qpms/oldtests/test_qpms_p.py

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"""
Unit tests for qpms_p
=====================
Covered functions
-----------------
plane_pq_y vs. vswf_yr1
Not covered
-----------
Everything else
"""
import unittest
import qpms
import numpy as np
from numpy import newaxis as ň
import warnings
# Some constants go here.
lengthOrdersOfMagnitude = [2.**i for i in range(-15,10,2)]
class PlaneWaveDecompositionTests(unittest.TestCase):
"""
covers plane_pq_y and vswf_yr1
"""
def testRandomInc(self):
# The "maximum" argument of the Bessel's functions, i.e. maximum wave number times the distance,
# for the "locally strongly varying fields"
maxx = 10
rfailtol = 0.01 # how much of the randomized test will be tolerated
lMax = 80 # To which order we decompose the waves
rtol = 1e-5 # relative required precision
atol = 1. # absolute tolerance, does not really play a role
nsamples = 4 # (frequency, direction, polarisation) samples per order of magnitude and test
npoints = 15 # points to evaluate per sample
failcounter = 0
passcounter = 0
for oom in lengthOrdersOfMagnitude:
k = np.random.randn(nsamples, 3) / oom
ksiz = np.linalg.norm(k, axis=-1)
kdir = k / ksiz[...,ň]
E_0 = np.cross(np.random.randn(nsamples, 3), k) * oom # ensure orthogonality
for s in range(nsamples):
testpoints = oom * maxx * np.random.randn(npoints, 3)
p, q = qpms.plane_pq_y(lMax, k[s], E_0[s])
planewave_1 = np.exp(1j*np.dot(testpoints,k[s]))[:,ň] * E_0[s,:]
for i in range(npoints):
sph = qpms.cart2sph(ksiz[s]*testpoints[i])
M̃_y, Ñ_y = qpms.vswf_yr1(sph, lMax, 1)
planewave_2_p = -1j*qpms.sph_loccart2cart(np.dot(p,Ñ_y)+np.dot(q,M̃_y),sph)
#self.assertTrue(np.allclose(planewave_2_p, planewave_1[i], rtol=rtol, atol=atol))
if not np.allclose(planewave_2_p, planewave_1[i], rtol=rtol, atol=atol):
False and warnings.warn('Planewave expansion test not passed; r = '
+str(testpoints[i])+', k = '+str(k[s])
+', E_0 = '+str(E_0[s])+', (original) E = '
+str(planewave_1[i])+', (reexpanded) E = '
+str(planewave_2_p)
+', x = '+str(np.dot(testpoints[i],k[s]))
+'; distance = '
+str(np.linalg.norm(planewave_1[i]-planewave_2_p))
+', required relative precision = '
+str(rtol)+'.')
failcounter += 1
else:
passcounter += 1
self.assertLess(failcounter / (failcounter + passcounter), rfailtol,
'%d / %d (%.2e) randomized numerical tests failed (tolerance %.2e)'
% (failcounter, failcounter + passcounter,
failcounter / (failcounter + passcounter), rfailtol))
return
def testCornerCases(self):
pass
class SphericalWaveTranslationTests(unittest.TestCase):
def testRandom1to1(self):
# The "maximum" argument of the Bessel's functions, i.e. maximum wave number times the distance,
# for the "locally strongly varying fields"
maxx = 10
rfailtol = 0.01 # how much of the randomized test fail proportion will be tolerated
lMax = 50 # To which order we decompose the waves
lMax_outgoing = 4 # To which order we try the outgoing waves
rtol = 1e-5 # relative required precision
atol = 1. # absolute tolerance, does not really play a role
nsamples = 4 # frequency samples per order of magnitude and test
npoints = 15 # points to evaluate per frequency and center
ncentres = 3 # number of spherical coordinate centres between which the translations are to be made
maxxd = 2000 # the center position standard deviation
failcounter = 0
passcounter = 0
my, ny = qpms.get_mn_y(lMax)
nelem_full = len(my)
nelem_out = lMax_outgoing * (lMax_outgoing + 2)
for oom in lengthOrdersOfMagnitude:
centres = oom * maxxd * np.random.randn(ncentres, 3)
ksizs = np.random.randn(nsamples)
for ksiz in ksizs:
for i in range(ncentres): # "source"
Rs = centres[i]
testr = oom * maxx * np.random.randn(npoints, 3)
for j in range(ncentres): # "destination"
if j == i:
continue
Rd = centres[j]
shift = Rd - Rs
shift_sph = qpms.cart2sph(shift)
shift_kr = ksiz * shift_sph[0]
shift_theta = shift_sph[1]
shift_phi = shift_sph[2]
A_yd_ys = np.empty((nelem_full,nelem_out), dtype = np.complex_)
B_yd_ys = np.empty((nelem_full,nelem_out), dtype = np.complex_)
for yd in range(nelem_full):
for ys in range(nelem_out):
A_yd_ys[yd, ys] = qpms.Ã(my[yd],ny[yd],my[ys],ny[ys],shift_kr, shift_theta, shift_phi, True, 1)
B_yd_ys[yd, ys] = qpms.B̃(my[yd],ny[yd],my[ys],ny[ys],shift_kr, shift_phi, shift_phi, True, 1)
for r in testr:
sph_ssys = qpms.cart2sph(r+Rd-Rs)
M_ssys, N_ssys = qpms.vswf_yr1(np.array([ksiz * sph_ssys[0], sph_ssys[1], sph_ssys[2]]), lMax_outgoing, J=1)
sph_dsys = qpms.cart2sph(r)
M_dsys, N_dsys = qpms.vswf_yr1(np.array([ksiz * sph_dsys[0], sph_dsys[1], sph_dsys[2]]), lMax, J=1)
for ys in range(nelem_out):
# Electrical waves
E_1 = -1j*qpms.sph_loccart2cart(N_ssys[ys], sph_ssys)
E_2 = -1j*qpms.sph_loccart2cart(np.dot(A_yd_ys[:,ys],N_dsys)+np.dot(B_yd_ys[:,ys],M_dsys),sph_dsys)
if not np.allclose(E_1, E_2, rtol=rtol, atol=atol):
failcounter += 1
else:
passcounter += 1
# Magnetic waves
E_1 = -1j*qpms.sph_loccart2cart(M_ssys[ys], sph_ssys)
E_2 = -1j*qpms.sph_loccart2cart(np.dot(A_yd_ys[:,ys],M_dsys)+np.dot(B_yd_ys[:,ys],N_dsys),sph_dsys)
if not np.allclose(E_1, E_2, rtol=rtol, atol=atol):
failcounter += 1
else:
passcounter += 1
self.assertLess(failcounter / (failcounter + passcounter), rfailtol,
'%d / %d (%.2e) randomized numerical tests failed (tolerance %.2e)'
% (failcounter, failcounter + passcounter,
failcounter / (failcounter + passcounter), rfailtol))
return
def testRandom3to1(self):
pass
def main():
unittest.main()
if __name__ == '__main__':
main()