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@squarednob
Created February 24, 2016 19:34
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Python: Pseudo integrate class
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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"import numpy as np\n",
"from matplotlib.pylab import plt\n",
"%matplotlib inline\n",
"\n",
"class PseudoIntegrate(object):\n",
" def __init__(self, x1=None, x2=None, x_number=None):\n",
" # defoult argument for x1, x2, x_number, y:\n",
" self.x1 = x1 or -10 # Left bound of x.\n",
" self.x2 = x2 or 10 # Right bound of x.\n",
" self.x_number = x_number or 300 # Number of numpy array element between x1 ~ x2.\n",
" \n",
" # Solve 1st order differential:\n",
" def integrate(self, fx, y_amount=None):\n",
" '''\n",
" fx = differential function\n",
" y_amount = initial amount of y:\n",
" '''\n",
" y_amount = y_amount or 0\n",
" \n",
" x_list = np.linspace(self.x1, self.x2, self.x_number)\n",
" y_list = []\n",
" \n",
" # Update y by adding dif:\n",
" for dx in x_list:\n",
" # dif=change in amount of y, dx=x in now, y_amout=Amount of y in now:\n",
" dif = fx(dx, y_amount)\n",
" y_list.append(y_amount+dif)\n",
" y_amount = y_amount + dif\n",
"\n",
" plt.plot(x_list, y_list)\n",
" \n",
" \n",
" # Solve 2nd order differential:\n",
" def integrate2ndOrder(self, fx, y_amount=None, dif_amount=None):\n",
" '''\n",
" fx = differential function,\n",
" y_amount = initial amount of y\n",
" dif_amount = initial amount of 1st order differential:\n",
" '''\n",
" # default value of argument:\n",
" y_amount = y_amount or 0\n",
" dif_amount = dif_amount or 0\n",
" \n",
" # make lists:\n",
" x_list = np.linspace(self.x1, self.x2, self.x_number)\n",
" y_list = []\n",
" \n",
" # Update dif_amount, then updata y.\n",
" for dx in x_list:\n",
" # dif=change in amount of y, dx=x in now, y=Amount of y in now:\n",
" dif_amount = dif_amount + fx(dx, y_amount)\n",
" y_amount = y_amount + dif_amount\n",
" y_list.append(y_amount)\n",
"\n",
" plt.plot(x_list, y_list)"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"p =PseudoIntegrate()"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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FFA4i0oS2bQvDRG+8AYsXhzDYtg369AmXxe7TB3r21JVQM5HCQUQarbIy9ADeeQdWrgz3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\nwkFERJIoHEREJInCQUREkvx/wLOZz68rMIcAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x104e3d780>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# dy/dx = 2 * x^2 + 1 \n",
"def fx(dx, y):\n",
" return 2*(dx**2) + 1\n",
"\n",
"p.integrate(fx)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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WLXPUUsztpvCbMubKxh0d5RWl1mawBuF3y4esji1btrzy9YYNvTh7trfU31VV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\nQ2CEbzAYDB0CI3yDwWDoEPx/FbRj838xbbwAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10d1f8668>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# d2y/dx2 = -0.1 * y:\n",
"def fx(dx, y):\n",
" return -0.1*y\n",
"\n",
"p.integrate2ndOrder(fx, 10, 1)"
]
}
],
"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": "3.4.4"
}
},
"nbformat": 4,
"nbformat_minor": 0
}
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