def test_LocalizationWindows():
print('\n---- testing SphericalCapCoef ----')
lmax = 15
theta = 50.
print('generating {:2.1f} degrees cap:'.format(theta))
coeffsm0 = shtools.SphericalCapCoef(np.radians(theta), lmax)
print(coeffsm0)
print('\n---- testing SHBias ----')
winpower = coeffsm0**2
ldata = 20
globalpower = np.random.rand(ldata)
localpower = shtools.SHBias(winpower, globalpower)
print(localpower[:min(ldata, 20)])
print('\n---- testing Curve2Mask ----')
# defines lat/lon square (bug!?)
nlat = 100
dlat = 180. / nlat
npoints = 4
points = np.empty((npoints, 2))
points[0] = [40., 20.]
points[1] = [40., 50.]
points[2] = [80., 50.]
points[3] = [80., 20.]
hasnorthpole = False
dhmask = shtools.Curve2Mask(nlat, points, hasnorthpole)
# compute covered area as a check
thetas = np.linspace(0 + dlat / 2., 180. - dlat / 2., nlat)
weights = 2 * np.sin(np.radians(thetas))
maskarea = np.sum(dhmask * weights[:, None] * dlat**2)
globearea = 4 * np.pi * (180 / np.pi)**2
print('mask covers {:2.2f}%% of the globe'.format(100 * maskarea /
globearea))
fig = plt.figure()
plt.imshow(dhmask)
fig.savefig('mask.png')
print('\n---- testing ComputeDMap ----')
nlat = 180
lmax = 20
dlat = 180. / nlat
lats = np.linspace(90. - dlat / 2., -90. + dlat / 2., nlat)
lons = np.linspace(0. + dlat, 360. - dlat / 2., nlat)
latgrid, longrid = np.meshgrid(lats, lons, indexing='ij')
dh_mask = np.logical_and(5. < latgrid, latgrid < 20.)
print('dij matrix[0,:lmax={:d}]:'.format(lmax))
dij_matrix = shtools.ComputeDMap(dh_mask, lmax)
print(dij_matrix[0, :lmax])
print('\n---- testing SHReturnTapersMap ----')
tapers, evalues = shtools.SHReturnTapersMap(dh_mask, lmax, ntapers=1)
print('best taper concentration: {:2.2f}'.format(evalues[0]))
def test_MultitaperSE():
print('\n---- testing SHReturnTapersM ----')
theta0_deg = 20.
theta0 = np.radians(theta0_deg)
lmax = 10
orderM = 2
print('creating spherical cap tapers with:', end=' ')
print('size {:1.0f} deg, bandwidth {:d}, order {:d}'.format(
theta0_deg, lmax, orderM))
tapers, concentrations = \
shtools.SHReturnTapersM(theta0, lmax, orderM)
print('first 3 taper concentrations:')
print(concentrations[:3])
print('\n---- testing SHReturnTapers ----')
theta0_deg = 20.
theta0 = np.radians(theta0_deg)
lmax = 20
print('creating spherical cap tapers of', end=' ')
print('size {:1.0f} deg with bandwidth {:d}'.format(theta0_deg, lmax))
tapers, concentrations, taperorder = \
shtools.SHReturnTapers(theta0, lmax)
print('first 10 taper concentrations:')
print(concentrations[:10])
print('\n---- testing SHMultiTaperSE ----')
lmax = 80
ntapers = 3
tapersk = tapers[:, :ntapers]
torders = taperorder[:ntapers]
coeffs = np.random.normal(size=(2, lmax + 1, lmax + 1))
localpower, localpower_sd = \
shtools.SHMultiTaperSE(coeffs, tapersk, torders)
print('total power:', np.sum(localpower))
print('\n---- testing SHMultiTaperCSE ----')
lmax = 80
ntapers = 3
tapersk = tapers[:, :ntapers]
torders = taperorder[:ntapers]
coeffs1 = np.random.normal(size=(2, lmax + 1, lmax + 1))
coeffs2 = 0.5 * (coeffs1 + np.random.normal(size=(2, lmax + 1, lmax + 1)))
print(coeffs1.shape, coeffs2.shape, tapersk.shape)
localpower, localpower_sd = \
shtools.SHMultiTaperCSE(coeffs1, coeffs2, tapersk, torders)
print('total power:', np.sum(localpower))
print('\n---- testing SHLocalizedAdmitCorr ----')
lat = 90.
lon = 0.
k = 3
admit, corr, dadmit, dcorr = \
shtools.SHLocalizedAdmitCorr(coeffs1, coeffs2, tapers, taperorder,
lat, lon, k=k)
print(admit)
print('\n---- testing ComputeDm ----')
theta0_deg = 20.
theta0 = np.radians(theta0_deg)
lmax = 10
m = 2
Dm = shtools.ComputeDm(lmax, m, theta0)
print(Dm[:3, :3])
print('\n---- testing ComputeDG82 ----')
theta0_deg = 20.
theta0 = np.radians(theta0_deg)
lmax = 10
m = 2
DG82 = shtools.ComputeDG82(lmax, m, theta0)
print(DG82[:3, :3])
print('\n---- testing SHFindLWin ----')
theta0_deg = 20.
theta0 = np.radians(theta0_deg)
m = 2
ntapers = 3
minconcentration = 0.8
lmax = shtools.SHFindLWin(theta0,
m,
minconcentration,
taper_number=ntapers)
print(lmax)
print('\n---- testing SHBiasK ----')
lmax = 80
power_unbiased = 1. / (1. + np.arange(lmax + 1))**2
power_biased = shtools.SHBiasK(tapers, power_unbiased)
print((power_biased[:lmax + 1] / power_unbiased)[:5])
print('\n---- testing SHBias ----')
lmax = 80
power_unbiased = 1. / (1. + np.arange(lmax + 1))**2
power_biased = shtools.SHBias(tapers[:, 2], power_unbiased)
print(tapers.shape)
print((power_biased[:lmax + 1] / power_unbiased)[:5])
print('\n---- testing SHBiasAdmitCorr ----')
lmax = 80
Stt = 1. / (1. + np.arange(lmax + 1))**2
Sgg = 1. / (1. + np.arange(lmax + 1))**2
Sgt = 0.5 / (1. + np.arange(lmax + 1))**2
admit, corr = shtools.SHBiasAdmitCorr(Sgt, Sgg, Stt, tapers[:, 2])
print(corr)