Experiments on showing how Taylor expansion works.
Probably will be added to the Math chapter once finalized.
This commit is contained in:
Roger Labbe
parent
727ca9bed9
commit
9950fb9ec8
277
experiments/Untitled.ipynb
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277
experiments/Untitled.ipynb
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"cells": [
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{
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"cell_type": "code",
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"execution_count": 3,
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"metadata": {
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"collapsed": true
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},
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"outputs": [],
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"source": [
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"%matplotlib inline\n",
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"\n",
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"import numpy as np\n",
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"import matplotlib.pyplot as plt\n",
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"from math import sin, cos, factorial\n",
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"\n",
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"\n",
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"def f_sin(x, p):\n",
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" if p == 0:\n",
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" return sin(x)\n",
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"\n",
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" return x\n",
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" if p % 4 == 1:\n",
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" return cos(x)\n",
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"\n",
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" if p % 4 == 2:\n",
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" return -sin(x)\n",
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"\n",
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" if p % 4 == 3:\n",
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" return -cos(x)\n",
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"\n",
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" return sin(x)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 4,
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"metadata": {
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"collapsed": true
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},
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"outputs": [],
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"source": [
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"def taylor(df, x, a, n):\n",
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"\n",
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" f = 0.0\n",
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"\n",
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" for i in range(n+1):\n",
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" term = df(a, i) * (x - a)**i / factorial(i)\n",
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" f += term\n",
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"\n",
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" return f"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 23,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"+EVEYkbBLyISMwp+EZGYUfCLiMSMgl9EJGYU/CIiMaPgFxGJmXR+bP1eM5tnZjPN7EUza1JJu0Fm\n",
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||||
"AAAAAElFTkSuQmCC\n"
|
||||
],
|
||||
"text/plain": [
|
||||
"<matplotlib.figure.Figure at 0x7ac3550>"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
"output_type": "display_data"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"\n",
|
||||
"from IPython.html.widgets import interact, interactive, fixed\n",
|
||||
"from IPython.html.widgets import FloatSliderWidget as fWidget\n",
|
||||
"from IPython.html.widgets import IntSliderWidget as iWidget\n",
|
||||
"\n",
|
||||
"x = 0.1\n",
|
||||
"a = 0.8\n",
|
||||
"n = 1\n",
|
||||
"\n",
|
||||
"def plot_data(a, n):\n",
|
||||
" xs = np.linspace(-2, 2, 50)\n",
|
||||
" ts = [taylor(f_sin, i, a, n) for i in xs]\n",
|
||||
"\n",
|
||||
" plt.plot(xs, np.sin(xs))\n",
|
||||
" plt.plot(xs, ts)\n",
|
||||
" plt.xlim(-2,2)\n",
|
||||
" plt.ylim(-2,2)\n",
|
||||
" plt.axvline(a)\n",
|
||||
" plt.show()\n",
|
||||
" \n",
|
||||
"interact(plot_data, \n",
|
||||
" a = fWidget(value=0.8, min=-1.9, max=1.9),\n",
|
||||
" n = iWidget(value=2, min=1, max=8))"
|
||||
]
|
||||
}
|
||||
],
|
||||
"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": "3.4.1"
|
||||
}
|
||||
},
|
||||
"nbformat": 4,
|
||||
"nbformat_minor": 0
|
||||
}
|
||||
56
experiments/taylor.py
Normal file
56
experiments/taylor.py
Normal file
@ -0,0 +1,56 @@
|
||||
# -*- coding: utf-8 -*-
|
||||
"""
|
||||
Created on Thu Mar 19 08:26:08 2015
|
||||
|
||||
@author: rlabbe
|
||||
"""
|
||||
|
||||
import numpy as np
|
||||
import matplotlib.pyplot as plt
|
||||
|
||||
from math import sin, cos, factorial
|
||||
def df(x, p):
|
||||
if p == 0:
|
||||
return sin(x)
|
||||
|
||||
return x
|
||||
if p % 4 == 1:
|
||||
return cos(x)
|
||||
|
||||
if p % 4 == 2:
|
||||
return -sin(x)
|
||||
|
||||
if p % 4 == 3:
|
||||
return -cos(x)
|
||||
|
||||
return sin(x)
|
||||
|
||||
|
||||
|
||||
|
||||
def taylor(df, x, a, n):
|
||||
|
||||
f = 0.0
|
||||
|
||||
for i in range(n+1):
|
||||
term = df(a, i) * (x - a)**i / factorial(i)
|
||||
f += term
|
||||
|
||||
return f
|
||||
|
||||
|
||||
x = 0.1
|
||||
a = 0.8
|
||||
n = 1
|
||||
|
||||
|
||||
|
||||
plt.cla()
|
||||
|
||||
xs = np.linspace(-2, 2, 100)
|
||||
ts = [taylor(df, i, a, n) for i in xs]
|
||||
|
||||
plt.plot(xs, np.sin(xs))
|
||||
plt.plot(xs, ts)
|
||||
|
||||
|
||||
Loading…
Reference in New Issue
Block a user