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lstagner/redux.ipynb

Last active August 29, 2015 14:16
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redux.ipynb
{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"%matplotlib inline"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#Lets see what happens if the velocity array fills up at every cell"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [
{
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],
"text/plain": [
"<matplotlib.figure.Figure at 0x34b19d0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"nvelocities = 200\n",
"fhi = np.arange(nvelocities/2) #first half of array\n",
"shi = nvelocities/2 + np.arange(nvelocities/2) #second half of array\n",
"esi = 2*fhi + 1 #every second index\n",
"ids = np.zeros(nvelocities,dtype=np.int) #position id of where velocity was generated\n",
"\n",
"#Assume worst case senario that it reduces at every grid cell\n",
"for i in range(100):\n",
" ids[fhi] = ids[esi]\n",
" ids[shi] = i+1\n",
"\n",
"plt.hist(ids);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##The first calculated cells are missing"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#How many unique cells are represented after each iteration"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false,
"scrolled": true
},
"outputs": [
{
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],
"text/plain": [
"<matplotlib.figure.Figure at 0x34b7e50>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"nvelocities = 10000\n",
"fhi = np.arange(nvelocities/2) #first half of array\n",
"shi = nvelocities/2 + np.arange(nvelocities/2) #second half of array\n",
"esi = 2*fhi + 1 #every second index\n",
"ids = np.zeros(nvelocities,dtype=np.int) #position id of where velocity was generated\n",
"\n",
"uniques = np.zeros(100)\n",
"#Assume worst case senario that it reduces at every grid cell\n",
"for i in range(100):\n",
" ids[fhi] = ids[esi]\n",
" ids[shi] = i+1\n",
" uniques[i] = np.unique(ids).size\n",
" \n",
"fig,ax = plt.subplots()\n",
"fig.set_size_inches(8,5)\n",
"ax.plot(uniques);\n",
"ax.set_xlabel('Iteration')\n",
"ax.set_ylabel('# unique')\n",
"ax.set_ylim(0,20);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##The number of unique cells represented saturates"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#Lets see how the that number changes with number of stored velocities"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"num_velocities = 10000\n",
"unique = np.zeros(num_velocities)\n",
"for num in range(num_velocities):\n",
" nvelocities=num+2\n",
" fhi = np.arange(nvelocities/2) #first half of array\n",
" shi = nvelocities/2 + np.arange(nvelocities/2) #second half of array\n",
" esi = 2*fhi + 1 #every second index\n",
" ids = np.zeros(nvelocities,dtype=np.int) #position id of where velocity was generated\n",
" nunique = 0\n",
" i=0\n",
" while True:\n",
" nunique_old=nunique\n",
" ids[fhi] = ids[esi]\n",
" ids[shi] = i+1\n",
" nunique = np.unique(ids).size\n",
" if nunique == nunique_old:\n",
" break\n",
" i=i+1\n",
" unique[num] = nunique\n"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
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],
"text/plain": [
"<matplotlib.figure.Figure at 0x36307d0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig,ax = plt.subplots()\n",
"fig.set_size_inches((8,5))\n",
"ax.plot(unique,'-')\n",
"ax.set_xlabel('# of velocities saved')\n",
"ax.set_ylabel('Max number of unique cells')\n",
"ax.set_xscale('log')"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": true
},
"source": [
"#This might be a problem"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.5+"
}
},
"nbformat": 4,
"nbformat_minor": 0
}
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