Source code for pygimli.utils.hankel

#!/usr/bin/env python
# -*- coding: utf-8 -*-
"""Stuff for Hankel transformation."""

import numpy as np


[docs]def hankelFC(order): """Filter coefficients for Hankel transformation. 10 data points per decade. DOCUMENTME .. Author RUB? Parameters ---------- order : int order=1: NY=+0.5 (SIN) order=2: NY=-0.5 (COS) order=3: NY=0.0 (J0) order=4: NY=1.0 (J1) Returns ------- fc : np.array() Filter coefficients nc0 : int fc[nc0] refers to zero argument """ if order == 1: # sin fc = np.array([ 2.59526236e-7, 3.66544843e-7, 5.17830795e-7, 7.31340622e-7, 1.03322805e-6, 1.45918500e-6, 2.06161065e-6, 2.91137793e-6, 4.11357863e-6, 5.80876420e-6, 8.20798075e-6, 1.15895083e-5, 1.63778560e-5, 2.31228459e-5, 3.26800649e-5, 4.61329334e-5, 6.52101085e-5, 9.20390575e-5, 1.30122935e-4, 1.83620431e-4, 2.59656626e-4, 3.66311982e-4, 5.18141184e-4, 7.30717340e-4, 1.03392184e-3, 1.45742714e-3, 2.06292302e-3, 2.90599911e-3, 4.11471902e-3, 5.79042763e-3, 8.20004722e-3, 1.15192930e-2, 1.63039133e-2, 2.28257757e-2, 3.22249222e-2, 4.47864328e-2, 6.27329625e-2, 8.57059100e-2, 1.17418314e-1, 1.53632655e-1, 1.97717964e-1, 2.28849849e-1, 2.40311038e-1, 1.65409220e-1, 2.84701476e-3, -2.88016057e-1, -3.69097406e-1, -2.50107514e-2, 5.71811256e-1, -3.92261572e-1, 7.63280044e-2, 5.16233994e-2, -6.48012082e-2, 4.89047141e-2, -3.26936331e-2, 2.10539842e-2, -1.33862549e-2, 8.47124695e-3, -5.35123972e-3, 3.37796651e-3, -2.13174466e-3, 1.34513833e-3, -8.48749612e-4, 5.35531006e-4, -3.37898780e-4, 2.13200109e-4, -1.34520273e-4, 8.48765787e-5, -5.35535069e-5, 3.37899801e-5, -2.13200365e-5, 1.34520337e-5, -8.48765949e-6, 5.35535110e-6, -3.37899811e-6, 2.13200368e-6, -1.34520338e-6, 8.48765951e-7, -5.35535110e-7, 3.37899811e-7], np.float) nc0 = np.int(40) elif order == 2: # cos fc = np.array([ 1.63740363e-7, 1.83719709e-7, 2.06136904e-7, 2.31289411e-7, 2.59510987e-7, 2.91176117e-7, 3.26704977e-7, 3.66569013e-7, 4.11297197e-7, 4.61483045e-7, 5.17792493e-7, 5.80972733e-7, 6.51862128e-7, 7.31401337e-7, 8.20645798e-7, 9.20779729e-7, 1.03313185e-6, 1.15919300e-6, 1.30063594e-6, 1.45933752e-6, 1.63740363e-6, 1.83719709e-6, 2.06136904e-6, 2.31289411e-6, 2.59510987e-6, 2.91176117e-6, 3.26704977e-6, 3.66569013e-6, 4.11297197e-6, 4.61483045e-6, 5.17792493e-6, 5.80972733e-6, 6.51862128e-6, 7.31401337e-6, 8.20645798e-6, 9.20779729e-6, 1.03313185e-5, 1.15919300e-5, 1.30063594e-5, 1.45933752e-5, 1.63740363e-5, 1.83719709e-5, 2.06136904e-5, 2.31289411e-5, 2.59510987e-5, 2.91176117e-5, 3.26704977e-5, 3.66569013e-5, 4.11297197e-5, 4.61483045e-5, 5.17792493e-5, 5.80972733e-5, 6.51862128e-5, 7.31401337e-5, 8.20645798e-5, 9.20779729e-5, 1.03313185e-4, 1.15919300e-4, 1.30063594e-4, 1.45933752e-4, 1.63740363e-4, 1.83719709e-4, 2.06136904e-4, 2.31289411e-4, 2.59510987e-4, 2.91176117e-4, 3.26704976e-4, 3.66569013e-4, 4.11297197e-4, 4.61483045e-4, 5.17792493e-4, 5.80972733e-4, 6.51862127e-4, 7.31401337e-4, 8.20645797e-4, 9.20779730e-4, 1.03313185e-3, 1.15919300e-3, 1.30063593e-3, 1.45933753e-3, 1.63740362e-3, 1.83719710e-3, 2.06136901e-3, 2.31289411e-3, 2.59510977e-3, 2.91176115e-3, 3.26704948e-3, 3.66569003e-3, 4.11297114e-3, 4.61483003e-3, 5.17792252e-3, 5.80972566e-3, 6.51861416e-3, 7.31400728e-3, 8.20643673e-3, 9.20777603e-3, 1.03312545e-2, 1.15918577e-2, 1.30061650e-2, 1.45931339e-2, 1.63734419e-2, 1.83711757e-2, 2.06118614e-2, 2.31263461e-2, 2.59454421e-2, 2.91092045e-2, 3.26529302e-2, 3.66298115e-2, 4.10749753e-2, 4.60613861e-2, 5.16081994e-2, 5.78193646e-2, 6.46507780e-2, 7.22544422e-2, 8.03873578e-2, 8.92661837e-2, 9.80670729e-2, 1.07049506e-1, 1.13757572e-1, 1.18327217e-1, 1.13965041e-1, 1.00497783e-1, 6.12958082e-2, -1.61234222e-4, -1.11788551e-1, -2.27536948e-1, -3.39004453e-1, -2.25128800e-1, 8.98279919e-2, 5.12510388e-1, -1.31991937e-1, -3.35136479e-1, 3.64868100e-1, -2.34039961e-1, 1.32085237e-1, -7.56739672e-2, 4.52296662e-2, -2.78297002e-2, 1.73727753e-2, -1.09136894e-2, 6.87397283e-3, -4.33413470e-3, 2.73388730e-3, -1.72477355e-3, 1.08821012e-3, -6.86602007e-4, 4.33213523e-4, -2.73338487e-4, 1.72464733e-4, -1.08817842e-4, 6.86594042e-5, -4.33211523e-5, 2.73337984e-5, -1.72464607e-5, 1.08817810e-5, -6.86593962e-6, 4.33211503e-6, -2.73337979e-6, 1.72464606e-6, -1.08817810e-6, 6.86593961e-7, -4.33211503e-7, 2.73337979e-7, -1.72464606e-7], np.float) nc0 = np.int(122) elif order == 3: # J0 fc = np.array([ 2.89878288e-7, 3.64935144e-7, 4.59426126e-7, 5.78383226e-7, 7.28141338e-7, 9.16675639e-7, 1.15402625e-6, 1.45283298e-6, 1.82900834e-6, 2.30258511e-6, 2.89878286e-6, 3.64935148e-6, 4.59426119e-6, 5.78383236e-6, 7.28141322e-6, 9.16675664e-6, 1.15402621e-5, 1.45283305e-5, 1.82900824e-5, 2.30258527e-5, 2.89878259e-5, 3.64935186e-5, 4.59426051e-5, 5.78383329e-5, 7.28141144e-5, 9.16675882e-5, 1.15402573e-4, 1.45283354e-4, 1.82900694e-4, 2.30258630e-4, 2.89877891e-4, 3.64935362e-4, 4.59424960e-4, 5.78383437e-4, 7.28137738e-4, 9.16674828e-4, 1.15401453e-3, 1.45282561e-3, 1.82896826e-3, 2.30254535e-3, 2.89863979e-3, 3.64916703e-3, 4.59373308e-3, 5.78303238e-3, 7.27941497e-3, 9.16340705e-3, 1.15325691e-2, 1.45145832e-2, 1.82601199e-2, 2.29701042e-2, 2.88702619e-2, 3.62691810e-2, 4.54794031e-2, 5.69408192e-2, 7.09873072e-2, 8.80995426e-2, 1.08223889e-1, 1.31250483e-1, 1.55055715e-1, 1.76371506e-1, 1.85627738e-1, 1.69778044e-1, 1.03405245e-1, -3.02583233e-2, -2.27574393e-1, -3.62173217e-1, -2.05500446e-1, 3.37394873e-1, 3.17689897e-1, -5.13762160e-1, 3.09130264e-1, -1.26757592e-1, 4.61967890e-2, -1.80968674e-2, 8.35426050e-3, -4.47368304e-3, 2.61974783e-3, -1.60171357e-3, 9.97717882e-4, -6.26275815e-4, 3.94338818e-4, -2.48606354e-4, 1.56808604e-4, -9.89266288e-5, 6.24152398e-5, -3.93805393e-5, 2.48472358e-5, -1.56774945e-5, 9.89181741e-6, -6.24131160e-6, 3.93800058e-6, -2.48471018e-6, 1.56774609e-6, -9.89180896e-7, 6.24130948e-7, -3.93800005e-7, 2.48471005e-7, -1.56774605e-7, 9.89180888e-8, -6.24130946e-8], np.float) nc0 = np.int(60) elif order == 4: # J1 fc = np.array([ 1.84909557e-13, 2.85321327e-13, 4.64471808e-13, 7.16694771e-13, 1.16670043e-12, 1.80025587e-12, 2.93061898e-12, 4.52203829e-12, 7.36138206e-12, 1.13588466e-11, 1.84909557e-11, 2.85321327e-11, 4.64471808e-11, 7.16694771e-11, 1.16670043e-10, 1.80025587e-10, 2.93061898e-10, 4.52203829e-10, 7.36138206e-10, 1.13588466e-9, 1.84909557e-9, 2.85321326e-9, 4.64471806e-9, 7.16694765e-9, 1.16670042e-8, 1.80025583e-8, 2.93061889e-8, 4.52203807e-8, 7.36138149e-8, 1.13588452e-7, 1.84909521e-7, 2.85321237e-7, 4.64471580e-7, 7.16694198e-7, 1.16669899e-6, 1.80025226e-6, 2.93060990e-6, 4.52201549e-6, 7.36132477e-6, 1.13587027e-5, 1.84905942e-5, 2.85312247e-5, 4.64449000e-5, 7.16637480e-5, 1.16655653e-4, 1.79989440e-4, 2.92971106e-4, 4.51975783e-4, 7.35565435e-4, 1.13444615e-3, 1.84548306e-3, 2.84414257e-3, 4.62194743e-3, 7.10980590e-3, 1.15236911e-2, 1.76434485e-2, 2.84076233e-2, 4.29770596e-2, 6.80332569e-2, 9.97845929e-2, 1.51070544e-1, 2.03540581e-1, 2.71235377e-1, 2.76073871e-1, 2.16691977e-1, -7.83723737e-2, -3.40675627e-1, -3.60693673e-1, 5.13024526e-1, -5.94724729e-2, -1.95117123e-1, 1.99235600e-1, -1.38521553e-1, 8.79320859e-2, -5.50697146e-2, 3.45637848e-2, -2.17527180e-2, 1.37100291e-2, -8.64656417e-3, 5.45462758e-3, -3.44138864e-3, 2.17130686e-3, -1.36998628e-3, 8.64398952e-4, -5.45397874e-4, 3.44122545e-4, -2.17126585e-4, 1.36997597e-4, -8.64396364e-5, 5.45397224e-5, -3.44122382e-5, 2.17126544e-5, -1.36997587e-5, 8.64396338e-6, -5.45397218e-6, 3.44122380e-6, -2.17126543e-6, 1.36997587e-6, -8.64396337e-7, 5.45397218e-7], np.float) nc0 = np.int(60) #return (np.reshape(fc, (-1, 1)), nc0) # (100,) -> (100, 1) return fc, nc0


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