def get_wavelet_fct(self, level):
# try to get it from cache
if self.wavelet_fct_level == level and self.wavelet_fct is not None:
return self.wavelet_fct
N = len(self.hk) - 1
#tabbed coef
hk = self.get_rec_hk()
gk = self.get_rec_gk()
tab_hk = np.r_[0, hk]
tab_gk = np.r_[0, gk]
# building the matrix
m = [0, 0]
p = [0, 0]
nn, kk = np.ogrid[1:N + 1, 1:N + 1]
index_m0 = nputils.clipreplace(2 * nn - kk, 1, N + 1, 0)
index_m1 = nputils.clipreplace(2 * nn - kk + 1, 1, N + 1, 0)
alpha = 2 / np.sum(hk)
m[0] = alpha * np.take(tab_hk, index_m0)
m[1] = alpha * np.take(tab_hk, index_m1)
p[0] = alpha * np.take(tab_gk, index_m0)
p[1] = alpha * np.take(tab_gk, index_m1)
x = np.arange(-N/2., N/2., pow(2, -level))
phi = np.zeros_like(x)
psi = np.zeros_like(x)
v = dict()
# compute the starting point
al, av = np.linalg.eig(m[0])
v_0 = av[:, np.argmin(abs(al - 1))]
v[0] = v_0 / v_0.sum()
pointsDone = np.empty(0)
for j in range(1, int(level + 1)):
points = np.setdiff1d(np.arange(0, 1, pow(2, -j)), pointsDone)
pointsDone = np.r_[points, pointsDone]
for point in points:
im = int(np.floor((point + 0.5)))
iv = (2 * point) % 1
v[point] = np.dot(m[im], v[iv])
phi[point * pow(2, level)::pow(2, level)] = np.real(v[point])
psi[point * pow(2, level)::pow(2, level)] = np.real(np.dot(p[im], v[iv]))
# cache result
self.wavelet_fct = (x, phi, psi)
self.wavelet_fct_level = level
return (x, phi, psi)
def get_wavelet_fct(self, level):
# try to get it from cache
if self.wavelet_fct_level == level and self.wavelet_fct is not None:
return self.wavelet_fct
N = len(self.hk) - 1
# tabbed coef
hk = self.get_rec_hk()
gk = self.get_rec_gk()
tab_hk = np.r_[0, hk]
tab_gk = np.r_[0, gk]
# building the matrix
m = [0, 0]
p = [0, 0]
nn, kk = np.ogrid[1 : N + 1, 1 : N + 1]
index_m0 = nputils.clipreplace(2 * nn - kk, 1, N + 1, 0)
index_m1 = nputils.clipreplace(2 * nn - kk + 1, 1, N + 1, 0)
alpha = 2 / np.sum(hk)
m[0] = alpha * np.take(tab_hk, index_m0)
m[1] = alpha * np.take(tab_hk, index_m1)
p[0] = alpha * np.take(tab_gk, index_m0)
p[1] = alpha * np.take(tab_gk, index_m1)
x = np.arange(-N / 2.0, N / 2.0, pow(2, -level))
phi = np.zeros_like(x)
psi = np.zeros_like(x)
v = dict()
# compute the starting point
al, av = np.linalg.eig(m[0])
v_0 = av[:, np.argmin(abs(al - 1))]
v[0] = v_0 / v_0.sum()
pointsDone = np.empty(0)
for j in range(1, int(level + 1)):
points = np.setdiff1d(np.arange(0, 1, pow(2, -j)), pointsDone)
pointsDone = np.r_[points, pointsDone]
for point in points:
im = int(np.floor((point + 0.5)))
iv = (2 * point) % 1
v[point] = np.dot(m[im], v[iv])
phi[point * pow(2, level) :: pow(2, level)] = np.real(v[point])
psi[point * pow(2, level) :: pow(2, level)] = np.real(np.dot(p[im], v[iv]))
# cache result
self.wavelet_fct = (x, phi, psi)
self.wavelet_fct_level = level
return (x, phi, psi)