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