mhjensen
188 lines
31 KiB
Plaintext
188 lines
31 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": 6,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"1.0110879714152359 2.0438571782842976\n",
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"[ 0. -2.20094088 -1.2269051 -0.59549218 0. 0.\n",
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" -0.00602718 -1.63131177 -1.41018017 -0.19538782 0. -0.29048766\n",
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" 0.18375465 1.12350786 -0.06959351 0. 0. 0.\n",
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" 0.25167654 0. ]\n",
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"(63014, 1) (63014,)\n"
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]
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},
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{
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"data": {
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"image/png": 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e5vWwQbvWxcCcgTZEU61u2VcMDQ2NRMRgq3LN7sVUhrslzYmItakJaV2aPgrM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\nThBmZpbLCcLMzHI5QZiZWa7/D84Ca9h1nC9AAAAAAElFTkSuQmCC\n",
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"text/plain": [
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"<matplotlib.figure.Figure at 0x10a1bb198>"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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},
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{
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"data": {
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"image/png": 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"text/plain": [
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"<matplotlib.figure.Figure at 0x1a129d77f0>"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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},
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{
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"data": {
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"image/png": 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8zCX4Pwccn+TYJMuB84Atww2SrE4yua/LgM1D265MMnkZ/wrgnoV3W5I0X7MGf7tSfx1w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\n/wfnQuc3ETNF1QAAAABJRU5ErkJggg==\n",
|
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"text/plain": [
|
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"<matplotlib.figure.Figure at 0x1119b1e80>"
|
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]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
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"source": [
|
|
"# Program to test the Metropolis algorithm with one particle at given temp in\n",
|
|
"# one dimension\n",
|
|
"#!/usr/bin/env python\n",
|
|
"import numpy as np\n",
|
|
"import matplotlib.mlab as mlab\n",
|
|
"import matplotlib.pyplot as plt\n",
|
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"import random\n",
|
|
"from math import sqrt, exp, log\n",
|
|
"from sklearn.preprocessing import PolynomialFeatures\n",
|
|
"from sklearn.linear_model import LinearRegression\n",
|
|
"# initialize the rng with a seed\n",
|
|
"random.seed()\n",
|
|
"# Hard coding of input parameters\n",
|
|
"MCcycles = 100000\n",
|
|
"Temperature = 2.0\n",
|
|
"beta = 1./Temperature\n",
|
|
"InitialVelocity = -2.0\n",
|
|
"CurrentVelocity = InitialVelocity\n",
|
|
"Energy = 0.5*InitialVelocity*InitialVelocity\n",
|
|
"VelocityRange = 10*sqrt(Temperature)\n",
|
|
"VelocityStep = 2*VelocityRange/10.\n",
|
|
"AverageEnergy = Energy\n",
|
|
"AverageEnergy2 = Energy*Energy\n",
|
|
"VelocityValues = np.zeros(MCcycles)\n",
|
|
"# The Monte Carlo sampling with Metropolis starts here\n",
|
|
"for i in range (1, MCcycles, 1):\n",
|
|
" TrialVelocity = CurrentVelocity + (2.0*random.random() - 1.0)*VelocityStep\n",
|
|
" EnergyChange = 0.5*(TrialVelocity*TrialVelocity -CurrentVelocity*CurrentVelocity);\n",
|
|
" if random.random() <= exp(-beta*EnergyChange):\n",
|
|
" CurrentVelocity = TrialVelocity\n",
|
|
" Energy += EnergyChange\n",
|
|
" VelocityValues[i] = CurrentVelocity\n",
|
|
" AverageEnergy += Energy\n",
|
|
" AverageEnergy2 += Energy*Energy\n",
|
|
"#Final averages\n",
|
|
"AverageEnergy = AverageEnergy/MCcycles\n",
|
|
"AverageEnergy2 = AverageEnergy2/MCcycles\n",
|
|
"Variance = AverageEnergy2 - AverageEnergy*AverageEnergy\n",
|
|
"print(AverageEnergy, Variance)\n",
|
|
"n, bins, patches = plt.hist(VelocityValues, 400, facecolor='green')\n",
|
|
"\n",
|
|
"plt.xlabel('$v$')\n",
|
|
"plt.ylabel('Velocity distribution P(v)')\n",
|
|
"plt.title(r'Velocity histogram at $k_BT=2$')\n",
|
|
"plt.axis([-5, 5, 0, 600])\n",
|
|
"plt.grid(True)\n",
|
|
"from collections import Counter\n",
|
|
"\n",
|
|
"#print (Counter(VelocityValues))\n",
|
|
"\n",
|
|
"print (VelocityValues[:20])\n",
|
|
"VelocityValues=list(Counter(VelocityValues).keys())\n",
|
|
"d=list(Counter(VelocityValues).values())\n",
|
|
"\n",
|
|
"VelocityValues=np.asarray(VelocityValues)[:, np.newaxis]\n",
|
|
"d=np.asarray(d)\n",
|
|
"print (VelocityValues.shape, d.shape)\n",
|
|
"\n",
|
|
"plt.scatter(VelocityValues, d)\n",
|
|
"plt.show()\n",
|
|
"\n",
|
|
"#2nd Degree Polynomial\n",
|
|
"poly_feat=PolynomialFeatures(degree=20, include_bias=False)\n",
|
|
"X_poly=poly_feat.fit_transform(VelocityValues)\n",
|
|
"lin_reg=LinearRegression()\n",
|
|
"poly_fit=lin_reg.fit(X_poly,d)\n",
|
|
"\n",
|
|
"y_plot=poly_fit.predict(X_poly)\n",
|
|
"plt.title(\"Polynomial Fit\")\n",
|
|
"plt.plot(VelocityValues, y_plot, color='black', label=\"Fit\")\n",
|
|
"plt.show()\n",
|
|
"\n",
|
|
"#Decision Trees\n",
|
|
"\n",
|
|
"from sklearn.tree import DecisionTreeRegressor\n",
|
|
"regr_1=DecisionTreeRegressor(max_depth=2)\n",
|
|
"regr_2=DecisionTreeRegressor(max_depth=5)\n",
|
|
"regr_3=DecisionTreeRegressor(max_depth=7)\n",
|
|
"regr_1.fit(VelocityValues, d)\n",
|
|
"regr_2.fit(VelocityValues, d)\n",
|
|
"regr_3.fit(VelocityValues, d)\n",
|
|
"\n",
|
|
"X_test = np.arange(0.0, MCcycles, 0.01)[:, np.newaxis]\n",
|
|
"y_1=regr_1.predict(X_test)\n",
|
|
"y_2=regr_2.predict(X_test)\n",
|
|
"y_3=regr_3.predict(X_test)\n",
|
|
"\n",
|
|
"plt.title(\"Decision Tree\")\n",
|
|
"plt.plot(X_test, y_1, color=\"red\", label=\"max_depth=2\", linewidth=2)\n",
|
|
"plt.plot(X_test, y_2, color=\"green\", label=\"max_depth=5\", linewidth=2)\n",
|
|
"plt.plot(X_test, y_3, color=\"m\", label=\"max_depth=7\", linewidth=2)\n",
|
|
"plt.show()\n",
|
|
"\n",
|
|
"#Separate each frequency not in one specific velocity, but in a range of values,\n",
|
|
"#i.e. frequency of all velocities in range -5 to -4.9, -4.9 to -4.8, etc..."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {},
|
|
"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": "3.6.3"
|
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}
|
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},
|
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"nbformat": 4,
|
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"nbformat_minor": 2
|
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}
|