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Last active February 23, 2023 15:45
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Examples of using an interpolated spherical potential as the potential for isotropic and anisotropic distribution functions in `galpy`
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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"%pylab is deprecated, use %matplotlib inline and import the required libraries.\n",
"Populating the interactive namespace from numpy and matplotlib\n"
]
}
],
"source": [
"import warnings\n",
"warnings.filterwarnings('ignore')\n",
"import numpy\n",
"from galpy import potential\n",
"from galpy.df import eddingtondf, constantbetadf, osipkovmerrittdf\n",
"%pylab inline\n",
"from galpy.util import plot as galpy_plot\n",
"galpy_plot.start_print(axes_labelsize=17.,text_fontsize=12.,\n",
" xtick_labelsize=15.,ytick_labelsize=15.)"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"pot= potential.HernquistPotential(amp=1.3,a=0.8)\n",
"ipot= potential.interpSphericalPotential(rforce=pot,rgrid=numpy.geomspace(0.001,100.,10001))"
]
},
{
"attachments": {},
"cell_type": "markdown",
"metadata": {},
"source": [
"## ``eddingtondf``"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"edf_orig= eddingtondf(pot=pot,denspot=pot)\n",
"edf_ip= eddingtondf(pot=ipot,denspot=pot)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(0.008620892753419304, 0.008620892766494453)"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"r= 1.2\n",
"edf_orig.vmomentdensity(r,0,0), edf_ip.vmomentdensity(r,0,0)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
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",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"figsize(6,4)\n",
"rs= numpy.geomspace(0.1,10.,101)\n",
"loglog(rs,[edf_orig.vmomentdensity(r,0,0) for r in rs])\n",
"loglog(rs,[edf_ip.vmomentdensity(r,0,0) for r in rs])\n",
"loglog(rs,[pot.dens(r,0) for r in rs])\n",
"xlabel(r'$r$')\n",
"ylabel(r'$\\rho(r)$');"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"rs= numpy.geomspace(0.1,10.,101)\n",
"semilogx(rs,[edf_orig.sigmar(r) for r in rs])\n",
"semilogx(rs,[edf_ip.sigmar(r) for r in rs])\n",
"xlabel(r'$r$')\n",
"ylabel(r'$\\sigma_r(r)$');"
]
},
{
"attachments": {},
"cell_type": "markdown",
"metadata": {},
"source": [
"## ``constantbetadf``\n",
"\n",
"### Half-integer value"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [],
"source": [
"twobeta= 1\n",
"cdf_orig= constantbetadf(pot=pot,denspot=pot,twobeta=twobeta)\n",
"cdf_ip= constantbetadf(pot=ipot,denspot=pot,twobeta=twobeta)"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(0.00862089451955567, 0.008620885260698473)"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"r= 1.2\n",
"cdf_orig.vmomentdensity(r,0,0), cdf_ip.vmomentdensity(r,0,0)"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"rs= numpy.geomspace(0.1,10.,101)\n",
"loglog(rs,[cdf_orig.vmomentdensity(r,0,0) for r in rs])\n",
"loglog(rs,[cdf_ip.vmomentdensity(r,0,0) for r in rs])\n",
"loglog(rs,[pot.dens(r,0) for r in rs])\n",
"xlabel(r'$r$')\n",
"ylabel(r'$\\rho(r)$');"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"rs= numpy.geomspace(0.1,10.,101)\n",
"semilogx(rs,[cdf_orig.sigmar(r) for r in rs])\n",
"semilogx(rs,[cdf_ip.sigmar(r) for r in rs])\n",
"xlabel(r'$r$')\n",
"ylabel(r'$\\sigma_r(r)$');"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"rs= numpy.geomspace(0.1,10.,101)\n",
"semilogx(rs,[cdf_orig.beta(r) for r in rs])\n",
"semilogx(rs,[cdf_ip.beta(r) for r in rs])\n",
"xlabel(r'$r$')\n",
"ylabel(r'$\\beta(r)$');"
]
},
{
"attachments": {},
"cell_type": "markdown",
"metadata": {},
"source": [
"## Arbitrary value of constant $\\beta$"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [],
"source": [
"twobeta= 1.8\n",
"cdf_orig= constantbetadf(pot=pot,denspot=pot,twobeta=twobeta)\n",
"cdf_ip= constantbetadf(pot=ipot,denspot=pot,twobeta=twobeta)"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [],
"source": [
"numpy.random.seed(10)\n",
"samp_orig= cdf_orig.sample(n=1000000)\n",
"samp_ip= cdf_ip.sample(n=1000000)"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"samp= samp_orig\n",
"bins= 31\n",
"for samp in [samp_orig,samp_ip]:\n",
" vrs= (samp.vR()*samp.R()+samp.vz()*samp.z())/samp.r()\n",
" vthetas=(samp.z()*samp.vR()-samp.R()*samp.vz())/samp.r()\n",
" vphis= samp.vT()\n",
" logrs= numpy.log(samp.r())\n",
" rmin= 0.1\n",
" rmax= 10\n",
" w,e= numpy.histogram(logrs,range=[numpy.log(rmin),numpy.log(rmax)],\n",
" bins=bins,weights=numpy.ones_like(logrs))\n",
" mvr2,_= numpy.histogram(logrs,range=[numpy.log(rmin),numpy.log(rmax)],\n",
" bins=bins,weights=vrs**2.)\n",
" mvt2,_= numpy.histogram(logrs,range=[numpy.log(rmin),numpy.log(rmax)],\n",
" bins=bins,weights=vthetas**2.)\n",
" mvp2,_= numpy.histogram(logrs,range=[numpy.log(rmin),numpy.log(rmax)],\n",
" bins=bins,weights=vphis**2.)\n",
" samp_sigr= numpy.sqrt(mvr2/w)\n",
" samp_sigt= numpy.sqrt(mvt2/w)\n",
" samp_sigp= numpy.sqrt(mvp2/w)\n",
" samp_beta= 1.-(samp_sigt**2.+samp_sigp**2.)/2./samp_sigr**2.\n",
" brs= numpy.exp((numpy.roll(e,-1)+e)[:-1]/2.)\n",
" plot(brs,samp_beta)\n",
"axhline(twobeta/2.)\n",
"ylim(0.5,1.)\n",
"xlabel(r'$r$')\n",
"ylabel(r'$\\beta(r)$');"
]
},
{
"attachments": {},
"cell_type": "markdown",
"metadata": {},
"source": [
"We can now swap $f(E)$ with its interpolated version (created during `sample`), to compute moments quickly:"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [],
"source": [
"cdf_orig.fE= cdf_orig._fE_interp\n",
"cdf_ip.fE= cdf_ip._fE_interp"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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+hznd5/KXqj+RZz9kxCMnauJdopZCRCQIjul4Eg+Pe5vL9h5AWVwtUz67k6vn9OWn8lKnSxMJqJgLES3xlVCJi49n4jl38ljWC3SvTKMg8VtG5PVi4fJ7nC5NpFG0xNcHLfEVp+QVzWTOlw/xXaKhe4WL6wYuoH27dKfLEtkjLfEVCQPDMi9j8YiX6Vt9EG8l/cQFL2ThfvZGp8sSaRaFiEgIuVqlcde4F8g9/Dr2ro3jgbJnGDfrJO3DJRFLISLigDNPPo/FF77N2bYT7yb/wkWFw3nwqcm6SVEiTlSEiDHGZYzJNMYMNcbkGmM00Cxhr0VKS/4x+klmHH07+1bH89DWZYyb043PvvrA6dJEGi0qQgQYDnS21i4BvgCmOFyPSKP16HI2C0e9zVBzJB8kbWPMinOZ+eQ16pVIRHAkRIwx6caYPGNM5m6vu4wxOZ4eRY4xpnNjjmetdVtrp3v+eCh1QSISMVKSW3DTRYv453HT2K86nlm/LGfcnG6s//ojp0sTaVDIQ8QTHOmer93lAUustUs8oZBrjHE18RSdvQJFJKJ0P34Ai0avZghH8n7yNkYXjWDWM9c5XZZIvUIeItbaImttEbDF+3VPWKRba0u8Xi4BMj3fz/b1tdsxcoBhwf0JRIIrKSmZm0ctYsbRt5NWHc/M8nwmuLux8YeSPb9ZJMTCaU4kAyjb7bUy4Az4bcjqD187GxpjhgJua23Z7sNkIpGoR5ezWXjRWwysPYzipJ+58IUsHn1xmtNliewinELExW69E2AzkLqnN3rmTnKBFcaYNfgeKgOgtLSUjIyM377cbnd9TUUc1yKlJbePeZo7O02lRa1heuljXDa7F5vLfnC6NIlibrd7l89JIK2+to5te2KMKQRyPUNbO3sSU621Xbza5ABdrbUBG6LSticSqcp/2cIti86lKOFb9q+GSzr+nbN7jHe6LIkBkbLtSRl1vRFv+/DH3kmzaANGiVSt90rl3vHLueHAbGqw/N+G+5g6byDbd2xzujSJUmG9AaOPnogL2GCtbePVZhZQ6Ln/IyDUE5Fo8MOmjdz81Lm8kVzOoZWGnBNy6XZsP6fLkigVET0Ra20ZULzb3eYZQFEgz6OeiESDdmnteSj7dS5rnUVpfA2Xr51M7sLxukFRAioseyKeSfBMYCpQDOTtXGXl6Y1kU7e0NxUottauDeT51RORaPNxyRpuK5rAh8lVHF+Rwv/1nc9hBx3ldFkSRRrqicTc80Q6duxoe/XqRVZWFllZWU6XIxIQ1dVVTHt8HE9Xr6WltYxvdz4X9ddNitI8+fn55OfnM3v27PXW2o6+2sRciKgnItFs5eonuee9m/kqCXpX7sct5z5B6732uEpepEERMScSKpoTkWjWq+sQ/jNyJadX7seKpB85//EevLb2OafLkggVlDkRY8zB1N3M5/K8VAaUWGu/9KPGkFNPRGLFghduZ86PC/nVGIYln8TkEbOIi493uiyJQM2eEzHGHA9MBNpQN+ldwu/3b6RSt3OuC/gJWGytfa/ZVQeJQkRiyWdfvcfNy8fyYXIVXXb8idsGPkb7/X0ObYvUq1khYoyZBqynbhVV+R7atqbu2R7p1tqpftYbVJpYl1hTXV3FHQtH8XTtB7SpsVx6yKUMOf0Sp8uSCNDsiXVjzHhr7Rx/Tt6c9waTeiISq5a+8SgzPs7lxwQYYDty0/mLSEpKdrosiQB+T6z7CgFjzN6NOWk4BohILOt3yoU8MmgpJ1TuzXNx67nw4ZP4uGSN02VJhGvS6ixjzEPAhiDVIiJB1i6tPbPGvcaYlB6UJFYx4eWLtL28NEtTl/gW0sA265FAS3wl1sXFx3PViJnMOG4arpo4ppc+xjVz+mkjR/mDgC/xNcYMAdZEynJeXzQnIvK7sq2buGHRMF5J2kSnijhu6vlvjunUzemyJMwE8mbDEqDIGHOnMeb05pcmIk5ytUpj5oSVTGrVj28Sq7n49QnMf/42p8uSCNLUEBlB3RME2wDTjTE1xpjVxph/K1REItclg6fzz4wZpNXEce/mJzS8JY3W1BBZDay21l5src2w1sYD1wLlQMCePigioXfS0X149NxX6FGZxvLEb7jokW58tH6V02VJmGtSiFhrnwSMd6/DWrvCWnuttXZSwKsLAk2si9Sv9V6pzJywkotb9WVjYjUXvzqWx5ZNd7oscUhYPk/EaZpYF2mcN99fyh3v5PB1ouUseyi3nP+Ebk6MUX5NrBtjWhtjBjfjpIMbe2OiiISfbsf249HhL9Gtsg3Px5Uwev7JlGxc53RZEmbqDRHPPlkrjDHTmjJpbozpbYy5Eyiy1v4ciCJFxBltWrfloezXGJ3cnc+SKhlXMJxnX9FmFPK7xu7i25u6iXMLrKFuqa+3dOqeh94GmGWtfSnAdQaMhrNE/FPw1uPcve52ShNgaEIXpp47T1vLx4iAPh7XEygufr9zvYy6UCne0y6/4UAhIuK/b/73Jdc9PYx3U3ZwYsVe3DnsSdq2OcDpsiTI9Ix1L9oKXqR5qquruPWx83nW/pcDq+C6rtPpflx/p8uSIAjKM9Y9k+UZwBfW2q8CUGdIqSciEhiLCmbw4DdzqDQwLnUQ2Wff7nRJEiQB2/bEs3fWl4Ab2OC5Y/2O5pcoIpFmZJ8r+fdp8ziwKp4Hyp7jmrn92FGx3emyJMSaesd6V2ttqrX2MGttHNAViDPGrA5CbSIS5o467EQWnP8qPSvTWJ7wDaMXnKJlwDHGn21PfmOtXWutvRYYYYy5JnBliUikaNXSxQMTVjImpQefJ1YxvmA4L77+iNNlSYg0NURSfd2AaK0tQQ+rEolpV42Yye2HTyXOwg3rp3PvYj3HPRY0de+s2cAJxpjlxpjxu92R3iawpTWNMSbT8zXLGONyshaRWNW32/nM7vckh1cmMX/Ha/xtdi+2bd/qdFkSRE3tieAZvroW6AOUGWM2G2M+B1zGmIMDXF+jGGM6A8OstUXU3beS6UQdIgKHHHgE80e9zpnVf+blpE2M+k93Pt3wrtNlSZA0OUQArLXvWmuHeybXz6ButVYfYK0nVBY3tG+WMSbdGJNnjMnc7XWXMSbHGDPU82vnRtaz1lo70dMDcQFF/vxcIhIYKcktuHvcUi5p1Z+vEmuY+NIFPPfqXKfLkiDwK0S8eT7A77LW9rHWplIXKvV+iHuCIx3fz2rPA5ZYa5dYa6cDuU0cmsoEvmhCexEJokmDc8k98mYSreHmkhncsyginhghTdDsENmdJ1Rm17f5orW2yDPstMX7dU9YpHsm6XcqwTM0ZYzJ9vW127GXeH47NVA/j4g0z+knDGXeWU9zREUSD1e8zuWzT9dTE6NIwEOkGTKom8/wVkZdzwZrrdvXF4Bn6Cvb6z2ukFQsIo3Sfv+OzBv9On2qDmRlUimjHzmF9V9/5HRZEgDhFCIuduudAJuB1Ea81w2UeIbKugBT6mtYWlpKRkbGb19ut9vfekWkCVKSW3DP+GVkt8ikJLGa7MIRLH9rodNliQ9ut3uXz0kgrb62jm3AaIwpBHI9Q1sYY4YCU621Xbza5FB3l3zAnt+uDRhFnLf8rYXk/vd2fo4zjG3dn0sG6xG84SgoGzAGio8QyaTuWSSHerXJBVzW2omBOq82YBQJD5999QHXL7+IT5Jr6Fd9EHeMeoaEhESnyxIfArYBY5AV88ehKxdQGMiTlJeXk52dTX5+fiAPKyJN1KnDMTx8wWucVrEPSxO+Zszck/lh00anyxIv+fn5ZGdnA7Sur03Y9ES8Xpu4c4WWMWYN0NtaWxao86onIhJeamtqmL5oAouq3uGAKril2z/pemRvp8sSL2HVEzHGdPbMdWQAU3ZbpjsMGOq52TAbmBDIABGR8BMXH8+158/j2gPGUR5vuWLV5SwquNfpsqSR9GRDEQkbq9et4KY3r+C7RBiZeALXnj/P6ZJiWlhPrDtFw1ki4e2HTRuZ/OQ5vJdSQc/KNHIvfJ4WKS2dLiumhdVwltM0sS4S3tqltWfumDd+28Bx7CPd2fj9506XFZPCemLdKeqJiESO+564nEe2v0TbargxYzrdj+vvdEkxST0REYlIfx9+PzcdfDm/xlkmr53Mf5bmOl2S7CbmQkTDWSKR5eye2dx/yizSauK468dHufOx0U6XFDM0nOWDhrNEItOPm79l8pODeDd5B70q2zLtwnxNuIeIhrNEJOLtt8+BzBn9OmdW/ZmVSaWMX3Aq3/zvS6fLinkKERGJGElJydw9filjUk7l4+RKsp8dQPG6l50uK6bFXIhoTkQk8l014l9MPTCb8njL31ddytMrH3K6pKikOREfNCciEj3e/rCAm1ddxf8SYFTL3lwx7J9OlxSVNCciIlHppKP7MHvAc3SqTGTO9pe4dt5AqqurnC4rpihERCSitW+XztwLXuXUija8EL+BifNOo2zrJqfLihkxFyKaExGJPi1btGLmuJUM4UjeSf6FcY/31jPcA0BzIj5oTkQkus165jpm//QcbWrgpi7T6H78AKdLiniaExGRmDFx0B3c0vEaKoxl8rtTWFQww+mSoppCRESizlndR3N/91mk1sSR+91c7l18qdMlRS2FiIhEpeMO787sQc/zl4ok5u94lSnzsqitqXG6rKijEBGRqHVA2w7MGfUap1Wm8mL8l2TP6c7WbWVOlxVVFCIiEtVapLTkgbEvMZi/sirlF8Y+1pOvvvvM6bKiRsyFiJb4isSeuPh4bhm1mEmt+lGSWE32i4NZvW6F02WFPS3x9UFLfEVi2zMrZ3H3hvsByDnsKgaeNs7hisKflviKiHgM6jWRu7vOoEWt4dYvZjDrmeucLimiKUREJOacdHQfHjpzMR2q4nmw7Dlue/QCrdzyk0JERGJSevsjmXvuCrpUtOSJ2ve5at6ZVFZWOF1WxIm6EDHGzHK6BhGJDK5Wacwa8yqZVfuzIulHsuefyk/lpU6XFVGiKkSMMZmAz8kfERFfkpKSmTG+gBFxx7M2eTvjFvemZOM6p8uKGI6EiDEm3RiT5/nQ937dZYzJMcYM9fzauQnHdAElwJYAlysiMeCGCx/hsjZn83ViLZOWj+CdD4ucLikihDxEPMGR7vnaXR6wxFq7xFo7Hcj1hENjZFhrSwJUpojEoOyzb+fG9L+zLc5y1eoryH91ntMlhb2EUJ/QWlsEYIzZpcfgCYv03YKgBMgElhhjsus5ntsYk7nzuCIizXF2j/Hsl3oQ/7fqKm754l5KyzcyNusmp8sKWyEPkQZkAGW7vVYGnEFd78TdwHu3GGOGen6frlARkeY46eg+/Kv1IiYvO49/bs7jfwu/5trz5jpdVlgKp4l1F3+cz9gMpO7pjdbatdbaJZ4/Nti+tLSUjIyM377c7oaySURi1WEHHcWc4QUcU5HCY1XvkDP3rJi5l8Ttdu/yOQmk1dfWsW1PjDGFQK7X8NZQYKq1totXmxygq7V2WKDOq21PRKQpdlRs5+oF/Xk1eTPdKlpz7wVLadmildNlhVSkbHtSRl1vxNs+BHi1lTZgFJGmSEluwQPjVnB2bSfeTC5nwqM9+HHzt06XFRJhvQGjj56IC9hgrW3j1WYWUOg1VNVs6omIiL/uXXwZj/z6Mh2qDHf1eZROHY5zuqSQiIieiLW2DCg2xngv/c0AAjpBrp6IiPjrqhEzuXrfC/g+oZZLCs/nzfeXOl1SUIVlT8RzA2EmMBUoBvJ2rrzy9EayqVvamwoUW2vXBvL86omISHMtfeNR7vx0GjVAzqFXcnaP8U6XFFQN9URi7nkiHTt2tL169SIrK4usrCynyxGRCLV63QpueOsKNsfDJWnDGZv1f06XFHD5+fnk5+cze/bs9dbajr7axFyIqCciIoGy/uuPmLzsPEqSarkwpTvXjHzI6ZKCIiLmREREIs1hBx2Fe9gyjq5IZkHFG1w//5yYuZdkp5gLEU2si0ggtW1zAO5Rr3JKhYvn4tZz+bzeUfNckrCcWHeahrNEJBhqa2q49uGBLE34mi47/sR9572Iq1W9N3pHFA1niYgEWVx8PNPHvcDI+C6sTd7OhMcz2fhD9G8sHnMhouEsEQmm6y94mEmts/giqZqL88/mo/WrnC7JbxrO8kHDWSISCosKZjDj2zm0rIVbO+fS/fgBTpfkNw1niYiE2Mg+V3LbETdQDUx5dwrPvjLH6ZKCIuZCRMNZIhIqfU4+l3tPepCWtYbbSu7j4Rduc7qkJtFwlg8azhKRUPvsqw+YXHA+XyVaRrc4nb8Pv9/pkppEw1kiIg7q1OEY3IOX8ZfKJOb+upJbHhnpdEkBoxAREQmB/fY5EPf5L3FCxV4sseu4es6ZVFdXOV1WsylERERCpFVLF7PGvsrplftSkPgdl8zryfYd25wuq1liLkQ0sS4iTkpISGTG2AIG1nbkreSfmbigBz+Vlzpdlk+aWPdBE+siEi6mL5zAfyrfolNlPDOyltB+f5+7rTtOE+siImEo57zZXOoaSElSDZOeH8y6LyLvP7gKERERB00cdAc5B4yjNKGWK1aO4q0PljldUpMoREREHDayz5Xccvh1VMTB5OKrWfbmY06X1GgKERGRMNC32/lMz7iHlFq46dM7WFx4n9MlNYpCREQkTJx8TF/+2WsBadVx5H47B/ez1ztd0h7FXIhoia+IhLMjD83goQFPcUhlPA/+9Cz3LJrkWC1a4uuDlviKSCTYXPYDly8+iw9SKhnCkdw8apFjtWiJr4hIhNnH1Q73hS9zYsVePMk6rp7Tl9qaGqfL+gOFiIhImGrZohUPjX2VXpVtKUj8lkvm9mRHxXany9pF1ISIMcbldA0iIoGWkJDIfWMLGVCbzhvJZVz8cE/Kf9nidFm/iZoQATYYY74wxuQ6XYiISCDFxcdz55hnGRnfmTUpvzJxYW9+3Pyt02UB0RUiw6y1h1prpzhdiIhIMFx/wQImtOjNJ0lVTHyqHxu+/cTpkpwJEWNMujEmzxiTudvrLmNMjjFmqOfXzk04rMsYkx7gUkVEwsrlw+7jirQRfJNQy6UvDuWj9ascrSfkIeIJjnTP1+7ygCXW2iXW2ulAbhPmOlKBLcaYXIWJiESzMQNu5NqDJrElwXLFK2N5+8MCx2oJeYhYa4ustUXALjNDnrBIt9aWeL1cAmR6vp/t68vruG5rbRmwGpgY7J9DRMRJQ3tfyi1HXE+lgZzVV1L49mJH6khw5Ky+ZQBlu71WBpxBXe/EXd8bd4ZJQ21ERKLNmSefR6sWbbih+Bpu/PhWfvn1J87pdXFIawiniXUXu/VOgM3UDVPtyRNAsTFmKNAVuLO+hqWlpWRkZPz25XYrd0QkcnU7th/3nTaXNjWG27+cyYIXbm/2Md1u9y6fk0BafW0d2/bEGFMI5HqGtvAEwFRrbRevNjlAV2vtsECdV9ueiEg0Ktm4jiuXjeTrRMv4vftx6eC7AnbsSNn2pIy63oi3ffhj76RZtAGjiESj9PZH8u9Bz9OxMoFZPy9l+sIJzT5mWG/A6KMn4gI2WGvbeLWZBRRaa5cE6rzqiYhINCvbuom/LezLeykVnMNfuHXUE80+ZkT0RDwrq4p3W56bARQF8jzqiYhINHO1SmPWqFc4ccdePM3HTJ7b3++NG8OyJ+K5gTATmAoUA3k7V1V5eiPZ1C3tTQWKrbVrA3l+9UREJBZUVlZw1YK+vJK0iR6Vadw7ahlJScl+HauhnkjMPU+kY8eOtlevXmRlZZGVleV0OSIiQVNbU8O1Dw9kacLXnLhjL+4fVUSLlJaNfn9+fj75+fnMnj17vbW2o682MRci6omISKy5acEIPqr4BPfw5ezjatfk9zfUEwmnmw1FRCQIbhm1mO07tjWpF9JYYTOxHiqaWBeRWORPgITlxLrTNJwlItI0EbHEV0REIk/MhYiGs0REGqcxw1kxFyKtW7fG7Xb7tbxXmzVKMOn6kmDy5/rKysra+b7y+trEXIg0h/6RSzDp+pJgCtb1FXMh8t133zU4nBWNw1yh+pkCeZ7mHKup721s+8a021MbXV/hcy5/jxWs66sxbUN9fWk4y4eqqqoGh7P0jzw8zqMQiRwKkcC1D7cQacxwVswt8TXGlAOfN9CkNfX/haUBmwJeVPA19DOF63mac6ymvrex7RvTbk9tdH2Fz7n8PVawrq/GtHXq+upgrW3r6xsxFyIiIhI4MTecJSIigaMQCSBjzFDPw7ZEms1zPXU2xmQ7XYtEn0B9XilEAiiQT2CU2GaMyQRSPc/TKTbG5Dhdk0SXQH1exWyIGGPSjTF5nn+s3q+7jDE5npTO8TxES6RZ/LjezqDu4WwAZZ4/i/jk5OdZTG4F7/UXne7j23nARGttiadtoTFmmOfxvSJN5s/1Bri82myh7kmfIn/g9OdZTIaItbYIwBizxft1z+N503f+hXuUUPc43yX1jU3vfLyviC9+Xm9l/B4kqdQFicgf+Pt5Fqjzx2SINCCDun+83sqoG0pYorCQAGvoesvj9/9ZpgNasCFN1eDnWaBOErNzIvVw8cf/8W2mkUMJxpihQLoxJtvzvwCRhrio53rz/O/S5Rmq6GytnR7q4iTiuWjg8yxQn1fqifyR32PPntUOWqElTVHv9eYVHEUhqkWiT0PXV0A+r9QT2VUZu05oAuyDxqMlOMrQ9SbBU0YIri+FyK6K+WNyu9B4tASHrjcJppBcXwoRL55lb8XGGO+lchloOEGCQNebBFOorq+Y3IDRc8NNJjCVurTO27nyyjPBlE3dUrhUoNhz17CIX3S9STA5fX3FZIiIiEhgaDhLRET8phARERG/KURERMRvChEREfGbQkRERPymEBEREb8pRERExG8KERER8ZtCRERE/Kat4EUc5HmmQ1dgMb8/hOoMa+1E56oSaTxteyLiEM+eR1C3Kd4U6p44twXYABwSyOdgiwSLhrNEnJPq2QyvC3WPXy6x1pZZa9soQCRSKEREHOJ5BC7U9UT0DBGJSBrOEnGYMcZaa43TdYj4Qz0REQcZYzIBPT9EIpZCRMRZZ1D3ICGRiKQQEXGWC8hzuggRf2lORERE/KaeiIiI+E0hIiIiflOIiIiI3xQiIiLiN4WIiIj4TSEiIiJ+U4iIiIjfFCIiIuI3hYiIiPjt/wE8mhPfEoPI0gAAAABJRU5ErkJggg==",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"rs= numpy.geomspace(0.1,10.,101)\n",
"loglog(rs,[cdf_orig.vmomentdensity(r,0,0) for r in rs])\n",
"loglog(rs,[cdf_ip.vmomentdensity(r,0,0) for r in rs])\n",
"loglog(rs,[pot.dens(r,0) for r in rs])\n",
"xlabel(r'$r$')\n",
"ylabel(r'$\\rho(r)$');"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"rs= numpy.geomspace(0.1,10.,101)\n",
"semilogx(rs,[cdf_orig.sigmar(r) for r in rs])\n",
"semilogx(rs,[cdf_ip.sigmar(r) for r in rs])\n",
"xlabel(r'$r$')\n",
"ylabel(r'$\\sigma_r(r)$');"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"rs= numpy.geomspace(0.1,10.,101)\n",
"semilogx(rs,[cdf_orig.beta(r) for r in rs])\n",
"semilogx(rs,[cdf_ip.beta(r) for r in rs])\n",
"xlabel(r'$r$')\n",
"ylabel(r'$\\beta(r)$');"
]
},
{
"attachments": {},
"cell_type": "markdown",
"metadata": {},
"source": [
"## ``osipkovmerrittdf``"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {},
"outputs": [],
"source": [
"ra= 1.4\n",
"odf_orig= osipkovmerrittdf(pot=pot,denspot=pot,ra=ra)\n",
"odf_ip= osipkovmerrittdf(pot=ipot,denspot=pot,ra=ra)"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(0.008620863632656803, 0.008620866870114893)"
]
},
"execution_count": 20,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"r= 1.2\n",
"odf_orig.vmomentdensity(r,0,0), odf_ip.vmomentdensity(r,0,0)"
]
},
{
"attachments": {},
"cell_type": "markdown",
"metadata": {},
"source": [
"We'll also sample first, then replace `f(Q)` with an interpolated version created during the sampling:"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {},
"outputs": [],
"source": [
"numpy.random.seed(10)\n",
"samp_orig= odf_orig.sample(n=1000000)\n",
"samp_ip= odf_ip.sample(n=1000000)"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"samp= samp_orig\n",
"bins= 31\n",
"for samp in [samp_orig,samp_ip]:\n",
" vrs= (samp.vR()*samp.R()+samp.vz()*samp.z())/samp.r()\n",
" vthetas=(samp.z()*samp.vR()-samp.R()*samp.vz())/samp.r()\n",
" vphis= samp.vT()\n",
" logrs= numpy.log(samp.r())\n",
" rmin= 0.1\n",
" rmax= 10\n",
" w,e= numpy.histogram(logrs,range=[numpy.log(rmin),numpy.log(rmax)],\n",
" bins=bins,weights=numpy.ones_like(logrs))\n",
" mvr2,_= numpy.histogram(logrs,range=[numpy.log(rmin),numpy.log(rmax)],\n",
" bins=bins,weights=vrs**2.)\n",
" mvt2,_= numpy.histogram(logrs,range=[numpy.log(rmin),numpy.log(rmax)],\n",
" bins=bins,weights=vthetas**2.)\n",
" mvp2,_= numpy.histogram(logrs,range=[numpy.log(rmin),numpy.log(rmax)],\n",
" bins=bins,weights=vphis**2.)\n",
" samp_sigr= numpy.sqrt(mvr2/w)\n",
" samp_sigt= numpy.sqrt(mvt2/w)\n",
" samp_sigp= numpy.sqrt(mvp2/w)\n",
" samp_beta= 1.-(samp_sigt**2.+samp_sigp**2.)/2./samp_sigr**2.\n",
" brs= numpy.exp((numpy.roll(e,-1)+e)[:-1]/2.)\n",
" plot(brs,samp_beta)\n",
"semilogx(brs,1./(1.+ra**2./brs**2.))\n",
"ylim(-0.5,1.)\n",
"xlabel(r'$r$')\n",
"ylabel(r'$\\beta(r)$');"
]
},
{
"attachments": {},
"cell_type": "markdown",
"metadata": {},
"source": [
"We can now swap $f(Q)$ with its interpolated version (created during `sample`), to compute moments quickly. This is a bit more complicated than above, because the log of the function is internally interpolated:"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {},
"outputs": [],
"source": [
"odf_orig.fQ= lambda Q: numpy.exp(odf_orig._logfQ_interp(Q))\n",
"odf_ip.fQ= lambda Q: numpy.exp(odf_ip._logfQ_interp(Q))"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"rs= numpy.geomspace(0.1,10.,11)\n",
"loglog(rs,[odf_orig.vmomentdensity(r,0,0) for r in rs])\n",
"loglog(rs,[odf_ip.vmomentdensity(r,0,0) for r in rs])\n",
"loglog(rs,[pot.dens(r,0) for r in rs])\n",
"xlabel(r'$r$')\n",
"ylabel(r'$\\rho(r)$');"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"rs= numpy.geomspace(0.1,10.,101)\n",
"semilogx(rs,[odf_orig.sigmar(r) for r in rs])\n",
"semilogx(rs,[odf_ip.sigmar(r) for r in rs])\n",
"xlabel(r'$r$')\n",
"ylabel(r'$\\sigma_r(r)$');"
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"rs= numpy.geomspace(0.1,10.,101)\n",
"semilogx(rs,[odf_orig.beta(r) for r in rs])\n",
"semilogx(rs,[odf_ip.beta(r) for r in rs])\n",
"semilogx(rs,1./(1.+ra**2./rs**2.))\n",
"xlabel(r'$r$')\n",
"ylabel(r'$\\beta(r)$');"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "py310",
"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": "3.10.6"
},
"orig_nbformat": 4,
"vscode": {
"interpreter": {
"hash": "b7f447f63c95a4eb49d6cb5a8a29fe4328fb8a8c4c8708123e006664154d1088"
}
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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