import numpy as np
import pandas as pd
import os
from functools import reduce
basepath = os.path.dirname(__file__)
coeff_fn = os.path.abspath(os.path.join(basepath,'coefficients','model_coefficients.csv'))
# read coefficient file and store in pandas DataFrame (this line will be replaced when
# there is a decision on new format, but the dataframe should be the same):
coeffs = pd.read_csv(coeff_fn, index_col=('n','m'))
# organize the coefficients in arrays that are used to calculate magnetic field values
names = ['const', 'sinca', 'cosca', 'epsilon', 'epsilon_sinca', 'epsilon_cosca',
'tilt', 'tilt_sinca', 'tilt_cosca', 'tilt_epsilon', 'tilt_epsilon_sinca',
'tilt_epsilon_cosca', 'tau', 'tau_sinca', 'tau_cosca', 'tilt_tau',
'tilt_tau_sinca', 'tilt_tau_cosca', 'f107']
m_matrix = np.array([np.hstack((coeffs['tor_c_' + ss].dropna().values,
coeffs['tor_s_' + ss].dropna().values,
coeffs['pol_c_' + ss].dropna().values,
coeffs['pol_s_' + ss].dropna().values)) for ss in names]).T
m_matrix_pol = np.array([np.hstack((coeffs['pol_c_' + ss].dropna().values,
coeffs['pol_s_' + ss].dropna().values)) for ss in names]).T
[docs]def get_model_vectors(v, By, Bz, tilt, f107, epsilon_multiplier = 1.):
""" tor_c, tor_s, pol_c, pol_s = get_model_vectors(v, By, Bz, tilt, F107)
returns column vectors ((K,1)-shaped) corresponding to the spherical harmonic coefficients of the toroidal
and poloidal parts, with _c and _s denoting cos and sin terms, respectively.
This function is used by amps.AMPS class
"""
ca = np.arctan2(By, Bz)
epsilon = v**(4/3.) * np.sqrt(By**2 + Bz**2)**(2/3.) * (np.sin(ca/2)**(8))**(1/3.) / 1000 * epsilon_multiplier # Newell coupling
tau = v**(4/3.) * np.sqrt(By**2 + Bz**2)**(2/3.) * (np.cos(ca/2)**(8))**(1/3.) / 1000 # Newell coupling - inverse
# make a dict of the 19 external parameters, where the keys are postfixes in the column names of coeffs:
external_params = {'const' : 1 ,
'sinca' : 1 * np.sin(ca),
'cosca' : 1 * np.cos(ca),
'epsilon' : epsilon ,
'epsilon_sinca' : epsilon * np.sin(ca),
'epsilon_cosca' : epsilon * np.cos(ca),
'tilt' : tilt ,
'tilt_sinca' : tilt * np.sin(ca),
'tilt_cosca' : tilt * np.cos(ca),
'tilt_epsilon' : tilt * epsilon ,
'tilt_epsilon_sinca': tilt * epsilon * np.sin(ca),
'tilt_epsilon_cosca': tilt * epsilon * np.cos(ca),
'tau' : tau ,
'tau_sinca' : tau * np.sin(ca),
'tau_cosca' : tau * np.cos(ca),
'tilt_tau' : tilt * tau ,
'tilt_tau_sinca' : tilt * tau * np.sin(ca),
'tilt_tau_cosca' : tilt * tau * np.cos(ca),
'f107' : f107 }
# The SH coefficients are the sums in the expansion in terms of external parameters, scaled by the ext. params.:
tor_c = reduce(lambda x, y: x+y, [coeffs['tor_c_' + param] * external_params[param] for param in external_params.keys()]).dropna()
tor_s = reduce(lambda x, y: x+y, [coeffs['tor_s_' + param] * external_params[param] for param in external_params.keys()]).fillna(0)
pol_c = reduce(lambda x, y: x+y, [coeffs['pol_c_' + param] * external_params[param] for param in external_params.keys()]).dropna()
pol_s = reduce(lambda x, y: x+y, [coeffs['pol_s_' + param] * external_params[param] for param in external_params.keys()]).fillna(0)
pol_s = pol_s.ix[pol_c.index] # equal number of sin and cos terms, but sin coeffs will be 0 where m = 0
tor_s = tor_s.ix[tor_c.index] #
return tor_c[:, np.newaxis], tor_s[:, np.newaxis], pol_c[:, np.newaxis], pol_s[:, np.newaxis], pol_c.index.values, tor_c.index.values