def TimingAccuracyDHC(sampling=1):
# ---- input parameters ----
maxdeg = 2800
ls = np.arange(maxdeg + 1)
beta = 1.5
print('Driscoll-Healy (complex), 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.zeros((2, (maxdeg + 1), (maxdeg + 1)), dtype=np.complex)
cilm.imag = np.random.normal(loc=0.,
scale=1.,
size=(2, maxdeg + 1, maxdeg + 1))
cilm.real = np.random.normal(loc=0.,
scale=1.,
size=(2, maxdeg + 1, maxdeg + 1))
old_power = spectralanalysis.spectrum(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 = expand.MakeGridDHC(cilm_trim, sampling=sampling)
tend = time.time()
tinverse = tend - tstart
# analysis / forward
tstart = time.time()
cilm2_trim = expand.SHExpandDHC(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
def example():
print('---- SHrtoc example ----')
# --- input data filename ---
infile = '../../ExampleDataFiles/MarsTopo719.shape'
coeffs1, lmax = shio.SHRead(infile, 719)
coeffs1 = coeffs1[:, :lmax + 1, :lmax + 1]
# --- convert to complex coefficients, fill negative order coefficients ---
coeffs2 = np.empty((2, lmax + 1, lmax + 1), dtype=np.complex)
coeffs2_buf = shio.SHrtoc(coeffs1, convention=1, switchcs=0)
coeffs2[0, :, :].real = coeffs2_buf[0, :, :]
coeffs2[0, :, :].imag = coeffs2_buf[1, :, :]
coeffs2[1] = (coeffs2[0].conjugate() *
((-1)**np.arange(lmax + 1))[np.newaxis, :])
# --- compute and plot grid ---
grid1 = expand.MakeGridDH(coeffs1, lmax, csphase=-1)
grid2 = expand.MakeGridDHC(coeffs2, lmax, csphase=-1)
gridmin = min(grid1.min(), grid2.real.min())
gridmax = max(grid1.max(), grid2.real.max())
norm = plt.Normalize(gridmin, gridmax)
fig, axes = plt.subplots(1, 2)
im1 = axes[0].imshow(grid1, norm=norm)
axes[0].set_title('from real coefficients')
im2 = axes[1].imshow(grid2.real, norm=norm)
axes[1].set_title('from complex coefficients')
fig.tight_layout(pad=1)
fig.savefig('topography_mars.png')
print('mars topography plotted and saved to file')
def spharm_to_surface(self, lmax=None):
"""
Inverse transform the SPHARM spectrum to surface using the given number of components.
Parameters
----------
lmax : int, optional
The maximum spherical harmonic degree to be used in the inverse transform.
If None, all degrees will be used.
Default is None.
Returns
-------
ndarray : reconstructed surface grid.
"""
grid = shtools.MakeGridDHC(self.harmonics_shtools, lmax_calc=lmax).real
return grid