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@aarontran
Created December 3, 2018 09:56
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Gala isochrone fit check"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"scrolled": true
},
"outputs": [],
"source": [
"from __future__ import division, print_function\n",
"import matplotlib as mpl\n",
"import matplotlib.pyplot as plt\n",
"import numpy as np\n",
"from scipy.optimize import minimize, leastsq\n",
"\n",
"import astropy.units as u\n",
"import gala.dynamics as gd\n",
"import gala.potential as gp\n",
"from gala.units import galactic\n",
"\n",
"%matplotlib inline\n",
"%load_ext autoreload\n",
"%autoreload 2"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"mwpot = gp.MilkyWayPotential(units=galactic)\n",
"\n",
"# Example 0\n",
"#dt = 0.1\n",
"#n_steps = 5000\n",
"#r0 = 3\n",
"#angle = 0.01\n",
"#vadj = 1\n",
"\n",
"# Example 1\n",
"dt = 0.01\n",
"n_steps = 50000\n",
"r0 = 0.3\n",
"angle = 0.01\n",
"vadj = 0.999\n",
"\n",
"# Example 2\n",
"#dt = 0.2\n",
"#n_steps = 500000\n",
"#r0 = 100\n",
"#angle = 0.1\n",
"#vadj = 1\n",
"\n",
"# Example 3\n",
"#dt = 0.001\n",
"#n_steps = 500000\n",
"#r0 = 3\n",
"#angle = 0.04\n",
"#vadj = 1"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"rvec = [r0,0,0]*u.kpc\n",
"vinit = mwpot.circular_velocity(rvec)[0].to(u.km/u.s).value\n",
"vvec = [0, vinit*np.cos(angle), vinit*np.sin(angle)]*u.km/u.s\n",
"vvec = vadj*vvec\n",
"\n",
"ics = gd.PhaseSpacePosition(pos=rvec, vel=vvec)\n",
"orbit = gp.Hamiltonian(mwpot).integrate_orbit(ics, dt=dt, n_steps=n_steps)\n",
"w = np.squeeze(orbit.w(mwpot.units))"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
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UEomKnRClDZLp06dXNYvvJbZt21bqsxEhRFkEVHUlXeXT+vXrdRLygYGBgg/c6+K0VJN8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EKFCpDL5ahcuTIUCgXKly+PRYsWQafTwcXFBd7e3pDL5Rg/fjyioqIIHZAxSwmmGAkXz6VDhw4o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\n4XA4ZRzu2HE4HA6Hw+FwOBxOGef/AWYEP7sQh1o4AAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7fdcb0989588>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig,axes = plt.subplots(1,3,figsize=(15,3),sharex=True)\n",
"axes[0].plot(orbit.x,orbit.y,'-k')\n",
"axes[1].plot(orbit.x,orbit.z,'-k')\n",
"axes[2].plot(orbit.y,orbit.z,'-k')\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"def fit_minimize(orbit, **kwargs):\n",
" m0 = 2E11\n",
" b0 = 1.\n",
" hpot = orbit.hamiltonian.potential\n",
" w = np.squeeze(orbit.w(hpot.units))\n",
"\n",
" def f(p, w):\n",
" logm, logb = p\n",
" potential = gp.IsochronePotential(m=np.exp(logm), b=np.exp(logb),\n",
" units=hpot.units)\n",
" H = (potential.value(w[:3]).decompose(hpot.units).value +\n",
" 0.5*np.sum(w[3:]**2, axis=0))\n",
" return np.sum(np.squeeze(H - np.mean(H))**2)\n",
"\n",
" res = minimize(f, x0=np.array([np.log(m0), np.log(b0)]), args=(w,), **kwargs)\n",
" if not res.success:\n",
" raise ValueError(\"Failed to fit toy potential to orbit.\")\n",
" logm, logb = np.abs(res.x)\n",
" m = np.exp(logm)\n",
" b = np.exp(logb)\n",
" \n",
" print(\"\\tfitting nit=\", res.nit)\n",
" print(\"\\tinit m0, b0\", m0, b0)\n",
" print(\"\\tfinal m, b \", m, b)\n",
"\n",
" return gp.IsochronePotential(m=m, b=b, units=hpot.units)"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def fit_leastsq(orbit):\n",
" m0 = 2E11\n",
" b0 = 1.\n",
" hpot = orbit.hamiltonian.potential\n",
" w = np.squeeze(orbit.w(hpot.units))\n",
"\n",
" def f(p,w):\n",
" logm,b = p\n",
" potential = gp.IsochronePotential(m=np.exp(logm), b=b, units=hpot.units)\n",
" H = potential.value(w[:3]).decompose(hpot.units).value + 0.5*np.sum(w[3:]**2, axis=0)\n",
" return np.squeeze(H - np.mean(H))\n",
"\n",
" p, cov_x, info, mesg, ier = leastsq(f, np.array([np.log(m0), b0]), args=(w,), full_output=True)\n",
" if ier < 1 or ier > 4:\n",
" raise ValueError(\"Failed to fit toy potential to orbit.\")\n",
" logm,b = np.abs(p)\n",
" m = np.exp(logm)\n",
" \n",
" print(\"\\tleastsq nfev=\", info['nfev'])\n",
" print(\"\\tinit m0, b0\", m0, b0)\n",
" print(\"\\tfinal m, b \", m, b)\n",
"\n",
" return gp.IsochronePotential(m=m, b=b, units=hpot.units)"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"scrolled": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\tfitting nit= 2\n",
"\tinit m0, b0 200000000000.0 1.0\n",
"\tfinal m, b 205190723715.43008 1.0753001604305725\n",
"\tfitting nit= 27\n",
"\tinit m0, b0 200000000000.0 1.0\n",
"\tfinal m, b 249224754151.42123 1.0000044223689473\n"
]
}
],
"source": [
"#iso_lsq = fit_leastsq(orbit)\n",
"iso_min = fit_minimize(orbit)\n",
"iso_min_nm = fit_minimize(orbit, method='Nelder-Mead')"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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w6IS1INsh2bVZhfV5JdZELNW+LVuPvXWF9Xk5G6Iyk/MKa0X62DFxi9t0mtab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O/LyVQ04ebsCSSXTIPls+Cwu1hLXZ6uexI07Q5fPwed9uK5xMEsT7VQunPBZ5RvWMBl2ZEkyurA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\n6Egfl+8AAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7fdcb03997b8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(10,4))\n",
"#H = iso_lsq.value(w[:3]).decompose(mwpot.units).value + 0.5*np.sum(w[3:]**2, axis=0)\n",
"#plt.plot(H - np.mean(H), label='lsq=levenberg-marquardt')\n",
"H = iso_min.value(w[:3]).decompose(mwpot.units).value + 0.5*np.sum(w[3:]**2, axis=0)\n",
"plt.plot(orbit.t, H - np.mean(H), label='BFGS')\n",
"H = iso_min_nm.value(w[:3]).decompose(mwpot.units).value + 0.5*np.sum(w[3:]**2, axis=0)\n",
"plt.plot(orbit.t, H - np.mean(H), label='Nelder-Mead')\n",
"plt.legend()\n",
"plt.xlabel('time (Myr)')\n",
"plt.ylabel('H_toy(xi,vi) - <H_toy(xi,vi)>')\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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LaZjZwwMiMherQzpRRPKBx4A/AfNE5BZgN3CFe/cPsG5x3Y51m+vNnp7HW3Jy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\nE4RSSqlmaYJQSinVLE0QSimlmvX/AbEITcKFMpcnAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7fdcb03ea7f0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"x = np.linspace(0.001,r0*1.2,1000)\n",
"r = [[xv,0,0]*u.kpc for xv in x]\n",
"r = np.array(r).T\n",
"plt.plot(x, mwpot.circular_velocity(r), '-k', label='mw')\n",
"#plt.plot(x, iso_lsq.circular_velocity(r), ':', label='lsq=LM')\n",
"plt.plot(x, iso_min.circular_velocity(r), ':', label='bfgs')\n",
"plt.plot(x, iso_min_nm.circular_velocity(r), ':', label='nm')\n",
"plt.legend()\n",
"plt.xlabel('r (kpc)')\n",
"plt.ylabel('vcirc (km/s)')\n",
"plt.axvline((np.sum(rvec**2)**0.5).to(u.kpc).value, color='k', linewidth=1)\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [],
"source": [
"m0 = 2e11\n",
"b0 = 1.\n",
"\n",
"iso = gp.IsochronePotential(m=m0, b=b0, units=mwpot.units)\n",
"H = iso.value(w[:3]).decompose(mwpot.units).value + 0.5*np.sum(w[3:]**2, axis=0)\n",
"chisq0 = np.sum(np.squeeze(H - np.mean(H))**2)\n",
"\n",
"chisq = np.empty((51,51))\n",
"for i,m in enumerate(m0*np.logspace(-3,3,chisq.shape[0])):\n",
" for j,b in enumerate(b0*np.logspace(-2,+2,chisq.shape[1])):\n",
" iso = gp.IsochronePotential(m=m, b=b, units=mwpot.units)\n",
" H = iso.value(w[:3]).decompose(mwpot.units).value + 0.5*np.sum(w[3:]**2, axis=0)\n",
" chisq[i,j] = np.sum(np.squeeze(H - np.mean(H))**2)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Compare performance in $\\chi^2$ space"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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REREXRMTTEXHvIK9HRJwdEQsi4ncR8bdDPUdJkiRJeeq9kjEbmL6B1w8DpvR9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\nSQYAADCp/w+EqEv8zDgMbQAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7fdcaeb46518>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(14,14))\n",
"plt.imshow(chisq.T/chisq0, origin='lower', extent=(-3,3,-2,2),\n",
" norm=mpl.colors.LogNorm())\n",
"plt.colorbar()\n",
"\n",
"#plt.scatter(np.log10(iso_lsq.parameters['m'].value/m0),\n",
"# np.log10(iso_lsq.parameters['b'].value/b0), color='w', marker='*', alpha=0.75, s=100,\n",
"# label='leastsq=levenberg-marquardt')\n",
"\n",
"plt.scatter(np.log10(iso_min.parameters['m'].value/m0),\n",
" np.log10(iso_min.parameters['b'].value/b0), color='y', marker='*', alpha=0.75, s=100,\n",
" label='min default BFGS')\n",
"\n",
"plt.scatter(np.log10(iso_min_nm.parameters['m'].value/m0),\n",
" np.log10(iso_min_nm.parameters['b'].value/b0), color='g', marker='*', alpha=0.75, s=100,\n",
" label='nelder-mead')\n",
"\n",
"plt.xlabel('log(m/m0)')\n",
"plt.ylabel('log(b/b0)')\n",
"plt.axvline(0,linewidth=1,color='magenta')\n",
"plt.axhline(0,linewidth=1,color='magenta')\n",
"plt.legend()\n",
"plt.show()"
]
}
],
"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"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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