{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# STSP == intuition\n",
    "\n",
    "Here are some sanity checks that STSP is behaving like we think it's behaving.\n",
    "\n",
    "Below are diagrams for each test case. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "        <iframe\n",
       "            width=\"600\"\n",
       "            height=\"800\"\n",
       "            src=\"stsp_diagram.pdf\"\n",
       "            frameborder=\"0\"\n",
       "            allowfullscreen\n",
       "        ></iframe>\n",
       "        "
      ],
      "text/plain": [
       "<IPython.lib.display.IFrame at 0x7f48ac9d1630>"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.display import IFrame\n",
    "IFrame(\"stsp_diagram.pdf\", width=600, height=800)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import sys\n",
    "sys.path.insert(0, '/astro/users/bmmorris/git/friedrich/')\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from copy import deepcopy\n",
    "\n",
    "from friedrich.stsp import STSP\n",
    "from friedrich.lightcurve import LightCurve, hat11_params_morris_experiment, hat11_params_morris\n",
    "import batman\n",
    "\n",
    "params = batman.TransitParams()\n",
    "params.t0 = 0.0\n",
    "params.a = 15.0\n",
    "params.rp = 0.05\n",
    "params.inc = 90\n",
    "params.b = 0\n",
    "params.limb_dark = 'quadratic'\n",
    "params.u = [0.64070, 0.04776]\n",
    "params.w = 18\n",
    "params.ecc = 0.27\n",
    "params.per = 5\n",
    "\n",
    "params.inc_stellar = 90\n",
    "params.per_rot = 29.2\n",
    "params.duration = 0.0979\n",
    "params.lam = 0\n",
    "\n",
    "params.rho_star = 1.8\n",
    "\n",
    "times = np.arange(-0.8*params.duration, 0.8*params.duration, 1./60/24)\n",
    "lc = LightCurve(times=times,\n",
    "                fluxes=np.ones(len(times)), \n",
    "                errors=np.ones(len(times)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**1)** Well-aligned star/planet system $\\hat{n_s} = \\hat{n_o}$, with a spot at $(\\theta, \\phi) = (90^\\circ,\\, 0^\\circ)$ or (lat, lon) = (0, 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f48acc95198>]"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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mpLI3REQP8Gf5fUm7gV1p3z3APan8ixRaFZLGkrVYzit5vGLr5ITHyy1btuyN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\nM7Oq/X+rD8SjJtMg5wAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f48acde2d68>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "radius, theta, phi = 0.1, np.radians(90), np.radians(0)\n",
    "\n",
    "s = STSP(lc, params, np.array([radius, theta, phi]))\n",
    "plt.plot(*s.stsp_lc(), '.')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*** \n",
    "\n",
    "**2)** Nearly-aligned star/planet system where $i_o = 89.3^\\circ$ (like HAT-11), with a spot at $(\\theta, \\phi) = (90^\\circ,\\, 0^\\circ)$ or (lat, lon) = (0, 0).\n",
    "\n",
    "The planet no longer occults the spot, since the planet's orbit carries the planet to negative $y$, below the spot at (lat, lon) = (0, 0)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f48accdea20>]"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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4eDArb5ReSbkBo2Dy5GzK83AburO+OXg4eFgvCkNaxXmRvNGjs0uhQDacs3Rp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\nFXPwMDOzijl4mJlZxf4/8VLlAbRUgngAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f48acd22a20>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "tmp_params = deepcopy(params)\n",
    "tmp_params.inc = 89.3\n",
    "\n",
    "radius, theta, phi = 0.1, np.radians(90), np.radians(0)\n",
    "\n",
    "s = STSP(lc, tmp_params, np.array([radius, theta, phi]))\n",
    "plt.plot(*s.stsp_lc(), '.')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***\n",
    "\n",
    "**3)** The planet will occult the spot if we send the spot to lower latitudes (in the southern hemisphere). \n",
    "\n",
    "Nearly-aligned star/planet system where $i_o = 89.3^\\circ$ (like HAT-11), with a spot at $(\\theta, \\phi) = (98^\\circ,\\, 0^\\circ)$ or (lat, lon) = $(-8^\\circ, 0^\\circ)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f48acbfd0f0>]"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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y97Y7Ojro6Ogo43asmRRqIsUTC/fsgStT4+n06bBiRXMGkUKz2GDN9yjM1zhy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\nABoLBu2bAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f48acc61ba8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "tmp_params = deepcopy(params)\n",
    "tmp_params.inc = 89.3\n",
    "\n",
    "radius, theta, phi = 0.1, np.radians(98), np.radians(0)\n",
    "\n",
    "s = STSP(lc, tmp_params, np.array([radius, theta, phi]))\n",
    "plt.plot(*s.stsp_lc(), '.')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The above plot confirms that the tilt of the planet's orbit $i_o$ sends the planet to negative $Y$ values when $X=0$, where it is occulting the southern hemisphere of the star in a nearly-aligned star/planet system.\n",
    "\n",
    "***\n",
    "\n",
    "**4)** Now let's misalign the planet/star so that $\\hat{n_s} \\perp \\hat{n_o}$, with $i_o = 90^\\circ$, with a spot at $(\\theta, \\phi) = (90^\\circ,\\, 0^\\circ)$ or (lat, lon) = $(0^\\circ, 0^\\circ)$.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f48acb55710>]"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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ss4+sJZGblspeExEl4M/z95J2A7vSuruAu1L5Fyi0KiSNJ2uxnFN2vmLr5HXn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\neJiZWc0cPMzMrGb/H/glxqW+g5rUAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f48acc221d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "del tmp_params\n",
    "tmp_params = deepcopy(params)\n",
    "tmp_params.lam = 90\n",
    "\n",
    "radius, theta, phi = 0.1, np.radians(90), np.radians(0)\n",
    "\n",
    "s = STSP(lc, tmp_params, np.array([radius, theta, phi]))\n",
    "plt.plot(*s.stsp_lc(), '.')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***\n",
    "\n",
    "**5)** If we now incline the planet's orbit $i_o = 89.3^\\circ$ (like HAT-11), the spot at $(\\theta, \\phi) = (90^\\circ,\\, 0^\\circ)$ or (lat, lon) = $(0^\\circ, 0^\\circ)$ will not be occulted again."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f48ad226240>]"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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4eDArb5ReSbkBo2Dy5GzK83AburO+OXg4eFgvCkNaxXmRvNGjs0uhQDacs3Rp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\nFXPwMDOzijl4mJlZxf4/8VLlAbRUgngAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f48ad369b70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "tmp_params = deepcopy(params)\n",
    "tmp_params.lam = 90\n",
    "tmp_params.inc = 89.3\n",
    "\n",
    "radius, theta, phi = 0.1, np.radians(90), np.radians(0)\n",
    "\n",
    "s = STSP(lc, tmp_params, np.array([radius, theta, phi]))\n",
    "plt.plot(*s.stsp_lc(), '.')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*** \n",
    "\n",
    "**6)** We could now occult the spot if we offset the spot longitude (in the +$\\hat{\\phi}$ direction), by moving the spot to $(\\theta, \\phi) = (90^\\circ,\\, 8^\\circ)$ or (lat, lon) = $(0^\\circ, 8^\\circ)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f48ad0934a8>]"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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RMCGlvSciuoAvFvYl7QX2pGMPAA+k9G+Qq1VIGklWY5lVdL987eR99ytYtmzZ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\nM6uYg4eZmVXMwcPMzCrm4GFmZhX7/4WN+etVwQFwAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f48ad2b8cc0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "tmp_params = deepcopy(params)\n",
    "tmp_params.lam = 90\n",
    "tmp_params.inc = 89.3\n",
    "tmp_params.inc_stellar = 90\n",
    "\n",
    "radius, theta, phi = 0.1, np.radians(90), np.radians(8)\n",
    "\n",
    "s = STSP(lc, tmp_params, np.array([radius, theta, phi]))\n",
    "plt.plot(*s.stsp_lc(), '.')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***\n",
    "\n",
    "**7)** Let's check that the planet is moving in the direction that we'd expect -- that is, it's traveling from left to right across the star, from $-\\hat{X}$ to $+\\hat{X}$. \n",
    "\n",
    "We'll check this by putting down two spots -- a small one on the center of the star, a larger one to the right at the same latitude, but greater longitude. If the planet is moving from $-\\hat{X}$ to $+\\hat{X}$, we would expect it to occult the smaller spot at mid-transit and the larger spot between mid-transit and egress.\n",
    "\n",
    "| spot | lat | lon | \n",
    "|--------|-----|-----|\n",
    "| spot 1 | 0  |  0  |\n",
    "| spot 2 | 0  |  30  |\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f48acde7780>]"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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9cD09Wc5j1iz/rEajrq4uurq6Sj/uoPM80gV+G3Ah8GvgceDSiNhS2GYCsC8i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\nOXiYmVnNHDzMzKxmDh5mZlaz/w8fYqsl13prBAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f48ace37438>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "tmp_params = deepcopy(params)\n",
    "\n",
    "radius1, theta1, phi1 = 0.02, np.radians(90), np.radians(0)\n",
    "radius2, theta2, phi2 = 0.1, np.radians(90), np.radians(30)\n",
    "\n",
    "s = STSP(lc, tmp_params, np.array([radius1, theta1, phi1, radius2, theta2, phi2]))\n",
    "plt.plot(*s.stsp_lc(), '.')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***\n",
    "\n",
    "**8)** For an antialigned star-planet system, you'd expect the same pattern as above, but reversed in time. Let's use the same spot positions as above, but set $\\lambda = 180^\\circ$, which effectively changes the direction of the planet's motion over the star.\n",
    "\n",
    "| spot | lat | lon | \n",
    "|--------|-----|-----|\n",
    "| spot 1 | 0  |  0  |\n",
    "| spot 2 | 0  |  30  |\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f48acd6f048>]"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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xelo3D1gaEe8vHGsG8F3gPLLuqkeBNyXMPc/D4Oioq7z7qlkjgfIANmVKlsDf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\nVjYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f48acd95cf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "tmp_params = deepcopy(params)\n",
    "tmp_params.lam = 180\n",
    "\n",
    "radius1, theta1, phi1 = 0.02, np.radians(90), np.radians(0)\n",
    "radius2, theta2, phi2 = 0.1, np.radians(90), np.radians(30)\n",
    "\n",
    "s = STSP(lc, tmp_params, np.array([radius1, theta1, phi1, radius2, theta2, phi2]))\n",
    "plt.plot(*s.stsp_lc(), '.')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***\n",
    "\n",
    "**9)** Now let's check the stellar inclination angle. Starting from the misaligned system from **(4)** with $\\hat{n_s} \\perp \\hat{n_o}$ with $i_o = 90^\\circ$, with a spot at $(\\theta, \\phi) = (90^\\circ,\\, 0^\\circ)$ or (lat, lon) = $(0^\\circ, 0^\\circ)$. \n",
    "\n",
    "We'll also offset the stellar inclination to $i_s = 60^\\circ$ rather than $i_s = 90^\\circ$ as it was in **(4)**, which we expect should move the spot occultation to earlier times, between ingress and mid-transit."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f48acae8400>]"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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jHfDRjx47ZwNg/Hg4cgSmTnVtYzSo1TyPfmseEdEj6TpgFVkfyd0RsVXSgmx3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\njDuULfIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f48acb42cf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "tmp_params = deepcopy(params)\n",
    "tmp_params.lam = 90\n",
    "tmp_params.inc_stellar = 60\n",
    "\n",
    "radius, theta, phi = 0.1, np.radians(90), np.radians(0)\n",
    "\n",
    "s = STSP(lc, tmp_params, np.array([radius, theta, phi]))\n",
    "plt.plot(*s.stsp_lc(), '.')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***\n",
    "\n",
    "**10)** Now let's check the stellar inclination angle going in the opposite direction. Starting from the misaligned system from **(4)** with $\\hat{n_s} \\perp \\hat{n_o}$ with, $i_o = 90^\\circ$, with a spot at $(\\theta, \\phi) = (90^\\circ,\\, 0^\\circ)$ or (lat, lon) = $(0^\\circ, 0^\\circ)$. \n",
    "\n",
    "We'll also offset the stellar inclination to $i_s = 120^\\circ$ rather than $i_s = 90^\\circ$ as it was in **(4)**, which we expect should move the spot occultation to later times, between mid-transit and egress."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f48aca74a90>]"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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E+YjVVzIdPDekEsVf+RszBp54Ist72Mg1ZAnzlOi+GlgJPEeWzN4sab6kK9Nm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\nDzMzq5qDh5mZVc3Bw8zMqubgYWZmVfv/V5gSJlZOxzQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f48acaaf748>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "tmp_params = deepcopy(params)\n",
    "tmp_params.lam = 90\n",
    "tmp_params.inc_stellar = 120\n",
    "\n",
    "radius, theta, phi = 0.1, np.radians(90), np.radians(0)\n",
    "\n",
    "s = STSP(lc, tmp_params, np.array([radius, theta, phi]))\n",
    "plt.plot(*s.stsp_lc(), '.')"
   ]
  }
 ],
 "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": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}