def __init__(self, G, Nf=6, lpfactor=20, scales=None, normalize=False):
self.lpfactor = lpfactor
self.normalize = normalize
lmin = G.lmax / lpfactor
if scales is None:
scales = utils.compute_log_scales(lmin, G.lmax, Nf - 1)
self.scales = scales
if len(scales) != Nf - 1:
raise ValueError('len(scales) should be Nf-1.')
def band_pass(x):
return x * np.exp(-x)
def low_pass(x):
return np.exp(-x**4)
kernels = [lambda x: 1.2 * np.exp(-1) * low_pass(x / 0.4 / lmin)]
for i in range(Nf - 1):
def kernel(x, i=i):
norm = np.sqrt(scales[i]) if normalize else 1
return norm * band_pass(scales[i] * x)
kernels.append(kernel)
super(MexicanHat, self).__init__(G, kernels)
def __init__(self, G, Nf=6, lpfactor=20, scales=None):
def kernel_abspline3(x, alpha, beta, t1, t2):
M = np.array([[1, t1, t1**2, t1**3],
[1, t2, t2**2, t2**3],
[0, 1, 2*t1, 3*t1**2],
[0, 1, 2*t2, 3*t2**2]])
v = np.array([1, 1, t1**(-alpha) * alpha * t1**(alpha - 1),
-beta*t2**(- beta - 1) * t2**beta])
a = np.linalg.solve(M, v)
r1 = x <= t1
r2 = (x >= t1)*(x < t2)
r3 = (x >= t2)
if isinstance(x, np.float64):
if r1:
r = x[r1]**alpha * t1**(-alpha)
if r2:
r = a[0] + a[1] * x + a[2] * x**2 + a[3] * x**3
if r3:
r = x[r3]**(-beta) * t2**beta
else:
r = np.zeros(x.shape)
x2 = x[r2]
r[r1] = x[r1]**alpha * t1**(-alpha)
r[r2] = a[0] + a[1] * x2 + a[2] * x2**2 + a[3] * x2**3
r[r3] = x[r3]**(-beta) * t2 ** beta
return r
self.lpfactor = lpfactor
lmin = G.lmax / lpfactor
if scales is None:
scales = utils.compute_log_scales(lmin, G.lmax, Nf - 1)
self.scales = scales
gb = lambda x: kernel_abspline3(x, 2, 2, 1, 2)
gl = lambda x: np.exp(-np.power(x, 4))
lminfac = .4 * lmin
g = [lambda x: 1.2 * np.exp(-1) * gl(x / lminfac)]
for i in range(0, Nf - 1):
g.append(lambda x, i=i: gb(self.scales[i] * x))
f = lambda x: -gb(x)
xstar = optimize.minimize_scalar(f, bounds=(1, 2),
method='bounded')
gamma_l = -f(xstar.x)
lminfac = .6 * lmin
g[0] = lambda x: gamma_l * gl(x / lminfac)
super(Abspline, self).__init__(G, g)
def __init__(self, G, Nf=6, lpfactor=20, scales=None):
def kernel_abspline3(x, alpha, beta, t1, t2):
M = np.array([[1, t1, t1**2, t1**3], [1, t2, t2**2, t2**3],
[0, 1, 2 * t1, 3 * t1**2], [0, 1, 2 * t2,
3 * t2**2]])
v = np.array([
1, 1, t1**(-alpha) * alpha * t1**(alpha - 1),
-beta * t2**(-beta - 1) * t2**beta
])
a = np.linalg.solve(M, v)
r1 = x <= t1
r2 = (x >= t1) * (x < t2)
r3 = (x >= t2)
if isinstance(x, np.float64):
if r1:
r = x[r1]**alpha * t1**(-alpha)
if r2:
r = a[0] + a[1] * x + a[2] * x**2 + a[3] * x**3
if r3:
r = x[r3]**(-beta) * t2**beta
else:
r = np.zeros(x.shape)
x2 = x[r2]
r[r1] = x[r1]**alpha * t1**(-alpha)
r[r2] = a[0] + a[1] * x2 + a[2] * x2**2 + a[3] * x2**3
r[r3] = x[r3]**(-beta) * t2**beta
return r
self.lpfactor = lpfactor
lmin = G.lmax / lpfactor
if scales is None:
scales = utils.compute_log_scales(lmin, G.lmax, Nf - 1)
self.scales = scales
gb = lambda x: kernel_abspline3(x, 2, 2, 1, 2)
gl = lambda x: np.exp(-np.power(x, 4))
lminfac = .4 * lmin
g = [lambda x: 1.2 * np.exp(-1) * gl(x / lminfac)]
for i in range(0, Nf - 1):
g.append(lambda x, i=i: gb(self.scales[i] * x))
f = lambda x: -gb(x)
xstar = optimize.minimize_scalar(f, bounds=(1, 2), method='bounded')
gamma_l = -f(xstar.x)
lminfac = .6 * lmin
g[0] = lambda x: gamma_l * gl(x / lminfac)
super(Abspline, self).__init__(G, g)