsrOxwmAeXkmOvcxcebZWcSEsxj06amViSTMkVVq8wqxcnAk8ATbsdtmD6O\nR6o4LiGEm4AAM1KsTRsYOrTsa44cMQmlLIcOmbJlS+mxWbOgWbPS10VFZpRa48amNGggAwNE5Vmd\n/FgMXK+UmodZoysOOAx8qbX+pRrjE0JYFBsL8+aZGs3evaXlwAHfQQEBASZxuMvIMMvLuISEmBpO\nfLwZeeYqsbGmeL9fCKjk5EfMhMVdmIRy0PlcCFFLxMSY4r7IZVGR2R9m/34zZ+aPP8wkTO+RYxkZ\nnq8LCsz16WX0mMbGmtWb3e3ZY+bYREeXlqgoUxo0KHtggqh/KjP5cR7wV8wwYFel+JhS6hGt9WPl\nvlkI4VdBQaVzZSoSHm4Wy8zIMPNp8ipYsjU21vdYWhp8+mn574mIMAkmMtJM7rzoIs/z6emQmWni\nCA8314eHm34faYarO6zWVGZi9kH5B2ZDrYOYjvqxwGylVJbWemG1RCiEqBGJiaaA6fTPzTX9MBkZ\nZjhzZqYpR46YkWXesrIqvv/x46VbAsTH+57/5hv47DPf4wEBJrmEhZU+9u0L55zjed2mTSbe0FDT\ndOd6dJXg4NLnoaGyLXR1qczkx9la64fdju0CvlVKZQOTMDPjhRD1gM1magoREWZ4shVnnmma1I4e\nNQkmO9uUrCyTTBxuCzk1aOD7/mNlLSmL6Q86dszzfFnrpa1bZxKLFVdfDYMHex5buNA0DQYFmRIc\n7Pk8MLD09ZAhvon1iy9KmxXLKgEBpc+TkkxydHE4TPOh6zr3YrP5HouI8Ky9ORym2Gz+r9VZTSox\nwPflnPsamFw14Qgh6ir3mo43u90kluxskxzKSirNm5uJn64aTW6uKUVFvteGlbFRhvc8noqElLFX\nbUaG5+KfFUlO9k0qH39c/ug7bw884Pl+ux0ercTEjCee8FzhOjPTbHHt4kpGroTk/jwoCObP971n\nVbGaVD4GbgXKajG9ClhRZREJIeqdgACTSMpKJi7Dh5virbDQ9O+4Sm5u2c1nyckmMeXnm0EGrkdX\nKSwsfV5WUin03uWpAmU1nRUX+x4rj/cgibKW7KmI96AHh9dyvhXdr7qb/aze/kvgEaXUz5jJj+mY\nnR9HAQOBp5RSrjzp0FrPrfJIhRCnpeBgU06094x3c1Zl3XOPSURFRSbBFBV5Pi8uLj3mPr/HZehQ\n8/7iYs9it3s+Fhf71rQcDtPMaLeXFofD872u1w5H2UnJZvNNLmWp7uYxq0llgfMxBphTxnn35i8H\nIElFCFGnlDWirTK8R7NVRkgI3H//yb+/SROzRA+U9q94JyJX7cVK4jkVVic/yghzIYSoA9z7T/xB\nkoUQQogqI0lFCCFElZGkIoQQosrInFIhhKjjHA4HDhzYHXbsDjshgZ5jpu0OO0fzjmJ3mN76+Igy\nxmRXkXKTilJqAfCU1nqXUqo1kK61rsRIbiGEqD9yCnLIL8qnoLiA+Ih4ny/unw/8THZ+NkX2Ivq0\n6ENEcITH+Y/0R2TlZ1FkL+LyTpcTGRLpcf5f3/+LY4XHKLYXM6nfJMKCPMcdT189ncLiQoodxcwb\nPo+ggNKv72JHMXcsN7uyBwYEsvBCzwVOcgtzmbpqKgARwRE8PeLpU/vDqEBFNZWJwJuY5Vh+A84G\nNlRbJEIIcYocDgf5xfkE2gIJDvTcgeyXg7+QnpNOXlEevZr3onlUc4/zr29+nR2ZO8gvzmdCjwkk\nxnkuD/Ds+mdJO5IGwJSBU2gf67lL2rKty9ifvR+ApLgkn6Ty7d5vOXT8EAAXnnGhT1LZdXgXOQVm\nSn5hcaFPUsnKz6KwuLDk53QXYCvtyXDVRtzZ3CanOKjeMcUVJZV04DGl1GeYVYlvVkqNLOdah9e6\nYEIIUaV2Zu7ktyO/kVOQQ9cmXX2+9Jf+vJSv93yNw+FgQvIEzm55tsf5r/d8zcb0jQA0a9DMJ6lk\nHM9gb9ZeAI4V+i5E5l4zcX25u3NPYkV237Vl3GsWZZ0PDCid0Vjs8J2e7544ih3FBFP6eTZs2Gw2\nbNgIDAjE4XB4JJJAWyANwxpis9kIDwr3uXdVqiip3Ac8A8zATGicUMG1DkCSihCiQnaHnaz8LAJs\nAUSHRnuc++b3b1ibtpbsgmyGthvKue3P9Ti/MX0jq3atAiA8KNwnqQTaAkt+gz9eeNzns91/888v\n8l0ozP18QXGBz/mYsBjiwuMIDgz2SAAuXZt0JSEqgeCAYJ9aCMCFHS4kryiPoIAgn58d4JZet2B3\n2AkMCKRBiO96NrOHzCbAFkCALYDQwFCPczabjUWjFvm8xyU0KJTHhz9e7vmqVG5S0Vq/DbwNoJSy\nAwO01uUtKimEEOQX5XMo9xA2bD41gTVpa3hzy5vYHXaGthvKlV2u9DifU5BT0ryUmZvpc2/3L9qy\nahKu5qaQwJAym4A6Ne5EeHA4oYGhtIz2Xbt/TMcxjEgaQWhQKDGhMT7nJ/acWMZPXGq0Gl3h+b4t\n+1Z43jtJemsY1rDC87WF1dFfQ4BfqzMQIUTdcLzwOLmFuT4jiDbs28DzG58HoGfzntzS+xaP85HB\nkSVf9kfyjvjc1/2396x8381Z2sW2Y2i7oUSGRNIhroPP+Qs6XMCoM0aVWYsA6NOiD31a9Cn352oS\n2aTcc8I6q8u0rFVKdVRKzQIGY9YAywC+AubIPvVC1H+7Du9i4YaFZOdn0yG+A5P7e+54ERteunhW\nWTUN12/aDUIa+IycAlOTuG/AfUSFRpVZU+jYqCMdG3UsNz7vjnnhH1a3E+4KrAOOAx8AB4DmwGhg\ntFLqbK31lmqLUghR7Y4VHGP59uXszdpLkb2I+wbc53E+OjSa7PxsAP7I+cPn/Y0iGhEYEEh8eDyN\nIxv7nG8f254FFywo98s/OjS6zL4GUbdYbf56HEgFhmitSxozlVKRwGrgEWBM1YcnhKhKdoedP3L+\n4Pejv3NWi7M8RggFBQTx+W+fl4wcKiwu9EgA8eHxJa+jQ6N9zseExvCvC/7lcU93gQGBBFJ205So\nP6wmlRRgvHtCAdBaH1NKzQMWV3lkQogq5XA4mLJySkl/xRnxZ3g0WYUGhdIksgkHcg7gcDhIz0mn\ndUzrkvM2m405Q+cQExpTZuIoL5mI04vVpHIcyp0x4wD59UOI2uBYwTG2HdrG9sztDG03lEYRjUrO\n2Ww2mjVoVpJU0o6keSQVgDFqDIEBgbSMbkl8uO9SHnVlBJLwH6tJ5VtgqlLqU611nuugUiocM5/l\nm+oITghROS/+9CKbD2wGoHmD5qS0SfE4nxiXyB85f9Auth3hwb6T4Hol9KqROEX9ZTWpTAO+B35T\nSn0I/AE0w3TUR2Oax4QQNeDgsYNsPrCZxpGN6da0m8e5jo06liSV7ZnbfZLKqDNGMUaNkaYqUW2s\nDineqpTqDzyI6ZCPAw4Da4HZlRn5pZQKxGxJfAMQBXwC3KG1PmDhvR8DDbTWg61+nhD1ybo961iy\naQkA3Zp2KzOptItth4pXdG7S2ef97kuFCFEdLP8L01pvBsZWwWfOBK4HrgMOAQuBd4GBFb1JKXUL\ncCEmkQlRrxXbi0nPSfeZ+d0hvnTSnz6kKbIXeSSKltEtmTpwao3FKYS3Gv21RSkVAtwF3Km1Xuk8\ndhWmWa2/1rrMvhmlVBLwKKZvR4h6K68ojze3vMlPf/yE3WHnifOe8Bi22ySyCa1iWhEXHkfXJl19\nVqsVwt9qui7cA9PktcZ1QGudppRKw/TL+CQVZ3PZEsxcmTOApBqIUwi/CA0MZduhbSULIv765690\nb9bd45oZKTOkT0TUWjW9nbCrLr/P6/h+oFU575mGGbb8RHUFJURNO5p3lM92fsbvR3/3OG6z2Tir\nxVmAWfYkv9h3NV1JKKI2q+maSgRgL2MHyXwgzPtipVQv4F6gj9barpSqgRCFqF6rdq3i3V/fxe6w\nM6jtIK7peo3H+XPanEPXpl1p17CdJBBR59R0TSUXCFBKeSezUMBjtr5SKgx4Bbhfa72jhuITotq1\nim5Vslrvhn0bfDZsig2PpX1se0kook6yuqCkDTMEeBQQiW8ycmitz7dwK1ddv7nbc4AEfJvE+gJn\nAo8rpVy7y4RiklIO0ElrvcdK/ELUNIfDwW9HfmPTH5u4uOPFHgnijPgzaBLZhJiwGAa0GuDHKIWo\nelabvx4FpmD2qt8L+O6AY80mIBsYBCwFUEq1BdoCX3pd+z3gvWnCo0AbYBymH0aIWsfhcPDkt0+y\n/dB2AHo060G72HYl5202GzPOmeGzB7kQ9YHVpHID8JTWevKJLqyI1jpfKbUQeEIplQEcxMxTWau1\n/s455DgOyNRa5wIezV5KqSwgV5rDRG1ms9loFNGoJKmsSVvjkVQASSii3rLapxINfFRFn3k/8Cqm\npvIFsBu43HmuP5DufBSi1svOz/YZwQUwrN0wggKCGNB6AMMTh/shMiH8w2pN5RtgAFUwm11rXYQZ\n0XVvGefWAOX2TmqtK94kWogacqzgGCu2r+DL3V/SKKIRDw560KPfpFVMK+afN79k33QhThdWk8oj\nwGvOUVvfYJbC91DebHgh6quv9nxFQXEB+7P3s+nAJno06+FxXhKKOB1ZTSqfOx9nOh/d14awIXuq\niNNMZEgkg9sO5tMdn9IyuiWhgaH+DkmIWsFqUhlSrVEIUUvlFuby2c7PaBzZmP6tPLv6zm1/Lklx\nSXRt0lXmlAjhZHXpe1kZWJx2dh3exYLvF3Cs4BgxYTH0TuhNSGBIyfno0GifpeeFON1ZXqZFKdUR\nmAUMBmKADOAr4GGt9a/VEp0QftQiqkXJsvJH847y3d7vOKfNOX6OSojazdKQYqVUV8xkxEHAB8B8\nzOZaQ4HvneeFqNO8l5EPDQpljBpDo4hG3Jh8IwNbV7jljxAC6zWVx4FUYIjWumSNLqVUJLAas5Pj\nmKoPT4jql5mbyXtb36NZg2aMOmOUx7l+rfrRt2Vf2TFRCIus/k9JAca7JxQArfUxpdQ8YHGVRyZE\nDdh9ZDfzv5lPYXEhwYHBDGg1gNjw2JLzAbYAAmw1ve6qEHWX1f8tx/EcRuxOhhOLOqtVTCuaNWgG\nQGFxIT/98ZOfIxKibrOaVL4FpjqXoy+hlAoH7qOMHRuFqAsCbAFc1eUqWse0ZnL/yQxpJ6PnhTgV\nVpu/pmE66n9TSn0I/AE0A0Zj1gVLqZ7whKgaRfYiPt3xKccKj3FF5ys8ziXFJTE9ZbrMNRGiClid\np7JVKdUfeBDTIR8HHMasBTZba72l+kIU4tTkFOQwb908DuQcwGaz0TuhN+1j23tcIwlFiKpheUiL\n1nozMLYaYxGiWkQGR9IksgkHcg7gcDj4cveXPklFCFE1yk0qSqlrgE+01pnO5xXSWr9WpZEJUUVs\nNhtXd7maPUf3MDJpJIPaDvJ3SELUWxXVVJYCZ2P6Upae4D4OQJKK8LsjeUdYv3c95yWe59GkFR8R\nz6PDHpX5JkJUs4r+h7XDbJjlei5ErfbN79/w1i9vkVuYS3xEPL0Tenucl4QiRPUr93+Z1nq328tB\nwHKt9SHv65RSzTB7xj9Z9eEJYd2uw7vILcwF4M0tb9K9aXeCA4P9HJUQpxer81ReBMrr2eyB2cRL\nCL+67MzLiA2PpXFkY27udbMkFCH8oKKO+o+BTs6XNuB9pVR+GZc2BXZWQ2xClCsrP4sGIQ08llAJ\nDw7nzr530iiikccS9UKImlNRI/Mc4Cbn85uADcCfXtcUA0eAl6s+NCF8ORwONuzfwOubX+fCMy7k\n3PbnepxPiErwU2RCCKi4T+U74DsA5970s7XWv9VUYEKU5Yf9P7B4o1m/dNnWZXRp0qVk7S4hhP9Z\n6lPRWk8AzlRKzXcdU0qdpZRaqZSSxZJEjUlunkyrmFYANAxrSF5Rnp8jEkK4s7pJ1xXAR5T2sQAc\nc77/M6XUiGqITQgfQQFB3Jh8I4PaDuKBQQ/QtmFbf4ckhHBjdfTXDOBfWusLXQe01r9orYcBi4DZ\n1RGcOL3tOryL1btW+xxPiErgmq7XEBYUVsa7hBD+ZHU2WBJwdznnlgETqiYcIcDusLNi+wqWb1uO\nAwetY1rTIb6Dv8MSQlhgtaZyAOhVzrluQGbVhCME2LCxI3MHdocdh8PBG1ve8Nk/XghRO1mtqbwK\nPKSUysHUTA4CjTH7qcwCFlZPeOJ0ZLPZuKHHDcxaM4sW0S2Y0GOCLE0vRB1hNanMBjpikse/3I7b\ngPcw+6wIcVLyi/IJDQr1ONYwrCH3DbiPpg2ayh7xQtQhVjfpKgTGKqW6AAMxm3QdBb7WWm+qxvhE\nPZeakcqLP77IVV2uIrl5sse55lHN/RSVEOJkVWrZVucOjz67PCqlGmitc6osKnFa2LBvA89vfB6A\nV35+hXax7WgY1tDPUQkhToWlpKKUCgHuxKxWHIJp9gLT0R+J6ayPtHivQMwSMDcAUcAnwB1a6wPl\nXH8lMA3ogFmK/3lgvta62Mrnidqrc5POxIXHkZmbiQ0bGcczJKkIUcdZrak8DtwFbAaaALmYdcC6\nYpLMzEp85kzgeuA64BCmn+ZdTLOaB6XUSMwggbuB/wHJwH+BYODhSnymqIUigiO4MflGPtnxCdf3\nuJ7o0Gh/hySEOEVWe0AvB57UWncHngV+0Fr3xdQe0qzex1njuQuYrrVeqbXeCFwFDFBK9S/jLbcC\n72qtF2itd2qt3wGeQubF1DnZ+dlsOejTckqH+A78re/fJKEIUU9YTSpNMTUFMLWVswC01vuAxzCJ\nwYoemCavNa4DWus0TGJKKeP6OZghy+7sQKzFzxO1wJaDW5i9djaLflhEenb6id8ghKizrCaVI5hm\nLoAdQCulVJTz9TagtcX7tHQ+7vM6vh9o5X2x1nqD1vpX12ulVDRwG6YfRtQBdoedZVuXkZWfRWFx\nIYt/XCwTGYWox6wmla+BvymlwoHtmMUkL3ae64sZXmxFBGB3DlF2lw9UuJCTUioCeB8IB6Za/Dzh\nZwG2AG5MvpGggCCiQ6O5pOMlMpFRiHrMalKZjelIX661LsJ0rj+nlFoPPIrpaLciFwhw7s/iLhST\nqMqklGoErAJ6AiO01rstfp6oYWXVQlpEt+CW3rfw4KAH6dyksx+iEkLUFKv7qfwEnIkZBQZmiO/D\nQAam32Oyxc/73fnoPastAd8mMQCUUm2Bb4B2wDla6w0WP0vUsMzcTP7x3T/Ymem7u3S3pt2ICo0q\n411CiPrE6jyVZ4GXtdafAmitHZgaSmVtArIx812WOu/dFmgLfFnG5zYBvsBsW9xfdp6svbb+uZVF\nPywiryiPjOMZPDDoAVmaXojTkNV5KjcBH57qh2mt85VSC4EnlFIZmIUpFwJrtdbfOYccxwGZWusC\nzDpjjYChQK5SyrVvrKO8yZLCP5o1aFayRteh3EOkZqTSo1kPP0clhKhpVvtUvqPsIb8n437MhMal\nmFrIbsw8GID+mFnz/Z2DAi4FGgDfO4+7SplNZcJ/YsNjuabrNTSObMx9A+6ThCLEacpqTWUjMEUp\ndTnwE+C9zpdDa32LlRs5O/rvdRbvc2soXQIGINBifKIG5RXlkZ6dTrvYdh7H+7ToQ49mPQgODPZT\nZEIIf7OaVC7DzCUJB/qVcV4mHpwmUjNSWbJpCXlFecwcPNNnJrwkFCFOb1aXvm934qtEfVdkL+KV\nTa9w6PghAF7Z9Aq397ld5p0IIUqU26eilBqqlGpQk8GI2i0oIIjx3ccDZjHIvi37SkIRQnioqKay\nEtPU9b3rgFLqL5gFHg9Vd2DC/+wOu8+uix0bdWR89/F0a9pNFoEUQvioaPSXx6+gzn1Q/g20qdaI\nRK2w5eAWHvziQfZn7/c5N7D1QEkoQogyVXbzb2nrOA38b/v/eHb9s/x57E9e/ull7A67v0MSQtQR\nlU0q4jTQo1kPggJMy+ih3EMcPHbQzxEJIeqKSu1RL04PzaOaM7LDSP489idjO4+lQYiM1xBCWHOi\npFLW/BOZk1JPFBQX8L/t/yMxLpEuTbp4nLuww4UysksIUWknSirvKKXyvY69X8Yxh9ZaVWFcoprt\nObqHRT8s4tDxQ8RHxDNz8ExCAkNKzktCEUKcjIqSystlHFtXXYGImhUfHk9eUR4Ah44fYt2edQxp\nN8TPUQkh6rpyk4rWekJNBiJqVmRIJJd0vIRlqcu49MxLGdBqgL9DEkLUA9JRX8/ZHXbW7VmHAwfn\ntDnH49zA1gPpldCLiOAIP0UnhKhvJKnUY5m5mTyz/hnSs9MJDQqlR7MeHpMWbTabJBQhRJWSeSr1\nWMOwhtic81Xzi/L5dMenfo5ICFHfSVKpRxwOz9HeAbYALut0GaFBoYzpOIYxHcf4KTIhxOlCmr/q\ngYzjGSzfthyA63tc73Guc+POzB02l8iQSH+EJoQ4zUhSqeMOHT/EA58/gN1hx2azMTxxOAlRCSXn\nbTabJBQhRI2R5q86Lj4ins5NOgOm+Wtj+kY/RySEOJ1JTaUOSTuSht1hp31se4/jo88YTUFxAaPP\nGE2H+A5+ik4IISSp1Anp2em8tvk1th3aRvvY9tw34D6PZVTaNGzDPf3u8WOEQghhSPNXHRARHMGu\nw7sA2HV4FzsP7/RzREIIUTZJKrVMenY6uYW5HsdiwmLo27IvAbYA+rbsS1RIlJ+iE0KIiknzVy2x\n9c+trNi+gm2HtnFF5ysY1n6Yx/nRZ4xm9BmjiQ2P9VOEQghxYpJUaonM3Ey2HdoGwNrdaxnabqhH\nv0mdSSZ2OxQXQ1GRKXZ7afGanInNZkpAgCmBgaYEBZlHWX5fiDpHkkoNO5J3hO2HttOnRR+P470S\nevHmL29SWFxIQlQCuUW5Nbcul8MB+fmQkwPHjsHx46WPubmmHD8OeXmlJT/flIICUwoLzaO9Cvez\nDwoyJSSktISFQWioKWFhpoSHl5aIiNISGWlKeLgkKCFqiCSVGmJ32Pnnd/9EH9IAdIjvQMOwhiXn\nw4LCmNhzIq2iW1VNrSQ/H7KySkt2dtnFlUiKi0/9M6uaq7aTl3dq97HZShNMgwaeJSqqtERHm8cG\nDUwyE0JUmvzPqSYOh8Oj+SrAFoDNZitZn+v7fd9zXuJ5Hu/p1rRbxTe1200iOHrUJIqjR8t+npVl\nkoo/2GylzVeuEhBQ2szlusbhKC2u5rHi4tKms6pMcg6HSZ45OXDggLX3RER4JproaM/ifiwk5MT3\nE+I0IUmlCh3IOcCG/Rv4+cDPpLROIaVNisf5Pgl9SM1IRcUrmjVoVnrCvVZRVqJwlexs336JqhIS\n4vnbvHszknvzkqvZydUEFRpq3hscbEpV9YU4HCa5uJrVXMXV7ObeFJebax6PH/csx46ZcjI1Hdc9\nrCSh0FDfpOOdeFzPQ0OlKU7Ua5JUqtDWjK18pD8CHEQSQkq4MonAmTB6H82k69HeRO8tgq8+gay3\nqq9WERRkvshiYjy/1FzNO9HRns1AwcFVH8OpsNlKE1XEKfYtFReb5OJq6nM1++XkeDYDujcTViZ5\n56tu7oUAAA+MSURBVOfDn3+aciKuvxfXn79785t7k5zrufQHiTpGksqJuDqxjx2jKPso+o8tpB7c\nyvHco4yP7F/65ZSTQ7esA7xesB4KC9nuWEf+0lRCCSy5VaiznJLISJMoXCU62vO1K5HIl1GpwMDS\nGoMVruYy1y8Ebr8YePRRuZ5XpqmuqAgOHzbFioAAzxqk67l7cQ1KcD26apUBMg1N1LwaTypKqUBg\nDnADEAV8AtyhtS6znUEp1Rv4J5AM7AMe1lovOekA9u0z/6Fdo5rcRze5Sm6u5ygo54imfFshz0R/\nC0AANq44etAjacQBI8Ka0Kq4AZ2KYj3OVSgoqPRL70QJQzqQq5/NVlp7SEio+FqHw/w78U405T0v\nLKxcLK5+tOzsyv8cYWG+zZcREaUj5twf3Yt3E2egxX/HQuCfmspM4HrgOuAQsBB4FxjofaFSqjHw\nKfAacBMwHFislPpDa/1ZpT/57bdh1aoKL/k65A900BF2BWYxOac7sY7SukWkI5gWxZHsCzyGHQfb\ng47SpSjO4/2X5LUzT0JDPZs5ympndxWpVdRd7iPLmjc/8fX5+WWPwPN+dJVTGfnm6nM6Va5h3d79\naK5H9xIc7Pm8vBIUVPro/jw4uHT+kqiTajSpKKVCgLuAO7XWK53HrgJ+U0r111p/4/WWicBR4C6t\ntR1IVUr1BCYDlU8qO3YAcMxWyN6AYzS2hxHnCPO4ZEPwQVKDjgCwKyiLXoWNzT90Z9PD2SEODoc6\n6BjdjqSGSRAd59seHhVV+/ooRO3g+lJu1Mja9UVFpQMOXInGVYvOyfGcU+Q+QKEqkol7DEVF5t41\nwX0EoSvpuE+K9X7uXdwn0rq/dp9k63q02TzPlVVcIxe9H8s67z6ht6zjFRX30ZHuidX7uoqucT0/\n0aMrrmpQ0zWVHpgmrzWuA1rrNKVUGpACeCeVFOBLZ0JxWQMsVErZtNaVGwp1xRW89eFcVudpCArk\nipj+DIvvU9osEB5OuyPfkZrxHQQFsbP9MHolX+vR5HReBbcXosoFBZU2f1aG3V46Is67qde9uCay\nuj/3fqyuEYflcThMM2FlmwqFdcHBMGoUjBhR5beu6aTS0vm4z+v4fqBVOdf/WMa1EUA8kFGpT09M\nJH7M1fDLWwDsbXUm9LjM45LkI82IOdyNtg3b0iqmFQRIH4aogwICSoeEnwrXF7xr9QT3VRTcn3uv\nrOD+vLCwdHi4q7heez8WF1ftqgyibIWFpivg/POrvMZS09+YEYBda+39K0g+EPb/7Z17sN3TFcc/\n95LQqgpS2lQmEcZXU1GPRhFBRko8IuJZqkRrKMVQFVQnXvVK1ShlGCoeqXeUNBpEuEGIZ71jjXe9\ngsQrQcUj/WPtX/Lzyzn33Nyeey/ntz4zZ37n7L1/57f3mnN+67f2XnutKu2Ldnzmf1upfU16r9Cb\nbkt1o9fyvej5zcWnIPr06EOfHn3a89VB0Hg0NS1aI+ksvvhi0ZRbfjNsvqwtr+Km2vz7bNNt9j7f\nvhivrtLnfHl+E29xU2+19/DlttVeWbviOcXzs8/FNtXKl1nGrZQOmALrbKXyMdAsaWkz+yxXvgzw\nYZX2RS/c7HOl9jVZc6U1OWfbc2huCnfLIPhK0tzc+YosqBudfWd9JR2LbjK9WHxKLGtfqe08fAF/\niWluag6FEgRB0EF0tqXyGDAX2AIYDyCpL9AXuKtC+3uA/QqL8kOA6YXF+yJLAcyaNas+vQ6CICgB\nuXtmuzcnNS3Iz711ApJOxzc+jgLewvep/NfMtkwuxysB75jZfEmrAgZcA5wNDAX+DAwzsztaucZm\nwN0dOY4gCIIGZrCZ3dOeE7vCtekPQDfcUulG2lGf6jYF7sStkRYze1PSMOAc3AvsZWCf1hRK4kHc\nHfkN4CsY0z0IguAryVL4ksOD7f2CTrdUgiAIgsYlVqyDIAiCuhFKJQiCIKgboVSCIAiCuhFKJQiC\nIKgbpQlstaR5XBqB5JI9Fo+D+Q3gfuBIM3sy1W+d6gU8CxxtZpO7qLsdjqSN8b1PQ82sJZWVQgaS\n9gdG4zH2ngaOyrwoyyADScsBpwO74OGf7sP/C0+n+oaWgaQLgKXNbP9cWatjlrQK8Ff8/jEfGAcc\nV4iGshhlslROYFEel83xYJUTurJDHYmkZuAfwFrACNxd+31gqqSVJfUHJgLX4QnQbgJulPTDLupy\nh5JuKleQ29RVFhlI2hc4D7+pDgCmARMl9S2LDPBEf0OB3YBN8JiCt0hatpFlIKlJ0knAgYXytox5\nAvBdfLP6KGA/4MRa1yyFS3HaVDkbz+NyaSrrC7wIDKqQx+Vrj6T1gUeA/mY2M5UtA7wDHAQMAmRm\nW+bOuRN41swO6PwedyySLsQV7JbAEDNrSWUNLQN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+ "text/plain": [
+ "| \n", + " | value | \n", + "
|---|---|
| S | \n", + "0.520453 | \n", + "
| I | \n", + "0.000615 | \n", + "
| R | \n", + "0.478933 | \n", + "
\n",
+ "\n",
+ "\n",
+ " \n",
+ "
\n",
+ "
"
+ ],
+ "text/plain": [
+ " S I R\n",
+ "0 0.988889 0.011111 0.000000\n",
+ "1 0.985226 0.011996 0.002778\n",
+ "2 0.981287 0.012936 0.005777\n",
+ "3 0.977055 0.013934 0.009011\n",
+ "4 0.972517 0.014988 0.012494"
+ ]
+ },
+ "execution_count": 79,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "tc = 3 # time between contacts in days \n",
+ "tr = 4 # recovery time in days\n",
+ "\n",
+ "beta = 1 / tc # contact rate in per day\n",
+ "gamma = 1 / tr # recovery rate in per day\n",
+ "\n",
+ "sir = make_system(beta, gamma)\n",
+ "run_simulation(system, update1)\n",
+ "system.results.head()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "We can extract the results and plot them."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 80,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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evJiQkBBSUkr7kW677TaWL1/Oc889R1paGmvWrOHBBx8kLCysZO96byeKOTIy\nkquuuop//OMffP755+zYsYPp06eTl5dXvX+4J6lS+/I5twN2Pd+JNHuJGnLeeWZU2KZN5vWRI7Bo\nEXTrZvZriY/3b3zCfxITE7nlllt49tlnGTNmDC+++CKPPfYY119/PTabjR49evDyyy8T7/xHct11\n15GXl8f8+fPJzMykQ4cOLFq0qCTpvPDCC8yfP5/LLruM8PBwhg4dyt///neP5qaRI0fyyCOPMGrU\nKILctjc955xzmDdvHs899xzPPPMMcXFxXHzxxUyaNKnc+MPCwk4Y85QpUwgLC2PGjBnk5+czduxY\nn36h2qKinR+3Y+agWOHQWpe72mRNk50f6yeHw9ROXn/dc4fJkBAYPdosue8cPCOEOAnVvfPjOqwn\nFSGqnc1m5rN07AjLlsGXX5rjBQVmU7BvvoFrrpGOfCH8qaIFJW+owTiEsCwiAsaNM0OQly6F/fvN\n8fR0+Pe/Ye5cKGcQjxCimlnqU1FK9T/RNVrrb049HCGsS0w0a4h9/jl89JFZM+ziiyWhCOFPVjvq\nv+bETWHSmi1qXGAgDB8OffrAmjVmuLG3nTuhfXvZs0WImmA1qQwp41gDIAUYj9nMSwi/adjQ1FK8\n7doF8+aZpHL55aZ2I4SoPlb3U1lbzqnlSqkc4H5gVJVFJUQVcDjgnXfMc1dySU42yadZM//GJkR9\nZXWV4op8hSx9L2qh4mJTM3GbRsCPP5qJk0uWlE6mFEJUnUpNfizHaCDrhFcJUcOCgsxyLoMGmSHI\nP/xgjjscsG6dWRU5JQVGjgTn6hhCiFNkdfTXZ2UcDgRaAYnA41UZlBBVqVEjuPlmMyt/2TLYutUc\nLyqCL76Ar7+GIUPg0kulM1+IU2W1phKC7+gvB2Yr4XnAC1UZlBDVoU0buPtuSE2F99+H334zxwsL\n4dAhSShCVAWrHfWDqzkOIWpMx44wZQr88otZqHL3bnBuh+Hh+HEz0VIIYV2l+lSUUiMxw4hjgQPA\n51rrL6sjMCGqk81mtjLu3NnUWLyXiMvLgxkzICnJNJslJUlNRggrrPapxAP/A3oD+cCfQBPgAWd/\nyyVa69q5DrMQFbDZzBwWb199ZWoqP/9sSqtWcO650Lu352gyIYQnq/89nsVsJzxaa73cdVApdRGw\nGHgMuNvKjZRSgcAc4AYgCvgEuENrfaCc61sC/wDOB3KBd4DJWuvjFmMXotKcG/SV+P13ePFFM+8l\nJcWUONlEjyzSAAAgAElEQVREWwgfVuepjMR8kS93P6i1/hCYBlxdic+cCVwPXAecA7QE3i3rQqVU\nKLASiAMGAFdiJlmWvYWaEFVk3DgznyUlxXMXyuxsWLECpk+HhQth82aw2/0WphC1jtWkUgQcKedc\nOmZ02AkppUKAu4DpWuuVWuuNmN0jB5SzaOU1QHPgMq31z1rrL4CHgLMsxi3ESWveHK69Fh57zMzC\nb9iw9JzDYTYMW7DAJBYhhGE1qSwEHlVKJbgfVEpFA1MxzWNW9MA0ea1xHXBuBJOGGQDg7Xxgpdb6\nsNv1L2qtJamIGtOggZkgOXcu3HqrGT3mEh1tOvzdFRWZ/hghTkdW+1QSnGWnUuprYD8Qj2mSigLy\n3SZIOrTW55dzH9cYm31ex/djJlJ6OwP4XCn1MHAtZm7Me8D9MjBA1LSAALN2WHIyHDhgJk02aOC7\n2+SmTfDCC9C1K5x1lnl0b0IToj6zmlSSgJ/c3tPa+dx1LBBrS99HAHatdaHX8XygrF0wooGbMCPP\nxgItgAWYkWfXWYxdiCrXtKlZAqYs335rais//mhKaKhJLD17mlpNaGjNxipETbI6+bGspe9PRi4Q\noJQK0loXuR0PBY6VcX0hkAmM11oXAz8opYKBt5VSk7TWh6ooLiGqRHGx6cx3l59v1h374QdTYznz\nTOjRA7p1g6go/8QpRHWp7OTHTsAgIAYzV+VrrbWuxC1+dz42d3sOpmnNu0kM57E8Z0Jx+dX52BaQ\npCJqlcBAmDbNNI99/z1s2GCeuxQWls59sdngnnvgjDP8F68QVc3q5McA4D/AjYD7vGKHUuoVYILW\n+kQ7QwJsArIxiWmp895tMQmirJn5XwE3K6WC3ZrMugDFmM59IWqlpk1h9GgYNQrS0+H//g82boT9\n+0uvCQw065G5c9VqzjxT5sGIuslqTWUqpg9jKvAqZomW5pghv7MpXViyQlrrfKXUQuAJpVQGcBAz\nsmyt1vo755DjOCBTa10ALAL+BixRSs3CdPTPB5ZI05eoC2w2SEgwZfRo+PNP05H/008QFubbv6K1\n2esFzOrKSpmaTIcOJsnIUjGitrOaVG4CHtFaz3c7theYp5QKc563OiHxfiAYU1MJxjmj3nmuP/AF\nZvviNVrrA0qpc4CngY1AjvN90yx+lhC1SuPGZrmXc88te9Kka1l+gIwMU9atM69jY80aZImJZmmZ\nli19R54J4W9Wk0pzYF05576hEl/yzg76e53F+9waPJvX0Fr/ipmvIkS9ElDGLLHWraFTJ9ixAwoK\nPM8dPmz6aDZsMK9TUszkTCFqE6tJZRfQD1hdxrl+mFn1QohT1K+fKUVFkJZmmsO2b4ddu0x/i7t2\n7Xzfv2gRZGWZBTBbtoQWLUyRYcyiplhNKs8Dc5VSx4A3MH0qTTFrfk0HHq2e8IQ4PQUFmaaupCTz\n2m43i1ru3GkSzK5dvqsrOxwmAeXkmOvcxcebZWcSEsxj06amViSTMkVVq8wqxcnAk8ATbsdtmD6O\nR6o4LiGEm4AAM1KsTRsYOrTsa44cMQmlLIcOmbJlS+mxWbOgWbPS10VFZpRa48amNGggAwNE5Vmd\n/FgMXK+UmodZoysOOAx8qbX+pRrjE0JYFBsL8+aZGs3evaXlwAHfQQEBASZxuMvIMMvLuISEmBpO\nfLwZeeYqsbGmeL9fCKjk5EfMhMVdmIRy0PlcCFFLxMSY4r7IZVGR2R9m/34zZ+aPP8wkTO+RYxkZ\nnq8LCsz16WX0mMbGmtWb3e3ZY+bYREeXlqgoUxo0KHtggqh/KjP5cR7wV8wwYFel+JhS6hGt9WPl\nvlkI4VdBQaVzZSoSHm4Wy8zIMPNp8ipYsjU21vdYWhp8+mn574mIMAkmMtJM7rzoIs/z6emQmWni\nCA8314eHm34faYarO6zWVGZi9kH5B2ZDrYOYjvqxwGylVJbWemG1RCiEqBGJiaaA6fTPzTX9MBkZ\nZjhzZqYpR46YkWXesrIqvv/x46VbAsTH+57/5hv47DPf4wEBJrmEhZU+9u0L55zjed2mTSbe0FDT\ndOd6dJXg4NLnoaGyLXR1qczkx9la64fdju0CvlVKZQOTMDPjhRD1gM1magoREWZ4shVnnmma1I4e\nNQkmO9uUrCyTTBxuCzk1aOD7/mNlLSmL6Q86dszzfFnrpa1bZxKLFVdfDYMHex5buNA0DQYFmRIc\n7Pk8MLD09ZAhvon1iy9KmxXLKgEBpc+TkkxydHE4TPOh6zr3YrP5HouI8Ky9ORym2Gz+r9VZTSox\nwPflnPsamFw14Qgh6ir3mo43u90kluxskxzKSirNm5uJn64aTW6uKUVFvteGlbFRhvc8noqElLFX\nbUaG5+KfFUlO9k0qH39c/ug7bw884Pl+ux0ercTEjCee8FzhOjPTbHHt4kpGroTk/jwoCObP971n\nVbGaVD4GbgXKajG9ClhRZREJIeqdgACTSMpKJi7Dh5virbDQ9O+4Sm5u2c1nyckmMeXnm0EGrkdX\nKSwsfV5WUin03uWpAmU1nRUX+x4rj/cgibKW7KmI96AHh9dyvhXdr7qb/aze/kvgEaXUz5jJj+mY\nnR9HAQOBp5RSrjzp0FrPrfJIhRCnpeBgU06094x3c1Zl3XOPSURFRSbBFBV5Pi8uLj3mPr/HZehQ\n8/7iYs9it3s+Fhf71rQcDtPMaLeXFofD872u1w5H2UnJZvNNLmWp7uYxq0llgfMxBphTxnn35i8H\nIElFCFGnlDWirTK8R7NVRkgI3H//yb+/SROzRA+U9q94JyJX7cVK4jkVVic/yghzIYSoA9z7T/xB\nkoUQQogqI0lFCCFElZGkIoQQosrInFIhhKjjHA4HDhzYHXbsDjshgZ5jpu0OO0fzjmJ3mN76+Igy\nxmRXkXKTilJqAfCU1nqXUqo1kK61rsRIbiGEqD9yCnLIL8qnoLiA+Ih4ny/unw/8THZ+NkX2Ivq0\n6ENEcITH+Y/0R2TlZ1FkL+LyTpcTGRLpcf5f3/+LY4XHKLYXM6nfJMKCPMcdT189ncLiQoodxcwb\nPo+ggNKv72JHMXcsN7uyBwYEsvBCzwVOcgtzmbpqKgARwRE8PeLpU/vDqEBFNZWJwJuY5Vh+A84G\nNlRbJEIIcYocDgf5xfkE2gIJDvTcgeyXg7+QnpNOXlEevZr3onlUc4/zr29+nR2ZO8gvzmdCjwkk\nxnkuD/Ds+mdJO5IGwJSBU2gf67lL2rKty9ifvR+ApLgkn6Ty7d5vOXT8EAAXnnGhT1LZdXgXOQVm\nSn5hcaFPUsnKz6KwuLDk53QXYCvtyXDVRtzZ3CanOKjeMcUVJZV04DGl1GeYVYlvVkqNLOdah9e6\nYEIIUaV2Zu7ktyO/kVOQQ9cmXX2+9Jf+vJSv93yNw+FgQvIEzm55tsf5r/d8zcb0jQA0a9DMJ6lk\nHM9gb9ZeAI4V+i5E5l4zcX25u3NPYkV237Vl3GsWZZ0PDCid0Vjs8J2e7544ih3FBFP6eTZs2Gw2\nbNgIDAjE4XB4JJJAWyANwxpis9kIDwr3uXdVqiip3Ac8A8zATGicUMG1DkCSihCiQnaHnaz8LAJs\nAUSHRnuc++b3b1ibtpbsgmyGthvKue3P9Ti/MX0jq3atAiA8KNwnqQTaAkt+gz9eeNzns91/888v\n8l0ozP18QXGBz/mYsBjiwuMIDgz2SAAuXZt0JSEqgeCAYJ9aCMCFHS4kryiPoIAgn58d4JZet2B3\n2AkMCKRBiO96NrOHzCbAFkCALYDQwFCPczabjUWjFvm8xyU0KJTHhz9e7vmqVG5S0Vq/DbwNoJSy\nAwO01uUtKimEEOQX5XMo9xA2bD41gTVpa3hzy5vYHXaGthvKlV2u9DifU5BT0ryUmZvpc2/3L9qy\nahKu5qaQwJAym4A6Ne5EeHA4oYGhtIz2Xbt/TMcxjEgaQWhQKDGhMT7nJ/acWMZPXGq0Gl3h+b4t\n+1Z43jtJemsY1rDC87WF1dFfQ4BfqzMQIUTdcLzwOLmFuT4jiDbs28DzG58HoGfzntzS+xaP85HB\nkSVf9kfyjvjc1/2396x8381Z2sW2Y2i7oUSGRNIhroPP+Qs6XMCoM0aVWYsA6NOiD31a9Cn352oS\n2aTcc8I6q8u0rFVKdVRKzQIGY9YAywC+AubIPvVC1H+7Du9i4YaFZOdn0yG+A5P7e+54ERteunhW\nWTUN12/aDUIa+IycAlOTuG/AfUSFRpVZU+jYqCMdG3UsNz7vjnnhH1a3E+4KrAOOAx8AB4DmwGhg\ntFLqbK31lmqLUghR7Y4VHGP59uXszdpLkb2I+wbc53E+OjSa7PxsAP7I+cPn/Y0iGhEYEEh8eDyN\nIxv7nG8f254FFywo98s/OjS6zL4GUbdYbf56HEgFhmitSxozlVKRwGrgEWBM1YcnhKhKdoedP3L+\n4Pejv3NWi7M8RggFBQTx+W+fl4wcKiwu9EgA8eHxJa+jQ6N9zseExvCvC/7lcU93gQGBBFJ205So\nP6wmlRRgvHtCAdBaH1NKzQMWV3lkQogq5XA4mLJySkl/xRnxZ3g0WYUGhdIksgkHcg7gcDhIz0mn\ndUzrkvM2m405Q+cQExpTZuIoL5mI04vVpHIcyp0x4wD59UOI2uBYwTG2HdrG9sztDG03lEYRjUrO\n2Ww2mjVoVpJU0o6keSQVgDFqDIEBgbSMbkl8uO9SHnVlBJLwH6tJ5VtgqlLqU611nuugUiocM5/l\nm+oITghROS/+9CKbD2wGoHmD5qS0SfE4nxiXyB85f9Auth3hwb6T4Hol9KqROEX9ZTWpTAO+B35T\nSn0I/AE0w3TUR2Oax4QQNeDgsYNsPrCZxpGN6da0m8e5jo06liSV7ZnbfZLKqDNGMUaNkaYqUW2s\nDineqpTqDzyI6ZCPAw4Da4HZlRn5pZQKxGxJfAMQBXwC3KG1PmDhvR8DDbTWg61+nhD1ybo961iy\naQkA3Zp2KzOptItth4pXdG7S2ef97kuFCFEdLP8L01pvBsZWwWfOBK4HrgMOAQuBd4GBFb1JKXUL\ncCEmkQlRrxXbi0nPSfeZ+d0hvnTSnz6kKbIXeSSKltEtmTpwao3FKYS3Gv21RSkVAtwF3Km1Xuk8\ndhWmWa2/1rrMvhmlVBLwKKZvR4h6K68ojze3vMlPf/yE3WHnifOe8Bi22ySyCa1iWhEXHkfXJl19\nVqsVwt9qui7cA9PktcZ1QGudppRKw/TL+CQVZ3PZEsxcmTOApBqIUwi/CA0MZduhbSULIv765690\nb9bd45oZKTOkT0TUWjW9nbCrLr/P6/h+oFU575mGGbb8RHUFJURNO5p3lM92fsbvR3/3OG6z2Tir\nxVmAWfYkv9h3NV1JKKI2q+maSgRgL2MHyXwgzPtipVQv4F6gj9barpSqgRCFqF6rdq3i3V/fxe6w\nM6jtIK7peo3H+XPanEPXpl1p17CdJBBR59R0TSUXCFBKeSezUMBjtr5SKgx4Bbhfa72jhuITotq1\nim5Vslrvhn0bfDZsig2PpX1se0kook6yuqCkDTMEeBQQiW8ycmitz7dwK1ddv7nbc4AEfJvE+gJn\nAo8rpVy7y4RiklIO0ElrvcdK/ELUNIfDwW9HfmPTH5u4uOPFHgnijPgzaBLZhJiwGAa0GuDHKIWo\nelabvx4FpmD2qt8L+O6AY80mIBsYBCwFUEq1BdoCX3pd+z3gvWnCo0AbYBymH0aIWsfhcPDkt0+y\n/dB2AHo060G72HYl5202GzPOmeGzB7kQ9YHVpHID8JTWevKJLqyI1jpfKbUQeEIplQEcxMxTWau1\n/s455DgOyNRa5wIezV5KqSwgV5rDRG1ms9loFNGoJKmsSVvjkVQASSii3rLapxINfFRFn3k/8Cqm\npvIFsBu43HmuP5DufBSi1svOz/YZwQUwrN0wggKCGNB6AMMTh/shMiH8w2pN5RtgAFUwm11rXYQZ\n0XVvGefWAOX2TmqtK94kWogacqzgGCu2r+DL3V/SKKIRDw560KPfpFVMK+afN79k33QhThdWk8oj\nwGvOUVvfYJbC91DebHgh6quv9nxFQXEB+7P3s+nAJno06+FxXhKKOB1ZTSqfOx9nOh/d14awIXuq\niNNMZEgkg9sO5tMdn9IyuiWhgaH+DkmIWsFqUhlSrVEIUUvlFuby2c7PaBzZmP6tPLv6zm1/Lklx\nSXRt0lXmlAjhZHXpe1kZWJx2dh3exYLvF3Cs4BgxYTH0TuhNSGBIyfno0GifpeeFON1ZXqZFKdUR\nmAUMBmKADOAr4GGt9a/VEp0QftQiqkXJsvJH847y3d7vOKfNOX6OSojazdKQYqVUV8xkxEHAB8B8\nzOZaQ4HvneeFqNO8l5EPDQpljBpDo4hG3Jh8IwNbV7jljxAC6zWVx4FUYIjWumSNLqVUJLAas5Pj\nmKoPT4jql5mbyXtb36NZg2aMOmOUx7l+rfrRt2Vf2TFRCIus/k9JAca7JxQArfUxpdQ8YHGVRyZE\nDdh9ZDfzv5lPYXEhwYHBDGg1gNjw2JLzAbYAAmw1ve6qEHWX1f8tx/EcRuxOhhOLOqtVTCuaNWgG\nQGFxIT/98ZOfIxKibrOaVL4FpjqXoy+hlAoH7qOMHRuFqAsCbAFc1eUqWse0ZnL/yQxpJ6PnhTgV\nVpu/pmE66n9TSn0I/AE0A0Zj1gVLqZ7whKgaRfYiPt3xKccKj3FF5ys8ziXFJTE9ZbrMNRGiClid\np7JVKdUfeBDTIR8HHMasBTZba72l+kIU4tTkFOQwb908DuQcwGaz0TuhN+1j23tcIwlFiKpheUiL\n1nozMLYaYxGiWkQGR9IksgkHcg7gcDj4cveXPklFCFE1yk0qSqlrgE+01pnO5xXSWr9WpZEJUUVs\nNhtXd7maPUf3MDJpJIPaDvJ3SELUWxXVVJYCZ2P6Upae4D4OQJKK8LsjeUdYv3c95yWe59GkFR8R\nz6PDHpX5JkJUs4r+h7XDbJjlei5ErfbN79/w1i9vkVuYS3xEPL0Tenucl4QiRPUr93+Z1nq328tB\nwHKt9SHv65RSzTB7xj9Z9eEJYd2uw7vILcwF4M0tb9K9aXeCA4P9HJUQpxer81ReBMrr2eyB2cRL\nCL+67MzLiA2PpXFkY27udbMkFCH8oKKO+o+BTs6XNuB9pVR+GZc2BXZWQ2xClCsrP4sGIQ08llAJ\nDw7nzr530iiikccS9UKImlNRI/Mc4Cbn85uADcCfXtcUA0eAl6s+NCF8ORwONuzfwOubX+fCMy7k\n3PbnepxPiErwU2RCCKi4T+U74DsA5970s7XWv9VUYEKU5Yf9P7B4o1m/dNnWZXRp0qVk7S4hhP9Z\n6lPRWk8AzlRKzXcdU0qdpZRaqZSSxZJEjUlunkyrmFYANAxrSF5Rnp8jEkK4s7pJ1xXAR5T2sQAc\nc77/M6XUiGqITQgfQQFB3Jh8I4PaDuKBQQ/QtmFbf4ckhHBjdfTXDOBfWusLXQe01r9orYcBi4DZ\n1RGcOL3tOryL1btW+xxPiErgmq7XEBYUVsa7hBD+ZHU2WBJwdznnlgETqiYcIcDusLNi+wqWb1uO\nAwetY1rTIb6Dv8MSQlhgtaZyAOhVzrluQGbVhCME2LCxI3MHdocdh8PBG1ve8Nk/XghRO1mtqbwK\nPKSUysHUTA4CjTH7qcwCFlZPeOJ0ZLPZuKHHDcxaM4sW0S2Y0GOCLE0vRB1hNanMBjpikse/3I7b\ngPcw+6wIcVLyi/IJDQr1ONYwrCH3DbiPpg2ayh7xQtQhVjfpKgTGKqW6AAMxm3QdBb7WWm+qxvhE\nPZeakcqLP77IVV2uIrl5sse55lHN/RSVEOJkVWrZVucOjz67PCqlGmitc6osKnFa2LBvA89vfB6A\nV35+hXax7WgY1tDPUQkhToWlpKKUCgHuxKxWHIJp9gLT0R+J6ayPtHivQMwSMDcAUcAnwB1a6wPl\nXH8lMA3ogFmK/3lgvta62Mrnidqrc5POxIXHkZmbiQ0bGcczJKkIUcdZrak8DtwFbAaaALmYdcC6\nYpLMzEp85kzgeuA64BCmn+ZdTLOaB6XUSMwggbuB/wHJwH+BYODhSnymqIUigiO4MflGPtnxCdf3\nuJ7o0Gh/hySEOEVWe0AvB57UWncHngV+0Fr3xdQe0qzex1njuQuYrrVeqbXeCFwFDFBK9S/jLbcC\n72qtF2itd2qt3wGeQubF1DnZ+dlsOejTckqH+A78re/fJKEIUU9YTSpNMTUFMLWVswC01vuAxzCJ\nwYoemCavNa4DWus0TGJKKeP6OZghy+7sQKzFzxO1wJaDW5i9djaLflhEenb6id8ghKizrCaVI5hm\nLoAdQCulVJTz9TagtcX7tHQ+7vM6vh9o5X2x1nqD1vpX12ulVDRwG6YfRtQBdoedZVuXkZWfRWFx\nIYt/XCwTGYWox6wmla+BvymlwoHtmMUkL3ae64sZXmxFBGB3DlF2lw9UuJCTUioCeB8IB6Za/Dzh\nZwG2AG5MvpGggCCiQ6O5pOMlMpFRiHrMalKZjelIX661LsJ0rj+nlFoPPIrpaLciFwhw7s/iLhST\nqMqklGoErAJ6AiO01rstfp6oYWXVQlpEt+CW3rfw4KAH6dyksx+iEkLUFKv7qfwEnIkZBQZmiO/D\nQAam32Oyxc/73fnoPastAd8mMQCUUm2Bb4B2wDla6w0WP0vUsMzcTP7x3T/Ymem7u3S3pt2ICo0q\n411CiPrE6jyVZ4GXtdafAmitHZgaSmVtArIx812WOu/dFmgLfFnG5zYBvsBsW9xfdp6svbb+uZVF\nPywiryiPjOMZPDDoAVmaXojTkNV5KjcBH57qh2mt85VSC4EnlFIZmIUpFwJrtdbfOYccxwGZWusC\nzDpjjYChQK5SyrVvrKO8yZLCP5o1aFayRteh3EOkZqTSo1kPP0clhKhpVvtUvqPsIb8n437MhMal\nmFrIbsw8GID+mFnz/Z2DAi4FGgDfO4+7SplNZcJ/YsNjuabrNTSObMx9A+6ThCLEacpqTWUjMEUp\ndTnwE+C9zpdDa32LlRs5O/rvdRbvc2soXQIGINBifKIG5RXlkZ6dTrvYdh7H+7ToQ49mPQgODPZT\nZEIIf7OaVC7DzCUJB/qVcV4mHpwmUjNSWbJpCXlFecwcPNNnJrwkFCFOb1aXvm934qtEfVdkL+KV\nTa9w6PghAF7Z9Aq397ld5p0IIUqU26eilBqqlGpQk8GI2i0oIIjx3ccDZjHIvi37SkIRQnioqKay\nEtPU9b3rgFLqL5gFHg9Vd2DC/+wOu8+uix0bdWR89/F0a9pNFoEUQvioaPSXx6+gzn1Q/g20qdaI\nRK2w5eAWHvziQfZn7/c5N7D1QEkoQogyVXbzb2nrOA38b/v/eHb9s/x57E9e/ull7A67v0MSQtQR\nlU0q4jTQo1kPggJMy+ih3EMcPHbQzxEJIeqKSu1RL04PzaOaM7LDSP489idjO4+lQYiM1xBCWHOi\npFLW/BOZk1JPFBQX8L/t/yMxLpEuTbp4nLuww4UysksIUWknSirvKKXyvY69X8Yxh9ZaVWFcoprt\nObqHRT8s4tDxQ8RHxDNz8ExCAkNKzktCEUKcjIqSystlHFtXXYGImhUfHk9eUR4Ah44fYt2edQxp\nN8TPUQkh6rpyk4rWekJNBiJqVmRIJJd0vIRlqcu49MxLGdBqgL9DEkLUA9JRX8/ZHXbW7VmHAwfn\ntDnH49zA1gPpldCLiOAIP0UnhKhvJKnUY5m5mTyz/hnSs9MJDQqlR7MeHpMWbTabJBQhRJWSeSr1\nWMOwhtic81Xzi/L5dMenfo5ICFHfSVKpRxwOz9HeAbYALut0GaFBoYzpOIYxHcf4KTIhxOlCmr/q\ngYzjGSzfthyA63tc73Guc+POzB02l8iQSH+EJoQ4zUhSqeMOHT/EA58/gN1hx2azMTxxOAlRCSXn\nbTabJBQhRI2R5q86Lj4ins5NOgOm+Wtj+kY/RySEOJ1JTaUOSTuSht1hp31se4/jo88YTUFxAaPP\nGE2H+A5+ik4IISSp1Anp2em8tvk1th3aRvvY9tw34D6PZVTaNGzDPf3u8WOEQghhSPNXHRARHMGu\nw7sA2HV4FzsP7/RzREIIUTZJKrVMenY6uYW5HsdiwmLo27IvAbYA+rbsS1RIlJ+iE0KIiknzVy2x\n9c+trNi+gm2HtnFF5ysY1n6Yx/nRZ4xm9BmjiQ2P9VOEQghxYpJUaonM3Ey2HdoGwNrdaxnabqhH\nv0mdSSZ2OxQXQ1GRKXZ7afGanInNZkpAgCmBgaYEBZlHWX5fiDpHkkoNO5J3hO2HttOnRR+P470S\nevHmL29SWFxIQlQCuUW5Nbcul8MB+fmQkwPHjsHx46WPubmmHD8OeXmlJT/flIICUwoLzaO9Cvez\nDwoyJSSktISFQWioKWFhpoSHl5aIiNISGWlKeLgkKCFqiCSVGmJ32Pnnd/9EH9IAdIjvQMOwhiXn\nw4LCmNhzIq2iW1VNrSQ/H7KySkt2dtnFlUiKi0/9M6uaq7aTl3dq97HZShNMgwaeJSqqtERHm8cG\nDUwyE0JUmvzPqSYOh8Oj+SrAFoDNZitZn+v7fd9zXuJ5Hu/p1rRbxTe1200iOHrUJIqjR8t+npVl\nkoo/2GylzVeuEhBQ2szlusbhKC2u5rHi4tKms6pMcg6HSZ45OXDggLX3RER4JproaM/ifiwk5MT3\nE+I0IUmlCh3IOcCG/Rv4+cDPpLROIaVNisf5Pgl9SM1IRcUrmjVoVnrCvVZRVqJwlexs336JqhIS\n4vnbvHszknvzkqvZydUEFRpq3hscbEpV9YU4HCa5uJrVXMXV7ObeFJebax6PH/csx46ZcjI1Hdc9\nrCSh0FDfpOOdeFzPQ0OlKU7Ua5JUqtDWjK18pD8CHEQSQkq4MonAmTB6H82k69HeRO8tgq8+gay3\nqq9WERRkvshiYjy/1FzNO9HRns1AwcFVH8OpsNlKE1XEKfYtFReb5OJq6nM1++XkeDYDujcTViZ5\n56tu7oUAAA+MSURBVOfDn3+aciKuvxfXn79785t7k5zrufQHiTpGksqJuDqxjx2jKPso+o8tpB7c\nyvHco4yP7F/65ZSTQ7esA7xesB4KC9nuWEf+0lRCCSy5VaiznJLISJMoXCU62vO1K5HIl1GpwMDS\nGoMVruYy1y8Ebr8YePRRuZ5XpqmuqAgOHzbFioAAzxqk67l7cQ1KcD26apUBMg1N1LwaTypKqUBg\nDnADEAV8AtyhtS6znUEp1Rv4J5AM7AMe1lovOekA9u0z/6Fdo5rcRze5Sm6u5ygo54imfFshz0R/\nC0AANq44etAjacQBI8Ka0Kq4AZ2KYj3OVSgoqPRL70QJQzqQq5/NVlp7SEio+FqHw/w78U405T0v\nLKxcLK5+tOzsyv8cYWG+zZcREaUj5twf3Yt3E2egxX/HQuCfmspM4HrgOuAQsBB4FxjofaFSqjHw\nKfAacBMwHFislPpDa/1ZpT/57bdh1aoKL/k65A900BF2BWYxOac7sY7SukWkI5gWxZHsCzyGHQfb\ng47SpSjO4/2X5LUzT0JDPZs5ympndxWpVdRd7iPLmjc/8fX5+WWPwPN+dJVTGfnm6nM6Va5h3d79\naK5H9xIc7Pm8vBIUVPro/jw4uHT+kqiTajSpKKVCgLuAO7XWK53HrgJ+U0r111p/4/WWicBR4C6t\ntR1IVUr1BCYDlU8qO3YAcMxWyN6AYzS2hxHnCPO4ZEPwQVKDjgCwKyiLXoWNzT90Z9PD2SEODoc6\n6BjdjqSGSRAd59seHhVV+/ooRO3g+lJu1Mja9UVFpQMOXInGVYvOyfGcU+Q+QKEqkol7DEVF5t41\nwX0EoSvpuE+K9X7uXdwn0rq/dp9k63q02TzPlVVcIxe9H8s67z6ht6zjFRX30ZHuidX7uoqucT0/\n0aMrrmpQ0zWVHpgmrzWuA1rrNKVUGpACeCeVFOBLZ0JxWQMsVErZtNaVGwp1xRW89eFcVudpCArk\nipj+DIvvU9osEB5OuyPfkZrxHQQFsbP9MHolX+vR5HReBbcXosoFBZU2f1aG3V46Is67qde9uCay\nuj/3fqyuEYflcThMM2FlmwqFdcHBMGoUjBhR5beu6aTS0vm4z+v4fqBVOdf/WMa1EUA8kFGpT09M\nJH7M1fDLWwDsbXUm9LjM45LkI82IOdyNtg3b0iqmFQRIH4aogwICSoeEnwrXF7xr9QT3VRTcn3uv\nrOD+vLCwdHi4q7heez8WF1ftqgyibIWFpivg/POrvMZS09+YEYBda+39K0g+EPb/7Z17sN3TFcc/\n95LQqgpS2lQmEcZXU1GPRhFBRko8IuJZqkRrKMVQFVQnXvVK1ShlGCoeqXeUNBpEuEGIZ71jjXe9\ngsQrQcUj/WPtX/Lzyzn33Nyeey/ntz4zZ37n7L1/57f3mnN+67f2XnutKu2Ldnzmf1upfU16r9Cb\nbkt1o9fyvej5zcWnIPr06EOfHn3a89VB0Hg0NS1aI+ksvvhi0ZRbfjNsvqwtr+Km2vz7bNNt9j7f\nvhivrtLnfHl+E29xU2+19/DlttVeWbviOcXzs8/FNtXKl1nGrZQOmALrbKXyMdAsaWkz+yxXvgzw\nYZX2RS/c7HOl9jVZc6U1OWfbc2huCnfLIPhK0tzc+YosqBudfWd9JR2LbjK9WHxKLGtfqe08fAF/\niWluag6FEgRB0EF0tqXyGDAX2AIYDyCpL9AXuKtC+3uA/QqL8kOA6YXF+yJLAcyaNas+vQ6CICgB\nuXtmuzcnNS3Iz711ApJOxzc+jgLewvep/NfMtkwuxysB75jZfEmrAgZcA5wNDAX+DAwzsztaucZm\nwN0dOY4gCIIGZrCZ3dOeE7vCtekPQDfcUulG2lGf6jYF7sStkRYze1PSMOAc3AvsZWCf1hRK4kHc\nHfkN4CsY0z0IguAryVL4ksOD7f2CTrdUgiAIgsYlVqyDIAiCuhFKJQiCIKgboVSCIAiCuhFKJQiC\nIKgbpQlstaR5XBqB5JI9Fo+D+Q3gfuBIM3sy1W+d6gU8CxxtZpO7qLsdjqSN8b1PQ82sJZWVQgaS\n9gdG4zH2ngaOyrwoyyADScsBpwO74OGf7sP/C0+n+oaWgaQLgKXNbP9cWatjlrQK8Ff8/jEfGAcc\nV4iGshhlslROYFEel83xYJUTurJDHYmkZuAfwFrACNxd+31gqqSVJfUHJgLX4QnQbgJulPTDLupy\nh5JuKleQ29RVFhlI2hc4D7+pDgCmARMl9S2LDPBEf0OB3YBN8JiCt0hatpFlIKlJ0knAgYXytox5\nAvBdfLP6KGA/4MRa1yyFS3HaVDkbz+NyaSrrC7wIDKqQx+Vrj6T1gUeA/mY2M5UtA7wDHAQMAmRm\nW+bOuRN41swO6PwedyySLsQV7JbAEDNrSWUNLQNJTfjv/HIzG5PKmvHfxlj8htHQMgCQNBs40czO\nTZ/7A08BG+I33IaTgaR+wN+AdYCPgCmZpVLrty9pEzwVST8zezHV7wucC3zHzD6hCmWxVCrmcQFe\nwjdJNiL/AXbAIxJkZKFtVsTH3VI4p4UGlIek7YDtgcMKVWWQgYA+eFQKAMzsCzNbz8yupBwyAHgb\n2EPSKukh81fAu8ALNK4MNsXjJw7AHyzy1BrzYODlTKHk6pfH76dVKcuaypLmcfnaY2ZzgJsLxYfh\nayu3ASdTAnlI6ok/re2H30TyrEbjy2CtdOwh6Q78qfUZ4JhkoZdBBgAH4FE83sSjbHwEbG1m70lq\nSBmY2XgWxVgsVtcac7V6Upv7q123LJbKkuZxaTgk7QicBpyVpsOq5appNHlcCEw0s1sq1JVBBt9O\nx8uAi4FhwJPAHZJ+QDlkALAmMAu3WAcBtwLXJ4VSFhnkqTXmxerT/XMBNeRSFktlSfO4NBSSRgEX\nAVfjHkBQPVdNw8gjzQGvD6xbpUnDywDIHqROSdNdSPoNPr1xECWQgaTV8d//ZmY2I5XtBcwEjqAE\nMqhArTEvVi+pG9BEDbmUxVJZ0jwuDYOk43BXwAvwYJzZukq1XDWNJI9RuBk/S9I8Fq0vTU4ulmWQ\nQTaWJ7KClEZiJrA65ZDBj3Gvv4eygvTU/W/cgimDDIrUGnO1eqghl7IolXweF6BmHpeGQNJofG/O\nGDM7NJeTBny/xhaFU4bQWPLYG+iPLyyuB2yTyvcHxlAOGTyCP1kOzAqSR1h/4HnKIYNX03GhxZqT\nwbOUQwZFao35HqCfpN6F+rnAo619cSlciqH1PC5d16uOQ9K6+A3lMuC4QvVcoB/wML7OchWwF3AU\nsEHmgtxopPnzV1jkUjyAEshA0sl4eon9cYvlYODXuKLtToPLIG18vgdYDh/7bOBw4Oe448K3aXwZ\ntADP5VyKW/3tJ6V7L76GcgiwKn4vOd/MTmjtWmWxVMDzuPwd94a4E8/NsmuX9qhj+Rlu8v8SzyuT\nfx1hZk8AI3EZPArsCAxvlD9RWyiRDMYAf8IT3T2Bb/7b2pyGl4GZfQ4Mxz2WrgZm4NNeg83s5TLI\noEitMadZjZG4t9zd+BT6xcBJtb67NJZKEARB0PGUyVIJgiAIOphQKkEQBEHdCKUSBEEQ1I1QKkEQ\nBEHdCKUSBEEQ1I1QKkEQBEHdKEvsr6DBkXQpnoStNaaZ2ZZpI9hnZja0wztWBUkr4ZtTh5rZc1Xa\njML3B/Q2s1crtemgvk0FLjSzazvrmkHjEEolaBROxuObZZwPfMaXc6h8kI4H4zuFu5JzgWurKZQu\n5ghgiqQWM3urqzsTfL0IpRI0BGb2PB7LCgBJH+DWyIwKbZ/uzL4VkTQQT2vbq1bbrsDMHpc0A49C\nUUxsFgStEkolKB3F6S9JC/CUspsDI/A8EufiYU3OBnbBQ4Ffhie3WpDOWxnP+z4Cz4j3MHC0mU2v\n0YWj8dSus3N9agZ+jyeT6oknUlssoKGkA1ObtfE10Zl4WPsJaUrtdWBsljo4nbMCnkvkd2Z2nqQ9\ngWPwBF5z07VGm9nruUtdCVwi6WQze7vGeIJgIbFQHwTOmXigwRHAJOBE4AE8Q+DOwA14LpqdASQt\nC0zFkz4di8dQeheYmiyRikj6Fh5naUKhaixwPB5faSQwB1dY+XMPA85L526PB0T8FLhK0vfN7B1g\nYirPsweeB+MqSYOAK9J3DAN+C2yFx8XLMwmPHbdTtbEEQSXCUgkC5xEzOxxA0mOkaNZmdkgquwO/\nWW+C35B/gYdS38jMHkptJuOK6FTgp1WuMxjoltqRzuuBTzOdaWZZwL5bJfXCb/wZq+NWyKm5c1/C\nLaRNgeuAS4DdJA3KWUz7AP80s3ckDcYV5Rlm9kn6jjnAQElNmRVmZh9KmomHO7+oTRIMAkKpBEHG\nwpzbZjZH0ueFsgWS3gV6pKKt8GRFj0rK/48mAcdK6m5m8ytcp186vpgr2xhXNDcV2l5LTqmY2RGw\nUAmtjUfaHZKqu6fjbXj+kL2B6ZLWwNPn7pDqpwGnAE9Kuh74F3CbmU2u0NeX8JxDQdBmYvorCJy5\nFcpaS5u6Mp5V8tPC63j8Bt+zynkrpONHubKV0rG4dvFG/oOkNSTdjk+zTcPzX3RL1U0AKbPn5cDu\nkrrjVsobwC2p/j5gO+AFfOrrLuA1SYdW6OuHuf4GQZsIpRIE7eN9fJF8YJXX7CrnZeUrVChbtdB2\n5exNWsi/GVdWA4HlzOxHFNZdEuNwRTUU2B0Yn3KKAGBmt5rZNsCKeJ6RJ4BzJG1Y+J4VWxlHEFQk\npr+CoH1MA7YFXs97TaUsi32ovhHz5XRcDXgvvb8X9y7bLb3PGJ573xMQcEi2hpPYNh0XPiCa2XOS\n7sIdC9bGvdey/p2BT5n9xMw+AiZJegVP1NQbX5/JWA14vMo4gqAioVSCoH2MAw4Fbpd0Kr6+sgM+\npXRituBdgbtxBbIZ8CSAmc1LyuiPkj4GWnDvroVKxczeSovyh0l6Hd/IuQ2eFhc8VW6xf+OABwv7\ncm7Hp80ulTQen6objVskLVmj5Ia8Dp4xMgjaTEx/BUE7MLN5uCfX/cBZ+IL3MODQ1nJ4J+tgMoss\njKz8NFxB7IG7BQ8AjiycvhO+PnI5cA2+wD8ceCb1Jc+kdBxXuM4UYE9cYdyA5yefBwwxs/dyTbcG\n5uNTbkHQZiKdcBB0MpI2AqYDfc3stQ66xj542Jrvmdn77Th/CvBU5mYdBG0lLJUg6GTM7AHgRha3\nRP5vJI1M03F/AS5qp0LZANiAyk4AQdAqoVSCoGs4GNhV0pp1/t6++DTafXjsrvZwFu4QMKtenQrK\nQ0x/BUEQBHUjLJUgCIKgboRSCYIgCOpGKJUgCIKgboRSCYIgCOpGKJUgCIKgboRSCYIgCOrG/wDK\ne236ks8bQQAAAABJRU5ErkJggg==\n",
+ "text/plain": [
+ "| \n", + " | S | \n", + "I | \n", + "R | \n", + "
|---|---|---|---|
| 0 | \n", + "0.988889 | \n", + "0.011111 | \n", + "0.000000 | \n", + "
| 1 | \n", + "0.985226 | \n", + "0.011996 | \n", + "0.002778 | \n", + "
| 2 | \n", + "0.981287 | \n", + "0.012936 | \n", + "0.005777 | \n", + "
| 3 | \n", + "0.977055 | \n", + "0.013934 | \n", + "0.009011 | \n", + "
| 4 | \n", + "0.972517 | \n", + "0.014988 | \n", + "0.012494 | \n", + "
\n",
+ "\n",
+ "\n",
+ " \n",
+ "
\n",
+ "
"
+ ],
+ "text/plain": [
+ " S I R\n",
+ "0 0.988889 0.011111 0.000000\n",
+ "1 0.985230 0.011992 0.002778\n",
+ "2 0.981296 0.012929 0.005776\n",
+ "3 0.977071 0.013921 0.009008\n",
+ "4 0.972541 0.014970 0.012488"
+ ]
+ },
+ "execution_count": 36,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "system = make_system(0.333, 0.25)\n",
+ "run_simulation(system, update1)\n",
+ "system.results.head()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 37,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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RGBBIbFisV/6MATMAsNlsRIVGeeX7S7lBRWu9FFgKoJQqAfprrctb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\no6FlACBpHnCWmV2S/u4DvABsgz9wG04GknoDfwI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+ "text/plain": [
+ "| \n", + " | S | \n", + "I | \n", + "R | \n", + "
|---|---|---|---|
| 0 | \n", + "0.988889 | \n", + "0.011111 | \n", + "0.000000 | \n", + "
| 1 | \n", + "0.985230 | \n", + "0.011992 | \n", + "0.002778 | \n", + "
| 2 | \n", + "0.981296 | \n", + "0.012929 | \n", + "0.005776 | \n", + "
| 3 | \n", + "0.977071 | \n", + "0.013921 | \n", + "0.009008 | \n", + "
| 4 | \n", + "0.972541 | \n", + "0.014970 | \n", + "0.012488 | \n", + "
\n",
+ "\n",
+ "\n",
+ " \n",
+ "
\n",
+ "
"
+ ],
+ "text/plain": [
+ " 0.1 0.3 0.5 0.7\n",
+ "0.10 0.084693 0.005444 0.002736 0.001827\n",
+ "0.18 0.708623 0.015914 0.006118 0.003783\n",
+ "0.26 0.900780 0.055380 0.011639 0.006427\n",
+ "0.34 0.956888 0.267864 0.022115 0.010191\n",
+ "0.42 0.977045 0.524563 0.047816 0.015946"
+ ]
+ },
+ "execution_count": 47,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "frame = sweep_parameters(beta_array, gamma_array)\n",
+ "frame.head()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "And here's how we can plot the results."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 48,
+ "metadata": {
+ "scrolled": true
+ },
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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zT7VKNe7t7sWskXHCViFohaGyksbSUjyGDUPdxeVrR20YrwAvthQLAFmW06z2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\no1XXv0iK8Vxo1825OMdSzXz6duzUgXlTpKtjiIN7TzHqC0T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vAf+QDUGnKXeS5P2zI4T4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\nrTA0Go1GkxRaYWg0Go0mKf4/WiN5xooTtR0AAAAASUVORK5CYII=\n",
+ "text/plain": [
+ "| \n", + " | 0.1 | \n", + "0.3 | \n", + "0.5 | \n", + "0.7 | \n", + "
|---|---|---|---|---|
| 0.10 | \n", + "0.084693 | \n", + "0.005444 | \n", + "0.002736 | \n", + "0.001827 | \n", + "
| 0.18 | \n", + "0.708623 | \n", + "0.015914 | \n", + "0.006118 | \n", + "0.003783 | \n", + "
| 0.26 | \n", + "0.900780 | \n", + "0.055380 | \n", + "0.011639 | \n", + "0.006427 | \n", + "
| 0.34 | \n", + "0.956888 | \n", + "0.267864 | \n", + "0.022115 | \n", + "0.010191 | \n", + "
| 0.42 | \n", + "0.977045 | \n", + "0.524563 | \n", + "0.047816 | \n", + "0.015946 | \n", + "
\n",
+ "\n",
+ "\n",
+ " \n",
+ "
\n",
+ "
"
+ ],
+ "text/plain": [
+ "temp 90\n",
+ "dtype: int64"
+ ]
+ },
+ "execution_count": 2,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "init = State(temp=90)\n",
+ "init"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "And a `System` object to contain the system parameters."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "| \n", + " | value | \n", + "
|---|---|
| temp | \n", + "90 | \n", + "
\n",
+ "\n",
+ "\n",
+ " \n",
+ "
\n",
+ "
"
+ ],
+ "text/plain": [
+ "init temp 90\n",
+ "dtype: int64\n",
+ "volume 300\n",
+ "r 0.01\n",
+ "T_env 22\n",
+ "t0 0\n",
+ "t_end 30\n",
+ "dt 1\n",
+ "dtype: object"
+ ]
+ },
+ "execution_count": 3,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "coffee = System(init=init,\n",
+ " volume=300,\n",
+ " r=0.01,\n",
+ " T_env=22,\n",
+ " t0=0, \n",
+ " t_end=30,\n",
+ " dt=1)\n",
+ "coffee"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "The `update` function implements Newton's law of cooling."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "def update(state, system):\n",
+ " \"\"\"Update the thermal transfer model.\n",
+ " \n",
+ " state: State (temp)\n",
+ " system: System object\n",
+ " \n",
+ " returns: State (temp)\n",
+ " \"\"\"\n",
+ " unpack(system)\n",
+ " T = state.temp\n",
+ " T += -r * (T - T_env) * dt\n",
+ "\n",
+ " return State(temp=T)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Here's how it works."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "| \n", + " | value | \n", + "
|---|---|
| init | \n", + "temp 90\n", + "dtype: int64 | \n", + "
| volume | \n", + "300 | \n", + "
| r | \n", + "0.01 | \n", + "
| T_env | \n", + "22 | \n", + "
| t0 | \n", + "0 | \n", + "
| t_end | \n", + "30 | \n", + "
| dt | \n", + "1 | \n", + "
\n",
+ "\n",
+ "\n",
+ " \n",
+ "
\n",
+ "
"
+ ],
+ "text/plain": [
+ "temp 89.32\n",
+ "dtype: float64"
+ ]
+ },
+ "execution_count": 6,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "update(init, coffee)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Now we can run simulations using the same function from the previous chapter."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "def run_simulation(system, update_func):\n",
+ " \"\"\"Runs a simulation of the system.\n",
+ " \n",
+ " Add a TimeFrame to the System: results\n",
+ " \n",
+ " system: System object\n",
+ " update_func: function that updates state\n",
+ " \"\"\"\n",
+ " unpack(system)\n",
+ " \n",
+ " frame = TimeFrame(columns=init.index)\n",
+ " frame.loc[t0] = init\n",
+ " ts = linrange(t0, t_end-dt, dt)\n",
+ " \n",
+ " for t in ts:\n",
+ " frame.loc[t+dt] = update_func(frame.loc[t], system)\n",
+ " \n",
+ " system.results = frame"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "And here's how it works."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "| \n", + " | value | \n", + "
|---|---|
| temp | \n", + "89.32 | \n", + "
\n",
+ "\n",
+ "\n",
+ " \n",
+ "
\n",
+ "
"
+ ],
+ "text/plain": [
+ " temp\n",
+ "0 90.000000\n",
+ "1 89.320000\n",
+ "2 88.646800\n",
+ "3 87.980332\n",
+ "4 87.320529\n",
+ "5 86.667323\n",
+ "6 86.020650\n",
+ "7 85.380444\n",
+ "8 84.746639\n",
+ "9 84.119173\n",
+ "10 83.497981\n",
+ "11 82.883001\n",
+ "12 82.274171\n",
+ "13 81.671430\n",
+ "14 81.074715\n",
+ "15 80.483968\n",
+ "16 79.899128\n",
+ "17 79.320137\n",
+ "18 78.746936\n",
+ "19 78.179466\n",
+ "20 77.617672\n",
+ "21 77.061495\n",
+ "22 76.510880\n",
+ "23 75.965771\n",
+ "24 75.426114\n",
+ "25 74.891852\n",
+ "26 74.362934\n",
+ "27 73.839305\n",
+ "28 73.320912\n",
+ "29 72.807702\n",
+ "30 72.299625"
+ ]
+ },
+ "execution_count": 8,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "run_simulation(coffee, update)\n",
+ "coffee.results"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Here's what the results look like."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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sbCxJQnQp3V0scbYz5ZfTOZxLuwxAdW09O4+kk5xRzPBgd8yM5alCdH0aTYFd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\nvPPOO20dpxCiE3JzMGditC+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+ "text/plain": [
+ "| \n", + " | temp | \n", + "
|---|---|
| 0 | \n", + "90.000000 | \n", + "
| 1 | \n", + "89.320000 | \n", + "
| 2 | \n", + "88.646800 | \n", + "
| 3 | \n", + "87.980332 | \n", + "
| 4 | \n", + "87.320529 | \n", + "
| 5 | \n", + "86.667323 | \n", + "
| 6 | \n", + "86.020650 | \n", + "
| 7 | \n", + "85.380444 | \n", + "
| 8 | \n", + "84.746639 | \n", + "
| 9 | \n", + "84.119173 | \n", + "
| 10 | \n", + "83.497981 | \n", + "
| 11 | \n", + "82.883001 | \n", + "
| 12 | \n", + "82.274171 | \n", + "
| 13 | \n", + "81.671430 | \n", + "
| 14 | \n", + "81.074715 | \n", + "
| 15 | \n", + "80.483968 | \n", + "
| 16 | \n", + "79.899128 | \n", + "
| 17 | \n", + "79.320137 | \n", + "
| 18 | \n", + "78.746936 | \n", + "
| 19 | \n", + "78.179466 | \n", + "
| 20 | \n", + "77.617672 | \n", + "
| 21 | \n", + "77.061495 | \n", + "
| 22 | \n", + "76.510880 | \n", + "
| 23 | \n", + "75.965771 | \n", + "
| 24 | \n", + "75.426114 | \n", + "
| 25 | \n", + "74.891852 | \n", + "
| 26 | \n", + "74.362934 | \n", + "
| 27 | \n", + "73.839305 | \n", + "
| 28 | \n", + "73.320912 | \n", + "
| 29 | \n", + "72.807702 | \n", + "
| 30 | \n", + "72.299625 | \n", + "
\n",
+ "\n",
+ "\n",
+ " \n",
+ "
\n",
+ "
"
+ ],
+ "text/plain": [
+ "temp 5.17\n",
+ "dtype: float64"
+ ]
+ },
+ "execution_count": 29,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "update(init,milk)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 30,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "| \n", + " | value | \n", + "
|---|---|
| temp | \n", + "5.17 | \n", + "
\n",
+ "\n",
+ "\n",
+ " \n",
+ "
\n",
+ "
"
+ ],
+ "text/plain": [
+ " temp\n",
+ "0 5.000000\n",
+ "1 5.170000\n",
+ "2 5.338300\n",
+ "3 5.504917\n",
+ "4 5.669868\n",
+ "5 5.833169\n",
+ "6 5.994837\n",
+ "7 6.154889\n",
+ "8 6.313340\n",
+ "9 6.470207\n",
+ "10 6.625505\n",
+ "11 6.779250\n",
+ "12 6.931457\n",
+ "13 7.082143\n",
+ "14 7.231321\n",
+ "15 7.379008"
+ ]
+ },
+ "execution_count": 30,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "run_simulation(milk, update)\n",
+ "milk.results"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 31,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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LJ89EKGRwLbsCv/x9C4XljaJ2EyMdvBzugqH+9lSvhJCnINccyj///INly5bB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\nhRSUNeDU1Xw0ttAy84SQ7oc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| 1 | \n", + "5.170000 | \n", + "
| 2 | \n", + "5.338300 | \n", + "
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| 4 | \n", + "5.669868 | \n", + "
| 5 | \n", + "5.833169 | \n", + "
| 6 | \n", + "5.994837 | \n", + "
| 7 | \n", + "6.154889 | \n", + "
| 8 | \n", + "6.313340 | \n", + "
| 9 | \n", + "6.470207 | \n", + "
| 10 | \n", + "6.625505 | \n", + "
| 11 | \n", + "6.779250 | \n", + "
| 12 | \n", + "6.931457 | \n", + "
| 13 | \n", + "7.082143 | \n", + "
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| 15 | \n", + "7.379008 | \n", + "
\n",
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+ },
+ "execution_count": 164,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "coffee.results - coffee2.results"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
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diff --git a/code/chap08mine.ipynb b/code/chap08mine.ipynb
new file mode 100644
index 00000000..59d9190e
--- /dev/null
+++ b/code/chap08mine.ipynb
@@ -0,0 +1,2954 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Modeling and Simulation in Python\n",
+ "\n",
+ "Chapter 8: Pharmacokinetics\n",
+ "\n",
+ "Copyright 2017 Allen Downey\n",
+ "\n",
+ "License: [Creative Commons Attribution 4.0 International](https://creativecommons.org/licenses/by/4.0)\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 436,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "# If you want the figures to appear in the notebook, \n",
+ "# and you want to interact with them, use\n",
+ "# %matplotlib notebook\n",
+ "\n",
+ "# If you want the figures to appear in the notebook, \n",
+ "# and you don't want to interact with them, use\n",
+ "# %matplotlib inline\n",
+ "\n",
+ "# If you want the figures to appear in separate windows, use\n",
+ "# %matplotlib qt5\n",
+ "\n",
+ "# tempo switch from one to another, you have to select Kernel->Restart\n",
+ "\n",
+ "%matplotlib inline\n",
+ "\n",
+ "from modsim import *"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Data\n",
+ "\n",
+ "We have data from Pacini and Bergman (1986), \"MINMOD: a computer program to calculate insulin sensitivity and pancreatic responsivity from the frequently sampled intravenous glucose tolerance test\", *Computer Methods and Programs in Biomedicine*, 23: 113-122.."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 437,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
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| 2 | \n", + "0.000000e+00 | \n", + "
| 3 | \n", + "0.000000e+00 | \n", + "
| 4 | \n", + "0.000000e+00 | \n", + "
| 5 | \n", + "0.000000e+00 | \n", + "
| 6 | \n", + "0.000000e+00 | \n", + "
| 7 | \n", + "0.000000e+00 | \n", + "
| 8 | \n", + "0.000000e+00 | \n", + "
| 9 | \n", + "0.000000e+00 | \n", + "
| 10 | \n", + "0.000000e+00 | \n", + "
| 11 | \n", + "0.000000e+00 | \n", + "
| 12 | \n", + "0.000000e+00 | \n", + "
| 13 | \n", + "-1.421085e-14 | \n", + "
| 14 | \n", + "-1.421085e-14 | \n", + "
| 15 | \n", + "0.000000e+00 | \n", + "
| 16 | \n", + "-1.421085e-14 | \n", + "
| 17 | \n", + "-1.421085e-14 | \n", + "
| 18 | \n", + "-1.421085e-14 | \n", + "
| 19 | \n", + "0.000000e+00 | \n", + "
| 20 | \n", + "-1.421085e-14 | \n", + "
| 21 | \n", + "0.000000e+00 | \n", + "
| 22 | \n", + "0.000000e+00 | \n", + "
| 23 | \n", + "0.000000e+00 | \n", + "
| 24 | \n", + "0.000000e+00 | \n", + "
| 25 | \n", + "0.000000e+00 | \n", + "
| 26 | \n", + "-1.421085e-14 | \n", + "
| 27 | \n", + "0.000000e+00 | \n", + "
| 28 | \n", + "-1.421085e-14 | \n", + "
| 29 | \n", + "0.000000e+00 | \n", + "
| 30 | \n", + "0.000000e+00 | \n", + "
\n",
+ "\n",
+ "\n",
+ " \n",
+ "
\n",
+ "
"
+ ],
+ "text/plain": [
+ " glucose insulin\n",
+ "time \n",
+ "0 92 11\n",
+ "2 350 26\n",
+ "4 287 130\n",
+ "6 251 85\n",
+ "8 240 51\n",
+ "10 216 49\n",
+ "12 211 45\n",
+ "14 205 41\n",
+ "16 196 35\n",
+ "19 192 30\n",
+ "22 172 30\n",
+ "27 163 27\n",
+ "32 142 30\n",
+ "42 124 22\n",
+ "52 105 15\n",
+ "62 92 15\n",
+ "72 84 11\n",
+ "82 77 10\n",
+ "92 82 8\n",
+ "102 81 11\n",
+ "122 82 7\n",
+ "142 82 8\n",
+ "162 85 8\n",
+ "182 90 7"
+ ]
+ },
+ "execution_count": 437,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "data = pd.read_csv('glucose_insulin.csv', index_col='time')\n",
+ "data"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Here's what the glucose time series looks like."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 438,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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iiFsD6UjKB3eSjcCnchMO5wN7ufuG6OclUfPYKDMbQ2je2jP5AjPrQJgZ36i+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\nMpTvS9gzPlWX6PWjHMSQSep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+ "text/plain": [
+ "| \n", + " | glucose | \n", + "insulin | \n", + "
|---|---|---|
| time | \n", + "\n", + " | \n", + " |
| 0 | \n", + "92 | \n", + "11 | \n", + "
| 2 | \n", + "350 | \n", + "26 | \n", + "
| 4 | \n", + "287 | \n", + "130 | \n", + "
| 6 | \n", + "251 | \n", + "85 | \n", + "
| 8 | \n", + "240 | \n", + "51 | \n", + "
| 10 | \n", + "216 | \n", + "49 | \n", + "
| 12 | \n", + "211 | \n", + "45 | \n", + "
| 14 | \n", + "205 | \n", + "41 | \n", + "
| 16 | \n", + "196 | \n", + "35 | \n", + "
| 19 | \n", + "192 | \n", + "30 | \n", + "
| 22 | \n", + "172 | \n", + "30 | \n", + "
| 27 | \n", + "163 | \n", + "27 | \n", + "
| 32 | \n", + "142 | \n", + "30 | \n", + "
| 42 | \n", + "124 | \n", + "22 | \n", + "
| 52 | \n", + "105 | \n", + "15 | \n", + "
| 62 | \n", + "92 | \n", + "15 | \n", + "
| 72 | \n", + "84 | \n", + "11 | \n", + "
| 82 | \n", + "77 | \n", + "10 | \n", + "
| 92 | \n", + "82 | \n", + "8 | \n", + "
| 102 | \n", + "81 | \n", + "11 | \n", + "
| 122 | \n", + "82 | \n", + "7 | \n", + "
| 142 | \n", + "82 | \n", + "8 | \n", + "
| 162 | \n", + "85 | \n", + "8 | \n", + "
| 182 | \n", + "90 | \n", + "7 | \n", + "
\n",
+ "\n",
+ "\n",
+ " \n",
+ "
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+ "
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+ ],
+ "text/plain": [
+ "G 287.03\n",
+ "X 0.00\n",
+ "dtype: float64"
+ ]
+ },
+ "execution_count": 450,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "update_func(init, 0, system)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Now run simulation is pretty much the same as it always is."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 451,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "def run_simulation(system, update_func):\n",
+ " \"\"\"Runs a simulation of the system.\n",
+ " \n",
+ " Adds a TimeFrame to `system` as `results`\n",
+ " \n",
+ " system: System object\n",
+ " update_func: function that updates state\n",
+ " \"\"\"\n",
+ " unpack(system)\n",
+ " \n",
+ " frame = TimeFrame(columns=init.index)\n",
+ " frame.loc[t0] = init\n",
+ " ts = linrange(t0, t_end-dt, dt)\n",
+ " \n",
+ " for t in ts:\n",
+ " frame.loc[t+dt] = update_func(frame.loc[t], t, system)\n",
+ " \n",
+ " system.results = frame"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "And here's how we run it. `%time` is a Jupyter magic command that runs the function and reports its run time."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 452,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Wall time: 700 ms\n"
+ ]
+ }
+ ],
+ "source": [
+ "%time run_simulation(system, update_func)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "The results are in a `TimeFrame object` with one column per state variable."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 453,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
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+ "... ... ...\n",
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+ "173.5 91.049626 -0.000591\n",
+ "174.0 91.090802 -0.000603\n",
+ "174.5 91.131899 -0.000614\n",
+ "175.0 91.172917 -0.000626\n",
+ "175.5 91.213861 -0.000638\n",
+ "176.0 91.254731 -0.000649\n",
+ "176.5 91.295531 -0.000661\n",
+ "177.0 91.336264 -0.000673\n",
+ "177.5 91.376932 -0.000684\n",
+ "178.0 91.417539 -0.000696\n",
+ "178.5 91.458085 -0.000708\n",
+ "179.0 91.498576 -0.000719\n",
+ "179.5 91.539013 -0.000731\n",
+ "180.0 91.579400 -0.000743\n",
+ "180.5 91.619739 -0.000755\n",
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+ "182.0 91.740501 -0.000791\n",
+ "\n",
+ "[365 rows x 2 columns]"
+ ]
+ },
+ "execution_count": 453,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "system.results"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "The following plot shows the results of the simulation along with the actual glucose data."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 454,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Saving figure to file chap08-fig03.pdf\n"
+ ]
+ },
+ {
+ "data": {
+ "image/png": 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k8gjKsEpv34RXgVeNMVWAX+GCh2eA2caYr3HBwyJvPwfx0717fuAAru9CYDMF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+ "text/plain": [
+ "| \n", + " | G | \n", + "X | \n", + "
|---|---|---|
| 0.0 | \n", + "290.000000 | \n", + "0.000000 | \n", + "
| 0.5 | \n", + "287.030000 | \n", + "0.000000 | \n", + "
| 1.0 | \n", + "284.104550 | \n", + "-0.000044 | \n", + "
| 1.5 | \n", + "281.229268 | \n", + "-0.000090 | \n", + "
| 2.0 | \n", + "278.403529 | \n", + "-0.000096 | \n", + "
| 2.5 | \n", + "275.620863 | \n", + "-0.000020 | \n", + "
| 3.0 | \n", + "272.869334 | \n", + "0.000179 | \n", + "
| 3.5 | \n", + "270.131906 | \n", + "0.000541 | \n", + "
| 4.0 | \n", + "267.386792 | \n", + "0.001052 | \n", + "
| 4.5 | \n", + "264.615400 | \n", + "0.001636 | \n", + "
| 5.0 | \n", + "261.809705 | \n", + "0.002223 | \n", + "
| 5.5 | \n", + "258.971601 | \n", + "0.002740 | \n", + "
| 6.0 | \n", + "256.112255 | \n", + "0.003160 | \n", + "
| 6.5 | \n", + "253.245932 | \n", + "0.003498 | \n", + "
| 7.0 | \n", + "250.384283 | \n", + "0.003770 | \n", + "
| 7.5 | \n", + "247.536483 | \n", + "0.003992 | \n", + "
| 8.0 | \n", + "244.709378 | \n", + "0.004176 | \n", + "
| 8.5 | \n", + "241.907820 | \n", + "0.004334 | \n", + "
| 9.0 | \n", + "239.134995 | \n", + "0.004478 | \n", + "
| 9.5 | \n", + "236.392528 | \n", + "0.004620 | \n", + "
| 10.0 | \n", + "233.680592 | \n", + "0.004763 | \n", + "
| 10.5 | \n", + "230.998839 | \n", + "0.004906 | \n", + "
| 11.0 | \n", + "228.347255 | \n", + "0.005044 | \n", + "
| 11.5 | \n", + "225.726142 | \n", + "0.005176 | \n", + "
| 12.0 | \n", + "223.136086 | \n", + "0.005300 | \n", + "
| 12.5 | \n", + "220.577749 | \n", + "0.005417 | \n", + "
| 13.0 | \n", + "218.051663 | \n", + "0.005528 | \n", + "
| 13.5 | \n", + "215.558239 | \n", + "0.005633 | \n", + "
| 14.0 | \n", + "213.097773 | \n", + "0.005732 | \n", + "
| 14.5 | \n", + "210.670550 | \n", + "0.005825 | \n", + "
| ... | \n", + "... | \n", + "... | \n", + "
| 167.5 | \n", + "90.548441 | \n", + "-0.000454 | \n", + "
| 168.0 | \n", + "90.590749 | \n", + "-0.000465 | \n", + "
| 168.5 | \n", + "90.632952 | \n", + "-0.000477 | \n", + "
| 169.0 | \n", + "90.675052 | \n", + "-0.000488 | \n", + "
| 169.5 | \n", + "90.717051 | \n", + "-0.000499 | \n", + "
| 170.0 | \n", + "90.758950 | \n", + "-0.000511 | \n", + "
| 170.5 | \n", + "90.800752 | \n", + "-0.000522 | \n", + "
| 171.0 | \n", + "90.842458 | \n", + "-0.000534 | \n", + "
| 171.5 | \n", + "90.884070 | \n", + "-0.000545 | \n", + "
| 172.0 | \n", + "90.925591 | \n", + "-0.000557 | \n", + "
| 172.5 | \n", + "90.967023 | \n", + "-0.000568 | \n", + "
| 173.0 | \n", + "91.008367 | \n", + "-0.000580 | \n", + "
| 173.5 | \n", + "91.049626 | \n", + "-0.000591 | \n", + "
| 174.0 | \n", + "91.090802 | \n", + "-0.000603 | \n", + "
| 174.5 | \n", + "91.131899 | \n", + "-0.000614 | \n", + "
| 175.0 | \n", + "91.172917 | \n", + "-0.000626 | \n", + "
| 175.5 | \n", + "91.213861 | \n", + "-0.000638 | \n", + "
| 176.0 | \n", + "91.254731 | \n", + "-0.000649 | \n", + "
| 176.5 | \n", + "91.295531 | \n", + "-0.000661 | \n", + "
| 177.0 | \n", + "91.336264 | \n", + "-0.000673 | \n", + "
| 177.5 | \n", + "91.376932 | \n", + "-0.000684 | \n", + "
| 178.0 | \n", + "91.417539 | \n", + "-0.000696 | \n", + "
| 178.5 | \n", + "91.458085 | \n", + "-0.000708 | \n", + "
| 179.0 | \n", + "91.498576 | \n", + "-0.000719 | \n", + "
| 179.5 | \n", + "91.539013 | \n", + "-0.000731 | \n", + "
| 180.0 | \n", + "91.579400 | \n", + "-0.000743 | \n", + "
| 180.5 | \n", + "91.619739 | \n", + "-0.000755 | \n", + "
| 181.0 | \n", + "91.660033 | \n", + "-0.000767 | \n", + "
| 181.5 | \n", + "91.700286 | \n", + "-0.000779 | \n", + "
| 182.0 | \n", + "91.740501 | \n", + "-0.000791 | \n", + "
365 rows × 2 columns
\n", + "\n",
+ "\n",
+ "\n",
+ " \n",
+ "
\n",
+ "
"
+ ],
+ "text/plain": [
+ " G X\n",
+ "time \n",
+ "0 290.000000 0.000000\n",
+ "2 278.503218 -0.000072\n",
+ "4 267.407044 0.001329\n",
+ "6 255.962566 0.003315\n",
+ "8 244.552487 0.004232\n",
+ "10 233.570125 0.004808\n",
+ "12 223.075469 0.005331\n",
+ "14 213.094204 0.005750\n",
+ "16 203.651201 0.006054\n",
+ "19 190.540814 0.006312\n",
+ "22 178.671483 0.006494\n",
+ "27 161.389180 0.006705\n",
+ "32 146.879018 0.006894\n",
+ "42 124.440473 0.007088\n",
+ "52 109.230932 0.006417\n",
+ "62 99.405510 0.005610\n",
+ "72 93.178906 0.004775\n",
+ "82 89.501328 0.003855\n",
+ "92 87.562395 0.002954\n",
+ "102 86.786289 0.002279\n",
+ "122 86.832321 0.001258\n",
+ "142 88.339444 0.000219\n",
+ "162 90.119786 -0.000323\n",
+ "182 91.759885 -0.000789"
+ ]
+ },
+ "execution_count": 460,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "system2.results"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Plotting the results from `run_simulation` and `run_odeint`, we can see that they are not very different."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 461,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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+ "text/plain": [
+ "| \n", + " | G | \n", + "X | \n", + "
|---|---|---|
| time | \n", + "\n", + " | \n", + " |
| 0 | \n", + "290.000000 | \n", + "0.000000 | \n", + "
| 2 | \n", + "278.503218 | \n", + "-0.000072 | \n", + "
| 4 | \n", + "267.407044 | \n", + "0.001329 | \n", + "
| 6 | \n", + "255.962566 | \n", + "0.003315 | \n", + "
| 8 | \n", + "244.552487 | \n", + "0.004232 | \n", + "
| 10 | \n", + "233.570125 | \n", + "0.004808 | \n", + "
| 12 | \n", + "223.075469 | \n", + "0.005331 | \n", + "
| 14 | \n", + "213.094204 | \n", + "0.005750 | \n", + "
| 16 | \n", + "203.651201 | \n", + "0.006054 | \n", + "
| 19 | \n", + "190.540814 | \n", + "0.006312 | \n", + "
| 22 | \n", + "178.671483 | \n", + "0.006494 | \n", + "
| 27 | \n", + "161.389180 | \n", + "0.006705 | \n", + "
| 32 | \n", + "146.879018 | \n", + "0.006894 | \n", + "
| 42 | \n", + "124.440473 | \n", + "0.007088 | \n", + "
| 52 | \n", + "109.230932 | \n", + "0.006417 | \n", + "
| 62 | \n", + "99.405510 | \n", + "0.005610 | \n", + "
| 72 | \n", + "93.178906 | \n", + "0.004775 | \n", + "
| 82 | \n", + "89.501328 | \n", + "0.003855 | \n", + "
| 92 | \n", + "87.562395 | \n", + "0.002954 | \n", + "
| 102 | \n", + "86.786289 | \n", + "0.002279 | \n", + "
| 122 | \n", + "86.832321 | \n", + "0.001258 | \n", + "
| 142 | \n", + "88.339444 | \n", + "0.000219 | \n", + "
| 162 | \n", + "90.119786 | \n", + "-0.000323 | \n", + "
| 182 | \n", + "91.759885 | \n", + "-0.000789 | \n", + "
\n",
+ "\n",
+ "\n",
+ " \n",
+ "
\n",
+ "
"
+ ],
+ "text/plain": [
+ " G X\n",
+ "2.0 -0.035794 34.378714\n",
+ "4.0 -0.007574 -20.903093\n",
+ "6.0 0.058481 -4.666342\n",
+ "8.0 0.064154 -1.328219\n",
+ "10.0 0.047295 -0.934767\n",
+ "12.0 0.027173 -0.582564\n",
+ "14.0 0.001675 -0.312059\n",
+ "16.0 -0.028931 -0.016229\n",
+ "19.0 -0.082709 0.204179\n",
+ "22.0 -0.136334 0.202042\n",
+ "27.0 -0.218693 0.299434\n",
+ "32.0 -0.286757 0.172747\n",
+ "42.0 -0.384822 0.409781\n",
+ "52.0 -0.455501 0.567695\n",
+ "62.0 -0.467895 0.466529\n",
+ "72.0 -0.440646 0.559205\n",
+ "82.0 -0.394390 0.516638\n",
+ "92.0 -0.339047 0.565098\n",
+ "102.0 -0.275395 0.164876\n",
+ "122.0 -0.170525 0.545027\n",
+ "142.0 -0.102344 -0.885106\n",
+ "162.0 -0.048847 1.056507\n",
+ "182.0 -0.021124 0.266167"
+ ]
+ },
+ "execution_count": 462,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "diff = system.results - system2.results\n",
+ "percent_diff = diff / system2.results * 100\n",
+ "percent_diff.dropna()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "**Exercise:** What happens to these errors if you run the simulation with a smaller value of `dt`?"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Optimization"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Now let's find the parameters that yield the best fit for the data."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 463,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "k1 = 0.03\n",
+ "k2 = 0.02\n",
+ "k3 = 1e-05\n",
+ "G0 = 290"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Again, we'll get basal levels from the initial values."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 464,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "Gb = data.glucose[0]\n",
+ "Ib = data.insulin[0]"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "And the slope function is the same."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 503,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "def slope_func(state, t, system):\n",
+ " \"\"\"Computes derivatives of the glucose minimal model.\n",
+ " \n",
+ " state: State object\n",
+ " t: time in min\n",
+ " system: System object\n",
+ " \n",
+ " returns: derivatives of G and X\n",
+ " \"\"\"\n",
+ " G, X = state\n",
+ " unpack(system)\n",
+ " \n",
+ " dGdt = -k1 * (G - Gb) - X*G\n",
+ " dXdt = k3 * (I(t) - Ib) - k2 * X\n",
+ " \n",
+ " return dGdt, dXdt"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "`make_system` takes the parameters and `DataFrame` and returns a `System` object."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 504,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "def make_system(G0, k1, k2, k3, data):\n",
+ " \"\"\"Makes a System object with the given parameters.\n",
+ " \n",
+ " G0: initial blood glucose\n",
+ " k1: rate parameter\n",
+ " k2: rate parameter\n",
+ " k3: rate parameter\n",
+ " data: DataFrame\n",
+ " \n",
+ " returns: System object\n",
+ " \"\"\"\n",
+ " init = State(G=G0, X=0)\n",
+ " system = System(init=init, \n",
+ " k1=k1, k2=k2, k3=k3,\n",
+ " Gb=Gb, Ib=Ib, \n",
+ " I=interpolate(data.insulin),\n",
+ " ts=data.index)\n",
+ " return system"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "`error_func` takes the parameters and actual data, makes a `System` object and runs it, then compares the results of the simulation to the data. It returns an array of errors."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 505,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "def error_func(params, data):\n",
+ " \"\"\"Computes an array of errors to be minimized.\n",
+ " \n",
+ " params: sequence of parameters\n",
+ " data: DataFrame of values to be matched\n",
+ " \n",
+ " returns: array of errors\n",
+ " \"\"\"\n",
+ " print(params)\n",
+ " \n",
+ " # make a System with the given parameters\n",
+ " system = make_system(*params, data)\n",
+ " \n",
+ " # solve the ODE\n",
+ " run_odeint(system, slope_func)\n",
+ " \n",
+ " # compute the difference between the model\n",
+ " # results and actual data\n",
+ " error = system.results.G - data.glucose\n",
+ " return error.loc[20:]"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "When we call `error_func`, we provide a sequence of parameters as a single object."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 506,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "(290, 0.027514300313941736, 0.014709983691870935, 1.2486091477939395e-05)"
+ ]
+ },
+ "execution_count": 506,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "params = G0, k1, k2, k3\n",
+ "params"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Here's how that works:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 507,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "(290, 0.027514300313941736, 0.014709983691870935, 1.2486091477939395e-05)\n"
+ ]
+ },
+ {
+ "data": {
+ "text/plain": [
+ "time\n",
+ "22 6.893990\n",
+ "27 -2.379341\n",
+ "32 3.126484\n",
+ "42 -3.041022\n",
+ "52 -0.590735\n",
+ "62 1.634997\n",
+ "72 2.808072\n",
+ "82 5.794733\n",
+ "92 -1.273543\n",
+ "102 -1.022659\n",
+ "122 -1.493460\n",
+ "142 0.796391\n",
+ "162 0.590536\n",
+ "182 -1.615481\n",
+ "dtype: float64"
+ ]
+ },
+ "execution_count": 507,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "error_func(params, data)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "`fit_leastsq` is a wrapper for `scipy.optimize.leastsq`"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 508,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "%psource fit_leastsq"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Here's how we call it."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 509,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "[ 2.90000000e+02 2.75143003e-02 1.47099837e-02 1.24860915e-05]\n",
+ "[ 2.90000000e+02 2.75143003e-02 1.47099837e-02 1.24860915e-05]\n",
+ "[ 2.90000000e+02 2.75143003e-02 1.47099837e-02 1.24860915e-05]\n",
+ "[ 2.90000004e+02 2.75143003e-02 1.47099837e-02 1.24860915e-05]\n",
+ "[ 2.90000000e+02 2.75143007e-02 1.47099837e-02 1.24860915e-05]\n",
+ "[ 2.90000000e+02 2.75143003e-02 1.47099839e-02 1.24860915e-05]\n",
+ "[ 2.90000000e+02 2.75143003e-02 1.47099837e-02 1.24860917e-05]\n",
+ "[ 2.89971197e+02 2.75197172e-02 1.47272414e-02 1.24866367e-05]\n",
+ "[ 2.89971201e+02 2.75197172e-02 1.47272414e-02 1.24866367e-05]\n",
+ "[ 2.89971197e+02 2.75197176e-02 1.47272414e-02 1.24866367e-05]\n",
+ "[ 2.89971197e+02 2.75197172e-02 1.47272416e-02 1.24866367e-05]\n",
+ "[ 2.89971197e+02 2.75197172e-02 1.47272414e-02 1.24866369e-05]\n",
+ "[ 2.89935997e+02 2.75207748e-02 1.47203978e-02 1.24871508e-05]\n",
+ "[ 2.89936001e+02 2.75207748e-02 1.47203978e-02 1.24871508e-05]\n",
+ "[ 2.89935997e+02 2.75207752e-02 1.47203978e-02 1.24871508e-05]\n",
+ "[ 2.89935997e+02 2.75207748e-02 1.47203981e-02 1.24871508e-05]\n",
+ "[ 2.89935997e+02 2.75207748e-02 1.47203978e-02 1.24871510e-05]\n",
+ "[ 2.89931213e+02 2.75153012e-02 1.47022586e-02 1.24883151e-05]\n",
+ "[ 2.89931217e+02 2.75153012e-02 1.47022586e-02 1.24883151e-05]\n",
+ "[ 2.89931213e+02 2.75153016e-02 1.47022586e-02 1.24883151e-05]\n",
+ "[ 2.89931213e+02 2.75153012e-02 1.47022588e-02 1.24883151e-05]\n",
+ "[ 2.89931213e+02 2.75153012e-02 1.47022586e-02 1.24883153e-05]\n",
+ "[ 2.89890576e+02 2.75142723e-02 1.47002334e-02 1.24875136e-05]\n",
+ "[ 2.89890581e+02 2.75142723e-02 1.47002334e-02 1.24875136e-05]\n",
+ "[ 2.89890576e+02 2.75142727e-02 1.47002334e-02 1.24875136e-05]\n",
+ "[ 2.89890576e+02 2.75142723e-02 1.47002337e-02 1.24875136e-05]\n",
+ "[ 2.89890576e+02 2.75142723e-02 1.47002334e-02 1.24875137e-05]\n",
+ "[ 2.89895707e+02 2.75134863e-02 1.47021764e-02 1.24873299e-05]\n",
+ "[ 2.89893213e+02 2.75139401e-02 1.47009835e-02 1.24874124e-05]\n",
+ "[ 2.89891911e+02 2.75141193e-02 1.47005720e-02 1.24874639e-05]\n",
+ "[ 2.89891298e+02 2.75141938e-02 1.47004070e-02 1.24874876e-05]\n",
+ "[ 2.89890914e+02 2.75142370e-02 1.47003116e-02 1.24875018e-05]\n",
+ "[ 2.89890749e+02 2.75142547e-02 1.47002727e-02 1.24875076e-05]\n",
+ "[ 2.89890753e+02 2.75142547e-02 1.47002727e-02 1.24875076e-05]\n",
+ "[ 2.89890749e+02 2.75142551e-02 1.47002727e-02 1.24875076e-05]\n",
+ "[ 2.89890749e+02 2.75142547e-02 1.47002729e-02 1.24875076e-05]\n",
+ "[ 2.89890749e+02 2.75142547e-02 1.47002727e-02 1.24875078e-05]\n",
+ "[ 2.89890811e+02 2.75142424e-02 1.47002736e-02 1.24875127e-05]\n",
+ "[ 2.89890815e+02 2.75142424e-02 1.47002736e-02 1.24875127e-05]\n",
+ "[ 2.89890811e+02 2.75142428e-02 1.47002736e-02 1.24875127e-05]\n",
+ "[ 2.89890811e+02 2.75142424e-02 1.47002739e-02 1.24875127e-05]\n",
+ "[ 2.89890811e+02 2.75142424e-02 1.47002736e-02 1.24875129e-05]\n",
+ "[ 2.89890807e+02 2.75142349e-02 1.47002742e-02 1.24875092e-05]\n",
+ "[ 2.89890811e+02 2.75142349e-02 1.47002742e-02 1.24875092e-05]\n",
+ "[ 2.89890807e+02 2.75142353e-02 1.47002742e-02 1.24875092e-05]\n",
+ "[ 2.89890807e+02 2.75142349e-02 1.47002744e-02 1.24875092e-05]\n",
+ "[ 2.89890807e+02 2.75142349e-02 1.47002742e-02 1.24875094e-05]\n",
+ "[ 2.89890797e+02 2.75142307e-02 1.47002743e-02 1.24875090e-05]\n",
+ "[ 2.89890803e+02 2.75142332e-02 1.47002742e-02 1.24875091e-05]\n",
+ "modsim.py: scipy.optimize.leastsq ran successfully\n",
+ " and returned the following message:\n",
+ "The relative error between two consecutive iterates is at most 0.000000\n"
+ ]
+ }
+ ],
+ "source": [
+ "best_params = fit_leastsq(error_func, params, data)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Now that we have `best_params`, we can use it to make a `System` object and run it.\n",
+ "\n",
+ "We have to use the scatter operator, `*`, to make `best_params` behave like four separate parameters, rather than a single object."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 510,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "system = make_system(*best_params, data)\n",
+ "run_odeint(system, slope_func)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Here are the results, along with the data. The first few points of the model don't fit the data, but we don't expect them to."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 511,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Saving figure to file chap08-fig04.pdf\n"
+ ]
+ },
+ {
+ "data": {
+ "image/png": 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FSqktmCG9PwDmY1YDBtgIfA68rJS6CfBOSnxMa13TLm8CGNI3nuhIO8erHVRU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\nPpCB2ZXQO0f6H8AAIBe4oyU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+ "text/plain": [
+ "| \n", + " | G | \n", + "X | \n", + "
|---|---|---|
| 2.0 | \n", + "-0.035794 | \n", + "34.378714 | \n", + "
| 4.0 | \n", + "-0.007574 | \n", + "-20.903093 | \n", + "
| 6.0 | \n", + "0.058481 | \n", + "-4.666342 | \n", + "
| 8.0 | \n", + "0.064154 | \n", + "-1.328219 | \n", + "
| 10.0 | \n", + "0.047295 | \n", + "-0.934767 | \n", + "
| 12.0 | \n", + "0.027173 | \n", + "-0.582564 | \n", + "
| 14.0 | \n", + "0.001675 | \n", + "-0.312059 | \n", + "
| 16.0 | \n", + "-0.028931 | \n", + "-0.016229 | \n", + "
| 19.0 | \n", + "-0.082709 | \n", + "0.204179 | \n", + "
| 22.0 | \n", + "-0.136334 | \n", + "0.202042 | \n", + "
| 27.0 | \n", + "-0.218693 | \n", + "0.299434 | \n", + "
| 32.0 | \n", + "-0.286757 | \n", + "0.172747 | \n", + "
| 42.0 | \n", + "-0.384822 | \n", + "0.409781 | \n", + "
| 52.0 | \n", + "-0.455501 | \n", + "0.567695 | \n", + "
| 62.0 | \n", + "-0.467895 | \n", + "0.466529 | \n", + "
| 72.0 | \n", + "-0.440646 | \n", + "0.559205 | \n", + "
| 82.0 | \n", + "-0.394390 | \n", + "0.516638 | \n", + "
| 92.0 | \n", + "-0.339047 | \n", + "0.565098 | \n", + "
| 102.0 | \n", + "-0.275395 | \n", + "0.164876 | \n", + "
| 122.0 | \n", + "-0.170525 | \n", + "0.545027 | \n", + "
| 142.0 | \n", + "-0.102344 | \n", + "-0.885106 | \n", + "
| 162.0 | \n", + "-0.048847 | \n", + "1.056507 | \n", + "
| 182.0 | \n", + "-0.021124 | \n", + "0.266167 | \n", + "
\n",
+ "\n",
+ "\n",
+ " \n",
+ "
\n",
+ "
"
+ ],
+ "text/plain": [
+ "S_G 0.027514\n",
+ "S_I 0.000849\n",
+ "dtype: float64"
+ ]
+ },
+ "execution_count": 513,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "indices(*best_params)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### The insulin minimal model\n",
+ "\n",
+ "In addition to the glucose minimal mode, Pacini and Bergman present an insulin minimal model, in which the concentration of insulin, $I$, is governed by this differential equation:\n",
+ "\n",
+ "$ \\frac{dI}{dt} = -k I(t) + \\gamma (G(t) - G_T) t $"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "**Exercise:** Write a version of `make_system` that takes the parameters of this model, `I0`, `k`, `gamma`, and `G_T` as parameters, along with a `DataFrame` containing the measurements, and returns a `System` object suitable for use with `run_simulation` or `run_odeint`.\n",
+ "\n",
+ "Use it to make a `System` object with the following parameters:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 571,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "I0 = 360\n",
+ "k = 0.25\n",
+ "gamma = 0.004\n",
+ "G_T = 80"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 572,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def make_system(I0,k,gamma,G_T,data):\n",
+ " init = State(I=I0)\n",
+ " system = System(init=init, I0=10, \n",
+ " gamma=gamma,k=k,G_T=G_T, G=interpolate(data.glucose), ts=data.index)\n",
+ " \n",
+ " return system"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 573,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "| \n", + " | value | \n", + "
|---|---|
| S_G | \n", + "0.027514 | \n", + "
| S_I | \n", + "0.000849 | \n", + "
\n",
+ "\n",
+ "\n",
+ " \n",
+ "
\n",
+ "
"
+ ],
+ "text/plain": [
+ "init I 360\n",
+ "dtype: int64\n",
+ "I0 10\n",
+ "gamma 0.004\n",
+ "k 0.25\n",
+ "G_T 80\n",
+ "G | \n", + " | value | \n", + "
|---|---|
| init | \n", + "I 360\n", + "dtype: int64 | \n", + "
| I0 | \n", + "10 | \n", + "
| gamma | \n", + "0.004 | \n", + "
| k | \n", + "0.25 | \n", + "
| G_T | \n", + "80 | \n", + "
| G | \n", + "<scipy.interpolate.interpolate.interp1d object... | \n", + "
| ts | \n", + "Int64Index([ 0, 2, 4, 6, 8, 10, 12,... | \n", + "
| \n", + " | I | \n", + "
|---|---|
| time | \n", + "\n", + " |
| 0 | \n", + "360.000000 | \n", + "
| 2 | \n", + "219.652719 | \n", + "
| 4 | \n", + "137.739127 | \n", + "
| 6 | \n", + "89.505898 | \n", + "
| 8 | \n", + "61.636133 | \n", + "
| 10 | \n", + "45.765330 | \n", + "
| 12 | \n", + "37.053121 | \n", + "
| 14 | \n", + "32.989732 | \n", + "
| 16 | \n", + "31.406589 | \n", + "
| 19 | \n", + "31.811071 | \n", + "
| 22 | \n", + "32.581632 | \n", + "
| 27 | \n", + "34.014287 | \n", + "
| 32 | \n", + "33.758216 | \n", + "
| 42 | \n", + "30.932902 | \n", + "
| 52 | \n", + "24.554216 | \n", + "
| 62 | \n", + "15.767804 | \n", + "
| 72 | \n", + "7.782053 | \n", + "
| 82 | \n", + "-0.382598 | \n", + "
| 92 | \n", + "0.598298 | \n", + "
| 102 | \n", + "1.943431 | \n", + "
| 122 | \n", + "3.415756 | \n", + "
| 142 | \n", + "4.413573 | \n", + "
| 162 | \n", + "11.170251 | \n", + "
| 182 | \n", + "25.702699 | \n", + "
\n",
+ "\n",
+ "\n",
+ " \n",
+ "
\n",
+ "
"
+ ],
+ "text/plain": [
+ "y 381 meter\n",
+ "v 0.0 meter / second\n",
+ "dtype: object"
+ ]
+ },
+ "execution_count": 79,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "init = State(y=381 * m, \n",
+ " v=0 * m/s)\n",
+ "init"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "collapsed": true
+ },
+ "source": [
+ "Acceleration due to gravity is about 9.8 m / s$^2$."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 80,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "g = 9.8 * m/s**2"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "collapsed": true
+ },
+ "source": [
+ "When we call `odeint`, we need an array of timestamps where we want to compute the solution.\n",
+ "\n",
+ "I'll start with a duration of 10 seconds."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 81,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "[ 0. 0.71428571 1.42857143 2.14285714 2.85714286 3.57142857 4.28571429 5. 5.71428571 6.42857143 7.14285714 7.85714286 8.57142857 9.28571429 10. ] second"
+ ],
+ "text/latex": [
+ "$[ 0. 0.71428571 1.42857143 2.14285714 2.85714286 3.57142857 4.28571429 5. 5.71428571 6.42857143 7.14285714 7.85714286 8.57142857 9.28571429 10. ] second$"
+ ],
+ "text/plain": [
+ "| \n", + " | value | \n", + "
|---|---|
| y | \n", + "381 meter | \n", + "
| v | \n", + "0.0 meter / second | \n", + "
\n",
+ "\n",
+ "\n",
+ " \n",
+ "
\n",
+ "
"
+ ],
+ "text/plain": [
+ " y v\n",
+ "0.000 381.000000 0.0000\n",
+ "0.191 380.821243 -1.8718\n",
+ "0.382 380.284972 -3.7436\n",
+ "0.573 379.391188 -5.6154\n",
+ "0.764 378.139890 -7.4872"
+ ]
+ },
+ "execution_count": 129,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "system.results.head()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 130,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "| \n", + " | y | \n", + "v | \n", + "
|---|---|---|
| 0.000 | \n", + "381.000000 | \n", + "0.0000 | \n", + "
| 0.191 | \n", + "380.821243 | \n", + "-1.8718 | \n", + "
| 0.382 | \n", + "380.284972 | \n", + "-3.7436 | \n", + "
| 0.573 | \n", + "379.391188 | \n", + "-5.6154 | \n", + "
| 0.764 | \n", + "378.139890 | \n", + "-7.4872 | \n", + "
\n",
+ "\n",
+ "\n",
+ " \n",
+ "
\n",
+ "
"
+ ],
+ "text/plain": [
+ " y v\n",
+ "18.336 -1266.423590 -179.6928\n",
+ "18.527 -1300.923672 -181.5646\n",
+ "18.718 -1335.781268 -183.4364\n",
+ "18.909 -1370.996377 -185.3082\n",
+ "19.100 -1406.569000 -187.1800"
+ ]
+ },
+ "execution_count": 130,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "system.results.tail()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "collapsed": true
+ },
+ "source": [
+ "The following function plots the results."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 131,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "def plot_position(results):\n",
+ " \"\"\"Plot the results.\n",
+ " \n",
+ " results: DataFrame with position, `y`\n",
+ " \"\"\"\n",
+ " newfig()\n",
+ " plot(results.y, label='y')\n",
+ " \n",
+ " decorate(xlabel='Time (s)',\n",
+ " ylabel='Position (m)')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "collapsed": true
+ },
+ "source": [
+ "Here's what it looks like."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 132,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Saving figure to file chap09-fig01.pdf\n"
+ ]
+ },
+ {
+ "data": {
+ "image/png": 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j32boJCQiEtEWzMrA7XKx77US/IEADU0dPPXKeT68VYloPA11TuibIV9/Y0Ki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\nrw4A7dtq5AAAAABJRU5ErkJggg==\n",
+ "text/plain": [
+ "| \n", + " | y | \n", + "v | \n", + "
|---|---|---|
| 18.336 | \n", + "-1266.423590 | \n", + "-179.6928 | \n", + "
| 18.527 | \n", + "-1300.923672 | \n", + "-181.5646 | \n", + "
| 18.718 | \n", + "-1335.781268 | \n", + "-183.4364 | \n", + "
| 18.909 | \n", + "-1370.996377 | \n", + "-185.3082 | \n", + "
| 19.100 | \n", + "-1406.569000 | \n", + "-187.1800 | \n", + "
\n",
+ "\n",
+ "\n",
+ " \n",
+ "
\n",
+ "
"
+ ],
+ "text/plain": [
+ " y v\n",
+ "0.0 381.0 8.0\n",
+ "1.0 384.1 -1.8\n",
+ "2.0 377.4 -11.6\n",
+ "3.0 360.9 -21.4\n",
+ "4.0 334.6 -31.2\n",
+ "5.0 298.5 -41.0\n",
+ "6.0 252.6 -50.8\n",
+ "7.0 196.9 -60.6\n",
+ "8.0 131.4 -70.4\n",
+ "9.0 56.1 -80.2\n",
+ "10.0 -29.0 -90.0"
+ ]
+ },
+ "execution_count": 134,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "system = make_system(10)\n",
+ "run_odeint(system, slope_func)\n",
+ "system.results"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "collapsed": true
+ },
+ "source": [
+ "To figure out when the penny hit the sidewalk, we use `interp_inverse`, which return a function that maps from height to time."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 135,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "y = system.results.y\n",
+ "T = interp_inverse(y, kind='cubic')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "collapsed": true
+ },
+ "source": [
+ "`T(0)` interpolates the time when the height was 0."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 136,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "array(9.663930979401997)"
+ ]
+ },
+ "execution_count": 136,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "T_sidewalk = T(0)\n",
+ "T_sidewalk"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "collapsed": true
+ },
+ "source": [
+ "We can compare that to the exact result. Without air resistance, we have\n",
+ "\n",
+ "$v = -g t$\n",
+ "\n",
+ "and\n",
+ "\n",
+ "$y = 381 - g t^2 / 2$\n",
+ "\n",
+ "Setting $y=0$ and solving for $t$ yields\n",
+ "\n",
+ "$t = \\sqrt{\\frac{2 y_{init}}{g}}$"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 137,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "8.817885349720552 second"
+ ],
+ "text/latex": [
+ "$8.817885349720552 second$"
+ ],
+ "text/plain": [
+ "| \n", + " | y | \n", + "v | \n", + "
|---|---|---|
| 0.0 | \n", + "381.0 | \n", + "8.0 | \n", + "
| 1.0 | \n", + "384.1 | \n", + "-1.8 | \n", + "
| 2.0 | \n", + "377.4 | \n", + "-11.6 | \n", + "
| 3.0 | \n", + "360.9 | \n", + "-21.4 | \n", + "
| 4.0 | \n", + "334.6 | \n", + "-31.2 | \n", + "
| 5.0 | \n", + "298.5 | \n", + "-41.0 | \n", + "
| 6.0 | \n", + "252.6 | \n", + "-50.8 | \n", + "
| 7.0 | \n", + "196.9 | \n", + "-60.6 | \n", + "
| 8.0 | \n", + "131.4 | \n", + "-70.4 | \n", + "
| 9.0 | \n", + "56.1 | \n", + "-80.2 | \n", + "
| 10.0 | \n", + "-29.0 | \n", + "-90.0 | \n", + "
\n",
+ "\n",
+ "\n",
+ " \n",
+ "
\n",
+ "
"
+ ],
+ "text/plain": [
+ "init y 381 meter\n",
+ "v 0.0 meter / secon...\n",
+ "g 9.8 meter / second ** 2\n",
+ "mass 0.0025 kilogram\n",
+ "rho 1.2 kilogram / meter ** 3\n",
+ "C_d 0.4445009981135434 dimensionless\n",
+ "area 0.0002835287369864788 meter ** 2\n",
+ "ts [0.0 second, 0.3 second, 0.6 second, 0.8999999...\n",
+ "dtype: object"
+ ]
+ },
+ "execution_count": 104,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "system = make_system(condition)\n",
+ "system"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "collapsed": true
+ },
+ "source": [
+ "Here's the slope function, including acceleration due to gravity and drag."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 105,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "def slope_func(state, t, system):\n",
+ " \"\"\"Compute derivatives of the state.\n",
+ " \n",
+ " state: position, velocity\n",
+ " t: time\n",
+ " system: System object containing g, rho,\n",
+ " C_d, area, and mass\n",
+ " \n",
+ " returns: derivatives of y and v\n",
+ " \"\"\"\n",
+ " y, v = state\n",
+ " unpack(system)\n",
+ " \n",
+ " f_drag = rho * v**2 * C_d * area / 2\n",
+ " a_drag = f_drag / mass\n",
+ " \n",
+ " dydt = v\n",
+ " dvdt = -g + a_drag\n",
+ " \n",
+ " return dydt, dvdt"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "collapsed": true
+ },
+ "source": [
+ "As always, let's test the slope function with the initial conditions."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 106,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "(| \n", + " | value | \n", + "
|---|---|
| init | \n", + "y 381 meter\n", + "v 0.0 meter / secon... | \n", + "
| g | \n", + "9.8 meter / second ** 2 | \n", + "
| mass | \n", + "0.0025 kilogram | \n", + "
| rho | \n", + "1.2 kilogram / meter ** 3 | \n", + "
| C_d | \n", + "0.4445009981135434 dimensionless | \n", + "
| area | \n", + "0.0002835287369864788 meter ** 2 | \n", + "
| ts | \n", + "[0.0 second, 0.3 second, 0.6 second, 0.8999999... | \n", + "
\n",
+ "\n",
+ "\n",
+ " \n",
+ "
\n",
+ "
"
+ ],
+ "text/plain": [
+ "init x 0 meter\n",
+ "y ...\n",
+ "g 9.8 meter / second ** 2\n",
+ "mass 0.145 kilogram\n",
+ "area 0.004185386812745002 meter ** 2\n",
+ "rho 1.2 kilogram / meter ** 3\n",
+ "C_d 0.3\n",
+ "ts [0.0 second, 0.051 second, 0.102 second, 0.153...\n",
+ "dtype: object"
+ ]
+ },
+ "execution_count": 29,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "system = make_system(condition)\n",
+ "system"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Here's the slope function that computes acceleration due to gravity and drag."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 30,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "def slope_func(state, t, system):\n",
+ " \"\"\"Computes derivatives of the state variables.\n",
+ " \n",
+ " state: State (x, y, x velocity, y velocity)\n",
+ " t: time\n",
+ " system: System object with g, rho, C_d, area, mass\n",
+ " \n",
+ " returns: sequence (vx, vy, ax, ay)\n",
+ " \"\"\"\n",
+ " x, y, vx, vy = state\n",
+ " unpack(system)\n",
+ " \n",
+ " a_grav = Vector(0, -g)\n",
+ "\n",
+ " v = Vector(vx, vy)\n",
+ " \n",
+ " f_drag = -rho * v.mag * v * C_d * area / 2\n",
+ " a_drag = f_drag / mass\n",
+ " \n",
+ " a = a_grav + a_drag\n",
+ " \n",
+ " return vx, vy, a.x, a.y"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Always test the slope function with the initial conditions."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 31,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "(| \n", + " | value | \n", + "
|---|---|
| init | \n", + "x 0 meter\n", + "y ... | \n", + "
| g | \n", + "9.8 meter / second ** 2 | \n", + "
| mass | \n", + "0.145 kilogram | \n", + "
| area | \n", + "0.004185386812745002 meter ** 2 | \n", + "
| rho | \n", + "1.2 kilogram / meter ** 3 | \n", + "
| C_d | \n", + "0.3 | \n", + "
| ts | \n", + "[0.0 second, 0.051 second, 0.102 second, 0.153... | \n", + "
\n",
+ "\n",
+ "\n",
+ " \n",
+ "
\n",
+ "
"
+ ],
+ "text/plain": [
+ " x y vx vy\n",
+ "0.000 0.000000 1.000000 10.352762 38.637033\n",
+ "0.051 0.525223 2.947460 10.244833 37.737037\n",
+ "0.102 1.045033 4.849486 10.140414 36.855149\n",
+ "0.153 1.559603 6.706980 10.039371 35.990594\n",
+ "0.204 2.069104 8.520808 9.941577 35.142638"
+ ]
+ },
+ "execution_count": 33,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "system.results.head()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "And the last few. The last value of `y` is negative, indicating that the ball hit the ground before the end of the simulation."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 34,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "| \n", + " | x | \n", + "y | \n", + "vx | \n", + "vy | \n", + "
|---|---|---|---|---|
| 0.000 | \n", + "0.000000 | \n", + "1.000000 | \n", + "10.352762 | \n", + "38.637033 | \n", + "
| 0.051 | \n", + "0.525223 | \n", + "2.947460 | \n", + "10.244833 | \n", + "37.737037 | \n", + "
| 0.102 | \n", + "1.045033 | \n", + "4.849486 | \n", + "10.140414 | \n", + "36.855149 | \n", + "
| 0.153 | \n", + "1.559603 | \n", + "6.706980 | \n", + "10.039371 | \n", + "35.990594 | \n", + "
| 0.204 | \n", + "2.069104 | \n", + "8.520808 | \n", + "9.941577 | \n", + "35.142638 | \n", + "
\n",
+ "\n",
+ "\n",
+ " \n",
+ "
\n",
+ "
"
+ ],
+ "text/plain": [
+ " x y vx vy\n",
+ "4.896 39.033848 42.325221 6.726804 -15.869290\n",
+ "4.947 39.376127 41.505021 6.695814 -16.294823\n",
+ "4.998 39.716812 40.663211 6.664295 -16.716737\n",
+ "5.049 40.055876 39.799976 6.632259 -17.134973\n",
+ "5.100 40.393294 38.915507 6.599718 -17.549471"
+ ]
+ },
+ "execution_count": 34,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "system.results.tail()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Visualizing the results\n",
+ "\n",
+ "We can extract the x and y components as `Series` objects."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 35,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "xs = system.results.x\n",
+ "ys = system.results.y"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "The simplest way to visualize the results is to plot x and y as functions of time."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 36,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "application/javascript": [
+ "/* Put everything inside the global mpl namespace */\n",
+ "window.mpl = {};\n",
+ "\n",
+ "\n",
+ "mpl.get_websocket_type = function() {\n",
+ " if (typeof(WebSocket) !== 'undefined') {\n",
+ " return WebSocket;\n",
+ " } else if (typeof(MozWebSocket) !== 'undefined') {\n",
+ " return MozWebSocket;\n",
+ " } else {\n",
+ " alert('Your browser does not have WebSocket support.' +\n",
+ " 'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
+ " 'Firefox 4 and 5 are also supported but you ' +\n",
+ " 'have to enable WebSockets in about:config.');\n",
+ " };\n",
+ "}\n",
+ "\n",
+ "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n",
+ " this.id = figure_id;\n",
+ "\n",
+ " this.ws = websocket;\n",
+ "\n",
+ " this.supports_binary = (this.ws.binaryType != undefined);\n",
+ "\n",
+ " if (!this.supports_binary) {\n",
+ " var warnings = document.getElementById(\"mpl-warnings\");\n",
+ " if (warnings) {\n",
+ " warnings.style.display = 'block';\n",
+ " warnings.textContent = (\n",
+ " \"This browser does not support binary websocket messages. \" +\n",
+ " \"Performance may be slow.\");\n",
+ " }\n",
+ " }\n",
+ "\n",
+ " this.imageObj = new Image();\n",
+ "\n",
+ " this.context = undefined;\n",
+ " this.message = undefined;\n",
+ " this.canvas = undefined;\n",
+ " this.rubberband_canvas = undefined;\n",
+ " this.rubberband_context = undefined;\n",
+ " this.format_dropdown = undefined;\n",
+ "\n",
+ " this.image_mode = 'full';\n",
+ "\n",
+ " this.root = $('');\n",
+ " this._root_extra_style(this.root)\n",
+ " this.root.attr('style', 'display: inline-block');\n",
+ "\n",
+ " $(parent_element).append(this.root);\n",
+ "\n",
+ " this._init_header(this);\n",
+ " this._init_canvas(this);\n",
+ " this._init_toolbar(this);\n",
+ "\n",
+ " var fig = this;\n",
+ "\n",
+ " this.waiting = false;\n",
+ "\n",
+ " this.ws.onopen = function () {\n",
+ " fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n",
+ " fig.send_message(\"send_image_mode\", {});\n",
+ " if (mpl.ratio != 1) {\n",
+ " fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n",
+ " }\n",
+ " fig.send_message(\"refresh\", {});\n",
+ " }\n",
+ "\n",
+ " this.imageObj.onload = function() {\n",
+ " if (fig.image_mode == 'full') {\n",
+ " // Full images could contain transparency (where diff images\n",
+ " // almost always do), so we need to clear the canvas so that\n",
+ " // there is no ghosting.\n",
+ " fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
+ " }\n",
+ " fig.context.drawImage(fig.imageObj, 0, 0);\n",
+ " };\n",
+ "\n",
+ " this.imageObj.onunload = function() {\n",
+ " this.ws.close();\n",
+ " }\n",
+ "\n",
+ " this.ws.onmessage = this._make_on_message_function(this);\n",
+ "\n",
+ " this.ondownload = ondownload;\n",
+ "}\n",
+ "\n",
+ "mpl.figure.prototype._init_header = function() {\n",
+ " var titlebar = $(\n",
+ " '');\n",
+ " var titletext = $(\n",
+ " '');\n",
+ " titlebar.append(titletext)\n",
+ " this.root.append(titlebar);\n",
+ " this.header = titletext[0];\n",
+ "}\n",
+ "\n",
+ "\n",
+ "\n",
+ "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
+ "\n",
+ "}\n",
+ "\n",
+ "\n",
+ "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
+ "\n",
+ "}\n",
+ "\n",
+ "mpl.figure.prototype._init_canvas = function() {\n",
+ " var fig = this;\n",
+ "\n",
+ " var canvas_div = $('');\n",
+ "\n",
+ " canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
+ "\n",
+ " function canvas_keyboard_event(event) {\n",
+ " return fig.key_event(event, event['data']);\n",
+ " }\n",
+ "\n",
+ " canvas_div.keydown('key_press', canvas_keyboard_event);\n",
+ " canvas_div.keyup('key_release', canvas_keyboard_event);\n",
+ " this.canvas_div = canvas_div\n",
+ " this._canvas_extra_style(canvas_div)\n",
+ " this.root.append(canvas_div);\n",
+ "\n",
+ " var canvas = $('');\n",
+ " canvas.addClass('mpl-canvas');\n",
+ " canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
+ "\n",
+ " this.canvas = canvas[0];\n",
+ " this.context = canvas[0].getContext(\"2d\");\n",
+ "\n",
+ " var backingStore = this.context.backingStorePixelRatio ||\n",
+ "\tthis.context.webkitBackingStorePixelRatio ||\n",
+ "\tthis.context.mozBackingStorePixelRatio ||\n",
+ "\tthis.context.msBackingStorePixelRatio ||\n",
+ "\tthis.context.oBackingStorePixelRatio ||\n",
+ "\tthis.context.backingStorePixelRatio || 1;\n",
+ "\n",
+ " mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
+ "\n",
+ " var rubberband = $('');\n",
+ " rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
+ "\n",
+ " var pass_mouse_events = true;\n",
+ "\n",
+ " canvas_div.resizable({\n",
+ " start: function(event, ui) {\n",
+ " pass_mouse_events = false;\n",
+ " },\n",
+ " resize: function(event, ui) {\n",
+ " fig.request_resize(ui.size.width, ui.size.height);\n",
+ " },\n",
+ " stop: function(event, ui) {\n",
+ " pass_mouse_events = true;\n",
+ " fig.request_resize(ui.size.width, ui.size.height);\n",
+ " },\n",
+ " });\n",
+ "\n",
+ " function mouse_event_fn(event) {\n",
+ " if (pass_mouse_events)\n",
+ " return fig.mouse_event(event, event['data']);\n",
+ " }\n",
+ "\n",
+ " rubberband.mousedown('button_press', mouse_event_fn);\n",
+ " rubberband.mouseup('button_release', mouse_event_fn);\n",
+ " // Throttle sequential mouse events to 1 every 20ms.\n",
+ " rubberband.mousemove('motion_notify', mouse_event_fn);\n",
+ "\n",
+ " rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
+ " rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
+ "\n",
+ " canvas_div.on(\"wheel\", function (event) {\n",
+ " event = event.originalEvent;\n",
+ " event['data'] = 'scroll'\n",
+ " if (event.deltaY < 0) {\n",
+ " event.step = 1;\n",
+ " } else {\n",
+ " event.step = -1;\n",
+ " }\n",
+ " mouse_event_fn(event);\n",
+ " });\n",
+ "\n",
+ " canvas_div.append(canvas);\n",
+ " canvas_div.append(rubberband);\n",
+ "\n",
+ " this.rubberband = rubberband;\n",
+ " this.rubberband_canvas = rubberband[0];\n",
+ " this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
+ " this.rubberband_context.strokeStyle = \"#000000\";\n",
+ "\n",
+ " this._resize_canvas = function(width, height) {\n",
+ " // Keep the size of the canvas, canvas container, and rubber band\n",
+ " // canvas in synch.\n",
+ " canvas_div.css('width', width)\n",
+ " canvas_div.css('height', height)\n",
+ "\n",
+ " canvas.attr('width', width * mpl.ratio);\n",
+ " canvas.attr('height', height * mpl.ratio);\n",
+ " canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n",
+ "\n",
+ " rubberband.attr('width', width);\n",
+ " rubberband.attr('height', height);\n",
+ " }\n",
+ "\n",
+ " // Set the figure to an initial 600x600px, this will subsequently be updated\n",
+ " // upon first draw.\n",
+ " this._resize_canvas(600, 600);\n",
+ "\n",
+ " // Disable right mouse context menu.\n",
+ " $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n",
+ " return false;\n",
+ " });\n",
+ "\n",
+ " function set_focus () {\n",
+ " canvas.focus();\n",
+ " canvas_div.focus();\n",
+ " }\n",
+ "\n",
+ " window.setTimeout(set_focus, 100);\n",
+ "}\n",
+ "\n",
+ "mpl.figure.prototype._init_toolbar = function() {\n",
+ " var fig = this;\n",
+ "\n",
+ " var nav_element = $('')\n",
+ " nav_element.attr('style', 'width: 100%');\n",
+ " this.root.append(nav_element);\n",
+ "\n",
+ " // Define a callback function for later on.\n",
+ " function toolbar_event(event) {\n",
+ " return fig.toolbar_button_onclick(event['data']);\n",
+ " }\n",
+ " function toolbar_mouse_event(event) {\n",
+ " return fig.toolbar_button_onmouseover(event['data']);\n",
+ " }\n",
+ "\n",
+ " for(var toolbar_ind in mpl.toolbar_items) {\n",
+ " var name = mpl.toolbar_items[toolbar_ind][0];\n",
+ " var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
+ " var image = mpl.toolbar_items[toolbar_ind][2];\n",
+ " var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
+ "\n",
+ " if (!name) {\n",
+ " // put a spacer in here.\n",
+ " continue;\n",
+ " }\n",
+ " var button = $('');\n",
+ " button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
+ " 'ui-button-icon-only');\n",
+ " button.attr('role', 'button');\n",
+ " button.attr('aria-disabled', 'false');\n",
+ " button.click(method_name, toolbar_event);\n",
+ " button.mouseover(tooltip, toolbar_mouse_event);\n",
+ "\n",
+ " var icon_img = $('');\n",
+ " icon_img.addClass('ui-button-icon-primary ui-icon');\n",
+ " icon_img.addClass(image);\n",
+ " icon_img.addClass('ui-corner-all');\n",
+ "\n",
+ " var tooltip_span = $('');\n",
+ " tooltip_span.addClass('ui-button-text');\n",
+ " tooltip_span.html(tooltip);\n",
+ "\n",
+ " button.append(icon_img);\n",
+ " button.append(tooltip_span);\n",
+ "\n",
+ " nav_element.append(button);\n",
+ " }\n",
+ "\n",
+ " var fmt_picker_span = $('');\n",
+ "\n",
+ " var fmt_picker = $('');\n",
+ " fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
+ " fmt_picker_span.append(fmt_picker);\n",
+ " nav_element.append(fmt_picker_span);\n",
+ " this.format_dropdown = fmt_picker[0];\n",
+ "\n",
+ " for (var ind in mpl.extensions) {\n",
+ " var fmt = mpl.extensions[ind];\n",
+ " var option = $(\n",
+ " '', {selected: fmt === mpl.default_extension}).html(fmt);\n",
+ " fmt_picker.append(option)\n",
+ " }\n",
+ "\n",
+ " // Add hover states to the ui-buttons\n",
+ " $( \".ui-button\" ).hover(\n",
+ " function() { $(this).addClass(\"ui-state-hover\");},\n",
+ " function() { $(this).removeClass(\"ui-state-hover\");}\n",
+ " );\n",
+ "\n",
+ " var status_bar = $('');\n",
+ " nav_element.append(status_bar);\n",
+ " this.message = status_bar[0];\n",
+ "}\n",
+ "\n",
+ "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
+ " // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
+ " // which will in turn request a refresh of the image.\n",
+ " this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
+ "}\n",
+ "\n",
+ "mpl.figure.prototype.send_message = function(type, properties) {\n",
+ " properties['type'] = type;\n",
+ " properties['figure_id'] = this.id;\n",
+ " this.ws.send(JSON.stringify(properties));\n",
+ "}\n",
+ "\n",
+ "mpl.figure.prototype.send_draw_message = function() {\n",
+ " if (!this.waiting) {\n",
+ " this.waiting = true;\n",
+ " this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
+ " }\n",
+ "}\n",
+ "\n",
+ "\n",
+ "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
+ " var format_dropdown = fig.format_dropdown;\n",
+ " var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
+ " fig.ondownload(fig, format);\n",
+ "}\n",
+ "\n",
+ "\n",
+ "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
+ " var size = msg['size'];\n",
+ " if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
+ " fig._resize_canvas(size[0], size[1]);\n",
+ " fig.send_message(\"refresh\", {});\n",
+ " };\n",
+ "}\n",
+ "\n",
+ "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
+ " var x0 = msg['x0'] / mpl.ratio;\n",
+ " var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
+ " var x1 = msg['x1'] / mpl.ratio;\n",
+ " var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\n",
+ " x0 = Math.floor(x0) + 0.5;\n",
+ " y0 = Math.floor(y0) + 0.5;\n",
+ " x1 = Math.floor(x1) + 0.5;\n",
+ " y1 = Math.floor(y1) + 0.5;\n",
+ " var min_x = Math.min(x0, x1);\n",
+ " var min_y = Math.min(y0, y1);\n",
+ " var width = Math.abs(x1 - x0);\n",
+ " var height = Math.abs(y1 - y0);\n",
+ "\n",
+ " fig.rubberband_context.clearRect(\n",
+ " 0, 0, fig.canvas.width, fig.canvas.height);\n",
+ "\n",
+ " fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
+ "}\n",
+ "\n",
+ "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
+ " // Updates the figure title.\n",
+ " fig.header.textContent = msg['label'];\n",
+ "}\n",
+ "\n",
+ "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
+ " var cursor = msg['cursor'];\n",
+ " switch(cursor)\n",
+ " {\n",
+ " case 0:\n",
+ " cursor = 'pointer';\n",
+ " break;\n",
+ " case 1:\n",
+ " cursor = 'default';\n",
+ " break;\n",
+ " case 2:\n",
+ " cursor = 'crosshair';\n",
+ " break;\n",
+ " case 3:\n",
+ " cursor = 'move';\n",
+ " break;\n",
+ " }\n",
+ " fig.rubberband_canvas.style.cursor = cursor;\n",
+ "}\n",
+ "\n",
+ "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
+ " fig.message.textContent = msg['message'];\n",
+ "}\n",
+ "\n",
+ "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
+ " // Request the server to send over a new figure.\n",
+ " fig.send_draw_message();\n",
+ "}\n",
+ "\n",
+ "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
+ " fig.image_mode = msg['mode'];\n",
+ "}\n",
+ "\n",
+ "mpl.figure.prototype.updated_canvas_event = function() {\n",
+ " // Called whenever the canvas gets updated.\n",
+ " this.send_message(\"ack\", {});\n",
+ "}\n",
+ "\n",
+ "// A function to construct a web socket function for onmessage handling.\n",
+ "// Called in the figure constructor.\n",
+ "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
+ " return function socket_on_message(evt) {\n",
+ " if (evt.data instanceof Blob) {\n",
+ " /* FIXME: We get \"Resource interpreted as Image but\n",
+ " * transferred with MIME type text/plain:\" errors on\n",
+ " * Chrome. But how to set the MIME type? It doesn't seem\n",
+ " * to be part of the websocket stream */\n",
+ " evt.data.type = \"image/png\";\n",
+ "\n",
+ " /* Free the memory for the previous frames */\n",
+ " if (fig.imageObj.src) {\n",
+ " (window.URL || window.webkitURL).revokeObjectURL(\n",
+ " fig.imageObj.src);\n",
+ " }\n",
+ "\n",
+ " fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
+ " evt.data);\n",
+ " fig.updated_canvas_event();\n",
+ " fig.waiting = false;\n",
+ " return;\n",
+ " }\n",
+ " else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
+ " fig.imageObj.src = evt.data;\n",
+ " fig.updated_canvas_event();\n",
+ " fig.waiting = false;\n",
+ " return;\n",
+ " }\n",
+ "\n",
+ " var msg = JSON.parse(evt.data);\n",
+ " var msg_type = msg['type'];\n",
+ "\n",
+ " // Call the \"handle_{type}\" callback, which takes\n",
+ " // the figure and JSON message as its only arguments.\n",
+ " try {\n",
+ " var callback = fig[\"handle_\" + msg_type];\n",
+ " } catch (e) {\n",
+ " console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
+ " return;\n",
+ " }\n",
+ "\n",
+ " if (callback) {\n",
+ " try {\n",
+ " // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
+ " callback(fig, msg);\n",
+ " } catch (e) {\n",
+ " console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
+ " }\n",
+ " }\n",
+ " };\n",
+ "}\n",
+ "\n",
+ "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
+ "mpl.findpos = function(e) {\n",
+ " //this section is from http://www.quirksmode.org/js/events_properties.html\n",
+ " var targ;\n",
+ " if (!e)\n",
+ " e = window.event;\n",
+ " if (e.target)\n",
+ " targ = e.target;\n",
+ " else if (e.srcElement)\n",
+ " targ = e.srcElement;\n",
+ " if (targ.nodeType == 3) // defeat Safari bug\n",
+ " targ = targ.parentNode;\n",
+ "\n",
+ " // jQuery normalizes the pageX and pageY\n",
+ " // pageX,Y are the mouse positions relative to the document\n",
+ " // offset() returns the position of the element relative to the document\n",
+ " var x = e.pageX - $(targ).offset().left;\n",
+ " var y = e.pageY - $(targ).offset().top;\n",
+ "\n",
+ " return {\"x\": x, \"y\": y};\n",
+ "};\n",
+ "\n",
+ "/*\n",
+ " * return a copy of an object with only non-object keys\n",
+ " * we need this to avoid circular references\n",
+ " * http://stackoverflow.com/a/24161582/3208463\n",
+ " */\n",
+ "function simpleKeys (original) {\n",
+ " return Object.keys(original).reduce(function (obj, key) {\n",
+ " if (typeof original[key] !== 'object')\n",
+ " obj[key] = original[key]\n",
+ " return obj;\n",
+ " }, {});\n",
+ "}\n",
+ "\n",
+ "mpl.figure.prototype.mouse_event = function(event, name) {\n",
+ " var canvas_pos = mpl.findpos(event)\n",
+ "\n",
+ " if (name === 'button_press')\n",
+ " {\n",
+ " this.canvas.focus();\n",
+ " this.canvas_div.focus();\n",
+ " }\n",
+ "\n",
+ " var x = canvas_pos.x * mpl.ratio;\n",
+ " var y = canvas_pos.y * mpl.ratio;\n",
+ "\n",
+ " this.send_message(name, {x: x, y: y, button: event.button,\n",
+ " step: event.step,\n",
+ " guiEvent: simpleKeys(event)});\n",
+ "\n",
+ " /* This prevents the web browser from automatically changing to\n",
+ " * the text insertion cursor when the button is pressed. We want\n",
+ " * to control all of the cursor setting manually through the\n",
+ " * 'cursor' event from matplotlib */\n",
+ " event.preventDefault();\n",
+ " return false;\n",
+ "}\n",
+ "\n",
+ "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
+ " // Handle any extra behaviour associated with a key event\n",
+ "}\n",
+ "\n",
+ "mpl.figure.prototype.key_event = function(event, name) {\n",
+ "\n",
+ " // Prevent repeat events\n",
+ " if (name == 'key_press')\n",
+ " {\n",
+ " if (event.which === this._key)\n",
+ " return;\n",
+ " else\n",
+ " this._key = event.which;\n",
+ " }\n",
+ " if (name == 'key_release')\n",
+ " this._key = null;\n",
+ "\n",
+ " var value = '';\n",
+ " if (event.ctrlKey && event.which != 17)\n",
+ " value += \"ctrl+\";\n",
+ " if (event.altKey && event.which != 18)\n",
+ " value += \"alt+\";\n",
+ " if (event.shiftKey && event.which != 16)\n",
+ " value += \"shift+\";\n",
+ "\n",
+ " value += 'k';\n",
+ " value += event.which.toString();\n",
+ "\n",
+ " this._key_event_extra(event, name);\n",
+ "\n",
+ " this.send_message(name, {key: value,\n",
+ " guiEvent: simpleKeys(event)});\n",
+ " return false;\n",
+ "}\n",
+ "\n",
+ "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
+ " if (name == 'download') {\n",
+ " this.handle_save(this, null);\n",
+ " } else {\n",
+ " this.send_message(\"toolbar_button\", {name: name});\n",
+ " }\n",
+ "};\n",
+ "\n",
+ "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
+ " this.message.textContent = tooltip;\n",
+ "};\n",
+ "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
+ "\n",
+ "mpl.extensions = [\"eps\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\"];\n",
+ "\n",
+ "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
+ " // Create a \"websocket\"-like object which calls the given IPython comm\n",
+ " // object with the appropriate methods. Currently this is a non binary\n",
+ " // socket, so there is still some room for performance tuning.\n",
+ " var ws = {};\n",
+ "\n",
+ " ws.close = function() {\n",
+ " comm.close()\n",
+ " };\n",
+ " ws.send = function(m) {\n",
+ " //console.log('sending', m);\n",
+ " comm.send(m);\n",
+ " };\n",
+ " // Register the callback with on_msg.\n",
+ " comm.on_msg(function(msg) {\n",
+ " //console.log('receiving', msg['content']['data'], msg);\n",
+ " // Pass the mpl event to the overriden (by mpl) onmessage function.\n",
+ " ws.onmessage(msg['content']['data'])\n",
+ " });\n",
+ " return ws;\n",
+ "}\n",
+ "\n",
+ "mpl.mpl_figure_comm = function(comm, msg) {\n",
+ " // This is the function which gets called when the mpl process\n",
+ " // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
+ "\n",
+ " var id = msg.content.data.id;\n",
+ " // Get hold of the div created by the display call when the Comm\n",
+ " // socket was opened in Python.\n",
+ " var element = $(\"#\" + id);\n",
+ " var ws_proxy = comm_websocket_adapter(comm)\n",
+ "\n",
+ " function ondownload(figure, format) {\n",
+ " window.open(figure.imageObj.src);\n",
+ " }\n",
+ "\n",
+ " var fig = new mpl.figure(id, ws_proxy,\n",
+ " ondownload,\n",
+ " element.get(0));\n",
+ "\n",
+ " // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
+ " // web socket which is closed, not our websocket->open comm proxy.\n",
+ " ws_proxy.onopen();\n",
+ "\n",
+ " fig.parent_element = element.get(0);\n",
+ " fig.cell_info = mpl.find_output_cell(\"\");\n",
+ " if (!fig.cell_info) {\n",
+ " console.error(\"Failed to find cell for figure\", id, fig);\n",
+ " return;\n",
+ " }\n",
+ "\n",
+ " var output_index = fig.cell_info[2]\n",
+ " var cell = fig.cell_info[0];\n",
+ "\n",
+ "};\n",
+ "\n",
+ "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
+ " var width = fig.canvas.width/mpl.ratio\n",
+ " fig.root.unbind('remove')\n",
+ "\n",
+ " // Update the output cell to use the data from the current canvas.\n",
+ " fig.push_to_output();\n",
+ " var dataURL = fig.canvas.toDataURL();\n",
+ " // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
+ " // the notebook keyboard shortcuts fail.\n",
+ " IPython.keyboard_manager.enable()\n",
+ " $(fig.parent_element).html('| \n", + " | x | \n", + "y | \n", + "vx | \n", + "vy | \n", + "
|---|---|---|---|---|
| 4.896 | \n", + "39.033848 | \n", + "42.325221 | \n", + "6.726804 | \n", + "-15.869290 | \n", + "
| 4.947 | \n", + "39.376127 | \n", + "41.505021 | \n", + "6.695814 | \n", + "-16.294823 | \n", + "
| 4.998 | \n", + "39.716812 | \n", + "40.663211 | \n", + "6.664295 | \n", + "-16.716737 | \n", + "
| 5.049 | \n", + "40.055876 | \n", + "39.799976 | \n", + "6.632259 | \n", + "-17.134973 | \n", + "
| 5.100 | \n", + "40.393294 | \n", + "38.915507 | \n", + "6.599718 | \n", + "-17.549471 | \n", + "
\n",
+ "\n",
+ "\n",
+ " \n",
+ "
\n",
+ "
"
+ ],
+ "text/plain": [
+ "init theta 0 radian\n",
+ "y 0 meter\n",
+ "r ...\n",
+ "k 2.7925531914893616e-05 meter\n",
+ "ts [0.0 second, 1.3 second, 2.6 second, 3.9000000...\n",
+ "dtype: object"
+ ]
+ },
+ "execution_count": 7,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "system = make_system(condition)\n",
+ "system"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "| \n", + " | value | \n", + "
|---|---|
| init | \n", + "theta 0 radian\n", + "y 0 meter\n", + "r ... | \n", + "
| k | \n", + "2.7925531914893616e-05 meter | \n", + "
| ts | \n", + "[0.0 second, 1.3 second, 2.6 second, 3.9000000... | \n", + "
\n",
+ "\n",
+ "\n",
+ " \n",
+ "
\n",
+ "
"
+ ],
+ "text/plain": [
+ "theta 0 radian\n",
+ "y 0 meter\n",
+ "r 0.02 meter\n",
+ "dtype: object"
+ ]
+ },
+ "execution_count": 8,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "system.init"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Now we can write a slope function based on the differential equations\n",
+ "\n",
+ "$\\omega = \\frac{d\\theta}{dt} = 10$\n",
+ "\n",
+ "$\\frac{dy}{dt} = r \\frac{d\\theta}{dt}$\n",
+ "\n",
+ "$\\frac{dr}{dt} = k \\frac{d\\theta}{dt}$\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "def slope_func(state, t, system):\n",
+ " \"\"\"Computes the derivatives of the state variables.\n",
+ " \n",
+ " state: State object with theta, y, r\n",
+ " t: time\n",
+ " system: System object with r, k\n",
+ " \n",
+ " returns: sequence of derivatives\n",
+ " \"\"\"\n",
+ " theta, y, r = state\n",
+ " unpack(system)\n",
+ " \n",
+ " omega = 10 * radian / s\n",
+ " dydt = r * omega\n",
+ " drdt = k * omega\n",
+ " \n",
+ " return omega, dydt, drdt"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Testing `slope_func`"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "(| \n", + " | value | \n", + "
|---|---|
| theta | \n", + "0 radian | \n", + "
| y | \n", + "0 meter | \n", + "
| r | \n", + "0.02 meter | \n", + "
\n",
+ "\n",
+ "\n",
+ " \n",
+ "
\n",
+ "
"
+ ],
+ "text/plain": [
+ " theta y r\n",
+ "124.8 1248.0 46.707064 0.054851\n",
+ "126.1 1261.0 47.422487 0.055214\n",
+ "127.4 1274.0 48.142630 0.055577\n",
+ "128.7 1287.0 48.867493 0.055940\n",
+ "130.0 1300.0 49.597074 0.056303"
+ ]
+ },
+ "execution_count": 12,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "system.results.tail()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Extracting one time series per variable (and converting `r` to radians):"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 13,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "thetas = system.results.theta\n",
+ "ys = system.results.y\n",
+ "rs = system.results.r * 1000"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Plotting `theta`"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 14,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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GF8f6wcOZr+MKSU/U5iGyf/3rX7h48SI+/PBDrF+/HoMGDUJwcDC8vLxgZWWF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\nQqHAkiVLIBaLERERgfj4eKhUKujKo9Z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+ "text/plain": [
+ "| \n", + " | theta | \n", + "y | \n", + "r | \n", + "
|---|---|---|---|
| 124.8 | \n", + "1248.0 | \n", + "46.707064 | \n", + "0.054851 | \n", + "
| 126.1 | \n", + "1261.0 | \n", + "47.422487 | \n", + "0.055214 | \n", + "
| 127.4 | \n", + "1274.0 | \n", + "48.142630 | \n", + "0.055577 | \n", + "
| 128.7 | \n", + "1287.0 | \n", + "48.867493 | \n", + "0.055940 | \n", + "
| 130.0 | \n", + "1300.0 | \n", + "49.597074 | \n", + "0.056303 | \n", + "
\n",
+ "\n",
+ "\n",
+ " \n",
+ "
\n",
+ "
"
+ ],
+ "text/plain": [
+ "init theta 0 radian\n",
+ "omega 0.0 radi...\n",
+ "k 2.7925531914893616e-05 meter / radian\n",
+ "rho_h 26.07109543981524 kilogram / meter ** 2\n",
+ "Rmin 0.02 meter\n",
+ "Rmax 0.055 meter\n",
+ "Mcore 0.015 kilogram\n",
+ "Mroll 0.215 kilogram\n",
+ "ts [0.0 second, 1.8 second, 3.6 second, 5.4 secon...\n",
+ "dtype: object"
+ ]
+ },
+ "execution_count": 25,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "system = make_system(condition)\n",
+ "system"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 26,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "| \n", + " | value | \n", + "
|---|---|
| init | \n", + "theta 0 radian\n", + "omega 0.0 radi... | \n", + "
| k | \n", + "2.7925531914893616e-05 meter / radian | \n", + "
| rho_h | \n", + "26.07109543981524 kilogram / meter ** 2 | \n", + "
| Rmin | \n", + "0.02 meter | \n", + "
| Rmax | \n", + "0.055 meter | \n", + "
| Mcore | \n", + "0.015 kilogram | \n", + "
| Mroll | \n", + "0.215 kilogram | \n", + "
| ts | \n", + "[0.0 second, 1.8 second, 3.6 second, 5.4 secon... | \n", + "
\n",
+ "\n",
+ "\n",
+ " \n",
+ "
\n",
+ "
"
+ ],
+ "text/plain": [
+ "theta 0 radian\n",
+ "omega 0.0 radian / second\n",
+ "y 47 meter\n",
+ "dtype: object"
+ ]
+ },
+ "execution_count": 26,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "system.init"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Here's how we compute `I` as a function of `r`:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 27,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "def moment_of_inertia(r, system):\n",
+ " \"\"\"Moment of inertia for a roll of toilet paper.\n",
+ " \n",
+ " r: current radius of roll in meters\n",
+ " system: System object with Mcore, rho, Rmin, Rmax\n",
+ " \n",
+ " returns: moment of inertia in kg m**2\n",
+ " \"\"\"\n",
+ " unpack(system)\n",
+ " Icore = Mcore * Rmin**2 \n",
+ " Iroll = pi * rho_h / 2 * (r**4 - Rmin**4)\n",
+ " return Icore + Iroll"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "When `r` is `Rmin`, `I` is small."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 28,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "6e-06 kilogram meter2"
+ ],
+ "text/latex": [
+ "$6e-06 kilogram \\cdot meter^{2}$"
+ ],
+ "text/plain": [
+ "| \n", + " | value | \n", + "
|---|---|
| theta | \n", + "0 radian | \n", + "
| omega | \n", + "0.0 radian / second | \n", + "
| y | \n", + "47 meter | \n", + "
\n",
+ "\n",
+ "\n",
+ " \n",
+ "
\n",
+ "
"
+ ],
+ "text/plain": [
+ " theta omega y\n",
+ "172.8 503.376998 6.830222 22.852269\n",
+ "174.6 515.788219 6.960580 22.346268\n",
+ "176.4 528.437150 7.094376 21.835001\n",
+ "178.2 541.330151 7.231802 21.318468\n",
+ "180.0 554.473940 7.373066 20.796665"
+ ]
+ },
+ "execution_count": 33,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "system.results.tail()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Extrating the time series"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 34,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "thetas = system.results.theta\n",
+ "omegas = system.results.omega\n",
+ "ys = system.results.y"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Plotting `theta`"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 35,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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ppZdaOk4hRAdWXa2w98gVTl28tVirp4stE6J6YGUhsw3aqgb9n3n88ccpKChg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\nzVJCQkKU++67T3n33XeVqqqq1gy7Xfn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+ "text/plain": [
+ "| \n", + " | theta | \n", + "omega | \n", + "y | \n", + "
|---|---|---|---|
| 172.8 | \n", + "503.376998 | \n", + "6.830222 | \n", + "22.852269 | \n", + "
| 174.6 | \n", + "515.788219 | \n", + "6.960580 | \n", + "22.346268 | \n", + "
| 176.4 | \n", + "528.437150 | \n", + "7.094376 | \n", + "21.835001 | \n", + "
| 178.2 | \n", + "541.330151 | \n", + "7.231802 | \n", + "21.318468 | \n", + "
| 180.0 | \n", + "554.473940 | \n", + "7.373066 | \n", + "20.796665 | \n", + "
\n",
+ "\n",
+ "\n",
+ " \n",
+ "
\n",
+ "
"
+ ],
+ "text/plain": [
+ "init theta 0 radian\n",
+ "omega 0.0 radi...\n",
+ "k 9.6e-05 meter / radian\n",
+ "Rmin 0.008 meter\n",
+ "Rmax 0.016 meter\n",
+ "mass 0.05 kilogram\n",
+ "I 3.0625000000000006e-05 kilogram * meter ** 2\n",
+ "g 9.8 meter / second ** 2\n",
+ "ts [0.0 second, 0.01 second, 0.02 second, 0.03 se...\n",
+ "dtype: object"
+ ]
+ },
+ "execution_count": 41,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "system = make_system(condition)\n",
+ "system"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 42,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "| \n", + " | value | \n", + "
|---|---|
| init | \n", + "theta 0 radian\n", + "omega 0.0 radi... | \n", + "
| k | \n", + "9.6e-05 meter / radian | \n", + "
| Rmin | \n", + "0.008 meter | \n", + "
| Rmax | \n", + "0.016 meter | \n", + "
| mass | \n", + "0.05 kilogram | \n", + "
| I | \n", + "3.0625000000000006e-05 kilogram * meter ** 2 | \n", + "
| g | \n", + "9.8 meter / second ** 2 | \n", + "
| ts | \n", + "[0.0 second, 0.01 second, 0.02 second, 0.03 se... | \n", + "
\n",
+ "\n",
+ "\n",
+ " \n",
+ "
\n",
+ "
"
+ ],
+ "text/plain": [
+ "theta 0 radian\n",
+ "omega 0.0 radian / second\n",
+ "y 1 meter\n",
+ "v 0.0 meter / second\n",
+ "dtype: object"
+ ]
+ },
+ "execution_count": 42,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "system.init"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Write a slope function for this system, using these results from the book:\n",
+ "\n",
+ "$ r = \\sqrt{2 k y + R_{min}^2} $ \n",
+ "\n",
+ "$ T = m g I / I^* $\n",
+ "\n",
+ "$ a = -m g r^2 / I^* $\n",
+ "\n",
+ "$ \\alpha = m g r / I^* $\n",
+ "\n",
+ "where $I^*$ is the augmented moment of inertia, $I + m r^2$.\n",
+ "\n",
+ "Hint: If `y` is less than 0, it means you have reached the end of the string, so the equation for `r` is no longer valid. In this case, the simplest thing to do it return the sequence of derivatives `0, 0, 0, 0`"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 55,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def slope_func(state,t,system):\n",
+ " theta, omega, y, v = state\n",
+ " unpack(system)\n",
+ " \n",
+ " if y < 0*m:\n",
+ " return 0,0,0,0\n",
+ "\n",
+ " \n",
+ " r=sqrt(2*k*y + Rmin**2)\n",
+ " alpha=mass*g*r/I*m*r**2\n",
+ " dydt= -r *omega\n",
+ " \n",
+ " \n",
+ " return omega, alpha, v, dydt"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Test your slope function with the initial conditions."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 56,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "(| \n", + " | value | \n", + "
|---|---|
| theta | \n", + "0 radian | \n", + "
| omega | \n", + "0.0 radian / second | \n", + "
| y | \n", + "1 meter | \n", + "
| v | \n", + "0.0 meter / second | \n", + "
\n",
+ "\n",
+ "\n",
+ " \n",
+ "
\n",
+ "
"
+ ],
+ "text/plain": [
+ " theta omega y v\n",
+ "0.96 0.030198 0.062912 0.999845 -0.000483\n",
+ "0.97 0.030831 0.063567 0.999841 -0.000493\n",
+ "0.98 0.031470 0.064222 0.999836 -0.000504\n",
+ "0.99 0.032115 0.064878 0.999830 -0.000514\n",
+ "1.00 0.032767 0.065533 0.999825 -0.000524"
+ ]
+ },
+ "execution_count": 60,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "system.results.tail()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Plot the results."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 61,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "thetas = system.results.theta\n",
+ "ys = system.results.y"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "`theta` should increase and accelerate."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 62,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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zsOoKqKqqinbtZOI9IUTrVqmtZeu+UxSX100sqlKpGBYTQrfO8ky4OVh1BTR1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\n",
+ "text/plain": [
+ "| \n", + " | theta | \n", + "omega | \n", + "y | \n", + "v | \n", + "
|---|---|---|---|---|
| 0.96 | \n", + "0.030198 | \n", + "0.062912 | \n", + "0.999845 | \n", + "-0.000483 | \n", + "
| 0.97 | \n", + "0.030831 | \n", + "0.063567 | \n", + "0.999841 | \n", + "-0.000493 | \n", + "
| 0.98 | \n", + "0.031470 | \n", + "0.064222 | \n", + "0.999836 | \n", + "-0.000504 | \n", + "
| 0.99 | \n", + "0.032115 | \n", + "0.064878 | \n", + "0.999830 | \n", + "-0.000514 | \n", + "
| 1.00 | \n", + "0.032767 | \n", + "0.065533 | \n", + "0.999825 | \n", + "-0.000524 | \n", + "
\n",
+ "\n",
+ "\n",
+ " \n",
+ "
\n",
+ "
"
+ ],
+ "text/plain": [
+ "0 0.000000\n",
+ "1 9.000000\n",
+ "2 10.530000\n",
+ "3 11.978100\n",
+ "4 13.614237\n",
+ "5 15.473489\n",
+ "6 17.586642\n",
+ "7 19.988378\n",
+ "8 22.718110\n",
+ "9 25.820630\n",
+ "10 29.346849\n",
+ "11 33.354630\n",
+ "dtype: float64"
+ ]
+ },
+ "execution_count": 15,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "run_simulation(system)\n",
+ "system.juveniles"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 16,
"metadata": {
"collapsed": true
},
@@ -307,11 +434,21 @@
" \"\"\"\n",
" newfig()\n",
" plot(system.adults, 'bo-', label='adults')\n",
+ " plot(system.juveniles, 'rs-', label='juveniles')\n",
" decorate(xlabel='Season', \n",
" ylabel='Rabbit population',\n",
" title=title)"
]
},
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": []
+ },
{
"cell_type": "markdown",
"metadata": {},
@@ -321,14 +458,14 @@
},
{
"cell_type": "code",
- "execution_count": 6,
+ "execution_count": 17,
"metadata": {},
"outputs": [
{
"data": {
- "image/png": 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hHoJGoz9tb48eSi3/6kySvxBCCPEQfv8dLlxQlq2soHt3k4ZjEEn+QgghxEPY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\nNmyY3KUZjREjRuDOnTuQJAk1NTW632va32Wpqan48MMPkZ2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+ "image/png": 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wfPnyMvsLCAjAmTNncPDgQZiYmGD69OmYPHnyB/lYGhsCriIPEUHIoW/fvjA1NcXevXsV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\nUalU1NTUaAWEhYUFixcvpry8XDN26NAhNm7cSG5uLpaWlvj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"text/plain": [
- "| \n", + " | value | \n", + "
|---|---|
| 0 | \n", + "0.000000 | \n", + "
| 1 | \n", + "9.000000 | \n", + "
| 2 | \n", + "10.530000 | \n", + "
| 3 | \n", + "11.978100 | \n", + "
| 4 | \n", + "13.614237 | \n", + "
| 5 | \n", + "15.473489 | \n", + "
| 6 | \n", + "17.586642 | \n", + "
| 7 | \n", + "19.988378 | \n", + "
| 8 | \n", + "22.718110 | \n", + "
| 9 | \n", + "25.820630 | \n", + "
| 10 | \n", + "29.346849 | \n", + "
| 11 | \n", + "33.354630 | \n", + "