def sharpness(t):
#h = cubicSymmetry(t)
h = numpy.array(t)
mass = getMass(h)
h /= mass
realSpace = pyshtools.MakeGridDH(h, sampling = 2)
#print numpy.sum((realSpace * numpy.log2(realSpace)).flatten())
#if numpy.any(realSpace < 0):
# print realSpace[numpy.where(realSpace < 0)]
#realSpaces.append(realSpace)
#plt.imshow(realSpace)
#plt.colorbar()
#plt.show()
# return mean# / std#getMass(pyshtools.SHExpandDH(1.0 / (1 + numpy.exp(-(realSpace - thresh) / realSpace)), sampling = 2)) / (4 * numpy.pi)
fm = getEnergies(h)
fm /= max(fm)
#plt.plot(fm)
#plt.xlabel('Harmonic number L')
#plt.ylabel('L2 norm across all M values for a given L (this is how you get rotation invariance)')
#plt.title('Rotation invariant feature detectors for ideal microstructures')
#plt.show()
print '75', get75percentile(fm[1:]), sum(fm[2::2]) / sum(fm[1:]), fm[0] / sum(fm[1:])
inf = -4 * numpy.pi * sum(pyshtools.SHCrossPowerSpectrum(h, pyshtools.SHExpandDH(numpy.log2(realSpace + 1e-10), sampling = 2)))
return inf
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, 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('SHRtopography_mars.png')
fig_spectrum.savefig('SHRspectrum_mars.png')
print 'mars topography and spectrum saved'
def example():
print '---- SHrtoc example ----'
#--- input data filename ---
infile = '../../ExampleDataFiles/MarsTopo719.shape'
coeffs1, lmax = shtools.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 = shtools.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)).reshape(1, 1, lmax + 1)
#--- compute and plot grid ---
grid1 = shtools.MakeGridDH(coeffs1, lmax, csphase=-1)
grid2 = shtools.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 TimingAccuracyDH():
#---- input parameters ----
maxdeg = 2800
ls = np.arange(maxdeg + 1)
sampling = 1
beta = -1.5
#---- create mask to filter out m<=l ----
mask = np.zeros(2 * (maxdeg + 1) * (maxdeg + 1), dtype=np.bool).reshape(2, maxdeg + 1, maxdeg + 1)
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))
random_numbers = np.random.normal(loc=0., scale=1., size=2 * (maxdeg + 1) * (maxdeg + 1))
cilm = random_numbers.reshape(2, maxdeg + 1, maxdeg + 1)
cilm[:, 1:, :] *= np.sqrt((ls[1:]**beta) / (2. * ls[1:] + 1.))[None, :, None]
#---- 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 = ((cilm_trim[mask_trim] - cilm2_trim[mask_trim]) / cilm_trim[mask_trim])**2
maxerr = np.sqrt(err.max())
rmserr = np.mean(err)
print '{:4d} {:1.2e} {:1.2e} {:1.1e}s {:1.1e}s'.\
format(lmax, maxerr, rmserr, tinverse, tforward)
lmax = lmax * 2
def TestCrustalThickness():
"""
Example routine that calculates the crustal thickness of Mars
"""
delta_max = 5.0
nmax = 6
degmax = 50
lmax = 200
rho_c = 2900.0
rho_m = 3500.0
filter_type = 0
half = 0
gravfile = '../../ExampleDataFiles/jgmro_110b_sha.tab'
pot, lmaxp, header = shtools.SHReadH(gravfile, degmax, 2)
gm = header[1] * 1.e9
mass = gm / shtools.constant.grav_constant
r_grav = header[0] * 1.e3
print r_grav, gm, mass, lmaxp
topofile = '../../ExampleDataFiles/MarsTopo719.shape'
hlm, lmaxt = shtools.SHRead(topofile, 719)
r0 = hlm[0, 0, 0]
d = r0 - 45.217409924028445e3
print r0, lmaxt
for l in range(2, lmaxp + 1):
pot[:, l, :l + 1] = pot[:, l, :l + 1] * (r_grav / r0)**l
topo_grid = shtools.MakeGridDH(hlm,
lmax=lmax,
sampling=2,
lmax_calc=degmax)
print "Maximum radius (km) = ", topo_grid.max() / 1.e3
print "Minimum radius (km) = ", topo_grid.min() / 1.e3
bc, r0 = shtools.CilmPlusDH(topo_grid, nmax, mass, rho_c, lmax=degmax)
ba = pot - bc
moho_c = np.zeros([2, degmax + 1, degmax + 1], dtype=float)
moho_c[0, 0, 0] = d
for l in range(1, degmax + 1):
if filter_type == 0:
moho_c[:, l, :l + 1] = ba[:, l, :l + 1] * mass * (2 * l + 1) * ((r0 / d)**l) \
/ (4.0 * np.pi * (rho_m - rho_c) * d**2)
elif filter_type == 1:
moho_c[:, l, :l + 1] = DownContFilterMA(l, half, r0, d) * ba[:, l, :l + 1] * mass * (2 * l + 1) * \
((r0 / d)**l) / (4.0 * np.pi * (rho_m - rho_c) * d**2)
else:
moho_c[:, l, :l + 1] = DownContFilterMC(l, half, r0, d) * ba[:, l, :l + 1] * mass * (2 * l + 1) *\
((r0 / d)**l) / (4.0 * np.pi * (rho_m - rho_c) * d**2)
moho_grid3 = shtools.MakeGridDH(moho_c,
lmax=lmax,
sampling=2,
lmax_calc=degmax)
print "Maximum Crustal thickness (km) = ", (topo_grid -
moho_grid3).max() / 1.e3
print "Minimum Crustal thickness (km) = ", (topo_grid -
moho_grid3).min() / 1.e3
moho_c = shtools.BAtoHilmDH(ba,
moho_grid3,
nmax,
mass,
r0, (rho_m - rho_c),
lmax=lmax,
filter_type=filter_type,
filter_deg=half,
lmax_calc=degmax)
moho_grid2 = shtools.MakeGridDH(moho_c,
lmax=lmax,
sampling=2,
lmax_calc=degmax)
print "Delta (km) = ", abs(moho_grid3 - moho_grid2).max() / 1.e3
temp_grid = topo_grid - moho_grid2
print "Maximum Crustal thickness (km) = ", temp_grid.max() / 1.e3
print "Minimum Crustal thickness (km) = ", temp_grid.min() / 1.e3
iter = 0
delta = 1.0e9
while delta > delta_max:
iter += 1
print "Iteration ", iter
moho_grid = (moho_grid2 + moho_grid3) / 2.0
print "Delta (km) = ", abs(moho_grid - moho_grid2).max() / 1.e3
temp_grid = topo_grid - moho_grid
print "Maximum Crustal thickness (km) = ", temp_grid.max() / 1.e3
print "Minimum Crustal thickness (km) = ", temp_grid.min() / 1.e3
moho_grid3 = moho_grid2
moho_grid2 = moho_grid
iter += 1
print "Iteration ", iter
moho_c = shtools.BAtoHilmDH(ba,
moho_grid2,
nmax,
mass,
r0,
rho_m - rho_c,
lmax=lmax,
filter_type=filter_type,
filter_deg=half,
lmax_calc=degmax)
moho_grid = shtools.MakeGridDH(moho_c,
lmax=lmax,
sampling=2,
lmax_calc=degmax)
delta = abs(moho_grid - moho_grid2).max()
print "Delta (km) = ", delta / 1.e3
temp_grid = topo_grid - moho_grid
print "Maximum Crustal thickness (km) = ", temp_grid.max() / 1.e3
print "Minimum Crustal thickness (km) = ", temp_grid.min() / 1.e3
moho_grid3 = moho_grid2
moho_grid2 = moho_grid
if temp_grid.max() > 100.e3:
print "Not converging"
exit(1)
fig_map = plt.figure()
plt.imshow(temp_grid)
fig_map.savefig('Mars_CrustalThicknes.png')
angles = ((0.0, 0.0), (0.0, 270.0), (0.0, 180.0), (0.0, 90.0), (90.0, 0.0), (90.0, 270.0), (90.0, 180.0), (90.0, 90.0), (180.0, 0.0), (180.0, 270.0), (180.0, 180.0), (180.0, 90.0))
totalSPH = numpy.zeros(o.shape)
for thetaphi in angles:
theta, phi = numpy.radians(thetaphi)
totalSPH += pyshtools.SHRotateRealCoef(o, (phi, theta, 0.0), dj)
return totalSPH
def getMass(output):
return 4 * numpy.pi * sum(pyshtools.SHCrossPowerSpectrum(output, pyshtools.SHExpandDH(numpy.ones(histogram.shape), sampling = 2)))
#print thetas.shape
#%%
plt.imshow(pyshtools.MakeGridDH(cubicSymmetry(output), sampling = 2))
#%%
if True:
#for g in range(len(stacks[:])):
#histogram = numpy.array(stacks[g])
output = pyshtools.SHExpandDH(histogram, sampling = 2)
#if True:
# output = numpy.array(lookup[0, 0])
output /= getMass(output)
histogram = pyshtools.MakeGridDH(output, sampling = 2)
#plt.imshow(histogram)
#plt.colorbar()
def reconstruct_grid(C):
return shtools.MakeGridDH(C, csphase=-1)
rpm_2D = np.zeros(shp, np.float64)
rpm_2D[:, :] = rpm_1D[:, np.newaxis]
return rpm_2D
#defining our colatitudes
co_lats = np.linspace(0., np.pi, num=T.shape[0], endpoint=True)
#defining the coordinates of our shell of radius r_i
rpm_2D = -make_Rpm(R_e=6371000., r_i=r_i, co_lats=co_lats, shp=T.shape)
#expanding to find SH coefficients for shell of radius r_i
rpm_2D_SH = sht.SHExpandDH(rpm_2D)
kernel = rpm_2D_SH[0, :, 0]
convolved = kernel[np.newaxis, :, np.newaxis] * T_SH
convolved[:, 1, 1] = 0.
#grid of gravitational source values on shell of radius r_i
tomo_r1 = sht.MakeGridDH(convolved, sampling=2, csphase=1)
#defining filter to be applied before backprojection
ramp_filter = np.linspace(0., 1., num=convolved.shape[1], endpoint=True)
cone_filter_2d = np.sqrt(
np.outer(ramp_filter * ramp_filter, ramp_filter * ramp_filter))
#convolution of coefficients and shell after filterning
filtered_convolved = cone_filter_2d[np.newaxis, :, :] * convolved
tomo_r1_filtered = sht.MakeGridDH(filtered_convolved, sampling=2, csphase=1)