Compound Astropy Models

Compound Models.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Some Models"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from astropy.modeling import FittableModel, Parameter\n",
    "import numpy as np\n",
    "from astropy.modeling import models, fitting\n",
    "import matplotlib.pyplot as plt\n",
    "import astropy.constants as c\n",
    "import astropy.units as u\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class Center(FittableModel):\n",
    "    \"\"\"Center a coordinate system in x,y space.\"\"\"\n",
    "    \n",
    "    inputs = (\"X\", \"Y\")\n",
    "    outputs = (\"X\", \"Y\")\n",
    "    \n",
    "    x_center = Parameter(min=0.0, max=70)\n",
    "    y_center = Parameter(min=0.0, max=70)\n",
    "    \n",
    "    @staticmethod\n",
    "    def evaluate(X, Y, x_center, y_center):\n",
    "        \"\"\"Recenter the coordinates.\"\"\"\n",
    "        return (X - x_center), (Y - y_center)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class InclinedDisk(FittableModel):\n",
    "    \"\"\"A coordinate transform for an inclined disk with a position angle.\"\"\"\n",
    "    \n",
    "    inputs = ('X', 'Y')\n",
    "    outputs = ('R', 'Theta')\n",
    "    \n",
    "    inclination = Parameter(min=0.01, max=80.0)\n",
    "    position_angle = Parameter(min=-360.0, max=360.0)\n",
    "    \n",
    "    @staticmethod\n",
    "    def evaluate(X, Y, inclination, position_angle):\n",
    "        \"\"\"Evaluate and return the coordinate transform.\"\"\"\n",
    "        # Handle some assumed units.\n",
    "        pa = np.radians(position_angle)\n",
    "        inc = np.radians(inclination)\n",
    "        \n",
    "        # Set up the coordinate system for this galaxy.\n",
    "        CC = (-X * np.sin(pa) + Y * np.cos(pa) ) ** 2.0\n",
    "        SS = (-X * np.cos(pa) - Y * np.sin(pa) ) ** 2.0\n",
    "        R = np.sqrt(CC + SS / (np.cos(inc) ** 2.0) )\n",
    "        Theta = ((-X * np.sin(pa) + Y * np.cos(pa)) / R) * np.sin(inclination)\n",
    "        return (R, Theta)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## A simple pipeline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class DiskCoordinates(Center | InclinedDisk):\n",
    "    r\"\"\"Coordinates for a disk given line-of-sight data.\n",
    "    \n",
    "    Converts ``x,y`` to ``r,theta`` given the following:\n",
    "    \n",
    "    .. math::\n",
    "        \n",
    "        c = -(x - x_{center}) \\sin(\\theta_{PA}) + (y - y_{center}) \\cos(\\theta_{PA})\n",
    "    \n",
    "    \"\"\"\n",
    "    pass"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
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       "kTsAAAAASUVORK5CYII=\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1107f7190>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X, Y = np.meshgrid(np.arange(200), np.arange(200))\n",
    "dc = DiskCoordinates(x_center_0=100.1, y_center_0=110.2, inclination_1=50.0, position_angle_1=10.0)\n",
    "R, Theta = dc(X, Y)\n",
    "plt.imshow(R)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Some fun with this pipeline:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class LOSV(FittableModel):\n",
    "    \"\"\"Line of sight velocity!\"\"\"\n",
    "    \n",
    "    inputs = ('vel', 'theta')\n",
    "    outputs = ('vel',)\n",
    "    \n",
    "    @staticmethod\n",
    "    def evaluate(vel, theta):\n",
    "        \"\"\"Velocity in the line-of-sight direction.\"\"\"\n",
    "        return vel * theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<class '__main__.PolyVelocityProfile'>\n",
       "Name: PolyVelocityProfile (CompoundModel28)\n",
       "Inputs: ('X', 'Y')\n",
       "Outputs: ('vel',)\n",
       "Fittable parameters: (u'x_center_0', u'y_center_0', u'inclination_1', u'position_angle_1', u'c0_2', u'c1_2', u'c2_2', u'c3_2')\n",
       "Expression: [0] | [1] | [2] & [3] | [4]\n",
       "Components: \n",
       "    [0]: <class '__main__.Center'>\n",
       "    Name: Center\n",
       "    Inputs: ('X', 'Y')\n",
       "    Outputs: ('X', 'Y')\n",
       "    Fittable parameters: ('x_center', 'y_center')\n",
       "\n",
       "    [1]: <class '__main__.InclinedDisk'>\n",
       "    Name: InclinedDisk\n",
       "    Inputs: ('X', 'Y')\n",
       "    Outputs: ('R', 'Theta')\n",
       "    Fittable parameters: ('inclination', 'position_angle')\n",
       "\n",
       "    [2]: <Polynomial1D(3, c0=0.0, c1=0.0, c2=0.0, c3=0.0)>\n",
       "\n",
       "    [3]: <Identity(1)>\n",
       "\n",
       "    [4]: <class '__main__.LOSV'>\n",
       "    Name: LOSV\n",
       "    Inputs: ('vel', 'theta')\n",
       "    Outputs: ('vel',)"
      ]
     },
     "execution_count": 143,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "class PolyVelocityProfile(DiskCoordinates | models.Polynomial1D(degree=3) & models.Identity(1) | LOSV):\n",
    "    \"\"\"A disk with a polynomial valued velocity profile.\"\"\"\n",
    "    pass\n",
    "PolyVelocityProfile"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 225,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "pvp = PolyVelocityProfile(x_center_0=100, y_center_0=100, inclination_1=10.0, position_angle_1=10.0,\n",
    "                          c0_2=0, c1_2=-2.0, c2_2=-0.005)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 226,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/alexrudy/Dropbox/Library/Development/Python/ipython/IPython/kernel/__main__.py:21: RuntimeWarning: invalid value encountered in divide\n"
     ]
    }
   ],
   "source": [
    "losv = pvp(X, Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 227,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar instance at 0x11c6f8f38>"
      ]
     },
     "execution_count": 227,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
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       "TaKTW0dHxybx7yYJePDx7rO1AAAAAElFTkSuQmCC\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11c60ac50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(losv)\n",
    "plt.colorbar()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 228,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x11c9b8350>]"
      ]
     },
     "execution_count": 228,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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       "PyJiCCX5R0QMoST/iIghlOQfETGE/j9INGBmnaPUWgAAAABJRU5ErkJggg==\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11c920990>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "R = np.linspace(0, 200, 200)\n",
    "plt.plot(R, pvp[2](R))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# A more physical model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 229,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class SpheriodalMass(FittableModel):\n",
    "    \"\"\"A model which encloses a spheroidal mass.\"\"\"\n",
    "    \n",
    "    inputs = ('R',)\n",
    "    outputs = ('vel',)\n",
    "    \n",
    "    # Log of the BH Mass in M_sun.\n",
    "    blackhole_mass = Parameter(min=0.0, max=10)\n",
    "    \n",
    "    @staticmethod\n",
    "    def evaluate(R, blackhole_mass):\n",
    "        \"\"\"Evaluate and return the velocity field for a spheroidal mass model.\"\"\"\n",
    "        # Handle logarithmic parameters:\n",
    "        blackhole_mass = (10.0 ** blackhole_mass)\n",
    "        \n",
    "        G = c.G.to((u.km / u.s)**2 / u.M_sun * 0.1 * u.pc).value\n",
    "        \n",
    "        velocity_circular = np.sqrt(G * blackhole_mass / R)\n",
    "                \n",
    "        return velocity_circular"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 230,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<class '__main__.BHVelocityProfile'>\n",
       "Name: BHVelocityProfile (CompoundModel52)\n",
       "Inputs: ('X', 'Y')\n",
       "Outputs: ('vel',)\n",
       "Fittable parameters: (u'x_center_0', u'y_center_0', u'inclination_1', u'position_angle_1', u'blackhole_mass_2')\n",
       "Expression: [0] | [1] | [2] & [3] | [4]\n",
       "Components: \n",
       "    [0]: <class '__main__.Center'>\n",
       "    Name: Center\n",
       "    Inputs: ('X', 'Y')\n",
       "    Outputs: ('X', 'Y')\n",
       "    Fittable parameters: ('x_center', 'y_center')\n",
       "\n",
       "    [1]: <class '__main__.InclinedDisk'>\n",
       "    Name: InclinedDisk\n",
       "    Inputs: ('X', 'Y')\n",
       "    Outputs: ('R', 'Theta')\n",
       "    Fittable parameters: ('inclination', 'position_angle')\n",
       "\n",
       "    [2]: <class '__main__.SpheriodalMass'>\n",
       "    Name: SpheriodalMass\n",
       "    Inputs: ('R',)\n",
       "    Outputs: ('vel',)\n",
       "    Fittable parameters: ('blackhole_mass',)\n",
       "\n",
       "    [3]: <Identity(1)>\n",
       "\n",
       "    [4]: <class '__main__.LOSV'>\n",
       "    Name: LOSV\n",
       "    Inputs: ('vel', 'theta')\n",
       "    Outputs: ('vel',)"
      ]
     },
     "execution_count": 230,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "class BHVelocityProfile(DiskCoordinates | SpheriodalMass & models.Identity(1) | LOSV):\n",
    "    \"\"\"A disk with a velocity profile set only by a central black hole.\"\"\"\n",
    "    pass\n",
    "BHVelocityProfile"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 231,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "BHv = BHVelocityProfile(x_center_0=100, y_center_0=100, inclination_1=10.0, position_angle_1=10.0, blackhole_mass_2=8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 232,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/alexrudy/Dropbox/Library/Development/Python/ipython/IPython/kernel/__main__.py:21: RuntimeWarning: invalid value encountered in divide\n",
      "/Users/alexrudy/Dropbox/Library/Development/Python/ipython/IPython/kernel/__main__.py:18: RuntimeWarning: divide by zero encountered in divide\n"
     ]
    }
   ],
   "source": [
    "losv = BHv(X, Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 233,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar instance at 0x11cb636c8>"
      ]
     },
     "execution_count": 233,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
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      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11c8d9ed0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.colors as mcolors\n",
    "plt.imshow(losv, norm=mcolors.SymLogNorm(100))\n",
    "plt.colorbar()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 234,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/alexrudy/Dropbox/Library/Development/Python/ipython/IPython/kernel/__main__.py:18: RuntimeWarning: divide by zero encountered in divide\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x11ca30d10>]"
      ]
     },
     "execution_count": 234,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
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      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11c719f10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(R, pvp[2](R))\n",
    "plt.plot(R, BHv[2](R))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}