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   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "#Vondr\u00e1k Precession Model\n",
      "There is another long-term precession model I found. Vondr\u00e1k's *[New precession expressions, valid for long time intervals](http://www.aanda.org/articles/aa/pdf/2011/10/aa17274-11.pdf)* (2011) describes this. He includes [code samples](http://www.aanda.org/articles/aa/olm/2011/10/aa17274-11/aa17274-11.html), depictions, and thoughts on the process that make this more readily available to me as a physics layman to comprehend. This method is not as long-term as Owen's, it *only* covers several hundreds of millennia (haha). One of the research goals is to \n",
      "\n",
      "> find relatively simple expressions of precession parameters, with accuracy comparable to the IAU 2006 model near the epoch J2000.0, and lower accuracy outside the interval \u00b11 millennium (up to several minutes of arc at the extreme epochs \u00b1200 millennia).\n",
      "\n",
      "See also:\n",
      "\n",
      "* *[New Long-Term Expressions for Precession](http://syrte.obspm.fr/jsr/journees2011/pdf/vondrak.pdf)* (2011) \n",
      "* *[Some New Thoughts About Long-Term Precession](http://syrte.obspm.fr/jsr/journees2010/pdf/Vondrak.pdf)* (2010)\n",
      "* *[New precession expressions, valid for long time intervals (Corrigendum)](http://www.aanda.org/articles/aa/abs/2012/05/aa17274e-11/aa17274e-11.html)* (2012)\n",
      "\n",
      "##Implementation in Software\n",
      "\n",
      "I've translated the [Fortran code by Vondr\u00e1k](http://www.aanda.org/articles/aa/olm/2011/10/aa17274-11/aa17274-11.html) into Python:\n",
      "\n",
      "> Here we present four computer subroutines that implement the long-term precession model. The chosen parameterization is P\u2090,Q\u2090 for the ecliptic pole and X\u2090,Y\u2090 for the equator pole. These results enable the precession matrix P to be computed. Two versions of the precession matrix are presented, the first for use with [J2000](https://en.wikipedia.org/wiki/Julian_year_%28astronomy%29).0 mean place and the second for use with Geocentric Celestial Reference System (GCRS) coordinates. Fortran code is used; implementations in other languages would be along very similar lines. The time argument for all four subroutines is Julian epoch ([TT](https://en.wikipedia.org/wiki/Terrestrial_Time))."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%pylab inline\n",
      "\n",
      "# 2Pi\n",
      "tau =  6.283185307179586476925287e0\n",
      "\n",
      "# Arcseconds to radians\n",
      "as2r = 4.848136811095359935899141e-6\n",
      "\n",
      "# Obliquity at J2000.0 (radians)\n",
      "eps0 = 84381.406 * as2r"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Populating the interactive namespace from numpy and matplotlib\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "##Precession of the ecliptic\n",
      "\n",
      "> The Fortran subroutine ltp_PECL generates the unit vector for the pole of the ecliptic, using the series for PA,QA (Eq. (8) and Table 1)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def ltp_PECL(epj):\n",
      "    '''Long-term precession of the ecliptic'''\n",
      "    \n",
      "    # There is a typographical error in the original coefficient \n",
      "    # C\u2087 for Q\u2090 should read 198.296701 instead of 198.296071\n",
      "    # Src: http://www.aanda.org/articles/aa/abs/2012/05/aa17274e-11/aa17274e-11.html\n",
      "\n",
      "    # Number of polynomial and periodic coefficients\n",
      "    npol = 4\n",
      "    nper = 8\n",
      "    \n",
      "    # Polynomial coefficients\n",
      "    pqpol = array([\n",
      "        [+5851.607687,-1600.886300],\n",
      "        [-0.1189000,+1.1689818],\n",
      "        [-0.00028913,-0.00000020],\n",
      "        [+0.000000101,-0.000000437],\n",
      "    ])\n",
      "\n",
      "    # Periodic coefficients\n",
      "    pqper = array([\n",
      "        [708.15, -5486.751211, -684.661560, 667.666730, -5523.863691],\n",
      "        [2309.00, -17.127623, 2446.283880, -2354.886252, -549.747450],\n",
      "        [1620.00, -617.517403, 399.671049, -428.152441, -310.998056],\n",
      "        [492.20, 413.442940, -356.652376, 376.202861, 421.535876],\n",
      "        [1183.00, 78.614193, -186.387003, 184.778874, -36.776172],\n",
      "        [622.00, -180.732815, -316.800070, 335.321713, -145.278396],\n",
      "        [882.00, -87.676083, 198.296701, -185.138669, -34.744450], # corrected coefficient per erratum\n",
      "        [547.00, 46.140315, 101.135679, -120.972830, 22.885731],\n",
      "    ])\n",
      "\n",
      "    # Centuries since J2000\n",
      "    T = (epj-2000.0)/100.0\n",
      "\n",
      "    # Initialize P\u2090 and Q\u2090 accumulators\n",
      "    P = 0.0\n",
      "    Q = 0.0\n",
      "    \n",
      "    # Periodic Terms\n",
      "    for i in range(0,nper):\n",
      "        W = tau*T\n",
      "        A = W/pqper[i][0]\n",
      "        S = sin(A)\n",
      "        C = cos(A)\n",
      "        P = P + C*pqper[i][1] + S*pqper[i][3]\n",
      "        Q = Q + C*pqper[i][2] + S*pqper[i][4]\n",
      "        \n",
      "    # Polynomial Terms\n",
      "    W = 1.0\n",
      "    for i in range(0,npol):\n",
      "        P = P + pqpol[i][0]*W\n",
      "        Q = Q + pqpol[i][1]*W\n",
      "        W = W*T\n",
      "        \n",
      "    # P\u2090 and Q\u2090 (radians)\n",
      "    P = P*as2r\n",
      "    Q = Q*as2r\n",
      "    \n",
      "    # Form the ecliptic pole vector\n",
      "    Z = sqrt(max(1.0-P*P-Q*Q,0.0))\n",
      "    S = sin(eps0)\n",
      "    C = cos(eps0)\n",
      "    vec0 = P\n",
      "    vec1 = -Q*C - Z*S\n",
      "    vec2 = -Q*S + Z*C\n",
      "    vec = array([vec0,vec1,vec2])\n",
      "    return vec"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "##Precession of the equator\n",
      "\n",
      "> The Fortran subroutine ltp_PEQU generates the unit vector for the pole of the equator, using the series for XA,YA (Eq. (9) and Table 2)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def ltp_PEQU(epj):\n",
      "    '''Long-term precession of the equator'''\n",
      "    \n",
      "    # Number of polynomial and periodic coefficients\n",
      "    npol = 4\n",
      "    nper = 14\n",
      "    \n",
      "    # Polynomial coefficients\n",
      "    xypol = array([\n",
      "        [+5453.282155,-73750.930350],\n",
      "        [+0.4252841,-0.7675452],\n",
      "        [-0.00037173,-0.00018725],\n",
      "        [-0.000000152,+0.000000231],\n",
      "    ])\n",
      "\n",
      "    # Periodic coefficients\n",
      "    xyper = array([\n",
      "        [256.75, -819.940624, 75004.344875, 81491.287984, 1558.515853],\n",
      "        [708.15, -8444.676815, 624.033993, 787.163481, 7774.939698,],\n",
      "        [274.20, 2600.009459, 1251.136893, 1251.296102, -2219.534038],\n",
      "        [241.45, 2755.175630, -1102.212834, -1257.950837, -2523.969396],\n",
      "        [2309.00, -167.659835, -2660.664980, -2966.799730, 247.850422],\n",
      "        [492.20, 871.855056, 699.291817, 639.744522, -846.485643],\n",
      "        [396.10, 44.769698, 153.167220, 131.600209, -1393.124055],\n",
      "        [288.90, -512.313065, -950.865637, -445.040117, 368.526116],\n",
      "        [231.10, -819.415595, 499.754645, 584.522874, 749.045012],\n",
      "        [1610.00, -538.071099, -145.188210, -89.756563, 444.704518],\n",
      "        [620.00, -189.793622, 558.116553, 524.429630, 235.934465],\n",
      "        [157.87, -402.922932, -23.923029, -13.549067, 374.049623],\n",
      "        [220.30, 179.516345, -165.405086, -210.157124, -171.330180],\n",
      "        [1200.00, -9.814756, 9.344131, -44.919798, -22.899655],\n",
      "    ])\n",
      "\n",
      "    # Centuries since J2000\n",
      "    T = (epj-2000.0)/100.0\n",
      "\n",
      "    # Initialize P\u2090 and Q\u2090 accumulators\n",
      "    X = 0.0\n",
      "    Y = 0.0\n",
      "    \n",
      "    # Periodic Terms\n",
      "    for i in range(0,nper):\n",
      "        W = tau*T\n",
      "        A = W/xyper[i][0]\n",
      "        S = sin(A)\n",
      "        C = cos(A)\n",
      "        X = X + C*xyper[i][1] + S*xyper[i][3]\n",
      "        Y = Y + C*xyper[i][2] + S*xyper[i][4]\n",
      "        \n",
      "    # Polynomial Terms\n",
      "    W = 1.0\n",
      "    for i in range(0,npol):\n",
      "        X = X + xypol[i][0]*W\n",
      "        Y = Y + xypol[i][1]*W\n",
      "        W = W*T\n",
      "        \n",
      "    # X and Y (direction cosines)\n",
      "    X = X*as2r\n",
      "    Y = Y*as2r\n",
      "    \n",
      "    # Form the equator pole vector\n",
      "    veq0 = X\n",
      "    veq1 = Y\n",
      "    W = X*X + Y*Y\n",
      "    veq2 = 0.0\n",
      "    if(W < 1.0):\n",
      "        veq2 = sqrt(1.0-W)\n",
      "    veq = array([veq0, veq1, veq2])\n",
      "    return veq"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "##Precession matrix, mean J2000.0\n",
      "\n",
      "> The Fortran subroutine ltp_PMAT generates the 3 \u00d7 3 rotation matrix **P**, constructed using Fabri parameterization (i.e. directly from the unit vectors for the ecliptic and equator poles \u2013 see Sect. 5.4). As well as calling the two previous subroutines, ltp_PMAT calls subroutines from the [IAU SOFA](http://www.iausofa.org/) library. The resulting matrix transforms vectors with respect to the mean equator and equinox of epoch 2000.0 into mean place of date.\n",
      "\n",
      "The original Fortran code uses the SOFA commands `pxp()` and `pn()`. They in return use a few more functions in the library. The modulus W returned from iau_PN is tossed out in the Fortran code. I just do similarly here so that everything is common between the functions. There are Python wrappers for both SOFA and [ERFA](https://github.com/liberfa/erfa), the open source version of SOFA, and there are elegant numpy linear algebra functions, but the following was simple enough and works too.\n",
      "\n",
      "* [iauPxp](http://www.iausofa.org/2013_1202_C/sofa/pxp.c) - `pxp()` - Outer (=vector=cross) product of two p-vectors\n",
      "* [iauPn](http://www.iausofa.org/2013_1202_C/sofa/pn.c) - `pn()` - normalize p\u2212vector returning modulus "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def pxp(a,b):\n",
      "    '''p-vector outer (=vector=cross) product.\n",
      "    Given: two p-vectors (a and b)\n",
      "    Return: a x b\n",
      "    '''\n",
      "    \n",
      "    xa = a[0]\n",
      "    ya = a[1]\n",
      "    za = a[2]\n",
      "    xb = b[0]\n",
      "    yb = b[1]\n",
      "    zb = b[2]\n",
      "    axb = array([])\n",
      "    axb = append(axb,ya*zb - za*yb)\n",
      "    axb = append(axb,za*xb - xa*zb)\n",
      "    axb = append(axb,xa*yb - ya*xb)\n",
      "    return axb\n",
      "\n",
      "def pn(p):\n",
      "    '''Convert a p-vector into modulus and unit vector.\n",
      "    Given: p-vector (p)\n",
      "    Return: modulus (r), and unit vector (u)\n",
      "    '''\n",
      "    \n",
      "    # Modulus of p-vector\n",
      "    # http://www.iausofa.org/2013_1202_C/sofa/pm.c\n",
      "    w = sqrt(p[0]*p[0] + p[1]*p[1] + p[2]*p[2])\n",
      "    u = array([])\n",
      "    if(w == 0.0):\n",
      "        # zero a p-vector\n",
      "        # http://www.iausofa.org/2013_1202_C/sofa/zp.c\n",
      "        u = append(u,[0.0, 0.0, 0.0])\n",
      "    else:\n",
      "        # unit vector\n",
      "        # http://www.iausofa.org/2013_1202_C/sofa/sxp.c\n",
      "        s = 1.0/w\n",
      "        u = append(u, s*p[0])\n",
      "        u = append(u, s*p[1])\n",
      "        u = append(u, s*p[2])\n",
      "    r = w\n",
      "    return r, u"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def ltp_PMAT(epj):\n",
      "    '''Long-term precession matrix\n",
      "    Given: EPJ d Julian epoch (TT)\n",
      "    Return: RP d precession matrix, J2000.0 to date\n",
      "    \n",
      "    The matrix is in the sense P_date = RP x P_J2000,\n",
      "    where P_J2000 is a vector with respect to the J2000.0 mean\n",
      "    equator and equinox and P_date is the same vector with respect to\n",
      "    the equator and equinox of epoch EPJ.\n",
      "    ''' \n",
      "    \n",
      "    # Equator pole (bottom row of matrix)\n",
      "    peqr = ltp_PEQU(epj)\n",
      "    \n",
      "    # Ecliptic pole\n",
      "    pecl = ltp_PECL(epj)\n",
      "\n",
      "    # Equinox (top row of matrix)\n",
      "    V = pxp(peqr, pecl) # P-vector outer product.\n",
      "    w, EQX = pn(V) # Convert a p-vector into modulus and unit vector\n",
      "\n",
      "    # Middle row of matrix\n",
      "    V = pxp(peqr, EQX)\n",
      "\n",
      "    # The matrix elements\n",
      "    rp = array([])\n",
      "    rp = append(rp, [EQX, V, peqr])\n",
      "    rp = rp.reshape(3,3)\n",
      "    return rp"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "##Precession matrix, GCRS\n",
      "\n",
      "> The Fortran subroutine ltp_PBMAT generates the 3 \u00d7 3 rotation matrix **P** \u00d7 **B**, where **B** is the \u201cframe bias matrix\u201d that expresses the relative orientation of the [GCRS](https://en.wikipedia.org/wiki/Barycentric_celestial_reference_system) and mean J2000.0 reference systems. A simple first-order implementation of the frame bias is used, the departure from rigor being well under 1 \u03bcas."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def ltp_PBMAT(epj):\n",
      "    '''Long-term precession matrix, including GCRS frame bias.\n",
      "    Given: EPJ d Julian epoch (TT)\n",
      "    Return: RPB d precession-bias matrix, J2000.0 to date\n",
      "    \n",
      "    The matrix is in the sense P_date = RPB x P_J2000,\n",
      "    where P_J2000 is a vector in the Geocentric Celestial Reference\n",
      "    System, and P_date is the vector with respect to the Celestial\n",
      "    Intermediate Reference System at that date but with nutation\n",
      "    neglected.\n",
      "    \n",
      "    A first order bias formulation is used, of sub-microarcsecond\n",
      "    accuracy compared with a full 3D rotation.\n",
      "    '''\n",
      "    \n",
      "    # Frame bias (IERS Conventions 2010, Eqs. 5.21 and 5.33)\n",
      "    DX = -0.016617 * as2r\n",
      "    DE = -0.0068192 * as2r\n",
      "    DR = -0.0146 * as2r\n",
      "    \n",
      "    # Precession matrix.\n",
      "    rp = ltp_PMAT(epj)\n",
      "    \n",
      "    # Apply the bias\n",
      "    rpb = array([])\n",
      "    rpb = append(rpb,  rp[0][0]    - rp[0][1]*DR + rp[0][2]*DX)\n",
      "    rpb = append(rpb,  rp[0][0]*DR + rp[0][1]    + rp[0][2]*DE)\n",
      "    rpb = append(rpb, -rp[0][0]*DX - rp[0][1]*DE + rp[0][2]   )\n",
      "    rpb = append(rpb,  rp[1][0]    - rp[1][1]*DR + rp[1][2]*DX)\n",
      "    rpb = append(rpb,  rp[1][0]*DR + rp[1][1]    + rp[1][2]*DE)\n",
      "    rpb = append(rpb, -rp[1][0]*DX - rp[1][1]*DE + rp[1][2]   )\n",
      "    rpb = append(rpb,  rp[2][0]    - rp[2][1]*DR + rp[2][2]*DX)\n",
      "    rpb = append(rpb,  rp[2][0]*DR + rp[2][1]    + rp[2][2]*DE)\n",
      "    rpb = append(rpb, -rp[2][0]*DX - rp[2][1]*DE + rp[2][2]   )\n",
      "    rpb = rpb.reshape(3,3)\n",
      "    return rpb"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "##Test Cases\n",
      "\n",
      "These test cases as well are translated from the original [Fortran code by Vondr\u00e1k](http://www.aanda.org/articles/aa/olm/2011/10/aa17274-11/aa17274-11.html) et al.\n",
      "\n",
      "> To assist in checking for correct use of the above subroutines, we present below the results of calling each of them for the following test date: -1374 (i.e. 1375\u2009BCE) May 3 (Gregorian calendar) at 13:52:19.2 TT. The equivalent [Julian date](https://en.wikipedia.org/wiki/Julian_day) and Julian [epoch](https://en.wikipedia.org/wiki/Epoch_%28astronomy%29) are 1219339.078000 (TT) and -1373.5959534565 (TT) respectively.\n",
      "\n",
      "The functions compute the precession matrix when given the date as a julian epoch. `epj` is based on the SOFA calendar helper function and is supplied in case it is useful."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def epj(dj):\n",
      "    '''Julian Date to Julian Epoch'''\n",
      "    # based on http://www.iausofa.org/2013_1202_C/sofa/epj.c\n",
      "    DJ00 = 2451545.0 # Reference epoch (J2000.0), Julian Date\n",
      "    DJY = 365.25 # Days per Julian year\n",
      "    epj = 2000.0 + (dj - DJ00)/DJY;\n",
      "    return epj\n",
      "\n",
      "print(epj(1219339.078000))\n",
      "epj = -1373.5959534565 # julian epoch"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "-1373.59595346\n"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "pecl = ltp_PECL(epj)\n",
      "pecl_test = array([+0.00041724785764001342,-0.40495491104576162693,+0.91433656053126552350])\n",
      "print(pecl)\n",
      "print(pecl_test)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[  4.17247858e-04  -4.04954914e-01   9.14336559e-01]\n",
        "[  4.17247858e-04  -4.04954911e-01   9.14336561e-01]\n"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "pequ = ltp_PEQU(epj)\n",
      "pequ_test = array([-0.29437643797369031532,-0.11719098023370257855,+0.94847708824082091796])\n",
      "print(pequ)\n",
      "print(pequ_test)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[-0.29437644 -0.11719098  0.94847709]\n",
        "[-0.29437644 -0.11719098  0.94847709]\n"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "rp = ltp_PMAT(epj)\n",
      "rp_test = array([\n",
      "                [+0.68473390570729557360,+0.66647794042757610444,+0.29486722236305384992],\n",
      "                [-0.66669482609418419936,+0.73625636097440967969,-0.11595076448202158534],\n",
      "                [-0.29437643797369031532,-0.11719098023370257855,+0.94847708824082091796],\n",
      "                ])\n",
      "print(rp)\n",
      "print(rp_test)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[[ 0.68473391  0.66647794  0.29486715]\n",
        " [-0.66669482  0.73625636 -0.11595076]\n",
        " [-0.29437644 -0.11719098  0.94847709]]\n",
        "[[ 0.68473391  0.66647794  0.29486722]\n",
        " [-0.66669483  0.73625636 -0.11595076]\n",
        " [-0.29437644 -0.11719098  0.94847709]]\n"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "rpxb = ltp_PBMAT(epj)\n",
      "rpxb_test = array([\n",
      "                  [+0.68473392912753224372,+0.66647788221176470103,+0.29486722236305384992],\n",
      "                  [-0.66669476463873305255,+0.73625641199831485100,-0.11595079385100924091],\n",
      "                  [-0.29437652267952261218,-0.11719099075396051880,+0.94847706065103424635],\n",
      "                  ])\n",
      "print(rpxb)\n",
      "print(rpxb_test)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[[ 0.68473393  0.66647788  0.29486722]\n",
        " [-0.66669476  0.73625642 -0.11595079]\n",
        " [-0.29437652 -0.11719099  0.94847706]]\n",
        "[[ 0.68473393  0.66647788  0.29486722]\n",
        " [-0.66669476  0.73625641 -0.11595079]\n",
        " [-0.29437652 -0.11719099  0.94847706]]\n"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "> The above computations were performed using quadruple precision (REAL*128) so that all the reported decimals (except perhaps for the least significant digit in rare critical cases) are correct. Note that on typical computers ordinary double precision has only 15\u201316 decimal places of precision, and this must be taken into account when comparing results.\n",
      "\n",
      "If there is an error, it will definitely will be due to a precision error. It is on my to-do list to massage these errors out.\n",
      "\n",
      "##Results\n",
      "\n",
      "Here are the periodic results from -200000 to 200000 years showing each component of the vector separately."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ecl_p_matrix_list = []\n",
      "equ_p_matrix_list = []\n",
      "year = arange(-200001.0, 200000.0, 100)\n",
      "for y in year:\n",
      "    p_ecl = ltp_PECL(y)\n",
      "    p_equ = ltp_PEQU(y)\n",
      "    ecl_p_matrix_list.append(p_ecl)\n",
      "    equ_p_matrix_list.append(p_equ)\n",
      "\n",
      "axis([-200000,200000,-.5,1])\n",
      "plot(year, ecl_p_matrix_list)\n",
      "#savefig('ecl_p_matrix.png')\n",
      "show()\n",
      "axis([-200000,200000,-.8,1.1])\n",
      "plot(year, equ_p_matrix_list)\n",
      "#savefig('equ_p_matrix.png')\n",
      "show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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GQEwM1NXZ+/n5cOgQzJwJ110H8+fDoEGdvQUinSMS30ehoOiCjhyBv/wF1q2Dv/4VPvsM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\nERERERERAfj/P8+FR4B8tjUAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f83519a31d0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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48caNxkpUY3HzzVTqGItnn6V8lxXIz5d7Y6AsPvxh4Cc/oZ9/8QuqJDOTXAao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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f8351963690>"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "##What's up with these vectors\n",
      "\n",
      "So what did we get? What are the units? How do we use it?\n",
      "\n",
      "The *[Report of the International Astronomical Union Division I Working Group on Precession and the Ecliptic](http://www.lunarplanner.com/Reference/cm06_94_PEWG.pdf)* (2006) discusses some of the different ways to compute the precession matrix **P**. **P** is the matrix we calculated above. This precession matrix is used to transform the current coordinates (of epoch J2000) to the coordinates of any date. \n",
      "\n",
      "The new positions (future or past of J2000) are optained by multiplying the coordinates of the standard epoch by the precession matrix. **p\u2081** = **P\u00b7p\u2080**, where **P** is the below precession matrix and **p\u2080** is the original position. The precession matrix is unitless.\n",
      "\n",
      "$$P = \\begin{pmatrix}\n",
      "P_{11} & P_{12} & P_{13} \\\\ \n",
      "P_{21} & P_{22} & P_{23} \\\\ \n",
      "P_{31} & P_{32} & P_{33} \n",
      "\\end{pmatrix}$$\n",
      "\n",
      "When these papers mention *the coordinate system based upon the mean equator and equinox*, they are talking about how the pole axis traces a cone (wobbles like a top) when they speak of equinox precession. The earth goes through one such rotation in approximately every 26,000 years. The [ecliptic plane](https://en.wikipedia.org/wiki/Ecliptic) is the path the Sun appears to traverse across the celestial sphere. The [ecliptic pole](https://en.wikipedia.org/wiki/Ecliptic_pole) is perpindicular to this. \n",
      "\n",
      "The pole of the equator is needed because the Earth's equatorial plane moves in respect to the celestial sphere and it is not perpendicular to the Ecliptic pole. The angle between the Earth's equatorial plane and the ecliptic pole, \u2208, is called the obliquity of the ecliptic and is about 23.4\u00b0. \n",
      "\n",
      "The term \"mean\" in mean equator, in respect to the Earth's equatorial plane, is used when [nutation](https://en.wikipedia.org/wiki/Nutation) is averaged out or omitted. I am not accounting for nutation in these examples, so we should note that the 'true pole' does not point at the epoch's celestial pole because it nutates away from the mean one in reality.\n",
      "\n",
      "The following gets the coordinates for Polaris (in respect to J2000) from PyEphem."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def compute_polaris(year):\n",
      "    polaris = ephem.star('Polaris')\n",
      "    polaris.compute(str(year),epoch='2000')\n",
      "    ra = polaris.a_ra\n",
      "    dec = polaris.a_dec\n",
      "    x = cos(dec) * cos(ra)\n",
      "    y = cos(dec) * sin(ra)\n",
      "    z = sin(dec)\n",
      "    p = array([[x], [y], [z]])\n",
      "    return p"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 13
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def ra_dec(v):\n",
      "    x = v[0][0]\n",
      "    y = v[1][0]\n",
      "    z = v[2][0]\n",
      "    ra = math.atan2(y,x)\n",
      "    dec = math.atan2(z,sqrt(x*x + y*y))\n",
      "    return ra, dec"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 14
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import ephem\n",
      "# renaming these so that they don't overwrite the pylab degrees\n",
      "from ephem import hours as hrs\n",
      "from ephem import degrees as deg\n",
      "p0 = compute_polaris(2000)\n",
      "(ra, dec) = ra_dec(p0)\n",
      "print('RA: {}'.format(hrs(ra)))\n",
      "print('DEC: {}'.format(deg(dec)))\n",
      "print('cartesian position of Polaris in the year=2000, epoch=2000:')\n",
      "x = p0[0][0]\n",
      "y = p0[1][0]\n",
      "z = p0[2][0]\n",
      "print('{}\\nthis vector has length {}'.format(\n",
      "      (x,y,z),sqrt(x*x + y*y + z*z)))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "RA: 2:31:47.10\n",
        "DEC: 89:15:51.0\n",
        "cartesian position of Polaris in the year=2000, epoch=2000:\n",
        "(0.010127331660770541, 0.007897050033378511, 0.99991753347673784)\n",
        "this vector has length 1.0\n"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This is then translated from -200000 to 200000. Where P is recomputed for every epoch date.\n",
      "\n",
      "$$p_{1} = P\\cdot p_{0} = \\begin{pmatrix}\n",
      "P_{11} & P_{12} & P_{13} \\\\ \n",
      "P_{21} & P_{22} & P_{23} \\\\ \n",
      "P_{31} & P_{32} & P_{33} \n",
      "\\end{pmatrix}\n",
      "\\begin{pmatrix}\n",
      "x\\\\ y\\\\ z\n",
      "\\end{pmatrix}\n",
      "=\n",
      "\\begin{pmatrix}\n",
      "P_{11}x + P_{12}y + P_{13}z \\\\ \n",
      "P_{21}x + P_{22}y + P_{23}z \\\\ \n",
      "P_{31}x + P_{32}y + P_{33}z \n",
      "\\end{pmatrix}$$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def pdp(a,b):\n",
      "    '''p-vector inner (=scalar=dot) product.'''\n",
      "    \n",
      "    # this is akin to the SOFA iauPdp, but it handles 3x3 square \n",
      "    # matrices times (dot) column vectors 3x1\n",
      "    # http://www.iausofa.org/2013_1202_C/sofa/pdp.c\n",
      "    row = []\n",
      "    for r in range(3):\n",
      "        w = a[r][0]*b[0] + a[r][1]*b[1] + a[r][2]*b[2]\n",
      "        row.append(w)\n",
      "    adb = array(row)\n",
      "    return adb"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 16
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "p0 = compute_polaris(2000)\n",
      "print('The position of Polaris at J2000 is')\n",
      "print(p0)\n",
      "epj = 100000\n",
      "P = ltp_PBMAT(epj) # Precession matrix, GCRS\n",
      "p1 = compute_polaris(epj)\n",
      "p1 = pdp(P, p1)\n",
      "print('The new position of Polaris in 100000 years is')\n",
      "print(p1)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The position of Polaris at J2000 is\n",
        "[[ 0.01012733]\n",
        " [ 0.00789705]\n",
        " [ 0.99991753]]\n",
        "The new position of Polaris in 100000 years is\n",
        "[[ 0.31728427]\n",
        " [-0.15847663]\n",
        " [ 0.9349951 ]]\n"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "(ra, dec) = ra_dec(p0)\n",
      "print('In hours of right ascension and degrees of declination')\n",
      "print('The position of Polaris at J2000 is')\n",
      "print(str(hrs(ra)),str(deg(dec)))\n",
      "print('The new position of Polaris in 100000 years is')\n",
      "(ra1, dec1) = ra_dec(p1)\n",
      "print(str(hrs(ra1)),str(deg(dec1)))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "In hours of right ascension and degrees of declination\n",
        "The position of Polaris at J2000 is\n",
        "('2:31:47.10', '89:15:51.0')\n",
        "The new position of Polaris in 100000 years is\n",
        "('-1:46:09.87', '69:13:38.5')\n"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Awesome, we were able to compute the position of Polaris in approximately 100000 years. These coordinates look to be in the right place too, and if we checked the length of the new cartesian vector it would be 1.0."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from mpl_toolkits.basemap import Basemap\n",
      "\n",
      "width = 9000000\n",
      "bm = Basemap(width=width, height=width, projection='aeqd', \n",
      "             lat_0=70.0, lon_0=280.0)\n",
      "bm.drawparallels(np.arange(-80,81,10))\n",
      "bm.drawmeridians(np.arange(-180,180,10))\n",
      "\n",
      "# Position of Polaris at J2000 is p0\n",
      "years = arange(-13001, 13000, 100)\n",
      "for year in years:\n",
      "    P = ltp_PBMAT(year) # Precession matrix, GCRS\n",
      "    p_1 = compute_polaris(year)\n",
      "    p_1 = pdp(P, p1)\n",
      "    (ra1, dec1) = ra_dec(p_1)\n",
      "    x, y = bm(degrees(ra1), degrees(dec1))\n",
      "    if(year == years[0]):\n",
      "        bm.plot(x,y, marker='s', color='r')\n",
      "    elif(year == years[-1]):\n",
      "        bm.plot(x,y, marker='o', color='b')\n",
      "    else:\n",
      "        bm.plot(x,y, marker='.', color='black', markersize=4)\n",
      "#savefig('images/polaris_one_precession.png')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Dhg2djEJ8Ph/Jycn4+eefUVRUZFKMtQUZGRlG3xGxp3hcUFBgUfaIreByuTh48CBKSkqw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\nCBHi/4V/ADwGGv5Qupg6AAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f83517873d0>"
       ]
      }
     ],
     "prompt_number": 19
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This is comparable to the results from the IAU precession model PyEphem inherits from libastro. See [github-issue-61.ipynb](https://github.com/brandon-rhodes/pyephem/blob/master/issues/github-issue-61.ipynb) ([nbviewer](http://nbviewer.ipython.org/github/brandon-rhodes/pyephem/blob/master/issues/github-issue-61.ipynb)) for further explanation. We also see that this precession model is periodic for 400000 years. The dates supplied are in Julian Epoch (TT). Because of this, the range of years \u00b113000 and \u00b1200000, are centered on Julian Epoch 0.0, and not epoch J2000."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "width = 9000000\n",
      "bm = Basemap(width=width, height=width, projection='aeqd', \n",
      "             lat_0=70.0, lon_0=280.0)\n",
      "bm.drawparallels(np.arange(-80,81,10))\n",
      "bm.drawmeridians(np.arange(-180,180,10))\n",
      "\n",
      "for year in range(-200001, 200000, 100):\n",
      "    P = ltp_PBMAT(year) # Precession matrix, GCRS\n",
      "    p_1 = compute_polaris(year)\n",
      "    p_1 = pdp(P, p_1)\n",
      "    (ra1, dec1) = ra_dec(p_1)\n",
      "    x, y = bm(degrees(ra1), degrees(dec1))\n",
      "    bm.plot(x,y, marker='o', color='blue', alpha=0.3, ms=3)\n",
      "#savefig('images/polaris_long_term.png')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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NjaUlS5bU+10ul5NUKqUDBw7QjRs36F//+hedP3+ezp07R4WFhS1ep7t16xaF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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f83517adb50>"
       ]
      }
     ],
     "prompt_number": 20
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "You can also convert the coordinates of another epoch to J2000 by inverting the precession matrix. We transpose this like so\n",
      "\n",
      "$$P^{-1} = \\begin{pmatrix}\n",
      "P_{11} & P_{12} & P_{13} \\\\ \n",
      "P_{21} & P_{22} & P_{23} \\\\ \n",
      "P_{31} & P_{32} & P_{33} \n",
      "\\end{pmatrix}$$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "I'm really glad I made a precession matrix and implemented it. Going through all of the steps makes it easier to comprehend. What started all of this was that I wanted to plot the Big Dipper 100000 years in the past and future in [proper-motion.ipynb](https://github.com/digitalvapor/asterisms/blob/master/notebooks/proper-motion.ipynb) ([nbviewer](http://nbviewer.ipython.org/github/digitalvapor/asterisms/blob/master/notebooks/proper-motion.ipynb)). Now I definitely am up to trying that again.\n",
      "\n",
      "If you would like a Python package of this precession model, see the source at [github.com/digitalvapor/vondrak](https://github.com/digitalvapor/vondrak) or the [Vondrak Package](https://pypi.python.org/pypi/vondrak) on PyPi. You can install with `pip install vondrak`."
     ]
    }
   ],
   "metadata": {}
  }
 ]
}