def test_real_forward_ssht_vs_ducc0(real_image, order, method, nthreads=1):
ssht_coeffs = ssht.forward(real_image,
order,
Reality=True,
Method=method,
Spin=0)
ducc0_coeffs = ssht.forward(
real_image,
order,
Reality=True,
Method=method,
Spin=0,
backend="ducc",
nthreads=nthreads,
)
assert ssht_coeffs == approx(ducc0_coeffs)
def test_real_forward_adjoint(rng: np.random.Generator, method, order):
shape = ssht.sample_shape(order, Method=method)
f = rng.standard_normal(shape, dtype="float64")
flm = ssht.forward(f, order, Reality=True, Method=method)
f = ssht.inverse(flm, order, Reality=True, Method=method)
f_prime = rng.standard_normal(shape, dtype="float64")
flm_prime = ssht.forward(f_prime, order, Reality=True, Method=method)
f_prime = ssht.forward_adjoint(flm_prime,
order,
Reality=True,
Method=method,
backend="ducc")
assert flm_prime.conj() @ flm == approx(
f_prime.flatten().conj() @ f.flatten())
def test_SHT(L, Method, Reality, Spin, nthreads=1):
if Reality:
# Generate random flms (of real signal).
flm = np.zeros((L * L), dtype=complex)
# Impose reality on flms.
for el in range(L):
m = 0
ind = ssht.elm2ind(el, m)
flm[ind] = np.random.randn()
for m in range(1, el + 1):
ind_pm = ssht.elm2ind(el, m)
ind_nm = ssht.elm2ind(el, -m)
flm[ind_pm] = np.random.randn() + 1j * np.random.randn()
flm[ind_nm] = (-1)**m * np.conj(flm[ind_pm])
else:
flm = np.random.randn(L * L) + 1j * np.random.randn(L * L)
t0 = time()
f = ssht.inverse(
flm,
L,
Reality=Reality,
Method=Method,
Spin=Spin,
backend="ducc",
nthreads=nthreads,
)
flm_syn = ssht.forward(
f,
L,
Reality=Reality,
Method=Method,
Spin=Spin,
backend="ducc",
nthreads=nthreads,
)
tducc = time() - t0
t0 = time()
f2 = ssht.inverse(flm, L, Reality=Reality, Method=Method, Spin=Spin)
flm_syn2 = ssht.forward(f2, L, Reality=Reality, Method=Method, Spin=Spin)
tssht = time() - t0
return (_l2error(f, f2) + _l2error(flm_syn, flm_syn2), tssht / tducc)
def test_complex_forward_ssht_vs_ducc0(complex_image,
order,
method,
spin,
nthreads=1):
ssht_coeffs = ssht.forward(complex_image,
order,
Reality=False,
Method=method,
Spin=spin)
ducc0_coeffs = ssht.forward(
complex_image,
order,
Reality=False,
Method=method,
Spin=spin,
backend="ducc",
nthreads=nthreads,
)
assert ssht_coeffs == approx(ducc0_coeffs)
# % function, using simplest interface with default options.
# %
# % Author: Christopher G R Wallis & Jason McEwen (www.christophergrwallis.org & www.jasonmcewen.org)
# %
# % pyssht python package to perform spin spherical harmonic transforms
# Define parameters.
L = 64
# Generate random flms (of complex signal).
flm = np.random.randn(L*L) + 1j*np.random.randn(L*L)
# Compute inverse then forward transform.
f = ssht.inverse(flm, L);
flm_syn = ssht.forward(f, L);
# Compute max error in harmonic space.
maxerr = np.abs(flm_syn - flm).max()
print "Max error: ", maxerr
# Plot function on sphere using mollweide projection
f_plot, mask_array = ssht.mollweide_projection(np.abs(f), L, resolution=200)
plt.figure()
imgplot = plt.imshow(f_plot,interpolation='nearest')
plt.colorbar(imgplot,fraction=0.025, pad=0.04)
plt.imshow(mask_array, interpolation='nearest', cmap=cm.gray, vmin=-1., vmax=1.)
plt.gca().set_aspect("equal")
plt.title("|f|")
plt.axis('off')
def test_inverse_spin_reality(self):
with self.assertRaises(ssht.ssht_spin_error) as context:
ssht.forward(f,L,Reality=True,Spin=2)
self.assertTrue('Reality set to True and Spin is not 0. However, spin signals must be complex.'
in context.exception)
def test_forward_method_type(self):
with self.assertRaises(ssht.ssht_input_error) as context:
ssht.forward(f,L,Method="DJ")
self.assertTrue('Method is not recognised, Methods are: MW, MW_pole, MWSS, DH and GL' in context.exception)
def test_forward_ndim(self):
with self.assertRaises(ssht.ssht_input_error) as context:
ssht.forward(flm,L)
self.assertTrue('f must be 2D numpy array' in context.exception)
import matplotlib.pyplot as plt # s2c test L=256 thetas, phis = ssht.sample_positions(L, Grid=True) f = np.zeros((L,2*L-1), dtype=np.float_) + np.random.randn(L,2*L-1) #ssht.plot_sphere(phis, L,Parametric=False, Output_File='test.pdf',Show=False, Color_Bar=True, Units='Radians') (x, y, z) = ssht.s2_to_cart(thetas, phis) (x, y, z) = ssht.spherical_to_cart( np.ones(thetas.shape), thetas, phis) #test rotations flm = ssht.forward(phis, L, Reality=True) f = ssht.inverse(flm,L, Reality=True) flm_prime = ssht.rotate_flms(flm, np.pi/4, np.pi/4, np.pi/4, L) f_prime = ssht.inverse(flm_prime, L, Reality=True) #ssht.plot_sphere(f, L,Parametric=False, Output_File='test_phi_sphere.pdf',Show=False, Color_Bar=True, Units='Radians') #ssht.plot_sphere(f_prime, L,Parametric=False, Output_File='test_phi_rot_sphere.pdf',Show=False, Color_Bar=True, Units='Radians') #plot = ssht.plot_mollweide(f, L, Close=True) #plt.show() #plot2 = ssht.plot_mollweide(f_prime, L, Close=True) #plt.show()
flm = np.zeros((L * L), dtype=complex)
# Impose reality on flms.
for el in range(L):
m = 0
ind = ssht.elm2ind(el, m)
flm[ind] = np.random.randn()
for m in range(1, el + 1):
ind_pm = ssht.elm2ind(el, m)
ind_nm = ssht.elm2ind(el, -m)
flm[ind_pm] = np.random.randn() + 1j * np.random.randn()
flm[ind_nm] = (-1)**m * np.conj(flm[ind_pm])
# Compute inverse then forward transform.
f = ssht.inverse(flm, L, Reality=True)
flm_syn = ssht.forward(f, L, Reality=True)
# Compute max error in harmonic space.
maxerr = np.abs(flm_syn - flm).max()
print "Max error: ", maxerr
# Plot function on sphere using mollweide projection
f_plot, mask_array = ssht.mollweide_projection(np.abs(f), L, resolution=200)
plt.figure()
imgplot = plt.imshow(f_plot, interpolation='nearest')
plt.colorbar(imgplot, fraction=0.025, pad=0.04)
plt.imshow(mask_array,
interpolation='nearest',
cmap=cm.gray,
vmin=-1.,
# % pyssht_demo_3 - Run demo3
# %
# % Demo to compute inverse and forward transform of spin function, using
# % standard interface with various options.
# %
# % Author: Christopher G R Wallis & Jason McEwen (www.christophergrwallis.org & www.jasonmcewen.org)
# %
# % pyssht python package to perform spin spherical harmonic transforms
# Define parameters.
L = 64
spin = 4
methods = ["MW", "MWSS", "GL", "DH"]
# Generate random flms (of complex signal).
flm = np.random.randn(L * L) + 1j * np.random.randn(L * L)
# Zero harmonic coefficients with el<|spin|.
ind_min = np.abs(spin)**2
flm[0:ind_min] = 0.0 + 1j * 0.0
# Compute inverse then forward transform.
for method in methods:
f = ssht.inverse(flm, L, Method=method, Spin=spin, Reality=False)
flm_syn = ssht.forward(f, L, Method=method, Spin=spin, Reality=False)
# Compute max error in harmonic space.
maxerr = np.abs(flm_syn - flm).max()
print("Method:", method, "\nMax error:", maxerr)
# % pyssht_demo_4 - Run demo4
# %
# % Demo to compute inverse and forward transform of spin function, using
# % polar interface.
# %
# % Author: Christopher G R Wallis & Jason McEwen (www.christophergrwallis.org & www.jasonmcewen.org)
# %
# % pyssht python package to perform spin spherical harmonic transforms
# Define parameters.
L = 64
Spin = 0
method = "MW_pole"
# Generate random flms (of complex signal).
flm = np.random.randn(L * L) + 1j * np.random.randn(L * L)
# Zero harmonic coefficients with el<|spin|.
ind_min = np.abs(Spin)**2
flm[0:ind_min] = 0.0 + 1j * 0.0
# Compute inverse then forward transform.
f, f_sp, phi_sp = ssht.inverse(flm, L, Spin=Spin, Method="MW_pole")
flm_syn = ssht.forward((f, f_sp, phi_sp), L, Spin=Spin, Method="MW_pole")
# Compute max error in harmonic space.
maxerr = np.abs(flm_syn - flm).max()
print("Max error:", maxerr)
def test_everything():
# Test indexing functions
ind2elm_check = [
pyssht.ind2elm(i) == sshtn.ind2elm(i) for i in range(L * L)
]
assert all(ind2elm_check), "ind2elm functions do not match"
elm2ind_check = [
pyssht.elm2ind(el, m) == sshtn.elm2ind(el, m) for el in range(L)
for m in range(-el, el)
]
assert all(elm2ind_check), "elm2ind functions do not match"
assert pyssht.sample_shape(L, Method="MW") == sshtn.mw_sample_shape(L)
assert pyssht.sample_shape(L, Method="MWSS") == sshtn.mwss_sample_shape(L)
py_theta, py_phi = pyssht.sample_positions(L, Method="MW", Grid=False)
nb_theta, nb_phi = sshtn.mw_sample_positions(L)
assert np.allclose(py_theta, nb_theta)
assert np.allclose(py_phi, nb_phi)
py_theta, py_phi = pyssht.sample_positions(L, Method="MWSS", Grid=False)
nb_theta, nb_phi = sshtn.mwss_sample_positions(L)
assert np.allclose(py_theta, nb_theta)
assert np.allclose(py_phi, nb_phi)
py_ttheta, py_pphi = pyssht.sample_positions(L, Method="MW", Grid=True)
nb_ttheta, nb_pphi = sshtn.mw_sample_grid(L)
assert np.allclose(py_ttheta, nb_ttheta)
assert np.allclose(py_pphi, nb_pphi)
py_ttheta, py_pphi = pyssht.sample_positions(L, Method="MWSS", Grid=True)
nb_ttheta, nb_pphi = sshtn.mwss_sample_grid(L)
assert np.allclose(py_ttheta, nb_ttheta)
assert np.allclose(py_pphi, nb_pphi)
# Generate random flms (of complex signal).
np.random.seed(89834)
flm = np.random.randn(L * L) + 1j * np.random.randn(L * L)
# Zero harmonic coefficients with el<|spin|.
ind_min = np.abs(s)**2
flm[0:ind_min] = 0.0 + 1j * 0.0
# MW inverse complex transform
f_py_mw = pyssht.inverse(flm, L, Spin=s, Method="MW")
f_nb_mw = np.empty(sshtn.mw_sample_shape(L), dtype=np.complex128)
sshtn.mw_inverse_sov_sym(flm, L, s, f_nb_mw)
assert np.allclose(f_py_mw, f_nb_mw)
# MW forward complex transform, recovering input
rec_flm_py_mw = pyssht.forward(f_py_mw, L, Spin=s, Method="MW")
rec_flm_nb_mw = np.empty(L * L, dtype=np.complex128)
sshtn.mw_forward_sov_conv_sym(f_nb_mw, L, s, rec_flm_nb_mw)
assert np.allclose(rec_flm_py_mw, rec_flm_nb_mw)
assert np.allclose(rec_flm_nb_mw, flm)
# MW forward real transform
f_re = np.random.randn(*sshtn.mw_sample_shape(L))
flm_py_re_mw = pyssht.forward(f_re, L, Spin=0, Method="MW", Reality=True)
flm_nb_re_mw = np.empty(L * L, dtype=np.complex128)
sshtn.mw_forward_sov_conv_sym_real(f_re, L, flm_nb_re_mw)
assert np.allclose(flm_py_re_mw, flm_nb_re_mw)
# MW inverse real transform
rec_f_re_py = pyssht.inverse(flm_py_re_mw,
L,
Spin=0,
Method="MW",
Reality=True)
rec_f_re_nb = np.empty(sshtn.mw_sample_shape(L), dtype=np.float64)
sshtn.mw_inverse_sov_sym_real(flm_nb_re_mw, L, rec_f_re_nb)
assert np.allclose(rec_f_re_py, rec_f_re_nb)
# Note that rec_f_re_{py,nb} != f_re since f_re is not band-limited at L
# MWSS invserse complex transform
f_py_mwss = pyssht.inverse(flm, L, Spin=s, Method="MWSS", Reality=False)
f_nb_mwss = np.empty(sshtn.mwss_sample_shape(L), dtype=np.complex128)
sshtn.mw_inverse_sov_sym_ss(flm, L, s, f_nb_mwss)
assert np.allclose(f_py_mwss, f_nb_mwss)
# MWSS forward complex transform
rec_flm_py_mwss = pyssht.forward(f_py_mwss,
L,
Spin=s,
Method="MWSS",
Reality=False)
rec_flm_nb_mwss = np.empty(L * L, dtype=np.complex128)
sshtn.mw_forward_sov_conv_sym_ss(f_nb_mwss, L, s, rec_flm_nb_mwss)
assert np.allclose(rec_flm_py_mwss, rec_flm_nb_mwss)
assert np.allclose(rec_flm_nb_mwss, flm)
# MWSS forward real transform
f_re2 = np.random.randn(*sshtn.mwss_sample_shape(L))
flm_py_re_mwss = pyssht.forward(f_re2,
L,
Spin=0,
Method="MWSS",
Reality=True)
flm_nb_re_mwss = np.empty(L * L, dtype=np.complex128)
sshtn.mw_forward_sov_conv_sym_ss_real(f_re2, L, flm_nb_re_mwss)
assert np.allclose(flm_py_re_mwss, flm_nb_re_mwss)
# MWSS inverse real transform
rec_f_re_py_mwss = pyssht.inverse(flm_py_re_mwss,
L,
Spin=0,
Method="MWSS",
Reality=True)
rec_f_re_nb_mwss = np.empty(sshtn.mwss_sample_shape(L), dtype=np.float64)
sshtn.mw_inverse_sov_sym_ss_real(flm_nb_re_mwss, L, rec_f_re_nb_mwss)
assert np.allclose(rec_f_re_py_mwss, rec_f_re_nb_mwss)
assert np.allclose(pyssht.generate_dl(np.pi / 2, 10),
sshtn.generate_dl(np.pi / 2, 10))