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@aflaxman
Forked from Tillsten/exp_sum_pymc.py
Created November 6, 2012 18:58
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Fit to an expontial sum in pymc
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{
"metadata": {
"name": "exp_sum_pymc"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "code",
"collapsed": false,
"input": [
"import pymc\n",
"import numpy as np"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 1
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Make test data\n",
"t=np.linspace(0,20,200)\n",
"decays = np.array([2.3,9])\n",
"x=np.linspace(-1,1, 32)\n",
"amp1 = 10*np.exp(-(x+0.5)**2/0.3)\n",
"amp2 = -8*np.exp(-(x-0.5)**2/0.4)\n",
"amps=np.column_stack((amp1,amp2))\n",
"d=amps.dot(np.exp(-t/decays[:,None]))"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 2
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"plot(x, amp1, label='amp1')\n",
"plot(x, amp2, label='amp2')\n",
"grid()\n",
"legend()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "pyout",
"prompt_number": 3,
"text": [
"<matplotlib.legend.Legend at 0xaf5de6c>"
]
},
{
"output_type": "display_data",
"png": 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pX5nZmdxIu0FyWjLX7lzj8u3LJKYkkpiSyIlrJ9hxfkfOdmJKIpnZmbg7uVOu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\n"
}
],
"prompt_number": 3
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Add Noise\n",
"noise1 = np.linspace(0,0.5,32)\n",
"np.random.shuffle(noise1)\n",
"dn=d+noise1[:,None]*np.random.randn(32,t.size)\n",
"dn+=np.random.randn(1, t.size)*0.4"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 4
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"plot(t, dn.T)\n",
"grid()\n",
"title('dn(t)')"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "pyout",
"prompt_number": 5,
"text": [
"<matplotlib.text.Text at 0xb025dec>"
]
},
{
"output_type": "display_data",
"png": 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E6pBtLEJlsaJp9+GKZiWVt0xkcU0N96ztBFSoejQEKcrIdv8vT+d6sWnsaF6c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\n5uYzxlBbeizk3pxL4+ozJ++pqq5G1l7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iwKvo7HXPcv/6O/lyyX2I+gLZmTGNk9qJWBRW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\npziR6AVBEE5x/x/EXlH4FiAnhAAAAABJRU5ErkJggg==\n"
}
],
"prompt_number": 5
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def model():\n",
" \n",
" sigma = pymc.Exponential('sigma', 1., value=.1*ones(32))\n",
" eta = pymc.Normal('eta', .4, .1**-2, value=.4, observed=True)\n",
" \n",
" amps = pymc.Uniform('amps', -20, 20, value=zeros((32,2)))\n",
" decays = pymc.Normal('decays', [2.3,9], .1**-2, value=[2.3,9], observed=True)\n",
" \n",
" base = pymc.exp(-t/decays[:,None])\n",
" model = pymc.LinearCombination('fit', [amps], [base])\n",
" \n",
" global_err = pymc.Normal('errs', 0, 1/eta**2, value=zeros_like(t), observed=True)\n",
" ch_errs=[]\n",
" for i in range(32):\n",
" x=pymc.Normal('err'+str(i), model[i,:]+global_err, tau=1/sigma[i]**2,\n",
" value=dn[i,:], observed=True) \n",
" ch_errs.append(x)\n",
" \n",
" return locals()"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 6
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"vars = model()\n",
"pymc.MAP([vars['amps'], vars['ch_errs']]).fit(method='fmin_powell', verbose=1)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Current log-probability : -451002.093578\n",
"Current log-probability : -232885.380200"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"Current log-probability : -139020.487273"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"Current log-probability : -98631.281777"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"Current log-probability : -81243.611057"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"Current log-probability : -73760.745946"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"Current log-probability : -70540.046207"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"Current log-probability : -69154.416981"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"Current log-probability : -68558.104993"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"Current log-probability : -68301.479353"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"Current log-probability : -68191.039314"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"Current log-probability : -68143.510929"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"Current log-probability : -68123.056868"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"Current log-probability : -68114.254367"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"Current log-probability : -68110.466170"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"Optimization terminated successfully.\n",
" Current function value: 68110.466166\n",
" Iterations: 15\n",
" Function evaluations: 8699\n"
]
}
],
"prompt_number": 7
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"m = pymc.MCMC(vars)\n",
"\n",
"m.use_step_method(pymc.AdaptiveMetropolis, m.sigma)\n",
"m.use_step_method(pymc.AdaptiveMetropolis, m.amps)\n",
"\n",
"%time m.sample(iter=100000, burn=50000, thin=5)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
" \r",
"[****************100%******************] 100000 of 100000 complete"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
" CPU times: user 232.93 s, sys: 10.06 s, total: 242.99 s\n",
"Wall time: 328.07 s\n"
]
}
],
"prompt_number": 8
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"plot(x, m.amps.trace().mean(0)[:,0], 'r-', label='predicted')\n",
"plot(x, m.amps.trace().mean(0)[:,1], 'r-')\n",
"\n",
"plot(x, pymc.utils.hpd(m.amps.trace(), .05).reshape(32,4), 'r--')\n",
"\n",
"plot(x, amp1, 'k-', label='truth')\n",
"plot(x, amp2, 'k-')\n",
"grid()\n",
"legend()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "pyout",
"prompt_number": 9,
"text": [
"<matplotlib.legend.Legend at 0xb57874c>"
]
},
{
"output_type": "display_data",
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TJ04IERwsRMmSQowaJYROp+rTwFR9Gk5WQna25eyL/tNTxsXFhY4dO/573h44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\n"
}
],
"prompt_number": 9
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"plot(t, m.model.trace().mean(0).T)\n",
"grid()\n",
"title('d_predicted(t)')"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "pyout",
"prompt_number": 10,
"text": [
"<matplotlib.text.Text at 0xb592b8c>"
]
},
{
"output_type": "display_data",
"png": 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Ivb5InDxZR5yLXCKcFziLQzGHbmkbMzdaXHRbIwx9+wlRWiqEKLsg2vnCBWEa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\nQfjyS0Ho6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}
],
"prompt_number": 10
},
{
"cell_type": "code",
"collapsed": false,
"input": [],
"language": "python",
"metadata": {},
"outputs": []
}
],
"metadata": {}
}
]
}
# -*- coding: utf-8 -*-
# <nbformat>3.0</nbformat>
# <codecell>
import pymc
import numpy as np
# <codecell>
# Make test data
t=np.linspace(0,20,200)
decays = np.array([2.3,9])
x=np.linspace(-1,1, 32)
amp1 = 10*np.exp(-(x+0.5)**2/0.3)
amp2 = -8*np.exp(-(x-0.5)**2/0.4)
amps=np.column_stack((amp1,amp2))
d=amps.dot(np.exp(-t/decays[:,None]))
# <codecell>
plot(x, amp1, label='amp1')
plot(x, amp2, label='amp2')
grid()
legend()
# <codecell>
#Add Noise
noise1 = np.linspace(0,0.5,32)
np.random.shuffle(noise1)
dn=d+noise1[:,None]*np.random.randn(32,t.size)
dn+=np.random.randn(1, t.size)*0.4
# <codecell>
plot(t, dn.T)
grid()
title('dn(t)')
# <codecell>
def model():
sigma = pymc.Exponential('sigma', 1., value=.1*ones(32))
eta = pymc.Normal('eta', .4, .1**-2, value=.4, observed=True)
amps = pymc.Uniform('amps', -20, 20, value=zeros((32,2)))
decays = pymc.Normal('decays', [2.3,9], .1**-2, value=[2.3,9], observed=True)
base = pymc.exp(-t/decays[:,None])
model = pymc.LinearCombination('fit', [amps], [base])
global_err = pymc.Normal('errs', 0, 1/eta**2, value=zeros_like(t), observed=True)
ch_errs=[]
for i in range(32):
x=pymc.Normal('err'+str(i), model[i,:]+global_err, tau=1/sigma[i]**2,
value=dn[i,:], observed=True)
ch_errs.append(x)
return locals()
# <codecell>
vars = model()
pymc.MAP([vars['amps'], vars['ch_errs']]).fit(method='fmin_powell', verbose=1)
# <codecell>
m = pymc.MCMC(vars)
m.use_step_method(pymc.AdaptiveMetropolis, m.sigma)
m.use_step_method(pymc.AdaptiveMetropolis, m.amps)
%time m.sample(iter=100000, burn=50000, thin=5)
# <codecell>
plot(x, m.amps.trace().mean(0)[:,0], 'r-', label='predicted')
plot(x, m.amps.trace().mean(0)[:,1], 'r-')
plot(x, pymc.utils.hpd(m.amps.trace(), .05).reshape(32,4), 'r--')
plot(x, amp1, 'k-', label='truth')
plot(x, amp2, 'k-')
grid()
legend()
# <codecell>
plot(t, m.model.trace().mean(0).T)
grid()
title('d_predicted(t)')
# <codecell>
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