def test_dsi_metrics():
btable = np.loadtxt(get_fnames('dsi4169btable'))
gtab = gradient_table(btable[:, 0], btable[:, 1:])
data, golden_directions = SticksAndBall(gtab,
d=0.0015,
S0=100,
angles=[(0, 0), (60, 0)],
fractions=[50, 50],
snr=None)
dsmodel = DiffusionSpectrumModel(gtab, qgrid_size=21, filter_width=4500)
rtop_signal_norm = dsmodel.fit(data).rtop_signal()
dsmodel.fit(data).rtop_pdf()
rtop_pdf = dsmodel.fit(data).rtop_pdf(normalized=False)
assert_almost_equal(rtop_signal_norm, rtop_pdf, 6)
dsmodel = DiffusionSpectrumModel(gtab, qgrid_size=21, filter_width=4500)
mevals = np.array(([0.0015, 0.0003, 0.0003], [0.0015, 0.0003, 0.0003]))
S_0, sticks_0 = MultiTensor(gtab,
mevals,
S0=100,
angles=[(0, 0), (60, 0)],
fractions=[50, 50],
snr=None)
S_1, sticks_0 = MultiTensor(gtab,
mevals * 2.0,
S0=100,
angles=[(0, 0), (60, 0)],
fractions=[50, 50],
snr=None)
MSD_norm_0 = dsmodel.fit(S_0).msd_discrete(normalized=True)
MSD_norm_1 = dsmodel.fit(S_1).msd_discrete(normalized=True)
assert_almost_equal(MSD_norm_0, 0.5 * MSD_norm_1, 4)
def test_shore_metrics():
gtab = get_gtab_taiwan_dsi()
mevals = np.array(([0.0015, 0.0003, 0.0003],
[0.0015, 0.0003, 0.0003]))
angl = [(0, 0), (60, 0)]
S, sticks = MultiTensor(gtab, mevals, S0=100.0, angles=angl,
fractions=[50, 50], snr=None)
# since we are testing without noise we can use higher order and lower lambdas, with respect to the default.
radial_order = 6
lambd = 1e-8
# test mapmri_indices
indices = mapmri_index_matrix(radial_order)
n_c = indices.shape[0]
F = radial_order / 2
n_gt = np.round(1 / 6.0 * (F + 1) * (F + 2) * (4 * F + 3))
assert_equal(n_c, n_gt)
# test MAPMRI fitting
mapm= MapmriModel(gtab, radial_order=radial_order, lambd=lambd)
mapfit = mapm.fit(S)
c_map=mapfit.mapmri_coeff
R = mapfit.mapmri_R
mu = mapfit.mapmri_mu
S_reconst = mapfit.predict(gtab, 1.0)
# test the signal reconstruction
S = S / S[0]
nmse_signal = np.sqrt(np.sum((S - S_reconst) ** 2)) / (S.sum())
assert_almost_equal(nmse_signal, 0.0, 3)
# test if the analytical integral of the pdf is equal to one
integral = 0
for i in range(indices.shape[0]):
n1,n2,n3 = indices[i]
integral += c_map[i] * int_func(n1) * int_func(n2) * int_func(n3)
assert_almost_equal(integral, 1.0, 3)
# compare the shore pdf with the ground truth multi_tensor pdf
sphere = get_sphere('symmetric724')
v = sphere.vertices
radius = 10e-3
r_points = v * radius
pdf_mt = multi_tensor_pdf(r_points, mevals=mevals,
angles=angl, fractions= [50, 50])
pdf_map = mapmri_EAP(r_points, radial_order, c_map, mu, R)
nmse_pdf = np.sqrt(np.sum((pdf_mt - pdf_map) ** 2)) / (pdf_mt.sum())
assert_almost_equal(nmse_pdf, 0.0, 2)
def test_multi_tensor():
sphere = get_sphere('symmetric724')
vertices = sphere.vertices
mevals = np.array(([0.0015, 0.0003, 0.0003], [0.0015, 0.0003, 0.0003]))
e0 = np.array([np.sqrt(2) / 2., np.sqrt(2) / 2., 0])
e1 = np.array([0, np.sqrt(2) / 2., np.sqrt(2) / 2.])
mevecs = [all_tensor_evecs(e0), all_tensor_evecs(e1)]
# odf = multi_tensor_odf(vertices, [0.5, 0.5], mevals, mevecs)
# assert_(odf.shape == (len(vertices),))
# assert_(np.all(odf <= 1) & np.all(odf >= 0))
fimg, fbvals, fbvecs = get_data('small_101D')
bvals, bvecs = read_bvals_bvecs(fbvals, fbvecs)
gtab = gradient_table(bvals, bvecs)
s1 = single_tensor(gtab, 100, mevals[0], mevecs[0], snr=None)
s2 = single_tensor(gtab, 100, mevals[1], mevecs[1], snr=None)
Ssingle = 0.5 * s1 + 0.5 * s2
S, sticks = MultiTensor(gtab,
mevals,
S0=100,
angles=[(90, 45), (45, 90)],
fractions=[50, 50],
snr=None)
assert_array_almost_equal(S, Ssingle)
def generate_signal_crossing(gtab, lambda1, lambda2, lambda3, angle2=60):
mevals = np.array(([lambda1, lambda2, lambda3],
[lambda1, lambda2, lambda3]))
angl = [(0, 0), (angle2, 0)]
S, sticks = MultiTensor(gtab, mevals, S0=100.0, angles=angl,
fractions=[50, 50], snr=None)
return S, sticks
def test_shore_metrics():
fetch_taiwan_ntu_dsi()
img, gtab = read_taiwan_ntu_dsi()
mevals = np.array(([0.0015, 0.0003, 0.0003],
[0.0015, 0.0003, 0.0003]))
angl = [(0, 0), (60, 0)]
S, sticks = MultiTensor(gtab, mevals, S0=100, angles=angl,
fractions=[50, 50], snr=None)
S = S / S[0, None].astype(np.float)
radial_order = 8
zeta = 800
lambdaN = 1e-12
lambdaL = 1e-12
asm = ShoreModel(gtab, radial_order=radial_order, zeta=zeta, lambdaN=lambdaN, lambdaL=lambdaL)
asmfit = asm.fit(S)
c_shore= asmfit.shore_coeff
cmat = SHOREmatrix(radial_order, zeta, gtab)
S_reconst = np.dot(cmat, c_shore)
nmse_signal = np.sqrt(np.sum((S - S_reconst) ** 2)) / (S.sum())
assert_almost_equal(nmse_signal, 0.0, 4)
mevecs2 = np.zeros((2, 3, 3))
angl = np.array(angl)
for i in range(2):
mevecs2[i] = all_tensor_evecs(sticks[i]).T
sphere = get_sphere('symmetric724')
v = sphere.vertices
radius = 10e-3
pdf_shore = asmfit.pdf(v * radius)
pdf_mt = multi_tensor_pdf(v * radius, [.5, .5], mevals=mevals, mevecs=mevecs2)
nmse_pdf = np.sqrt(np.sum((pdf_mt - pdf_shore) ** 2)) / (pdf_mt.sum())
assert_almost_equal(nmse_pdf, 0.0, 2)
rtop_shore_signal = asmfit.rtop_signal()
rtop_shore_pdf = asmfit.rtop_pdf()
assert_almost_equal(rtop_shore_signal, rtop_shore_pdf, 9)
rtop_mt = multi_tensor_rtop([.5, .5], mevals=mevals)
assert_equal(rtop_mt/rtop_shore_signal < 1.12 and rtop_mt/rtop_shore_signal > 0.9 , True)
msd_mt = multi_tensor_msd([.5, .5], mevals=mevals)
msd_shore = asmfit.msd()
assert_equal(msd_mt/msd_shore < 1.05 and msd_mt/msd_shore > 0.95 , True)
def test_multivox_forecast():
gtab = get_3shell_gtab()
mevals = np.array(([0.0017, 0.0003, 0.0003], [0.0017, 0.0003, 0.0003]))
angl1 = [(0, 0), (60, 0)]
angl2 = [(90, 0), (45, 90)]
angl3 = [(0, 0), (90, 0)]
S = np.zeros((3, 1, 1, len(gtab.bvals)))
S[0, 0, 0], sticks = MultiTensor(gtab,
mevals,
S0=1.0,
angles=angl1,
fractions=[50, 50],
snr=None)
S[1, 0, 0], sticks = MultiTensor(gtab,
mevals,
S0=1.0,
angles=angl2,
fractions=[50, 50],
snr=None)
S[2, 0, 0], sticks = MultiTensor(gtab,
mevals,
S0=1.0,
angles=angl3,
fractions=[50, 50],
snr=None)
fm = ForecastModel(gtab, sh_order=8, dec_alg='CSD')
f_fit = fm.fit(S)
S_predict = f_fit.predict()
assert_equal(S_predict.shape, S.shape)
mse1 = np.sum((S_predict[0, 0, 0] - S[0, 0, 0])**2) / len(gtab.bvals)
assert_almost_equal(mse1, 0.0, 3)
mse2 = np.sum((S_predict[1, 0, 0] - S[1, 0, 0])**2) / len(gtab.bvals)
assert_almost_equal(mse2, 0.0, 3)
mse3 = np.sum((S_predict[2, 0, 0] - S[2, 0, 0])**2) / len(gtab.bvals)
assert_almost_equal(mse3, 0.0, 3)
def setup():
data.gtab = get_3shell_gtab()
data.mevals = np.array(([0.0017, 0.0003, 0.0003],
[0.0017, 0.0003, 0.0003]))
data.angl = [(0, 0), (60, 0)]
data.S, data.sticks = MultiTensor(
data.gtab, data.mevals, S0=100.0, angles=data.angl,
fractions=[50, 50], snr=None)
data.sh_order = 6
data.lambda_lb = 1e-8
data.lambda_csd = 1.0
sphere = get_sphere('repulsion100')
data.sphere = sphere.vertices[0:int(sphere.vertices.shape[0]/2), :]
def setup():
data.gtab = get_gtab_taiwan_dsi()
data.mevals = np.array(([0.0015, 0.0003, 0.0003], [0.0015, 0.0003,
0.0003]))
data.angl = [(0, 0), (60, 0)]
data.S, sticks = MultiTensor(data.gtab,
data.mevals,
S0=100.0,
angles=data.angl,
fractions=[50, 50],
snr=None)
data.radial_order = 6
data.zeta = 700
data.lambdaN = 1e-12
data.lambdaL = 1e-12
def test_forecast_indices():
# check anisotropic tensor
fm = ForecastModel(data.gtab,
sh_order=2,
lambda_lb=data.lambda_lb,
dec_alg='WLS')
f_fit = fm.fit(data.S)
d_par = f_fit.dpar
d_perp = f_fit.dperp
assert_almost_equal(d_par, data.mevals[0, 0], 5)
assert_almost_equal(d_perp, data.mevals[0, 1], 5)
gt_fa = np.sqrt(0.5 * (2 * (data.mevals[0, 0] - data.mevals[0, 1])**2) /
(data.mevals[0, 0]**2 + 2 * data.mevals[0, 1]**2))
gt_md = (data.mevals[0, 0] + 2 * data.mevals[0, 1]) / 3.0
assert_almost_equal(f_fit.fractional_anisotropy(), gt_fa, 2)
assert_almost_equal(f_fit.mean_diffusivity(), gt_md, 5)
# check isotropic tensor
mevals = np.array(([0.003, 0.003, 0.003], [0.003, 0.003, 0.003]))
data.angl = [(0, 0), (60, 0)]
S, sticks = MultiTensor(data.gtab,
mevals,
S0=100.0,
angles=data.angl,
fractions=[50, 50],
snr=None)
fm = ForecastModel(data.gtab,
sh_order=data.sh_order,
lambda_lb=data.lambda_lb,
dec_alg='WLS')
f_fit = fm.fit(S)
d_par = f_fit.dpar
d_perp = f_fit.dperp
assert_almost_equal(d_par, 3e-03, 5)
assert_almost_equal(d_perp, 3e-03, 5)
assert_almost_equal(f_fit.fractional_anisotropy(), 0.0, 5)
assert_almost_equal(f_fit.mean_diffusivity(), 3e-03, 10)
def test_mapmri_odf():
gtab = get_3shell_gtab()
# load symmetric 724 sphere
sphere = get_sphere('symmetric724')
# load icosahedron sphere
sphere2 = create_unit_sphere(5)
evals = np.array(([0.0017, 0.0003, 0.0003], [0.0017, 0.0003, 0.0003]))
data, golden_directions = MultiTensor(gtab,
evals,
S0=1.0,
angles=[(0, 0), (90, 0)],
fractions=[50, 50],
snr=None)
map_model = MapmriModel(gtab, radial_order=4)
# symmetric724
mapfit = map_model.fit(data)
odf = mapfit.odf(sphere)
directions, _, _ = peak_directions(odf, sphere, .35, 25)
assert_equal(len(directions), 2)
assert_almost_equal(angular_similarity(directions, golden_directions), 2,
1)
# 5 subdivisions
odf = mapfit.odf(sphere2)
directions, _, _ = peak_directions(odf, sphere2, .35, 25)
assert_equal(len(directions), 2)
assert_almost_equal(angular_similarity(directions, golden_directions), 2,
1)
sb_dummies = sticks_and_ball_dummies(gtab)
for sbd in sb_dummies:
data, golden_directions = sb_dummies[sbd]
mapfit = map_model.fit(data)
odf = mapfit.odf(sphere2)
directions, _, _ = peak_directions(odf, sphere2, .35, 25)
if len(directions) <= 3:
assert_equal(len(directions), len(golden_directions))
if len(directions) > 3:
assert_equal(gfa(odf) < 0.1, True)
def test_shore_metrics():
gtab = get_gtab_taiwan_dsi()
mevals = np.array(([0.0015, 0.0003, 0.0003],
[0.0015, 0.0003, 0.0003]))
angl = [(0, 0), (60, 0)]
S, sticks = MultiTensor(gtab, mevals, S0=100.0, angles=angl,
fractions=[50, 50], snr=None)
# test shore_indices
n = 7
l = 6
m = -4
radial_order, c = shore_order(n, l, m)
n2, l2, m2 = shore_indices(radial_order, c)
assert_equal(n, n2)
assert_equal(l, l2)
assert_equal(m, m2)
radial_order = 6
c = 41
n, l, m = shore_indices(radial_order, c)
radial_order2, c2 = shore_order(n, l, m)
assert_equal(radial_order, radial_order2)
assert_equal(c, c2)
# since we are testing without noise we can use higher order and lower lambdas, with respect to the default.
radial_order = 8
zeta = 700
lambdaN = 1e-12
lambdaL = 1e-12
asm = ShoreModel(gtab, radial_order=radial_order,
zeta=zeta, lambdaN=lambdaN, lambdaL=lambdaL)
asmfit = asm.fit(S)
c_shore = asmfit.shore_coeff
cmat = shore_matrix(radial_order, zeta, gtab)
S_reconst = np.dot(cmat, c_shore)
# test the signal reconstruction
S = S / S[0]
nmse_signal = np.sqrt(np.sum((S - S_reconst) ** 2)) / (S.sum())
assert_almost_equal(nmse_signal, 0.0, 4)
# test if the analytical integral of the pdf is equal to one
integral = 0
for n in range(int((radial_order)/2 +1)):
integral += c_shore[n] * (np.pi**(-1.5) * zeta **(-1.5) * genlaguerre(n,0.5)(0)) ** 0.5
assert_almost_equal(integral, 1.0, 10)
# test if the integral of the pdf calculated on a discrete grid is equal to one
pdf_discrete = asmfit.pdf_grid(17, 40e-3)
integral = pdf_discrete.sum()
assert_almost_equal(integral, 1.0, 1)
# compare the shore pdf with the ground truth multi_tensor pdf
sphere = get_sphere('symmetric724')
v = sphere.vertices
radius = 10e-3
pdf_shore = asmfit.pdf(v * radius)
pdf_mt = multi_tensor_pdf(v * radius, mevals=mevals,
angles=angl, fractions= [50, 50])
nmse_pdf = np.sqrt(np.sum((pdf_mt - pdf_shore) ** 2)) / (pdf_mt.sum())
assert_almost_equal(nmse_pdf, 0.0, 2)
# compare the shore rtop with the ground truth multi_tensor rtop
rtop_shore_signal = asmfit.rtop_signal()
rtop_shore_pdf = asmfit.rtop_pdf()
assert_almost_equal(rtop_shore_signal, rtop_shore_pdf, 9)
rtop_mt = multi_tensor_rtop([.5, .5], mevals=mevals)
assert_equal(rtop_mt / rtop_shore_signal <1.10 and rtop_mt / rtop_shore_signal > 0.95, True)
# compare the shore msd with the ground truth multi_tensor msd
msd_mt = multi_tensor_msd([.5, .5], mevals=mevals)
msd_shore = asmfit.msd()
assert_equal(msd_mt / msd_shore < 1.05 and msd_mt / msd_shore > 0.95, True)
def test_shore_metrics():
gtab = get_gtab_taiwan_dsi()
mevals = np.array(([0.0015, 0.0003, 0.0003], [0.0015, 0.0003, 0.0003]))
angl = [(0, 0), (60, 0)]
S, sticks = MultiTensor(gtab,
mevals,
S0=100.0,
angles=angl,
fractions=[50, 50],
snr=None)
# test shore_indices
n = 7
l = 6
m = -4
radial_order, c = shore_order(n, l, m)
n2, l2, m2 = shore_indices(radial_order, c)
assert_equal(n, n2)
assert_equal(l, l2)
assert_equal(m, m2)
radial_order = 6
c = 41
n, l, m = shore_indices(radial_order, c)
radial_order2, c2 = shore_order(n, l, m)
assert_equal(radial_order, radial_order2)
assert_equal(c, c2)
# since we are testing without noise we can use higher order and lower lambdas, with respect to the default.
radial_order = 8
zeta = 700
lambdaN = 1e-12
lambdaL = 1e-12
asm = ShoreModel(gtab,
radial_order=radial_order,
zeta=zeta,
lambdaN=lambdaN,
lambdaL=lambdaL)
asmfit = asm.fit(S)
c_shore = asmfit.shore_coeff
cmat = shore_matrix(radial_order, zeta, gtab)
S_reconst = np.dot(cmat, c_shore)
# test the signal reconstruction
S = S / S[0]
nmse_signal = np.sqrt(np.sum((S - S_reconst)**2)) / (S.sum())
assert_almost_equal(nmse_signal, 0.0, 4)
# test if the analytical integral of the pdf is equal to one
integral = 0
for n in range(int((radial_order) / 2 + 1)):
integral += c_shore[n] * (np.pi**(-1.5) * zeta**(-1.5) *
genlaguerre(n, 0.5)(0))**0.5
assert_almost_equal(integral, 1.0, 10)
# test if the integral of the pdf calculated on a discrete grid is equal to one
pdf_discrete = asmfit.pdf_grid(17, 40e-3)
integral = pdf_discrete.sum()
assert_almost_equal(integral, 1.0, 1)
# compare the shore pdf with the ground truth multi_tensor pdf
sphere = get_sphere('symmetric724')
v = sphere.vertices
radius = 10e-3
pdf_shore = asmfit.pdf(v * radius)
pdf_mt = multi_tensor_pdf(v * radius,
mevals=mevals,
angles=angl,
fractions=[50, 50])
nmse_pdf = np.sqrt(np.sum((pdf_mt - pdf_shore)**2)) / (pdf_mt.sum())
assert_almost_equal(nmse_pdf, 0.0, 2)
# compare the shore rtop with the ground truth multi_tensor rtop
rtop_shore_signal = asmfit.rtop_signal()
rtop_shore_pdf = asmfit.rtop_pdf()
assert_almost_equal(rtop_shore_signal, rtop_shore_pdf, 9)
rtop_mt = multi_tensor_rtop([.5, .5], mevals=mevals)
assert_equal(
rtop_mt / rtop_shore_signal < 1.10
and rtop_mt / rtop_shore_signal > 0.95, True)
# compare the shore msd with the ground truth multi_tensor msd
msd_mt = multi_tensor_msd([.5, .5], mevals=mevals)
msd_shore = asmfit.msd()
assert_equal(msd_mt / msd_shore < 1.05 and msd_mt / msd_shore > 0.95, True)
def test_mapmri_metrics():
gtab = get_gtab_taiwan_dsi()
mevals = np.array(([0.0015, 0.0003, 0.0003], [0.0015, 0.0003, 0.0003]))
angl = [(0, 0), (60, 0)]
S, sticks = MultiTensor(gtab,
mevals,
S0=100.0,
angles=angl,
fractions=[50, 50],
snr=None)
# since we are testing without noise we can use higher order and lower
# lambdas, with respect to the default.
radial_order = 6
lambd = 1e-8
# test mapmri_indices
indices = mapmri_index_matrix(radial_order)
n_c = indices.shape[0]
F = radial_order / 2
n_gt = np.round(1 / 6.0 * (F + 1) * (F + 2) * (4 * F + 3))
assert_equal(n_c, n_gt)
# test MAPMRI fitting
mapm = MapmriModel(gtab, radial_order=radial_order, lambd=lambd)
mapfit = mapm.fit(S)
c_map = mapfit.mapmri_coeff
R = mapfit.mapmri_R
mu = mapfit.mapmri_mu
S_reconst = mapfit.predict(gtab, 1.0)
# test the signal reconstruction
S = S / S[0]
nmse_signal = np.sqrt(np.sum((S - S_reconst)**2)) / (S.sum())
assert_almost_equal(nmse_signal, 0.0, 3)
# test if the analytical integral of the pdf is equal to one
integral = 0
for i in range(indices.shape[0]):
n1, n2, n3 = indices[i]
integral += c_map[i] * int_func(n1) * int_func(n2) * int_func(n3)
assert_almost_equal(integral, 1.0, 3)
# compare the shore pdf with the ground truth multi_tensor pdf
sphere = get_sphere('symmetric724')
v = sphere.vertices
radius = 10e-3
r_points = v * radius
pdf_mt = multi_tensor_pdf(r_points,
mevals=mevals,
angles=angl,
fractions=[50, 50])
pdf_map = mapmri_EAP(r_points, radial_order, c_map, mu, R)
nmse_pdf = np.sqrt(np.sum((pdf_mt - pdf_map)**2)) / (pdf_mt.sum())
assert_almost_equal(nmse_pdf, 0.0, 2)
# test MAPMRI metrics
tau = 1 / (4 * np.pi**2)
angl = [(0, 0), (0, 0)]
S, sticks = MultiTensor(gtab,
mevals,
S0=100.0,
angles=angl,
fractions=[50, 50],
snr=None)
mapm = MapmriModel(gtab, radial_order=radial_order, lambd=lambd)
mapfit = mapm.fit(S)
# RTOP
gt_rtop = 1.0 / np.sqrt(
(4 * np.pi * tau)**3 * mevals[0, 0] * mevals[0, 1] * mevals[0, 2])
rtop = mapfit.rtop()
assert_almost_equal(rtop, gt_rtop, 4)
# RTAP
gt_rtap = 1.0 / np.sqrt((4 * np.pi * tau)**2 * mevals[0, 1] * mevals[0, 2])
rtap = mapfit.rtap()
assert_almost_equal(rtap, gt_rtap, 4)
# RTPP
gt_rtpp = 1.0 / np.sqrt((4 * np.pi * tau) * mevals[0, 0])
rtpp = mapfit.rtpp()
assert_almost_equal(rtpp, gt_rtpp, 4)
