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May 5, 2015 22:07
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Compound Astropy Models
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| { | |
| "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": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "<matplotlib.image.AxesImage at 0x10fe2fcd0>" | |
| ] | |
| }, | |
| "execution_count": 50, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| }, | |
| { | |
| "data": { | |
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| ], | |
| "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" | |
| }, | |
| { | |
| "data": { | |
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| ], | |
| "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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| ], | |
| "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" | |
| }, | |
| { | |
| "data": { | |
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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" | |
| }, | |
| { | |
| "data": { | |
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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 | |
| } |
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