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   "source": [
    "# Finding unit vector in QD northward direction\n",
    "\n",
    "How to find a unit vector in teh QD northward direction (along QD meridians) at any location, using apexpy:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
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   "source": [
    "import apexpy\n",
    "import numpy as np\n",
    "\n",
    "epoch = 2015 # year at which IGRF coefficients are evaluated\n",
    "a = apexpy.Apex(epoch)\n",
    "\n",
    "glat, glon = 60, 30 # set geodetic latitude and longitude\n",
    "f1, f2 = a.basevectors_qd(glat, glon, 0, coords = 'geo') # last param is height - set to ground here\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\bf{f}_2$ is a vector that points along contours of constant longitude - i.e., along magnetic meridians. The apexpy function returns the east and north-components of this vector. However, it is not a unit vector, so the last step to find a QD northward unit vector is normalize $\\bf{f}_2$:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "QD north at (glat, glon) = (60.0, 30.0) is -0.177 east, 0.984 north\n"
     ]
    }
   ],
   "source": [
    "qd_north = f2 / np.linalg.norm(f2)\n",
    "print('QD north at (glat, glon) = (%.1f, %.1f) is %.3f east, %.3f north' % (glat, glon, qd_north[0], qd_north[1]))"
   ]
  }
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