def example():
"""
example that plots the power spectrum of Mars topography data
"""
# --- input data filename ---
infile = '../../ExampleDataFiles/MarsTopo719.shape'
coeffs, lmax = shtools.SHRead(infile, 719)
lmax = coeffs.shape[1] - 1
# --- plot grid ---
grid = shtools.MakeGridDH(coeffs, lmax, csphase=-1)
fig_map = plt.figure()
plt.imshow(grid)
# ---- compute spectrum ----
ls = np.arange(lmax + 1)
pspectrum = shtools.SHPowerSpectrum(coeffs)
pdensity = shtools.SHPowerSpectrumDensity(coeffs)
# ---- plot spectrum ----
fig_spectrum, ax = plt.subplots(1, 1)
ax.set_xscale('log')
ax.set_yscale('log')
ax.set_xlabel('degree l')
ax.grid(True, which='both')
ax.plot(ls[1:], pspectrum[1:], label='power per degree l')
ax.plot(ls[1:], pdensity[1:], label='power per degree l and order m')
ax.legend()
fig_map.savefig('SHCtopography_mars.png')
fig_spectrum.savefig('SHCspectrum_mars.png')
print('mars topography and spectrum saved')
def test_RealSpectralAnalysis():
# ---- input parameters ----
lmax = 5
ls = np.arange(lmax + 1)
mask = np.zeros((2, lmax + 1, lmax + 1), dtype=np.bool)
for l in np.arange(lmax + 1):
mask[:, l, :l + 1] = True
mask[1, :, 0] = False
print('\n---- testing SHPower/DensityL, SHPowerSpectrum/Density ----')
print('generating normal distributed coefficients with variance 1...')
coeffs1 = np.random.normal(size=(2, lmax + 1, lmax + 1))
coeffs1[np.invert(mask)] = 0.
spec1 = np.array([shtools.SHPowerL(coeffs1, l) for l in ls])
spec2 = shtools.SHPowerSpectrum(coeffs1)
print('tot power computed with SHPowerL={:2.2f}'.format(np.sum(spec1)))
print('tot power computed with SHPowerSpectrum={:2.2f}'.format(
np.sum(spec2)))
spec1 = np.array([shtools.SHPowerDensityL(coeffs1, l) for l in ls])
spec2 = shtools.SHPowerSpectrumDensity(coeffs1)
print('tot power computed with SHPowerDensityL={:2.2f}'.format(
np.sum(spec1 * (2 * ls + 1))))
print('tot power computed with SHPowerSpectrumDensity={:2.2f}'.format(
np.sum(spec2 * (2 * ls + 1))))
print('\n---- testing SHCrossCrossPower/DensityL, ' +
'SHCrossCrossPowerSpectrum/Density ----')
print('generating two sets of normal distributed coefficients ' +
'with variance 1...')
coeffs2 = np.random.normal(size=(2, lmax + 1, lmax + 1))
coeffs2[np.invert(mask)] = 0.
spec1 = np.array([shtools.SHCrossPowerL(coeffs1, coeffs2, l) for l in ls])
spec2 = shtools.SHCrossPowerSpectrum(coeffs1, coeffs2)
print('tot cpower computed with SHCrossPowerL={:2.2f}'.format(
np.sum(spec1)))
print('tot cpower computed with SHCrossPowerSpectrum={:2.2f}'.format(
np.sum(spec2)))
spec1 = np.array(
[shtools.SHCrossPowerDensityL(coeffs1, coeffs2, l) for l in ls])
spec2 = shtools.SHCrossPowerSpectrumDensity(coeffs1, coeffs2)
print('tot cpower computed with SHCrossPowerDensityL={:2.2f}'.format(
np.sum(spec1 * (2 * ls + 1))))
print(
'tot cpower computed with SHCrossPowerSpectrumDensity={:2.2f}'.format(
np.sum(spec2 * (2 * ls + 1))))
print('\n---- testing SHAdmitCorr and SHConfidence ----')
admit, dadmit, corr = shtools.SHAdmitCorr(coeffs1, coeffs2)
confidence = np.array([shtools.SHConfidence(l, corr[l]) for l in ls])
print('admittance:', admit)
print('admittance error:', dadmit)
print('correlation:', corr)
print('confidence:', confidence)
def TimingAccuracyDH(sampling=1):
# ---- input parameters ----
maxdeg = 2800
ls = np.arange(maxdeg + 1)
beta = 1.5
print('Driscoll-Healy (real) sampling =', sampling)
# ---- create mask to filter out m<=l ----
mask = np.zeros((2, maxdeg + 1, maxdeg + 1), dtype=np.bool)
mask[0, 0, 0] = True
for l in ls:
mask[:, l, :l + 1] = True
mask[1, :, 0] = False
# ---- create Gaussian powerlaw coefficients ----
print('creating {:d} random coefficients'.format(2 * (maxdeg + 1) *
(maxdeg + 1)))
np.random.seed(0)
cilm = np.random.normal(loc=0., scale=1., size=(2, maxdeg + 1, maxdeg + 1))
old_power = shtools.SHPowerSpectrum(cilm)
new_power = 1. / (1. + ls)**beta # initialize degrees > 0 to power-law
cilm[:, :, :] *= np.sqrt(new_power / old_power)[None, :, None]
cilm[~mask] = 0.
# ---- time spherical harmonics transform for lmax set to increasing
# ---- powers of 2.
lmax = 2
print('lmax maxerror rms tinverse tforward')
while lmax <= maxdeg:
# trim coefficients to lmax
cilm_trim = cilm[:, :lmax + 1, :lmax + 1]
mask_trim = mask[:, :lmax + 1, :lmax + 1]
# synthesis / inverse
tstart = time.time()
grid = shtools.MakeGridDH(cilm_trim, sampling=sampling)
tend = time.time()
tinverse = tend - tstart
# analysis / forward
tstart = time.time()
cilm2_trim = shtools.SHExpandDH(grid, sampling=sampling)
tend = time.time()
tforward = tend - tstart
# compute error
err = np.abs(cilm_trim[mask_trim] - cilm2_trim[mask_trim]) / \
np.abs(cilm_trim[mask_trim])
maxerr = err.max()
rmserr = np.mean(err**2)
print('{:4d} {:1.2e} {:1.2e} {:1.1e}s {:1.1e}s'.format(
lmax, maxerr, rmserr, tinverse, tforward))
lmax = lmax * 2