PmagPy_calculations.ipynb

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    "# Calculations with PmagPy\n",
    "\n",
    "This notebook demonstrates many of the PmagPy calculation functions such as those that rotate directions, return statistical parameters, and simulate data from specified distributions.\n",
    "\n",
    "## Guide to PmagPy\n",
    "\n",
    "The notebook is one of a series of notebooks that demonstrate the functionality of PmagPy. The other notebooks are:\n",
    "\n",
    "- [PmagPy_introduction.ipynb](PmagPy_introduction.ipynb) This notebook introduces PmagPy and lists the functions that are demonstrated in the other notebooks. \n",
    "- [PmagPy_plots_analysis.ipynb](PmagPy_plots_analysis.ipynb) This notebook demonstrates PmagPy functions that can be used to visualize data as well as those that conduct statistical tests that have associated visualizations.\n",
    "- [PmagPy_MagIC.ipynb](PmagPy_MagIC.ipynb) This notebook demonstrates how PmagPy can be used to read and write data to and from the MagIC database format including conversion from many individual lab measurement file formats.\n",
    "\n",
    "## Customizing this notebook\n",
    "\n",
    "If you want to make changes to this notebook, you should make a copy (see File menu).  Otherwise each time you update **PmagPy**, your changes will be overwritten.\n",
    "\n",
    "## Get started\n",
    "\n",
    "To use the functions in this notebook, we have to   import the **PmagPy** modules **pmagplotlib**, **pmag** and **ipmag** and some other handy functions for use in the notebook.  This is done in the following code block which must be executed before running any other code block. To execute, click on the code block and then click on the \"Run\" button in the menu.  \n",
    "\n",
    "In order to access the example data, this notebook is meant to be run in the PmagPy-data directory (PmagPy directory for developers).\n",
    "\n",
    "Try it!  Run the code block below (click on the cell and then click 'Run'):"
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    "import pmagpy.pmag as pmag\n",
    "import pmagpy.pmagplotlib as pmagplotlib\n",
    "import pmagpy.ipmag as ipmag\n",
    "import matplotlib.pyplot as plt # our plotting buddy\n",
    "from pmagpy import convert_2_magic as convert\n",
    "import numpy as np # the fabulous NumPy package\n",
    "import pandas as pd # and of course Pandas\n",
    "has_basemap, Basemap = pmag.import_basemap()\n",
    "has_cartopy, Cartopy = pmag.import_cartopy()\n",
    "from IPython.display import Image\n",
    "%matplotlib inline "
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    "## Functions demonstrated within this notebook:\n",
    "\n",
    "- Functions in **PmagPy_calculations.ipynb**:\n",
    "    - [aarm_magic](#aarm_magic) : calculate AARM tensors\n",
    "    - [atrm_magic](#aarm_magic) : calculate ATRM tensors\n",
    "    - [angle](#angle) : calculates the angle between two vectors\n",
    "    - [apwp](#apwp) : returns predicted paleolatitudes, directions and pole latitude/longitude from apparent polar wander paths of Besse and Courtillot (2002).\n",
    "    - [b_vdm](#b_vdm) : converts B (in microT) and (magnetic) latitude to V(A)DM (see [vdm_b](#vdm_b))\n",
    "    - [bootams](#bootams) : calculates bootstrap statistics for tensor data\n",
    "    - [cart_dir](#cart_dir) : converts cartesian coordinates (x,y,z) to declination, inclination, intensity (see [dir_cart](#dir_cart))\n",
    "    - [di_eq](#di_eq) : maps declination, inclinatitions to X,Y for plotting in equal area projections\n",
    "    - [di_geo](#di_geo) : rotates declination, inclination in specimen coordinates to geographic coordinates\n",
    "    - [di_rot](#di_rot) : rotates directions to a  coordinate system with D,I as center\n",
    "    - [di_tilt](#di_tilt) : rotates directions to stratigraphic coordinates\n",
    "    - [di_vgp](#di_vgp) : converts direction to Virtual Geomagnetic Pole (see [vgp_di](#vgp_di))\n",
    "    - [dia_vgp](#dia_vgp) : converts direction and $\\alpha_{95}$ to Virtual Geomagnetic Pole and dp,dm\n",
    "    - [dipole_pinc](#dipole_pinc) : calculates inclination given latitude assuming geocentric axial dipole\n",
    "    - [dipole_plat](#dipole_plat) : calculates latitude given inclination assuming geocentric axial dipole\n",
    "    - [dir_cart](#dir_cart) : converts declination, inclination, intensity to cartesian coordinates (see [cart_dir](#cart_dir))\n",
    "    - [eigs_s](#eigs_s) : converts eigenparameters to equivalent 6 element tensor (see [s_eigs](#s_eigs))\n",
    "    - [eq_di](#eq_di) : takes X,Y from equal area projection (e.g., from digitized coordinates) and  converts to declination, inclination\n",
    "    - [fcalc](#fcalc) : returns the value from an F table, given the degrees of freedom.\n",
    "    - [fisher](#fisher) : generates sets of directions drawn from Fisher distributions with vertical true mean\n",
    "    - [fishrot](#fishrot) : generates sets of directions drawn from Fisher distributions with arbitrary true mean\n",
    "    - [flip](#flip) : flips a second mode (reverse directions) to their antipodes\n",
    "    - [gaussian](#gaussian) : generates data drawn from a normal distribution\n",
    "    - [gobing](#gobing) : calculates Bingham statistics from a set of directions\n",
    "    - [gofish](#gofish) : calculates Fisher statistics from a set of directions\n",
    "    - [gokent](#gokent) : calculates Kent statistics from a set of directions\n",
    "    - [goprinc](#goprinc) : calculates principal directions statistics\n",
    "    - [igrf](#igrf) : calculates geomagnetic field vectors for location, age given a field model (e.g., IGRF) including paleofield models (e.g., cals10k)\n",
    "    - [incfish](#incfish) : estimates the true mean inclination from inclination only data\n",
    "    - [pca](#pca) : calculates the best-fit line or plane for demagnetization data and associated statistics\n",
    "    - [pt_rot](#pt_rot) : rotates point given finite rotation pole\n",
    "    - [s_eigs](#s_eigs) : takes a 6 element tensor and calculates eigen parameters (see [eigs_s](#eigs_s))\n",
    "    - [s_geo](#s_geo) : rotates 6 element tensors to geographic coordinates\n",
    "    - [s_hext](#s_hext) : calculates Hext statistics from 6 element tensors\n",
    "    - [s_tilt](#s_tilt) : rotates 6 element tensors to stratigraphic coordinates\n",
    "    - [s_magic](#s_tilt) :\n",
    "    - [scalc](#scalc) : calculates  VGP scatter\n",
    "    - [scalc_magic](#scalc) : calculates  VGP scatter\n",
    "    - [separate_directions](#separate_directions) : separates a set of directions into two modes (normal and reverse)\n",
    "    - [squish](#squish): flattens inclination data given flattening factor (see [unsquish](#unsquish))\n",
    "    - [sundec](#sundec) : calulates direction to sun for location, date, time and sun azimuth\n",
    "    - [tk03](#tk03) : generates sets of directions consistent with the TK03 field model\n",
    "    - [uniform](#uniform) : generates sets of uniformly distributed directions\n",
    "    - [unsquish](#unsquish) : unsquishes flattened inclinations, given flattening factor (see [squish](#squish))\n",
    "    - [vdm_b](#vdm_b) : calculates intensity at given location from specified virtual dipole moment (see [b_vdm](#b_vdm))\n",
    "    - [vector_mean](#vector_mean) : calculates vector mean for sets of vectors (declination, inclination, intensity)\n",
    "    - [vgp_di](#vgp_di) : calculates direction at given location from virtual geomagnetic pole (see [di_vgp](#di_vgp))\n",
    "    - [watsons_f](#watsons_f) : calculates Watson's F statistic for testing for common mean"
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    "## aarm_magic\n",
    "\n",
    "[\\[command line version\\]](https://pmagpy.github.io/PmagPy-cli.html#aarm_magic.py)\n",
    "\n",
    "Anisotropy of anhysteretic or other remanence can be converted to a tensor and used to correct natural remanence data for the effects of anisotropy remanence acquisition. For example, directions may be deflected from the geomagnetic field direction or intensities may be biased by strong anisotropies in the magnetic fabric of the specimen. By imparting an anhysteretic or thermal remanence in many specific orientations, the anisotropy of remanence acquisition can be characterized and used for correction. We do this for anisotropy of anhysteretic remanence (AARM) by imparting an ARM in 9, 12 or 15 positions. Each ARM must be preceded by an AF demagnetization step. The 15 positions are shown in the [k15_magic](#k15_magic) example.\n",
    "\n",
    "For the 9 position scheme, **aarm_magic** assumes that the AARMs are imparted in positions 1,2,3, 6,7,8, 11,12,13. Someone (a.k.a. Josh Feinberg) has kindly made the measurements and saved them an SIO formatted measurement file named aarm_magic_example.dat in the datafile directory called aarm_magic. Note the special format of these files - the treatment column (column #2) has the position number (1,2,3,6, etc.) followed by either a “00” for the obligatory zero field baseline step or a “10” for the in-field step. These could also be ‘0‘ and ‘1’.\n",
    "\n",
    "We need to first import these into the measurements format and then calculate the anisotropy tensors. These can then be plotted or used to correct paleointensity or directional data for anisotropy of remanence.\n",
    "\n",
    "So, first follow the instructions in  [sio_magic](#sio_magic) to import the AARM data into the MagIC format. The DC field was 50 μT, the peak AC field was 180 mT, the location was \"Bushveld\" and the lab protocol was AF and Anisotropy. The naming convention used Option # 3 (see help menu).\n",
    "\n",
    "Then we need  to calculate the best-fit tensor and write them out to the specimens.txt MagIC tables which can be used to correct remanence data for anisotropy. \n",
    "\n",
    "The **aarm_magic** program takes a measurements.txt formatted file with anisotropy of ARM data in it and calculates the tensors, rotates it into the desired coordinate system and stores the data in a specimens.txt format file.  To do this in a notebook, use **ipmag.aarm_magic()**.  "
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      "-I- Using online data model\n",
      "-I- Getting method codes from earthref.org\n",
      "-I- Importing controlled vocabularies from https://earthref.org\n",
      "-I- overwriting /Users/nebula/Python/PmagPy/data_files/aarm_magic/specimens.txt\n",
      "-I- 7 records written to specimens file\n",
      "-I- overwriting /Users/nebula/Python/PmagPy/data_files/aarm_magic/samples.txt\n",
      "-I- 1 records written to samples file\n",
      "-I- overwriting /Users/nebula/Python/PmagPy/data_files/aarm_magic/sites.txt\n",
      "-I- 1 records written to sites file\n",
      "-I- overwriting /Users/nebula/Python/PmagPy/data_files/aarm_magic/locations.txt\n",
      "-I- 1 records written to locations file\n",
      "-I- overwriting /Users/nebula/Python/PmagPy/data_files/aarm_magic/aarm_measurements.txt\n",
      "-I- 126 records written to measurements file\n"
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    "convert.sio('arm_magic_example.dat',dir_path='data_files/aarm_magic/',specnum=3,\n",
    "           location='Bushveld',codelist='AF:ANI',samp_con='3',\n",
    "           meas_file='aarm_measurements.txt',peakfield=180,labfield=50, phi=-1, theta=-1)"
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      "Help on function aarm_magic in module pmagpy.ipmag:\n",
      "\n",
      "aarm_magic(infile, dir_path='.', input_dir_path='', spec_file='specimens.txt', samp_file='samples.txt', data_model_num=3, coord='s')\n",
      "    Converts AARM  data to best-fit tensor (6 elements plus sigma)\n",
      "    \n",
      "    Parameters\n",
      "    ----------\n",
      "    infile : str\n",
      "        input measurement file\n",
      "    dir_path : str\n",
      "        output directory, default \".\"\n",
      "    input_dir_path : str\n",
      "        input file directory IF different from dir_path, default \"\"\n",
      "    spec_file : str\n",
      "        input/output specimen file name, default \"specimens.txt\"\n",
      "    samp_file : str\n",
      "        input sample file name, default \"samples.txt\"\n",
      "    data_model_num : number\n",
      "        MagIC data model [2, 3], default 3\n",
      "    coord : str\n",
      "        coordinate system specimen/geographic/tilt-corrected,\n",
      "        ['s', 'g', 't'], default 's'\n",
      "    \n",
      "    Returns\n",
      "    ---------\n",
      "    Tuple : (True or False indicating if conversion was sucessful, output file name written)\n",
      "    \n",
      "    Info\n",
      "    ---------\n",
      "        Input for is a series of baseline, ARM pairs.\n",
      "      The baseline should be the AF demagnetized state (3 axis demag is\n",
      "      preferable) for the following ARM acquisition. The order of the\n",
      "      measurements is:\n",
      "    \n",
      "           positions 1,2,3, 6,7,8, 11,12,13 (for 9 positions)\n",
      "           positions 1,2,3,4, 6,7,8,9, 11,12,13,14 (for 12 positions)\n",
      "           positions 1-15 (for 15 positions)\n",
      "\n"
     ]
    }
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   "source": [
    "help(ipmag.aarm_magic)"
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      "7  records written to file  /Users/nebula/Python/PmagPy/data_files/aarm_magic/specimens.txt\n",
      "specimen data stored in /Users/nebula/Python/PmagPy/data_files/aarm_magic/specimens.txt\n"
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    "ipmag.aarm_magic('aarm_measurements.txt',dir_path='data_files/aarm_magic/')"
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot the data generated by aarm_magic:\n",
    "ipmag.aniso_magic_nb(infile='data_files/aarm_magic/specimens.txt', save_plots=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## atrm_magic\n",
    "\n",
    "[\\[command line version\\]](https://pmagpy.github.io/PmagPy-cli.html#atrm_magic.py)\n",
    "\n",
    "Anisotropy of thermal remanence (ATRM) is similar to anisotropy of anhysteretic remanence (AARM) and the procedure for obtaining the tensor is also similar. Therefore, the **atrm_magic** is quite similar to [aarm_magic](#aarm_magic). However, the SIO lab procedures for the two experiments are somewhat different. In the ATRM experiment, there is a single, zero field step at the chosen temperature which is used as a baseline. We use only six positions (as opposed to nine for AARM) because of the additional risk of alteration at each temperature step. The positions are also different:\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 7,
     "metadata": {
      "image/png": {
       "width": 500
      }
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Image('data_files/Figures/atrm_meas.png',width=500)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The file atrm_magic_example.dat in the data_files/atrm_magic directory is an SIO formatted data file containing ATRM measurement data done in a temperature of 520∘C. Note the special format of these files - the treatment column (column 2) has the temperature in centigrade followed by either a “00” for the obligatory zero field baseline step or a “10” for the first postion, and so on. These could also be ‘0‘ and ‘1’, etc..\n",
    "\n",
    "Follow the instructions for  [sio_magic](#sio_magic) to import the ATRM data into the MagIC format. The DC field was 40 μT. The sample/site naming convention used option # 1 (see help menu) and the specimen and sample name are the same (specnum=0). \n",
    "\n",
    "We will use **ipmag.atrm_magic()** to calculate the best-fit tensor and write out the MagIC tables which can be used to correct remanence data  for the effects of remanent anisotropy.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-I- overwriting /Users/nebula/Python/PmagPy/data_files/atrm_magic/specimens.txt\n",
      "-I- 30 records written to specimens file\n",
      "-I- overwriting /Users/nebula/Python/PmagPy/data_files/atrm_magic/samples.txt\n",
      "-I- 30 records written to samples file\n",
      "-I- overwriting /Users/nebula/Python/PmagPy/data_files/atrm_magic/sites.txt\n",
      "-I- 10 records written to sites file\n",
      "-I- overwriting /Users/nebula/Python/PmagPy/data_files/atrm_magic/locations.txt\n",
      "-I- 1 records written to locations file\n",
      "-I- overwriting /Users/nebula/Python/PmagPy/data_files/atrm_magic/measurements.txt\n",
      "-I- 210 records written to measurements file\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(True, '/Users/nebula/Python/PmagPy/data_files/atrm_magic/measurements.txt')"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "convert.sio('atrm_magic_example.dat',dir_path='data_files/atrm_magic/',specnum=0,\n",
    "           location='unknown',codelist='T:ANI',samp_con='1',\n",
    "           meas_file='measurements.txt',labfield=40, phi=-1, theta=-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on function atrm_magic in module pmagpy.ipmag:\n",
      "\n",
      "atrm_magic(meas_file, dir_path='.', input_dir_path='', input_spec_file='specimens.txt', output_spec_file='specimens.txt', data_model_num=3)\n",
      "    Converts ATRM  data to best-fit tensor (6 elements plus sigma)\n",
      "    \n",
      "    Parameters\n",
      "    ----------\n",
      "    meas_file : str\n",
      "        input measurement file\n",
      "    dir_path : str\n",
      "        output directory, default \".\"\n",
      "    input_dir_path : str\n",
      "        input file directory IF different from dir_path, default \"\"\n",
      "    input_spec_file : str\n",
      "        input specimen file name, default \"specimens.txt\"\n",
      "    output_spec_file : str\n",
      "        output specimen file name, default \"specimens.txt\"\n",
      "    data_model_num : number\n",
      "        MagIC data model [2, 3], default 3\n",
      "    \n",
      "    Returns\n",
      "    ---------\n",
      "    Tuple : (True or False indicating if conversion was sucessful, output file name written)\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(ipmag.atrm_magic)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "30  records written to file  /Users/nebula/Python/PmagPy/data_files/atrm_magic/specimens.txt\n",
      "specimen data stored in /Users/nebula/Python/PmagPy/data_files/atrm_magic/specimens.txt\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(True, '/Users/nebula/Python/PmagPy/data_files/atrm_magic/specimens.txt')"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ipmag.atrm_magic('measurements.txt',dir_path='data_files/atrm_magic')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## angle\n",
    "\n",
    "[\\[Essentials Appendix A.3.4\\]](https://earthref.org/MagIC/books/Tauxe/Essentials/WebBook3ap1.html#x20-215000A.3.4) [\\[command line version\\]](https://pmagpy.github.io/PmagPy-cli.html#angle.py)\n",
    "\n",
    "**angle** calculates the angle $\\alpha$ between two declination,inclination pairs.\n",
    "\n",
    "There are several ways to use this function from the notebook - one loading the data into a Pandas dataframe, then converting to the desired arrays, or load directly into a **Numpy** array of desired shape.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on function angle in module pmagpy.pmag:\n",
      "\n",
      "angle(D1, D2)\n",
      "    Calculate the angle between two directions.\n",
      "    \n",
      "    Parameters\n",
      "    ----------\n",
      "    D1 : Direction 1 as an array of [declination, inclination] pair or pairs\n",
      "    D2 : Direction 2 as an array of [declination, inclination] pair or pairs\n",
      "    \n",
      "    Returns\n",
      "    -------\n",
      "    angle : angle between the directions as a single-element array\n",
      "    \n",
      "    Examples\n",
      "    --------\n",
      "    >>> pmag.angle([350.0,10.0],[320.0,20.0])\n",
      "    array([ 30.59060998])\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(pmag.angle)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Pandas way:\n",
    "di=pd.read_csv('data_files/angle/angle.dat',delim_whitespace=True,header=None)\n",
    "#rename column headers\n",
    "di.columns=['Dec1','Inc1','Dec2','Inc2']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's the sort of data  in the file: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Dec1</th>\n",
       "      <th>Inc1</th>\n",
       "      <th>Dec2</th>\n",
       "      <th>Inc2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>11.2</td>\n",
       "      <td>32.9</td>\n",
       "      <td>6.4</td>\n",
       "      <td>-42.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>11.5</td>\n",
       "      <td>63.7</td>\n",
       "      <td>10.5</td>\n",
       "      <td>-55.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>11.9</td>\n",
       "      <td>31.4</td>\n",
       "      <td>358.1</td>\n",
       "      <td>-71.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>349.6</td>\n",
       "      <td>36.2</td>\n",
       "      <td>356.3</td>\n",
       "      <td>-45.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>60.3</td>\n",
       "      <td>63.5</td>\n",
       "      <td>58.9</td>\n",
       "      <td>-56.6</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    Dec1  Inc1   Dec2  Inc2\n",
       "0   11.2  32.9    6.4 -42.9\n",
       "1   11.5  63.7   10.5 -55.4\n",
       "2   11.9  31.4  358.1 -71.8\n",
       "3  349.6  36.2  356.3 -45.0\n",
       "4   60.3  63.5   58.9 -56.6"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "di.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we will use **pmag.angle()** to calculate the angles.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 75.92745193, 119.10251273, 103.65330599,  81.42586582,\n",
       "       120.1048559 , 100.8579262 ,  95.07347774,  74.10981614,\n",
       "        78.41266977, 120.05285684, 114.36156914,  66.30664335,\n",
       "        85.38356936,  95.07546203,  93.84174   ,  93.116631  ,\n",
       "       105.39087299,  71.78167883, 104.04746653,  93.84450445,\n",
       "        93.29827337,  96.34377954,  90.14271929, 112.17559328,\n",
       "        90.06592091, 120.00493016,  75.31604123,  86.19902246,\n",
       "        85.85667799,  82.64834934, 115.51261896,  99.28623007,\n",
       "        65.9466766 ,  90.55185269,  90.50418859,  84.49253198,\n",
       "        93.00731365,  67.47153733,  76.84279617,  83.80354   ,\n",
       "       128.3068145 ,  91.690954  ,  46.87441241, 110.66917836,\n",
       "       103.69699188,  64.35444341,  81.94448359,  94.01817998,\n",
       "       121.19588845,  83.64445512, 113.72812352,  76.38276774,\n",
       "       113.38742874,  74.09024232,  79.42493098,  74.92842387,\n",
       "        90.5556631 ,  91.44844861, 112.71773111,  77.26775912,\n",
       "        77.06338144,  62.41361128,  88.42053203, 106.29965884,\n",
       "       100.55759278, 143.79308212, 104.94537375,  91.83604987,\n",
       "        96.21780532,  85.58941479,  65.61977586,  88.64226464,\n",
       "        75.64540868,  93.36044834, 101.25961804, 115.14897178,\n",
       "        86.70974597,  92.32998728,  91.89347431, 102.39692204,\n",
       "        78.93051946,  93.41996659,  88.08998457,  94.50358255,\n",
       "        76.96036419, 110.40068516,  89.23179785,  80.90505187,\n",
       "       100.40590063,  91.88885371, 107.05953781, 115.8185023 ,\n",
       "       111.2919312 , 124.61718069,  88.12341445,  66.94129884,\n",
       "        99.90439898,  76.73639992,  71.37398958, 100.7789606 ])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# call pmag.angle\n",
    "pmag.angle(di[['Dec1','Inc1']].values,di[['Dec2','Inc2']].values)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here is the other (equally valid) way using **np.loadtext()**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 75.92745193, 119.10251273, 103.65330599,  81.42586582,\n",
       "       120.1048559 , 100.8579262 ,  95.07347774,  74.10981614,\n",
       "        78.41266977, 120.05285684, 114.36156914,  66.30664335,\n",
       "        85.38356936,  95.07546203,  93.84174   ,  93.116631  ,\n",
       "       105.39087299,  71.78167883, 104.04746653,  93.84450445,\n",
       "        93.29827337,  96.34377954,  90.14271929, 112.17559328,\n",
       "        90.06592091, 120.00493016,  75.31604123,  86.19902246,\n",
       "        85.85667799,  82.64834934, 115.51261896,  99.28623007,\n",
       "        65.9466766 ,  90.55185269,  90.50418859,  84.49253198,\n",
       "        93.00731365,  67.47153733,  76.84279617,  83.80354   ,\n",
       "       128.3068145 ,  91.690954  ,  46.87441241, 110.66917836,\n",
       "       103.69699188,  64.35444341,  81.94448359,  94.01817998,\n",
       "       121.19588845,  83.64445512, 113.72812352,  76.38276774,\n",
       "       113.38742874,  74.09024232,  79.42493098,  74.92842387,\n",
       "        90.5556631 ,  91.44844861, 112.71773111,  77.26775912,\n",
       "        77.06338144,  62.41361128,  88.42053203, 106.29965884,\n",
       "       100.55759278, 143.79308212, 104.94537375,  91.83604987,\n",
       "        96.21780532,  85.58941479,  65.61977586,  88.64226464,\n",
       "        75.64540868,  93.36044834, 101.25961804, 115.14897178,\n",
       "        86.70974597,  92.32998728,  91.89347431, 102.39692204,\n",
       "        78.93051946,  93.41996659,  88.08998457,  94.50358255,\n",
       "        76.96036419, 110.40068516,  89.23179785,  80.90505187,\n",
       "       100.40590063,  91.88885371, 107.05953781, 115.8185023 ,\n",
       "       111.2919312 , 124.61718069,  88.12341445,  66.94129884,\n",
       "        99.90439898,  76.73639992,  71.37398958, 100.7789606 ])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Numpy way:\n",
    "di=np.loadtxt('data_files/angle/angle.dat').transpose() # read in file\n",
    "D1=di[0:2].transpose() # assign to first array\n",
    "D2=di[2:].transpose() # assign to second array\n",
    "pmag.angle(D1,D2) # call pmag.angle"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can always save your output using **np.savetxt()**.   "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "angles=pmag.angle(D1,D2) # assign the returned array to angles"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## apwp\n",
    "\n",
    "[\\[Essentials Chapter 16\\]](https://earthref.org/MagIC/books/Tauxe/Essentials/WebBook3ch16.html#x15-15600016)  [\\[command line version\\]](https://pmagpy.github.io/PmagPy-cli.html#apwp.py)\n",
    "\n",
    "The program **apwp** calculates paleolatitude, declination, inclination from a pole latitude and longitude based on the paper Besse and Courtillot (2002; see [Essentials Chapter 16](https://earthref.org/MagIC/books/Tauxe/Essentials/WebBook3ch16.html#x15-15600016)   for complete discussion). Here we will  calculate the expected direction for 100 million year old rocks at a locality in La Jolla Cove (Latitude: 33$^{\\circ}$N, Longitude 117$^{\\circ}$W). Assume that we are on the North American Plate! (Note that there IS no option for the Pacific plate in the program **apwp**, and that La Jolla was on the North American plate until a few million years ago (6?). \n",
    "\n",
    "\n",
    "Within the notebook we will call **pmag.apwp**.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on function apwp in module pmagpy.pmag:\n",
      "\n",
      "apwp(data, print_results=False)\n",
      "    calculates expected pole positions and directions for given plate, location and age\n",
      "    Parameters\n",
      "    _________\n",
      "        data : [plate,lat,lon,age]\n",
      "            plate : [NA, SA, AF, IN, EU, AU, ANT, GL]\n",
      "                NA : North America\n",
      "                SA : South America\n",
      "                AF : Africa\n",
      "                IN : India\n",
      "                EU : Eurasia\n",
      "                AU : Australia\n",
      "                ANT: Antarctica\n",
      "                GL : Greenland\n",
      "             lat/lon : latitude/longitude in degrees N/E\n",
      "             age : age in millions of years\n",
      "        print_results : if True will print out nicely formatted results\n",
      "    Returns\n",
      "    _________\n",
      "        if print_results is False, [Age,Paleolat, Dec, Inc, Pole_lat, Pole_lon]\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(pmag.apwp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " Age   Paleolat.   Dec.   Inc.   Pole_lat.  Pole_Long.\n",
      "  100.0    38.8   352.4    58.1    81.5    198.3\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# here are the desired plate, latitude, longitude and age:\n",
    "data=['NA',33,-117,100] # North American plate, lat and lon of San Diego at 100 Ma\n",
    "pmag.apwp(data,print_results=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## b_vdm\n",
    "\n",
    "[\\[Essentials Chapter 2\\]](https://earthref.org/MagIC/books/Tauxe/Essentials/WebBook3ch2.html#x15-1560002)  [\\[command line version\\]](https://pmagpy.github.io/PmagPy-cli.html#b_vdm.py)\n",
    "\n",
    "\n",
    "\n",
    "**b_vdm** converts geomagnetic field intensity observed at the earth's surface at a particular (paleo)latitude and calculates the Virtual \\[Axial\\] Dipole Moment (vdm or vadm).  We will call **pmag.b_vdm()** directly from within the notebook. \\[See also [**vdm_b**](#vdm_b).\\]\n",
    "\n",
    "Here we use the function  **pmag.b_vdm()** to convert an estimated paleofield value of 33 $\\mu$T obtained from a lava flow at 22$^{\\circ}$ N latitude to the equivalent Virtual Dipole Moment (VDM) in Am$^2$. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on function b_vdm in module pmagpy.pmag:\n",
      "\n",
      "b_vdm(B, lat)\n",
      "    Converts a magnetic field value (input in units of tesla) to a virtual\n",
      "    dipole moment (VDM) or a virtual axial dipole moment (VADM); output\n",
      "    in units of Am^2)\n",
      "    \n",
      "    Parameters\n",
      "    ----------\n",
      "    B: local magnetic field strength in tesla\n",
      "    lat: latitude of site in degrees\n",
      "    \n",
      "    Returns\n",
      "    ----------\n",
      "    V(A)DM in units of Am^2\n",
      "    \n",
      "    Examples\n",
      "    --------\n",
      "    >>> pmag.b_vdm(33e-6,22)*1e-21\n",
      "    \n",
      "    71.58815974511788\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(pmag.b_vdm)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   71.6  ZAm^2\n"
     ]
    }
   ],
   "source": [
    "print ('%7.1f'%(pmag.b_vdm(33e-6,22)*1e-21),' ZAm^2')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "71.58815974511788"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pmag.b_vdm(33e-6,22)*1e-21"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## bootams\n",
    "\n",
    "[\\[Essentials Chapter 13\\]](https://earthref.org/MagIC/books/Tauxe/Essentials/WebBook3ch13.html#x15-15600013)  [\\[command line version\\]](https://pmagpy.github.io/PmagPy-cli.html#bootams.py)\n",
    "\n",
    " **bootams** calculates bootstrap statistics for anisotropy tensor data in the form of:\n",
    "\n",
    "x11 x22 x33 x12 x23 x13\n",
    "\n",
    "It does this by selecting para-data sets and calculating the Hext average eigenparameters. It has an optional parametric bootstrap whereby the $\\sigma$ for the data set as a whole is used to draw new para data sets. The bootstrapped eigenparameters are assumed to be Kent distributed and the program calculates Kent error ellipses for each set of eigenvectors. It also estimates the standard deviations of the bootstrapped eigenvalues.\n",
    "\n",
    "**bootams**   reads in a file with data for the six tensor elements (x11 x22 x33 x12 x23 x13) for specimens, calls **pmag.s_boot()**  using a parametric or non-parametric bootstrap as desired. If all that is desired is the bootstrapped eigenparameters, **pmag.s_boot()** has all we need, but if the Kent ellipses are required, and we can call **pmag.sbootpars()** to calculated these more derived products and  print them out.\n",
    "\n",
    "Note that every time the bootstrap program gets called, the output will be slightly different because this depends on calls to random number generators. If the answers are different by a lot, then the number of bootstrap calculations is too low. The number of bootstraps can be changed with the nb option below. \n",
    "\n",
    "\n",
    "We can do all this from within the notebook as follows: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on function s_boot in module pmagpy.pmag:\n",
      "\n",
      "s_boot(Ss, ipar=0, nb=1000)\n",
      "    Returns bootstrap parameters for S data\n",
      "    \n",
      "    Parameters\n",
      "    __________\n",
      "    Ss : nested array of [[x11 x22 x33 x12 x23 x13],....] data\n",
      "    ipar : if True, do a parametric bootstrap\n",
      "    nb : number of bootstraps\n",
      "    \n",
      "    Returns\n",
      "    ________\n",
      "    Tmean : average eigenvalues\n",
      "    Vmean : average eigvectors\n",
      "    Taus : bootstrapped eigenvalues\n",
      "    Vs :  bootstrapped eigenvectors\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(pmag.s_boot)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So we will:\n",
    "- read in the AMS tensor data\n",
    "- get the bootstrapped eigenparameters\n",
    "- print out the formatted results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tau tau_sigma V_dec V_inc V_eta V_eta_dec V_eta_inc V_zeta V_zeta_dec V_zeta_inc\n",
      "\n",
      "0.33505 0.00022     5.3    14.7    10.2   263.6    33.0    13.3   116.3    52.3\n",
      "0.33334 0.00020   124.5    61.7     6.0   225.5     5.9    17.0   318.8    28.8\n",
      "0.33161 0.00014   268.8    23.6    10.5     5.0    18.1    12.3   128.3    59.2\n"
     ]
    }
   ],
   "source": [
    "Ss=np.loadtxt('data_files/bootams/bootams_example.dat')\n",
    "Tmean,Vmean,Taus,Vs=pmag.s_boot(Ss) # get the bootstrapped eigenparameters\n",
    "bpars=pmag.sbootpars(Taus,Vs) # calculate kent parameters for bootstrap\n",
    "print(\"\"\"tau tau_sigma V_dec V_inc V_eta V_eta_dec V_eta_inc V_zeta V_zeta_dec V_zeta_inc\n",
    "\"\"\")\n",
    "outstring='%7.5f %7.5f %7.1f %7.1f %7.1f %7.1f %7.1f %7.1f %7.1f %7.1f'%(\\\n",
    "          Tmean[0],bpars[\"t1_sigma\"],Vmean[0][0],Vmean[0][1],\\\n",
    "          bpars[\"v1_zeta\"],bpars[\"v1_zeta_dec\"],bpars[\"v1_zeta_inc\"],\\\n",
    "          bpars[\"v1_eta\"],bpars[\"v1_eta_dec\"],bpars[\"v1_eta_inc\"])\n",
    "print(outstring)\n",
    "outstring='%7.5f %7.5f %7.1f %7.1f %7.1f %7.1f %7.1f %7.1f %7.1f %7.1f'%(\\\n",
    "          Tmean[1],bpars[\"t2_sigma\"],Vmean[1][0],Vmean[1][1],\\\n",
    "          bpars[\"v2_zeta\"],bpars[\"v2_zeta_dec\"],bpars[\"v2_zeta_inc\"],\\\n",
    "          bpars[\"v2_eta\"],bpars[\"v2_eta_dec\"],bpars[\"v2_eta_inc\"])\n",
    "print(outstring)\n",
    "outstring='%7.5f %7.5f %7.1f %7.1f %7.1f %7.1f %7.1f %7.1f %7.1f %7.1f'%(\\\n",
    "          Tmean[2],bpars[\"t3_sigma\"],Vmean[2][0],Vmean[2][1],\\\n",
    "          bpars[\"v3_zeta\"],bpars[\"v3_zeta_dec\"],bpars[\"v3_zeta_inc\"],\\\n",
    "          bpars[\"v3_eta\"],bpars[\"v3_eta_dec\"],bpars[\"v3_eta_inc\"])\n",
    "print(outstring)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tau tau_sigma V_dec V_inc V_eta V_eta_dec V_eta_inc V_zeta V_zeta_dec V_zeta_inc\n",
      "\n",
      "0.33505 0.00021     5.3    14.7    10.1   266.7    30.1    22.6   116.7    56.2\n",
      "0.33334 0.00022   124.5    61.7    19.2   237.3    11.4    23.7   332.5    24.0\n",
      "0.33161 0.00026   268.8    23.6    10.5     7.3    19.5    20.3   133.9    59.3\n"
     ]
    }
   ],
   "source": [
    "# with parametric bootstrap: \n",
    "Ss=np.loadtxt('data_files/bootams/bootams_example.dat')\n",
    "Tmean,Vmean,Taus,Vs=pmag.s_boot(Ss,ipar=1,nb=5000) # get the bootstrapped eigenparameters\n",
    "bpars=pmag.sbootpars(Taus,Vs) # calculate kent parameters for bootstrap\n",
    "print(\"\"\"tau tau_sigma V_dec V_inc V_eta V_eta_dec V_eta_inc V_zeta V_zeta_dec V_zeta_inc\n",
    "\"\"\")\n",
    "outstring='%7.5f %7.5f %7.1f %7.1f %7.1f %7.1f %7.1f %7.1f %7.1f %7.1f'%(\\\n",
    "          Tmean[0],bpars[\"t1_sigma\"],Vmean[0][0],Vmean[0][1],\\\n",
    "          bpars[\"v1_zeta\"],bpars[\"v1_zeta_dec\"],bpars[\"v1_zeta_inc\"],\\\n",
    "          bpars[\"v1_eta\"],bpars[\"v1_eta_dec\"],bpars[\"v1_eta_inc\"])\n",
    "print(outstring)\n",
    "outstring='%7.5f %7.5f %7.1f %7.1f %7.1f %7.1f %7.1f %7.1f %7.1f %7.1f'%(\\\n",
    "          Tmean[1],bpars[\"t2_sigma\"],Vmean[1][0],Vmean[1][1],\\\n",
    "          bpars[\"v2_zeta\"],bpars[\"v2_zeta_dec\"],bpars[\"v2_zeta_inc\"],\\\n",
    "          bpars[\"v2_eta\"],bpars[\"v2_eta_dec\"],bpars[\"v2_eta_inc\"])\n",
    "print(outstring)\n",
    "outstring='%7.5f %7.5f %7.1f %7.1f %7.1f %7.1f %7.1f %7.1f %7.1f %7.1f'%(\\\n",
    "          Tmean[2],bpars[\"t3_sigma\"],Vmean[2][0],Vmean[2][1],\\\n",
    "          bpars[\"v3_zeta\"],bpars[\"v3_zeta_dec\"],bpars[\"v3_zeta_inc\"],\\\n",
    "          bpars[\"v3_eta\"],bpars[\"v3_eta_dec\"],bpars[\"v3_eta_inc\"])\n",
    "print(outstring)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## cart_dir\n",
    "\n",
    "[\\[Essentials Chapter 2\\]](https://earthref.org/MagIC/books/Tauxe/Essentials/WebBook3ch2.html#x15-1560002)  [\\[command line version\\]](https://pmagpy.github.io/PmagPy-cli.html#cart_dir.py)\n",
    "\n",
    "**cart_dir** converts cartesian coordinates (X,Y,Z) to polar coordinates (Declination, Inclination, Intensity).  We will call **pmag.cart2dir()**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on function cart2dir in module pmagpy.pmag:\n",
      "\n",
      "cart2dir(cart)\n",
      "    Converts a direction in cartesian coordinates into declination, inclinations\n",
      "    \n",
      "    Parameters\n",
      "    ----------\n",
      "    cart : input list of [x,y,z] or list of lists [[x1,y1,z1],[x2,y2,z2]...]\n",
      "    \n",
      "    Returns\n",
      "    -------\n",
      "    direction_array : returns an array of [declination, inclination, intensity]\n",
      "    \n",
      "    Examples\n",
      "    --------\n",
      "    >>> pmag.cart2dir([0,1,0])\n",
      "    array([ 90.,   0.,   1.])\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(pmag.cart2dir)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Input: \n",
      " [[ 0.3971 -0.1445  0.9063]\n",
      " [-0.5722  0.04   -0.8192]]\n",
      "Output: \n",
      "  340.0    65.0 1.000e+00\n",
      "  176.0   -55.0 1.000e+00\n"
     ]
    }
   ],
   "source": [
    "# read in data file from example file\n",
    "cart=np.loadtxt('data_files/cart_dir/cart_dir_example.dat')\n",
    "print ('Input: \\n',cart) # print out the cartesian coordinates\n",
    "# print out the  results\n",
    "dirs = pmag.cart2dir(cart)\n",
    "print (\"Output: \")\n",
    "for d in dirs:\n",
    "    print ('%7.1f %7.1f %8.3e'%(d[0],d[1],d[2]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## di_eq\n",
    "\n",
    "[\\[Essentials Appendix B\\]](https://earthref.org/MagIC/books/Tauxe/Essentials/WebBook3ap2.html#equal_area) \n",
    "[\\[command line version\\]](https://pmagpy.github.io/PmagPy-cli.html#di_eq.py)\n",
    "\n",
    "Paleomagnetic data are frequently plotted in equal area projection. PmagPy has several plotting options which do this (e.g., [**eqarea**](#eqarea), but occasionally it is handy to be able to convert the directions to X,Y coordinates directly, without plotting them at all.  Here is an example transcript of a session using the datafile di_eq_example.dat: \n",
    "\n",
    "The program **di_eq**  program calls **pmag.dimap()** which we can do from within a Jupyter notebook."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on function dimap in module pmagpy.pmag:\n",
      "\n",
      "dimap(D, I)\n",
      "    Function to map directions  to x,y pairs in equal area projection\n",
      "    \n",
      "    Parameters\n",
      "    ----------\n",
      "    D : list or array of declinations (as float)\n",
      "    I : list or array or inclinations (as float)\n",
      "    \n",
      "    Returns\n",
      "    -------\n",
      "    XY : x, y values of directions for equal area projection [x,y]\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(pmag.dimap)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-0.23941025 -0.8934912 ]\n",
      " [ 0.43641303  0.71216134]\n",
      " [ 0.06384422  0.76030049]\n",
      " [ 0.32144709  0.68621606]\n",
      " [ 0.32271993  0.67056248]\n",
      " [ 0.40741223  0.54065429]\n",
      " [ 0.5801562   0.34037562]\n",
      " [ 0.10535089  0.65772758]\n",
      " [ 0.24717308  0.59968683]\n",
      " [ 0.18234908  0.61560016]\n",
      " [ 0.17481507  0.60171742]\n",
      " [ 0.282746    0.54547233]\n",
      " [ 0.26486315  0.53827299]\n",
      " [ 0.23575838  0.5345358 ]\n",
      " [ 0.29066509  0.50548208]\n",
      " [ 0.26062905  0.51151332]\n",
      " [ 0.23208983  0.51642328]\n",
      " [ 0.24444839  0.50566578]\n",
      " [ 0.27792652  0.46438138]\n",
      " [ 0.2505103   0.47715181]\n",
      " [ 0.29177004  0.44081644]\n",
      " [ 0.10876949  0.51614821]\n",
      " [ 0.19670646  0.48201446]\n",
      " [ 0.34938995  0.38129223]\n",
      " [ 0.1684068   0.47556614]\n",
      " [ 0.20628586  0.44644351]\n",
      " [ 0.17570082  0.45064929]\n",
      " [ 0.30110381  0.37853937]\n",
      " [ 0.20495497  0.42396971]\n",
      " [ 0.19975473  0.4225844 ]\n",
      " [ 0.34691999  0.30800998]\n",
      " [ 0.11902989  0.44114437]\n",
      " [ 0.23984794  0.37648585]\n",
      " [ 0.26952843  0.34250954]\n",
      " [ 0.08545091  0.42378931]\n",
      " [ 0.19222399  0.38723272]\n",
      " [ 0.17260777  0.39508358]\n",
      " [ 0.27200846  0.32074137]\n",
      " [ 0.39398077  0.11745077]\n",
      " [-0.01772645  0.40600235]\n",
      " [ 0.15427268  0.36700021]\n",
      " [ 0.21390276  0.33576007]\n",
      " [ 0.10322076  0.37220205]\n",
      " [ 0.23183349  0.28324518]\n",
      " [ 0.07216042  0.35153814]\n",
      " [ 0.00780196  0.31923589]\n",
      " [ 0.15258303  0.26535002]\n",
      " [ 0.24813332  0.13641245]]\n"
     ]
    }
   ],
   "source": [
    "DIs=np.loadtxt('data_files/di_eq/di_eq_example.dat').transpose() # load in the data\n",
    "print (pmag.dimap(DIs[0],DIs[1])) # call the function"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## di_geo\n",
    "\n",
    "[\\[Essentials Chapter 9\\]](https://earthref.org/MagIC/books/Tauxe/Essentials/WebBook3ch9.html) \n",
    "and [Changing coordinate systems](http://earthref.org/MAGIC/books/Tauxe/Essentials/WebBook3ap1.html#Changing_coordinate_systems)\n",
    "[\\[command line version\\]](https://pmagpy.github.io/PmagPy-cli.html#di_geo.py)\n",
    "\n",
    "Here we will convert D = 8.1,I = 45.2 from specimen coordinates to geographic-adjusted coordinates. The orientation of laboratory arrow on the specimen was: azimuth = 347; plunge = 27. To do this we will call **pmag.dogeo()**. There is also **pmag.dogeo_V** for arrays of data. \n",
    "\n",
    "So let's start with **pmag.dogeo()**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on function dogeo in module pmagpy.pmag:\n",
      "\n",
      "dogeo(dec, inc, az, pl)\n",
      "    Rotates declination and inclination into geographic coordinates using the\n",
      "    azimuth and plunge of the X direction (lab arrow) of a specimen.\n",
      "    \n",
      "    Parameters\n",
      "    ----------\n",
      "    dec : declination in specimen coordinates\n",
      "    inc : inclination in specimen coordinates\n",
      "    \n",
      "    Returns\n",
      "    -------\n",
      "    rotated_direction : tuple of declination, inclination in geographic coordinates\n",
      "    \n",
      "    Examples\n",
      "    --------\n",
      "    >>> pmag.dogeo(0.0,90.0,0.0,45.5)\n",
      "    (180.0, 44.5)\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(pmag.dogeo)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(94.83548541337562, 43.02168490109632)"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pmag.dogeo(dec=81,inc=45.2,az=347,pl=27)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's check out the version that takes many data points at once. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on function dogeo_V in module pmagpy.pmag:\n",
      "\n",
      "dogeo_V(indat)\n",
      "    Rotates declination and inclination into geographic coordinates using the\n",
      "    azimuth and plunge of the X direction (lab arrow) of a specimen.\n",
      "    \n",
      "    Parameters\n",
      "    ----------\n",
      "    indat: nested list of [dec, inc, az, pl] data\n",
      "    \n",
      "    Returns\n",
      "    -------\n",
      "    rotated_directions : arrays of Declinations and Inclinations\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(pmag.dogeo_V)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 288.1   35.8   67.   -36. ]\n",
      " [ 256.8   22.5   84.   -81. ]\n",
      " [ 262.4   19.1   91.   -48. ]\n",
      " [ 258.6   19.6   89.   -61. ]\n",
      " [ 259.9   54.7   49.   -76. ]\n",
      " [ 279.1   27.9   62.   -41. ]\n",
      " [ 228.3  -47.5  141.   -84. ]\n",
      " [ 249.8   25.    60.   -82. ]\n",
      " [ 239.8  -33.9  108.   -91. ]\n",
      " [ 271.7   50.8   28.   -52. ]\n",
      " [ 266.8   67.1   16.   -67. ]\n",
      " [ 238.9   51.9   27.   -76. ]\n",
      " [ 238.9   55.3   17.   -90. ]\n",
      " [ 252.6   41.    43.   -73. ]\n",
      " [ 112.7   17.1  282.6  -78. ]\n",
      " [ 134.9   -8.9  234.   -56. ]\n",
      " [ 138.6   -1.1  244.6  -73. ]\n",
      " [  83.5   31.1  292.   -28. ]\n",
      " [ 151.1  -35.2  196.6  -69. ]\n",
      " [ 146.8  -14.5  217.   -51. ]\n",
      " [  13.8   35.   332.6  -44. ]\n",
      " [ 293.1    3.9   53.5  -25.5]\n",
      " [  99.5  -11.   243.6  -30. ]\n",
      " [ 267.8  -12.7   91.5  -49. ]\n",
      " [  47.    12.8  298.6  -28. ]\n",
      " [  45.8   -9.   297.   -33.5]\n",
      " [  81.7  -26.8  254.6  -51. ]\n",
      " [  79.7  -25.7  256.   -60. ]\n",
      " [  84.7  -20.9  256.6  -60. ]\n",
      " [ 303.3   66.7    3.6  -71.5]\n",
      " [ 104.6   32.2  297.  -100.5]\n",
      " [ 262.8   77.9  357.1  -87. ]\n",
      " [  63.3   53.2  316.   -63. ]\n",
      " [  37.7   60.1  331.6  -57. ]\n",
      " [ 109.3    5.4  255.6  -58.5]\n",
      " [ 119.3    5.5  252.6  -52. ]\n",
      " [ 108.7   23.6  287.6  -79. ]]\n"
     ]
    }
   ],
   "source": [
    "indata=np.loadtxt('data_files/di_geo/di_geo_example.dat')\n",
    "print (indata)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's take a look at these data in equal area projection: (see [eqarea](#eqarea) for details)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ipmag.plot_net(1)\n",
    "ipmag.plot_di(dec=indata.transpose()[0],inc=indata.transpose()[1],color='red',edge='black')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The data are highly scattered and we hope that the geographic coordinate system looks better! To find out try: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "decs,incs=pmag.dogeo_V(indata)\n",
    "ipmag.plot_net(1)\n",
    "ipmag.plot_di(dec=decs,inc=incs,color='red',edge='black')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "These data are clearly much better grouped. \n",
    "\n",
    "And here they are printed out."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1.23907966e+01  1.89735424e+01]\n",
      " [ 1.49830732e+01  1.55593373e+01]\n",
      " [ 1.06667819e+01  1.81693342e+01]\n",
      " [ 1.14047553e+01  1.89951632e+01]\n",
      " [ 1.24483163e+01  1.72036203e+01]\n",
      " [ 3.57299071e+02  1.51561580e+01]\n",
      " [ 3.53883281e+02  2.17091208e+01]\n",
      " [ 3.53789196e+02  2.16365727e+01]\n",
      " [ 3.40503777e+02  2.52889275e+01]\n",
      " [ 3.42563974e+02  2.75374519e+01]\n",
      " [ 3.51164668e+02  2.23293805e+01]\n",
      " [ 3.49415385e+02  2.99754627e+01]\n",
      " [ 3.46335983e+02  1.71006907e+01]\n",
      " [ 3.50937970e+02  2.40567015e+01]\n",
      " [ 3.59146910e+02  2.49558990e+01]\n",
      " [ 5.20812064e-01  2.94481211e+01]\n",
      " [ 3.54368265e+02  4.53644133e+01]\n",
      " [ 9.11626301e-01  2.42403293e+01]\n",
      " [ 3.50170459e+02  2.74704564e+01]\n",
      " [ 3.54249362e-02  2.81645605e+01]\n",
      " [ 3.43981389e+02 -8.04836591e+00]\n",
      " [ 3.46130907e+02 -6.14959601e+00]\n",
      " [ 3.47283278e+02 -4.83219850e+00]\n",
      " [ 3.50443170e+02 -6.65953274e+00]\n",
      " [ 3.44495997e+02 -6.69629260e+00]\n",
      " [ 3.52433892e+02 -3.06972914e+01]\n",
      " [ 1.55709734e+00 -2.25743459e+01]\n",
      " [ 4.40491709e+00 -2.08767482e+01]\n",
      " [ 2.54671945e+00 -1.46610862e+01]\n",
      " [ 3.44221055e+02  4.90397368e+00]\n",
      " [ 3.52498530e+02  6.46629212e+00]\n",
      " [ 3.45060173e+02  4.43967268e+00]\n",
      " [ 3.48635524e+02  7.10612965e+00]\n",
      " [ 3.49534584e+02  8.12663013e+00]\n",
      " [ 3.51173216e+02  1.92524262e+01]\n",
      " [ 3.57092897e+02  2.62872553e+01]\n",
      " [ 3.56384865e+02  2.13946656e+01]]\n"
     ]
    }
   ],
   "source": [
    "print(np.column_stack([decs,incs]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## di_rot \n",
    "\n",
    "[\\[Essentials Chapter 11\\]](https://earthref.org/MagIC/books/Tauxe/Essentials/WebBook3ch11.html) \n",
    "[\\[command line version\\]](https://pmagpy.github.io/PmagPy-cli.html#di_rot.py)\n",
    "\n",
    "\n",
    "**di_rot**   rotates dec inc pairs to a new origin.  We can call **pmag.dodirot()** for single [dec,inc,Dbar,Ibar] data or **pmag.dodirot_V()** for an array of Dec, Inc pairs.  We can use the data from the [di_geo](#di_geo) example and rotate the geographic coordinate data such that the center of the distribution is the principal direction.   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We do it like this: \n",
    "- read in a data set with dec inc pairs\n",
    "- make an equal area projection of the data to remind us what they look like\n",
    "- calculate the principal component with **pmag.doprinc())**\n",
    "- rotate the data to the principal direction\n",
    "- plot the rotated data in an equal area projection. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "di_block=np.loadtxt('data_files/di_rot/di_rot_example.txt') # read in some data\n",
    "ipmag.plot_net(1) # make the plot\n",
    "ipmag.plot_di(di_block=di_block,title='geographic',color='red',edge='black')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we calculate the principal direction using the method described inthe [goprinc](#goprinc) section."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "princ=pmag.doprinc(di_block)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And note we use **pmag.dodirot_V** to do the rotation.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on function dodirot_V in module pmagpy.pmag:\n",
      "\n",
      "dodirot_V(di_block, Dbar, Ibar)\n",
      "    Rotate an array of dec/inc pairs to coordinate system with Dec,Inc as 0,90\n",
      "    \n",
      "    Parameters\n",
      "    ___________________\n",
      "    di_block : array of [[Dec1,Inc1],[Dec2,Inc2],....]\n",
      "    Dbar : declination of desired center\n",
      "    Ibar : inclination of desired center\n",
      "    \n",
      "    Returns\n",
      "    __________\n",
      "    array of rotated decs and incs: [[rot_Dec1,rot_Inc1],[rot_Dec2,rot_Inc2],....]\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(pmag.dodirot_V)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
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       "       [312.48926048,  79.65647491],\n",
       "       [200.97503066,  60.43114047],\n",
       "       [ 82.81519452,  80.55563807],\n",
       "       [  4.47891063,  78.31133276],\n",
       "       [152.93461275,  86.9201173 ],\n",
       "       [130.61844695,  86.22975549],\n",
       "       [ 73.38056924,  83.81526149],\n",
       "       [183.81900156,  71.53579093]])"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rot_block=pmag.dodirot_V(di_block,princ['dec'],princ['inc'])\n",
    "rot_block"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And of course look at what we have done!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ipmag.plot_net(1) # make the plot\n",
    "ipmag.plot_di(di_block=rot_block,color='red',title='rotated',edge='black')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## di_tilt\n",
    "\n",
    "[\\[Essentials Chapter 9\\]](https://earthref.org/MagIC/books/Tauxe/Essentials/WebBook3ch9.html) [\\[Changing coordinate systems\\]](http://earthref.org/MAGIC/books/Tauxe/Essentials/WebBook3ap1.html#Changing_coordinate_systems)\n",
    "[\\[command line version\\]](https://pmagpy.github.io/PmagPy-cli.html#di_tilt.py)\n",
    "\n",
    "**di_tilt** can rotate a direction of Declination = 5.3 and Inclination = 71.6 to “stratigraphic” coordinates, assuming the  strike was 135 and the dip was 21. The convention in this program is to use the dip direction, which is to the “right” of this strike. \n",
    "\n",
    "We can perform this calculation by calling  **pmag.dotilt** or **pmag.dotilt_V()** depending on if we have a single point or an array to rotate."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on function dotilt in module pmagpy.pmag:\n",
      "\n",
      "dotilt(dec, inc, bed_az, bed_dip)\n",
      "    Does a tilt correction on a direction (dec,inc) using bedding dip direction\n",
      "    and bedding dip.\n",
      "    \n",
      "    Parameters\n",
      "    ----------\n",
      "    dec : declination directions in degrees\n",
      "    inc : inclination direction in degrees\n",
      "    bed_az : bedding dip direction\n",
      "    bed_dip : bedding dip\n",
      "    \n",
      "    Returns\n",
      "    -------\n",
      "    dec,inc : a tuple of rotated dec, inc values\n",
      "    \n",
      "    Examples\n",
      "    -------\n",
      "    >>> pmag.dotilt(91.2,43.1,90.0,20.0)\n",
      "    (90.952568837153436, 23.103411670066617)\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(pmag.dotilt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on function dotilt_V in module pmagpy.pmag:\n",
      "\n",
      "dotilt_V(indat)\n",
      "    Does a tilt correction on an array with rows of dec,inc bedding dip direction and dip.\n",
      "    \n",
      "    Parameters\n",
      "    ----------\n",
      "    input : declination, inclination, bedding dip direction and bedding dip\n",
      "    nested array of [[dec1, inc1, bed_az1, bed_dip1],[dec2,inc2,bed_az2,bed_dip2]...]\n",
      "    \n",
      "    Returns\n",
      "    -------\n",
      "    dec,inc : arrays of rotated declination, inclination\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(pmag.dotilt_V)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# read in some data\n",
    "data=np.loadtxt('data_files/di_tilt/di_tilt_example.dat') # load up the data\n",
    "di_block=data[:,[0,1]] # let's look at the data first! \n",
    "ipmag.plot_net(1)\n",
    "ipmag.plot_di(di_block=di_block)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can rotate them"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "Dt,It=pmag.dotilt_V(data) # rotate them\n",
    "ipmag.plot_net(1) # and take another look\n",
    "ipmag.plot_di(dec=Dt,inc=It)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Use the handy function **np.column_stack** to pair the decs and incs together"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 3.74524673e+01,  4.95794971e+01],\n",
       "       [ 3.36467520e+02,  6.09447203e+01],\n",
       "       [ 3.38016562e+02,  2.29922937e+01],\n",
       "       [ 3.55656248e+02,  7.51556739e+00],\n",
       "       [ 8.17695697e+00,  5.86079487e+01],\n",
       "       [ 6.24312543e+00,  2.98149642e+01],\n",
       "       [ 3.57033733e+02,  5.00073921e+01],\n",
       "       [ 3.42811107e+02,  5.85702274e+01],\n",
       "       [ 3.39284414e+02,  3.48942163e-01],\n",
       "       [ 3.85757431e+00,  2.17049062e+01],\n",
       "       [ 3.54347623e+02,  4.89864710e+01],\n",
       "       [ 2.83925013e-01,  4.85556186e+01],\n",
       "       [ 3.35776430e+02,  6.39503873e+01],\n",
       "       [ 1.81481921e+01,  3.27972491e+01],\n",
       "       [ 3.53945383e+02,  3.12870301e+01],\n",
       "       [ 3.08201120e+01,  4.80808730e+01],\n",
       "       [ 2.80340193e+01,  4.25855265e+01],\n",
       "       [ 3.52849360e+02,  3.85903328e+01],\n",
       "       [ 3.51431548e+02,  4.79200709e+01],\n",
       "       [ 1.49895755e+01,  5.82971278e+00],\n",
       "       [ 2.01405693e+02, -2.73644346e+01],\n",
       "       [ 1.94529222e+02, -6.03000930e+01],\n",
       "       [ 1.51711653e+02, -3.44278588e+01],\n",
       "       [ 2.02439369e+02, -5.45796578e+01],\n",
       "       [ 1.78129642e+02,  1.35071395e+01],\n",
       "       [ 1.74193635e+02, -3.83557833e+01],\n",
       "       [ 1.92458609e+02, -4.42202097e+01],\n",
       "       [ 1.82404516e+02, -1.00854450e+01],\n",
       "       [ 1.87192313e+02, -5.16833347e+01],\n",
       "       [ 1.58078673e+02,  5.20435367e-01],\n",
       "       [ 1.81335139e+02, -3.65993719e+01],\n",
       "       [ 1.94115720e+02, -4.70131320e+01],\n",
       "       [ 1.58208438e+02, -6.99710447e+00],\n",
       "       [ 2.04050923e+02, -2.39690981e+01],\n",
       "       [ 1.77668058e+02, -3.69335311e+01],\n",
       "       [ 1.79312818e+02, -5.36825261e+01],\n",
       "       [ 1.73740461e+02, -2.78039697e+01],\n",
       "       [ 1.86273785e+02,  1.48376413e+01],\n",
       "       [ 1.68858936e+02, -3.72957242e+01],\n",
       "       [ 1.68155763e+02, -2.35094484e+01],\n",
       "       [ 1.33030870e+01,  4.22794606e+01],\n",
       "       [ 3.48352284e+02,  5.58391509e+01],\n",
       "       [ 3.53867446e+02,  5.47913351e+01],\n",
       "       [ 8.65352111e+00,  3.91760462e+01],\n",
       "       [ 3.40000000e+02,  7.00000000e+00],\n",
       "       [ 3.36154223e+02,  4.78755564e+01],\n",
       "       [ 3.81797572e+00,  2.54089397e+01],\n",
       "       [ 1.43419909e+01,  1.56898879e+01],\n",
       "       [ 3.23928409e+02,  3.67361188e+01],\n",
       "       [ 1.27352972e+01,  5.63798793e+01],\n",
       "       [ 1.42359910e+01,  5.15897401e+01],\n",
       "       [ 3.48737862e+02,  1.13663807e+01],\n",
       "       [ 3.45111147e+02,  2.68299034e+01],\n",
       "       [ 3.50355082e+02,  4.74111159e+01],\n",
       "       [ 3.52271716e+02,  7.31725552e+00],\n",
       "       [ 3.89741169e+00,  3.22117431e+01],\n",
       "       [ 3.19005940e+01,  6.79140326e+01],\n",
       "       [ 8.12324186e+00,  4.71819989e+01],\n",
       "       [ 3.25923242e+01,  4.86194246e+01],\n",
       "       [ 1.89143987e+01,  1.46150626e+00],\n",
       "       [ 1.59511050e+02, -4.84321911e+01],\n",
       "       [ 1.64070130e+02, -8.83925684e+00],\n",
       "       [ 1.68071076e+02, -4.98009543e+01],\n",
       "       [ 1.73357015e+02, -3.80292679e+01],\n",
       "       [ 1.69578333e+02, -2.55976667e+01],\n",
       "       [ 2.01113352e+02, -3.85750376e+01],\n",
       "       [ 1.89188527e+02,  3.16419245e+00],\n",
       "       [ 1.68193460e+02, -2.28496326e+01],\n",
       "       [ 1.66316564e+02, -5.16025617e+01],\n",
       "       [ 1.78511559e+02, -2.65720102e+01],\n",
       "       [ 1.79619680e+02, -2.69659149e+01],\n",
       "       [ 1.80072436e+02, -2.90190442e+01],\n",
       "       [ 1.72017252e+02, -4.69940123e+01],\n",
       "       [ 1.71028729e+02, -3.88734330e+01],\n",
       "       [ 1.77793107e+02, -5.79993286e+01],\n",
       "       [ 1.94987994e+02, -2.57291361e+01],\n",
       "       [ 1.88426223e+02, -5.68143203e+01],\n",
       "       [ 1.66302864e+02, -2.70024954e+01],\n",
       "       [ 1.82295485e+02, -5.75960780e+01],\n",
       "       [ 1.81867322e+02, -4.00131799e+01]])"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.column_stack((Dt,It)) # if you want to see the output: "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## di_vgp\n",
    "\n",
    "[\\[Essentials Chapter 2\\]](https://earthref.org/MagIC/books/Tauxe/Essentials/WebBook3ch2.html) \n",
    "[\\[command line version\\]](https://pmagpy.github.io/PmagPy-cli.html#di_vgp.py)\n",
    "\n",
    "\n",
    "**di_vgp** converts directions (declination,inclination) to Virtual Geomagnetic Pole positions.   This is the inverse of [**vgp_di**](#vgp_di). \n",
    "To do so, we will call **pmag.dia_vgp()** from within the notebook."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on function dia_vgp in module pmagpy.pmag:\n",
      "\n",
      "dia_vgp(*args)\n",
      "    Converts directional data (declination, inclination, alpha95) at a given\n",
      "    location (Site latitude, Site longitude) to pole position (pole longitude,\n",
      "    pole latitude, dp, dm)\n",
      "    \n",
      "    Parameters\n",
      "    ----------\n",
      "    Takes input as (Dec, Inc, a95, Site latitude, Site longitude)\n",
      "    Input can be as individual values (5 parameters)\n",
      "    or\n",
      "    as a list of lists: [[Dec, Inc, a95, lat, lon],[Dec, Inc, a95, lat, lon]]\n",
      "    \n",
      "    Returns\n",
      "    ----------\n",
      "    if input is individual values for one pole the return is:\n",
      "    pole longitude, pole latitude, dp, dm\n",
      "    \n",
      "    if input is list of lists the return is:\n",
      "    list of pole longitudes, list of pole latitude, list of dp, list of dm\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(pmag.dia_vgp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 11.   63.   55.   13. ]\n",
      " [154.  -58.   45.5 -73. ]]\n"
     ]
    }
   ],
   "source": [
    "data=np.loadtxt('data_files/di_vgp/di_vgp_example.dat') # read in some data\n",
    "print (data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The data are almost in the correct format, but there is no a95 field, so that will have to be inserted (as zeros). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0., 0.])"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a95=np.zeros(len(data))\n",
    "a95"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 11.   63.    0.   55.   13. ]\n",
      " [154.  -58.    0.   45.5 -73. ]]\n"
     ]
    }
   ],
   "source": [
    "DIs=data.transpose()[0:2].transpose() # get the DIs\n",
    "LatLons=data.transpose()[2:].transpose() # get the Lat Lons\n",
    "newdata=np.column_stack((DIs,a95,LatLons)) # stitch them back together\n",
    "print (newdata)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[154.65869784  77.3180885    0.           0.        ]\n",
      " [  6.62978666 -69.63701906   0.           0.        ]]\n"
     ]
    }
   ],
   "source": [
    "vgps=np.array(pmag.dia_vgp(newdata)) # get a tuple with lat,lon,dp,dm, convert to array\n",
    "print (vgps.transpose()) #  print out the vgps"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## dipole_pinc\n",
    "\n",
    "[\\[Essentials Chapter 2\\]](https://earthref.org/MagIC/books/Tauxe/Essentials/WebBook3ch2.html) \n",
    "[\\[command line version\\]](https://pmagpy.github.io/PmagPy-cli.html#dipole_pinc.py)\n",
    "\n",
    "If we assume a geocentric axial dipole, we can calculate an expected inclination at a given latitude and that is what **dipole_pinc** does.   It calls **pmag.pinc()** and so will we to find the expected inclination at a paleolatitude of 24$^{\\circ}$S! \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on function pinc in module pmagpy.pmag:\n",
      "\n",
      "pinc(lat)\n",
      "    calculate paleoinclination from latitude using dipole formula: tan(I) = 2tan(lat)\n",
      "    Parameters\n",
      "    ________________\n",
      "    \n",
      "    lat : either a single value or an array of latitudes\n",
      "    \n",
      "    Returns\n",
      "    -------\n",
      "    \n",
      "    array of inclinations\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(pmag.pinc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-41.68370203503222"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lat=-24\n",
    "pmag.pinc(-24)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Or as an array"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "lats=range(-90,100,10)\n",
    "incs=pmag.pinc(lats)\n",
    "plt.plot(incs,lats)\n",
    "plt.ylim(100,-100)\n",
    "plt.xlabel('Latitude')\n",
    "plt.ylabel('Inclination')\n",
    "plt.axhline(0,color='black')\n",
    "plt.axvline(0,color='black');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## dipole_plat\n",
    "\n",
    "[\\[Essentials Chapter 2\\]](https://earthref.org/MagIC/books/Tauxe/Essentials/WebBook3ch2.html) \n",
    "[\\[command line version\\]](https://pmagpy.github.io/PmagPy-cli.html#dipole_plat.py)\n",
    "\n",
    "**dipole_plat** is similar to [dipole_pinc](#dipole_pinc) but calculates the paleolatitude from the inclination.  We will call **pmag.plat()**:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on function plat in module pmagpy.pmag:\n",
      "\n",
      "plat(inc)\n",
      "    calculate paleolatitude from inclination using dipole formula: tan(I) = 2tan(lat)\n",
      "    Parameters\n",
      "    ________________\n",
      "    \n",
      "    inc : either a single value or an array of inclinations\n",
      "    \n",
      "    Returns\n",
      "    -------\n",
      "    \n",
      "    array of latitudes\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(pmag.plat)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "24.237370383549177"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "inc=42\n",
    "pmag.plat(inc)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## dir_cart\n",
    "\n",
    "[\\[Essentials Chapter 2\\]](https://earthref.org/MagIC/books/Tauxe/Essentials/WebBook3ch2.html#x15-1560002)  [\\[command line version\\]](https://pmagpy.github.io/PmagPy-cli.html#dir_cart.py)\n",
    "\n",
    "**pmag.dir2cart()** converts directions (Declination, Inclination, Intensity) to cartesian coordinates (X,Y,Z). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on function dir2cart in module pmagpy.pmag:\n",
      "\n",
      "dir2cart(d)\n",
      "    Converts a list or array of vector directions in degrees (declination,\n",
      "    inclination) to an array of the direction in cartesian coordinates (x,y,z)\n",
      "    \n",
      "    Parameters\n",
      "    ----------\n",
      "    d : list or array of [dec,inc] or [dec,inc,intensity]\n",
      "    \n",
      "    Returns\n",
      "    -------\n",
      "    cart : array of [x,y,z]\n",
      "    \n",
      "    Examples\n",
      "    --------\n",
      "    >>> pmag.dir2cart([200,40,1])\n",
      "    array([-0.71984631, -0.26200263,  0.64278761])\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(pmag.dir2cart)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Input: \n",
      " [[ 20.   46.    1.3]\n",
      " [175.  -24.    4.2]]\n",
      "Output: \n",
      "8.4859e-01 3.0886e-01 9.3514e-01\n",
      "-3.8223e+00 3.3441e-01 -1.7083e+00\n"
     ]
    }
   ],
   "source": [
    "# read in data file from example file\n",
    "dirs=np.loadtxt('data_files/dir_cart/dir_cart_example.dat')\n",
    "print ('Input: \\n',dirs) # print out the cartesian coordinates\n",
    "# print out the  results\n",
    "carts = pmag.dir2cart(dirs)\n",
    "print (\"Output: \")\n",
    "for c in carts:\n",
    "    print ('%8.4e %8.4e %8.4e'%(c[0],c[1],c[2]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## eigs_s\n",
    "\n",
    "[\\[Essentials Chapter 13\\]](https://earthref.org/MagIC/books/Tauxe/Essentials/WebBook3ch13.html#x15-156000813) [\\[command line version\\]](https://pmagpy.github.io/PmagPy-cli.html#eigs_s.py)\n",
    "\n",
    "This program converts eigenparameters to the six tensor elements.  This is the inverse of [s_eigs](#s_eigs).\n",
    "There is a function **ipmag.eigs_s()** which will do this in a notebook:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on function eigs_s in module pmagpy.ipmag:\n",
      "\n",
      "eigs_s(infile='', dir_path='.')\n",
      "    Converts eigenparamters format data to s format\n",
      "    \n",
      "    Parameters\n",
      "    ___________________\n",
      "    Input:\n",
      "        file : input file name with eigenvalues (tau) and eigenvectors (V) with  format:\n",
      "            tau_1 V1_dec V1_inc tau_2 V2_dec V2_inc tau_3 V3_dec V3_inc\n",
      "    Output\n",
      "         the six tensor elements as a nested array\n",
      "          [[x11,x22,x33,x12,x23,x13],....]\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(ipmag.eigs_s)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.33416328, 0.33280227, 0.33303446, -0.00016631071, 0.0012316267, 0.0013552071]\n",
      "[0.33555713, 0.33197427, 0.3324687, 0.00085685047, 0.00025266458, 0.0009815096]\n",
      "[0.335853, 0.33140355, 0.3327435, 0.0013230764, 0.0011778723, 4.5534102e-06]\n",
      "[0.3347939, 0.33140817, 0.33379796, -0.0004308845, 0.0004885784, 0.00045610438]\n",
      "[0.33502916, 0.33117944, 0.3337915, -0.00106313, 0.00029828132, 0.00035882858]\n",
      "[0.33407047, 0.3322691, 0.33366045, -6.384468e-06, 0.0009844461, 5.9963346e-05]\n",
      "[0.33486328, 0.33215088, 0.3329859, -0.0003427944, 0.00038177703, 0.0002014497]\n",
      "[0.33509853, 0.33195898, 0.33294258, 0.000769761, 0.00056717254, 0.00011960149]\n"
     ]
    }
   ],
   "source": [
    "Ss=ipmag.eigs_s(infile=\"eigs_s_example.dat\", dir_path='data_files/eigs_s')\n",
    "for s in Ss:\n",
    "    print (s)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## eq_di\n",
    "\n",
    "[\\[Essentials Appendix B\\]](https://earthref.org/MagIC/books/Tauxe/Essentials/WebBook3ap2.html#x21-227000B#x15-156000813) [\\[command line version\\]](https://pmagpy.github.io/PmagPy-cli.html#eq_di.py)\n",
    "\n",
    " Data are frequently published as equal area projections and not listed in data tables. These data can be digitized as x,y data (assuming the outer rim is unity) and converted to approximate directions with the program **eq_di**. To use this program, install a graph digitizer (GraphClick from http://www.arizona-software.ch/graphclick/ works on Macs).\n",
    "\n",
    "Digitize the data from the equal area projection saved in the file eqarea.png in the eq_di directory. You should only work on one hemisphere at a time (upper or lower) and save each hemisphere in its own file. Then you can convert the X,Y data to approximate dec and inc data - the quality of the data depends on your care in digitizing and the quality of the figure that you are digitizing.\n",
    "\n",
    "Here we will try this out on a datafile already prepared, which are the digitized data from the lower hemisphere of a plot.  You  check your work with [eqarea](#eqarea).  \n",
    "\n",
    "To do this in a notebook, we can use **pmag.doeqdi()**.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on function doeqdi in module pmagpy.pmag:\n",
      "\n",
      "doeqdi(x, y, UP=False)\n",
      "    Takes digitized x,y, data and returns the dec,inc, assuming an\n",
      "    equal area projection\n",
      "    Parameters\n",
      "    __________________\n",
      "        x : array of digitized x from point on equal area projection\n",
      "        y : array of  igitized y from point on equal area projection\n",
      "        UP : if True, is an upper hemisphere projection\n",
      "    Output :\n",
      "        dec : declination\n",
      "        inc : inclination\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(pmag.doeqdi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# read in the data into an array\n",
    "# x is assumed first column, y, second\n",
    "xy=np.loadtxt('data_files/eq_di/eq_di_example.dat').transpose()\n",
    "decs,incs=pmag.doeqdi(xy[0],xy[1])\n",
    "ipmag.plot_net(1)\n",
    "ipmag.plot_di(dec=decs,inc=incs,color='r',edge='black')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## fcalc\n",
    "\n",
    "**pmag.fcalc()** returns the values of an F-test from  an F table."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on function fcalc in module pmagpy.pmag:\n",
      "\n",
      "fcalc(col, row)\n",
      "    looks up an F-test stastic from F tables F(col,row), where row is number of degrees of freedom - this is 95% confidence (p=0.05).\n",
      "    \n",
      "      Parameters\n",
      "      _________\n",
      "          col : degrees of freedom column\n",
      "          row : degrees of freedom row\n",
      "    \n",
      "      Returns\n",
      "          F : value for 95% confidence from the F-table\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(pmag.fcalc)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## fisher\n",
    "\n",
    "[\\[Essentials Chapter 11\\]](https://earthref.org/MagIC/books/Tauxe/Essentials/WebBook3ch11.html) \n",
    "[\\[command line version\\]](https://pmagpy.github.io/PmagPy-cli.html#fisher.py)\n",
    "\n",
    "**fisher**  draws $N$  directions  from a Fisher distribution with specified $\\kappa$ and a vertical mean. (For other directions see [fishrot](#fishrot)).  To do this, we can just call the function **pmag.fshdev()** $N$ times."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on function fshdev in module pmagpy.pmag:\n",
      "\n",
      "fshdev(k)\n",
      "    Generate a random draw from a Fisher distribution with mean declination\n",
      "    of 0 and inclination of 90 with a specified kappa.\n",
      "    \n",
      "    Parameters\n",
      "    ----------\n",
      "    k : kappa (precision parameter) of the distribution\n",
      "        k can be a single number or an array of values\n",
      "    \n",
      "    Returns\n",
      "    ----------\n",
      "    dec, inc : declination and inclination of random Fisher distribution draw\n",
      "               if k is an array, dec, inc are returned as arrays, otherwise, single values\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(pmag.fshdev)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# set the number, N, and kappa\n",
    "N,kappa=100,20\n",
    "# a basket to put our fish in\n",
    "fish=[]\n",
    "# get the Fisherian deviates\n",
    "for i in range(N):\n",
    "    d,i=pmag.fshdev(kappa)\n",
    "    fish.append([d,i])\n",
    "ipmag.plot_net(1)\n",
    "ipmag.plot_di(di_block=fish,color='r',edge='black')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## fishrot\n",
    "\n",
    "\n",
    "[\\[Essentials Chapter 11\\]](https://earthref.org/MagIC/books/Tauxe/Essentials/WebBook3ch11.html) \n",
    "[\\[command line version\\]](https://pmagpy.github.io/PmagPy-cli.html#fishrot.py)\n",
    "\n",
    "This program is similar to [fisher](#fisher), but allows you to specify the mean direction. \n",
    "This has been implemented as **ipmag.fishrot()**. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on function fishrot in module pmagpy.ipmag:\n",
      "\n",
      "fishrot(k=20, n=100, dec=0, inc=90, di_block=True)\n",
      "    Generates Fisher distributed unit vectors from a specified distribution\n",
      "    using the pmag.py fshdev and dodirot functions.\n",
      "    \n",
      "    Parameters\n",
      "    ----------\n",
      "    k : kappa precision parameter (default is 20)\n",
      "    n : number of vectors to determine (default is 100)\n",
      "    dec : mean declination of distribution (default is 0)\n",
      "    inc : mean inclination of distribution (default is 90)\n",
      "    di_block : this function returns a nested list of [dec,inc,1.0] as the default\n",
      "    if di_block = False it will return a list of dec and a list of inc\n",
      "    \n",
      "    Returns\n",
      "    ---------\n",
      "    di_block : a nested list of [dec,inc,1.0] (default)\n",
      "    dec, inc : a list of dec and a list of inc (if di_block = False)\n",
      "    \n",
      "    Examples\n",
      "    --------\n",
      "    >>> ipmag.fishrot(k=20, n=5, dec=40, inc=60)\n",
      "    [[44.766285502555775, 37.440866867657235, 1.0],\n",
      "     [33.866315796883725, 64.732532250463436, 1.0],\n",
      "     [47.002912770597163, 54.317853800896977, 1.0],\n",
      "     [36.762165614432547, 56.857240672884252, 1.0],\n",
      "     [71.43950604474395, 59.825830945715431, 1.0]]\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(ipmag.fishrot)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   35.1    45.9\n",
      "   47.4    20.6\n",
      "   20.2    34.6\n",
      "   48.9    28.6\n",
      "   33.1    34.2\n"
     ]
    }
   ],
   "source": [
    "rotdi=ipmag.fishrot(k=50,n=5,dec=33,inc=41)\n",
    "for di in rotdi:\n",
    "    print ('%7.1f %7.1f'%(di[0],di[1]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ipmag.plot_net(1)\n",
    "ipmag.plot_di(di_block=rotdi)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## flip\n",
    "\n",
    "Fisher statistics requires unimodal data (all in one direction with no reversals) but many paleomagnetic data sets are bimodal.  To flip bimodal data into a single mode, we can use **pmag.flip( )**.  This function calculates the principle direction and flips all the 'reverse' data to the 'normal' direction along the principle axis.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on function flip in module pmagpy.pmag:\n",
      "\n",
      "flip(di_block, combine=False)\n",
      "    determines 'normal' direction along the principle eigenvector, then flips the antipodes of\n",
      "    the reverse mode to the antipode\n",
      "    \n",
      "    Parameters\n",
      "    ___________\n",
      "    di_block : nested list of directions\n",
      "    Return\n",
      "    D1 : normal mode\n",
      "    D2 : flipped reverse mode as two DI blocks\n",
      "    combine : if True return combined D1, D2, nested D,I pairs\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(pmag.flip)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#read in the data into an array\n",
    "vectors=np.loadtxt('data_files/eqarea_ell/tk03.out').transpose()\n",
    "di_block=vectors[0:2].transpose() # decs are di_block[0], incs are di_block[1]\n",
    "# flip the reverse directions to their normal antipodes\n",
    "normal,flipped=pmag.flip(di_block)\n",
    "# and plot them up\n",
    "ipmag.plot_net(1)\n",
    "ipmag.plot_di(di_block=di_block,color='red')\n",
    "ipmag.plot_di(di_block=flipped,color='b')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## gaussian\n",
    "\n",
    "[\\[Essentials Chapter 11\\]](https://earthref.org/MagIC/books/Tauxe/Essentials/WebBook3ch11.html) \n",
    "[\\[command line version\\]](https://pmagpy.github.io/PmagPy-cli.html#gaussian.py)\n",
    "\n",
    "This program generates sets of data drawn from a normal distribution with a given mean and standard deviation.  It is just a wrapper for a call to  **pmag.gaussdev()** which just calls **numpy.random.normal()** which we could do, but we would have to import it, so it is easiest just to call the **pmag** version which we have already imported.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on function gaussdev in module pmagpy.pmag:\n",
      "\n",
      "gaussdev(mean, sigma, N=1)\n",
      "        returns a number randomly drawn from a gaussian distribution with the given mean, sigma\n",
      "        Parmeters:\n",
      "        _____________________________\n",
      "        mean : mean of the gaussian distribution from which to draw deviates\n",
      "        sigma : standard deviation of same\n",
      "        N : number of deviates desired\n",
      "    \n",
      "        Returns\n",
      "        -------\n",
      "    \n",
      "        N deviates from the normal distribution from\n",
      "    .\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(pmag.gaussdev)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYsAAAEKCAYAAADjDHn2AAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMi4zLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvIxREBQAAHI1JREFUeJzt3X2UXFWZ7/HvjyCvahAIXk2ADhJf4ogMFNE7o6gwYNA1RO4ECTIz4OVOvErWXHV8iS6vYlwzDr7hGol3iBcUcRAQgekZcCKCoy6HgVR4TzDXnpiQJixphAEReWny3D/OLjypVPU51V2nq7r791mrVp+XvU89VV3VT5999tlbEYGZmdlYdut1AGZm1v+cLMzMrJCThZmZFXKyMDOzQk4WZmZWyMnCzMwKOVmYmVkhJwszMyvkZGFmZoV273UA3XLggQfGwMBAr8MwM5tS1q9f/1BEzCkqN22SxcDAAPV6vddhmJlNKZK2lilXaTOUpMWSNkkakrSyxf5jJd0maVTS0qZ9h0j6vqR7JW2UNFBlrGZm1l5lyULSLGA1cBKwEDhd0sKmYvcBZwGXtTjEN4HPR8SrgEXAg1XFamZmY6uyGWoRMBQRmwEkXQ4sATY2CkTElrRvR75iSiq7R8QNqdzjFcZpZmYFqmyGmgtsy60Pp21lvBz4T0lXS7pd0ufTmcpOJC2XVJdUHxkZ6ULIZmbWSpXJQi22lZ08Y3fgjcCHgGOAw8iaq3Y+WMSaiKhFRG3OnMKL+WZmNk5VJoth4ODc+jxgewd1b4+IzRExClwLHNXl+MzMrKQqk8U6YIGk+ZL2AJYBgx3UfZGkxunCceSudZiZ2eSqLFmkM4IVwFrgXuDKiNggaZWkkwEkHSNpGDgVuFDShlT3WbImqBsl3U3WpPW1qmI1M7OxabrMwV2r1cI35ZmZdUbS+oioFZXz2FBmfW5gYABJSMJD2livTJvhPsymq61bt9JoAZBadTI0q57PLMzMrJCThZmZFXKyMDOzQk4WZmZWyMnCZqR8DyP3MjIr5t5QNiPlexiBexmZFfGZhZmZFXKyMDOzQk4WZmZWyMnCzMwKOVmYmVkhJwuzksoM6Ff1oH+HHnqou/taT7jrrFlJZQb0q3rQvy1btjy37O6+Npl8ZmFmZoWcLMzMrFClyULSYkmbJA1JWtli/7GSbpM0Kmlpi/0vlHS/pAuqjNPMzMZWWbKQNAtYDZwELAROl7Swqdh9wFnAZW0O8xngR1XFaGZm5VR5ZrEIGIqIzRHxNHA5sCRfICK2RMRdwI7mypKOBl4MfL/CGM3MrIQqk8VcYFtufThtKyRpN+CLwIcriMvMzDpUZbJo1a8vWmxr5X3A9RGxbaxCkpZLqkuqj4yMdBygmZmVU+V9FsPAwbn1ecD2knX/K/BGSe8Dng/sIenxiNjpInlErAHWANRqtbKJyMzMOlRlslgHLJA0H7gfWAa8q0zFiDijsSzpLKDWnCjMzGzyVNYMFRGjwApgLXAvcGVEbJC0StLJAJKOkTQMnApcKGlDVfGYmdn4KT9b2FRWq9WiXq/3OgybIiTtMlNe0XchX6Zd+TJlJhprJzGbFZG0PiJqReV8B7eZmRVysjAzs0JOFmZmVsjJwszMCjlZmJlZIScLMzMr5GRhNg6dTm/aD1Oymk2Ep1U1G4dOpzfthylZzSbCZxZmZlbIycLMzAo5WZiZWSEnCzMzK+RkYWZmhZwszCZZp91uu8Vdc20i3HXWbJJ12u22W9w11ybCZxZmZlbIycLMzAo5WZiZWaFKk4WkxZI2SRqStLLF/mMl3SZpVNLS3PYjJd0saYOkuySdVmWcZmY2tsqShaRZwGrgJGAhcLqkhU3F7gPOAi5r2v4E8OcR8WpgMfBlSftVFatZO/keRIceemivw+lYp/Hnyzf3mnJvqpmtyt5Qi4ChiNgMIOlyYAmwsVEgIrakfTvyFSPi/+WWt0t6EJgD/GeF8ZrtIt+DaCrqNP7m8vleU+5NNbNV2Qw1F9iWWx9O2zoiaRGwB/AfXYrLzMw6VGWyaPWvR0f/okl6CXAp8O6I2NFi/3JJdUn1kZGRcYZpZmZFqkwWw8DBufV5wPaylSW9ELgO+ERE/HurMhGxJiJqEVGbM2fOhII1M7P2qkwW64AFkuZL2gNYBgyWqZjKXwN8MyK+U2GMZmZWQmXJIiJGgRXAWuBe4MqI2CBplaSTASQdI2kYOBW4UNKGVP2dwLHAWZLuSI8jq4rVbCrq1RhTNjNpKvf0yKvValGv13sdhk0Rknbp9dPqu9Bue7syZZa7VbdMnBPdPpGYbGqQtD4iakXlfAe3mZkVcrIwM7NCThZmZlbIycLMzAo5WZiZWSEnC7Meynd/ncyBCst2u+1VfNZ/PK2qWQ/lp1jt1fOONShgr+Kz/uMzCzMzK+RkYWZmhZwszMyskJOFmZkV8gVus4o0ehI1lierrlkVnCzMKjKRnkTuhWT9xs1QZmZWyMnCzMwKOVmYmVkhJwszMytUabKQtFjSJklDkla22H+spNskjUpa2rTvTEk/T48zq4zTzMzGVllvKEmzgNXACcAwsE7SYERszBW7DzgL+FBT3f2BTwE1IID1qe4jVcVrNpXlu9o2bzfrhiq7zi4ChiJiM4Cky4ElwHPJIiK2pH07muq+FbghIh5O+28AFgPfrjBesynLXW2talU2Q80FtuXWh9O2quuamVmXlUoWkn5vHMduNe5xdLOupOWS6pLqIyMjHQVnZmbllT2z+HtJt0p6n6T9StYZBg7Orc8DtnezbkSsiYhaRNTmzJlT8tBmZtapUskiIt4AnEH2B7wu6TJJJxRUWwcskDRf0h7AMmCwZFxrgRMlvUjSi4AT0zYzM+uB0tcsIuLnwCeAjwJvAv5O0s8k/bc25UeBFWR/5O8FroyIDZJWSToZQNIxkoaBU4ELJW1IdR8GPkOWcNYBqxoXu82qNjAw4KlEzZooovgygqQjgHcDbwduAC6KiNskvRS4OSJ6/o2q1WpRr9d7HYZNEZLIf/bz6837OjlWp3X7wXjin4qv01qTtD4iakXlynadvQD4GvDxiPhtY2NEbJf0iXHGaGZmU0TZZPE24LcR8SyApN2AvSLiiYi4tLLozMysL5S9ZvEDYO/c+j5pm5mZzQBlk8VeEfF4YyUt71NNSGZm1m/KJovfSDqqsSLpaOC3Y5Q3M7NppOw1i/cD35HUuDHuJcBp1YRkNrV4vuxiAwMDbN26FcjeI49lNfWUShYRsU7SK4FXkA3F8bOIeKbSyMymCP/hK7Z169aduufa1NPJqLPHAAOpzu+nftbfrCQqMzPrK6WShaRLgZcBdwDPps0BOFmYmc0AZc8sasDC8C2bZmYzUtneUPcA/6XKQMzMrH+VTRYHAhslrZU02HhUGZhZN+QHBRwYGOh1ONOS3+OZoWwz1LlVBmFWFffCqZ7f45mhbNfZH0k6FFgQET+QtA8wq9rQzMysX5SdVvUvgKuAC9OmucC1VQVlZmb9pew1i3OAPwQeg+cmQjqoqqDMzKy/lE0WT0XE040VSbuT3WdhZmYzQNlk8SNJHwf2TnNvfwf4p+rCMjOzflI2WawERoC7gfcA15PNxz0mSYslbZI0JGlli/17Sroi7b9F0kDa/jxJl0i6W9K9kj5W9gWZmVn3le0NtYNsWtWvlT2wpFnAauAEYBhYJ2kwIjbmip0NPBIRh0taBpxHNprtqcCeEfGa1PNqo6RvR8SWss9vZmbdU3ZsqF/Q4hpFRBw2RrVFwFBEbE7HuBxYAuSTxRJ+dw/HVcAFyjpqB7BvujayN/A06eK6mZlNvk7GhmrYi+w///0L6swFtuXWh4HXtSsTEaOSHgUOIEscS4AHyGbk+0BEPFwyVjMz67JS1ywi4le5x/0R8WXguIJqrW7lbD47aVdmEdnoti8F5gN/JWmXsxhJyyXVJdVHRkaKX4iZmY1L2Waoo3Kru5GdabygoNowcHBufR6wvU2Z4dTkNBt4GHgX8C9pgqUHJf00PefmfOWIWAOsAajVau7Ka2ZWkbLNUF/MLY8CW4B3FtRZByyQNB+4H1hGlgTyBoEzgZuBpcBNERGS7gOOk/Qtsmao1wNfLhmrmXXA08JaGWV7Q72l0wOnaxArgLVk40hdHBEbJK0C6hExCFwEXCppiOyMYlmqvhr4OtnQ6AK+HhF3dRqDmRXztLBWRtlmqA+OtT8ivtRm+/Vk92Tkt30yt/wk2cXy5nqPt9puZma90UlvqGPImo0A/hj4MTv3djIzs2mqbLI4EDgqIn4NIOlc4DsR8T+qCszMzPpH2eE+DiG7Ma7haWCg69GYmVlfKntmcSlwq6RryO6DOAX4ZmVRmZlZXynbG+qvJX0PeGPa9O6IuL26sMwml7uPmo2t7JkFZPc7PBYRX5c0R9L8iPhFVYGZTSZ3HzUbW9lpVT8FfBRoDBX+POBbVQVlZmb9pewF7lOAk4HfAETEdoqH+zAzs2mibLJ4OiKCNBCgpH2rC8nMzPpN2WRxpaQLgf0k/QXwAzqYCMnMzKa2skOUf4FsjonvAq8APhkRX6kyMLPxGhgYQBKS3LOpIo3eY83vcX57/tHp7yH/OxwYGOhy9DYehb2h0vSoayPij4Abqg/JbGK2bt1K1mpqVWnXe6xbvcryv8NGl2brrcIzi4h4FnhC0uxJiMfMzPpQ2fssngTulnQDqUcUQET8ZSVRmZlZXymbLK5LDzMzm4HGTBaSDomI+yLikskKyMzM+k/RNYtrGwuSvltxLGZm1qeKkkW+G8JhVQZiVoa7VJr1RlGyiDbLpUhaLGmTpCFJK1vs31PSFWn/LZIGcvuOkHSzpA2S7pa0V6fPb9NPo0tlRLB169Zeh2M2YxRd4H6tpMfIzjD2Tsuk9YiIF7armO7PWA2cAAwD6yQNRsTGXLGzgUci4nBJy4DzgNMk7U42UOGfRcSdkg4AnhnPCzQzs4kbM1lExKwJHHsRMBQRmwEkXQ4sAfLJYglwblq+CrhA2R04JwJ3RcSdKY5fTSAOMzOboLJjQ43HXGBbbn04bWtZJiJGgUeBA4CXAyFpraTbJH2k1RNIWi6pLqk+MjLS9RdgZmaZKpNFq3v0m697tCuzO/AG4Iz08xRJx+9SMGJNRNQiojZnzpyJxmtmZm1UmSyGgYNz6/OA7e3KpOsUs4GH0/YfRcRDEfEEcD1wVIWxmtkkaTfYYLvebfny7gHXO1Umi3XAAknzJe0BLAMGm8oMAmem5aXATWnejLXAEZL2SUnkTex8rcPMpqgtW7Y816Mt/2jXuy1f3j3geqeTObg7EhGjklaQ/eGfBVwcERskrQLqETEIXARcKmmI7IxiWar7iKQvkSWcAK6PCA83YmbWI5ouQznXarWo1+u9DsMqJmmnoatbfX7LbG9XxnpnIr9bGz9J6yOiVlSuymYoMzObJpwszMyskJOFmZkVcrKwKavTLpXt5o226cWDTVajst5QZlXLz/dcZp7mbs0Pbf3N83dXw2cWZmZWyMnCzMwKOVmYmVkhJwszMyvkZGF9L9+7xb2YrMG9niaXe0NZ38v3bjFrcK+nyeUzCzMzK+RkYWZmhZwszMyskJOFmZkVcrIwM7NCThZmNuO4223nKk0WkhZL2iRpSNLKFvv3lHRF2n+LpIGm/YdIelzSh6qM08xmlka3W8/rXV5lyULSLGA1cBKwEDhd0sKmYmcDj0TE4cD5wHlN+88HvldVjGZmVk6VZxaLgKGI2BwRTwOXA0uayiwBLknLVwHHK91dI+kdwGZgQ4UxmplZCVUmi7nAttz6cNrWskxEjAKPAgdI2hf4KPDpCuMzM7OSqkwWre6/bx6zoV2ZTwPnR8TjYz6BtFxSXVJ9ZGRknGGamVmRKseGGgYOzq3PA7a3KTMsaXdgNvAw8DpgqaTPAfsBOyQ9GREX5CtHxBpgDUCtVvPgQTNYY8rUxrKZdVeVyWIdsEDSfOB+YBnwrqYyg8CZwM3AUuCmyEYGe2OjgKRzgcebE4VZnqdMNatWZckiIkYlrQDWArOAiyNig6RVQD0iBoGLgEslDZGdUSyrKh4zMxs/TZehn2u1WtTr9V6HYRWQ5CHKZ4D877nd77xdmTLLnT7XTCFpfUTUisr5Dm4zMyvkZGFmZoWcLMzMrJCThU2KMgO3eXC3ma3R/Xk8c61PpK6V4zm4bVKUmS/ZcyrPbBPp/uyu09XzmYWZmRVysjAzs0JOFmZmVsjJwszMCjlZWE/le0C5F4tZ/3JvKOupfA8oM+tfPrMwM7NCThZmZlbIycLMzAo5WZiZWSEnC9tFp+M45R8e08mmC49VtjP3hrJddDqOU57HdLLpwmOV7cxnFmZmVqjSZCFpsaRNkoYkrWyxf09JV6T9t0gaSNtPkLRe0t3p53FVxmlmZmOrLFlImgWsBk4CFgKnS1rYVOxs4JGIOBw4HzgvbX8I+OOIeA1wJnBpVXGamVmxKs8sFgFDEbE5Ip4GLgeWNJVZAlySlq8CjpekiLg9Iran7RuAvSTtWWGsZmY2hiqTxVxgW259OG1rWSYiRoFHgQOayvwJcHtEPNX8BJKWS6pLqo+MjHQtcDMz21mVyaJV94Hm7jNjlpH0arKmqfe0eoKIWBMRtYiozZkzZ9yBWjllBv3LT2/Zrruhp8C08er0s5Mvn3/k65YpY9V2nR0GDs6tzwO2tykzLGl3YDbwMICkecA1wJ9HxH9UGKeVVGbQv/z0lu26G3oKTBuvTj87Zcr781hOlWcW64AFkuZL2gNYBgw2lRkku4ANsBS4KSJC0n7AdcDHIuKnFcZoZmYlVJYs0jWIFcBa4F7gyojYIGmVpJNTsYuAAyQNAR8EGt1rVwCHA/9b0h3pcVBVsZqZ2dg0XeYSqNVqUa/Xex3GtCBppztXWy1P5DhV1zXrtun8GZS0PiJqReV8B7eZmRVysphB2g3+V1XPpV7VNetnU3WAQjdDzSBjnUq72cesvW5+J/rtu+ZmKDMz6xonCzMzK+RkYWZmhZwszMyskJOFmZkVcrKY5soM/mdm49euK2y7rupT9XvoObinuTKD/5nZ+LWbq3u6ffd8ZmFmZoWcLMzMrJCThZmZFXKyMDOzQk4WSb8N7tVpPP0Wv9l00m7q1bGmaO102tdOv+dlBgLtJg8kmPTh4F4dxTPROSj67fWbzTSdfs87rTvGMT2QoJmZdUelyULSYkmbJA1JWtli/56Srkj7b5E0kNv3sbR9k6S3VhmnmZmNrbJkIWkWsBo4CVgInC5pYVOxs4FHIuJw4HzgvFR3IbAMeDWwGPhqOp6ZmfVAlWcWi4ChiNgcEU8DlwNLmsosAS5Jy1cBxyu7BXIJcHlEPBURvwCG0vHMzKwHqkwWc4FtufXhtK1lmYgYBR4FDihZ18zMJkmVY0Opxbbmy/XtypSpi6TlwPK0+rikTR1FuOvxWi6Pw4HAQxM5wHjiaVe+7Gvp4uvvRFfeqxnA71M5U/p96vR73mndnPz7VGpkwyqTxTBwcG59HrC9TZlhSbsDs4GHS9YlItYAa7oYc1dIqpfpimZ+r8ry+1SO36dyxvM+VdkMtQ5YIGm+pD3ILlgPNpUZBM5My0uBmyLrLDwILEu9peYDC4BbK4zVzMzGUNmZRUSMSloBrAVmARdHxAZJq4B6RAwCFwGXShoiO6NYlupukHQlsBEYBc6JiGeritXMzMY2be7g7ieSlqcmMivg96ocv0/l+H0qZzzvk5OFmZkV8nAfZmZWyMmiy4qGOLGMpC2S7pZ0h6TxjwA5DUm6WNKDku7Jbdtf0g2Sfp5+vqiXMfaDNu/TuZLuT5+rOyS9rZcx9gNJB0v6oaR7JW2Q9L/S9o4+U04WXVRyiBP7nbdExJHu6riLb5ANc5O3ErgxIhYAN6b1me4b7Po+AZyfPldHRsT1kxxTPxoF/ioiXgW8Hjgn/V3q6DPlZNFdZYY4MRtTRPyYrHdgXn5onEuAd0xqUH2ozftkTSLigYi4LS3/GriXbESMjj5TThbd5WFKygvg+5LWpzvxbWwvjogHIPvyAwf1OJ5+tkLSXamZasY31+Wlkb1/H7iFDj9TThbdVWqYEgPgDyPiKLImu3MkHdvrgGxa+D/Ay4AjgQeAL/Y2nP4h6fnAd4H3R8RjndZ3suiuUsOUGETE9vTzQeAaPKpwkV9KeglA+vlgj+PpSxHxy4h4NiJ2AF/DnysAJD2PLFH8Q0RcnTZ39JlysuiuMkOczHiS9pX0gsYycCJwz9i1Zrz80DhnAv/Yw1j6VuOPX3IK/lyRpn24CLg3Ir6U29XRZ8o35XVZ6qr3ZX43xMlf9zikviPpMLKzCciGnLnM79PvSPo28GaykUF/CXwKuBa4EjgEuA84NSJm9MXdNu/Tm8maoALYAryn0S4/U0l6A/AT4G5gR9r8cbLrFqU/U04WZmZWyM1QZmZWyMnCzMwKOVmYmVkhJwszMyvkZGFmZoWcLGxKkfRiSZdJ2pyGCrlZ0imT8Lw1SX/XpWP9axqZ+C5JP5N0gaT9JnC8fyvYv5+k9433+GbgZGFTSLq56FrgxxFxWEQcTXbj47yqnzsi6hHxl1085BkRcQRwBPAUE7jJLiL+oKDIfoCThU2Ik4VNJccBT0fE3zc2RMTWiPgKZIOkSfqJpNvS4w/S9jdL+udGnfSf/Flp+W8lbUz/5X8hbTtV0j2S7pT04+ZjSFok6d8k3Z5+viJtP0vS1ZL+Jc0R8LmiF5RGJ/4IcIik16bj/KmkW9N8DBdKmiXpvfnjpedqvO7H08/nS7oxvfa7JTVGPP5b4GXpeJ9PZT8saV163Z9O2/aVdF163fdIOq3TX5BNX7v3OgCzDrwauG2M/Q8CJ0TEk5IWAN8G2s6VIWl/siEhXhkRkWsK+iTw1oi4v03z0M+AYyNiVNIfAX8D/EnadyTZqJ5PAZskfSUitrU4xnMi4llJdwKvlPQ0cBrZQIvPSPoqcAZwFXAzWWIhlWm+6/1J4JSIeEzSgcC/Sxokm6fg9yLiyPS6TwQWkI2bJGAwDeQ4B9geEW9P5WaPFbfNLE4WNmVJWg28gexs4xjgecAFko4EngVeXnCIx8j+wP5fSdcBjbOPnwLfkHQlcHWLerOBS1JCivS8DTdGxKMpvo3Aoew8bH3bl5N+Hg8cDazLWt3YG3gwIkbSdZrXAz8HXpHibD7G36Q//DvIhsd/cYvnOjE9bk/rzydLHj8BviDpPOCfI+InJeK2GcLJwqaSDfzuP3gi4pz0H3RjWtYPkI0R9FqyJtYn0/ZRdm5y3SvVH5W0iOwP9DJgBXBcRPxPSa8D3g7ckZJP3meAH0bEKWl+gH/N7Xsqt/wsJb5jymZYfA3ZpDQHAZdExMdaFL0CeCfZmc01setYPWeQnR0cnc5KtjRea/NTAp+NiAtbxHI08Dbgs5K+HxGriuK3mcHXLGwquQnYS9J7c9v2yS3PBh5Iw1P/GdlgjgBbgYWS9kxNK8fDc+P7z05Tb76frAkJSS+LiFsi4pPAQ+w87Hzjee5Py2dN5AUpGzr6s8C2iLiLbHrLpZIOSvv3l3RoKn412Wxmp5Mljmazyc5CnpH0FrKzGoBfAy/IlVsL/Pf0+pE0V9JBkl4KPBER3wK+ABw1kddm04vPLGzKSNcV3gGcL+kjwAjwG+CjqchXge9KOhX4YdpHRGxLTUp3kTXhNJpfXgD8o6S9yP7b/kDa/vnUxCSyP953Am/KhfI5smaoD5IlsPH4B0lPAXsCPyBNvxsRGyV9gmwWwd2AZ4BzgK0R8Uhq2loYEbe2OibwT5LqwB1kZyBExK8k/VTSPcD3IuLDkl4F3Jyauh4H/hQ4PL32Hel539viOWyG8qizZmZWyM1QZmZWyMnCzMwKOVmYmVkhJwszMyvkZGFmZoWcLMzMrJCThZmZFXKyMDOzQv8fgCvRYUHg5vgAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "N=1000\n",
    "bins=100\n",
    "norm=pmag.gaussdev(10,3,N)\n",
    "plt.hist(norm,bins=bins,color='black',histtype='step',density=True)\n",
    "plt.xlabel('Gaussian Deviates')\n",
    "plt.ylabel('Frequency');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x560 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# alternatively we can plot with ipmag.histplot:\n",
    "ipmag.histplot(data=norm, xlab='Gaussian Deviates', save_plots=False, norm=-1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## gobing\n",
    "\n",
    " \n",
    "[\\[Essentials Chapter 12\\]](https://earthref.org/MagIC/books/Tauxe/Essentials/WebBook3ch12.html) \n",
    "[\\[command line version\\]](https://pmagpy.github.io/PmagPy-cli.html#gobing.py)\n",
    "\n",
    "**gobing** calculates Bingham statistics for sets of directional data (see the section for eqarea_ell in the PmagPy_plots_analysis documentation for nice examples).  We do this by calling **pmag.dobingham()**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on function dobingham in module pmagpy.pmag:\n",
      "\n",
      "dobingham(di_block)\n",
      "    Calculates the Bingham mean and associated statistical parameters from\n",
      "    directions that are input as a di_block\n",
      "    \n",
      "    Parameters\n",
      "    ----------\n",
      "    di_block : a nested list of [dec,inc] or [dec,inc,intensity]\n",
      "    \n",
      "    Returns\n",
      "    -------\n",
      "    bpars : dictionary containing the Bingham mean and associated statistics\n",
      "    dictionary keys\n",
      "        dec : mean declination\n",
      "        inc : mean inclination\n",
      "        n : number of datapoints\n",
      "        Eta : major ellipse\n",
      "        Edec : declination of major ellipse axis\n",
      "        Einc : inclination of major ellipse axis\n",
      "        Zeta : minor ellipse\n",
      "        Zdec : declination of minor ellipse axis\n",
      "        Zinc : inclination of minor ellipse axis\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(pmag.dobingham)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'dec': 357.77952733337463,\n",
       " 'inc': 60.3168380083183,\n",
       " 'Edec': 105.71735145158095,\n",
       " 'Einc': 9.956900268236785,\n",
       " 'Zdec': 20.99389065755772,\n",
       " 'Zinc': -27.647853556651516,\n",
       " 'n': 20,\n",
       " 'Zeta': 4.480026907803641,\n",
       " 'Eta': 4.4907543191720025}"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "di_block=np.loadtxt('data_files/gobing/gobing_example.txt')\n",
    "pmag.dobingham(di_block)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## gofish\n",
    "\n",
    "[\\[Essentials Chapter 11\\]](https://earthref.org/MagIC/books/Tauxe/Essentials/WebBook3ch11.html) \n",
    "[\\[command line version\\]](https://pmagpy.github.io/PmagPy-cli.html#gofish.py)\n",
    "\n",
    "**gofish** calculates Fisher statistics for sets of directional data.  (see the section for eqarea_ell in the PmagPy_plots_analysis documentation for nice examples).\n",
    "This can be done with **ipmag.fisher_mean()**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on function fisher_mean in module pmagpy.ipmag:\n",
      "\n",
      "fisher_mean(dec=None, inc=None, di_block=None)\n",
      "    Calculates the Fisher mean and associated parameters from either a list of\n",
      "    declination values and a separate list of inclination values or from a\n",
      "    di_block (a nested list a nested list of [dec,inc,1.0]). Returns a\n",
      "    dictionary with the Fisher mean and statistical parameters.\n",
      "    \n",
      "    Parameters\n",
      "    ----------\n",
      "    dec : list of declinations or longitudes\n",
      "    inc : list of inclinations or latitudes\n",
      "    di_block : a nested list of [dec,inc,1.0]\n",
      "        A di_block can be provided instead of dec, inc lists in which case it\n",
      "        will be used. Either dec, inc lists or a di_block need to be provided.\n",
      "    \n",
      "    Returns\n",
      "    -------\n",
      "    fisher_mean : dictionary containing the Fisher mean parameters\n",
      "    \n",
      "    Examples\n",
      "    --------\n",
      "    Use lists of declination and inclination to calculate a Fisher mean:\n",
      "    \n",
      "    >>> ipmag.fisher_mean(dec=[140,127,142,136],inc=[21,23,19,22])\n",
      "    {'alpha95': 7.292891411309177,\n",
      "    'csd': 6.4097743211340896,\n",
      "    'dec': 136.30838974272072,\n",
      "    'inc': 21.347784026899987,\n",
      "    'k': 159.69251473636305,\n",
      "    'n': 4,\n",
      "    'r': 3.9812138971889026}\n",
      "    \n",
      "    Use a di_block to calculate a Fisher mean (will give the same output as the\n",
      "    example with the lists):\n",
      "    \n",
      "    >>> ipmag.fisher_mean(di_block=[[140,21],[127,23],[142,19],[136,22]])\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(ipmag.fisher_mean)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'dec': 10.783552984917437,\n",
       " 'inc': 39.602582993520244,\n",
       " 'n': 10,\n",
       " 'r': 9.848433230859508,\n",
       " 'k': 59.379770717798884,\n",
       " 'alpha95': 6.320446730051139,\n",
       " 'csd': 10.511525802823254}"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "di_block=np.loadtxt('data_files/gofish/fishrot.out')\n",
    "ipmag.fisher_mean(di_block=di_block)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### fisher mean on pandas DataFrames\n",
    "There is also a function **pmag.dir_df_fisher_mean()** that calculates Fisher statistics on a Pandas DataFrame with directional data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on function dir_df_fisher_mean in module pmagpy.pmag:\n",
      "\n",
      "dir_df_fisher_mean(dir_df)\n",
      "    calculates fisher mean for Pandas data frame\n",
      "    \n",
      "    Parameters\n",
      "    __________\n",
      "    dir_df: pandas data frame with columns:\n",
      "        dir_dec : declination\n",
      "        dir_inc : inclination\n",
      "    Returns\n",
      "    -------\n",
      "    fpars : dictionary containing the Fisher mean and statistics\n",
      "        dec : mean declination\n",
      "        inc : mean inclination\n",
      "        r : resultant vector length\n",
      "        n : number of data points\n",
      "        k : Fisher k value\n",
      "        csd : Fisher circular standard deviation\n",
      "        alpha95 : Fisher circle of 95% confidence\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(pmag.dir_df_fisher_mean)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'dec': 10.78355298491744,\n",
       " 'inc': 39.60258299352024,\n",
       " 'n': 10,\n",
       " 'r': 9.848433230859508,\n",
       " 'k': 59.379770717798884,\n",
       " 'alpha95': 6.320446730051139,\n",
       " 'csd': 10.511525802823254}"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# make the data frame\n",
    "dir_df=pd.read_csv('data_files/gofish/fishrot.out',delim_whitespace=True, header=None)\n",
    "dir_df.columns=['dir_dec','dir_inc']\n",
    "pmag.dir_df_fisher_mean(dir_df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## gokent\n",
    "\n",
    "[\\[Essentials Chapter 12\\]](https://earthref.org/MagIC/books/Tauxe/Essentials/WebBook3ch12.html) \n",
    "[\\[command line version\\]](https://pmagpy.github.io/PmagPy-cli.html#gokent.py)\n",
    "\n",
    "With **gokent** we can calculate Kent statistics on sets of directional data (see the section for eqarea_ell in the PmagPy_plots_analysis documentation for nice examples).  \n",
    "\n",
    "This calls **pmag.dokent()** (see also **eqarea_ell** example)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on function dokent in module pmagpy.pmag:\n",
      "\n",
      "dokent(data, NN)\n",
      "    gets Kent  parameters for data\n",
      "    Parameters\n",
      "    ___________________\n",
      "    data :  nested pairs of [Dec,Inc]\n",
      "    NN  : normalization\n",
      "        NN is the number of data for Kent ellipse\n",
      "        NN is 1 for Kent ellipses of bootstrapped mean directions\n",
      "    \n",
      "    Return\n",
      "    kpars dictionary keys\n",
      "        dec : mean declination\n",
      "        inc : mean inclination\n",
      "        n : number of datapoints\n",
      "        Eta : major ellipse\n",
      "        Edec : declination of major ellipse axis\n",
      "        Einc : inclination of major ellipse axis\n",
      "        Zeta : minor ellipse\n",
      "        Zdec : declination of minor ellipse axis\n",
      "        Zinc : inclination of minor ellipse axis\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(pmag.dokent)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'dec': 359.1530456710398,\n",
       " 'inc': 55.03341554254794,\n",
       " 'n': 20,\n",
       " 'Zdec': 246.82080930796928,\n",
       " 'Zinc': 14.881429411175574,\n",
       " 'Edec': 147.69921287231705,\n",
       " 'Einc': 30.819395154843157,\n",
       " 'Zeta': 7.805151237185049,\n",
       " 'Eta': 9.304659303299626}"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "di_block=np.loadtxt('data_files/gokent/gokent_example.txt')\n",
    "pmag.dokent(di_block,di_block.shape[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## goprinc\n",
    "\n",
    "[\\[Essentials Chapter 12\\]](https://earthref.org/MagIC/books/Tauxe/Essentials/WebBook3ch12.html) \n",
    "[\\[command line version\\]](https://pmagpy.github.io/PmagPy-cli.html#goprinc.py)\n",
    "\n",
    "**goprinc** calculates the principal directions (and their eigenvalues) for sets of paleomagnetic vectors.  It doesn't do any statistics on them, unlike the other programs. \n",
    "We will call **pmag.doprinc()**:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on function doprinc in module pmagpy.pmag:\n",
      "\n",
      "doprinc(data)\n",
      "    Gets principal components from data in form of a list of [dec,inc] data.\n",
      "    \n",
      "    Parameters\n",
      "    ----------\n",
      "    data : nested list of dec, inc directions\n",
      "    \n",
      "    Returns\n",
      "    -------\n",
      "    ppars : dictionary with the principal components\n",
      "        dec : principal directiion declination\n",
      "        inc : principal direction inclination\n",
      "        V2dec : intermediate eigenvector declination\n",
      "        V2inc : intermediate eigenvector inclination\n",
      "        V3dec : minor eigenvector declination\n",
      "        V3inc : minor eigenvector inclination\n",
      "        tau1 : major eigenvalue\n",
      "        tau2 : intermediate eigenvalue\n",
      "        tau3 : minor eigenvalue\n",
      "        N  : number of points\n",
      "        Edir : elongation direction [dec, inc, length]\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(pmag.doprinc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'Edir': array([151.85261736,  29.07891169,   1.        ]),\n",
       " 'dec': 3.869443846664467,\n",
       " 'inc': 56.740159941913355,\n",
       " 'N': 20,\n",
       " 'tau1': 0.8778314142896239,\n",
       " 'tau2': 0.07124540042876253,\n",
       " 'tau3': 0.05092318528161358,\n",
       " 'V2dec': 151.85261735984162,\n",
       " 'V2inc': 29.078911691227447,\n",
       " 'V3dec': 250.25426093396385,\n",
       " 'V3inc': 14.721055437689328}"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "di_block=np.loadtxt('data_files/goprinc/goprinc_example.txt')\n",
    "pmag.doprinc(di_block)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## igrf\n",
    "\n",
    "[\\[Essentials Chapter 2\\]](https://earthref.org/MagIC/books/Tauxe/Essentials/WebBook3ch2.html) \n",
    "[\\[command line version\\]](https://pmagpy.github.io/PmagPy-cli.html#igrf.py)\n",
    "\n",
    "\n",
    "This program gives geomagnetic field vector data for a specified place at a specified time.  It has many built in models including  IGRFs, GUFM and several archeomagnetic models.   It calls the  function **ipmag.igrf()** for this so that is what we will do.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on function igrf in module pmagpy.ipmag:\n",
      "\n",
      "igrf(input_list, mod='', ghfile='')\n",
      "    Determine Declination, Inclination and Intensity from the IGRF model.\n",
      "    (http://www.ngdc.noaa.gov/IAGA/vmod/igrf.html)\n",
      "    \n",
      "    Parameters\n",
      "    ----------\n",
      "    input_list : list with format [Date, Altitude, Latitude, Longitude]\n",
      "        date must be in decimal year format XXXX.XXXX (Common Era)\n",
      "    mod :  desired model\n",
      "        \"\" : Use the IGRF\n",
      "        custom : use values supplied in ghfile\n",
      "        or choose from this list\n",
      "        ['arch3k','cals3k','pfm9k','hfm10k','cals10k.2','cals10k.1b']\n",
      "        where:\n",
      "            arch3k (Korte et al., 2009)\n",
      "            cals3k (Korte and Constable, 2011)\n",
      "            cals10k.1b (Korte et al., 2011)\n",
      "            pfm9k  (Nilsson et al., 2014)\n",
      "            hfm10k is the hfm.OL1.A1 of Constable et al. (2016)\n",
      "            cals10k.2 (Constable et al., 2016)\n",
      "            the first four of these models, are constrained to agree\n",
      "            with gufm1 (Jackson et al., 2000) for the past four centuries\n",
      "    \n",
      "    \n",
      "    gh : path to file with l m g h data\n",
      "    \n",
      "    Returns\n",
      "    -------\n",
      "    igrf_array : array of IGRF values (0: dec; 1: inc; 2: intensity (in nT))\n",
      "    \n",
      "    Examples\n",
      "    --------\n",
      "    >>> local_field = ipmag.igrf([2013.6544, .052, 37.87, -122.27])\n",
      "    >>> local_field\n",
      "    array([  1.39489916e+01,   6.13532008e+01,   4.87452644e+04])\n",
      "    >>> ipmag.igrf_print(local_field)\n",
      "    Declination: 13.949\n",
      "    Inclination: 61.353\n",
      "    Intensity: 48745.264 nT\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(ipmag.igrf)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will calculate the field for San Diego from 3000 BCE to 1950 in 50 year increments using the hfm.OL1.A1 model of Constable et al. (2016, doi: 10.1016/j.epsl.2016.08.015).  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x648 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# make a list of desired dates\n",
    "dates=range(-3000,1950,50) # list of dates in +/- Common Era\n",
    "mod = 'hfm10k' # choose the desired model\n",
    "lat,lon,alt=33,-117,0 # desired latitude, longitude and alitude\n",
    "Vecs=[] # list for Dec,Inc,Int outputs\n",
    "for date in dates: # step through the dates\n",
    "    Vecs.append(ipmag.igrf([date,alt,lat,lon],mod=mod)) # append to list\n",
    "vector_df = pd.DataFrame(Vecs)   # make it into a Pandas dataframe\n",
    "vector_df.columns=['dec','inc','int']\n",
    "vector_df['vadms']=pmag.b_vdm(vector_df.int.values*1e-9, lat) # calculate the VADMs\n",
    "vector_df['dec_adj']=vector_df['dec'] \n",
    "vector_df.loc[vector_df.dec>180,['dec_adj']]=vector_df.dec-360 # adjust declinations to be -180 => 180\n",
    "fig=plt.figure(1,figsize=(7,9)) # set up the figure\n",
    "fig.add_subplot(411) # make 4 rows of plots, this is the first\n",
    "plt.plot(dates,vector_df.dec_adj) # plot the adjusted declinations\n",
    "plt.ylabel('Declination ($^{\\circ}$)')\n",
    "plt.title('Geomagnetic field evaluated at Lat: '+str(lat)+' / Lon: '+str(lon))\n",
    "fig.add_subplot(412) # this is the second\n",
    "plt.plot(dates,vector_df.inc) # plot  the inclinations\n",
    "plt.ylabel('Inclination ($^{\\circ}$)')\n",
    "fig.add_subplot(413)\n",
    "plt.plot(dates,vector_df.int*1e-3) # plot the intensites (in uT instead of nT)\n",
    "plt.ylabel('Intensity ($\\mu$T)')\n",
    "fig.add_subplot(414) # plot the VADMs \n",
    "plt.plot(dates,vector_df.vadms*1e-21) # plot as ZAm^2\n",
    "plt.ylabel('VADM (ZAm$^2$)')\n",
    "plt.xlabel('Dates (CE)');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## incfish\n",
    "\n",
    "[\\[Essentials Chapter 11\\]](https://earthref.org/MagIC/books/Tauxe/Essentials/WebBook3ch11.html) \n",
    "[\\[command line version\\]](https://pmagpy.github.io/PmagPy-cli.html#incfish.py)\n",
    "\n",
    "You can't get a meaningful average inclination from inclination only data because of the exponential relationship between inclinations and the true mean inclination for Fisher distributions (except exactly at the pole and the equator).  So, McFadden and Reid (1982, doi:  10.1111/j.1365-246X.1982.tb04950.x) developed a maximum liklihood estimate for getting an estimate for true mean absent declination.   **pmag.doincfish()** is an implementation of that concept. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on function doincfish in module pmagpy.pmag:\n",
      "\n",
      "doincfish(inc)\n",
      "    gets fisher mean inc from inc only data\n",
      "    input: list of inclination values\n",
      "    output: dictionary of\n",
      "        'n' : number of inclination values supplied\n",
      "        'ginc' : gaussian mean of inclinations\n",
      "        'inc' : estimated Fisher mean\n",
      "        'r' : estimated Fisher R value\n",
      "        'k' : estimated Fisher kappa\n",
      "        'alpha95' : estimated fisher alpha_95\n",
      "        'csd' : estimated circular standard deviation\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(pmag.doincfish)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'n': 100,\n",
       " 'ginc': 57.135000000000005,\n",
       " 'inc': 61.024999999999764,\n",
       " 'r': 92.8908144677846,\n",
       " 'k': 13.925645849497057,\n",
       " 'alpha95': 0.9966295962964244,\n",
       " 'csd': 21.70587740469687}"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "incs=np.loadtxt('data_files/incfish/incfish_example_inc.dat')\n",
    "pmag.doincfish(incs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## pca\n",
    "\n",
    "[\\[Essentials Chapter 11\\]](https://earthref.org/MagIC/books/Tauxe/Essentials/WebBook3ch11.html) [\\[command line version\\]](https://pmagpy.github.io/PmagPy-cli.html#pca.py)\n",
    "\n",
    "**pca**  calculates best-fit lines, planes or Fisher means through selected treatment steps along with Kirschvink (1980, doi:  10.1111/j.1365-246X.1980.tb02601.x) MAD values. The file format is a simple space delimited file with specimen name, treatment step, intensity, declination and inclination. **pca.py**  calls **pmag.domean()**, so that is what we will do here. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on function domean in module pmagpy.pmag:\n",
      "\n",
      "domean(data, start, end, calculation_type)\n",
      "    Gets average direction using Fisher or principal component analysis (line\n",
      "    or plane) methods\n",
      "    \n",
      "    Parameters\n",
      "    ----------\n",
      "    data : nest list of data: [[treatment,dec,inc,int,quality],...]\n",
      "    start : step being used as start of fit (often temperature minimum)\n",
      "    end : step being used as end of fit (often temperature maximum)\n",
      "    calculation_type : string describing type of calculation to be made\n",
      "    'DE-BFL' (line), 'DE-BFL-A' (line-anchored), 'DE-BFL-O' (line-with-origin),\n",
      "    'DE-BFP' (plane), 'DE-FM' (Fisher mean)\n",
      "    \n",
      "    Returns\n",
      "    -------\n",
      "    mpars : dictionary with the keys \"specimen_n\",\"measurement_step_min\",\n",
      "    \"measurement_step_max\",\"specimen_mad\",\"specimen_dec\",\"specimen_inc\"\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(pmag.domean)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'calculation_type': 'DE-BFL',\n",
       " 'center_of_mass': [1.9347888195464598e-05,\n",
       "  -2.1736620227095438e-05,\n",
       "  2.5042313896882542e-05],\n",
       " 'specimen_direction_type': 'l',\n",
       " 'specimen_dec': 334.9058336155927,\n",
       " 'specimen_inc': 51.50973235790523,\n",
       " 'specimen_mad': 8.75370050160012,\n",
       " 'specimen_n': 10,\n",
       " 'specimen_dang': 19.257783100769142,\n",
       " 'measurement_step_min': 2.5,\n",
       " 'measurement_step_max': 70.0}"
      ]
     },
     "execution_count": 87,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# read in data as space delimited file\n",
    "data=pd.read_csv('data_files/pca/pca_example.txt',\\\n",
    "                 delim_whitespace=True,header=None)\n",
    "# we need to add a column for quality\n",
    "data['quality']='g'\n",
    "# strip off the specimen name and reorder records \n",
    "#  from:  int,dec,inc to: dec,inc,int \n",
    "data=data[[1,3,4,2,'quality']].values.tolist()\n",
    "pmag.domean(data,1,10,'DE-BFL')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## pt_rot\n",
    "\n",
    "\n",
    "[\\[Essentials Chapter 16\\]](https://earthref.org/MagIC/books/Tauxe/Essentials/WebBook3ch16.html) \n",
    "[\\[Essentials Appendix A.3.5\\]](https://earthref.org/MagIC/books/Tauxe/Essentials/WebBook3ap1.html)\n",
    "[\\[command line version\\]](https://pmagpy.github.io/PmagPy-cli.html#pt_rot.py)\n",
    "\n",
    "\n",
    "\n",
    "This program finds rotation poles  for a specified location, age and destination plate, then rotates the point into the destination plate coordinates using the roations and methods described in Essentials Appendix A.3.5.  \n",
    "This can be done for you using the function **frp.get_pole()** in the finite rotation pole module called **pmagpy.frp**. You then call **pmag.pt_rot()** to do the rotation.  Let's do this for to rotate the Cretaceous poles from Europe (sane data as in the polemap_magic example) and rotate them to South African coordinates.  \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on function get_pole in module pmagpy.frp:\n",
      "\n",
      "get_pole(continent, age)\n",
      "    returns rotation poles and angles for specified continents and ages\n",
      "    assumes fixed Africa.  \n",
      "    Parameters\n",
      "    __________\n",
      "        continent : \n",
      "            aus : Australia\n",
      "            eur : Eurasia\n",
      "            mad : Madacascar\n",
      "            [nwaf,congo] : NW Africa  [choose one]\n",
      "            col :  Colombia\n",
      "            grn : Greenland\n",
      "            nam : North America\n",
      "            par : Paraguay\n",
      "            eant :  East Antarctica\n",
      "            ind : India\n",
      "            [neaf,kala] : NE Africa [choose one]\n",
      "            [sac,sam] :  South America [choose one]\n",
      "            ib : Iberia\n",
      "            saf : South Africa\n",
      "      Returns\n",
      "      _______\n",
      "          [pole longitude, pole latitude, rotation angle] : for the continent at specified age\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# need to load this special module\n",
    "import pmagpy.frp as frp\n",
    "help(frp.get_pole)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[40.2, -12.5, 28.5]"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Prot=frp.get_pole('eur',100)\n",
    "Prot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on function pt_rot in module pmagpy.pmag:\n",
      "\n",
      "pt_rot(EP, Lats, Lons)\n",
      "    Rotates points on a globe by an Euler pole rotation using method of\n",
      "    Cox and Hart 1986, box 7-3.\n",
      "    \n",
      "    Parameters\n",
      "    ----------\n",
      "    EP : Euler pole list [lat,lon,angle]\n",
      "    Lats : list of latitudes of points to be rotated\n",
      "    Lons : list of longitudes of points to be rotated\n",
      "    \n",
      "    Returns\n",
      "    _________\n",
      "    RLats : rotated latitudes\n",
      "    RLons : rotated longitudes\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(pmag.pt_rot)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [],
   "source": [
    "data=pd.read_csv('data_files/polemap_magic/locations.txt',sep='\\t',header=1)\n",
    "lats=data['pole_lat'].values\n",
    "lons=data['pole_lon'].values\n",
    "RLats,RLons=rot_pts=pmag.pt_rot(Prot,lats,lons)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And now we can plot them using **pmagplotlib.plot_map()**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "gridlines only supported for PlateCarree, Lambert Conformal, and Mercator plots currently\n"
     ]
    },
    {
     "data": {
      "image/png": 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dwMErroLH+iD/t7Msy7rd0IMIFSIibTMi0g4JIcQ43v6lA/zsKnj3x+Dl74Nx44sFdDlA10gz8PfWuTTvzjGQaqQ7ZmusquSwnlWl1mvG/ihJBqXDKeerEYco61qeG5tD58EGihn+MnjC6D0ELf2y8TkX1QoPcvlTswr6EbTuFuhg0Yq7POH86sSlHChz1zW7dS5fcQuAHZ2ZxZw7fCVc3Hotbdb9fOPXJ/Hwmq8yvuMMnrnhJzOcRWIjVImFU4W17aW11SHujEj7qIQQopXmhX9mchz+67/h4AuKO/VXfh+/5ItXXMvlXEXz7hx3zV0E2IT9Qb5SdM2TyDqfGeW3+j1oQjPI08IPOvFlAtpRsRSvZ4ZuAae9BO5XxtNeuTeWsD7k6nZn36IVij93xtmfpdS3fXPcG0S0tOhV4uYFvybuaeNba94JwK6B6Wy8fCs7/+cfNPQ99vqhoaFfEqEqRKRtRkTaARBCTOBNn9xP53dg1X/BO99he4RkCWeJqsiEbDSLR4dVtW73d5j2dYQtv1Ih4jDRmPr+ENdFWriu1auvolMLwvi+L1bKqD7e4GYS7OzvsGWRdHE74N2nT5Km4Vsr3kmSAn+8a4hvvfMBDp6wCH73k+MsyzInZongi4i0zYhI2wdCiMXMfeGfSJ0E77kOZqZqC4KBUnlA15yz3nIqjLmwM5Qmkap1kk+ZjAO81qchMKhx6YCbYU/ClNFPndRLrylm4HMjFKt5Q/DrPxXUI9uU0acqpOyDd9+iVjunSx9NbP3YspL/8/I1t9BBJ7nnEvz6ii56btgOH/oyfHxVQ5QSNjwi0jYjIm0NQogpLH//PjZvgHd+3fYKeUSUP1BFuck6HdliGaM0AsErxqBsrwcUSUFaxZJ4TSlY5fJgEiqBq9AXUZDWK0DuY83+XjfDFbhjgkreWeX7Bkh/odhfPfGW60qoDHgdiU7a6ObP2w5w68U/57n4ybD5t8dblrVrRM5ljCMibTPGHe4OjCYIIc6k6YTb2PsEfOMvMDATalmwSpsoK/HF1lGOgNUJTunpIFGpTBEEn2PVaErpDgi2C6KEamWb8ms3pgfsBFGbbW8YGSCUS/tMfuYw+3API+S5tbfa7o2bNl4AabxaeKt3kYfG9ADJNUUXzmSiwKbtF7CJC7h44bV8YNv5/PGLW9i8c9rD4t+vg+9eErMs69DInVWEIwWRpQ0IIaZz3sV7+NPv4F3fgYWvqd/rOpRPlmTaFuTr7UzeGd3sKglu8YPmr9xOV+BqNDokQasTrKrvONgTk59c8XGa6OMqLi8mcTL1N+vTUCag/351hcFir4bt8Spx3nLU9K+6pw9Qkgt8+YpbaKObx3c8wY8vvoM9zzfB/XfPtyzrwSp6eFQgsrTNOOpJWwjRypwT/szLO+ANV8PkAB/l4UAl2qv8zJSZmFSj/aCyiT7FR1ol2jD6ewkxB71ZZGxXOSkzfG77leX1eUMdvgg7UAZBlUpk35zBXPp8g+Yu6Fx7vzzfLfTQNzSLf177v/z1s5vg8m9jXXpBhfrb0YGItM04quUR8eWfWsyYBe+7Eqa+Bfqx/6DyCa1KUYtLXtbHX1utUw0UCarXMLnotpE1+FHr10WNelSQTBRAjfgk7iXlTFFWMa1kY+yf2kYW88StLhnpx1QSlamXUVz/BjfE2coyN7Q9RZ7cUvttQaaK7Uisd1MKSP27kw7ysRQd//kEzac38dvz/pPYo1utQ1+5JpJLIoTCUWlpCyEaeNfHh/jVevjqL2DSS+wd5eSJeqCaOqWOXU/XOLXuMPvCuv9lnK+OLlyyCrsWVQiUd2GsZoBz+iJztqhZ/zyTuyYJSo3EXOwto65R6V6TtC1/yDUq5bl30OkZkCR5r2U1ue3NXNx6Lc8V9vL7C27Eisfp+9X90y3LerqCsz2isXCmsLZ1lC8XBPGjI8/SPupIWwgxjWWvfYp9T8M1P4W9Bo12OOUR1WIdKRnGTyrQCCnwuC2GbQHHqIsL+5I20HipQeapVJfXiNqtO21LGPq6mJ6cImrdemDUFrt/g7m4/eYi90nPHRWbcRNNyVQFct1L6dpoQgedHDowxP+9/9c88fu/sm/nI5HO7SAibTOOKnlECHEyJ8x/kOPmwpt+BnsbR7YDmjfJsMKvHUnWKsHp5GgiTT/i9/FaUcPWS/qlkKSc6EwmCnS2dngnJNV2g+QqxZdazSsO+JKlX52NKwc8EZEl+VFylITtuxa3tM5X2EVlki91LU7ZN2n9d9JBx/hOzrx2Bff+d4YHPv6TnbFY7NyhoaHf+Hc8wtGMo8bSjsVi5xyaNvM3vO9KeOm7zIVGcgJyuNotNwGX1sqYJIIw9YYZgPz6opB2eo0tJbiLFZiSSIUZ6DLeyVnVzVD1eDEuuxb2Gmh9chNsGaIj02t63eyMnXS4fehIdJZU1UeT+zbQ+4cCO86/Et70n/CNjx7VwTiRpW3GEU/aQgjBf/7XIX70TfjST2DGEnPBw0XY9Wg7yKpWYfKGqKZ9aS0HDRC6hZxRymQJ1uf9zkfdninj3WJC1tA/iUqIWw58GYq5SFQJxSmzfM0t7s/Ofpt9ViXWA+aFJproo41u/pSby53nXceBmS+Ezh8ftUucRaRtRsPh7sBwQggxmY43H+L2n8HN9xxZhJ3GazVLrVX3njB4nnj05Wra14/x8zlX/7LaftmvxXakYfoLveUt6nJ9zhb/GtMDpFt7Sbf22uSe1Y7b4vxpln8oyPKb7YCbZKJgTz7KnCbOoLZp+wXuIR2JTjualCQFkuRJ2avFb29m68Zl5EnRRTt5Urw+vY2z77qMmck9cErbM0KI40P2LEIVEELEhBBdQohfOb9PEELcI4T4uxDix0KIRmf7BOd3r7M/o9TxUWf7g0KIGoeaYByxpC2EmMcpbc8wvhG+dxc85/NE1puwq9Wswx5nImIJqan6YYvyVw9Iwgvqu+pil8VL3o7XhbqwgqdeKB2EFAzm4u6fjlCWt6lNtY2VpW2WLHqcs6WdQn+SxqUDxVB3R+OWFrZEkgJ9NBUlG6e+3MZmctub6aSDPpqYPekp/uWmi5n3niUw67isEOIVlZ1QhArw/4Adyu+rga9alnUSsAe42Nl+MbDHsqxm4KtOOYQQL8S+W14EvBq4TggRG67OHpGkLYTIkDr+YV7zb/DOm+CxSeaClbqSmaxY+adbuWFQS/vl6io3iVhP6BZwuX5qfU1SMEda+rnkpfGSf5ZSSz5bJFMjgauTkH5eKn6DYLb0ODl4pMizaM1d9v2w1J6Q7ey3iThFngJJz1Jwpj5f3X8Z6/tXIYTg1A+8glk//C+YcewdsVjsVeYDI1QLIUQaOBe4wfktgH8FfuoUuQl4vfP9dc5vnP1nOuVfB2ywLOt5y7L+CfQCi4arz0ec94hD2P/kog/D4kv8C1Yz+ea3LVNBvSYSKndcGLIOCpQZaZgGEIM7HWl7Eq6PpmKwUCX9zhra0todTCuThGG9d7LY/1O1/FInyvGaeOkgscF2DZQRkgDLW2+xB6PWpC2TJPAna/DcQ9LzpivRTged/MvZSaxNb+NXy3/QGYvFOoaGhn4X4iwihMPXgI8AU53fM4GnlGXjcsAc5/scYDeAZVkHhRBPO+Xn4H1/VY+pO44oS7tuhF3OqpXIOJ9ZggnEpMXKNvw0Wl2z9qtX/17Oe8QPYc+5FlQ7qJj6FlaP16WgSrV8pexgLl7UrSWyzr4NcbZut7Vpz/qd4EmulZSqtpJ8S61H/cxtbObG7ZfQRxPtSyaxYNOnOTRtZudRY3GPB1I1/sEsIcQ25e/dsnohxGuBgmVZ9ymtmlIKWGX2BR1TdxwxlnZdCTsIGUofML1eP+t3JJDTPkc5ZLCLC90dsRJJSIVq2Vd6LTLK96zymQnYnwM2QG5DM6Rh0+YLSK+xozFVzV56iqTIU0gn7fD+rFZXRvmdha3ZZeRXpEgtyXPspm/y+PL3RRZ3eDwR4D2yBFghhHgNMBGIY1ve04UQ4xxrOw1uWGsOmAvkhBDjgGnYiS/kdgn1mLrjiLC0ayZsn4i6EmRKkyJ5rDbd2vXTY9OGsmEs67Copo5qPUnKQdeONUu3nS6PrGA8Vu9jmH7W4h0jkVW+b8D8NpXxaXsz5D7WTBN9dNDpLt5shF5HlhKNPrexme7+Nk5YMptjN33z6LK4hwmWZX3Usqy0ZVkZ7InE31uW9Vbg/4DznWIXAXLJuI3Ob5z9v3f86DcCKx3vkhOAk4Ctw9XvMW9p15WwyyHr6I06KYfwdPBtt5I+mHRrk1U/mqzsgAnS9JpeVy7YmltmLh+EclZ0mPmCIGQoWtjqEmVhj10JbXTb2jblU9oaF1yWbxs5+97bmllG44IBxt38Aw6+9W2RxT08uAzYIIT4PNAF3OhsvxFYL4ToxbawVwJYlvVXIcRPgAeAg8AllmUNDVfnxjRpewh75SX+eZcreWizBK9sbiKCemvBfm1kDNsJ2FYraY0ACiTtDHhhJ2j1az3cElTG+fRzkwxxjQsk6cR2/cuTKiXwrPaZUb4bBvRkokDqnIm8cNOr+f7rfxsRdx1gWdYdwB3O94cweH9YlrUfuEDf7uy7Erhy+HpYxJiVR2om7FqkiOGUEWT9JgvVzwXNVFelE32HAbnrmt3FFWTiqOJO/AcnP9lJ34ahbL0Q5hpncYSRDjr7O9xcJDJxlTGkXiKD0StJynN5UsSWnMaS//lPmDk9kkqOIoxJS7tiwpbWWFhyMtWXobpV0CtFpfXr5OTnpljGNe6wYDOwBlroIZ9Ikcv6JJkywfT/DGt1m8rpg2aY9oOOzwKLcUPV2xLdbv7wwCRW4OZNKfQ7E5VQMp+S297MjdlmGpcOMPMXJ/PkeWsii/sowZgjbSHE8XWXRIKQcT6zdagziFTqUfdIoZwVq7/SB2jthf4kPYkWz9Jkge2G8f4JmoAMc50qkVxWar83U7xXMnhSw0oEknbGcS3UXAJLJsCx2xjcEOfplecw8xfXsee8f++MxWKvGhoaujVk7yOMQYwp0hZCHMNJLVlWvL0ywq5k8shUp187QTA9+LX6UteCICIyvYmEIb06DBSDG+KwJmRh0/Ws9M1CHlNp3/2uzWYt2x/Y99HSon92G7Z3TDdtQNHtL4cyUDn9kuSc29jsGewG03H3vHJLvSsKDW6I8/jSN7Pg54/zjzd8/HdCiBdalqWGZUc4gjBmSFsIITj7/L0NyYkcWvWByohUPnAZ59Pv2Cxm96taoFqbw2kNh42szGHuk58m7NeOjqDJUSWqsCR3R9q2PNOtveQyzZWtvG4aQEwDY9BgGabuMhi8RvMoykL6C73uUmMSUtMGXC3fNRSU9mTYfeNKZQEG9e1hA8Wc6LLNzbBj6XuZcfU+Dl11/QNCiBmWZT0V/iwijBWMGdLmvZ8/xF2/InbTRg7dG7AOajlvgyBktN/ZgHqDsNSwbbit67B1+VnKYd3nKtmfcT6z2qcCucJNoT9pSw0btAJZzCRu8uHWfeCD+lYL1IFOLoAg29wMLHX8zyn6n0vy1qWRxvSAG2DTuNQJhU/YATVgW+u5bHOp5KMv/5YDNsCexZfT8IosYt5De5wAkWFzPRt2NALzDncnRh/GBGnHYrHlHJuCm7dy4N5j/Qv6PawZigELGUrIpHFp6crZVRO2c2x6Ra8d8aau4CLrLCc9HI6JwbBtmvzCy5FiBvOcgHJcW6K76KutH6vDTxJR+xcGpjePSiAnHAFW2gv6QpGY5XJjgMfNT83yp953g5vj7qo36RW97vbGpT6LQ5gGqi1wqOWbTOhdRuNl7z6IOcQ6whjGqCdtIcQCZs3ayDU/hWdm+xcM8pvOYn74nW0ews5W3kcPHH9qz8SaXqefVVtvsq5lEDBNIupasCp3qGVlmSzm0G/5fbN97QsACUP7tb49qH0yoVpPkxyw2FkLck3Rik5ScCMfTcE0eVLuepF+95y6ALFcYAEoLjbs12+1n4+O5/l3bOLgJ9sZd824txw8ePBHIc40whjBqCZtIcR05p30AO/8GLSeFs61z4RM6SZ1aSoXpvqH0+qtZ2BIkKZbKXnLV3FJ0hnvIrlJCm4+ja7Wdvd7Jx100W4PWJudY7P4a9RKHwv9SVuYgBmSAAAgAElEQVQqULPyyTL1uEayjqzzKftUqTtkDlhZzOIndWtVr25ychf20eRu66LdJWx5rjJpVI5mz70niVqmlU239kKiQG6zwcPGb67kgVkMvf9X8JmzfiiE2GlZVpehVIQxiFG73JgQIsaSVx8kcwp85GvBhB3m9VxDY9ogiUD1sojaB9letrRYVXWHabMSmCQOeR0dPV6SitRmW+gxVlUg6SEssJfSkqTVSYed9U5aidp1kh4W0qNi6/Zltq4d1m86aAJV6r7OwCPPyzeoJYO/a6ezrfHSAXsVGgNhm1KvSuLuoYVOOujubwu876QsktvYXNS4KSbWcmUSvzdLre/jTrqJ8Z/5MM89/HiTZVlaasHRjYXzhLXt0trqEP/vyFtubPRa2m//yEEe2AYfvCaY/CqwriVCEbasuxJyzWBOyF9v1Gp96r7MadtTIZkosJq1JZajCvnaLxejNZWTBC/3Xdi6jq7Wdm7cfkmJ5V3oT5amKfUjIdMbg48bYOPKAdpWlE4EJimQSuRpai0SrLqwLq3FiEVTMIwcxOS560Sd0pK7tQ11U4glXeu7JdFDT6KFrduXed/2Mnjvm4z01y72PZXIs3XpstLJWl26Uq7JwZkX8aK3/pA9m3f0CSEaLcs6QIQxjVFJ2uLqH1ncegvcvBVyIbqYUb5nCSRsTznT8dVAeotkffZnyuwPizr7SJO2J7k6Ep0eItJRIOl5vZe4nKtcEu+i3f0u64IigXfQSao1z9XpyzyTs6ZAkpJBKWxAjOMb3UGnR7KRbwryPPTz1M85SYEWejz6tErs0npuos8l6TwpD2Enh4p1Nu/OuYk7pYXe0trjrtKuGhFuGtdW+2Pr9mUsb73FbXt56y1syl4QfmHkLfDn1G+ZO7WVBZcsGySamBzzGHWkLYR4CTOOhetvgxmz4GmtQAbj0lIlyOJ5JYaifu2xsjMBdZSzZpXXbt/Xbb99ftayyZqst8tazmtZm6QPSVTdtNmEbFoOzJk8lITe3W8Hj8jkSMlEwZOWtIUeViXWk1qRt2WTjcsgY1vbkvAb0wMMZuPhznlx0U2uhR7a6fIQcIFk4MRgEFQLOujNQ0K3sAuxpIe4k0MF8rEUTfTRThd5UrTTxbrEhe51I4NHB0+Rh1b7+koyT1KwvUky2urvQR5JuQbOuPnt3H7aFZx+w1utu995c0TcYxijirSFELOYPe8+PvRlOLm1lOwyISvSj/PblzFskwhD2CoyVBYYEqZOv21BkP0wQZEOLktcbSRrd7LMsUqNZK2hnS5b205413os9CdZzyo6Ex0e0mmiz257BWzduKyYXwObtF0XzM0lTdlY6bWo/Qg1ScE9HzmQpMh7ZA95vLpQgVx815UlFEJOkS8GxmiQbyGuJR7ro22o23OsLCPrvJB1dCQ66U60sWn7BW6ukkJ/kvaE3afu/jb6EnZ/ZN/ldfC9Rqo7Yw4ap03i6l++gHedvhHxLrHYsqx6Le8cYYQxqiYixblvtUg0wYe/EjxRZIK+L2MoY9qv1xdosSjfZXumdvzaHAlk/NuVUkgHnSUWqbSqoajpliPstkQ3F7LOPaabNpfsVGJT61E9UMC2ynMbm92+q0tzuV4oEmnHzQ5bblEHHdUylqQpiVo9RwjO/SHJVFruLfSUWNF5Ul4dXGtXbVMOUqqMoqOPJt83G9fDZGMzi1bcVTqR6QTzuN8ltMF++Ypb+AofpPPnz/GZyw/w+N8HJluW9ZzvhRgFWHiisLZdXVsd4oJoInLYEIvFXsucE+CW7eEIOxNQxrTPBFlfWO8EVQ7x68NoQQbXE6JxpZesVW1WWtSAm6w/DGGDbQE2JeyVWZro82jZfTQVX/sV5Em5Fm4b3axmLZ0rHKkkAI0rB1iVWA/YZNhCjy9pSgLULWTZvhw0dI1e7pdlpcUNuBZzIWZfF32QUAcFCfVaqDq47I9sS36XA1kb3eQTdr+kZZ1akS8Sdhb/oKOAezlPio435Pn1hmf5+xte9yyRvj0mMSpIWwgxjab0Jj713zBpsndnhuDfOvz2Z4v70629xeCXct4JlbQ92pCxLdMLWeexrFVyk1C9QgCP1HHFxAmc2xjj14NDXLH/eU8Tnf0ddCW8mmuBpJGwJaTEIINRWuihZ0Unn9t+pcebpDE9wODSuOsjri7ZJdvzs5r1SUO1bXWdRjXgRSJPqkQ6kmStyhvqMdK9UW1fDWNX+6ISvkrcKtQJXPm/uTCxjq5EOz2ttvdJUHoAwPPWpV6Hb3ztIIvbNyGuFi/VFrWNMAYwKkib89/zFJYFi15ZkVeHr+ueRBavhe7Ul9veHJxqNSiPRiXtHw5k7Y/0it6SSUadyCSRS8Lw6KXYxP1hZvA+aypCCFpiMYAS4i70Jz2EVQ6S7Nb3ryKVyNNCDy30cHHrtdy4/RJyzjVd1HoXTQm7z5IAValBhU7OYSHrUiWbHlo8bZjqVvVr+XYit8sBRcpNspwkYEnCJsnE9PagDrhSx+9o7aS7tY1N113gex+7ebnTSftNZoXdVltTgS98UfCez5y6LXIDHHs47KQthDiDpjT87C/eHZniVxM5hibMbLE+T2BFSD9nmdDI1FbZ9rOGbRmf7ZUg49+OiazBHPghIaUGSTZS0wY4h4sQwn6LFkJwbmOMK/ZX120ZrAPFLHdX91/mTop20GlbkY5XSQednMVtbp/8CDsIemSiCdLSlddMfjcdq7+lrONCj5yUTBQnMVW5qIt2T04SWY9u9avn5/cWIdfVbKGH5JqCPS/wMSVa0pFJpDtlW6Kb/IqiDt8da+OVFz5CesMBckuujNwAxxgOK2kLISYzr/n/+NBXYOo0e2PGW8ZDzsq+wVy8PHFnDNuyyvcyUXeSsH37Uw6m9oP6laEmX+/lK24pmWQsN1kmofstSwI7wCws3oRAYGHx68HqksZJwjZ5elzdfxmrEuttC5JOtmaWeSYkTfKBuq/cSjBBUINuJILeTlSYthX6k5BwLFpFHmmnq2TyUmrdTfSFPgc5WMj+dtBpX4MvpOzgJXUycjPQWgyrV/GomMOXv/M8b37JlxHi4/Mty9oZqgMRDjsOr6V90aXP0JeDM5Ybd+urdcgEOkZ/6xAY3KyUDwp/xkvYcoDQ+1VXaSSjfGaL38u2lbXLXdx6rUfzhfCEHYS/cjPPMIXpnMHdPMl1kw+QnEyoiUoVkrBVy1LV1Nf3266Bhf4kn2z9uEeukP7OUleW2wqxZCiy87O2TYRdKSQhejxVHF2+kw73f2KSpvTJy3LkbZqDkANsCz2kWvOsbV1N7rrifE3uumZSa/Kuu6B6Txx3/ATe/9mpfO1b83eM+TSuRxEOG2kLIV7GzCb4qTmnhU7QQMnvYUPG+9O41NMwt6+2mUwUXJ23xEMmU0rYQTkwqkGW6+nkYedXMXCmUuKWuTpMfZGTj8lEweMZossF5fTsSoNoVKjEavIOUaH7anckOkvdHBOUELd061PPRboGmiYqVZgGlx5a3DeDFnpYzVo+l77S8+a4deMyGpcO0EkHZyVu8xz/uv9IcvuG7fS86xtRGtcxgsPipy2EaOSklud5x+Xwmn8zlpEyhE6YVZN2NkSZTLFtP4SSZXwQ1kKX0oAp57IHWbh4hdnClrJBLWRtgmodrmV1KOKWkZGqni1DuNUyktRXsd6jXzfvzjGQavREGapWdjnS9rsGuqXtN9gF1akf00mH0R9cvmnIyV7V/1sSuF9SrjBQE3d10sGN113iLbDUvv9WJda7vvUSux58jjVLdrL3yQMnWJaVrboTdUbkp23G4bG013z2eXrugXPe4m5SiVD9rhJ3JUTpOSZbpnCm9Lhy9dYqkejHq+2WJWsHy1fc4onkA3/vinpBToKBTURdiXBRkyr8+pcnxYWsKyHC3rnhw0JNiw6EgdqmrpPrFq4b0WmA3C7JXqarlVa46dzVZclMQUJhIOUW6UbZs6al6PueK6bWNWnrE07JsPzSA/xw47x/CiEarNEScTceCEihf7RixElbCPFCZsyCDfeDKL6NmaxqqE6akK5OoVb49mmr3Ot/WLLW+y+XkwIn3aZPvY3pAfc85EPd2d/hlkm39rKK9Z5j9SWt6m1l63A1aud8TNerJIMfXgtU3a9PouZJecLAC7FkiY6tenPok6nliFsnL0nW6vUrl8XPD2rAjOqNI9FDCwWS7mSlKWNgGM8XFer5X8o1fHBFyo42XVqMXpUWvt6f137oRP70k7vZPW7cRcD3QzcaYcQxoqQthBC0vfyvsbedz9BxdtozP6khSBYJkifkPlcDzpbpVMbbnkoi1ei2aj9UyHr9dFnwnqMkazC/tq9mbVX9qifa6SJF3g29ludoTLdKqRWshsFL0lJJSiXs7ph/sE45qPWqwTFBiaD8co9UAnncpVzDela5bn+ybX0NST+/bdmXSgfh1azlc5krATzujPo59dHEuPEN/PuNbVzZsWWtEOJXlmU9UcUpRxgBjLSl/Vox+DQNF61mSHkOTNa0SpiVWLUVyRUZb3sm+BF3pfKIJDI1o50KfVCSE1mgJMB3pJ7lK25xH0I/lzTdK8G0Xe6r1iJ3vTsci1uSjfp2IPe30+X+XsV637cEE1GaCDvM5KNqbZvOU9eyTRa2H2FL75VykMevYr1H05btBbkyyjJBPvZ+KGDn8JbRv7p+LucJumNt7rXZ176U0974MLePf/3jRJOSoxYjRtpCCMEpbRtjl12KaGgAzGTtp2H7TUzqx3qQ9SmY8f5Mt/aWWDlhLexK5Bu/OpOJAjiErp5DibyTtYNnJOHp6UNVBD3oprzQ6u9KoGbIUy1X1Sdbz7dRjoRcrwofUqxG61X7ERSBqPfXD2rfdKlBDZRRA2rkZGwfTe6gq0eh+tVZ6f9Gnvdq1tLdWkwEBhgzD0rXxdkfO4ktp34L8c2vN1mWVfloEWHYMWKk3dDQcJ414RDi3NcGWqeSBFXCctfTq0SuyCrfM4ZtSt2m11LV8q5WItHrOpvJLNw/k9sPDPGrAwd9y/tKP0sHfGWRoCxyKvyIvhb92538cvyA9eAePXFTmCx7EF6bL+dnreddCeOpEUTY5a6xGtKu1yUnMVXpSz0/vyyA1aCFHlYNrXcHGJn3fH1sFS1zi+d/DZe6HjsvmjvA2W+bxSPjjn+MI9zaFkLMBdYBxwGHgOsty/q6ECIB/Jiig+2bLMvaI+zQ4K8DrwGeBd5uWdb9Tl0XAZ9wqv68ZVk3DVe/R4S0hRANNL/4Z+Mu/7gbEl0NdEtUtXJLiC5jqEDbpi6uGvQg6tJJ0ISb7sYmf5/NZL5pzWbKRMFFEywu3PecS9xBg4Iq+XQkOit+VQ4TFl2vCUtdspHtm4Jj9D7qRFfPfqkIe/3ChpQHQSd+N3vgUIF4ftD+nvIGCZkSUdWC+JZB4tJpe4lt2V/F5Z5gpz6aPIE3b/vobC560X2Ir4qUZVnD54p0+HEQ+JBlWfcLIaYC9wkhbgXeDtxuWdZVQojLgcuBy4BzgJOcv9OAbwOnOST/aWAhYDn1bLQsa89wdHqkSPsCa+JkxKvCJxVSyaqWCUG9LhVy0VQTTJaWqtmCP3nr2wv9SRZOnsCUifaANUUIzhwfM1rbJg8Wd5JUcbcr19dKUIuuLY8PA6kDmxYDqLa9amUDvR4dtRJ2WMTzNqlK8lZRybmZol/7aKJ3Sdpe7kxDF+3IBSHypFjLatflcubsRi5YPYk9g5Mf4Qi2ti3LehR41Pm+VwixA5gDvA44wyl2E3AHNmm/DljnuERuEUJMF0LMdsreallWP4BD/K8GfjQc/R520hZCxDhh/oZxn74MIYTRL9kPskzQRCCUWtkmzxM/bw4J01p/Jp1Y9bdtT3QZAykk1H7ffmCIiyZYTBGCZyyL2w+YI4ZVrxFZ52AuzqLWu0p8ssM81EGTXcMBvzUTwWxp10qI1ejxcuDzm6z1Q6VE7nftC7EkpOw+SIvbhFoGUzVRVdfcdve3XNxBuiGq3iSddJAiz1ncxrsvm0rH/McQ3xJzLcvaXVUnxhCEEBmgHbgHaHIIHcuyHhVCyBt3DqBei5yzzW/7sGAkSHulNW0m4pVnVnys6mutB7VIlCNsdZsk6iAS07VGVaMtkKyaALdOzfM+JnM6k7lbPMvWqc8afR5k/TIftTw/k3uaLkNImBL7V4IwRPgi3kqKReTZyhN8xVhGkoJO1n79KUeKpvMdLitYn0iUkFJPkvC5T4IwkGosabdWmDxP1P/lKtaznlVA8T6TS5vJsk1JePO79/HY05N2Mbat7VlCiG3K7+sty7peLSCEOAb4GfB+y7IGAiRc0w4rYPuwYFhJWwgxjnkn/cBkZbclul1XNhPURPhBCLKgTYnl1cT3QQjjUuabMc/HffBWnuVWni3pn+q7KwNoJPykHTVUPQhhyK1cmLe+/0W8lQVO5r9pZNjFMzzMd0vaCZKYwsBvUFKhej/UWwMvdy7qdtN5hfU+MSHsuYSReEzXpwMnV0rCJm5533XTxg8Sb6OPJi7/QBcveeEziO+IzGEJb28E5tVcyxNBYexCiPHYhH2zZVk/dzb3CSFmO1b2bHCtpRwwVzk8DeSd7Wdo2++ouec+GF5L+7NrD4jffY+GZa8o2VXu4Q0ic339PFOghJ5AybR+X5gHo1Yi0IlZt+DcgSvhf00a0wMlVrac4MvHHJ1dWfmbWKkHQyVQ/ZT173bbixCOcWET9yvBIW0TKiU0db/qDy2/e84VIGY+h0oQJJWok6kSOumW0+lHUqaSbbl9Vq6PmmVQBkfJpc0AN44gSYFtTa/mXf/+ax57rOGfjG1r2wjHG+RGYIdlWerr4kbgIuAq5/OXyvb3CiE2YE9EPu0QeyfwBSHEDKfcq4CPDle/h420hRDjOf54Yt/6NlCaY6PSiUU9UlGd/VYJ22R56PmYpdtVgSTruDBU+ybfZvVB93sgg3ypdTLzuyZ+S22pULXRODmYW9urdlAq0zxbmUbGzbH9NP9nrCOMDBIEP6LUids0wVmt77kfYcfzgyVShkTY62yy3FUyN0VC6v0Kcz7udYh5r6EeBSkntlezlrWsdve9d/sNfLL14wC8+dL7eNVJecT3RLNlWcUk50cGlgCrgB4hhPRK+Bg2Wf9ECHExsAu4wNn3G2x3v15sl7/VAJZl9QshPgfc65T7rJyUHA4MW5a/cV/7hnXof37B+J/bg1S5wJggSC8PuZSTuiKInrNBlwyCrCSZBa+HlrLLZQW9hgbJC/qDV84nVw0BL/QnaUt0cynXlNSrP+jLdm+1by/ndbJ3brosmZhyawSRtYrjeQ8zOZ0nuduVRsKgGsL2kxJMZWr1c/ZzV1RRbkK1GlnIT+oyZRMsN4Fa7hrr/u8ysZWUSOT9JxdYOPjpq8n+0+KH64ZG1Npe2Cqsbb+urQ4xL8ryFwpCiAmk5zLuhu+528IStu4yl0wUc1LIm0gNjDBZnSqhmSwO1TKTkJ4hYWUTFWp/pOWvJgmS9en1Gie6FMmnI9HpiTb0lFNeffOk6J2bJpnyJlsqB79owHJ5nQEe5rsVk7VpUk8nQBNJloPH8takElXPrSYcXL7B+FnZso1q9oUpFxSxWa10p88DJCnQRjd9iabic9CfJJWwn4+lHzyV65vvRwhximVZD1bVaIS6YbhI+3xOPJGGly1yPUBMCZl0OSDIH1uNIpMTgy30GPMrQ1ESUUnA7xVXPgTSFUpdkNUEkywjsYCTmcGr2MNWdjiShjoQ2Jn9iiufq94q+huE2jeww48LsSTNf3D8budhu445g1J8yyDMs61sP8stzORlrZN6prcd9bNcsI1EmNwean3yu3qcHjpvskKDrPpK0sLqqKdni2nQ8RuEdMklzNtNCz1uf7/CB7kmcal77D+ntfPW9/ZSeHRoJ0egtj3WMDya9tLTfxC76O0AnuAQ8CcNqVN30uEhb78ltDwk7hC2TIQDeKQCFZK49YdbJ0tTm377JWaziAV8iBiTOI7lPMWXeZStnqAYNeeE7LMppFpKIGr0nOy3xECq0d6XKhD/haNpz6udLMK8Eaj7JEwE4een7GdRq5OO1UIn4UonAE1vAJVESNbbDbGaAdSklZuugzpAy+cP7MyEb9q+kYtbr6WJPk6/+AW8o7UH8V0x2bKsZ0sqijBiqDtpCyFOYOZMxKtfU7JPt7J1y9rV2Jx97qKljpatWp8y6U08P0h8V45mck5sk4PZBBI34Fqp6uSVmsxHhcmqKc2Y10aMSQDEmMQJnMwhNpV2wFCfnllOJWsdvUvSLjHpbw7lLMNKCEX2KazFHoYkJMJY2dV4nYD/G1UlfamV+OsJeV+Gka1UVOqvL3PIyCXS0q293Lj9Ei5uvZZUuokFp/2TezsH3gD8oKoTiVAX1J20Gy79yEPs3YuYMAEoTkCqOT4kUauELTW0ZKLAV/igvc1xPTqL24IfmvuU7/K+DOHfKa1U6TYH4SZ2dA8Fiee5gyHOJMYkDrKfPWw1tqu7hzX/IefKGq7MIQeg2c653ANxBmE2FJaU1jlwXqOnb6a2ysFk0fm5/wXVWUmbOmp1jZMDnfpGBeGlFhMqraOW8w+61yq1uMP2Q61bXbKsnS5SrcUFmM+9+FgG9x9aT0TahxV1JW0hRIw5acb9cIO7rVyubPlbQhK2TBWpppGUkA9kIZa03dvOw7aqJSp0yNf1v3K5kqW2XIof00c/kzmdHH+ln7uNx+sP0sBim3BLrGv5/KpvEI8WSSS+pSiJ1KK9lkM1r+dhPRjC1KGWLUfqrmQERlkpDPEGyTdq36p9EwiCfn66G6O0uKuZVNVhqhu8k/vruJA+mmijm+blJ/PP/8gihDjRsqx/1NyBMhhqFAykxtdYi3+agLGKelvaZ4pZs2h4cYsxCEaHun01azmL4krR8sZVX3XdBy5l0HU1olYfXn17ST80Twxdt1bJ3CUEciV1FWJJjhm6GbiZibEkbdokqGxfX6A2ENLSdqQe2aZ6znKbLku43jMhEcYroZJXdD+ZpFyfKrG2K5VC1ACdsJaz3zyICcMRVu9HrpUeqwZ3BUFNqtVBJ9200U0bTRP6WPLWuUycOq6XaELysKGuftqx895gxc8+lZPXvBKww2P1sHL9pm6ny10b0DTDX87/1ZPBTFrbZSxtfRBQgyf0VVJU7dyvnnLQj1UHlEoIR4cpEX+5aDzTQ1utb3O5xQLK9akcTJa2n+80eAk8nh/0zGmo11m/bn79d99otAHXLyCmHla2Wo+uq6supNVY2uX+T7JuHZ10uOtZxrf/gavOvYcnc/vHWZZlznpWJ7QvbLDuvKc2S3vauMHIT9sPQoiZxKcxee0ngH0uYQfNuF/OVZ7JRb2sfnPq4bkeMlTlER/4Wd9yH3ilD0872qRmNWRbC1mrROMmLVIsP78IOz0a1PTgmggoDNSJyqD/c5iJSROC+qP+H32vpYGww9avWuT68fWYlDRZ7Wq9+sCUHCpOmlcrjcj/U1hvEjmnlMLWtfOkaGptZvpx3TyZ23828L9VdSRCTagbacf+64tPWPfdS8P0OLCvhLB1qIStB8jI9KdBkY4QTMIm6JNUEvLh9HiV4G9dx/ODoV/L62FRQ3UucH4WWz1Ryat6rZOMso4kBeP/Xr3GfveGKXLSz1o2XXM/P/BKoA66ar9qcXMMC9P8gK8briOTyHiEFHmSFHjlO+Zx7AlP/JZIIjksaKhXRYd+uJ6Gf3sb7XS5N4CqqaoEvJq1rhyiW9JdtJdsl1Ct7ErJx0Saav/U+owDgaInD6Qay5KwJHa9zmrIO+y5hiEPP2JQX72rmXg0HeMni9Sq+8rrEfR/CEvYpv6Vg34Ngwai5FChJPgnLNR7KJ4fJDkUbAhVCr83MNPzpy7MvOQtc/hz5+MIIWbVrTMRQqMulrYQ4iXMm4c4fRlwq3ECspghzg4m0clavmrrMoncD6WRb+6DaZJGDD7auvWlt6PvD0OwuoVUTvsOQ96VRAr6+UqXC16pB/R8GH4ug37H1APq9Te9/ajzFxWFlMcqI9iwZKpLb0HBRB593kFyqFC3XN7l3nz8/ldTpo/npa9tonnR9GjV9sOAupB2w8Xvuk8ceyzts7Yb96s3x4WsKxtYoiMw2MSPsBWEIV81WCVIcpnAFcQazuVpcQd7+FKoB1snE70/+n71gQ7ziu53LirCWJm1LG8Vtr5KV4sxQfXw0c9VXku/icdK2pB5TMqlZQ2CX1nTHIUf/DyeJHkHJUTzg99zph9jykXTRxP/evE8vv/+vyDeL4Q1XFnnIhhRM2kLISaSSDD+93cC/a4erWbmU3NP6Es9FUi6EYh+uSmMhK37Ze8yfHcQpH2a4Ld/AlfQ2HA5QggS7iIKHy45Nqg96U+th6ObEPQwl5vIUhHGKqsm/3S9reZKoLrthbWIK9Gf1WupE2w9AnZUhD0H01ta0HF+HkP6NfAzAuQxJqPq0BlJntt7EOAleMPbIgwz6mFpv0q88EU0nTox9AEqQfgRtoRL2H7eIfO0T/27fpyzz8/S0R8MDwE3vQZiSvJ/6wxlHRr/9f7i+UEjWYdBOTlF9701WV3D4TsMw7NaeliY/On9UCvJlpswrAeJV5pzJUjGKxnMYt590kLXYfL60XVveXxfrINzVs2g/9nZ2xgmieQg4+owMJYuajzWUTNpN1z8rl+KdDEaT410NGlmcpkvVdfWCUcNZggkbCjxxS0hzkexA1Q0mF6rJYz17ALim2B8KwiBZVkMHQqX7FdP9KS3aSJk00PpdwP7XT8oP7F2OIm3Vmtdvx6mYKeSScBYeNlA3r9h5hikBV5v7xwTwsyLVGIc+PVZvzfU82uij5NefQI3/Edpnp4Iw4uaSfvQnXeQ/MmXAH83Kgk1Q5+axQ7MN46HOPWAmXucTwMhu/Ah+3Luer7+33/5JLwYmLScwdhveJ4rPBZS2AnHcm6KOmGHIQKT78tNnBIAACAASURBVPpIEEitGA6ZpZbz1uU8k+Fhqn8krrVuTARNeqv3pUlG8pPX1Oe2XPRl86LpPP7wswghmizLOnxa2VGGmkhbCDGXmTMZf+oCd5sMX5errqhoo7uEsNWw8BLoEY6mrH1KXo64Kc+ATupOHUZSDZJgZNsDn2TgmM8B3gdVfwAKcz0/Ay2fSnzNw8DPyj6cVnUQapmcLDdJWI21raJsyLfB6PCzuMNY4vXy19bb8quzUr9ztXxsXAMvPGMm237Zdybww5o7HSEUarW0z2pY9gpEg9fdW3X1k5ZKB52lhL1FIyuFkOP5Qa+0oRPqaco2NaGSrm37aNpqkExgeWVfOZlChRp9VtYdLLEBJp4J+2+H/pXuZjVsGsItIjCQaoTYT5nI6cznXu7km2X7OpYRJo9LpcRdLjTdz6PH77fsV7n7Jgyp1xJV6+elpF+/crlO1H2tZx3LMYnGm4lIe8RQE2k3vPH870075yXGferNrhJ221B3eZ0avPtNniEqOecppmQN8CJREdp9cJ734QiTMEgPHQ9EYgNMfhMIYX8C9K80yiKuv7phAk6WjfM9juUsBIJjOYvTmMgmbgJwE9zrx+sLTRxOhJVLwkgW9YaqcZvyktQDlXjElJP59DpMmr9aTk+LoAfGma5x69nH8surexEicv0bKVRN2kKIhoZjE0z48ns92/WHSU212jbUXWpdaxhINRbLmKQN03cVJ98FiYWwbxuwLPgkdBiCcVRUQwzyevhp38c0nEmDcCbfheDQ5DPZN9FrYevojrX5vsamWYSg6OEyg4Wsw36W/FKJyoxuMgn+WINf4iw9V00tUKN8yw3I1Ugc1UZN6vAbREypG/z6YSJuP7SdvE/6jpwC7Ky23xHCoxZLu6Vhepxxx89xN6g3cws9LgF4CFtN7q9iXhlrJchyTjn1vfguiC+1rdb4Uvv3X5YVj9dQzjoy+eeWI+6ymdRi+p4/MZXXIhBYWOwTfyrJNBhUn/7qWmA7c1nq1ncHB8iT8l170yVsZ6UgmSRotKOc7zHUJ7FTWO1bJ0uVuP1yv1RLzmFy7pRY4buKcz5q7vVKg7f06yGEoOWsY7nz+7mziEh7RFB17pFpX7qse8JZL/eVAi5kHR1Dnf4W9jz8s+aZUqvuwnbhN7nxywFgykKbsMH+nLLQHiS0dvwi5gqxpOcPYAYfJk0nE7jC0LAXYTRSPfdGgTXs5VcM8hSPcxvdfL5sO34okOSzbGczu3mKQW7jcdZUQMAp8nTRTg8tLpmb2lD/hgNhJ0xV61dFUNIn+b+tV/4TE8qRsZ6PpFz9fnMXFUkyj5o3q/d6Sbh8yEGl9exjeeny5JE9eTKKULWlvf+2P3LMe4qTZuqDciHrXO26LaURtsHCVuHeOKrHCNg3nfTg8PG9Zs82mOVY2pZl/1brsDvqQdAk0Qw+TIL32VZrbAH7mAJ8qaRc2AktX7mjSqJWyU1d8f1L3KPsC0dOMiFQE3100U4e77qcUPSxl1bucEZEhtW2/dKNBhFOLYRtyldjQpC3hgq/IBnTYFOpB5LH+j/N2wc11D1F3jcDZpi3lZYzZ3HDf2xHCDHOsqyDZQ+IUBOqIm0hxERxzBQmbPgasK9kfwedJUs+udByHAclrvcQdl7Zrt5HKnn/bRk03mVb2M9ss38rN6tEWM1xijOhB7Y+PIWz2GMgbQi+uXW/X/sUarP0/KxRlbyrhWmAkfmUVeu6iT6PHl4LqlkDsRzC6rjVwO/+qffEZFBbYRHGpdSVXHZprrMpb9vqeqpumHuyiVSmkd4/H1wE/LGmzio4wPg6RPMeeRGR1cojLx//omYnd3YReVJcyDrvTVZm7Ubjzb0LszufCfr+gWXw6GT7U9PJK32QnuE2LGcSz8LiGWU5NAk/bdV0s9V6A5bzSvFbfCAMVMJUz0nKIOp+mVu5z7XNm2qSSqRFXc6y9sskaLKy9SCjMEmUKkFYN75KUOKCWit24X2W8E9R7JbHWz5sfxaeHWf1FXP+UFU/I1SEqiztqR/999uJNXhm6OU/ftXQ+lD/aGkFqZ+Al9jvUb7LZ63c29ouivJJmZVLykFa1VM4i2e4zdfK1lELefohiKzrYV2X62MYQoXaLW5Te/q5Ba1TqWZrDEphWytM+UjCRivq2/SylSY4M5V11xA1JE9T17uUz24hlvQGuJkC2bBXdpIT5erg/qqzD/LVz+2DT4fuaoQqURVp77/tj0z/0kdKtrsr0Mh/uMHbw5SISX+NdffNxt/SVn2zUdpTypcLAQ9jJe3hS6HJ+nCiHla86btKwkkKdNPmS8zVEreqX9eqk/v5to8EjPewD1SJrtIVmILa9q1HMWbiuxxCTxWJ27PWagWQ13fh0kYe6n4SIcRUy7L2VlVZhFCoWB4RQsQO9DzI+IUtJVLAKtYXCxoiEf2kCr/E9cyjdMIxhZes1YjJedga9mkwsDi8O18l8JM96rEiS7l2g9qo54omct3HkUS1q+WYovWG8/8h69Q9jBpjXb4eRiZPD92tzt2vyRlQSsQVySimtA+PAvcUV8Px1cx3mds3Yc/kNCecMg7gheE6NjoghHi1EOJBIUSvEOLyw92fMKjG0j4h1jSLhimTPRsL/UnaE12hkyGpS3eZJgY91oeUOky5SPBuq+cEkAkmSWik4EdsSQolunKlfTNNBKoWcznNWm2vjyY35e5wQ18BaSSgygK6hxFD8LxG3kGRiyX3vsndtQJ4nhv1+VDfWOX4/nWILx70GkZ+nlkK/O79ExeM5y/3HViAV9gctRBCxIBrgbOxZyzvFUJstCzrgcPbs2BUQ9rzx81/QcnGVYn19s1XJnS80oVxffNka79NdQ1XaHMbn2AipxPnXnbyibrXr+csyZMqa4m20FN3LV0G2kjN3LUy8a4Ar5bXIReFDYNKM/6N5CIMfkvgHcc5Hg+jWMO5cOiKwDw1fpZtpTJJqGdIJ+E83md0C/Zz9FLsGIiU4RgFftGSfTTxgvk7ed1lzWuB74c+icOLRUCvZVkPAQghNgCvA0Y1aVcjjywYv+DEku0Xsi70DSdfF9VXzDDHlPte72x5EuqrdpLrmMpraWQ6x3IW86v0sZ7P51lMZ8XHF/01Shdf7aATdXUgwM24WA5yUJDnKr1DemhxCVt+D4L0NummjW7aqloRZzTCL4DnSe72eBg9Le7wlJPyg77ijZ7oSv75Bc2EvbdLyuUpWtk6Yau4FpvAy0AdcPSBLLEgySM7xpScPQfYrfzOOdtGNSq2tCetfuMXxxlIe9nurWWPDZoY9JNITHXo++oxkWOCyVKdzMs9ltVMlrGYTp6qwOqez+c9SZ0Az7Gq/KKTmGp9Q6msUSJLJOyPcsTd3d9GU6LUcjVZz300kaRQ4u4o90lIbbxSqSQMcR/Opc4kUuR5mO8CMJPTeZ7f2pPWWiImU25rCbWMvgSd3z3tyc8T5mVKTtrvMmwjYLsBpudX/i+emz+JR3aU89EdccwSQmxTfl9vWdb1znfTijujPulVxaR9cMc/mHLReRT6k24KVvfBVRcmMOjOpjSjlaASvbqe0oja12f5oydXSAONxJhgJF8/TOdlHuKfzstKypgI24+oTMSta70yz3kQOvs7SCaKPth6/er/rpIcJfUKwFFRr8UTTOlzK5WVHua7LnmrR5pye+u/TflJQsFH+1aDZIw6tgpJZQuxO65b4gHatukazWmewJO7nkUIMcGyrOcDeh8KBxhfjzevJyzLWuizLweome/TlHcqPuyoSB4RQogDOx9Ct7Qv5ZqSsgOpRs/EoZqkxg+qXFIp6fbOTdM7N12R5BIGpbptMVfIIQ6UJV8TnuJezyv1U9xrLGdatd7PK0IvKwNg1O1qnnM/FPqTdPe3uX+mwUPVtmV/TL7icnJULvY8WuFnQJh0bL/rrwY+VUL6prwffjBFGQceJ0m4XBrkvP038AsYkDKJPHXFg0R6m+iQ5z2+sYGm4ycANJc9mdGBe4GThBAnCCEagZXAxsPcp7Ko1NJOCiFomJWAPcWNJRbPPPtmjM+zfT8lYYe1sk3EXY/0mpUgOJ/IGvKkPDJHEPnqkNb4dF5WVlapxZqUk4C1erqYjpWWbphISJXQ621tQ23XyCTxyOsV9prp1nqlb5E6GfuuUWpXHh7lyDqoLnnsSzEG2vid4ykLYPffmA/8NVQfDyMsyzoohHgv0Imdf/N7lmWN+n5XStrzxy04ESG8UlDbUHdJwTwpmFv/sGEJv3SX1UIfUPyITt2+k08wkf1M5uX0c39FniR62eFYK1EStkz0VA2kpBLGSjdBnlc3bbRRvE9Gi1RSjmD97gNJ0tUStUQoY0QPK/eJVvRAnXxUu583fHekkfhplMZBUNqWrsur1+fEBeN58cLGnzJMK7TXG5Zl/Qb4zeHuRyWolLRLPEfa6bInRZR/bO/cdMU3caVad73d+fysq3L9qiWVqopaCdtP+2uiz50IDKttm6CTt0m6CeqbJG41b4nsk9TH9ayCIwG//29YyWQ4YFxYWpKwltLYF7MpkrLfJ8pvndg14vabT5LXT/4/XzD/72zrfDpEByNUi4pIu+n/nf/t/XO9Ptquni1vrtPKW9eHKzilFozmvpoWxlXliHa6XBkj7HmolrWcdK6G7NU+yr6pmrjU6U2Tm1KTL0fkI+VJUglhhzVCAjVpv6RpWpCZ7q89kGq0Q9Xtjugd8zq5aQtQu6gyyGfagtn845o95QtGqBoVTUQ+t+Nhxi040fPw6q5+d81dFKquYM14eBBU9+Ek5WpnyP2y3oF5YtL9HiB1JBMFj1dQirz7u1qJRO2PKimoHil5Uu4CDHIRhjBBRbKekUC5+8fPl9vvOFcaCTNZ6APdr9sNcdeJ3plsJIVN1JKsdyv71c+XAudR7J8BupUNMPeUiTz4kL0cYeVnEyEMKrK09+/cxWQ9GlId9Z3R2WT5VYJa3AJNdYVNZ3o872Emp/Mkd7suXCOBSq9RkCugSd+VkoRn0jDh77ttul7S6jXVb0rrarL41Xp7aAkkQXlcveSIWlz6TG6BKtT69O9ykDIdX3FsgY8LnjEyUu+qfsq7sYl7N17LW0PvknRFTgDPTJtDfPr9PPMsaaoeiiIEITRpCyEmN0yaQOz4OWCQrAZSjXTH2twoOrD9hWshcPUBCHpgTCuXVFI32IQ9j9XOYge2x9JIEndYlLue5a6xZ78PcesEo5KwKlfoniN+rog6YXfTFvimpRNsOYmk0vuqGmmu1sFDP95jZUuYKO5R7bv6O0jC2IWZuINOY7dSTlmmL+yiIfJ+OP6UCTyaf34+EWkPCyqxtGfGEnFEzF6ZdjAXtx8j5x+rEraccKok70Q5mCwVE6n7zfSbvquYyeken+s0/waMTuKuBn7EpmvVatCUp5zh/yjzkpRLNqUTdhftJe2ov9Uwer/7p9o3OD/voHJvZH71jAj8PEB22dt907KaSFr9HWBhg3fyMUzK2y7aaaeLmckGgJnBtZfHAcYP2zqkYxmVkPbU2NRJ7gPemB6gI9FJb6L4+iQJWz7A+montcJE0n4+tpXiSe5mCs2uz3WMicxjNTC6iLvcslyBCwQ4JFuyP0AqUcuZrq1aZzmohA3lQ+ub6DOSo6qPQzi5I2wZP8MgiKSD7jnTPasvmFArSrxNTMvyqdgNA3mI6x4i6jbDMn3lrqEMpJoydQPA1LIdj1AVKpksmBqLT/Fs6KCTPCl3JQtJ2HJSSf4ejomiek9kPsx32cVahtiv5RY5veo+BiHB6ZzIh0jUsf5ywSZ6MqlykPXIYyqK9NPSxMp7otCfZDAXZzBnL1UnJz79JjnzpMr2uVKvjkoCZ4Laq8vkdTkvjdmYg2BShmPLiRGm5f70SzcXWFwM8KlkcQTph/9E/ASISHvYUAlpx2NTJ3seriQF2oa6ixaEk0QIbCtKruotMZyz/LU+iGATd44fekLMn+TuenTPgwSns4DPMYc3MZ/P1424gyQDKVfpnht5UoEWr55TW/6p28Jk/uukg9z2ZpesG9MDoc4pDCHXy/PHbwLW1FZd2jRM4htJ3LQQiHq8CfPwkr36fa5tUeuEHTcF1uyC5t25kvNVvYB0HJw6HSFE3LgzQs2oTB6JFxc+GMzF7ddqR+tSZ/u7+9vq2cdA1NtVT83aNlxeJDNYRIxJAIxjIjNYRL8yOFS7iov+3SSlyHkGuV0n7DBufSb5y1NXojiAyFfm3PbSdBR+ban+2UEDUT2s5WrKhpkjqQRu2LrPEn1Acek9gweJcY3VlPKnb/c79bm4+UriWwbpXZKm2Vk3Ur0GMiJSd8mU1yIT7+fB95//KaIVI4cFlZB2vGFqkbQb0wOhJ4NGQxrNSqBmbRsO7GErx7GcGJMY4jn2sDWUv7WpTFAIt2lysETTTpQeFxTUIuuUSaD8SF89VifsdGtviYeICaYIyXpl9qvl2GqJukQzn2eINFQtbX2lJh2OJ0n8Fw5hqzr0aRQTRkmr2+e0XS1bugHm7bqTQwV3QChZ4d4QlCP/X7dNHcfecC9SEapAZZq2QtqXJa6mbaib5FBREqnHjPqIzsofJvRzNzv4JI/wE3bwSfq5u4SMTIscmPyjqyEx3Z1P/wvr9eMnq8jFGMBO96oiLGFLIQa8Cz/UE4HrIwZAvVZB2ypFSa54PWRd/pZuf5KkZZa+gHVXAa8boCOR6JORbn1b7AlOuTCDStgDqUbXyl7PqpLUu5OmjuPZ3WMi9ciYRCV+2nFVHpH5LOL5QU8o7FizquuNsAE6/dztkUTCwi/AxVROwk8i8UM5n2jftSoTdsi8S9h0uBo2hCNsOWiMtcG7nBugbqGXyw3vm+lPi3SM/2LQo0Mb6/V7MXCCazzEvVv5PA/yc1N2/rtUwQ3icbNwOmTdRTsXsq4om8Wb4ZnI1B4uhLa0x48fP121tIHi6hkOWujxrMhezYM3mnN8QLDeLAN0juEk5rGa43lPRXXXy6IMImxJyOqEpLpP3V/J/08StvQg6KbNqGNLBBF2G92uUWB6u6i3R1IYazso0x+Uv9dNpK7m0jatyCR/G5cgkxa41LhPMyRRkx4mJt9s3UfblIPkF47HkaNhy3z18lq4Epk2Gb13agqeGVPLjo0phCbtiRMnJmLxKe4rcRN98Kh5ZG9LlKZqPZLgRxx6gE4Yd8FKyKdSsvJzAZQTfG10l+xTydpEVB6SV9z1VMLOk2LT9gs8x0lvET8vH9Pko25xjzRR66iXQaEv1KEGx/j5b/tmtZwHzPaxsPUFfSXKBNUAJSSuu0rq/4v1rHJzxmSnvhhxIMr0N1wILY+MGzcuEZs6yY2gC7IsRoNEUu8sgn6EoUoVeoBOGHfBeq0+HrTP1HfVqg5znVRrSroJyqXJZH1y3/r+VWXrc+vVIiOlL7meEbDe0BfW9UO59v0GoNABP7HSYBvT9zi5ojQSsAyYB/OwV1gHc1i7ibzVRFJvMFfrNyHeSQdN9BGLD9HwzFMhO+mPg4wbVjfhsYrQpN3Q0DBd9R5JDhVgNm5gjap1dtBJJx3IvBESI03m9UoAVe7GkcRdb3fBWpL7y2N1Ddmkb4eJdNNhcteThK3q2GBb2Xp5PT93Cz2u94Hs93BKZWEtbf2tQ891I1H3vqrrrUJp1j4VjlSiD0JxlMAYOVmZ9/pou3p2GOu7DKQlfuzUBxB7I3lkuBCatC3LisuIyGSiAEOUuCJJ4h7pRPYmzODDJEYwAZRK3CMxQAQd104XbUPdJYl+khTcHDFh2zOhnS73WJXMTBq2JGyd/NScJ24K2ID7plJ3x7AoZ2XrmrVJ3gkbIal7Wfm+raq+2iayVvy5BxbbK7PHKerinpVlKk3ZJN3+lGPDLjgiB7NYfDJDA/sqbDhCWFRC2sfEjrEDQuRDGwRpQekEMZzWtmoBTeCcEn05iEz9rPJ6aMiVHGs6Xr1uQSuy6/Wor93qrL/6VqTLEDrxyIUJTMTUR5Mbll4OJfUGRGFK7d50Tqay1VzvSiSRaiSSqqAueuBnYTv6tUrSakY+FbKcCaaISBP0pcWgfP6bhgmNYIEQotGyrPolWYkAVBZcMzh9sMAAxRwDQW5LKoEeDuu7En15tKRlDUPIYV39pJUtyVpajfrEnvp/MRF2LQgbqq62p/ZnuPRMPx06bNl6QF/j1CNlgNnCno1LzuVcBl1oE5BBSaJcyURa2ttkFd6D9P+L/tsaGsIaOgRwMFwnI1SC0N4jDQ0NAwcHngOKPtrgf7NfyDr3+0i48en9kAmg9vF3drE2kISr8fqoJ8KSk57dTsLPPa871kZ3zJu7unl3jubdOdqGip4jel4SHQWSdNPmaUuuLONnZUtZxKR9q3q2mqu72oG9FnLXZY/hvlf9rrGHhGdjnmyc531jAmXS8v+3d+7xcVR1/3+fhqbltpQFNnRJy6IFQX+piVSogghaDA8qiBdApSD6eANURBQQihdEuVm8gqKAtKCAPiJU4YlUQawPUMAEArZAKNt22ZJtCW1aSps0Ob8/Zs7smbNnZmc3mzRJ5/165ZXd2bmcvcxnvvM938sq4znu3cRQ3o7Fzx3ls35p0xQm7LYzUsrBIRw9JoDIlvbg4OCGXTa+HHnHejYbFK2o4XKR6P5C9TiqfznIKh+KGER5n7USG32ZrRSoIjVQKN6Cp6F5oKPEx20TlQIpXyd1vWKfDdOPrY/TJti1uAur9ne1vfICyvqJA9wiXmKLmmxc5Vromnskke8rppmrOO0IrpCS7MhplTXQVp/l2lWTYfe4yN9wUYlov9q/cWvJ8rAffQvtniC000IrbVUMsTKqOQltUR9DvTWPIiDVtBnzrFL39jpf53+/zQP+GHnlJvESONxJrMQjToGi9DR/swHTf95NQ4n4qs5EJuXcIWbESBBRfNk2hjKnMFIETWIW6lIkprsCbE4eum4RWyMCVdCJRyExta/Ut30o8Ec8qzkwegRtmVpQbUTJxo0M7rpHlRvHlCOyaPf19b3a37ulxBKLcqKMhVjLWhWJqqVgDCWV27tNThd8y7zJKbeZbCpdoKEuOOrHzK5UbhGbld2XS/jC+3SBMtfXrWzdRaKOs6MQtW6P6cP2Pls9Fls9x3iufNaPEhlbkwTwX1CD5jzkpk1QH4v2cBFZtF9//fVX+jduYSL+Ezmq26OZjpKJppjKSJP3Uoeps6+jh/l1TWsE/JNePuHW9lsuyqedlpJ05Sjx2FC+Q423Xvz7cNCLQmmTjzNW50p82qZVbkuDV991kIVt4kWVWLrXRGLTRth16O6RfiZuN/fVaKaSkL/e+t5X3PYARcx2U0fzA/ZkBgVWsVDzg9ayX+RwU42lFxbhUelte5C/GooRHUFxywAtde2eT1Nl3ekWd6EuRWFacIKJafWqSUgVlx01zA/C25iZDX/V+xvq72S4Q0uHC1+RKNtEpNsTEjTLXPd9u9uU+KFn47hI8EeKmMKti3p2C8wsM97AVnMbN8KucQ+E4aKS0qwb+zaWhlw20M15PfPppoGj+QF782Z2YhJTmcF3OXZEZuRHE0GCbT5Wz231RMzPTBXt8TLejBPF3IfqGKRnQJr1LoIK+evp7Uqw1f5t32N9Y6/3F6WBgpqATOHUK2mi0xeNpITA7JCzw6GVZdWtZyXqFdVOOcn9P81vaffm/bHa+uPMZGB2sA8+DLlpU00s7Rg7lcRp927t3UqjxYJJJQvczJnMY39f6NybSADryma7gRMr3cBsXmMxz3BbBcMaHdiSY8Ks4XLYKsJFvfg10O1lREKxGlsD3eTrill+qgSBDeXysn5vSSjgd4+Y9UOC/N76Ovq+y3WpqZSxam3rdE1rJJUuFF1eRoQI6YK/0QH2aI/edD2JdJ8zWWnGZIf9pA4Nfil0sji2tIeVSkR7Y+9G4Qv90n8guadm8NzMtbyZvb3QuU6ciUs9Ztt2IunJLZM4hLfAmBTuarFV2jMxozbMwvP6frwiTgOFEt+3LYU66GLQRKcXQZKn2GC3iU46k02e2yRs3EGUa/AwVMaqYCsXibKu9fKtJol8X7EQ1GzC65NYvuIgwc5ucSzt3tlFCz/IZad+k77fUI182jF2KnGP9PZv3OolYZh1LRpndvH/ntqHNXSxjT7+wzq+x184nQVlrWwzuWVX5lTzXrYreh3sKCVUg+pmBwl20P5MF4K+vWoTpZovm33+1PdnRm/oKAu4hXbfn239oFR4k6EI9nB0sBkN5El7LixVt9pG17RGp0P6KpyiUrNxqvG5X22g22Q6Tk0Rd64j1MIGEifZrXb9N6S7tRSFnpTjHrnpim+GH2H0I4S4WgixXAjxlBDiLiHEFO21i4QQXUKIZ4UQrdry49xlXUKIC7XlBwghHhVCPC+EuEMIETGltZSKLO3+3i2+BepLbaWNAilyzOBffA1w6uvqDREUtttWM7nlNRaXJIoMN8MVZlYulK2cACnB1sXZNrEZlNFoC/2zUc5KNo+vxmD6sc0kGh2z7vZQCKt/Md5EXQlxb7reEWyTgK/OJ+BpIsddZyYDHw5u/FAWp8LfeCjzdz9wkZRymxDiSuAi4AIhxJuBU4G34Hyyi4UQB7nb/Bw4FsgBjwkh7pFS/ge4ErhWSnm7EOIXwGeA66sZVEWivWVjP+D8GHR/qLLiFvExCqRoojPQuradUCo+ej85i4HBv/Bq3XUVDGt0UUmdEJNywqmLlDp5ShocGLWZFWaPP3ULrhcEMi1x09JSndXbaC2pg+2tUya8L0XBaqHVirEs2GHZrHpnG69zuyosFSVEL2oNbtxJypPC6woFjRuATZtgHIi2lPKv2tNHgI+6j08EbpdSbgVeFEJ0AYe5r3VJKVcACCFuB04UQiwD3gN8wl3nFuDbVCnalbhHNmxd/zop7KIAjotETXpVmv24kl+SFe9ntSbYw90n0IzeMG+9bQKgr9Og7cHcb5RjR0XFR5v1McyKhTbZrAAAIABJREFUe1YraJX25+IV1jciEZTLJCwyoZOmqgRbRY2Y32k1n13Y72I8J+YU6lLOd/Yo9pKrlZZh1QhKpimH7RyRvb0A461J5KeB+9zH++G/b8m5y4KW7wWsl1JuM5ZXRSWW9iuyfxuvre93fhxaO6ImOmmjlTR5r2yrefsaxQLS6xenuI5deCcJ/s1yLqlgmJVj87Ha/NKVNnQwre1KrUDdl+25HbQJSDMCo5sGf8U48yS2nNRekk3aXsbVHLs52RnldlkJtprYtDGexXaoWP3b5qTjKrxoD+tF110/TJy9kD9bv8gArHfUK7MAL0bfi51+JtYi7HNvIcTj2vMbpJQ3qCdCiMXAvpbtLpZS3u2uczFOxUIVHWFrNS+xG8EyZP2qqCS5Ru729oN5evlEmF56kqlZ5KEmRuRJ08wl7M4HEAj2cSclh0O4w0S0mouOjVqEnqlsRIWtt2PVuOFiJdXhAmimg+5kg3eBNeceVH9QsyWZ3plmuBkLNUiqxXOPrMKJv1bincdJZ58dsKHmHgkSbm/ZOZS4P4PQXyv0pJDbtiFXrAB4rtx7GSHWSSlnBb0opQyNehBCnAF8AHivlFIJbQ7/pa2RopPKtnwdMEUIsZNrbevrV0wl7hEmH7I/zy0LrraYJ81C5oZaqFHYhXf6okmSvK2i7WtFkPsjyna2x5UQZMHWOp4ZKHGf6Jaa2chVT4Yxx9GabPOs6TR5mpMdXgJNkGBHibQJYjirKG5PKnYLPkKxPVkV+ET8JEJ94+bYSuYnVq6EvfZFSrm5+hGNDoQQxwEXACcY7+ce4FQhxCQhxAHAgcBS4DHgQDdSpB5nsvIeV+wfoOgTPwO4u9pxVSTa63/7t0uyy7c6IUnGbYs6MaOeKGHr9fBvpHv3IJHIgb9b/aGjDXOMlYirbrHqQhl0e6hnLqp1WmgvCu4Q/Ju61a3ej37xaqHdV68kTZ5W2mimwyfOrbTRStuwWNij/bdQLWHvy3chn+7GUSsLWoXyBU1C31W6P2s25OxizZpKSSULHP3yL+ENh1S1/SjkZ8DuwP1CiA436gMp5TPAncB/gP8FzpZSDrhW9DlAG7AMuNNdFxzxP8+dtNwLuLHaQVXi02ZgYOA/W5attCZttNBOOy0VTcIF3cYqV0iSt7GZ/wNOA0ojHGD71UM2MTvCVLutGZNtCrftpFbWd9nUZkudiiCCokoUTXR6LjF1wTZfHw31Zmrh4hpNFOpSJA7Vwv7W4ASdqT+tPomHm4BjthcrKSA1DTi8+nNqPudx97IuyBxX1fajDSlladPT4muXA5dblt8L3GtZvoJihMmQqMjSBpa/smwdhbpUiZiomhG1umVdziX8H8dT4KyKCrFvL8zIDn3CLsx6ah7o8MXe6p9PJ8WsQ2VZ24RQj9G2RvasITxbzkK5z7yFdvKkrfHhBVK+SdJaJsToUTJhSUEm+npp7dsaTUS1sntn15fMQ5DHcZOs8S9P5PvgCei1WNpMc8Ra92VHbWNmC09soJue5Wvh1ms/F2knMVVRkaUNdG1Y3cvWrbswZ9JiFruThHqBIWWBqRM1is8ybLKumoI12xPbe9WjYswfux52pzc06KTJSx0v15JLFZQyW08BFYs12E9c07dtS59XrzfTURIpot5/LfzMulvGLCtrI0zYRzqJK2wcUXHaiBVI3GVcoIN2YXOVTcPfeR3g8PB6NEGorOc0eVYuex1gecU7iYlMRZa2lLJ/t8zePPb8nkBw12qzmIxukesV3GxZfuUYqT5+tbg42PYRZb9KsAEvZVz3YSvUhdETbGNCsRrBtmEKtsJ0iagxDWfyjI1qQilHg1BXgxf6GfXu81HAiBZJmNmRaeDD5a1sWx9N9X030I2UklXLt4Djz40ZJip1jzDlkAb1xdBJk0+YVUKN2R/SrOY2HjmY7zGbNg7n6yWvhfmse9P19KbrvV6NumAXY9aDO8o0D3QUBVunUsE2O57gFzfbRVVVAtRfUy4c021Sa5HUk42gfCLUWCb0s7PYAEp8E/k+X2SJzxWiUM8PrawfpI113YNsqpuClHLdkHYUE0rFot13cBPPLHNmIRvopoNmX/RCpRNy1VjbUJkIlLOch2pVH8z32Ic51DOFaRzpE27bOE1BCztZggQ7Tb4o2DpV+K+txx0obVAQhK3an62a4HCH4FUaojlarO1qfn/epHOaYksx3ZpWmZPurs1JSA+34FTv7Hrr51HJ2JYu3wOmj5vIkVFLxaK95orbzvjXsr0BJ6SrmwbaafFu381bpyhUK9zgLzVqirOZ/BH0ernty/1wExzmiytPuT0/bCeB+f5sgt1CO620BboZSsajrOxKxDpgXb0kaJiVrVDzFm20Bq6jT1TVkihzJUNNix9tRBlr4hFXsB/BZ4n35vH7sNXjCn3ZQRfltmX71zTcr5+J2mW4ur/xSMWiDSyvX+6ISROdJcIUtebIYXyIU/gWb+GTQHAVuTDKNUUNqtMRtk01FHjKF1de4CnfezB9gepCpy9X0ThhYXINdHtRG8NNFMFWmHMYYeMbaeEe1+SxTz7eRYlgAyRU0owq0ToLODQ8LjvsuzSFe/nyCYg//vpr0QYfUy2VRo8ALF/z7CYGByUTJhRT6jtpCq0toSiQ4jA+xCzej0DwbhrppsFremDW0lDU4mQfitiFRRk8ytUApJhJgad4lKs9CxSChaUSwVEukdSAc0fjFQ+qxspWqCpxULb7SRTypH13BypqZqTcENWWvrWl448kenRRVBKPBESOPAI8bqw8DRLTcNwneYqulK84d1ZB77tcCKL5+ivL1iKljCchh5mKRVtK2Tttb8HAitVMmFGcvTJPWCg9idQt9PEc6XMnvI3p3Ob6RVW4mElQIo4ZQlfuBzgcJ2YD3WQ5n6xvSbhgm5QrjKMEWwlqRT0Cw9CFm8ramqnqg/p3ohJuzOW1qMESxFCsbfNzHY2YE7pp8sWLdBpHqIsrFMVZsRonNV29NhvPwg77rk1hDhNxKSWvP/0ixJEjw041ljbvPgqe+dtaml3RNiv8qZraNm6852wyb4KLDwIhnC/7PrHViwZop4U0+cCON0HiXYmlUmsfZi2jJIJcI3nSXhx3YMSIfwNzkDXFdGc10O2FcZouHhVLPdKujLEYOWKzYE3DpOSCPRvn+/6jt5Kfw7XlHwamQtcR4YJtHtsck/l81bNbEBN3AlhZdqcxQ6Ianza33cWZSxYNAP5YXVVL2yasBVKepT3vWbj8OXhyA1zxeh9X8yp50uSemkGhx7H0dmYes1jAIFc4RfctHch1dJ9x2ATiUATb9sMN21/UspK2fo9gj4YIjBjRsQ0paJgh6eyVzCvoSTf672C0RGgEkScdmq4/0mPRHwfFkxe7EeF8f1PxX8D1t6Fv/mHnX1CkiEnQ79u27QP3S7a961i0Sngxw0RVljaw+O8PwQ397Zw/8Rq+ztWeeyRMqHJPzYCM83jes84fmUnUN7rbZKGPBGdNnsSZu9QjEGTYg9fYlT+RKnGdRLnlVi6Tavx2YfsL+jGXRIdEFO6g1PTAydYhFISyosVpp8l7wmtDdbCxjUu9X5UVCyM3WTiUiormpNpIX2xMwQ7F/O6n4wi1meGo0HdXZdajf3fF71x1sfrb4tcZvOfWj3NraYvBmNpSlaUtpcztk4AXFjjtx5roDOxaovs4NaevI96Z4tO+XMJ5kIXjxSSfz3u2a2+2uXXjylHJCVerk9Mm2DpRw5FUhIgphqmBAjNW56qzsoMIsLLDPhMl2J00hQp7B80j7g4ZyvHMC/tI1Sap+jgq/np2ffAFXP8apwOHR6vgZ/WhB1CoS/FS/z7k//ECwN/L7jxmyFQl2gDHvgMWP4DnfwZ/hqQS6zxpL8uv/shev3C79OUSzvKc87doFaibLCkld28W3knVSZNPuINO1LDby1oTdAwV2tdGKx00B47JtLLNll8lLpFaWNlTcU5k9Uf5NGbl4tKzNsOSWfKka9F5pCKG6ju3ifdIEOU4Pn+2O0RVECpkI8fnfVL5iUdzHFF93o8tFexyQAop5fhMdx5lVOse4ad/4IT3HsQ9F6zOkZ+WpjnZQUdPM03JTufHpQmRiufuW1K0pnUrGwCt2uS8Z53/H5wOi3oFl03cCluKfQnVBUHFhFcT6qVTaciVLUrFHINeoU9hlliN6t7xUYvaIq5gmyKtIkdsn6cp1urOqjvZ4HODmPMY3TSMaOkCs+NQtYwGl0lFpHEaGEDxbksNd2rRwo4a2hjmBlQoI+rBxWvY5digljnV08/E0f2ZbyeqtrSBfzz6EnTvORGA87kG8Bc76qTJm6hMk/csacAR7mzAnnOOcDc/D/O6HUu8L5fwJikhuq84DPWDLDdhVs5it/mx9Qk6m0vEtj8leHpYn88lUk6ww647luEX6lK+ULcgn/xC5vq+V/8hw32x6sQebnSLv1ZRI8OZkBV0jCDUsQt1KefOSHdtBd155XGs7On6omjHK7ee+q200Ur2/hd4+erby/stY2pC1Za2lLL3yIMFT13ZzwGX5Tlq9VJO2xU6eprJJ9O+4lElApvD6ZIGocINlPi9CwBJ57lK6LERNS446m0p2JNFbCKn3Dc2i88cl1lcCwgus6oYioUNJVZ20MSUei+2i5rejV33bQd97gVSI2px1youfKTca2EJPnoseZ60l9GYGigUk2zMgl9agk1vur6msehKsDtpIt+7G70dWYB/1mTnMWUZiqXNu06ewP1PuU/ucnoEqsauUKz45p30+hxIjvLkKBF1ZXFDaaEik3K3yab4RvH3RZmkK3dslbJum/jyXUSi+q6D0pmdHfus7N7Z9V5zWN1vbt4JqPeillVycbOJ83ALtvl5j7UY7XJ3c3rSk1q3UJfy+7NPougigaLf2xX2qD5qW+ih/lj//Sb/cTepw/dHSvl6pDcaM2SqtrQBrrhs8MiWA1hy1R9ycKjjIvkkt3knrzpxVDPYGznbv4Oowq3IFB/qLpiw+s3lLC59Qk09jzoZYwqF6ppuq8Fhip7u6/VK2LoiWjZCxP8GoqHdTuv7D5tE1e+Qooig594Z4clHxXBmXZZjONPgg/brXXSnA4dqJVmn91nXH8oYTdeZSoJ76f6/csix+1e1z5jqGJJoA0tXdMPa52Cfw50fRSttdNLENZzPbW4xKO/LzhBNqMugu0naaC3JwNMJO4nVSV6Lk11lAwYVTbIJuP6/6s4zZsqyWmbiukQS+T5fJT8I9snbYsfDQhXDiOoeMfdT6Xc0XoXbdiz94ts7u977PhNp4yRb41rbs4t1a6KOMyjvIE2eJjq56f61vLT8xVlcOIQ3E1MRQ3KPSCn73/LeKfz9ueKyVtrIk/ZZj+pxfWNvdQcyJy+z+CYmo8Rum4TVBjGzKyvZXxTUvr3mt5V0npmq/Sls599U47G73960c3J31DVbT1wVthnk6jAFMWr96nKfT9B+Kp1c3N5ukZGK7QaKv5V08QI8Y3XOuYhbXGuJfJ/nFqtmnOad17O5XdlQ2ArQEbhRTM0ZkmgDPPznDV++fzWwCp9Y6ydp80CHY2klh+DXNC30bFG4VSx0JUQ5ucslXOj7qCijrdzxbY0MTKGGUuFWf1Pt2+j9KG3Yojxsrg49HiasPozavlzEz/YW2qGyvdLfe2fXw6HF56mBQlGsLZ2IFNbmz2XQ5zhU/sH/LE5S/94jkFIOVLzDmKoZsmhLKf/yP5070dcPR/1rKQBncjMdPc1cYdwzBWVNVk3WEe7cUzNoo5VrOL+kTklUCzhK4fQgMTZdI1FQYldywoe5Q6Zb/kyL+nBKkmY8VhVP2KD0c4XKzGymg2Y6fJ091fjNyCD987MJt/L5B7G9a3/UipF6H174n1sQKpHvs2fI6uV3K0D/DpVRpCe5Lf/9M7z6h3+cUc3YY6pnqD5tpJQrWo5JcMfa15krtnm+LoCFPXO5MHmFt+4FySu5jMurP5geKqjIAhnnglAgRT7pZOHpdUqCKgMGEeYXtYX7KQGrpEBSmmKH9bIV+7RkGD2Gu1CXYoZxC2KmKXuvryrdR9QGBykKNNEZGG9txp/r8e9qH0qs22nxwkHV+x/rYl1pclYtj5tKF8yFRbQa6TphNbRtLGSu7zvupoH2p1P0/6sDpPyfykYdnW3bdqq9oTcOGLJoAzz5j02nX7dLYsHcMzcw41858kekSSULFHqcOF8VPRKJRuziDMGTmFmn0BRAAWhPOmF3YROU5ah0QquFdrt7wf3RVewa0i3o6cUUZDWufJ0jFF3TGr2Y3UJdqqQeSH6a65ufVow1Lxc/rlvMQS4gJcK2hCFTxGziraiF2OljGOuulij4vgd3UjFN3mvg6xHgIokSr60+0zZavUgRZZQUelIM3vFDJpz4IQZu+c1r1b6PmOqoiWhLKf/nmYc3LVh+/UQOFv2kyXMmN3MlF7CA07nabXRbUmBIF2ddpMvXtLGTdcRbCXeKgq/9mSnEZpF+k0osdBWTHuhC6fH79H3iOQ1S6YK/G8l0AqM89P9eREedfVxhE67lQvPUe9EvfKZYV2KxddPgXbxtn2k1kReV3kUNF9sr3dr7jsx5ChVVZAwripWtwj31uSIl1uDUAxr47a2wYsVsbvlNDd5FTCXUSrQ3n/iFFD+8dRI/vMAfe9zR0+zVpxiyVRUi5vWNvdAIfUsSnnB3Jpt87hqwn+TVnPg2EfSJm3FbZ1ranTR5jZG9bTXLqDdd78tUDHJlVOJHNzvN2CxUU4z1yWX1etRJXPP7bqKTVtpq6hapVa2RsYwv/E/XYzVJqX5Xq5zQv6OmL7UWj1Kfo8qEVUaW+i2rSpw7rboPMbEeCUuH4/3EhDPkiUjFPb9ce/h9N62le8I+gHOC6gWerP7eqBmSGUoLTFnwhDHr/MA6epqtDRRgaGU8w7aNmjmouwr0k653dj1dRzTSUdccaXI0KupY5p2GHmpXznrW/dKVWpZKsHXMaobVsr2t7O1JSfifQqviaKveaIb96b+xBZxeclfslU4GBm+7lQmfPC1ueLCdqJloA4/VT57A//5zd8D5MbXQTl8uwZU9FwBlOrUrATfFOwPzZl7MvJkXRxJuj2xRuBdwutXfXKkghq2vYiuqpTdd700S6q4TZfWoi4/51+nOGJQ7dumWBd+dQdD7Ur5M9aeLtbp7KtfRxybYY33ycTQR5cLnCbfFz21GiYRdkCcmcsj7FjFw6SU7zO2NEOJ8IYQUQuztPhdCiJ8IIbqEEE8JId6mrXuGEOJ59+8MbfmhQohOd5ufCCGE7VhRqIl7BEBKKc+5dn/uvWkd/3XUZMAR6UV8zLlKJy0bhU04asvVrXZ9Yy992YR1PS9LUifr+Lg7aPaOX23Kezlx1+t0hKGLlYqkyJOGOkrEWhdJva6JrT2Z+oxsxagUNreICtsr12XGN/nVUxpzbx5b37/eki5mmJhOSbhfiYWtCbbNOFDNLXQKPSm/lX33XXDku5F/XrRD1M4WQkwDjsV/L/NfwIHu3+HA9cDhQogk8C1gFiCBJ4QQ90gpX3XX+RxOG+Z7geOA+6oZU81EG+Dn561K7TalrvB8bzMHJopZkH1LErTNbOV0FjDvrIu57Dot7E8Jr25h60KexV+zJEOxiJQh+PqPS99eF+6hRJQEoVvZlboNfJ19sIuzfpxyz5vpsL7HMBeCuW7U96CiCtTxTOtZXUiifN5x3eTqKdSlSKzKlUQc6eGhvpR3i7vErDUTxOCtC5GPP/bBIQ967HAt8A3gbm3ZicAC1z30iBBiihBiKnA0cL+UsgdACHE/cJwQ4kEgIaV82F2+APgQVYp2Ld0jSCnXvu09Cf59xwuAY2lfkLwScLqwA8xhcXGDIJdIGeqP7HW64Ohknb+g18q5ShTV1tbwWcXaJGQqWSiJGtFRafiqI49KQFGWdpQ/71gR66+Yvmwdm/iWrGO8n6BtzElgdWy9NvRoaao7FvFKDZjukenFeH0l2Mr9Zsbpq9+drWKmOZk+cdNSxEsrAf635m9mFCKEOAF4SUr5pPHSfjgdORU5d1nY8pxleVXU1NIGeOiPr36gN1//51M+uxuguSMyRffDB8/6PYuu+5h/Q90lYrpNsvj82SoG3IYSlFwmAUvw1e1WFreq9x3qY68AX/afIdg2VFaZXg2xmizOoWATyaAomjzpklKyUQi17l2hUQISFMmwI08yVoQReaQISlnPk2Yhcz33WElhKCNiBGCvu67ltdM/RO8Vv9xWw5EHIvvr7HfPlbG3EEKrLs4NUsob1BMhxGJgX8t2FwPfBN5nec3mj5ZVLK+Kmos20LZm1TZ6OrtJNjkiXX9kL325BCc/dQ93zjyBuSxkER8L34tNuL2XZjgPMsZrGdcHtyRRvK4ZDRdUOGBb0pnYa6WtxEK1+barSW8vRy1cAl5hroguH9ukoTkWld0ZlQIpa02WsDHVqiD/johuYavPURdq87NV1rW+vpnhqAj6TU5seIVXFv6V/u6eN3HFL2vzRkaGdVLKWUEvSinn2JYLIZqAA4An3TnDRuDfQojDcFRF73vfiBMVn8NxkejLH6RUzdT6VVFT9wiAlHLbnDMaWHjzgGdNzU+e572ugvXnnXWxsyAskcbmNskYz7P+x6lkwd5/UqsUaBaaKufLKydgygqtNuW22P7A/heEKY5BLgY1fv1kN8PtzIlE3YUSxXVR0tkmQLBt+wp6j+PJyq5V6GbzQAczVue8787sSBMm2ArlkjMnsm3uPUXm4V8w6cD9kFI+V/LiOERK2SmlTEkpM1LKDI6CvE1K+TJwD3C6G0UyG9ggpVwDtAHvE0LsKYTYE8dKb3Nf2yiEmO1GjZyO30deETUXbYDbfrDmjb9bOMjgMreqHAXqG3upb+z1BNIaxZEz/qBUuLMEtyjLQO6pGcGvW2inhQWcXlW4ngq5G06CBDPMmi0XAeLVXTa611QzFhUSGJXxOuEYllEbZNVWQhqnpZ9yd6gyqwqz3yfgE3a1jt55Jk0+1O3luSak5OX5d/Lav54+rarBjz/uBVYAXcCvgLMA3AnIy4DH3L/vqklJ4IvAr91tXqDKSUgYHvcIUsoVHzlzV664Ywv//f+cE/2C5JXczJm+Wer6U3vpuz1RGj2iMCNLAtwlOvWNvU4dkrD9ZYtuEgCS/k4yEO3kKlcgKop/2yTMqjUtT5uFXa11GlSTRL1WDiUCYcevVer6WML8TKv5fpoHOkLLqc5Y7fzYzYJiQREjKtmtg+aSJBqblb134RY2FdYjpby94sGPE1xrWz2WYLbh8l67CbjJsvxx4P/VYizDItoAf/zN5jcm9+KFj351kHTSiSJood1X2nN+8jzO4dfhO9IFOyiuW6OSiQtv3WSBDpqjF7WiGG6nZzWSLMa1Rm34YDYNDiIo/tps7aaPL7RaYV2a9LRipxVTXNQElX5SmwJrZtSZrduqpdJiXaOB4RpvOcH2KkROdx+nC/6qkUYn9m4aAhtP64KtW9m9l/6Y/udWfzyumz06GDbRllKu+NRn6/jdVS/zrct3ciI16opXeTMjD+CyOfDBQ2DRMpi3OGDHNqvbJEt56z1bXFRoTNGddO4Aok7o6SLl8xknIZdLRBJuXfTKCbY5riDr2jwRzVt0/T1GTQayWeGVWve2eiPj2cquhf9afVZmmzgwokJCGh6o7ZUFrtx5TXT6GocEzcfs9dKNbN64gT4p76zmPcTUnmETbYBbfj24/5TkhJUnf20v9tqnzgtta6fFs2qVi+SyD8PFh4IQMNMNwPEJt2ll688zFQ7MYrFXk3Sj+8HV++nosXeIt2UR2ghygUD5iUawC6EZIWITlKD3H8XdYbppTFdT0D5sPRXNCobjiaG8H5tw29bxmO5fZlrZOqZgm1b2wLKVH5VSDlY9+JiaMiwTkQop5ar3n7ozv7pqo7dMncxK8G5NOnMbH8w4gg3O/w8eYtmhaTnnSpd51m2FCTtRM8IUSuR0C9bc3nTVlIsuMV0gUS8ieqSJ7T3okQFh0Slh7cCUv9psNaYSa4Isb70+SWAySABh1mqtojFGijDB1t9H2B2X3uBCT5bpTdfTNa3Rm4xUQm2W9tXrinjuvSDBBg7M/gC2bWNwcPCuSG8yZkQYVksb4LbrXmvcY0+Ru+DcrbCfU+azk6aS9OZFWZi5lyPYUjouEitB3WsgssV92WHORWJRFuZVGS2pi1UHzYGTkkFukqCTU7da9ebCQeF/NqGt5OJjXhj0uib6a6peeJCVbtunEmxdpM0oh2o7mI9mK7zSycegRhN50szIFycZdZTVHRQxoof6qfZg6rwrGy0CTEyv56XTb6b/ya4TYyt7dDHsoi2lfOlT5+7OtVdt5tQfO8vO5xqvo02BFDTCPLcy7wf3C/BpZymKss1V4tK3JHwi8rLDNDfMXsDuMC+XIJ9Ml9zWl0OdbKoudljMdznXiC0LUX88lAqCUYiSgaj3hTTXt9U6MQV7vFPO8o9SIkF3C6XJh7YMAy1KRFtPF3NV4rcNp/ZPNw3czJmh46xv7GW3vy9k68Q6gEWhKw8nW6kofHdHYdhFG+CWH2+aOmVP1nz5a+0UprfQQLc1hXxe3hXvKEk1NiK4RErcMPvCvJXO80ojSCopymT6lc00dtv+oDKr2fQDBzU5MI9n9nWMasVG/ay8WuEh/ljbOPX/5uujjXKunEq2Vd/BjH/5Q/lUIo26EPqiRFSFP1e49aSbTpo4n2uc5W7VRfOYupX91j2e4Olvzef1/2SPj2tmjz6G1aetkFK+fNxn9uWHVwz43AKqVjQZ/FEhUdqNVeizVizKOu4XZ1ywaIs7lh5/eyVFJ01cw/ksZK6vpnUl9OUS1ltSM3VcoVe81glqiqAvC1sHSkVP1T1XW5UTYmVlV3Jx87a1pK5Xkg05WgV7OEiT95oYgD9Rxkys0Uuymo2dO2nidBZYwzPT5Em/Kx9SAAAgAElEQVQlCz7Brm/spefOBxhITIEdpDDUWGNELG2A2695ObVnksK5X++GA4pRDM100NbYSl9jorRnZDlhtvm3y1QO9NwwmaJPW68KqIRZiWgnTXT0NJNKFn3Y1YhHoSdlrylOZVmNUV/XsZVOtaWd2+p064Rms4ZgWtjjMdQvLOyymn2lBgpW10hYzLaOavJsu6MN+vwbZ3Yxddsq2r99K9uee/F9sZU9Ohkx0ZZSrj3tm2mu+UE3F9+Q91l+qWSBXGPCHoNdqUUdtP6Rbrbk7QnmLS2KNzh+cF24SxoQ44hugRT5pPODt1UJDDtZzSYNQT5uW8W1StEbIiixtpVnDTuuEnFzMnKo1EKwx0o4YJRyvrZtjlq91OmsPtVSO0QJuV6S320tppr25uvS3mek3CRBd3oqeqS+sZc0edb97m8M7DUVeDEoUyJmOzNiog1w2w/W7L3nXhPWnXpePw0HF8uRttBO4ciUk9JeztqOYoGb6+NYEQC5I92SrTq5oqgqMQ0Kz1PLb8ydTdvMVlpp8yJI8qRDMzL1SBJv/wHW91AoJ9hhvm/b8+1B2BhGu2Cr8ZVkM7qCa2uqq7Y76l9L4Ql8DXp9Pmy1H53plESSNNBN80AHYM9kNfMJmpMdDL6+lZXfXohcsfqY2MoevYyoaEspX/nKT/fnks++zNX/mE5qQsFfbUwJclQ3SRTfN0CmOBHolXU1yTr7M5NgAkU4C7nsDG7MzPCF9NU39laUSq+7TYLCAPXQv7DlZpx3FMHW92X6PavxWwcRZO2NV5oHOkg80lfaAmx2vfVzaKHdmXhU60911gWng3ogrvtE/3z1JhNRUAbNS9++mYEZ70C+sOrBSBvGbBdGVLQBfvLlVXVNR+w2cPf1BU46u1gbPJUskCPhF25Fpda1Tg7IwNKnjqJxZpcjqo2WglK50phqT3yz+KNXsv7HfQy5UDsQXn8kyB+tC7MSarNfpM1q1V0dyh2k1w4J64ITtZgWAHX25aPdWq6WNHmngNOjxguuCHfUNXvfpR4zrYo+MRU4vJgB6bOqdbfIGrz2YkFROUEXyTxpn2GSJs+mx5ez5ubFsHZtA9wR+f3GjDwjLtpSykEhxCGrlm9Z9o4PTKF1/zYWMre4Qga7QNus8KgsAY7UaoMQUFlwCfQdaTQIzhr/bajXMpQKvIEt2Ua5Ssq1JdNRomzLptPD9xRBBafU+mr/Qdb1UEV2PFvZ+gV1xupcUVhdodbD9VTsuhLkGeSKk41anLXVun60uF8OL64LpXH9NrppYCFzS8JPX+rfh/ynzobT5iPnn7bjBNaPUUZctAGklMs/+/1p/PALWa66tx6EK1wZdwWzHKvtsaICEfd+zBmCRThbheWcqWx1m3Drgq3C78qVflUocTYtcJMg67mSCoOVoEIPbdb5WJlMLEeJZT21+L93tmMtJ1Y5P9rEdO3H+6i2ruGjTqwyBFt3sbiTjuBPU4/6edoKfz3x7fuRe06Da+dOYP4oKpndT/V32OOY7SLaAL++OFc/o3mXvraFrzD39IW0J1vI5RKOmNqa89hKtDYS3XWyxPFB1x/pNGOgEWfis0Z4E53MKGttK5T7pb6x1+dLN7PirB1Fkn6x1QXb1kw3SLA7abIWvtK3NQlzu9gIcomMdeH2Cba65mmiWmItWyI+rK9BiS/c28ZFTTyG1UE3uYbzS4yB9v+bzMAvr4dXXtk/nnwcG4xIco0NKWV/V8fmQ2/4epaJ3TlaaXPENIPdcjZFHKqKIulbkvA6pB921kNwpLHvIV7ZG2d2lXaDD0B181EUeoqTSWGCplvlHT3NdPQ0+7a1YSbqFEixkLleF+5yCUNm0afhIqgQ1GgT9+aBDmfiUFnYh7p/yu9sirCNoHVMy9r9651dT+/sYnEoXbDLfT6LmeOt09HTTAvtyIEB+s86Fz52GVLKKCOOGQVsN0sbQEr57y9clOCGLy3nzDvbaEu2OtY22GO2g8TV1iAhxG2Su2eGE1EyM+9MTGYNH3fW/Z+J+EayTk3uSjBdJFE724Sh/NxBwqpqKataJqbPu5JekLUICwyy4kfTZKXt4ulFhoBnMXdNa/T7s02UVR1VGpUlvqroF1d3VqZ1HaV8gro4t9NCa9LJL3j5qruhfyf4xVl1XP/FiAOL2d5sV9EG+OUVG3c54KCdNj971zLmn3QepzXe6ohoFExXSdBrNrKwNHtU6TZQlbXdtyRB4wmui+SpgLBCjSidbcoJY1AsuW0S05YSr5OiYJ2EVKI1nBOJY8Gy1inUpWC2c5HtqGumkyaa6HQmFYNQSTFBLhFtuS7Ses9v/S4kiotKCbZemiFNnnZa6O54nYGrvgjrX3lTXMVvbLHdRVtK+boQ4qgfn7Pyod8cnWBuciE3Ztz2a2HRIo3GfxtRJigz2uOssV3USU53H9V2YzfJk7YW9VHYok2Ue0Q1mrChn/C6KLbSFqlpgU7U0L8ojGaBNpOQCqRYzBzydf5J37NX3xju7phKaQswI0Vd91PrVJNopN81tdHKXBYCsJC5LH3yXfDF98EJX0fecsEO0V19PLHdRRtASvnPk85u4LrzV3HBjQtIz8xzWfZyv8siw7CWafTcJDqVhhZq+9Ixk21sVrY+Eakny5QTRi/ML2lvC6ajqiuGpaMPp4CO1YnHbhropKnkjkV9jnNYHM0/bUR9gL8CYjnBruazu4ILaaaDBrpZzBwWPfUx6h66joG1PfDIhRO55YKK9xmzfRkVog3wp+sKiYbp9b2PL95A05xO6o/sdWpjK+HMaisHWcAZ7MKeMZ5ntWXu475cwr+sBqSSBQo9qUiuEFOwo6CyKb0MuB57BUJV7CpMsMt1Vinnfx6vqJ6mNsFOk+d0FnglVH2oCUmVADO7tGEBAOliCdWg1PZKMSOK5uCUEbnsqcth7RoGvvVteHVts5RyW8U7j9nujBrRllJurKur+68rP/3ifb98bBdubTiNk7nHv1KGYtNek4yxTsayjrmu+7gk9dy2bTZkfyEo4W5OFutA2NwbQ8GMszZLbULllflMhircY9HC7qSJdlqs1Q9baKeVtmImo47m/tBrgliLNtXVdq5A/x0sZo7XoGMhc2HbNrjkDDj288g7LnuypgeOGTFGjWgDDAwM/O8Zl+7HpR99nmv/VsdnTvg5N95ztn+lDIEC6olvJvj1INRrQa4ML+Em4NhqW98FwBXlVLLgE9YgsbbVECmHcquUCII7zj4SxXEMoUrfUER3JATbFq8ehaBJ0G4aSgS7hXav7VpJMSiwJr1UM6ZqMUsd6J/7oqc+xoSbvsTg6xLu/N5E7rhsRMY0JPqIk2ssjCrRBlhwWb7uiBOmDPzkK6s47fo2bqQo2p6AKt9zxr4PU4DN0LqwCUN9W2shKP2Y2dIx6KJvHqdAcEf2MLdIuT6K6jjWQlVZN+Fnpr+MrF52daiiGhbJMJR9l3vfts9MVbbTXRGViGaBlM9/rcRa3an40tAVFl/19kZvnXce8+EvtzF4972QW7FX7BYZ24w60XZrk+yx/yGTNxx4QyeNn+ty4qophtUVjrQLlE1obZQrvxq0bckEY4Xp7qZgm6JTjcDp79ln5WcouSvQfbJR+2FWMnloukqq9cfqdyWm9ah3dA+rYufrTVkXTbgLpLziWQVSNNPBHBb7jgmljQhMsa5lRcOgyo629fTa2eq7KJAiN38DXHEu9K5rklL21GRgMduNUSfaAFLKXiHEQTfNyz333TefwJcy//EJUHOygw6aSyzpvlzCEzEzHA5KRVMX7yhCbhLkUomCfjJGFTd1lxDpeFn/0zZaS1wIKr1dDwUcysRiFMEOcmOUKztrW8dcF/CqCpoNhaN0fVfjL5DymlzYGhN7FfhczM7oQxXsSrNOgxooN9DNn7rfAT84iQmbej4yIOXTQxpYzKhAjOZyA3V1dcft2VB332WPvpuzXr3fEyKVxKILmM0yVpN/UCoCQXU7ggiKjdaxFYJSBEWHmE12lTVsE099ErMi4c44/xpndtFCu3c85aMtx3D5pKOKU1AhrHLCH7Yf8H/GupWtokJsQhjU7kv1ZqxWsCv9LMz11VivqTvfixZ5qW8fPnH4enjTe5G3f0cwxhBTZ0nOfHxoO/mBeEJKOas2IxodbLfaI1EYGBj43+POncE1Jz3G8Qfe5omPyjhMJQsl9TsUanIu7HZSfxz2p/YXZKkrbJX79O1M61r5SVVrr0oaBkcJI/TIOv8KPY6PtpmOyIJdC8Is5EpFTv9mbOhCmxooeH9hKMEu4JROncPiwG1sfmuzPKru2rH9lhTV1nMJEuy2ulZfE9+LvrwVJu0Nd3y3rmQnMZEQQnxJCPGsEOIZIcRV2vKLhBBd7mut2vLj3GVdQogLteUHCCEeFUI8L4S4QwhR9QTIqLa0AYQQ4oiP7zc4oQ5WLHiAlzoP9CYAVWU90wo2u88oTH8p+CfRbI8VUcukmsfTj2FidmDXj2WOzaz0FzTpGNisAee1D878vZdsEVW0yzWtrZUlHiZeUT570/esCPIxK5+vsrDVhKOazAxCt7bN7ucjjXqvpn//+l/sxPxrJ8Fzz+4hpazgCj962N6WthDiGOBi4P1Syq1CiJSUsiCEeDPwO+AwnMZwi4GD3M2eA47FiXt5DPi4lPI/Qog7gT9KKW8XQvwCeFJKeX014xqVPm0dKaUUQux6QEvitffM/xB3nPmwEz2SdYo0NSc7fH0W0+S97EDASwfXrTOzYHyUCUG9xnVUTGG0ZdPpURzl6kjo4y6JLc8SLtgu7bSQwrkLiWptm+OqtUgH1fMOEqQwdMGOMiFohvKFXTj0Ho16sky5euTDhXlxUhOR9/1zd35x6UpYu/mgsSrYo4QvAldIKbcCSCnVB34icLu7/EUhRBeOgAN0SSlXAAghbgdOFEIsA94DfMJd5xbg28D4FG0AKeVmIcT+619+YeXXm97H1Uf+lb4lCfqWJMifYPdVm9XQTNEza1OrbfV9KWydzJXYddIUScT0Meko14hNsNtpKfG7W0MWs5SGP2YoFe6sc6FrSzqTkp000UpbpMSbWgi17U5HLYfS6IxqQ+iCxNo2EauiaJRgh7lSvI4y051CUWqf21OwC3XOnULrgBPSuWb1Nr5zShdbXhk4Tkr5/IgPbHxxEPAuIcTlwBbgfCnlY8B+wCPaejl3GcBqY/nhwF7Aei3UUl+/YsaEaANIKVcJIY762dz2hy7613/zncydQKkrxBaFENhIwKVkmdEh3SY0ykI2JxL1MQS5YoLSlXXh1u8KdMFXdxK+btqZkt35l2eLz/tyCXK5BDmchsT5ZJpW2kKt7loJtv5f4Yt5NgsqVUiedEl4X7mQOb3ZRDnftxpn17RG33elEm3MjuiKcuGJlaKPM0/aE+xVffvw3x96lfWfn8fAt+a1BW2/g7G3EEL3sdwgpbxBPRFCLAb2tWx3MY4+7gnMBt4O3CmEeANgm9SV2OcIZcj6VTFmRBucwlKfv+Gt/OK4v3DKA9/jjlcvoS/n9nRMBm+nC1xYhEcYugBXExZXiT88SNSjumdKQhEzWK3uvmyCXCbBjczgsJkP0UTniE1Qeunfq/A1qVVUE0IXdGFQRJmUtuGz/NP4YrlVPLfCJtDm80rcPmERLF3TGr0LxjP77MdnP7qJ3JuPZeDbl07gW/PK7nvU00ct6gCtC/NpSynnBL0mhPgijh9aAkuFEIPA3jiWslY0l0aKvYtsy9cBU4QQO7nWtr5+xYwp0Qb45eeeFFtee4tsO+YHvPWBg3ny1Y864qRFaPisUA0lYmFhghAc121acLaa1OZ6+vqBvltNJH1haOoOIOm/Y0iTd7rX5yyp9Zniw5JkGxtZvG71HY3NLGQuzckOn9ukFgkzoFnVZkU8o/WWOblXTlRNodSFTlnAgBfDbft+oob3KbcI+Ceso7pyzOgWNW6bkJtj0j+73tn13uvP7LMf//2RTUzetY7Nt949MW4bVjP+hOOLflAIcRBQjyPA9wC/FULMx5mIPBBYimNRHyiEOAB4CTgV+IQ7L/cA8FHgduAM4O5qBzXmRBvglq8+I97CGfL5Y85h3wcaePnVd/ncJM3JDjp6msta1eVinXPa9mECrgjLHlQuDmUxm75s2ySpOq4u3jYBi9LezGd9Z4vbqOdQLA+wNHMUSzmKz8z8Oa3477KrLa9qFWy98L8reroogv/9hrkvglwQupja4ro9t5khnlC8eCjLGooXrQLFzMOOuuYh+bVNIVdYL3Dg+9xW9+/jCfaDv++ZGKeo15SbgJuEEE/j2P1nuBfEZ9xokP8A24CzpZQDAEKIc4A2HBPhJinlM+6+LgBuF0J8D2gHbqx2UGNStAGe+eotYgoXy7XHnMbEu+6jL/dmn5tEWaJl3SFZ939Ge54pvqy2t/nCdSE3fdDKlaFn2anbaCXY4Pdz21wf+nFVKVb12NauzAsJXOK3sL3XiZB+n3X+3cjZFGamvAL65bAJl08otY7lXUc0Bror9JBHfXK4UJcqK9xgdzvon2/Q3IK57zxpFjOHDppJUfAuYCpMME0+0JUUNBb9PQS5R6xirVxI04sXotX9+3D2R15h8q67xII9DEgp+wBre3op5eXA5Zbl9wL3WpavoBhhMiRGfZx2OXa6/Ady4MZfMfHuP9Mv30zjzC7PggpM+c4SvamCu145azasroguDrrPWGUnAl5yh+cvDbhIhEbBuOjWc2iJ2mzIa4qMEw9/IVeU7W6jT+aZt/l6Z3Il2GVFnnDXjLn9jNU5X4U9fV/lwhZtE5EL6+b6Kv0BPv81OCVv1b70YlW2WPEgSmqahPSR7DqikdRAgS1bJCefXIcYx4It9polaR1inPbvxl9G5Ji1tBXbLr5I7ASy/8QPsO8/bqHQ81bSyeLJ7Pl1s8aG5vMg3PX6lthLvipr15bQo4cGKgFRFloD3bTR6hNwZZmbwqXfLZiCbX1v+jiz2IU761yIlP+6gW7aafEq3Ol9LnNPzeCKmRcyn/MsO7ITZk3OWJ3zT9do2IRcCa4pvJ00+cL1dFdIaqAQWijK1jxY9XtUr6tKf94+taqI+uOgDMUolFQMBM/98dC0w0rcQzuKYMcEM+ZFGxzhFusny5fffQb7/uMW53bWTR9XboSyzYJt3d/NDjlZY5uMUYrV/a9S6PUT2kzo8VWs0wRATf6ZKe0qVK9kLLZ6w+Yy930cdsJDtNJGnjSdM534ctXNRj92Nw0wU72nlCfmbbSGRpeokDso+pi9ZbMLvigM5XrQLVWwZDVaErCV4JpJSVHaqJnCb14Q1Hs1LXHVqUZ9RhXVPA9w16TJ+z4Tc5JTkSbvRdsUkhNjwd7BGReiDSCv/qoQINcecxr7PHArudy7aJzZVZzIy2C3rk1hDhA8K1kC/d+ppFM9r4PSiTXl79bFWw9X0wU70L2jj00fc6M2piX2YfusN0smoJnG3VTXWXEEie6eUMJdmOb3EysfsT656SURuQKsLGaFuhgqfNE2xmRiOWvbN17tM9dDK5VVrV+szItM0F2FLV5cub+Uvz4/LV3yPtTrahsl2Fu2EAt2zPgRbfAL98S77qPQ0+hZ3LklAZa2KXo2bFa4Iuv+zzj/TFeGftKb6FEhbbSWF8MsfleHEugM/guS/lh7Dx09zTQki8ewWaa2W/vmgQ5rrHFQXWllMepCpB4ri11Z+eAImXlRCIrI0O9c9G1UL8cGur0WXp6g1gVP9JrjM8Vbn4As9/2oY6jEK73rjVqu0MsX6OjJPuAX7OPOnRwLdsz4Em0oCvfAiR9g4p8WUWAaqWSBxhO6HD9t1l0xzII2MS3ZMqiEn75cgkKjY3XrNVCUL1r523PaeuCfXNQjRPoI8M1nAt5To7bcJUy4zLodUV9TKBFPT8t7FqXZxdzmymig2/MlQ1HQTCE3KzOqLun6e2uj1fPR28ZqduzRQy5tY1QX27BJUPMi5d0lGPVlbPVmdGLBNojbjVkZd6INrnBPqJODx7+X5O9/Cu9wBKRxZpfTeiuLVdAi8Yi2renvzhSfKreGEmwVdZAnzULm+idIM85EZ47Syc6SlmcYkSFZ/G4Q28XIfd63JMHSzFFekwgzBjtIjG3Wd6EuRWFa6Tq6W6RAqsQ9pGihvcSvbwq8Wq5cRmriUaVtK7dJB83eBVF3Myl/uS7+ZiJTgRQLOL3E591At6+QVBjmxUShFy3Tn6v9664VFV2jClEpwX6WiZx8GqRm7Mri376y4wh2TCDjUrQB5JVfFnXXfPX9a0846891877F1C8fB1A6KRnmzzbXyQWsZ4pkFp/42uqSlFToU2Kb9e8qsB9mxvivu3DcZSXt0dyLRB8JWpJtJZOAOlHioaEo9LpYKzFso9V7bvMTK5TVnCddMgnYSZOvV6N+LJXgYtZsUeLdRqsvbl7fhx7KZ5bk1Sdng9AvEFHT423zBmZMduKRPhLTc7AKHl4LJ50zyAlnT+VX38xNiDMdY2AcxGmXQwjxJmYcuJxZrey34CzExImOeyLIxx3Vvw1Ff3gjpcKdcURzbnIhLbQ7zat6Wu0heua+w1ww5joZ43Vt3/VH9vpcLn25BI0zuziTm0uiIMqFremxx77UcIoiqrsr9KzPNlpLXB0qTV6foFMir49HjU+tq18Y2mj1skpt2Y46tsJeOlGt6nJUkhlZkiW6pvjaTU/ABTdCzysTPjAwMPCXIQ1qjCJ2nyVpGWKc9j/jOO0xh5TyWSHEFKYetP6ld57F1HuvILUPTnNgm3DrQgx2f3ZYmJ1aJ+tYtJ3JJs+S9B0vLGolisvGXCfjuH/SM/M+y7Gjp7kkOzJPusTKLrEWLaF2SriDBLtAqqTMq/LlBvnSzcQjfbug+tYq+sRsDhHUIUjtL+gY1abmDwWfYGti3b8azrsL2gqwbi0HSznw7IgOLGbUM+5FG0BKuUEIsRP//c1ta5pPIfWXn8D0FPVHWhJvMsbGpog3astMd4m5bhaWZp06HlYq9acHWPMK5QZQ/vMSf/ISyGVn0HZCeFedctai7vvW3ROmFau38dJRSURBE3U6NtdDE5100Ox7TYV2qhh58z3ok5MmtRTsoJrsVgzBXrsBTr4RJu0veP6fcoqUckPNBhYzbhj37hETcfWdkh+cTd3VVzH1M+8C8EeVQPQUd7ALt/7ftm6l2PaVcQS7NRlcNlm3RJWgg+OKUN3Gy6WG69jikW2hdKZYB1nZTXRaw+milr7VJy5Nv7Zyd6ha4Wr5SBJU2dFL69cEu+NF+NB8+MgZE5h/5eBOqgDRjkzsHrGzQ1jaOvLrJwvxjVOaBy79bnu+8ySm/vDz/qgM3YIO8y1ntMd6kouZ8GKG4AW5Xkz07TLBZWTVrb3eSQecUqtQ3K412UaafGA0h8KWEGKblNR9y+q4apkehqeqGkJpa6+hEtRxR12M1HFGWqwVQcf14tvdGuJ3/A3O+TFccl2Sr5zyivjhFSM0wJgxyQ4n2gBSyg4hREo+8Xghf9zTTP39FUyY6XRzAfzWsyGevom+xl5opNRXrWMLwStncZeJBTd9t+20eLHdzUmnaW99o1NXBBzxaKPVV0CrzU1TN9PSgyYm9c4sug9bz/pU4Xm69VzJxJzZBqwctrog+vOR9lNHQb8ADgzAvF/Dbx+AdT20fOWUV8I7CsfEsIOKNoCUcq0Qon7CZz/fl591Cg13/YjGmZQK9yM4zYagJOvQK3GawR/7beIKd/2RvfTdHjD5WQazxokq9ASO71pFXqiQt75cwhNTJd4k8eqXFHqcXpGqZKyyTL2sQt2SrsNX4EmvRthKG3NY7L1mbfJQpoBSNa24dMEu19OzGsq1KasGvdrhuvXwqfmwYZtgZU6mpJRrh3yA8UacXGNlhxVtACllPyB2+vkvZPcxZ5D40ifZ76LPs7ax0bGelZWsEmrC4rEzFIU7itujkh9j1v+0L+skyTTMdCYdzW43ZoeepbmAiVAXvd5HkHVsJqiczgKgtEmBTYBtDQaCxhAVM+vQpFrhHkozA1vjZoWKFpHT4I5FcO534OS5E/jp/MF693cYExOJHW4iMgghRKNoPW513UsrSN74feoPe2txgtKWTJPRnmctO4wqylFT6TNl1/DvdmZXSa1tvc3aBckrS5JcggohQXgbrHJE7Y6+vQi6OzAnXKNub4sgSQ0UyL8k+do521jxAiz/j5wtpXyUmEDEpFmS/YY4EfliPBE5bpFS5oQQE+QNNw6uO+ELpE57L4d+99N0Ns4uWt2W2OjAsq9RClGVI+N/apuMVK6Pjp5mz9et6py0JNt9rbJwU+r1/o8KU2D0YlC96fqKhVoR5vqIItbD4aaohiArulxRK4Cp8iV+8+sBvnvJAJ/94gTuXTQ4WUq5dXhHHDNeiS1tC0KIfXb+xAcLg4/+mwN+dT6bjvkAuXuKTQFK6o9kjB1kLTu1CXhAKJ8NNbGo6mErH7YKZ9PdF7og65Xm9HocOmGCDdGb1nrHDKgfHZUwF0VY0+ShEMUtUi7r0rZ+4rl2zjuznw19gn8/LmdKKe0hLzElxJa2ndjStuBOCom6uroPrDj9+4v2OP7vvO2qL/Dvlcc7gjybonDbxDhjPM8S3Q3iYnNvqAnCVto4nQVeKrct/VtZ2+AIt95U2KyXbU2ldsPRmF6atm5jqBZ1VIKEMqi9W5T9RB1fJf7u1QNTefjaJ5j//QG+elEdl3xjII69jqkJsaVdBiHEHvt8/oT1G/7yMPtf91VWHnF2MYtSt7jRHmeKi3xd0BXZgIMZ25ntyxTKxQH+8p82zJofTXTSPNBh70eomseCr4FsEFGiPqoR7KFMBpY7bi32Xe64m55eyUWf6WGPnbfxz3/IA6WUXcN60HFKbGnbiUU7IkKIoye9cb8Hdn37m9j4nV8h9t7bEWK9LKoZ041jMYO/RrZVwN31lVjbamnYbs/1mOgokRRqgrGkL4oBgxIAAAxwSURBVCGU1BRRBEWFlKNSwa6VoNoShGzr1FLA86TZu+8l7rzgJX6+AM69YgqXfG59XJlvCMSibScW7QoQQuyy7/mnvvbKwr8y9cJPsObkefSvS/kjTAzhVlX1VCPftp5W3z6t7cTwW9pmnRCz/ZVOJbWfh5Ny0RaV+ocrPfZIvU8AKSVL/9jN9y/axhv3h0WLaZRSvjRiAxinxKJtJxbtKhBCvHXKiUd2bHz8efjy15kw93TEpEnFKBPwuUrqG3uZnzzPc1XczJnevky/tY4u2qoQlM2irjQmWbfchyJulQhv1MiLWqPuKrqmlZ9UMO8oynXrkVLywF+28PNLe5ASOjvkCcCfY+u6NsSibSeeiKwCKeWTgBBCzBKL//rYwE9+RN3XzoejzoLMxJKmBqmZxdKkaiJRWZttydaS/ZuuEVOwa5U4YhPN4QqpG0nLF/xRMDbfvK9rjhHOaKslriOlZMlft/KjSzewZbOk6z/iI4ODg3+SUg7W8j3s8PQRvXDbDkRsadcAIcRscfQxD8sXV1D3tW8wcMTnIFd6PTzshIe8TELVIGABpwPBlqgSbLNpQTWE+XdrQTXCHBb/XY0f3eevX4U3oar2ZSa+mNa0Kfb6GKSUPPLAVn58aS/rewZZsXzgFCnlH2KxHh6EmCURQ7S05fiztGPRriFCiHcx6+iH6FlF3dcvZMJHPkr/mj1Lyr4qf7WKsW7rabVGiijRVu2voPZ1NYYzWaWaOiQ2ooh3iVgDTHf+maJtxqVHOe5j/9zKj+ZtoJAfZGXXwGlSytvjEL7hJRZtO7FoDwNCiGNoPuLvbHiFuou/wYQTT6I/PyW02YIKDdTFW5+ArLVwDzfl2pdVQlSL2xblUi70z1YjXKf94a386NJeVr2wjXMuTXDhma/GzXVHiFi07cSiPUwIIQRwrHjboW11fRtJfPMLbHz3JxGTJzsTlhms4X5QKtx6U9rRWnJUJ8zCLpdtWY1LxKTc3UM5N87goOSxh7byq6s28fwz/Zx1ye5c8rn1cWGnESYWbTuxaA8zrni/f9Kcdy7qb18GHz6Zvc86nkzzFE9cvMJUGb9wq7RzXbjHomCD0RNRc1uYRBXtat06YYK9JreNu27ZzB9ueo2ddxG8/6z9uPaslXGdkO3E9hZtIUQz8AtgMrANOEtKudQ9p38MHA9sBj4lpfy3u80ZwCXuLr4npbzFXX4o8BtgZ+Be4CvVRhnFoj2CCCEyfPHbL/Lnm0jsXcf0Tx9Dzye+SGNys1/AKdYaUS25RrtY2wizuG3iXIl7Y6jjUGzdKvn7Pa/zh5te46ml/Rx/ys789vrX3g48EYfubV9GgWj/FbhWSnmfEOJ44BtSyqPdx1/CEe3DgR9LKQ8XQiSBx4FZgASeAA6VUr4qhFgKfAUnj/pe4CdSyvuqGdeEajaKqQ4pZVZe9y3B6lV1ve0vHvufB3vpfsMxdH38O+x6/91MHcxR39jrWdsjnSQyVJz2C8U/G4W6VKBgq/+6/ztsX1HHpKMuAsuf6uN7567nXY1r+O31r/HPtr7T1vcM7nrbdZuElPLxWLBjcIRXZb/tAd6P6URggXR4BJgihJgKtAL3Syl7pJSvAvcDx7mvJaSUD7u/qwXAh6odVBynvR1wQ8QW43hP9uxJfLhn44XXI9ZdzaQzT2bLhz6LmL4/LbR7FrbqKDNaiSqsQQk5KtxuOFAXv971gzzwu+f4w42vsa57kI+cuQuvrht848N/37JiWA4cM9Y5F2gTQlyDY+C+012+H7BaWy/nLgtbnrMsr4pYtLcz7hVZwNkIIZr7nhDtXPseyLyVRUefxqIPfpefzbnUawUGYyN6RKcSF0fUxgPlUBeDTRsHWfbgC1xz+2Ye/MsWZrXuydNP9B8HLP7Zd3sHfvbdqg8RM+wMgLQ3tK6AvYXw+VhukFLeoJ4IIRYD+1q2uxh4L/BVKeX/CCFOBm4E5gDCsr6sYnlVxD7tUYgQYjJwAu/48B10PgDJNLz1WHjfHH74qTuZtturQGkhKJ3t0SygkuQds/6IbfxhdbLNWHNVCKu/X7L4iSn83+Kt/Ov+LSzr6Ofgw3fniBOn8NOvrNpbSvlKNe8tZuQRokXCP4a4lz2G4tPeAEyRUkp38nGDlDIhhPgl8KCU8nfues8CR6s/KeXn3eW/BB50/x6QUh7sLv+4vl7F44pFe3QjhKgDDuWT33uUJxdD12PwhreROPVtfOPYJ3jjrD1I7+T0hA1KS7fVGhkOUR+utPiwiBQpJc8/Cw8sHuSBxYP86yHJfm+YyDvnTOLGaza1AkuklJuHPIiYEWcUiPYy4ItSygeFEO8FrpJSHiqEeD9wDsWJyJ9IKQ9zJyKfAN7m7uLfOBORPUKIx3AmLx/FmYj8qZTy3qrGFYv22EIIsSvwLk487z6eXAxrV7HvsQdy6pwCs45N0HjgZIQQZUuSjsa+jBAcXeJLN++WPPi3QR78m+RvfxMIAUccO4k/3LT548DfpZTD4xyPGVFGgWgfiRPatxOwBSfk7wnX6v4ZcBxOyN+ZUsrH3W0+DXzT3cXlUsqb3eWzKIb83Qd8KQ7520ERQjQA7+U9n7qNp++HiYK3v30bBx0i2P+QnZl+8GQOP3g9u+1eGii0PYU7imjvsbmbwv/1s6wLnizU8exyyZOdE3g5N8DhR09i8d1bz5ZSLgaej6M9xh/bW7RHK7FojyNcC+AgYCYf/86dE/o62e2Fx+l7bhW771nH9EN2Zv9DdmbmwVt54yE78YaDJ9K/byPOZkOnWtfLpg3bWLlsC6uWv87KZVsoLH+VF5ZtY82qbUzbHzKHTOYNB0/khis3fgp4BuiIU8nHP7Fo24lFewdACDEBJw/xYCHEIXt/9gPzpy57kJXLXmegXzL9kMlMf9POJPbaiV0Tdey8+wR2TdSxy+7un/tYvbbL7nXUTyq13Ldtk7y+cYDNGwd4rdf5//rGQe/xZvV/4yCb1m8j9/wWVi3fwuaNA0x/02RSh+zJHgfvy58veeIjwHKgS0pZ2mInZocgFm07sWjv4Agh9gYOxrHQk5xy6dVM7GUCrzBp6zp227iGZO9K+jdu8YT3td5BJkyAXXavY+fdJvD667B54wDbtg4yYfddYffdGNx1Cuy2G/XJSUzYfVdEYjcm7L4rm3dKMXjtDy8ENgAv4IhzLnZvxJjEom0nFu2YinHdMJOA3YHdgNeBjcDmWHxjakUs2nbi5JqYinGFeYv7t3Y7Dydm3BK3rrER1x6JiYmJGUPEoh0TExMzhohFOyYmJmYMEYt2TExMzBgiFu2YmJiYMUQs2jExMTFjiFi0Y2JiYsYQsWjHxMTEjCFi0Y6JiYkZQ8QZkTExMaOUrUDX9h7EqCO2tGNiYmLGELFox8TExIwhYtGOiYmJGUPEoh0TExMzhohFOyYmJmYMEYt2TExMzBgiFu2YmJiYMUQs2jExMTFjiDi5JiYmZpSylbjdWCmxpR0TExMzhohFOyYmJmYMEYt2TExMzBgiFu2YmJiYMUQs2jExMTEWhBAfE0I8I4QYFELMMl67SAjRJYR4VgjRqi0/zl3WJYS4UFt+gBDiUSHE80KIO4QQ9e7ySe7zLvf1TLlxxaIdExMTY+dp4MPAQ/pCIcSbgVOBtwDHAdcJIeqEEHXAz4H/At4MfNxdF+BK4Fop5YHAq8Bn3OWfAV6VUs4ArnXXCyUW7ZiYmBgLUsplUspnLS+dCNwupdwqpXwRp+j3Ye5fl5RyhZSyD7gdOFEIIYD3AH9wt78F+JC2r1vcx38A3uuuH0gs2jExMTGVsR+wWnuec5cFLd8LWC+l3GYs9+3LfX2Du34gcXJNTEzMKCXXBl/be4g7mSyEeFx7foOU8gb1RAixGNjXst3FUsq7A/Zps4QldiNYhqwftq9AYtGOiYkZlUgpjxuBY8ypYrMcME173gjk3ce25euAKUKInVxrWl9f7SsnhNgJ2APoCTt47B6JiYmJqYx7gFPdyI8DgAOBpcBjwIFupEg9zmTlPVJKCTwAfNTd/gzgbm1fZ7iPPwr83V0/EFHm9ZiYmJgdEiHEScBPgX2A9UCHlLLVfe1i4NPANuBcKeV97vLjgR8BdcBNUsrL3eVvwJmYTALtwGlSyq1CiMnAQqAFx8I+VUq5InRcsWjHxMTEjB1i90hMTEzMGCIW7ZiYmJgxRCzaMTExMWOIWLRjYmJixhCxaMfExMSMIWLRjomJiRlDxKIdExMTM4aIRTsmJiZmDPH/AWGAOAGuxDG2AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "Opts={}\n",
    "Opts['sym']='wo' # sets the symbol\n",
    "Opts['symsize']=10\n",
    "Opts['proj']='ortho'\n",
    "Opts['edge']='black'\n",
    "Opts['lat_0']=90\n",
    "Opts['details']={}\n",
    "Opts['details']['fancy']=True # warning : this option takes a few minutes\n",
    "if has_cartopy:\n",
    "    plt.figure(1,(6,6)) # optional - make a map\n",
    "    pmagplotlib.plot_map(1, RLats, RLons, Opts)\n",
    "elif has_basemap:\n",
    "    plt.figure(1,(6,6)) # optional - make a map\n",
    "    pmagplotlib.plot_map_basemap(1, RLats, RLons, Opts)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## s_eigs\n",
    "\n",
    "\n",
    "[\\[Essentials Chapter 13\\]](https://earthref.org/MagIC/books/Tauxe/Essentials/WebBook3ch13.html#x15-156000813) [\\[command line version\\]](https://pmagpy.github.io/PmagPy-cli.html#s_eigs.py)\n",
    "\n",
    "This program converts  the six tensor elements to eigenparameters - the inverse of [eigs_s](#eigs_s).  \n",
    "We can call the function **pmag.doseigs()** from the notebook.  \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on function doseigs in module pmagpy.pmag:\n",
      "\n",
      "doseigs(s)\n",
      "    convert s format for eigenvalues and eigenvectors\n",
      "    \n",
      "    Parameters\n",
      "    __________\n",
      "    s=[x11,x22,x33,x12,x23,x13] : the six tensor elements\n",
      "    \n",
      "    Return\n",
      "    __________\n",
      "        tau : [t1,t2,t3]\n",
      "           tau is an list of eigenvalues in decreasing order:\n",
      "        V : [[V1_dec,V1_inc],[V2_dec,V2_inc],[V3_dec,V3_inc]]\n",
      "            is an list of the eigenvector directions\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(pmag.doseigs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.331272   239.53    44.70 0.333513   126.62    21.47 0.335215    19.03    37.54\n",
      "0.331779   281.12     6.18 0.332183   169.79    73.43 0.336039    12.82    15.32\n",
      "0.330470   283.57    27.30 0.333283   118.37    61.91 0.336247    16.75     6.13\n",
      "0.331238   261.36    12.07 0.333776   141.40    66.82 0.334986   355.70    19.48\n",
      "0.330857   255.71     7.13 0.333792   130.85    77.65 0.335352   346.97    10.03\n",
      "0.331759   268.51    26.79 0.334050   169.66    16.95 0.334190    51.04    57.53\n",
      "0.331950   261.59    20.68 0.333133    92.18    68.99 0.334917   352.93     3.54\n",
      "0.331576   281.42    21.32 0.333121   117.04    67.94 0.335303    13.54     5.41\n"
     ]
    }
   ],
   "source": [
    "Ss=np.loadtxt('data_files/s_eigs/s_eigs_example.dat')\n",
    "for s in Ss:\n",
    "    tau,V=pmag.doseigs(s)\n",
    "    print ('%f %8.2f %8.2f %f %8.2f %8.2f %f %8.2f %8.2f'%\\\n",
    "           (tau[2],V[2][0],V[2][1],tau[1],V[1][0],V[1][1],tau[0],V[0][0],V[0][1]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## s_geo\n",
    "\n",
    "[\\[Essentials Chapter 13\\]](https://earthref.org/MagIC/books/Tauxe/Essentials/WebBook3ch13.html#x15-156000813) [\\[command line version\\]](https://pmagpy.github.io/PmagPy-cli.html#s_geo.py)\n",
    "\n",
    "**s_geo** takes the 6 tensor elements in specimen coordinates and applies the rotation similar to [**di_geo**](#di_geo).  To do this we will call **pmag.dosgeo()** from within the notebook.   \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on function dosgeo in module pmagpy.pmag:\n",
      "\n",
      "dosgeo(s, az, pl)\n",
      "    rotates  matrix a to az,pl returns  s\n",
      "    Parameters\n",
      "    __________\n",
      "    s : [x11,x22,x33,x12,x23,x13] - the six tensor elements\n",
      "    az : the azimuth of the specimen X direction\n",
      "    pl : the plunge (inclination) of the specimen X direction\n",
      "    \n",
      "    Return\n",
      "    s_rot : [x11,x22,x33,x12,x23,x13] - after rotation\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(pmag.dosgeo)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 3.3412680e-01  3.3282733e-01  3.3304587e-01 -1.5288725e-04\n",
      "  1.2484333e-03  1.3572115e-03]\n",
      "[3.3556300e-01 3.3198264e-01 3.3245432e-01 8.7258930e-04 2.4140846e-04\n",
      " 9.6166186e-04]\n",
      "[3.3584908e-01 3.3140627e-01 3.3274469e-01 1.3184461e-03 1.1881561e-03\n",
      " 2.9863901e-05]\n",
      "[ 0.33479756  0.3314253   0.3337772  -0.00047493  0.00049539  0.00044303]\n",
      "[ 3.3505613e-01  3.3114848e-01  3.3379540e-01 -1.0137478e-03\n",
      "  2.8535718e-04  3.4851654e-04]\n",
      "[ 3.3406156e-01  3.3226916e-01  3.3366925e-01 -2.2665596e-05\n",
      "  9.8547747e-04  5.5531069e-05]\n",
      "[ 3.3486596e-01  3.3216032e-01  3.3297369e-01 -3.5492037e-04\n",
      "  3.9253550e-04  1.5402706e-04]\n",
      "[3.3510646e-01 3.3196402e-01 3.3292958e-01 7.5965287e-04 5.7242444e-04\n",
      " 1.0112141e-04]\n"
     ]
    }
   ],
   "source": [
    "Ss=np.loadtxt('data_files/s_geo/s_geo_example.dat')\n",
    "for s in Ss:\n",
    "    print(pmag.dosgeo(s[0:6],s[6],s[7]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## s_hext\n",
    "\n",
    "[\\[Essentials Chapter 13\\]](https://earthref.org/MagIC/books/Tauxe/Essentials/WebBook3ch13.html#x15-156000813) [\\[command line version\\]](https://pmagpy.github.io/PmagPy-cli.html#s_hext.py)\n",
    "\n",
    "**s_hext** calculates Hext (1963, doi: 10.2307/2333905) statistics for anisotropy data in the six tensor element format.  \n",
    "It  calls **pmag.dohext()**.   "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on function dohext in module pmagpy.pmag:\n",
      "\n",
      "dohext(nf, sigma, s)\n",
      "    calculates hext parameters for nf, sigma and s\n",
      "    \n",
      "    Parameters\n",
      "    __________\n",
      "    nf :  number of degrees of freedom (measurements - 6)\n",
      "    sigma : the sigma of the measurements\n",
      "    s : [x11,x22,x33,x12,x23,x13] - the six tensor elements\n",
      "    \n",
      "    Return\n",
      "    hpars : dictionary of Hext statistics with keys:\n",
      "        'F_crit' : critical value for anisotropy\n",
      "        'F12_crit' : critical value for tau1>tau2, tau2>3\n",
      "        'F' : value of F\n",
      "        'F12' : value of F12\n",
      "        'F23' : value of F23\n",
      "        'v1_dec': declination of principal eigenvector\n",
      "        'v1_inc': inclination of principal eigenvector\n",
      "        'v2_dec': declination of major eigenvector\n",
      "        'v2_inc': inclination of major eigenvector\n",
      "        'v3_dec': declination of minor eigenvector\n",
      "        'v3_inc': inclination of minor eigenvector\n",
      "        't1': principal eigenvalue\n",
      "        't2': major eigenvalue\n",
      "        't3': minor eigenvalue\n",
      "        'e12': angle of confidence ellipse of principal eigenvector in direction of major eigenvector\n",
      "        'e23': angle of confidence ellipse of major eigenvector in direction of minor eigenvector\n",
      "        'e13': angle of confidence ellipse of principal eigenvector in direction of minor eigenvector\n",
      "    \n",
      "    If working with data set with no sigmas and the average is desired, use nf,sigma,avs=pmag.sbar(Ss) as input\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(pmag.dohext)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We are working with data that have no sigmas attached to them and want to average all the values in the file together.  Let's look at the rotated data from the [**s_geo**](#s_geo) example.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'F_crit': '2.4377', 'F12_crit': '3.2199', 'F': 5.752167064666719, 'F12': 3.5510601243464004, 'F23': 3.663557566868797, 'v1_dec': 5.330894345303252, 'v1_inc': 14.682483596068828, 'v2_dec': 124.47233106679136, 'v2_inc': 61.71700837018042, 'v3_dec': 268.75792759495505, 'v3_inc': 23.599173682479822, 't1': 0.3350527, 't2': 0.33334228, 't3': 0.331605, 'e12': 25.45983619637674, 'e23': 25.114754046379378, 'e13': 13.28977437428862}\n"
     ]
    }
   ],
   "source": [
    "# read in the data\n",
    "Ss=np.loadtxt('data_files/s_geo/s_geo_example.dat')\n",
    "# make a container for the rotated S values\n",
    "SGeos=[]\n",
    "for s in Ss:\n",
    "    SGeos.append(pmag.dosgeo(s[0:6],s[6],s[7]))\n",
    "nf,sigma,avs=pmag.sbar(SGeos)  # get the average over all the data\n",
    "hpars=pmag.dohext(nf,sigma,avs)\n",
    "print(hpars)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## s_magic\n",
    "\n",
    "[\\[command line version\\]](https://pmagpy.github.io/PmagPy-cli.html#s_magic.py)\n",
    "\n",
    "NEED TO ADD THIS ONE....  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## s_tilt\n",
    "\n",
    "[\\[Essentials Chapter 13\\]](https://earthref.org/MagIC/books/Tauxe/Essentials/WebBook3ch13.html#x15-156000813) [\\[command line version\\]](https://pmagpy.github.io/PmagPy-cli.html#s_tilt.py)\n",
    "\n",
    "**s_tilt** takes the 6 tensor elements in geographic coordinates and applies the rotation similar to [**di_tilt**](#di_tilt) into stratigraphic coordinates.  It  calls **pmag.dostilt()**.  But be careful!  **s_tilt.py** (the command line program) assumes that the bedding info is the strike, with the dip to the right of strike unlike **pmag.dostilt** which assumes that the azimuth is the dip direction.     "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on function dostilt in module pmagpy.pmag:\n",
      "\n",
      "dostilt(s, bed_az, bed_dip)\n",
      "    Rotates \"s\" tensor to stratigraphic coordinates\n",
      "    \n",
      "    Parameters\n",
      "    __________\n",
      "    s : [x11,x22,x33,x12,x23,x13] - the six tensor elements\n",
      "    bed_az : bedding dip direction\n",
      "    bed_dip :  bedding dip\n",
      "    \n",
      "    Return\n",
      "    s_rot : [x11,x22,x33,x12,x23,x13] - after rotation\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(pmag.dostilt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.3345571   0.33192658  0.3335163  -0.00043562  0.00092779  0.00105006]\n",
      "[ 3.3585501e-01  3.3191565e-01  3.3222935e-01  5.5959972e-04\n",
      " -5.3161417e-05  6.4731773e-04]\n",
      "[3.3586669e-01 3.3084923e-01 3.3328408e-01 1.4226610e-03 1.3233915e-04\n",
      " 9.2028757e-05]\n",
      "[ 3.3488664e-01  3.3138493e-01  3.3372843e-01 -5.6597008e-04\n",
      " -3.9085373e-04  4.8729391e-05]\n",
      "[ 3.3506602e-01  3.3127019e-01  3.3366373e-01 -1.0519302e-03\n",
      " -5.7256600e-04 -2.9959495e-04]\n",
      "[3.3407688e-01 3.3177567e-01 3.3414748e-01 7.0073889e-05 1.8446925e-04\n",
      " 5.0731825e-05]\n",
      "[ 3.3483925e-01  3.3197853e-01  3.3318222e-01 -2.8446535e-04\n",
      "  3.5184901e-05 -2.9261652e-04]\n",
      "[ 3.3513144e-01  3.3175036e-01  3.3311823e-01  7.7914412e-04\n",
      " -6.4021988e-05  4.6115947e-05]\n"
     ]
    }
   ],
   "source": [
    "# note that the data in this example are Ss and strike and dip (not bed_az,bed_pl)\n",
    "Ss=np.loadtxt('data_files/s_tilt/s_tilt_example.dat')\n",
    "for s in Ss:\n",
    "    print(pmag.dostilt(s[0:6],s[6]+90.,s[7])) # make the bedding azimuth dip direction, not strike. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## scalc\n",
    "\n",
    "[\\[Essentials Chapter 14\\]](https://earthref.org/MagIC/books/Tauxe/Essentials/WebBook3ch14.html#x15-156000813) [\\[command line version\\]](https://pmagpy.github.io/PmagPy-cli.html#scalc.py)\n",
    "\n",
    "\n",
    "This program reads in data files with vgp_lon, vgp_lat and optional kappa, N, and site latitude.\n",
    "It allows some filtering based on the requirements of the study, such as:\n",
    "- Fisher k cutoff\n",
    "- VGP latitudinal cutoff\n",
    "- Vandamme (1994, doi: 10.1016/0031-9201(94)90012-4) iterative cutoff\n",
    "- flipping the reverse mode to antipodes\n",
    "- rotating principle direction to the spin axis\n",
    "- bootstrap confidence bounds\n",
    "- optionally calculates the scatter (Sp or Sf of McElhinny & McFadden, 1997) of VGPs\n",
    "with  correction for within site scatter.  \n",
    "\n",
    "The filtering is just what **Pandas** was designed for, so we can  calls **pmag.scalc_vgp_df()** which works on a suitably constructed  **Pandas** DataFrame.   \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on function scalc_vgp_df in module pmagpy.pmag:\n",
      "\n",
      "scalc_vgp_df(vgp_df, anti=0, rev=0, cutoff=180.0, kappa=0, n=0, spin=0, v=0, boot=0, mm97=0, nb=1000)\n",
      "    Calculates Sf for a dataframe with VGP Lat., and optional Fisher's k, site latitude and N information can be used to correct for within site scatter (McElhinny & McFadden, 1997)\n",
      "    \n",
      "    Parameters\n",
      "    _________\n",
      "    df : Pandas Dataframe with columns\n",
      "        REQUIRED:\n",
      "        vgp_lat :  VGP latitude\n",
      "        ONLY REQUIRED for MM97 correction:\n",
      "        dir_k : Fisher kappa estimate\n",
      "        dir_n_samples : number of samples per site\n",
      "        lat : latitude of the site\n",
      "        mm97 : if True, will do the correction for within site scatter\n",
      "        OPTIONAL:\n",
      "        boot : if True. do bootstrap\n",
      "        nb : number of bootstraps, default is 1000\n",
      "    \n",
      "    Returns\n",
      "    _____________\n",
      "        N : number of VGPs used in calculation\n",
      "        S : S\n",
      "        low : 95% confidence lower bound [0 if boot=0]\n",
      "        high  95% confidence upper bound [0 if boot=0]\n",
      "        cutoff : cutoff used in calculation of  S\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(pmag.scalc_vgp_df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To just calculate the value of S (without the within site scatter) we read in a data file and attach the correct headers to it depending on what is in it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "100    21.8    180.0 \n"
     ]
    }
   ],
   "source": [
    "vgp_df=pd.read_csv('data_files/scalc/scalc_example.txt',delim_whitespace=True,header=None)\n",
    "if len(list(vgp_df.columns))==2:\n",
    "    vgp_df.columns=['vgp_lon','vgp_lat']\n",
    "    vgp_df['dir_k'],vgp_df['dir_n'],vgp_df['lat']=0,0,0\n",
    "else:\n",
    "    vgp_df.columns=['vgp_lon','vgp_lat','dir_k','dir_n_samples','lat']\n",
    "pmag.scalc_vgp_df\n",
    "N,S_B,low,high,cutoff=pmag.scalc_vgp_df(vgp_df)\n",
    "print(N, '%7.1f  %7.1f ' % (S_B, cutoff))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To apply a cutoff for the Fisher k value, we just filter the DataFrame prior to calculating S_b. Let's filter for kappa>50"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "73    18.5    180.0 \n"
     ]
    }
   ],
   "source": [
    "N,S_B,low,high,cutoff=pmag.scalc_vgp_df(vgp_df,kappa=50)\n",
    "print(N, '%7.1f  %7.1f ' % (S_B, cutoff))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To apply the Vandamme (1994) approach, we set v to True"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "89    15.2     32.3 \n"
     ]
    }
   ],
   "source": [
    "N,S_B,low,high,cutoff=pmag.scalc_vgp_df(vgp_df,v=True)\n",
    "print(N, '%7.1f  %7.1f ' % (S_B, cutoff))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To flip the \"reverse\" directions, we set anti to 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "flipping reverse\n",
      "100    21.1    180.0 \n"
     ]
    }
   ],
   "source": [
    "N,S_B,low,high,cutoff=pmag.scalc_vgp_df(vgp_df,anti=True)\n",
    "print(N, '%7.1f  %7.1f ' % (S_B, cutoff))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And, to do relative to the spin axis, set spin to True: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "100    21.6    180.0 \n"
     ]
    }
   ],
   "source": [
    "N,S_B,low,high,cutoff=pmag.scalc_vgp_df(vgp_df,spin=True)\n",
    "print(N, '%7.1f  %7.1f ' % (S_B, cutoff))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## scalc_magic\n",
    "\n",
    "[\\[Essentials Chapter 14\\]](https://earthref.org/MagIC/books/Tauxe/Essentials/WebBook3ch14.html#x15-156000813) [\\[command line version\\]](https://pmagpy.github.io/PmagPy-cli.html#scalc_magic.py)\n",
    "\n",
    "\n",
    "This program does the same thing as [**scalc**](#scalc), but reads in a MagIC formatted file. So, we can do that easy-peasy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "flipping reverse\n",
      "21    17.3    180.0 \n"
     ]
    }
   ],
   "source": [
    "vgp_df=pd.read_csv('data_files/scalc_magic/sites.txt',sep='\\t',header=1)\n",
    "N,S_B,low,high,cutoff=pmag.scalc_vgp_df(vgp_df,anti=True)\n",
    "print(N, '%7.1f  %7.1f ' % (S_B, cutoff))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "flipping reverse\n",
      "21    16.8    180.0 \n"
     ]
    }
   ],
   "source": [
    "vgp_df=pd.read_csv('data_files/scalc_magic/sites.txt',sep='\\t',header=1)\n",
    "N,S_B,low,high,cutoff=pmag.scalc_vgp_df(vgp_df,anti=True,spin=True)\n",
    "print(N, '%7.1f  %7.1f ' % (S_B, cutoff))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## separate_directions\n",
    "\n",
    "Like [pmag.flip( )](#flip), **pmag.separate_directions** divides a directional data set into two modes.  Unlike [pmag.flip( )](#flip), it returns the two separate modes (e.g., normal and reverse)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on function separate_directions in module pmagpy.pmag:\n",
      "\n",
      "separate_directions(di_block)\n",
      "    Separates set of directions into two modes based on principal direction\n",
      "    \n",
      "    Parameters\n",
      "    _______________\n",
      "    di_block : block of nested dec,inc pairs\n",
      "    \n",
      "    Return\n",
      "    mode_1_block,mode_2_block :  two lists of nested dec,inc pairs\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(pmag.separate_directions)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#read in the data into an array\n",
    "vectors=np.loadtxt('data_files/eqarea_ell/tk03.out').transpose()\n",
    "di_block=vectors[0:2].transpose() # decs are di_block[0], incs are di_block[1]\n",
    "# flip the reverse directions to their normal antipodes\n",
    "normal,reverse=pmag.separate_directions(di_block)\n",
    "# and plot them up\n",
    "ipmag.plot_net(1)\n",
    "ipmag.plot_di(di_block=normal,color='red')\n",
    "ipmag.plot_di(di_block=reverse,color='b')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## squish\n",
    "\n",
    "[\\[Essentials Chapter 7\\]](https://earthref.org/MagIC/books/Tauxe/Essentials/WebBook3ch7.html#x15-156000813) [\\[command line version\\]](https://pmagpy.github.io/PmagPy-cli.html#squish.py)\n",
    "\n",
    "\n",
    "\n",
    "This program reads in dec/inc data and \"squishes\" the inclinations using the formula from King \n",
    "(1955, doi: 10.1111/j.1365-246X.1955.tb06558.x)  $\\tan(I_o)=flat \\tan(I_f)$.  \\[See also [unsquish](#unsquish)\\]. \n",
    "We can call **pmag.squish()** from within the notebook.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on function squish in module pmagpy.pmag:\n",
      "\n",
      "squish(incs, f)\n",
      "    returns 'flattened' inclination, assuming factor, f and King (1955) formula:\n",
      "    tan (I_o) = f tan (I_f)\n",
      "    \n",
      "    Parameters\n",
      "    __________\n",
      "    incs : array of inclination (I_f)  data to flatten\n",
      "    f : flattening factor\n",
      "    \n",
      "    Returns\n",
      "    _______\n",
      "    I_o :  inclinations after flattening\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(pmag.squish)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {},
   "outputs": [],
   "source": [
    "di_block=np.loadtxt('data_files/squish/squish_example.dat').transpose()\n",
    "decs=di_block[0]\n",
    "incs=di_block[1]\n",
    "flat=0.4\n",
    "fincs=pmag.squish(incs,flat)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ipmag.plot_net(1)\n",
    "ipmag.plot_di(dec=decs,inc=incs,title='Original',color='blue')\n",
    "ipmag.plot_net(2)\n",
    "ipmag.plot_di(dec=decs,inc=fincs,title='Squished',color='red')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## stats\n",
    "\n",
    "[\\[Essentials Chapter 11\\]](https://earthref.org/MagIC/books/Tauxe/Essentials/WebBook3ch11.html#x15-156000813) [\\[command line version\\]](https://pmagpy.github.io/PmagPy-cli.html#/stats.py)\n",
    "\n",
    "This program just calculates the N, mean, sum, sigma and sigma % for data.  There are numerous ways to do that in **Numpy**, so let's just use those."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "100 9.949869990000002 994.9869990000001 0.9533644867617789\n"
     ]
    }
   ],
   "source": [
    "data=np.loadtxt('data_files/gaussian/gauss.out')\n",
    "print (data.shape[0],data.mean(),data.sum(),data.std())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## strip_magic\n",
    "\n",
    "[\\[Essentials Chapter 15\\]](https://earthref.org/MagIC/books/Tauxe/Essentials/WebBook3ch15.html)\n",
    "[\\[MagIC Database\\]](https://earthref.org/MagIC)\n",
    "[\\[command line version\\]](https://pmagpy.github.io/PmagPy-cli.html#strip_magic.py)\n",
    "\n",
    "We can do this easily using the wonders of **Pandas** and **matplotlib** as demonstrated here.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['site', 'location', 'age', 'age_unit', 'dir_dec', 'dir_inc',\n",
       "       'core_depth', 'lat', 'lon', 'geologic_classes', 'geologic_types',\n",
       "       'lithologies', 'citations', 'vgp_lat', 'vgp_lon', 'paleolatitude',\n",
       "       'vgp_lat_rev', 'vgp_lon_rev'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 115,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# read in the data\n",
    "data=pd.read_csv('data_files/strip_magic/sites.txt',sep='\\t',header=1)\n",
    "# see what's there\n",
    "data.columns\n",
    "\n",
    "# you might have to use **df.dropna()** to clean off unwanted NaN lines or other data massaging\n",
    "# but not for this example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(1,(10,4)) # make the figure\n",
    "plt.plot(data.age,data.vgp_lat,'b-') # plot as blue line\n",
    "plt.plot(data.age,data.vgp_lat,'ro',markeredgecolor=\"black\") # plot as red dots with black rims\n",
    "plt.xlabel('Age (Ma)') # label the time axis\n",
    "plt.ylabel('VGP Lat.$^{\\circ}$')\n",
    "plt.ylim(-90,90) # set the plot limits\n",
    "plt.axhline(color='black'); # put on a zero line"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## sundec\n",
    "\n",
    "[\\[Essentials Chapter 9\\]](https://earthref.org/MagIC/books/Tauxe/Essentials/WebBook3ch9.html)\n",
    "[\\[command line version\\]](https://pmagpy.github.io/PmagPy-cli.html#sundec.py)\n",
    "\n",
    "Paleomagnetists often use the sun to orient their cores, especially if the sampling site is strongly magnetic and would deflect the magnetic compass.  The information required is: where are you (e.g., latitude and longitude), what day is it, what time is it in Greenwhich Mean Time (a.k.a. Universal Time) and where is the sun (e.g., the antipode of the angle the shadow of a gnomon makes with the desired direction)?\n",
    "\n",
    "This calculation is surprisingly accurate and is implemented in the function \n",
    " **pmag.dosundec()**.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on function dosundec in module pmagpy.pmag:\n",
      "\n",
      "dosundec(sundata)\n",
      "    returns the declination for a given set of suncompass data\n",
      "    Parameters\n",
      "    __________\n",
      "      sundata : dictionary with these keys:\n",
      "          date: time string with the format 'yyyy:mm:dd:hr:min'\n",
      "          delta_u: time to SUBTRACT from local time for Universal time\n",
      "          lat: latitude of location (negative for south)\n",
      "          lon: longitude of location (negative for west)\n",
      "          shadow_angle: shadow angle of the desired direction with respect to the sun.\n",
      "    Returns\n",
      "    ________\n",
      "       sunaz : the declination of the desired direction wrt true north.\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(pmag.dosundec)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "Say you (or your elderly colleague) were located at 35$^{\\circ}$ N and 33$^{\\circ}$ E. The local time was three hours ahead of Universal Time. The shadow angle for the drilling direction was 68$^{\\circ}$  measured at 16:09 on May 23, 1994. **pmag.dosundec()** requires a dictionary with the necessary information: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  154.2\n"
     ]
    }
   ],
   "source": [
    "sundata={'delta_u':3,'lat':35,'lon':33,\\\n",
    "         'date':'1994:05:23:16:9','shadow_angle':68}\n",
    "print ('%7.1f'%(pmag.dosundec(sundata)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## tk03\n",
    "\n",
    "[\\[Essentials Chapter 16\\]](https://earthref.org/MagIC/books/Tauxe/Essentials/WebBook3ch16.html)\n",
    "[\\[command line version\\]](https://pmagpy.github.io/PmagPy-cli.html#tk03.py)\n",
    "\n",
    "Sometimes it is useful to generate a distribution of synthetic geomagnetic field vectors that you might expect to find from paleosecular variation of the geomagnetic field. The program **tk03** generates distributions of field vectors from the PSV model of Tauxe and Kent (2004, doi: 10.1029/145GM08).  This program was implemented for notebook use as **ipmag.tk03()**.  \\[See also [**find_ei**](#find_ei)\\]. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on function tk03 in module pmagpy.ipmag:\n",
      "\n",
      "tk03(n=100, dec=0, lat=0, rev='no', G2=0, G3=0)\n",
      "    Generates vectors drawn from the TK03.gad model of secular\n",
      "    variation (Tauxe and Kent, 2004) at given latitude and rotated\n",
      "    about a vertical axis by the given declination. Return a nested list of\n",
      "    of [dec,inc,intensity].\n",
      "    \n",
      "    Parameters\n",
      "    ----------\n",
      "    n : number of vectors to determine (default is 100)\n",
      "    dec : mean declination of data set (default is 0)\n",
      "    lat : latitude at which secular variation is simulated (default is 0)\n",
      "    rev : if reversals are to be included this should be 'yes' (default is 'no')\n",
      "    G2 : specify average g_2^0 fraction (default is 0)\n",
      "    G3 : specify average g_3^0 fraction (default is 0)\n",
      "    \n",
      "    Returns\n",
      "    ----------\n",
      "    tk_03_output : a nested list of declination, inclination, and intensity (in nT)\n",
      "    \n",
      "    Examples\n",
      "    --------\n",
      "    >>> ipmag.tk03(n=5, dec=0, lat=0)\n",
      "    [[14.752502674158681, -36.189370642603834, 16584.848620957589],\n",
      "     [9.2859465437113311, -10.064247301056071, 17383.950391596223],\n",
      "     [2.4278460589582913, 4.8079990844938019, 18243.679003572055],\n",
      "     [352.93759572283585, 0.086693343935840397, 18524.551174838372],\n",
      "     [352.48366219759953, 11.579098286352332, 24928.412830772766]]\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(ipmag.tk03)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "di_block=ipmag.tk03(lat=30)\n",
    "ipmag.plot_net(1)\n",
    "ipmag.plot_di(di_block=di_block,color='red',edge='black')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## uniform\n",
    "\n",
    "[\\[command line version\\]](https://pmagpy.github.io/PmagPy-cli.html#uniform.py)\n",
    "\n",
    "It is at times handy to be able to generate a uniformly distributed set of directions (or geographic locations). This is done using a technique described by Fisher et al. (Fisher, N. I., Lewis, T., & Embleton, B. J. J. (1987). Statistical Analysis of Spherical Data. Cambridge: Cambridge University Press).   We do this by calling  **pmag.get_unf()**.   "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on function get_unf in module pmagpy.pmag:\n",
      "\n",
      "get_unf(N=100)\n",
      "    Generates N uniformly distributed directions\n",
      "    using the way described in Fisher et al. (1987).\n",
      "    Parameters\n",
      "    __________\n",
      "    N : number of directions, default is 100\n",
      "    \n",
      "    Returns\n",
      "    ______\n",
      "    array of nested dec,inc pairs\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(pmag.get_unf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "di_block=pmag.get_unf()\n",
    "ipmag.plot_net(1)\n",
    "ipmag.plot_di(di_block=di_block,color='red',edge='black')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## unsquish\n",
    "\n",
    "[\\[Essentials Chapter 7\\]](https://earthref.org/MagIC/books/Tauxe/Essentials/WebBook3ch7.html#x15-156000813) \n",
    "[\\[Essentials Chapter 16\\]](https://earthref.org/MagIC/books/Tauxe/Essentials/WebBook3ch16.html#x15-156000813) \n",
    "[\\[command line version\\]](https://pmagpy.github.io/PmagPy-cli.html#unsquish.py)\n",
    "\n",
    "\n",
    "\n",
    "This program is just the inverse of [**squish**](#squish) in that it takes \"squished\" data and \"unsquishes\" them, assuming a King (1955, doi: 10.1111/j.1365-246X.1955.tb06558.x)  relationship:  $\\tan(I_o)=flat \\tan(I_f)$. So, $\\tan(I_f) = \\tan(I_o)/flat$. \n",
    "\n",
    "It calls **pmag.unquish()**.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on function unsquish in module pmagpy.pmag:\n",
      "\n",
      "unsquish(incs, f)\n",
      "    returns 'unflattened' inclination, assuming factor, f and King (1955) formula:\n",
      "    tan (I_o) = tan (I_f)/f\n",
      "    \n",
      "    Parameters\n",
      "    __________\n",
      "    incs : array of inclination (I_f)  data to unflatten\n",
      "    f : flattening factor\n",
      "    \n",
      "    Returns\n",
      "    _______\n",
      "    I_o :  inclinations after unflattening\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(pmag.unsquish)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "metadata": {},
   "outputs": [],
   "source": [
    "di_block=np.loadtxt('data_files/unsquish/unsquish_example.dat').transpose()\n",
    "decs=di_block[0]\n",
    "incs=di_block[1]\n",
    "flat=.4\n",
    "fincs=pmag.unsquish(incs,flat)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ipmag.plot_net(1)\n",
    "ipmag.plot_di(dec=decs,inc=incs,title='Squished',color='red')\n",
    "ipmag.plot_net(2)\n",
    "ipmag.plot_di(dec=decs,inc=fincs,title='Unsquished',color='blue')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## vdm_b\n",
    "\n",
    "[\\[Essentials Chapter 2\\]](https://earthref.org/MagIC/books/Tauxe/Essentials/WebBook3ch2.html#x15-1560002)  [\\[command line version\\]](https://pmagpy.github.io/PmagPy-cli.html#vdm_b.py)\n",
    "\n",
    "\n",
    "\n",
    "**vdm_b** is the inverse of [**b_vdm**](#b_vdm) in that it converts a virtual \\[axial\\] dipole moment (vdm or vadm) to a predicted geomagnetic field intensity observed at the earth's surface at a particular (paleo)latitude. This  program calls **pmag.vdm_b()**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on function vdm_b in module pmagpy.pmag:\n",
      "\n",
      "vdm_b(vdm, lat)\n",
      "    Converts a virtual dipole moment (VDM) or a virtual axial dipole moment\n",
      "    (VADM; input in units of Am^2) to a local magnetic field value (output in\n",
      "    units of tesla)\n",
      "    \n",
      "    Parameters\n",
      "    ----------\n",
      "    vdm : V(A)DM in units of Am^2\n",
      "    lat: latitude of site in degrees\n",
      "    \n",
      "    Returns\n",
      "    -------\n",
      "    B: local magnetic field strength in tesla\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(pmag.vdm_b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   33.0 microtesla\n"
     ]
    }
   ],
   "source": [
    "print ('%7.1f microtesla'%(pmag.vdm_b(7.159e22,22)*1e6))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## vector_mean\n",
    "\n",
    "[\\[Essentials Chapter 2\\]](https://earthref.org/MagIC/books/Tauxe/Essentials/WebBook3ch2.html#x15-1560002)  [\\[command line version\\]](https://pmagpy.github.io/PmagPy-cli.html#vector_mean.py)\n",
    "\n",
    "**vector_mean** calculates the vector mean for a set of vectors in polar coordinates (e.g., declination, inclination, intensity).  This is similar to the Fisher mean ([**gofish**](#gofish)) but uses vector length instead of unit vectors.  It calls\n",
    "calls **pmag.vector_mean()**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on function vector_mean in module pmagpy.pmag:\n",
      "\n",
      "vector_mean(data)\n",
      "    calculates the vector mean of a given set of vectors\n",
      "    Parameters\n",
      "    __________\n",
      "    data :  nested array of [dec,inc,intensity]\n",
      "    \n",
      "    Returns\n",
      "    _______\n",
      "    dir : array of [dec, inc, 1]\n",
      "    R : resultant vector length\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(pmag.vector_mean)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "100     1.3    49.6 2289431.981383\n"
     ]
    }
   ],
   "source": [
    "data=np.loadtxt('data_files/vector_mean/vector_mean_example.dat')\n",
    "Dir,R=pmag.vector_mean(data)\n",
    "print (('%i %7.1f %7.1f %f')%(data.shape[0],Dir[0],Dir[1],R))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## vgp_di\n",
    "\n",
    "[\\[Essentials Chapter 2\\]](https://earthref.org/MagIC/books/Tauxe/Essentials/WebBook3ch2.html) \n",
    "[\\[command line version\\]](https://pmagpy.github.io/PmagPy-cli.html#vgp_di.py)\n",
    "\n",
    "\n",
    "We use **vgp_di** to convert virtual geomagnetic pole positions to predicted directions at a given location.  \\[See also [**di_vgp**](#di_vgp)\\].\n",
    "\n",
    "This program uses the function **pmag.vgp_di()**.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on function vgp_di in module pmagpy.pmag:\n",
      "\n",
      "vgp_di(plat, plong, slat, slong)\n",
      "    Converts a pole position (pole latitude, pole longitude) to a direction\n",
      "    (declination, inclination) at a given location (slat, slong) assuming a\n",
      "    dipolar field.\n",
      "    \n",
      "    Parameters\n",
      "    ----------\n",
      "    plat : latitude of pole (vgp latitude)\n",
      "    plong : longitude of pole (vgp longitude)\n",
      "    slat : latitude of site\n",
      "    slong : longitude of site\n",
      "    \n",
      "    Returns\n",
      "    ----------\n",
      "    dec,inc : tuple of declination and inclination\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(pmag.vgp_di)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  335.6    62.9\n"
     ]
    }
   ],
   "source": [
    "d,i=pmag.vgp_di(68,191,33,243)\n",
    "print ('%7.1f %7.1f'%(d,i))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## watsons_f\n",
    "\n",
    "[\\[Essentials Chapter 11\\]](https://earthref.org/MagIC/books/Tauxe/Essentials/WebBook3ch11.html) \n",
    "[\\[command line version\\]](https://pmagpy.github.io/PmagPy-cli.html#watsons_f.py)\n",
    "\n",
    "There are several different ways of testing whether two sets of directional data share a common mean.  One popular (although perhaps not the best) way is to use Watson's F test (Watson, 1956, doi: 10.1111/j.1365-246X.1956.tb05560.x).   \\[See also [**watsons_v**](#watsons_v) or  Lisa Tauxe's bootstrap way: [**common_mean**](#common_mean)\\].  \n",
    "\n",
    "If you still want to use Waston's F, then try \n",
    " **pmag.watsons_f()** for this."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on function watsons_f in module pmagpy.pmag:\n",
      "\n",
      "watsons_f(DI1, DI2)\n",
      "    calculates Watson's F statistic (equation 11.16 in Essentials text book).\n",
      "    \n",
      "    Parameters\n",
      "    _________\n",
      "    DI1 : nested array of [Dec,Inc] pairs\n",
      "    DI2 : nested array of [Dec,Inc] pairs\n",
      "    \n",
      "    Returns\n",
      "    _______\n",
      "    F : Watson's F\n",
      "    Fcrit : critical value from F table\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(pmag.watsons_f)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   5.23    3.26\n"
     ]
    }
   ],
   "source": [
    "DI1=np.loadtxt('data_files/watsons_f/watsons_f_example_file1.dat')\n",
    "DI2=np.loadtxt('data_files/watsons_f/watsons_f_example_file2.dat')\n",
    "F,Fcrit=pmag.watsons_f(DI1,DI2)\n",
    "print ('%7.2f %7.2f'%(F,Fcrit))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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