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# -*- coding: utf-8 -*- |
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"""Classes that make up the core of apexpy.""" |
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import datetime as dt |
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import numpy as np |
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import os |
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import warnings |
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from apexpy import helpers |
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# Below try..catch required for autodoc to work on readthedocs |
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try: |
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from apexpy import fortranapex as fa |
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except ImportError as ierr: |
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warnings.warn("".join(["fortranapex module could not be imported, so ", |
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"apexpy probably won't work. Make sure you have ", |
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"a gfortran compiler. Failed with error: ", |
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str(ierr)])) |
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# Make sure invalid warnings are always shown |
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warnings.filterwarnings('always', message='.*set to NaN where*', |
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module='apexpy.apex') |
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class ApexHeightError(ValueError): |
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"""Specialized ValueError definition, to be used when apex height is wrong. |
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""" |
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pass |
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class Apex(object): |
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"""Calculates coordinate conversions, field-line mapping, and base vectors. |
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Parameters |
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---------- |
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date : NoneType, float, :class:`dt.date`, or :class:`dt.datetime`, optional |
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Determines which IGRF coefficients are used in conversions. Uses |
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current date as default. If float, use decimal year. If None, uses |
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current UTC. (default=None) |
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refh : float, optional |
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Reference height in km for apex coordinates, the field lines are mapped |
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to this height. (default=0) |
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datafile : str or NoneType, optional |
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Path to custom coefficient file, if None uses `apexsh.dat` file |
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(default=None) |
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fortranlib : str or NoneType, optional |
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Path to Fortran Apex CPython library, if None uses linked library file |
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(default=None) |
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Attributes |
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---------- |
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year : float |
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Decimal year used for the IGRF model |
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RE : float |
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Earth radius in km, defaults to mean Earth radius |
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refh : float |
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Reference height in km for apex coordinates |
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datafile : str |
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Path to coefficient file |
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fortranlib : str |
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Path to Fortran Apex CPython library |
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igrf_fn : str |
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IGRF coefficient filename |
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Notes |
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----- |
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The calculations use IGRF-13 with coefficients from 1900 to 2025 [1]_. |
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The geodetic reference ellipsoid is WGS84. |
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References |
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---------- |
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.. [1] Thébault, E. et al. (2015), International Geomagnetic Reference |
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Field: the 12th generation, Earth, Planets and Space, 67(1), 79, |
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:doi:`10.1186/s40623-015-0228-9`. |
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""" |
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# ------------------------ |
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# Define the magic methods |
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def __init__(self, date=None, refh=0, datafile=None, fortranlib=None): |
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if datafile is None: |
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datafile = os.path.join(os.path.dirname(__file__), 'apexsh.dat') |
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if fortranlib is None: |
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fortranlib = fa.__file__ |
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self.RE = 6371.009 # Mean Earth radius in km |
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self.set_refh(refh) # Reference height in km |
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if date is None: |
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self.year = helpers.toYearFraction(dt.datetime.utcnow()) |
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else: |
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try: |
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# Convert date/datetime object to decimal year |
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self.year = helpers.toYearFraction(date) |
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except AttributeError: |
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# Failed while finding datetime attribute, so |
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# date is probably an int or float; use directly |
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self.year = date |
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if not os.path.isfile(datafile): |
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raise IOError('Data file does not exist: {}'.format(datafile)) |
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if not os.path.isfile(fortranlib): |
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raise IOError('Fortran library does not exist: {}'.format( |
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fortranlib)) |
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self.datafile = datafile |
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self.fortranlib = fortranlib |
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# Set the IGRF coefficient text file name |
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self.igrf_fn = os.path.join(os.path.dirname(__file__), |
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'igrf13coeffs.txt') |
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if not os.path.exists(self.igrf_fn): |
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raise OSError("File {} does not exist".format(self.igrf_fn)) |
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# Update the Fortran epoch using the year defined above |
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self.set_epoch(self.year) |
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# Vectorize the fortran functions |
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self._geo2qd = np.frompyfunc( |
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lambda glat, glon, height: fa.apxg2q(glat, (glon + 180) % 360 - 180, |
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height, 0)[:2], 3, 2) |
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self._geo2apex = np.frompyfunc( |
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lambda glat, glon, height: fa.apxg2all(glat, (glon + 180) % 360 |
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- 180, height, self.refh, |
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0)[2:4], 3, 2) |
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self._geo2apexall = np.frompyfunc( |
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lambda glat, glon, height: fa.apxg2all(glat, (glon + 180) % 360 |
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- 180, height, self.refh, |
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1), 3, 14) |
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self._qd2geo = np.frompyfunc( |
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lambda qlat, qlon, height, precision: fa.apxq2g(qlat, (qlon + 180) |
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% 360 - 180, height, |
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precision), 4, 3) |
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self._basevec = np.frompyfunc( |
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lambda glat, glon, height: fa.apxg2q(glat, (glon + 180) % 360 - 180, |
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height, 1)[2:4], 3, 2) |
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# Vectorize other nonvectorized functions |
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self._apex2qd = np.frompyfunc(self._apex2qd_nonvectorized, 3, 2) |
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self._qd2apex = np.frompyfunc(self._qd2apex_nonvectorized, 3, 2) |
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self._get_babs = np.frompyfunc(self._get_babs_nonvectorized, 3, 1) |
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return |
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def __repr__(self): |
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"""Produce an evaluatable representation of the Apex class.""" |
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rstr = "".join(["apexpy.Apex(date=", self.year.__repr__(), ", refh=", |
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self.refh.__repr__(), ", datafile=", |
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self.datafile.__repr__(), ", fortranlib=", |
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self.fortranlib.__repr__(), ")"]) |
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return rstr |
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def __str__(self): |
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"""Produce a user-friendly representation of the Apex class.""" |
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out_str = '\n'.join(["Apex class conversions performed with", |
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"-------------------------------------", |
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"Decimal year: {:.8f}".format(self.year), |
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"Reference height: {:.3f} km".format(self.refh), |
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"Earth radius: {:.3f} km".format(self.RE), '', |
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"Coefficient file: '{:s}'".format(self.datafile), |
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"Cython Fortran library: '{:s}'".format( |
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self.fortranlib)]) |
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return out_str |
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def __eq__(self, comp_obj): |
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"""Performs equivalency evaluation. |
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Parameters |
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---------- |
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comp_obj |
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Object of any time to be compared to the class object |
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Returns |
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------- |
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bool or NotImplemented |
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True if self and comp_obj are identical, False if they are not, |
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and NotImplemented if the classes are not the same |
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""" |
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if isinstance(comp_obj, self.__class__): |
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# Objects are the same if all the attributes are the same |
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for apex_attr in ['year', 'refh', 'RE', 'datafile', 'fortranlib', |
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'igrf_fn']: |
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bad_attr = False |
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if hasattr(self, apex_attr): |
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aval = getattr(self, apex_attr) |
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if hasattr(comp_obj, apex_attr): |
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cval = getattr(comp_obj, apex_attr) |
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if cval != aval: |
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# Not equal, as the attribute values differ |
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bad_attr = True |
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else: |
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# The comparison object is missing an attribute |
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bad_attr = True |
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else: |
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if hasattr(comp_obj, apex_attr): |
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# The current object is missing an attribute |
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bad_attr = True |
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if bad_attr: |
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return False |
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# If we arrive here, all expected attributes exist in both classes |
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# and have the same values |
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return True |
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return NotImplemented |
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# ------------------------- |
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# Define the hidden methods |
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View Code Duplication |
def _apex2qd_nonvectorized(self, alat, alon, height): |
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"""Convert from apex to quasi-dipole (not-vectorised) |
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Parameters |
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----------- |
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alat : (float) |
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Apex latitude in degrees |
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alon : (float) |
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Apex longitude in degrees |
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height : (float) |
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Height in km |
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Returns |
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--------- |
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qlat : (float) |
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Quasi-dipole latitude in degrees |
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qlon : (float) |
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Quasi-diplole longitude in degrees |
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""" |
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# Evaluate the latitude |
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alat = helpers.checklat(alat, name='alat') |
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# Convert modified apex to quasi-dipole, longitude is the same |
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qlon = alon |
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# Get the apex height |
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h_apex = self.get_apex(alat) |
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if h_apex < height: |
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if np.isclose(h_apex, height, rtol=0, atol=1e-5): |
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# Allow for values that are close |
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h_apex = height |
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else: |
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estr = ''.join(['height {:.3g} is > '.format(np.max(height)), |
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'apex height {:.3g} for alat {:.3g}'.format( |
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h_apex, alat)]) |
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raise ApexHeightError(estr) |
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# Convert the latitude |
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salat = np.sign(alat) if alat != 0 else 1 |
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qlat = salat * np.degrees(np.arccos(np.sqrt((self.RE + height) |
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/ (self.RE + h_apex)))) |
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return qlat, qlon |
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View Code Duplication |
def _qd2apex_nonvectorized(self, qlat, qlon, height): |
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"""Converts quasi-dipole to modified apex coordinates. |
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Parameters |
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---------- |
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qlat : float |
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Quasi-dipole latitude |
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qlon : float |
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Quasi-dipole longitude |
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height : float |
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Altitude in km |
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Returns |
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------- |
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alat : float |
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Modified apex latitude |
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alon : float |
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Modified apex longitude |
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Raises |
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------ |
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ApexHeightError |
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if apex height < reference height |
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""" |
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# Evaluate the latitude |
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qlat = helpers.checklat(qlat, name='qlat') |
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# Get the longitude and apex height |
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alon = qlon |
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h_apex = self.get_apex(qlat, height) |
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if h_apex < self.refh: |
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if np.isclose(h_apex, self.refh, rtol=0, atol=1e-5): |
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# Allow for values that are close |
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h_apex = self.refh |
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else: |
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estr = ''.join(['apex height ({:.3g}) is < '.format(h_apex), |
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'reference height ({:.3g})'.format(self.refh), |
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' for qlat {:.3g}'.format(qlat)]) |
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raise ApexHeightError(estr) |
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# Convert the latitude |
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sqlat = np.sign(qlat) if qlat != 0 else 1 |
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alat = sqlat * np.degrees(np.arccos(np.sqrt((self.RE + self.refh) |
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/ (self.RE + h_apex)))) |
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return alat, alon |
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def _map_EV_to_height(self, alat, alon, height, newheight, data, ev_flag): |
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"""Maps electric field related values to a desired height |
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Parameters |
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---------- |
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alat : array-like |
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Apex latitude in degrees. |
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alon : array-like |
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Apex longitude in degrees. |
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height : array-like |
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Current altitude in km. |
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new_height : array-like |
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Desired altitude to which EV values will be mapped in km. |
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data : array-like |
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3D value(s) for the electric field or electric drift |
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ev_flag : str |
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Specify if value is an electric field ('E') or electric drift ('V') |
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Returns |
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------- |
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data_mapped : array-like |
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Data mapped along the magnetic field from the old height to the |
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new height. |
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Raises |
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------ |
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ValueError |
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If an unknown `ev_flag` or badly shaped data input is supplied. |
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""" |
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# Ensure the E-V flag is correct |
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ev_flag = ev_flag.upper() |
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if ev_flag not in ['E', 'V']: |
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raise ValueError('unknown electric field/drift flag') |
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# Make sure data is array of correct shape |
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if not (np.ndim(data) == 1 |
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and np.size(data) == 3) and not (np.ndim(data) == 2 |
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and np.shape(data)[0] == 3): |
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# Raise ValueError because if passing e.g. a (6,) ndarray the |
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|
# reshape below will work even though the input is invalid |
359
|
|
|
raise ValueError('{:} must be (3, N) or (3,) ndarray'.format( |
360
|
|
|
ev_flag)) |
361
|
|
|
|
362
|
|
|
data = np.reshape(data, (3, np.size(data) // 3)) |
363
|
|
|
|
364
|
|
|
# Get the necessary base vectors at the current and new height |
365
|
|
|
v1 = list() |
366
|
|
|
v2 = list() |
367
|
|
|
for i, alt in enumerate([height, newheight]): |
368
|
|
|
_, _, _, _, _, _, d1, d2, _, e1, e2, _ = self.basevectors_apex( |
369
|
|
|
alat, alon, alt, coords='apex') |
370
|
|
|
|
371
|
|
|
if ev_flag == 'E' and i == 0 or ev_flag == 'V' and i == 1: |
372
|
|
|
v1.append(e1) |
373
|
|
|
v2.append(e2) |
374
|
|
|
else: |
375
|
|
|
v1.append(d1) |
376
|
|
|
v2.append(d2) |
377
|
|
|
|
378
|
|
|
# Make sure v1 and v2 have shape (3, N) |
379
|
|
|
v1[-1] = np.reshape(v1[-1], (3, v1[-1].size // 3)) |
380
|
|
|
v2[-1] = np.reshape(v2[-1], (3, v2[-1].size // 3)) |
381
|
|
|
|
382
|
|
|
# Take the dot product between the data value and each base vector |
383
|
|
|
# at the current height |
384
|
|
|
data1 = np.sum(data * v1[0], axis=0) |
385
|
|
|
data2 = np.sum(data * v2[0], axis=0) |
386
|
|
|
|
387
|
|
|
# Map the data to the new height, removing any axes of length 1 |
388
|
|
|
# after the calculation |
389
|
|
|
data_mapped = np.squeeze(data1[np.newaxis, :] * v1[1] |
390
|
|
|
+ data2[np.newaxis, :] * v2[1]) |
391
|
|
|
|
392
|
|
|
return data_mapped |
393
|
|
|
|
394
|
|
|
def _get_babs_nonvectorized(self, glat, glon, height): |
395
|
|
|
"""Get the absolute value of the B-field in Tesla |
396
|
|
|
|
397
|
|
|
Parameters |
398
|
|
|
---------- |
399
|
|
|
glat : float |
400
|
|
|
Geodetic latitude in degrees |
401
|
|
|
glon : float |
402
|
|
|
Geodetic longitude in degrees |
403
|
|
|
height : float |
404
|
|
|
Altitude in km |
405
|
|
|
|
406
|
|
|
Returns |
407
|
|
|
------- |
408
|
|
|
babs : float |
409
|
|
|
Absolute value of the magnetic field in Tesla |
410
|
|
|
|
411
|
|
|
""" |
412
|
|
|
# Evaluate the latitude |
413
|
|
|
glat = helpers.checklat(glat, name='qlat') |
414
|
|
|
|
415
|
|
|
# Get the magnetic field output: North, East, Down, Absolute value |
416
|
|
|
bout = fa.feldg(1, glat, glon, height) |
417
|
|
|
|
418
|
|
|
# Convert the absolute value from Gauss to Tesla |
419
|
|
|
babs = bout[-1] / 10000.0 |
420
|
|
|
|
421
|
|
|
return babs |
422
|
|
|
|
423
|
|
|
# ----------------------- |
424
|
|
|
# Define the user methods |
425
|
|
|
|
426
|
|
|
def convert(self, lat, lon, source, dest, height=0, datetime=None, |
427
|
|
|
precision=1e-10, ssheight=50 * 6371): |
428
|
|
|
"""Converts between geodetic, modified apex, quasi-dipole and MLT. |
429
|
|
|
|
430
|
|
|
Parameters |
431
|
|
|
---------- |
432
|
|
|
lat : array_like |
433
|
|
|
Latitude in degrees |
434
|
|
|
lon : array_like |
435
|
|
|
Longitude in degrees or MLT in hours |
436
|
|
|
source : str |
437
|
|
|
Input coordinate system, accepts 'geo', 'apex', 'qd', or 'mlt' |
438
|
|
|
dest : str |
439
|
|
|
Output coordinate system, accepts 'geo', 'apex', 'qd', or 'mlt' |
440
|
|
|
height : array_like, optional |
441
|
|
|
Altitude in km |
442
|
|
|
datetime : :class:`datetime.datetime` |
443
|
|
|
Date and time for MLT conversions (required for MLT conversions) |
444
|
|
|
precision : float, optional |
445
|
|
|
Precision of output (degrees) when converting to geo. A negative |
446
|
|
|
value of this argument produces a low-precision calculation of |
447
|
|
|
geodetic lat/lon based only on their spherical harmonic |
448
|
|
|
representation. |
449
|
|
|
A positive value causes the underlying Fortran routine to iterate |
450
|
|
|
until feeding the output geo lat/lon into geo2qd (APXG2Q) reproduces |
451
|
|
|
the input QD lat/lon to within the specified precision (all |
452
|
|
|
coordinates being converted to geo are converted to QD first and |
453
|
|
|
passed through APXG2Q). |
454
|
|
|
ssheight : float, optional |
455
|
|
|
Altitude in km to use for converting the subsolar point from |
456
|
|
|
geographic to magnetic coordinates. A high altitude is used |
457
|
|
|
to ensure the subsolar point is mapped to high latitudes, which |
458
|
|
|
prevents the South-Atlantic Anomaly (SAA) from influencing the MLT. |
459
|
|
|
|
460
|
|
|
Returns |
461
|
|
|
------- |
462
|
|
|
lat : ndarray or float |
463
|
|
|
Converted latitude (if converting to MLT, output latitude is apex) |
464
|
|
|
lon : ndarray or float |
465
|
|
|
Converted longitude or MLT |
466
|
|
|
|
467
|
|
|
Raises |
468
|
|
|
------ |
469
|
|
|
ValueError |
470
|
|
|
For unknown source or destination coordinate system or a missing |
471
|
|
|
or badly formed latitude or datetime input |
472
|
|
|
|
473
|
|
|
""" |
474
|
|
|
# Test the input values |
475
|
|
|
source = source.lower() |
476
|
|
|
dest = dest.lower() |
477
|
|
|
|
478
|
|
|
if source not in ['geo', 'apex', 'qd', 'mlt'] \ |
479
|
|
|
or dest not in ['geo', 'apex', 'qd', 'mlt']: |
480
|
|
|
estr = 'Unknown coordinate transformation: {} -> {}'.format(source, |
481
|
|
|
dest) |
482
|
|
|
raise ValueError(estr) |
483
|
|
|
|
484
|
|
|
if datetime is None and ('mlt' in [source, dest]): |
485
|
|
|
raise ValueError('datetime must be given for MLT calculations') |
486
|
|
|
|
487
|
|
|
lat = helpers.checklat(lat) |
488
|
|
|
|
489
|
|
|
if source == dest: |
490
|
|
|
# The source and destination are the same, no conversion necessary |
491
|
|
|
return lat, lon |
492
|
|
|
else: |
493
|
|
|
# Select the correct conversion method |
494
|
|
|
if source == 'geo': |
495
|
|
|
if dest == 'qd': |
496
|
|
|
lat, lon = self.geo2qd(lat, lon, height) |
497
|
|
|
else: |
498
|
|
|
lat, lon = self.geo2apex(lat, lon, height) |
499
|
|
|
if dest == 'mlt': |
500
|
|
|
lon = self.mlon2mlt(lon, datetime, ssheight=ssheight) |
501
|
|
|
elif source == 'apex': |
502
|
|
|
if dest == 'geo': |
503
|
|
|
lat, lon, _ = self.apex2geo(lat, lon, height, |
504
|
|
|
precision=precision) |
505
|
|
|
elif dest == 'qd': |
506
|
|
|
lat, lon = self.apex2qd(lat, lon, height=height) |
507
|
|
|
elif dest == 'mlt': |
508
|
|
|
lon = self.mlon2mlt(lon, datetime, ssheight=ssheight) |
509
|
|
|
elif source == 'qd': |
510
|
|
|
if dest == 'geo': |
511
|
|
|
lat, lon, _ = self.qd2geo(lat, lon, height, |
512
|
|
|
precision=precision) |
513
|
|
|
else: |
514
|
|
|
lat, lon = self.qd2apex(lat, lon, height=height) |
515
|
|
|
if dest == 'mlt': |
516
|
|
|
lon = self.mlon2mlt(lon, datetime, ssheight=ssheight) |
517
|
|
|
elif source == 'mlt': |
518
|
|
|
# From MLT means that the input latitude is assumed to be apex, |
519
|
|
|
# so we don't need to update latitude for apex conversions. |
520
|
|
|
lon = self.mlt2mlon(lon, datetime, ssheight=ssheight) |
521
|
|
|
if dest == 'geo': |
522
|
|
|
lat, lon, _ = self.apex2geo(lat, lon, height, |
523
|
|
|
precision=precision) |
524
|
|
|
elif dest == 'qd': |
525
|
|
|
lat, lon = self.apex2qd(lat, lon, height=height) |
526
|
|
|
|
527
|
|
|
return lat, lon |
528
|
|
|
|
529
|
|
|
def geo2apex(self, glat, glon, height): |
530
|
|
|
"""Converts geodetic to modified apex coordinates. |
531
|
|
|
|
532
|
|
|
Parameters |
533
|
|
|
---------- |
534
|
|
|
glat : array_like |
535
|
|
|
Geodetic latitude |
536
|
|
|
glon : array_like |
537
|
|
|
Geodetic longitude |
538
|
|
|
height : array_like |
539
|
|
|
Altitude in km |
540
|
|
|
|
541
|
|
|
Returns |
542
|
|
|
------- |
543
|
|
|
alat : ndarray or float |
544
|
|
|
Modified apex latitude |
545
|
|
|
alon : ndarray or float |
546
|
|
|
Modified apex longitude |
547
|
|
|
|
548
|
|
|
""" |
549
|
|
|
|
550
|
|
|
glat = helpers.checklat(glat, name='glat') |
551
|
|
|
|
552
|
|
|
alat, alon = self._geo2apex(glat, glon, height) |
553
|
|
|
|
554
|
|
|
if np.any(alat == -9999): |
555
|
|
|
warnings.warn(''.join(['Apex latitude set to NaN where undefined ', |
556
|
|
|
'(apex height may be < reference height)'])) |
557
|
|
|
if np.isscalar(alat): |
558
|
|
|
alat = np.nan |
559
|
|
|
else: |
560
|
|
|
alat[alat == -9999] = np.nan |
561
|
|
|
|
562
|
|
|
# If array is returned, dtype is object, so convert to float |
563
|
|
|
return np.float64(alat), np.float64(alon) |
564
|
|
|
|
565
|
|
|
def apex2geo(self, alat, alon, height, precision=1e-10): |
566
|
|
|
"""Converts modified apex to geodetic coordinates. |
567
|
|
|
|
568
|
|
|
Parameters |
569
|
|
|
---------- |
570
|
|
|
alat : array_like |
571
|
|
|
Modified apex latitude |
572
|
|
|
alon : array_like |
573
|
|
|
Modified apex longitude |
574
|
|
|
height : array_like |
575
|
|
|
Altitude in km |
576
|
|
|
precision : float, optional |
577
|
|
|
Precision of output (degrees). A negative value of this argument |
578
|
|
|
produces a low-precision calculation of geodetic lat/lon based only |
579
|
|
|
on their spherical harmonic representation. A positive value causes |
580
|
|
|
the underlying Fortran routine to iterate until feeding the output |
581
|
|
|
geo lat/lon into geo2qd (APXG2Q) reproduces the input QD lat/lon to |
582
|
|
|
within the specified precision. |
583
|
|
|
|
584
|
|
|
Returns |
585
|
|
|
------- |
586
|
|
|
glat : ndarray or float |
587
|
|
|
Geodetic latitude |
588
|
|
|
glon : ndarray or float |
589
|
|
|
Geodetic longitude |
590
|
|
|
error : ndarray or float |
591
|
|
|
The angular difference (degrees) between the input QD coordinates |
592
|
|
|
and the qlat/qlon produced by feeding the output glat and glon |
593
|
|
|
into geo2qd (APXG2Q) |
594
|
|
|
|
595
|
|
|
""" |
596
|
|
|
# Evaluate the latitude |
597
|
|
|
alat = helpers.checklat(alat, name='alat') |
598
|
|
|
|
599
|
|
|
# Perform the two-step convertion to geodetic coordinates |
600
|
|
|
qlat, qlon = self.apex2qd(alat, alon, height=height) |
601
|
|
|
glat, glon, error = self.qd2geo(qlat, qlon, height, precision=precision) |
602
|
|
|
|
603
|
|
|
return glat, glon, error |
604
|
|
|
|
605
|
|
|
def geo2qd(self, glat, glon, height): |
606
|
|
|
"""Converts geodetic to quasi-dipole coordinates. |
607
|
|
|
|
608
|
|
|
Parameters |
609
|
|
|
---------- |
610
|
|
|
glat : array_like |
611
|
|
|
Geodetic latitude |
612
|
|
|
glon : array_like |
613
|
|
|
Geodetic longitude |
614
|
|
|
height : array_like |
615
|
|
|
Altitude in km |
616
|
|
|
|
617
|
|
|
Returns |
618
|
|
|
------- |
619
|
|
|
qlat : ndarray or float |
620
|
|
|
Quasi-dipole latitude |
621
|
|
|
qlon : ndarray or float |
622
|
|
|
Quasi-dipole longitude |
623
|
|
|
|
624
|
|
|
""" |
625
|
|
|
# Evaluate the latitude |
626
|
|
|
glat = helpers.checklat(glat, name='glat') |
627
|
|
|
|
628
|
|
|
# Convert to quasi-dipole coordinates |
629
|
|
|
qlat, qlon = self._geo2qd(glat, glon, height) |
630
|
|
|
|
631
|
|
|
# If array is returned, dtype is object, so convert to float |
632
|
|
|
return np.float64(qlat), np.float64(qlon) |
633
|
|
|
|
634
|
|
|
def qd2geo(self, qlat, qlon, height, precision=1e-10): |
635
|
|
|
"""Converts quasi-dipole to geodetic coordinates. |
636
|
|
|
|
637
|
|
|
Parameters |
638
|
|
|
---------- |
639
|
|
|
qlat : array_like |
640
|
|
|
Quasi-dipole latitude |
641
|
|
|
qlon : array_like |
642
|
|
|
Quasi-dipole longitude |
643
|
|
|
height : array_like |
644
|
|
|
Altitude in km |
645
|
|
|
precision : float, optional |
646
|
|
|
Precision of output (degrees). A negative value of this argument |
647
|
|
|
produces a low-precision calculation of geodetic lat/lon based only |
648
|
|
|
on their spherical harmonic representation. A positive value causes |
649
|
|
|
the underlying Fortran routine to iterate until feeding the output |
650
|
|
|
geo lat/lon into geo2qd (APXG2Q) reproduces the input QD lat/lon to |
651
|
|
|
within the specified precision. |
652
|
|
|
|
653
|
|
|
Returns |
654
|
|
|
------- |
655
|
|
|
glat : ndarray or float |
656
|
|
|
Geodetic latitude |
657
|
|
|
glon : ndarray or float |
658
|
|
|
Geodetic longitude |
659
|
|
|
error : ndarray or float |
660
|
|
|
The angular difference (degrees) between the input QD coordinates |
661
|
|
|
and the qlat/qlon produced by feeding the output glat and glon |
662
|
|
|
into geo2qd (APXG2Q) |
663
|
|
|
|
664
|
|
|
""" |
665
|
|
|
# Evaluate the latitude |
666
|
|
|
qlat = helpers.checklat(qlat, name='qlat') |
667
|
|
|
|
668
|
|
|
# Convert to geodetic coordinates |
669
|
|
|
glat, glon, error = self._qd2geo(qlat, qlon, height, precision) |
670
|
|
|
|
671
|
|
|
# If array is returned, dtype is object, so convert to float |
672
|
|
|
return np.float64(glat), np.float64(glon), np.float64(error) |
673
|
|
|
|
674
|
|
|
def apex2qd(self, alat, alon, height): |
675
|
|
|
"""Converts modified apex to quasi-dipole coordinates. |
676
|
|
|
|
677
|
|
|
Parameters |
678
|
|
|
---------- |
679
|
|
|
alat : array_like |
680
|
|
|
Modified apex latitude |
681
|
|
|
alon : array_like |
682
|
|
|
Modified apex longitude |
683
|
|
|
height : array_like |
684
|
|
|
Altitude in km |
685
|
|
|
|
686
|
|
|
Returns |
687
|
|
|
------- |
688
|
|
|
qlat : ndarray or float |
689
|
|
|
Quasi-dipole latitude |
690
|
|
|
qlon : ndarray or float |
691
|
|
|
Quasi-dipole longitude |
692
|
|
|
|
693
|
|
|
Raises |
694
|
|
|
------ |
695
|
|
|
ApexHeightError |
696
|
|
|
if `height` > apex height |
697
|
|
|
|
698
|
|
|
""" |
699
|
|
|
# Convert the latitude to apex, latitude check performed in the |
700
|
|
|
# hidden method |
701
|
|
|
qlat, qlon = self._apex2qd(alat, alon, height) |
702
|
|
|
|
703
|
|
|
# If array is returned, the dtype is object, so convert to float |
704
|
|
|
return np.float64(qlat), np.float64(qlon) |
705
|
|
|
|
706
|
|
|
def qd2apex(self, qlat, qlon, height): |
707
|
|
|
"""Converts quasi-dipole to modified apex coordinates. |
708
|
|
|
|
709
|
|
|
Parameters |
710
|
|
|
---------- |
711
|
|
|
qlat : array_like |
712
|
|
|
Quasi-dipole latitude |
713
|
|
|
qlon : array_like |
714
|
|
|
Quasi-dipole longitude |
715
|
|
|
height : array_like |
716
|
|
|
Altitude in km |
717
|
|
|
|
718
|
|
|
Returns |
719
|
|
|
------- |
720
|
|
|
alat : ndarray or float |
721
|
|
|
Modified apex latitude |
722
|
|
|
alon : ndarray or float |
723
|
|
|
Modified apex longitude |
724
|
|
|
|
725
|
|
|
Raises |
726
|
|
|
------ |
727
|
|
|
ApexHeightError |
728
|
|
|
if apex height < reference height |
729
|
|
|
|
730
|
|
|
""" |
731
|
|
|
# Perform the conversion from quasi-dipole to apex coordinates |
732
|
|
|
alat, alon = self._qd2apex(qlat, qlon, height) |
733
|
|
|
|
734
|
|
|
# If array is returned, the dtype is object, so convert to float |
735
|
|
|
return np.float64(alat), np.float64(alon) |
736
|
|
|
|
737
|
|
|
def mlon2mlt(self, mlon, dtime, ssheight=318550): |
738
|
|
|
"""Computes the magnetic local time at the specified magnetic longitude |
739
|
|
|
and UT. |
740
|
|
|
|
741
|
|
|
Parameters |
742
|
|
|
---------- |
743
|
|
|
mlon : array_like |
744
|
|
|
Magnetic longitude (apex and quasi-dipole longitude are always |
745
|
|
|
equal) |
746
|
|
|
dtime : :class:`datetime.datetime` |
747
|
|
|
Date and time |
748
|
|
|
ssheight : float, optional |
749
|
|
|
Altitude in km to use for converting the subsolar point from |
750
|
|
|
geographic to magnetic coordinates. A high altitude is used |
751
|
|
|
to ensure the subsolar point is mapped to high latitudes, which |
752
|
|
|
prevents the South-Atlantic Anomaly (SAA) from influencing the MLT. |
753
|
|
|
The current default is 50 * 6371, roughly 50 RE. (default=318550) |
754
|
|
|
|
755
|
|
|
Returns |
756
|
|
|
------- |
757
|
|
|
mlt : ndarray or float |
758
|
|
|
Magnetic local time in hours [0, 24) |
759
|
|
|
|
760
|
|
|
Notes |
761
|
|
|
----- |
762
|
|
|
To compute the MLT, we find the apex longitude of the subsolar point at |
763
|
|
|
the given time. Then the MLT of the given point will be computed from |
764
|
|
|
the separation in magnetic longitude from this point (1 hour = 15 |
765
|
|
|
degrees). |
766
|
|
|
|
767
|
|
|
""" |
768
|
|
|
# Get the subsolar location |
769
|
|
|
ssglat, ssglon = helpers.subsol(dtime) |
770
|
|
|
|
771
|
|
|
# Convert the subsolar location to apex coordinates |
772
|
|
|
_, ssalon = self.geo2apex(ssglat, ssglon, ssheight) |
773
|
|
|
|
774
|
|
|
# Calculate the magnetic local time (0-24 h range) from apex longitude. |
775
|
|
|
# np.float64 will ensure lists are converted to arrays |
776
|
|
|
mlt = (180 + np.float64(mlon) - ssalon) / 15 % 24 |
777
|
|
|
|
778
|
|
|
return mlt |
779
|
|
|
|
780
|
|
|
def mlt2mlon(self, mlt, dtime, ssheight=318550): |
781
|
|
|
"""Computes the magnetic longitude at the specified MLT and UT. |
782
|
|
|
|
783
|
|
|
Parameters |
784
|
|
|
---------- |
785
|
|
|
mlt : array_like |
786
|
|
|
Magnetic local time |
787
|
|
|
dtime : :class:`datetime.datetime` |
788
|
|
|
Date and time |
789
|
|
|
ssheight : float, optional |
790
|
|
|
Altitude in km to use for converting the subsolar point from |
791
|
|
|
geographic to magnetic coordinates. A high altitude is used |
792
|
|
|
to ensure the subsolar point is mapped to high latitudes, which |
793
|
|
|
prevents the South-Atlantic Anomaly (SAA) from influencing the MLT. |
794
|
|
|
The current default is 50 * 6371, roughly 50 RE. (default=318550) |
795
|
|
|
|
796
|
|
|
Returns |
797
|
|
|
------- |
798
|
|
|
mlon : ndarray or float |
799
|
|
|
Magnetic longitude [0, 360) (apex and quasi-dipole longitude are |
800
|
|
|
always equal) |
801
|
|
|
|
802
|
|
|
Notes |
803
|
|
|
----- |
804
|
|
|
To compute the magnetic longitude, we find the apex longitude of the |
805
|
|
|
subsolar point at the given time. Then the magnetic longitude of the |
806
|
|
|
given point will be computed from the separation in magnetic local time |
807
|
|
|
from this point (1 hour = 15 degrees). |
808
|
|
|
""" |
809
|
|
|
# Get the location of the subsolar point at this time |
810
|
|
|
ssglat, ssglon = helpers.subsol(dtime) |
811
|
|
|
|
812
|
|
|
# Convert the location of the subsolar point to apex coordinates |
813
|
|
|
_, ssalon = self.geo2apex(ssglat, ssglon, ssheight) |
814
|
|
|
|
815
|
|
|
# Calculate the magnetic longitude (0-360 h range) from MLT. |
816
|
|
|
# np.float64 will ensure lists are converted to arrays |
817
|
|
|
mlon = (15 * np.float64(mlt) - 180 + ssalon + 360) % 360 |
818
|
|
|
|
819
|
|
|
return mlon |
820
|
|
|
|
821
|
|
|
def map_to_height(self, glat, glon, height, newheight, conjugate=False, |
822
|
|
|
precision=1e-10): |
823
|
|
|
"""Performs mapping of points along the magnetic field to the closest |
824
|
|
|
or conjugate hemisphere. |
825
|
|
|
|
826
|
|
|
Parameters |
827
|
|
|
---------- |
828
|
|
|
glat : array_like |
829
|
|
|
Geodetic latitude |
830
|
|
|
glon : array_like |
831
|
|
|
Geodetic longitude |
832
|
|
|
height : array_like |
833
|
|
|
Source altitude in km |
834
|
|
|
newheight : array_like |
835
|
|
|
Destination altitude in km |
836
|
|
|
conjugate : bool, optional |
837
|
|
|
Map to `newheight` in the conjugate hemisphere instead of the |
838
|
|
|
closest hemisphere |
839
|
|
|
precision : float, optional |
840
|
|
|
Precision of output (degrees). A negative value of this argument |
841
|
|
|
produces a low-precision calculation of geodetic lat/lon based only |
842
|
|
|
on their spherical harmonic representation. A positive value causes |
843
|
|
|
the underlying Fortran routine to iterate until feeding the output |
844
|
|
|
geo lat/lon into geo2qd (APXG2Q) reproduces the input QD lat/lon to |
845
|
|
|
within the specified precision. |
846
|
|
|
|
847
|
|
|
Returns |
848
|
|
|
------- |
849
|
|
|
newglat : ndarray or float |
850
|
|
|
Geodetic latitude of mapped point |
851
|
|
|
newglon : ndarray or float |
852
|
|
|
Geodetic longitude of mapped point |
853
|
|
|
error : ndarray or float |
854
|
|
|
The angular difference (degrees) between the input QD coordinates |
855
|
|
|
and the qlat/qlon produced by feeding the output glat and glon |
856
|
|
|
into geo2qd (APXG2Q) |
857
|
|
|
|
858
|
|
|
Notes |
859
|
|
|
----- |
860
|
|
|
The mapping is done by converting glat/glon/height to modified apex |
861
|
|
|
lat/lon, and converting back to geographic using newheight (if |
862
|
|
|
conjugate, use negative apex latitude when converting back) |
863
|
|
|
|
864
|
|
|
""" |
865
|
|
|
|
866
|
|
|
alat, alon = self.geo2apex(glat, glon, height) |
867
|
|
|
if conjugate: |
868
|
|
|
alat = -alat |
869
|
|
|
try: |
870
|
|
|
newglat, newglon, error = self.apex2geo(alat, alon, newheight, |
871
|
|
|
precision=precision) |
872
|
|
|
except ApexHeightError: |
873
|
|
|
raise ApexHeightError("input height is > apex height") |
874
|
|
|
|
875
|
|
|
return newglat, newglon, error |
876
|
|
|
|
877
|
|
|
def map_E_to_height(self, alat, alon, height, newheight, edata): |
878
|
|
|
"""Performs mapping of electric field along the magnetic field. |
879
|
|
|
|
880
|
|
|
It is assumed that the electric field is perpendicular to B. |
881
|
|
|
|
882
|
|
|
Parameters |
883
|
|
|
---------- |
884
|
|
|
alat : (N,) array_like or float |
885
|
|
|
Modified apex latitude |
886
|
|
|
alon : (N,) array_like or float |
887
|
|
|
Modified apex longitude |
888
|
|
|
height : (N,) array_like or float |
889
|
|
|
Source altitude in km |
890
|
|
|
newheight : (N,) array_like or float |
891
|
|
|
Destination altitude in km |
892
|
|
|
edata : (3,) or (3, N) array_like |
893
|
|
|
Electric field (at `alat`, `alon`, `height`) in geodetic east, |
894
|
|
|
north, and up components |
895
|
|
|
|
896
|
|
|
Returns |
897
|
|
|
------- |
898
|
|
|
out : (3, N) or (3,) ndarray |
899
|
|
|
The electric field at `newheight` (geodetic east, north, and up |
900
|
|
|
components) |
901
|
|
|
|
902
|
|
|
""" |
903
|
|
|
# Call hidden mapping method with flag for the electric field |
904
|
|
|
out = self._map_EV_to_height(alat, alon, height, newheight, edata, 'E') |
905
|
|
|
|
906
|
|
|
return out |
907
|
|
|
|
908
|
|
|
def map_V_to_height(self, alat, alon, height, newheight, vdata): |
909
|
|
|
"""Performs mapping of electric drift velocity along the magnetic field. |
910
|
|
|
|
911
|
|
|
It is assumed that the electric field is perpendicular to B. |
912
|
|
|
|
913
|
|
|
Parameters |
914
|
|
|
---------- |
915
|
|
|
alat : (N,) array_like or float |
916
|
|
|
Modified apex latitude |
917
|
|
|
alon : (N,) array_like or float |
918
|
|
|
Modified apex longitude |
919
|
|
|
height : (N,) array_like or float |
920
|
|
|
Source altitude in km |
921
|
|
|
newheight : (N,) array_like or float |
922
|
|
|
Destination altitude in km |
923
|
|
|
vdata : (3,) or (3, N) array_like |
924
|
|
|
Electric drift velocity (at `alat`, `alon`, `height`) in geodetic |
925
|
|
|
east, north, and up components |
926
|
|
|
|
927
|
|
|
Returns |
928
|
|
|
------- |
929
|
|
|
out : (3, N) or (3,) ndarray |
930
|
|
|
The electric drift velocity at `newheight` (geodetic east, north, |
931
|
|
|
and up components) |
932
|
|
|
|
933
|
|
|
""" |
934
|
|
|
# Call hidden mapping method with flag for the electric drift velocities |
935
|
|
|
out = self._map_EV_to_height(alat, alon, height, newheight, vdata, 'V') |
936
|
|
|
|
937
|
|
|
return out |
938
|
|
|
|
939
|
|
|
def basevectors_qd(self, lat, lon, height, coords='geo', precision=1e-10): |
940
|
|
|
"""Get quasi-dipole base vectors f1 and f2 at the specified coordinates. |
941
|
|
|
|
942
|
|
|
Parameters |
943
|
|
|
---------- |
944
|
|
|
lat : (N,) array_like or float |
945
|
|
|
Latitude |
946
|
|
|
lon : (N,) array_like or float |
947
|
|
|
Longitude |
948
|
|
|
height : (N,) array_like or float |
949
|
|
|
Altitude in km |
950
|
|
|
coords : {'geo', 'apex', 'qd'}, optional |
951
|
|
|
Input coordinate system |
952
|
|
|
precision : float, optional |
953
|
|
|
Precision of output (degrees) when converting to geo. A negative |
954
|
|
|
value of this argument produces a low-precision calculation of |
955
|
|
|
geodetic lat/lon based only on their spherical harmonic |
956
|
|
|
representation. |
957
|
|
|
A positive value causes the underlying Fortran routine to iterate |
958
|
|
|
until feeding the output geo lat/lon into geo2qd (APXG2Q) reproduces |
959
|
|
|
the input QD lat/lon to within the specified precision (all |
960
|
|
|
coordinates being converted to geo are converted to QD first and |
961
|
|
|
passed through APXG2Q). |
962
|
|
|
|
963
|
|
|
Returns |
964
|
|
|
------- |
965
|
|
|
f1 : (2, N) or (2,) ndarray |
966
|
|
|
f2 : (2, N) or (2,) ndarray |
967
|
|
|
|
968
|
|
|
Notes |
969
|
|
|
----- |
970
|
|
|
The vectors are described by Richmond [1995] [2]_ and |
971
|
|
|
Emmert et al. [2010] [3]_. The vector components are geodetic east and |
972
|
|
|
north. |
973
|
|
|
|
974
|
|
|
References |
975
|
|
|
---------- |
976
|
|
|
.. [2] Richmond, A. D. (1995), Ionospheric Electrodynamics Using |
977
|
|
|
Magnetic Apex Coordinates, Journal of geomagnetism and |
978
|
|
|
geoelectricity, 47(2), 191–212, :doi:`10.5636/jgg.47.191`. |
979
|
|
|
|
980
|
|
|
.. [3] Emmert, J. T., A. D. Richmond, and D. P. Drob (2010), |
981
|
|
|
A computationally compact representation of Magnetic-Apex |
982
|
|
|
and Quasi-Dipole coordinates with smooth base vectors, |
983
|
|
|
J. Geophys. Res., 115(A8), A08322, :doi:`10.1029/2010JA015326`. |
984
|
|
|
|
985
|
|
|
""" |
986
|
|
|
# Convert from current coordinates to geodetic coordinates |
987
|
|
|
glat, glon = self.convert(lat, lon, coords, 'geo', height=height, |
988
|
|
|
precision=precision) |
989
|
|
|
|
990
|
|
|
# Get the geodetic base vectors |
991
|
|
|
f1, f2 = self._basevec(glat, glon, height) |
992
|
|
|
|
993
|
|
|
# If inputs are not scalar, each vector is an array of arrays, |
994
|
|
|
# so reshape to a single array |
995
|
|
|
if f1.dtype == object: |
996
|
|
|
f1 = np.vstack(f1).T |
997
|
|
|
f2 = np.vstack(f2).T |
998
|
|
|
|
999
|
|
|
return f1, f2 |
1000
|
|
|
|
1001
|
|
|
def basevectors_apex(self, lat, lon, height, coords='geo', precision=1e-10): |
1002
|
|
|
"""Returns base vectors in quasi-dipole and apex coordinates. |
1003
|
|
|
|
1004
|
|
|
Parameters |
1005
|
|
|
---------- |
1006
|
|
|
lat : array_like or float |
1007
|
|
|
Latitude in degrees; input must be broadcastable with `lon` and |
1008
|
|
|
`height`. |
1009
|
|
|
lon : array_like or float |
1010
|
|
|
Longitude in degrees; input must be broadcastable with `lat` and |
1011
|
|
|
`height`. |
1012
|
|
|
height : array_like or float |
1013
|
|
|
Altitude in km; input must be broadcastable with `lon` and `lat`. |
1014
|
|
|
coords : str, optional |
1015
|
|
|
Input coordinate system, expects one of 'geo', 'apex', or 'qd' |
1016
|
|
|
(default='geo') |
1017
|
|
|
precision : float, optional |
1018
|
|
|
Precision of output (degrees) when converting to geo. A negative |
1019
|
|
|
value of this argument produces a low-precision calculation of |
1020
|
|
|
geodetic lat/lon based only on their spherical harmonic |
1021
|
|
|
representation. |
1022
|
|
|
A positive value causes the underlying Fortran routine to iterate |
1023
|
|
|
until feeding the output geo lat/lon into geo2qd (APXG2Q) reproduces |
1024
|
|
|
the input QD lat/lon to within the specified precision (all |
1025
|
|
|
coordinates being converted to geo are converted to QD first and |
1026
|
|
|
passed through APXG2Q). |
1027
|
|
|
|
1028
|
|
|
Returns |
1029
|
|
|
------- |
1030
|
|
|
f1 : (3, N) or (3,) ndarray |
1031
|
|
|
Quasi-dipole base vector equivalent to e1, tangent to contours of |
1032
|
|
|
constant lambdaA |
1033
|
|
|
f2 : (3, N) or (3,) ndarray |
1034
|
|
|
Quasi-dipole base vector equivalent to e2 |
1035
|
|
|
f3 : (3, N) or (3,) ndarray |
1036
|
|
|
Quasi-dipole base vector equivalent to e3, tangent to contours of |
1037
|
|
|
PhiA |
1038
|
|
|
g1 : (3, N) or (3,) ndarray |
1039
|
|
|
Quasi-dipole base vector equivalent to d1 |
1040
|
|
|
g2 : (3, N) or (3,) ndarray |
1041
|
|
|
Quasi-dipole base vector equivalent to d2 |
1042
|
|
|
g3 : (3, N) or (3,) ndarray |
1043
|
|
|
Quasi-dipole base vector equivalent to d3 |
1044
|
|
|
d1 : (3, N) or (3,) ndarray |
1045
|
|
|
Apex base vector normal to contours of constant PhiA |
1046
|
|
|
d2 : (3, N) or (3,) ndarray |
1047
|
|
|
Apex base vector that completes the right-handed system |
1048
|
|
|
d3 : (3, N) or (3,) ndarray |
1049
|
|
|
Apex base vector normal to contours of constant lambdaA |
1050
|
|
|
e1 : (3, N) or (3,) ndarray |
1051
|
|
|
Apex base vector tangent to contours of constant V0 |
1052
|
|
|
e2 : (3, N) or (3,) ndarray |
1053
|
|
|
Apex base vector that completes the right-handed system |
1054
|
|
|
e3 : (3, N) or (3,) ndarray |
1055
|
|
|
Apex base vector tangent to contours of constant PhiA |
1056
|
|
|
|
1057
|
|
|
Notes |
1058
|
|
|
----- |
1059
|
|
|
The vectors are described by Richmond [1995] [4]_ and |
1060
|
|
|
Emmert et al. [2010] [5]_. The vector components are geodetic east, |
1061
|
|
|
north, and up (only east and north for `f1` and `f2`). |
1062
|
|
|
|
1063
|
|
|
`f3`, `g1`, `g2`, and `g3` are not part of the Fortran code |
1064
|
|
|
by Emmert et al. [2010] [5]_. They are calculated by this |
1065
|
|
|
Python library according to the following equations in |
1066
|
|
|
Richmond [1995] [4]_: |
1067
|
|
|
|
1068
|
|
|
* `g1`: Eqn. 6.3 |
1069
|
|
|
* `g2`: Eqn. 6.4 |
1070
|
|
|
* `g3`: Eqn. 6.5 |
1071
|
|
|
* `f3`: Eqn. 6.8 |
1072
|
|
|
|
1073
|
|
|
References |
1074
|
|
|
---------- |
1075
|
|
|
.. [4] Richmond, A. D. (1995), Ionospheric Electrodynamics Using |
1076
|
|
|
Magnetic Apex Coordinates, Journal of geomagnetism and |
1077
|
|
|
geoelectricity, 47(2), 191–212, :doi:`10.5636/jgg.47.191`. |
1078
|
|
|
|
1079
|
|
|
.. [5] Emmert, J. T., A. D. Richmond, and D. P. Drob (2010), |
1080
|
|
|
A computationally compact representation of Magnetic-Apex |
1081
|
|
|
and Quasi-Dipole coordinates with smooth base vectors, |
1082
|
|
|
J. Geophys. Res., 115(A8), A08322, :doi:`10.1029/2010JA015326`. |
1083
|
|
|
|
1084
|
|
|
""" |
1085
|
|
|
# Convert to geodetic coordinates from current coordinate system |
1086
|
|
|
glat, glon = self.convert(lat, lon, coords, 'geo', height=height, |
1087
|
|
|
precision=precision) |
1088
|
|
|
|
1089
|
|
|
# Retrieve the desired magnetic locations and base vectors |
1090
|
|
|
returnvals = list(self._geo2apexall(glat, glon, height)) |
1091
|
|
|
qlat = np.float64(returnvals[0]) |
1092
|
|
|
alat = np.float64(returnvals[2]) |
1093
|
|
|
bvec_ind = [4, 5, 7, 8, 9, 11, 12, 13] |
1094
|
|
|
|
1095
|
|
|
# If inputs are not scalar, each vector is an array of arrays, |
1096
|
|
|
# so reshape to a single array |
1097
|
|
|
if returnvals[4].dtype == object: |
1098
|
|
|
for i in bvec_ind: |
1099
|
|
|
returnvals[i] = np.vstack(returnvals[i]).T |
1100
|
|
|
|
1101
|
|
|
# Make sure the base vector arrays are 2D |
1102
|
|
|
for i in bvec_ind: |
1103
|
|
|
if i in [4, 5]: |
1104
|
|
|
rsize = (2, returnvals[i].size // 2) |
1105
|
|
|
else: |
1106
|
|
|
rsize = (3, returnvals[i].size // 3) |
1107
|
|
|
returnvals[i] = returnvals[i].reshape(rsize) |
1108
|
|
|
|
1109
|
|
|
# Assign the reshaped base vectors |
1110
|
|
|
f1, f2 = returnvals[4:6] |
1111
|
|
|
d1, d2, d3 = returnvals[7:10] |
1112
|
|
|
e1, e2, e3 = returnvals[11:14] |
1113
|
|
|
|
1114
|
|
|
# Compute f3, g1, g2, g3 (outstanding quasi-dipole base vectors) |
1115
|
|
|
# |
1116
|
|
|
# Start by calculating the D equivalent, F (F_scalar) |
1117
|
|
|
f1_stack = np.vstack((f1, np.zeros_like(f1[0]))) |
1118
|
|
|
f2_stack = np.vstack((f2, np.zeros_like(f2[0]))) |
1119
|
|
|
F_scalar = np.cross(f1_stack.T, f2_stack.T).T[-1] |
1120
|
|
|
|
1121
|
|
|
# Get the cosine of the magnetic inclination |
1122
|
|
|
cos_mag_inc = helpers.getcosIm(alat) |
1123
|
|
|
|
1124
|
|
|
# Define the k base vectors |
1125
|
|
|
k_unit = np.array([0, 0, 1], dtype=np.float64).reshape((3, 1)) |
1126
|
|
|
|
1127
|
|
|
# Calculate the remaining quasi-dipole base vectors |
1128
|
|
|
g1 = ((self.RE + np.float64(height)) |
1129
|
|
|
/ (self.RE + self.refh)) ** (3 / 2) * d1 / F_scalar |
1130
|
|
|
g2 = -1.0 / (2.0 * F_scalar * np.tan(np.radians(qlat))) * ( |
1131
|
|
|
k_unit + ((self.RE + np.float64(height)) |
1132
|
|
|
/ (self.RE + self.refh)) * d2 / cos_mag_inc) |
1133
|
|
|
g3 = k_unit * F_scalar |
1134
|
|
|
f3 = np.cross(g1.T, g2.T).T |
1135
|
|
|
|
1136
|
|
|
# Reshape the output |
1137
|
|
|
out = [f1, f2, f3, g1, g2, g3, d1, d2, d3, e1, e2, e3] |
1138
|
|
|
|
1139
|
|
|
if np.any(alat == -9999): |
1140
|
|
|
warnings.warn(''.join(['Base vectors g, d, e, and f3 set to NaN ', |
1141
|
|
|
'where apex latitude is undefined (apex ', |
1142
|
|
|
'height may be < reference height)'])) |
1143
|
|
|
mask = alat == -9999 |
1144
|
|
|
for i in range(len(out) - 2): |
1145
|
|
|
out[i + 2] = np.where(mask, np.nan, out[i + 2]) |
1146
|
|
|
|
1147
|
|
|
out = tuple(np.squeeze(bvec) for bvec in out) |
1148
|
|
|
|
1149
|
|
|
return out |
1150
|
|
|
|
1151
|
|
|
def get_apex(self, lat, height=None): |
1152
|
|
|
""" Calculate apex height |
1153
|
|
|
|
1154
|
|
|
Parameters |
1155
|
|
|
---------- |
1156
|
|
|
lat : float |
1157
|
|
|
Apex latitude in degrees |
1158
|
|
|
height : float or NoneType |
1159
|
|
|
Height above the surface of the Earth in km or NoneType to use |
1160
|
|
|
reference height (default=None) |
1161
|
|
|
|
1162
|
|
|
Returns |
1163
|
|
|
------- |
1164
|
|
|
apex_height : float |
1165
|
|
|
Height of the field line apex in km |
1166
|
|
|
|
1167
|
|
|
""" |
1168
|
|
|
# Check the latitude |
1169
|
|
|
lat = helpers.checklat(lat, name='alat') |
1170
|
|
|
|
1171
|
|
|
# Ensure the height is set |
1172
|
|
|
if height is None: |
1173
|
|
|
height = self.refh |
1174
|
|
|
|
1175
|
|
|
# Calculate the apex height |
1176
|
|
|
cos_lat_squared = np.cos(np.radians(lat)) ** 2 |
1177
|
|
|
apex_height = (self.RE + height) / cos_lat_squared - self.RE |
1178
|
|
|
|
1179
|
|
|
return apex_height |
1180
|
|
|
|
1181
|
|
|
def get_height(self, lat, apex_height): |
1182
|
|
|
"""Calculate the height given an apex latitude and apex height. |
1183
|
|
|
|
1184
|
|
|
Parameters |
1185
|
|
|
---------- |
1186
|
|
|
lat : float |
1187
|
|
|
Apex latitude in degrees |
1188
|
|
|
apex_height : float |
1189
|
|
|
Maximum height of the apex field line above the surface of the |
1190
|
|
|
Earth in km |
1191
|
|
|
|
1192
|
|
|
Returns |
1193
|
|
|
------- |
1194
|
|
|
height : float |
1195
|
|
|
Height above the surface of the Earth in km |
1196
|
|
|
|
1197
|
|
|
""" |
1198
|
|
|
# Check the latitude |
1199
|
|
|
lat = helpers.checklat(lat, name='alat') |
1200
|
|
|
|
1201
|
|
|
# Calculate the height from the apex height |
1202
|
|
|
cos_lat_squared = np.cos(np.radians(lat)) ** 2 |
1203
|
|
|
height = cos_lat_squared * (apex_height + self.RE) - self.RE |
1204
|
|
|
|
1205
|
|
|
return height |
1206
|
|
|
|
1207
|
|
|
def set_epoch(self, year): |
1208
|
|
|
"""Updates the epoch for all subsequent conversions. |
1209
|
|
|
|
1210
|
|
|
Parameters |
1211
|
|
|
---------- |
1212
|
|
|
year : float |
1213
|
|
|
Decimal year |
1214
|
|
|
|
1215
|
|
|
""" |
1216
|
|
|
# Set the year and load the data file |
1217
|
|
|
self.year = np.float64(year) |
1218
|
|
|
fa.loadapxsh(self.datafile, self.year) |
1219
|
|
|
|
1220
|
|
|
# Call the Fortran routine to set time |
1221
|
|
|
fa.cofrm(self.year, self.igrf_fn) |
1222
|
|
|
return |
1223
|
|
|
|
1224
|
|
|
def set_refh(self, refh): |
1225
|
|
|
"""Updates the apex reference height for all subsequent conversions. |
1226
|
|
|
|
1227
|
|
|
Parameters |
1228
|
|
|
---------- |
1229
|
|
|
refh : float |
1230
|
|
|
Apex reference height in km |
1231
|
|
|
|
1232
|
|
|
Notes |
1233
|
|
|
----- |
1234
|
|
|
The reference height is the height to which field lines will be mapped, |
1235
|
|
|
and is only relevant for conversions involving apex (not quasi-dipole). |
1236
|
|
|
|
1237
|
|
|
""" |
1238
|
|
|
self.refh = refh |
1239
|
|
|
|
1240
|
|
|
def get_babs(self, glat, glon, height): |
1241
|
|
|
"""Returns the magnitude of the IGRF magnetic field in tesla. |
1242
|
|
|
|
1243
|
|
|
Parameters |
1244
|
|
|
---------- |
1245
|
|
|
glat : array_like |
1246
|
|
|
Geodetic latitude in degrees |
1247
|
|
|
glon : array_like |
1248
|
|
|
Geodetic longitude in degrees |
1249
|
|
|
height : array_like |
1250
|
|
|
Altitude in km |
1251
|
|
|
|
1252
|
|
|
Returns |
1253
|
|
|
------- |
1254
|
|
|
babs : ndarray or float |
1255
|
|
|
Magnitude of the IGRF magnetic field in Tesla |
1256
|
|
|
|
1257
|
|
|
""" |
1258
|
|
|
# Get the absolute value of the magnetic field at the desired location |
1259
|
|
|
babs = self._get_babs(glat, glon, height) |
1260
|
|
|
|
1261
|
|
|
# If array is returned, the dtype is object, so convert to float |
1262
|
|
|
return np.float64(babs) |
1263
|
|
|
|
1264
|
|
|
def bvectors_apex(self, lat, lon, height, coords='geo', precision=1e-10): |
1265
|
|
|
"""Returns the magnetic field vectors in apex coordinates. |
1266
|
|
|
|
1267
|
|
|
Parameters |
1268
|
|
|
---------- |
1269
|
|
|
lat : (N,) array_like or float |
1270
|
|
|
Latitude |
1271
|
|
|
lon : (N,) array_like or float |
1272
|
|
|
Longitude |
1273
|
|
|
height : (N,) array_like or float |
1274
|
|
|
Altitude in km |
1275
|
|
|
coords : {'geo', 'apex', 'qd'}, optional |
1276
|
|
|
Input coordinate system |
1277
|
|
|
precision : float, optional |
1278
|
|
|
Precision of output (degrees) when converting to geo. A negative |
1279
|
|
|
value of this argument produces a low-precision calculation of |
1280
|
|
|
geodetic lat/lon based only on their spherical harmonic |
1281
|
|
|
representation. |
1282
|
|
|
A positive value causes the underlying Fortran routine to iterate |
1283
|
|
|
until feeding the output geo lat/lon into geo2qd (APXG2Q) reproduces |
1284
|
|
|
the input QD lat/lon to within the specified precision (all |
1285
|
|
|
coordinates being converted to geo are converted to QD first and |
1286
|
|
|
passed through APXG2Q). |
1287
|
|
|
|
1288
|
|
|
Returns |
1289
|
|
|
------- |
1290
|
|
|
main_mag_e3: (1, N) or (1,) ndarray |
1291
|
|
|
IGRF magnitude divided by a scaling factor, D (d_scale) to give |
1292
|
|
|
the main B field magnitude along the e3 base vector |
1293
|
|
|
e3 : (3, N) or (3,) ndarray |
1294
|
|
|
Base vector tangent to the contours of constant V_0 and Phi_A |
1295
|
|
|
main_mag_d3: (1, N) or (1,) ndarray |
1296
|
|
|
IGRF magnitude multiplied by a scaling factor, D (d_scale) to give |
1297
|
|
|
the main B field magnitudee along the d3 base vector |
1298
|
|
|
d3 : (3, N) or (3,) ndarray |
1299
|
|
|
Base vector equivalent to the scaled main field unit vector |
1300
|
|
|
|
1301
|
|
|
Notes |
1302
|
|
|
----- |
1303
|
|
|
See Richmond, A. D. (1995) [4]_ equations 3.8-3.14 |
1304
|
|
|
|
1305
|
|
|
The apex magnetic field vectors described by Richmond [1995] [4]_ and |
1306
|
|
|
Emmert et al. [2010] [5]_, specfically the Be3 (main_mag_e3) and Bd3 |
1307
|
|
|
(main_mag_d3) components. The vector components are geodetic east, |
1308
|
|
|
north, and up. |
1309
|
|
|
|
1310
|
|
|
References |
1311
|
|
|
---------- |
1312
|
|
|
Richmond, A. D. (1995) [4]_ |
1313
|
|
|
Emmert, J. T. et al. (2010) [5]_ |
1314
|
|
|
|
1315
|
|
|
""" |
1316
|
|
|
# Convert the current coordinates to geodetic coordinates |
1317
|
|
|
glat, glon = self.convert(lat, lon, coords, 'geo', height=height, |
1318
|
|
|
precision=precision) |
1319
|
|
|
|
1320
|
|
|
# Get the magnitude of the magnetic field at the desired location |
1321
|
|
|
babs = self.get_babs(glat, glon, height) |
1322
|
|
|
|
1323
|
|
|
# Retrieve the necessary base vectors |
1324
|
|
|
_, _, _, _, _, _, d1, d2, d3, _, _, e3 = self.basevectors_apex( |
1325
|
|
|
glat, glon, height, coords='geo') |
1326
|
|
|
|
1327
|
|
|
# Perform the calculations described in [4] |
1328
|
|
|
d1_cross_d2 = np.cross(d1.T, d2.T).T |
1329
|
|
|
d_scale = np.sqrt(np.sum(d1_cross_d2 ** 2, axis=0)) # D in [4] 3.13 |
1330
|
|
|
|
1331
|
|
|
main_mag_e3 = babs / d_scale # Solve for b0 in [4] 3.13 |
1332
|
|
|
main_mag_d3 = babs * d_scale # Solve for b0 in [4] 3.10 |
1333
|
|
|
|
1334
|
|
|
return main_mag_e3, e3, main_mag_d3, d3 |
1335
|
|
|
|