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 test_SHConversions():
print('---- testing SHrtoc and SHctor ----')
lmax = 10
coeffs1 = np.random.normal(loc=0., scale=1., size=(2, lmax + 1, 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
coeffs2 = shio.SHrtoc(coeffs1)
coeffs3 = shio.SHctor(coeffs2)
error = np.sqrt(np.sum((coeffs3[mask] - coeffs1[mask])**2))
print('error after real to complex to real conversion: ', error)