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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 importlib import resources |
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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-14 with coefficients from 1900 to 2030 [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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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.now( |
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tz=dt.timezone.utc)) |
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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 datafile is not specified, use the package default, otherwise |
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# check that the provided file exists |
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if datafile is None: |
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datafile = os.path.join(resources.files(__package__), 'apexsh.dat') |
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else: |
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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 fortranlib is not specified, use the package default, otherwise |
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# check that the provided file exists |
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if fortranlib is None: |
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fortranlib = fa.__file__ |
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else: |
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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(resources.files(__package__), |
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'igrf14coeffs.txt') |
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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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315
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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) |
|
318
|
|
|
/ (self.RE + h_apex)))) |
|
319
|
|
|
|
|
320
|
|
|
return alat, alon |
|
321
|
|
|
|
|
322
|
|
|
def _map_EV_to_height(self, alat, alon, height, newheight, data, ev_flag): |
|
323
|
|
|
"""Maps electric field related values to a desired height |
|
324
|
|
|
|
|
325
|
|
|
Parameters |
|
326
|
|
|
---------- |
|
327
|
|
|
alat : array-like |
|
328
|
|
|
Apex latitude in degrees. |
|
329
|
|
|
alon : array-like |
|
330
|
|
|
Apex longitude in degrees. |
|
331
|
|
|
height : array-like |
|
332
|
|
|
Current altitude in km. |
|
333
|
|
|
new_height : array-like |
|
334
|
|
|
Desired altitude to which EV values will be mapped in km. |
|
335
|
|
|
data : array-like |
|
336
|
|
|
3D value(s) for the electric field or electric drift |
|
337
|
|
|
ev_flag : str |
|
338
|
|
|
Specify if value is an electric field ('E') or electric drift ('V') |
|
339
|
|
|
|
|
340
|
|
|
Returns |
|
341
|
|
|
------- |
|
342
|
|
|
data_mapped : array-like |
|
343
|
|
|
Data mapped along the magnetic field from the old height to the |
|
344
|
|
|
new height. |
|
345
|
|
|
|
|
346
|
|
|
Raises |
|
347
|
|
|
------ |
|
348
|
|
|
ValueError |
|
349
|
|
|
If an unknown `ev_flag` or badly shaped data input is supplied. |
|
350
|
|
|
|
|
351
|
|
|
""" |
|
352
|
|
|
# Ensure the E-V flag is correct |
|
353
|
|
|
ev_flag = ev_flag.upper() |
|
354
|
|
|
if ev_flag not in ['E', 'V']: |
|
355
|
|
|
raise ValueError('unknown electric field/drift flag') |
|
356
|
|
|
|
|
357
|
|
|
# Make sure data is array of correct shape |
|
358
|
|
|
if not (np.ndim(data) == 1 |
|
359
|
|
|
and np.size(data) == 3) and not (np.ndim(data) == 2 |
|
360
|
|
|
and np.shape(data)[0] == 3): |
|
361
|
|
|
# Raise ValueError because if passing e.g. a (6,) ndarray the |
|
362
|
|
|
# reshape below will work even though the input is invalid |
|
363
|
|
|
raise ValueError('{:} must be (3, N) or (3,) ndarray'.format( |
|
364
|
|
|
ev_flag)) |
|
365
|
|
|
|
|
366
|
|
|
data = np.reshape(data, (3, np.size(data) // 3)) |
|
367
|
|
|
|
|
368
|
|
|
# Get the necessary base vectors at the current and new height |
|
369
|
|
|
v1 = list() |
|
370
|
|
|
v2 = list() |
|
371
|
|
|
for i, alt in enumerate([height, newheight]): |
|
372
|
|
|
_, _, _, _, _, _, d1, d2, _, e1, e2, _ = self.basevectors_apex( |
|
373
|
|
|
alat, alon, alt, coords='apex') |
|
374
|
|
|
|
|
375
|
|
|
if ev_flag == 'E' and i == 0 or ev_flag == 'V' and i == 1: |
|
376
|
|
|
v1.append(e1) |
|
377
|
|
|
v2.append(e2) |
|
378
|
|
|
else: |
|
379
|
|
|
v1.append(d1) |
|
380
|
|
|
v2.append(d2) |
|
381
|
|
|
|
|
382
|
|
|
# Make sure v1 and v2 have shape (3, N) |
|
383
|
|
|
v1[-1] = np.reshape(v1[-1], (3, v1[-1].size // 3)) |
|
384
|
|
|
v2[-1] = np.reshape(v2[-1], (3, v2[-1].size // 3)) |
|
385
|
|
|
|
|
386
|
|
|
# Take the dot product between the data value and each base vector |
|
387
|
|
|
# at the current height |
|
388
|
|
|
data1 = np.sum(data * v1[0], axis=0) |
|
389
|
|
|
data2 = np.sum(data * v2[0], axis=0) |
|
390
|
|
|
|
|
391
|
|
|
# Map the data to the new height, removing any axes of length 1 |
|
392
|
|
|
# after the calculation |
|
393
|
|
|
data_mapped = np.squeeze(data1[np.newaxis, :] * v1[1] |
|
394
|
|
|
+ data2[np.newaxis, :] * v2[1]) |
|
395
|
|
|
|
|
396
|
|
|
return data_mapped |
|
397
|
|
|
|
|
398
|
|
|
def _get_babs_nonvectorized(self, glat, glon, height): |
|
399
|
|
|
"""Get the absolute value of the B-field in Tesla |
|
400
|
|
|
|
|
401
|
|
|
Parameters |
|
402
|
|
|
---------- |
|
403
|
|
|
glat : float |
|
404
|
|
|
Geodetic latitude in degrees |
|
405
|
|
|
glon : float |
|
406
|
|
|
Geodetic longitude in degrees |
|
407
|
|
|
height : float |
|
408
|
|
|
Altitude in km |
|
409
|
|
|
|
|
410
|
|
|
Returns |
|
411
|
|
|
------- |
|
412
|
|
|
babs : float |
|
413
|
|
|
Absolute value of the magnetic field in Tesla |
|
414
|
|
|
|
|
415
|
|
|
""" |
|
416
|
|
|
# Evaluate the latitude |
|
417
|
|
|
glat = helpers.checklat(glat, name='qlat') |
|
418
|
|
|
|
|
419
|
|
|
# Get the magnetic field output: North, East, Down, Absolute value |
|
420
|
|
|
bout = fa.feldg(1, glat, glon, height) |
|
421
|
|
|
|
|
422
|
|
|
# Convert the absolute value from Gauss to Tesla |
|
423
|
|
|
babs = bout[-1] / 10000.0 |
|
424
|
|
|
|
|
425
|
|
|
return babs |
|
426
|
|
|
|
|
427
|
|
|
# ----------------------- |
|
428
|
|
|
# Define the user methods |
|
429
|
|
|
|
|
430
|
|
|
def convert(self, lat, lon, source, dest, height=0, datetime=None, |
|
431
|
|
|
precision=1e-10, ssheight=50 * 6371): |
|
432
|
|
|
"""Converts between geodetic, modified apex, quasi-dipole and MLT. |
|
433
|
|
|
|
|
434
|
|
|
Parameters |
|
435
|
|
|
---------- |
|
436
|
|
|
lat : array_like |
|
437
|
|
|
Latitude in degrees |
|
438
|
|
|
lon : array_like |
|
439
|
|
|
Longitude in degrees or MLT in hours |
|
440
|
|
|
source : str |
|
441
|
|
|
Input coordinate system, accepts 'geo', 'apex', 'qd', or 'mlt' |
|
442
|
|
|
dest : str |
|
443
|
|
|
Output coordinate system, accepts 'geo', 'apex', 'qd', or 'mlt' |
|
444
|
|
|
height : array_like, optional |
|
445
|
|
|
Altitude in km |
|
446
|
|
|
datetime : :class:`datetime.datetime` |
|
447
|
|
|
Date and time for MLT conversions (required for MLT conversions) |
|
448
|
|
|
precision : float, optional |
|
449
|
|
|
Precision of output (degrees) when converting to geo. A negative |
|
450
|
|
|
value of this argument produces a low-precision calculation of |
|
451
|
|
|
geodetic lat/lon based only on their spherical harmonic |
|
452
|
|
|
representation. |
|
453
|
|
|
A positive value causes the underlying Fortran routine to iterate |
|
454
|
|
|
until feeding the output geo lat/lon into geo2qd (APXG2Q) reproduces |
|
455
|
|
|
the input QD lat/lon to within the specified precision (all |
|
456
|
|
|
coordinates being converted to geo are converted to QD first and |
|
457
|
|
|
passed through APXG2Q). |
|
458
|
|
|
ssheight : float, optional |
|
459
|
|
|
Altitude in km to use for converting the subsolar point from |
|
460
|
|
|
geographic to magnetic coordinates. A high altitude is used |
|
461
|
|
|
to ensure the subsolar point is mapped to high latitudes, which |
|
462
|
|
|
prevents the South-Atlantic Anomaly (SAA) from influencing the MLT. |
|
463
|
|
|
|
|
464
|
|
|
Returns |
|
465
|
|
|
------- |
|
466
|
|
|
lat : ndarray or float |
|
467
|
|
|
Converted latitude (if converting to MLT, output latitude is apex) |
|
468
|
|
|
lon : ndarray or float |
|
469
|
|
|
Converted longitude or MLT |
|
470
|
|
|
|
|
471
|
|
|
Raises |
|
472
|
|
|
------ |
|
473
|
|
|
ValueError |
|
474
|
|
|
For unknown source or destination coordinate system or a missing |
|
475
|
|
|
or badly formed latitude or datetime input |
|
476
|
|
|
|
|
477
|
|
|
""" |
|
478
|
|
|
# Test the input values |
|
479
|
|
|
source = source.lower() |
|
480
|
|
|
dest = dest.lower() |
|
481
|
|
|
|
|
482
|
|
|
if source not in ['geo', 'apex', 'qd', 'mlt'] \ |
|
483
|
|
|
or dest not in ['geo', 'apex', 'qd', 'mlt']: |
|
484
|
|
|
estr = 'Unknown coordinate transformation: {} -> {}'.format(source, |
|
485
|
|
|
dest) |
|
486
|
|
|
raise ValueError(estr) |
|
487
|
|
|
|
|
488
|
|
|
if datetime is None and ('mlt' in [source, dest]): |
|
489
|
|
|
raise ValueError('datetime must be given for MLT calculations') |
|
490
|
|
|
|
|
491
|
|
|
lat = helpers.checklat(lat) |
|
492
|
|
|
|
|
493
|
|
|
if source == dest: |
|
494
|
|
|
# The source and destination are the same, no conversion necessary |
|
495
|
|
|
return lat, lon |
|
496
|
|
|
else: |
|
497
|
|
|
# Select the correct conversion method |
|
498
|
|
|
if source == 'geo': |
|
499
|
|
|
if dest == 'qd': |
|
500
|
|
|
lat, lon = self.geo2qd(lat, lon, height) |
|
501
|
|
|
else: |
|
502
|
|
|
lat, lon = self.geo2apex(lat, lon, height) |
|
503
|
|
|
if dest == 'mlt': |
|
504
|
|
|
lon = self.mlon2mlt(lon, datetime, ssheight=ssheight) |
|
505
|
|
|
elif source == 'apex': |
|
506
|
|
|
if dest == 'geo': |
|
507
|
|
|
lat, lon, _ = self.apex2geo(lat, lon, height, |
|
508
|
|
|
precision=precision) |
|
509
|
|
|
elif dest == 'qd': |
|
510
|
|
|
lat, lon = self.apex2qd(lat, lon, height=height) |
|
511
|
|
|
elif dest == 'mlt': |
|
512
|
|
|
lon = self.mlon2mlt(lon, datetime, ssheight=ssheight) |
|
513
|
|
|
elif source == 'qd': |
|
514
|
|
|
if dest == 'geo': |
|
515
|
|
|
lat, lon, _ = self.qd2geo(lat, lon, height, |
|
516
|
|
|
precision=precision) |
|
517
|
|
|
else: |
|
518
|
|
|
lat, lon = self.qd2apex(lat, lon, height=height) |
|
519
|
|
|
if dest == 'mlt': |
|
520
|
|
|
lon = self.mlon2mlt(lon, datetime, ssheight=ssheight) |
|
521
|
|
|
elif source == 'mlt': |
|
522
|
|
|
# From MLT means that the input latitude is assumed to be apex, |
|
523
|
|
|
# so we don't need to update latitude for apex conversions. |
|
524
|
|
|
lon = self.mlt2mlon(lon, datetime, ssheight=ssheight) |
|
525
|
|
|
if dest == 'geo': |
|
526
|
|
|
lat, lon, _ = self.apex2geo(lat, lon, height, |
|
527
|
|
|
precision=precision) |
|
528
|
|
|
elif dest == 'qd': |
|
529
|
|
|
lat, lon = self.apex2qd(lat, lon, height=height) |
|
530
|
|
|
|
|
531
|
|
|
return lat, lon |
|
532
|
|
|
|
|
533
|
|
|
def geo2apex(self, glat, glon, height): |
|
534
|
|
|
"""Converts geodetic to modified apex coordinates. |
|
535
|
|
|
|
|
536
|
|
|
Parameters |
|
537
|
|
|
---------- |
|
538
|
|
|
glat : array_like |
|
539
|
|
|
Geodetic latitude |
|
540
|
|
|
glon : array_like |
|
541
|
|
|
Geodetic longitude |
|
542
|
|
|
height : array_like |
|
543
|
|
|
Altitude in km |
|
544
|
|
|
|
|
545
|
|
|
Returns |
|
546
|
|
|
------- |
|
547
|
|
|
alat : ndarray or float |
|
548
|
|
|
Modified apex latitude |
|
549
|
|
|
alon : ndarray or float |
|
550
|
|
|
Modified apex longitude |
|
551
|
|
|
|
|
552
|
|
|
""" |
|
553
|
|
|
|
|
554
|
|
|
glat = helpers.checklat(glat, name='glat') |
|
555
|
|
|
|
|
556
|
|
|
alat, alon = self._geo2apex(glat, glon, height) |
|
557
|
|
|
|
|
558
|
|
|
if np.any(alat == -9999): |
|
559
|
|
|
warnings.warn(''.join(['Apex latitude set to NaN where undefined ', |
|
560
|
|
|
'(apex height may be < reference height)'])) |
|
561
|
|
|
if np.isscalar(alat): |
|
562
|
|
|
alat = np.nan |
|
563
|
|
|
else: |
|
564
|
|
|
alat[alat == -9999] = np.nan |
|
565
|
|
|
|
|
566
|
|
|
# If array is returned, dtype is object, so convert to float |
|
567
|
|
|
alat = helpers.set_array_float(alat) |
|
568
|
|
|
alon = helpers.set_array_float(alon) |
|
569
|
|
|
|
|
570
|
|
|
return alat, alon |
|
571
|
|
|
|
|
572
|
|
|
def apex2geo(self, alat, alon, height, precision=1e-10): |
|
573
|
|
|
"""Converts modified apex to geodetic coordinates. |
|
574
|
|
|
|
|
575
|
|
|
Parameters |
|
576
|
|
|
---------- |
|
577
|
|
|
alat : array_like |
|
578
|
|
|
Modified apex latitude |
|
579
|
|
|
alon : array_like |
|
580
|
|
|
Modified apex longitude |
|
581
|
|
|
height : array_like |
|
582
|
|
|
Altitude in km |
|
583
|
|
|
precision : float, optional |
|
584
|
|
|
Precision of output (degrees). A negative value of this argument |
|
585
|
|
|
produces a low-precision calculation of geodetic lat/lon based only |
|
586
|
|
|
on their spherical harmonic representation. A positive value causes |
|
587
|
|
|
the underlying Fortran routine to iterate until feeding the output |
|
588
|
|
|
geo lat/lon into geo2qd (APXG2Q) reproduces the input QD lat/lon to |
|
589
|
|
|
within the specified precision. |
|
590
|
|
|
|
|
591
|
|
|
Returns |
|
592
|
|
|
------- |
|
593
|
|
|
glat : ndarray or float |
|
594
|
|
|
Geodetic latitude |
|
595
|
|
|
glon : ndarray or float |
|
596
|
|
|
Geodetic longitude |
|
597
|
|
|
error : ndarray or float |
|
598
|
|
|
The angular difference (degrees) between the input QD coordinates |
|
599
|
|
|
and the qlat/qlon produced by feeding the output glat and glon |
|
600
|
|
|
into geo2qd (APXG2Q) |
|
601
|
|
|
|
|
602
|
|
|
""" |
|
603
|
|
|
# Evaluate the latitude |
|
604
|
|
|
alat = helpers.checklat(alat, name='alat') |
|
605
|
|
|
|
|
606
|
|
|
# Perform the two-step convertion to geodetic coordinates |
|
607
|
|
|
qlat, qlon = self.apex2qd(alat, alon, height=height) |
|
608
|
|
|
glat, glon, error = self.qd2geo(qlat, qlon, height, precision=precision) |
|
609
|
|
|
|
|
610
|
|
|
return glat, glon, error |
|
611
|
|
|
|
|
612
|
|
|
def geo2qd(self, glat, glon, height): |
|
613
|
|
|
"""Converts geodetic to quasi-dipole coordinates. |
|
614
|
|
|
|
|
615
|
|
|
Parameters |
|
616
|
|
|
---------- |
|
617
|
|
|
glat : array_like |
|
618
|
|
|
Geodetic latitude |
|
619
|
|
|
glon : array_like |
|
620
|
|
|
Geodetic longitude |
|
621
|
|
|
height : array_like |
|
622
|
|
|
Altitude in km |
|
623
|
|
|
|
|
624
|
|
|
Returns |
|
625
|
|
|
------- |
|
626
|
|
|
qlat : ndarray or float |
|
627
|
|
|
Quasi-dipole latitude |
|
628
|
|
|
qlon : ndarray or float |
|
629
|
|
|
Quasi-dipole longitude |
|
630
|
|
|
|
|
631
|
|
|
""" |
|
632
|
|
|
# Evaluate the latitude |
|
633
|
|
|
glat = helpers.checklat(glat, name='glat') |
|
634
|
|
|
|
|
635
|
|
|
# Convert to quasi-dipole coordinates |
|
636
|
|
|
qlat, qlon = self._geo2qd(glat, glon, height) |
|
637
|
|
|
|
|
638
|
|
|
# If array is returned, dtype is object, so convert to float |
|
639
|
|
|
qlat = helpers.set_array_float(qlat) |
|
640
|
|
|
qlon = helpers.set_array_float(qlon) |
|
641
|
|
|
|
|
642
|
|
|
return qlat, qlon |
|
643
|
|
|
|
|
644
|
|
|
def qd2geo(self, qlat, qlon, height, precision=1e-10): |
|
645
|
|
|
"""Converts quasi-dipole to geodetic coordinates. |
|
646
|
|
|
|
|
647
|
|
|
Parameters |
|
648
|
|
|
---------- |
|
649
|
|
|
qlat : array_like |
|
650
|
|
|
Quasi-dipole latitude |
|
651
|
|
|
qlon : array_like |
|
652
|
|
|
Quasi-dipole longitude |
|
653
|
|
|
height : array_like |
|
654
|
|
|
Altitude in km |
|
655
|
|
|
precision : float, optional |
|
656
|
|
|
Precision of output (degrees). A negative value of this argument |
|
657
|
|
|
produces a low-precision calculation of geodetic lat/lon based only |
|
658
|
|
|
on their spherical harmonic representation. A positive value causes |
|
659
|
|
|
the underlying Fortran routine to iterate until feeding the output |
|
660
|
|
|
geo lat/lon into geo2qd (APXG2Q) reproduces the input QD lat/lon to |
|
661
|
|
|
within the specified precision. |
|
662
|
|
|
|
|
663
|
|
|
Returns |
|
664
|
|
|
------- |
|
665
|
|
|
glat : ndarray or float |
|
666
|
|
|
Geodetic latitude |
|
667
|
|
|
glon : ndarray or float |
|
668
|
|
|
Geodetic longitude |
|
669
|
|
|
error : ndarray or float |
|
670
|
|
|
The angular difference (degrees) between the input QD coordinates |
|
671
|
|
|
and the qlat/qlon produced by feeding the output glat and glon |
|
672
|
|
|
into geo2qd (APXG2Q) |
|
673
|
|
|
|
|
674
|
|
|
""" |
|
675
|
|
|
# Evaluate the latitude |
|
676
|
|
|
qlat = helpers.checklat(qlat, name='qlat') |
|
677
|
|
|
|
|
678
|
|
|
# Convert to geodetic coordinates |
|
679
|
|
|
glat, glon, error = self._qd2geo(qlat, qlon, height, precision) |
|
680
|
|
|
|
|
681
|
|
|
# If array is returned, dtype is object, so convert to float |
|
682
|
|
|
glat = helpers.set_array_float(glat) |
|
683
|
|
|
glon = helpers.set_array_float(glon) |
|
684
|
|
|
error = helpers.set_array_float(error) |
|
685
|
|
|
|
|
686
|
|
|
return glat, glon, error |
|
687
|
|
|
|
|
688
|
|
|
def apex2qd(self, alat, alon, height): |
|
689
|
|
|
"""Converts modified apex to quasi-dipole coordinates. |
|
690
|
|
|
|
|
691
|
|
|
Parameters |
|
692
|
|
|
---------- |
|
693
|
|
|
alat : array_like |
|
694
|
|
|
Modified apex latitude |
|
695
|
|
|
alon : array_like |
|
696
|
|
|
Modified apex longitude |
|
697
|
|
|
height : array_like |
|
698
|
|
|
Altitude in km |
|
699
|
|
|
|
|
700
|
|
|
Returns |
|
701
|
|
|
------- |
|
702
|
|
|
qlat : ndarray or float |
|
703
|
|
|
Quasi-dipole latitude |
|
704
|
|
|
qlon : ndarray or float |
|
705
|
|
|
Quasi-dipole longitude |
|
706
|
|
|
|
|
707
|
|
|
Raises |
|
708
|
|
|
------ |
|
709
|
|
|
ApexHeightError |
|
710
|
|
|
if `height` > apex height |
|
711
|
|
|
|
|
712
|
|
|
""" |
|
713
|
|
|
# Convert the latitude to apex, latitude check performed in the |
|
714
|
|
|
# hidden method |
|
715
|
|
|
qlat, qlon = self._apex2qd(alat, alon, height) |
|
716
|
|
|
|
|
717
|
|
|
# If array is returned, the dtype is object, so convert to float |
|
718
|
|
|
qlat = helpers.set_array_float(qlat) |
|
719
|
|
|
qlon = helpers.set_array_float(qlon) |
|
720
|
|
|
|
|
721
|
|
|
return qlat, qlon |
|
722
|
|
|
|
|
723
|
|
|
def qd2apex(self, qlat, qlon, height): |
|
724
|
|
|
"""Converts quasi-dipole to modified apex coordinates. |
|
725
|
|
|
|
|
726
|
|
|
Parameters |
|
727
|
|
|
---------- |
|
728
|
|
|
qlat : array_like |
|
729
|
|
|
Quasi-dipole latitude |
|
730
|
|
|
qlon : array_like |
|
731
|
|
|
Quasi-dipole longitude |
|
732
|
|
|
height : array_like |
|
733
|
|
|
Altitude in km |
|
734
|
|
|
|
|
735
|
|
|
Returns |
|
736
|
|
|
------- |
|
737
|
|
|
alat : ndarray or float |
|
738
|
|
|
Modified apex latitude |
|
739
|
|
|
alon : ndarray or float |
|
740
|
|
|
Modified apex longitude |
|
741
|
|
|
|
|
742
|
|
|
Raises |
|
743
|
|
|
------ |
|
744
|
|
|
ApexHeightError |
|
745
|
|
|
if apex height < reference height |
|
746
|
|
|
|
|
747
|
|
|
""" |
|
748
|
|
|
# Perform the conversion from quasi-dipole to apex coordinates |
|
749
|
|
|
alat, alon = self._qd2apex(qlat, qlon, height) |
|
750
|
|
|
|
|
751
|
|
|
# If array is returned, the dtype is object, so convert to float |
|
752
|
|
|
alat = helpers.set_array_float(alat) |
|
753
|
|
|
alon = helpers.set_array_float(alon) |
|
754
|
|
|
|
|
755
|
|
|
return alat, alon |
|
756
|
|
|
|
|
757
|
|
View Code Duplication |
def mlon2mlt(self, mlon, dtime, ssheight=318550): |
|
|
|
|
|
|
758
|
|
|
"""Computes the magnetic local time at the specified magnetic longitude |
|
759
|
|
|
and UT. |
|
760
|
|
|
|
|
761
|
|
|
Parameters |
|
762
|
|
|
---------- |
|
763
|
|
|
mlon : array_like |
|
764
|
|
|
Magnetic longitude (apex and quasi-dipole longitude are always |
|
765
|
|
|
equal) |
|
766
|
|
|
dtime : :class:`datetime.datetime` |
|
767
|
|
|
Date and time |
|
768
|
|
|
ssheight : float, optional |
|
769
|
|
|
Altitude in km to use for converting the subsolar point from |
|
770
|
|
|
geographic to magnetic coordinates. A high altitude is used |
|
771
|
|
|
to ensure the subsolar point is mapped to high latitudes, which |
|
772
|
|
|
prevents the South-Atlantic Anomaly (SAA) from influencing the MLT. |
|
773
|
|
|
The current default is 50 * 6371, roughly 50 RE. (default=318550) |
|
774
|
|
|
|
|
775
|
|
|
Returns |
|
776
|
|
|
------- |
|
777
|
|
|
mlt : ndarray or float |
|
778
|
|
|
Magnetic local time in hours [0, 24) |
|
779
|
|
|
|
|
780
|
|
|
Notes |
|
781
|
|
|
----- |
|
782
|
|
|
To compute the MLT, we find the apex longitude of the subsolar point at |
|
783
|
|
|
the given time. Then the MLT of the given point will be computed from |
|
784
|
|
|
the separation in magnetic longitude from this point (1 hour = 15 |
|
785
|
|
|
degrees). |
|
786
|
|
|
|
|
787
|
|
|
""" |
|
788
|
|
|
# Get the subsolar location |
|
789
|
|
|
ssglat, ssglon = helpers.subsol(dtime) |
|
790
|
|
|
|
|
791
|
|
|
# Convert the subsolar location to apex coordinates |
|
792
|
|
|
_, ssalon = self.geo2apex(ssglat, ssglon, ssheight) |
|
793
|
|
|
|
|
794
|
|
|
# Calculate the magnetic local time (0-24 h range) from apex longitude. |
|
795
|
|
|
# Ensure lists are converted to arrays |
|
796
|
|
|
mlt = (180 + np.asarray(mlon) - ssalon) / 15 % 24 |
|
797
|
|
|
|
|
798
|
|
|
if mlt.shape == (): |
|
799
|
|
|
mlt = np.float64(mlt) |
|
800
|
|
|
|
|
801
|
|
|
return mlt |
|
802
|
|
|
|
|
803
|
|
View Code Duplication |
def mlt2mlon(self, mlt, dtime, ssheight=318550): |
|
|
|
|
|
|
804
|
|
|
"""Computes the magnetic longitude at the specified MLT and UT. |
|
805
|
|
|
|
|
806
|
|
|
Parameters |
|
807
|
|
|
---------- |
|
808
|
|
|
mlt : array_like |
|
809
|
|
|
Magnetic local time |
|
810
|
|
|
dtime : :class:`datetime.datetime` |
|
811
|
|
|
Date and time |
|
812
|
|
|
ssheight : float, optional |
|
813
|
|
|
Altitude in km to use for converting the subsolar point from |
|
814
|
|
|
geographic to magnetic coordinates. A high altitude is used |
|
815
|
|
|
to ensure the subsolar point is mapped to high latitudes, which |
|
816
|
|
|
prevents the South-Atlantic Anomaly (SAA) from influencing the MLT. |
|
817
|
|
|
The current default is 50 * 6371, roughly 50 RE. (default=318550) |
|
818
|
|
|
|
|
819
|
|
|
Returns |
|
820
|
|
|
------- |
|
821
|
|
|
mlon : ndarray or float |
|
822
|
|
|
Magnetic longitude [0, 360) (apex and quasi-dipole longitude are |
|
823
|
|
|
always equal) |
|
824
|
|
|
|
|
825
|
|
|
Notes |
|
826
|
|
|
----- |
|
827
|
|
|
To compute the magnetic longitude, we find the apex longitude of the |
|
828
|
|
|
subsolar point at the given time. Then the magnetic longitude of the |
|
829
|
|
|
given point will be computed from the separation in magnetic local time |
|
830
|
|
|
from this point (1 hour = 15 degrees). |
|
831
|
|
|
""" |
|
832
|
|
|
# Get the location of the subsolar point at this time |
|
833
|
|
|
ssglat, ssglon = helpers.subsol(dtime) |
|
834
|
|
|
|
|
835
|
|
|
# Convert the location of the subsolar point to apex coordinates |
|
836
|
|
|
_, ssalon = self.geo2apex(ssglat, ssglon, ssheight) |
|
837
|
|
|
|
|
838
|
|
|
# Calculate the magnetic longitude (0-360 h range) from MLT. |
|
839
|
|
|
# Ensure lists are converted to arrays |
|
840
|
|
|
mlon = (15 * np.asarray(mlt) - 180 + ssalon + 360) % 360 |
|
841
|
|
|
|
|
842
|
|
|
if mlon.shape == (): |
|
843
|
|
|
mlon = np.float64(mlon) |
|
844
|
|
|
|
|
845
|
|
|
return mlon |
|
846
|
|
|
|
|
847
|
|
|
def map_to_height(self, glat, glon, height, newheight, conjugate=False, |
|
848
|
|
|
precision=1e-10): |
|
849
|
|
|
"""Performs mapping of points along the magnetic field to the closest |
|
850
|
|
|
or conjugate hemisphere. |
|
851
|
|
|
|
|
852
|
|
|
Parameters |
|
853
|
|
|
---------- |
|
854
|
|
|
glat : array_like |
|
855
|
|
|
Geodetic latitude |
|
856
|
|
|
glon : array_like |
|
857
|
|
|
Geodetic longitude |
|
858
|
|
|
height : array_like |
|
859
|
|
|
Source altitude in km |
|
860
|
|
|
newheight : array_like |
|
861
|
|
|
Destination altitude in km |
|
862
|
|
|
conjugate : bool, optional |
|
863
|
|
|
Map to `newheight` in the conjugate hemisphere instead of the |
|
864
|
|
|
closest hemisphere |
|
865
|
|
|
precision : float, optional |
|
866
|
|
|
Precision of output (degrees). A negative value of this argument |
|
867
|
|
|
produces a low-precision calculation of geodetic lat/lon based only |
|
868
|
|
|
on their spherical harmonic representation. A positive value causes |
|
869
|
|
|
the underlying Fortran routine to iterate until feeding the output |
|
870
|
|
|
geo lat/lon into geo2qd (APXG2Q) reproduces the input QD lat/lon to |
|
871
|
|
|
within the specified precision. |
|
872
|
|
|
|
|
873
|
|
|
Returns |
|
874
|
|
|
------- |
|
875
|
|
|
newglat : ndarray or float |
|
876
|
|
|
Geodetic latitude of mapped point |
|
877
|
|
|
newglon : ndarray or float |
|
878
|
|
|
Geodetic longitude of mapped point |
|
879
|
|
|
error : ndarray or float |
|
880
|
|
|
The angular difference (degrees) between the input QD coordinates |
|
881
|
|
|
and the qlat/qlon produced by feeding the output glat and glon |
|
882
|
|
|
into geo2qd (APXG2Q) |
|
883
|
|
|
|
|
884
|
|
|
Notes |
|
885
|
|
|
----- |
|
886
|
|
|
The mapping is done by converting glat/glon/height to modified apex |
|
887
|
|
|
lat/lon, and converting back to geographic using newheight (if |
|
888
|
|
|
conjugate, use negative apex latitude when converting back) |
|
889
|
|
|
|
|
890
|
|
|
""" |
|
891
|
|
|
|
|
892
|
|
|
alat, alon = self.geo2apex(glat, glon, height) |
|
893
|
|
|
if conjugate: |
|
894
|
|
|
alat = -alat |
|
895
|
|
|
try: |
|
896
|
|
|
newglat, newglon, error = self.apex2geo(alat, alon, newheight, |
|
897
|
|
|
precision=precision) |
|
898
|
|
|
except ApexHeightError: |
|
899
|
|
|
raise ApexHeightError("input height is > apex height") |
|
900
|
|
|
|
|
901
|
|
|
return newglat, newglon, error |
|
902
|
|
|
|
|
903
|
|
|
def map_E_to_height(self, alat, alon, height, newheight, edata): |
|
904
|
|
|
"""Performs mapping of electric field along the magnetic field. |
|
905
|
|
|
|
|
906
|
|
|
It is assumed that the electric field is perpendicular to B. |
|
907
|
|
|
|
|
908
|
|
|
Parameters |
|
909
|
|
|
---------- |
|
910
|
|
|
alat : (N,) array_like or float |
|
911
|
|
|
Modified apex latitude |
|
912
|
|
|
alon : (N,) array_like or float |
|
913
|
|
|
Modified apex longitude |
|
914
|
|
|
height : (N,) array_like or float |
|
915
|
|
|
Source altitude in km |
|
916
|
|
|
newheight : (N,) array_like or float |
|
917
|
|
|
Destination altitude in km |
|
918
|
|
|
edata : (3,) or (3, N) array_like |
|
919
|
|
|
Electric field (at `alat`, `alon`, `height`) in geodetic east, |
|
920
|
|
|
north, and up components |
|
921
|
|
|
|
|
922
|
|
|
Returns |
|
923
|
|
|
------- |
|
924
|
|
|
out : (3, N) or (3,) ndarray |
|
925
|
|
|
The electric field at `newheight` (geodetic east, north, and up |
|
926
|
|
|
components) |
|
927
|
|
|
|
|
928
|
|
|
""" |
|
929
|
|
|
# Call hidden mapping method with flag for the electric field |
|
930
|
|
|
out = self._map_EV_to_height(alat, alon, height, newheight, edata, 'E') |
|
931
|
|
|
|
|
932
|
|
|
return out |
|
933
|
|
|
|
|
934
|
|
|
def map_V_to_height(self, alat, alon, height, newheight, vdata): |
|
935
|
|
|
"""Performs mapping of electric drift velocity along the magnetic field. |
|
936
|
|
|
|
|
937
|
|
|
It is assumed that the electric field is perpendicular to B. |
|
938
|
|
|
|
|
939
|
|
|
Parameters |
|
940
|
|
|
---------- |
|
941
|
|
|
alat : (N,) array_like or float |
|
942
|
|
|
Modified apex latitude |
|
943
|
|
|
alon : (N,) array_like or float |
|
944
|
|
|
Modified apex longitude |
|
945
|
|
|
height : (N,) array_like or float |
|
946
|
|
|
Source altitude in km |
|
947
|
|
|
newheight : (N,) array_like or float |
|
948
|
|
|
Destination altitude in km |
|
949
|
|
|
vdata : (3,) or (3, N) array_like |
|
950
|
|
|
Electric drift velocity (at `alat`, `alon`, `height`) in geodetic |
|
951
|
|
|
east, north, and up components |
|
952
|
|
|
|
|
953
|
|
|
Returns |
|
954
|
|
|
------- |
|
955
|
|
|
out : (3, N) or (3,) ndarray |
|
956
|
|
|
The electric drift velocity at `newheight` (geodetic east, north, |
|
957
|
|
|
and up components) |
|
958
|
|
|
|
|
959
|
|
|
""" |
|
960
|
|
|
# Call hidden mapping method with flag for the electric drift velocities |
|
961
|
|
|
out = self._map_EV_to_height(alat, alon, height, newheight, vdata, 'V') |
|
962
|
|
|
|
|
963
|
|
|
return out |
|
964
|
|
|
|
|
965
|
|
|
def basevectors_qd(self, lat, lon, height, coords='geo', precision=1e-10): |
|
966
|
|
|
"""Get quasi-dipole base vectors f1 and f2 at the specified coordinates. |
|
967
|
|
|
|
|
968
|
|
|
Parameters |
|
969
|
|
|
---------- |
|
970
|
|
|
lat : (N,) array_like or float |
|
971
|
|
|
Latitude |
|
972
|
|
|
lon : (N,) array_like or float |
|
973
|
|
|
Longitude |
|
974
|
|
|
height : (N,) array_like or float |
|
975
|
|
|
Altitude in km |
|
976
|
|
|
coords : {'geo', 'apex', 'qd'}, optional |
|
977
|
|
|
Input coordinate system |
|
978
|
|
|
precision : float, optional |
|
979
|
|
|
Precision of output (degrees) when converting to geo. A negative |
|
980
|
|
|
value of this argument produces a low-precision calculation of |
|
981
|
|
|
geodetic lat/lon based only on their spherical harmonic |
|
982
|
|
|
representation. |
|
983
|
|
|
A positive value causes the underlying Fortran routine to iterate |
|
984
|
|
|
until feeding the output geo lat/lon into geo2qd (APXG2Q) reproduces |
|
985
|
|
|
the input QD lat/lon to within the specified precision (all |
|
986
|
|
|
coordinates being converted to geo are converted to QD first and |
|
987
|
|
|
passed through APXG2Q). |
|
988
|
|
|
|
|
989
|
|
|
Returns |
|
990
|
|
|
------- |
|
991
|
|
|
f1 : (2, N) or (2,) ndarray |
|
992
|
|
|
f2 : (2, N) or (2,) ndarray |
|
993
|
|
|
|
|
994
|
|
|
Notes |
|
995
|
|
|
----- |
|
996
|
|
|
The vectors are described by Richmond [1995] [2]_ and |
|
997
|
|
|
Emmert et al. [2010] [3]_. The vector components are geodetic east and |
|
998
|
|
|
north. |
|
999
|
|
|
|
|
1000
|
|
|
References |
|
1001
|
|
|
---------- |
|
1002
|
|
|
.. [2] Richmond, A. D. (1995), Ionospheric Electrodynamics Using |
|
1003
|
|
|
Magnetic Apex Coordinates, Journal of geomagnetism and |
|
1004
|
|
|
geoelectricity, 47(2), 191–212, :doi:`10.5636/jgg.47.191`. |
|
1005
|
|
|
|
|
1006
|
|
|
.. [3] Emmert, J. T., A. D. Richmond, and D. P. Drob (2010), |
|
1007
|
|
|
A computationally compact representation of Magnetic-Apex |
|
1008
|
|
|
and Quasi-Dipole coordinates with smooth base vectors, |
|
1009
|
|
|
J. Geophys. Res., 115(A8), A08322, doi:10.1029/2010JA015326. |
|
1010
|
|
|
|
|
1011
|
|
|
""" |
|
1012
|
|
|
# Convert from current coordinates to geodetic coordinates |
|
1013
|
|
|
glat, glon = self.convert(lat, lon, coords, 'geo', height=height, |
|
1014
|
|
|
precision=precision) |
|
1015
|
|
|
|
|
1016
|
|
|
# Get the geodetic base vectors |
|
1017
|
|
|
f1, f2 = self._basevec(glat, glon, height) |
|
1018
|
|
|
|
|
1019
|
|
|
# If inputs are not scalar, each vector is an array of arrays, |
|
1020
|
|
|
# so reshape to a single array |
|
1021
|
|
|
if f1.dtype == object: |
|
1022
|
|
|
f1 = np.vstack(f1).T |
|
1023
|
|
|
f2 = np.vstack(f2).T |
|
1024
|
|
|
|
|
1025
|
|
|
return f1, f2 |
|
1026
|
|
|
|
|
1027
|
|
|
def basevectors_apex(self, lat, lon, height, coords='geo', precision=1e-10): |
|
1028
|
|
|
"""Returns base vectors in quasi-dipole and apex coordinates. |
|
1029
|
|
|
|
|
1030
|
|
|
Parameters |
|
1031
|
|
|
---------- |
|
1032
|
|
|
lat : array_like or float |
|
1033
|
|
|
Latitude in degrees; input must be broadcastable with `lon` and |
|
1034
|
|
|
`height`. |
|
1035
|
|
|
lon : array_like or float |
|
1036
|
|
|
Longitude in degrees; input must be broadcastable with `lat` and |
|
1037
|
|
|
`height`. |
|
1038
|
|
|
height : array_like or float |
|
1039
|
|
|
Altitude in km; input must be broadcastable with `lon` and `lat`. |
|
1040
|
|
|
coords : str, optional |
|
1041
|
|
|
Input coordinate system, expects one of 'geo', 'apex', or 'qd' |
|
1042
|
|
|
(default='geo') |
|
1043
|
|
|
precision : float, optional |
|
1044
|
|
|
Precision of output (degrees) when converting to geo. A negative |
|
1045
|
|
|
value of this argument produces a low-precision calculation of |
|
1046
|
|
|
geodetic lat/lon based only on their spherical harmonic |
|
1047
|
|
|
representation. |
|
1048
|
|
|
A positive value causes the underlying Fortran routine to iterate |
|
1049
|
|
|
until feeding the output geo lat/lon into geo2qd (APXG2Q) reproduces |
|
1050
|
|
|
the input QD lat/lon to within the specified precision (all |
|
1051
|
|
|
coordinates being converted to geo are converted to QD first and |
|
1052
|
|
|
passed through APXG2Q). |
|
1053
|
|
|
|
|
1054
|
|
|
Returns |
|
1055
|
|
|
------- |
|
1056
|
|
|
f1 : (3, N) or (3,) ndarray |
|
1057
|
|
|
Quasi-dipole base vector equivalent to e1, tangent to contours of |
|
1058
|
|
|
constant lambdaA |
|
1059
|
|
|
f2 : (3, N) or (3,) ndarray |
|
1060
|
|
|
Quasi-dipole base vector equivalent to e2 |
|
1061
|
|
|
f3 : (3, N) or (3,) ndarray |
|
1062
|
|
|
Quasi-dipole base vector equivalent to e3, tangent to contours of |
|
1063
|
|
|
PhiA |
|
1064
|
|
|
g1 : (3, N) or (3,) ndarray |
|
1065
|
|
|
Quasi-dipole base vector equivalent to d1 |
|
1066
|
|
|
g2 : (3, N) or (3,) ndarray |
|
1067
|
|
|
Quasi-dipole base vector equivalent to d2 |
|
1068
|
|
|
g3 : (3, N) or (3,) ndarray |
|
1069
|
|
|
Quasi-dipole base vector equivalent to d3 |
|
1070
|
|
|
d1 : (3, N) or (3,) ndarray |
|
1071
|
|
|
Apex base vector normal to contours of constant PhiA |
|
1072
|
|
|
d2 : (3, N) or (3,) ndarray |
|
1073
|
|
|
Apex base vector that completes the right-handed system |
|
1074
|
|
|
d3 : (3, N) or (3,) ndarray |
|
1075
|
|
|
Apex base vector normal to contours of constant lambdaA |
|
1076
|
|
|
e1 : (3, N) or (3,) ndarray |
|
1077
|
|
|
Apex base vector tangent to contours of constant V0 |
|
1078
|
|
|
e2 : (3, N) or (3,) ndarray |
|
1079
|
|
|
Apex base vector that completes the right-handed system |
|
1080
|
|
|
e3 : (3, N) or (3,) ndarray |
|
1081
|
|
|
Apex base vector tangent to contours of constant PhiA |
|
1082
|
|
|
|
|
1083
|
|
|
Notes |
|
1084
|
|
|
----- |
|
1085
|
|
|
The vectors are described by Richmond [1995] [4]_ and |
|
1086
|
|
|
Emmert et al. [2010] [5]_. The vector components are geodetic east, |
|
1087
|
|
|
north, and up (only east and north for `f1` and `f2`). |
|
1088
|
|
|
|
|
1089
|
|
|
`f3`, `g1`, `g2`, and `g3` are not part of the Fortran code |
|
1090
|
|
|
by Emmert et al. [2010] [5]_. They are calculated by this |
|
1091
|
|
|
Python library according to the following equations in |
|
1092
|
|
|
Richmond [1995] [4]_: |
|
1093
|
|
|
|
|
1094
|
|
|
* `g1`: Eqn. 6.3 |
|
1095
|
|
|
* `g2`: Eqn. 6.4 |
|
1096
|
|
|
* `g3`: Eqn. 6.5 |
|
1097
|
|
|
* `f3`: Eqn. 6.8 |
|
1098
|
|
|
|
|
1099
|
|
|
References |
|
1100
|
|
|
---------- |
|
1101
|
|
|
.. [4] Richmond, A. D. (1995), Ionospheric Electrodynamics Using |
|
1102
|
|
|
Magnetic Apex Coordinates, Journal of geomagnetism and |
|
1103
|
|
|
geoelectricity, 47(2), 191–212, :doi:`10.5636/jgg.47.191`. |
|
1104
|
|
|
|
|
1105
|
|
|
.. [5] Emmert, J. T., A. D. Richmond, and D. P. Drob (2010), |
|
1106
|
|
|
A computationally compact representation of Magnetic-Apex |
|
1107
|
|
|
and Quasi-Dipole coordinates with smooth base vectors, |
|
1108
|
|
|
J. Geophys. Res., 115(A8), A08322, doi:10.1029/2010JA015326. |
|
1109
|
|
|
|
|
1110
|
|
|
""" |
|
1111
|
|
|
# Convert to geodetic coordinates from current coordinate system |
|
1112
|
|
|
glat, glon = self.convert(lat, lon, coords, 'geo', height=height, |
|
1113
|
|
|
precision=precision) |
|
1114
|
|
|
|
|
1115
|
|
|
# Retrieve the desired magnetic locations and base vectors |
|
1116
|
|
|
returnvals = list(self._geo2apexall(glat, glon, height)) |
|
1117
|
|
|
qlat = np.float64(returnvals[0]) |
|
1118
|
|
|
alat = np.float64(returnvals[2]) |
|
1119
|
|
|
bvec_ind = [4, 5, 7, 8, 9, 11, 12, 13] |
|
1120
|
|
|
|
|
1121
|
|
|
# If inputs are not scalar, each vector is an array of arrays, |
|
1122
|
|
|
# so reshape to a single array |
|
1123
|
|
|
if returnvals[4].dtype == object: |
|
1124
|
|
|
for i in bvec_ind: |
|
1125
|
|
|
returnvals[i] = np.vstack(returnvals[i]).T |
|
1126
|
|
|
|
|
1127
|
|
|
# Make sure the base vector arrays are 2D |
|
1128
|
|
|
for i in bvec_ind: |
|
1129
|
|
|
if i in [4, 5]: |
|
1130
|
|
|
rsize = (2, returnvals[i].size // 2) |
|
1131
|
|
|
else: |
|
1132
|
|
|
rsize = (3, returnvals[i].size // 3) |
|
1133
|
|
|
returnvals[i] = returnvals[i].reshape(rsize) |
|
1134
|
|
|
|
|
1135
|
|
|
# Assign the reshaped base vectors |
|
1136
|
|
|
f1, f2 = returnvals[4:6] |
|
1137
|
|
|
d1, d2, d3 = returnvals[7:10] |
|
1138
|
|
|
e1, e2, e3 = returnvals[11:14] |
|
1139
|
|
|
|
|
1140
|
|
|
# Compute f3, g1, g2, g3 (outstanding quasi-dipole base vectors) |
|
1141
|
|
|
# |
|
1142
|
|
|
# Start by calculating the D equivalent, F (F_scalar) |
|
1143
|
|
|
f1_stack = np.vstack((f1, np.zeros_like(f1[0]))) |
|
1144
|
|
|
f2_stack = np.vstack((f2, np.zeros_like(f2[0]))) |
|
1145
|
|
|
F_scalar = np.cross(f1_stack.T, f2_stack.T).T[-1] |
|
1146
|
|
|
|
|
1147
|
|
|
# Get the cosine of the magnetic inclination |
|
1148
|
|
|
cos_mag_inc = helpers.getcosIm(alat) |
|
1149
|
|
|
|
|
1150
|
|
|
# Define the k base vectors |
|
1151
|
|
|
k_unit = np.array([0, 0, 1], dtype=np.float64).reshape((3, 1)) |
|
1152
|
|
|
|
|
1153
|
|
|
# Calculate the remaining quasi-dipole base vectors |
|
1154
|
|
|
g1 = ((self.RE + np.asarray(height)) |
|
1155
|
|
|
/ (self.RE + self.refh)) ** (3 / 2) * d1 / F_scalar |
|
1156
|
|
|
g2 = -1.0 / (2.0 * F_scalar * np.tan(np.radians(qlat))) * ( |
|
1157
|
|
|
k_unit + ((self.RE + np.asarray(height)) |
|
1158
|
|
|
/ (self.RE + self.refh)) * d2 / cos_mag_inc) |
|
1159
|
|
|
g3 = k_unit * F_scalar |
|
1160
|
|
|
f3 = np.cross(g1.T, g2.T).T |
|
1161
|
|
|
|
|
1162
|
|
|
# Reshape the output |
|
1163
|
|
|
out = [f1, f2, f3, g1, g2, g3, d1, d2, d3, e1, e2, e3] |
|
1164
|
|
|
|
|
1165
|
|
|
if np.any(alat == -9999): |
|
1166
|
|
|
warnings.warn(''.join(['Base vectors g, d, e, and f3 set to NaN ', |
|
1167
|
|
|
'where apex latitude is undefined (apex ', |
|
1168
|
|
|
'height may be < reference height)'])) |
|
1169
|
|
|
mask = alat == -9999 |
|
1170
|
|
|
for i in range(len(out) - 2): |
|
1171
|
|
|
out[i + 2] = np.where(mask, np.nan, out[i + 2]) |
|
1172
|
|
|
|
|
1173
|
|
|
out = tuple(np.squeeze(bvec) for bvec in out) |
|
1174
|
|
|
|
|
1175
|
|
|
return out |
|
1176
|
|
|
|
|
1177
|
|
|
def get_apex(self, lat, height=None): |
|
1178
|
|
|
"""Calculate the apex height along a field line. |
|
1179
|
|
|
|
|
1180
|
|
|
Parameters |
|
1181
|
|
|
---------- |
|
1182
|
|
|
lat : float |
|
1183
|
|
|
Apex latitude in degrees |
|
1184
|
|
|
height : float or NoneType |
|
1185
|
|
|
Height above the surface of the Earth in km or NoneType to use |
|
1186
|
|
|
reference height (default=None) |
|
1187
|
|
|
|
|
1188
|
|
|
Returns |
|
1189
|
|
|
------- |
|
1190
|
|
|
apex_height : float |
|
1191
|
|
|
Height of the field line apex in km |
|
1192
|
|
|
|
|
1193
|
|
|
""" |
|
1194
|
|
|
# Check the latitude |
|
1195
|
|
|
lat = helpers.checklat(lat, name='alat') |
|
1196
|
|
|
|
|
1197
|
|
|
# Ensure the height is set |
|
1198
|
|
|
if height is None: |
|
1199
|
|
|
height = self.refh |
|
1200
|
|
|
|
|
1201
|
|
|
# Calculate the apex height |
|
1202
|
|
|
cos_lat_squared = np.cos(np.radians(lat)) ** 2 |
|
1203
|
|
|
apex_height = (self.RE + height) / cos_lat_squared - self.RE |
|
1204
|
|
|
|
|
1205
|
|
|
return apex_height |
|
1206
|
|
|
|
|
1207
|
|
|
def get_height(self, lat, apex_height): |
|
1208
|
|
|
"""Calculate the height given an apex latitude and apex height. |
|
1209
|
|
|
|
|
1210
|
|
|
Parameters |
|
1211
|
|
|
---------- |
|
1212
|
|
|
lat : float |
|
1213
|
|
|
Apex latitude in degrees |
|
1214
|
|
|
apex_height : float |
|
1215
|
|
|
Maximum height of the apex field line above the surface of the |
|
1216
|
|
|
Earth in km |
|
1217
|
|
|
|
|
1218
|
|
|
Returns |
|
1219
|
|
|
------- |
|
1220
|
|
|
height : float |
|
1221
|
|
|
Height above the surface of the Earth in km |
|
1222
|
|
|
|
|
1223
|
|
|
""" |
|
1224
|
|
|
# Check the latitude |
|
1225
|
|
|
lat = helpers.checklat(lat, name='alat') |
|
1226
|
|
|
|
|
1227
|
|
|
# Calculate the height from the apex height |
|
1228
|
|
|
cos_lat_squared = np.cos(np.radians(lat)) ** 2 |
|
1229
|
|
|
height = cos_lat_squared * (apex_height + self.RE) - self.RE |
|
1230
|
|
|
|
|
1231
|
|
|
return height |
|
1232
|
|
|
|
|
1233
|
|
|
def set_epoch(self, year): |
|
1234
|
|
|
"""Updates the epoch for all subsequent conversions. |
|
1235
|
|
|
|
|
1236
|
|
|
Parameters |
|
1237
|
|
|
---------- |
|
1238
|
|
|
year : float |
|
1239
|
|
|
Decimal year |
|
1240
|
|
|
|
|
1241
|
|
|
""" |
|
1242
|
|
|
# Set the year and load the data file |
|
1243
|
|
|
self.year = np.float64(year) |
|
1244
|
|
|
fa.loadapxsh(self.datafile, self.year) |
|
1245
|
|
|
|
|
1246
|
|
|
# Call the Fortran routine to set time |
|
1247
|
|
|
fa.cofrm(self.year, self.igrf_fn) |
|
1248
|
|
|
return |
|
1249
|
|
|
|
|
1250
|
|
|
def set_refh(self, refh): |
|
1251
|
|
|
"""Updates the apex reference height for all subsequent conversions. |
|
1252
|
|
|
|
|
1253
|
|
|
Parameters |
|
1254
|
|
|
---------- |
|
1255
|
|
|
refh : float |
|
1256
|
|
|
Apex reference height in km |
|
1257
|
|
|
|
|
1258
|
|
|
Notes |
|
1259
|
|
|
----- |
|
1260
|
|
|
The reference height is the height to which field lines will be mapped, |
|
1261
|
|
|
and is only relevant for conversions involving apex (not quasi-dipole). |
|
1262
|
|
|
|
|
1263
|
|
|
""" |
|
1264
|
|
|
self.refh = refh |
|
1265
|
|
|
|
|
1266
|
|
|
def get_babs(self, glat, glon, height): |
|
1267
|
|
|
"""Returns the magnitude of the IGRF magnetic field in tesla. |
|
1268
|
|
|
|
|
1269
|
|
|
Parameters |
|
1270
|
|
|
---------- |
|
1271
|
|
|
glat : array_like |
|
1272
|
|
|
Geodetic latitude in degrees |
|
1273
|
|
|
glon : array_like |
|
1274
|
|
|
Geodetic longitude in degrees |
|
1275
|
|
|
height : array_like |
|
1276
|
|
|
Altitude in km |
|
1277
|
|
|
|
|
1278
|
|
|
Returns |
|
1279
|
|
|
------- |
|
1280
|
|
|
babs : ndarray or float |
|
1281
|
|
|
Magnitude of the IGRF magnetic field in Tesla |
|
1282
|
|
|
|
|
1283
|
|
|
""" |
|
1284
|
|
|
# Get the absolute value of the magnetic field at the desired location |
|
1285
|
|
|
babs = self._get_babs(glat, glon, height) |
|
1286
|
|
|
|
|
1287
|
|
|
# If array is returned, the dtype is object, so convert to float |
|
1288
|
|
|
babs = helpers.set_array_float(babs) |
|
1289
|
|
|
|
|
1290
|
|
|
return babs |
|
1291
|
|
|
|
|
1292
|
|
|
def bvectors_apex(self, lat, lon, height, coords='geo', precision=1e-10): |
|
1293
|
|
|
"""Returns the magnetic field vectors in apex coordinates. |
|
1294
|
|
|
|
|
1295
|
|
|
Parameters |
|
1296
|
|
|
---------- |
|
1297
|
|
|
lat : (N,) array_like or float |
|
1298
|
|
|
Latitude |
|
1299
|
|
|
lon : (N,) array_like or float |
|
1300
|
|
|
Longitude |
|
1301
|
|
|
height : (N,) array_like or float |
|
1302
|
|
|
Altitude in km |
|
1303
|
|
|
coords : {'geo', 'apex', 'qd'}, optional |
|
1304
|
|
|
Input coordinate system |
|
1305
|
|
|
precision : float, optional |
|
1306
|
|
|
Precision of output (degrees) when converting to geo. A negative |
|
1307
|
|
|
value of this argument produces a low-precision calculation of |
|
1308
|
|
|
geodetic lat/lon based only on their spherical harmonic |
|
1309
|
|
|
representation. |
|
1310
|
|
|
A positive value causes the underlying Fortran routine to iterate |
|
1311
|
|
|
until feeding the output geo lat/lon into geo2qd (APXG2Q) reproduces |
|
1312
|
|
|
the input QD lat/lon to within the specified precision (all |
|
1313
|
|
|
coordinates being converted to geo are converted to QD first and |
|
1314
|
|
|
passed through APXG2Q). |
|
1315
|
|
|
|
|
1316
|
|
|
Returns |
|
1317
|
|
|
------- |
|
1318
|
|
|
main_mag_e3: (1, N) or (1,) ndarray |
|
1319
|
|
|
IGRF magnitude divided by a scaling factor, D (d_scale) to give |
|
1320
|
|
|
the main B field magnitude along the e3 base vector |
|
1321
|
|
|
e3 : (3, N) or (3,) ndarray |
|
1322
|
|
|
Base vector tangent to the contours of constant V_0 and Phi_A |
|
1323
|
|
|
main_mag_d3: (1, N) or (1,) ndarray |
|
1324
|
|
|
IGRF magnitude multiplied by a scaling factor, D (d_scale) to give |
|
1325
|
|
|
the main B field magnitudee along the d3 base vector |
|
1326
|
|
|
d3 : (3, N) or (3,) ndarray |
|
1327
|
|
|
Base vector equivalent to the scaled main field unit vector |
|
1328
|
|
|
|
|
1329
|
|
|
Notes |
|
1330
|
|
|
----- |
|
1331
|
|
|
See Richmond, A. D. (1995) [4]_ equations 3.8-3.14 |
|
1332
|
|
|
|
|
1333
|
|
|
The apex magnetic field vectors described by Richmond [1995] [4]_ and |
|
1334
|
|
|
Emmert et al. [2010] [5]_, specfically the Be3 (main_mag_e3) and Bd3 |
|
1335
|
|
|
(main_mag_d3) components. The vector components are geodetic east, |
|
1336
|
|
|
north, and up. |
|
1337
|
|
|
|
|
1338
|
|
|
References |
|
1339
|
|
|
---------- |
|
1340
|
|
|
Richmond, A. D. (1995) [4]_ |
|
1341
|
|
|
Emmert, J. T. et al. (2010) [5]_ |
|
1342
|
|
|
|
|
1343
|
|
|
""" |
|
1344
|
|
|
# Convert the current coordinates to geodetic coordinates |
|
1345
|
|
|
glat, glon = self.convert(lat, lon, coords, 'geo', height=height, |
|
1346
|
|
|
precision=precision) |
|
1347
|
|
|
|
|
1348
|
|
|
# Get the magnitude of the magnetic field at the desired location |
|
1349
|
|
|
babs = self.get_babs(glat, glon, height) |
|
1350
|
|
|
|
|
1351
|
|
|
# Retrieve the necessary base vectors |
|
1352
|
|
|
_, _, _, _, _, _, d1, d2, d3, _, _, e3 = self.basevectors_apex( |
|
1353
|
|
|
glat, glon, height, coords='geo') |
|
1354
|
|
|
|
|
1355
|
|
|
# Perform the calculations described in [4] |
|
1356
|
|
|
d1_cross_d2 = np.cross(d1.T, d2.T).T |
|
1357
|
|
|
d_scale = np.sqrt(np.sum(d1_cross_d2 ** 2, axis=0)) # D in [4] 3.13 |
|
1358
|
|
|
|
|
1359
|
|
|
main_mag_e3 = babs / d_scale # Solve for b0 in [4] 3.13 |
|
1360
|
|
|
main_mag_d3 = babs * d_scale # Solve for b0 in [4] 3.10 |
|
1361
|
|
|
|
|
1362
|
|
|
return main_mag_e3, e3, main_mag_d3, d3 |
|
1363
|
|
|
|