def example():
"""
example that plots the power spectrum of Mars topography data
"""
# --- input data filename ---
infile = os.path.join(os.path.dirname(__file__),
'../../ExampleDataFiles/MarsTopo719.shape')
coeffs, lmax = shio.shread(infile)
# --- plot grid ---
grid = expand.MakeGridDH(coeffs, csphase=-1)
fig_map = plt.figure()
plt.imshow(grid)
# ---- compute spectrum ----
ls = np.arange(lmax + 1)
pspectrum = spectralanalysis.spectrum(coeffs, unit='per_l')
pdensity = spectralanalysis.spectrum(coeffs, unit='per_lm')
# ---- 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():
"""
example that plots the power spectrum of Mars topography data
"""
# --- input data filename ---
infile = os.path.join(os.path.dirname(__file__),
'../../ExampleDataFiles/MarsTopo719.shape')
coeffs, lmax = shio.shread(infile)
# --- plot grid ---
grid = expand.MakeGridDH(coeffs, csphase=-1)
fig_map = plt.figure()
plt.imshow(grid)
# ---- compute spectrum ----
ls = np.arange(lmax + 1)
pspectrum = spectralanalysis.spectrum(coeffs, unit='per_l')
pdensity = spectralanalysis.spectrum(coeffs, unit='per_lm')
# ---- 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 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 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
#plt.plot((1.0/np.pi)*lon,(1.0/np.pi)*lat,'.')
#plt.xlim([-1.0,+1.0])
#plt.ylim([-0.5,+0.5])
#plt.show()
levs = np.logspace(-8, 4, 200)
print levs
xx = np.linspace(-1.0 * np.pi, +1.0 * np.pi, nLon)
yy = np.linspace(-0.5 * np.pi, +0.5 * np.pi, nLat)
XX, YY = np.meshgrid(xx, yy)
#plt.contourf(XX, YY, ke2, 100, locator=ticker.LogLocator())
plt.contourf(XX, YY, ke2, norm=LogNorm(), levels=levs)
plt.colorbar(orientation='horizontal',
ticks=[1.0e-8, 1.0e-6, 1.0e-4, 1.0e-2, 1.0e+0, 1.0e+2, 1.0e+4])
plt.savefig('kinetic_energy_galewsky_7days.png')
plt.show()
coeffs = SHExpandDH(ke2, sampling=2)
power = spectrum(coeffs, unit='per_l')
nl = coeffs.shape[1] / 2
plt.loglog(np.arange(nl), power[:nl])
#plt.loglog(np.arange(nl-6)+6, 1.0e+7*np.power(np.arange(nl-6)+6,-3.0))
plt.loglog(
np.arange(nl - 6) + 6, 8.0e+6 * np.power(np.arange(nl - 6) + 6, -3.0))
#plt.loglog([50.0,50.0],[1.0e+5,1.0e-1])
plt.xlabel('$k$')
plt.ylabel('$KE$')
plt.savefig('ke_spectra_galewsky_7days.png')
plt.show()
def TimingAccuracyGLQ():
# ---- input parameters ----
maxdeg = 2800
ls = np.arange(maxdeg + 1)
beta = 1.5
print('Driscoll-Healy (real)')
# ---- 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)))
cilm = np.random.normal(loc=0., scale=1., size=(2, maxdeg + 1, maxdeg + 1))
cilm[:, 1:, :] *= np.sqrt((ls[1:]**beta) / (2. * ls[1:] + 1.))[None, :,
None]
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 tprecompute tinverse tforward')
while lmax <= maxdeg:
# trim coefficients to lmax
cilm_trim = cilm[:, :lmax + 1, :lmax + 1]
mask_trim = mask[:, :lmax + 1, :lmax + 1]
# precompute grid nodes and associated Legendre functions
tstart = time.time()
zeros, weights = expand.SHGLQ(lmax)
tend = time.time()
tprecompute = tend - tstart
# synthesis / inverse
tstart = time.time()
grid = expand.MakeGridGLQ(cilm_trim, zeros)
tend = time.time()
tinverse = tend - tstart
# analysis / forward
tstart = time.time()
cilm2_trim = expand.SHExpandGLQ(grid, weights, zeros)
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 '
'{:1.1e}s'.format(lmax, maxerr, rmserr, tprecompute, tinverse,
tforward))
if maxerr > 100.:
raise RuntimeError('Tests Failed. Maximum relative error = ',
maxerr)
lmax = lmax * 2
def TimingAccuracyGLQ():
# ---- input parameters ----
maxdeg = 2800
ls = np.arange(maxdeg + 1)
beta = 1.5
print('Driscoll-Healy (real)')
# ---- 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)))
cilm = np.random.normal(loc=0., scale=1., size=(2, maxdeg + 1, maxdeg + 1))
cilm[:, 1:, :] *= np.sqrt((ls[1:]**beta) /
(2. * ls[1:] + 1.))[None, :, None]
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 tprecompute tinverse tforward')
while lmax <= maxdeg:
# trim coefficients to lmax
cilm_trim = cilm[:, :lmax + 1, :lmax + 1]
mask_trim = mask[:, :lmax + 1, :lmax + 1]
# precompute grid nodes and associated Legendre functions
tstart = time.time()
zeros, weights = expand.SHGLQ(lmax)
tend = time.time()
tprecompute = tend - tstart
# synthesis / inverse
tstart = time.time()
grid = expand.MakeGridGLQ(cilm_trim, zeros)
tend = time.time()
tinverse = tend - tstart
# analysis / forward
tstart = time.time()
cilm2_trim = expand.SHExpandGLQ(grid, weights, zeros)
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 '
'{:1.1e}s'.format(lmax, maxerr, rmserr, tprecompute, tinverse,
tforward))
lmax = lmax * 2
