Replaced methods with functions.

master
Per A Brodtkorb 8 years ago
parent e287f3b5d5
commit 311437f05c

@ -24,14 +24,15 @@ dea3 = nd.dea3
class PolyBasis(object):
def derivative(self, t, k, n=1):
@staticmethod
def derivative(t, k, n=1):
c = np.zeros(k + 1)
c[k] = 1
dc = polynomial.polyder(c, m=n)
return polynomial.polyval(t, dc)
def eval(self, t, c):
@staticmethod
def eval(t, c):
return polynomial.polyval(t, c)
def __call__(self, t, k):
@ -40,15 +41,16 @@ poly_basis = PolyBasis()
class ChebyshevBasis(object):
def derivative(self, t, k, n=1):
@staticmethod
def derivative(t, k, n=1):
c = np.zeros(k + 1)
c[k] = 1
cheb = Chebyshev(c)
dcheb = cheb.deriv(m=n)
return chebval(t, dcheb.coef)
def eval(self, t, c):
@staticmethod
def eval(t, c):
return chebval(t, c)
def __call__(self, t, k):
@ -70,45 +72,45 @@ def richardson(Q, k):
def evans_webster_weights(omega, gg, dgg, x, basis, *args, **kwds):
def Psi(t, k):
return dgg(t, *args, **kwds) * basis(t, k)
def Psi(t, k):
return dgg(t, *args, **kwds) * basis(t, k)
j_w = 1j * omega
nn = len(x)
A = np.zeros((nn, nn), dtype=complex)
F = np.zeros((nn,), dtype=complex)
j_w = 1j * omega
nn = len(x)
A = np.zeros((nn, nn), dtype=complex)
F = np.zeros((nn,), dtype=complex)
dbasis = basis.derivative
lim_gg = Limit(gg)
b1 = np.exp(j_w*lim_gg(1, *args, **kwds))
if np.isnan(b1):
b1 = 0.0
a1 = np.exp(j_w*lim_gg(-1, *args, **kwds))
if np.isnan(a1):
a1 = 0.0
lim_Psi = Limit(Psi)
for k in range(nn):
F[k] = basis(1, k)*b1 - basis(-1, k)*a1
A[k] = (dbasis(x, k, n=1) + j_w * lim_Psi(x, k))
dbasis = basis.derivative
lim_gg = Limit(gg)
b1 = np.exp(j_w*lim_gg(1, *args, **kwds))
if np.isnan(b1):
b1 = 0.0
a1 = np.exp(j_w*lim_gg(-1, *args, **kwds))
if np.isnan(a1):
a1 = 0.0
LS = linalg.lstsq(A, F)
return LS[0]
lim_Psi = Limit(Psi)
for k in range(nn):
F[k] = basis(1, k)*b1 - basis(-1, k)*a1
A[k] = (dbasis(x, k, n=1) + j_w * lim_Psi(x, k))
LS = linalg.lstsq(A, F)
return LS[0]
def osc_weights(omega, g, dg, x, basis, ab, *args, **kwds):
def gg(t):
return g(scale * t + offset, *args, **kwds)
def dgg(t):
return scale * dg(scale * t + offset, *args, **kwds)
w = []
for a, b in zip(ab[::2], ab[1::2]):
scale = (b - a) / 2
offset = (a + b) / 2
def gg(t):
return g(scale * t + offset, *args, **kwds)
def dgg(t):
return scale * dg(scale * t + offset, *args, **kwds)
w.append(evans_webster_weights(omega, gg, dgg, x, basis))
return np.asarray(w).ravel()
@ -131,7 +133,8 @@ class QuadOsc(object):
self.precision = precision
self.full_output = full_output
def _change_interval_to_0_1(self, f, g, dg, a, b):
@staticmethod
def _change_interval_to_0_1(f, g, dg, a, b):
def f1(t, *args, **kwds):
den = 1-t
return f(a + t / den, *args, **kwds) / den ** 2
@ -142,9 +145,10 @@ class QuadOsc(object):
def dg1(t, *args, **kwds):
den = 1-t
return dg(a + t / den, *args, **kwds) / den ** 2
return f1, g2, dg1, 0., 1.
return f1, g1, dg1, 0., 1.
def _change_interval_to_m1_0(self, f, g, dg, a, b):
@staticmethod
def _change_interval_to_m1_0(f, g, dg, a, b):
def f2(t, *args, **kwds):
den = 1 + t
return f(b + t / den, *args, **kwds) / den ** 2
@ -157,7 +161,8 @@ class QuadOsc(object):
return dg(b + t / den, *args, **kwds) / den ** 2
return f2, g2, dg2, -1.0, 0.0
def _change_interval_to_m1_1(self, f, g, dg, a, b):
@staticmethod
def _change_interval_to_m1_1(f, g, dg, a, b):
def f2(t, *args, **kwds):
den = (1 - t**2)
return f(t / den, *args, **kwds) * (1+t**2) / den ** 2
@ -197,42 +202,43 @@ class QuadOsc(object):
def __call__(self, omega, *args, **kwds):
f, g, dg, a, b, reverse = self._get_functions()
Q, err = self._quad_osc(f, g, dg, a, b, omega, *args, **kwds)
val, err = self._quad_osc(f, g, dg, a, b, omega, *args, **kwds)
if reverse:
Q = -Q
val = -val
if self.full_output:
return Q, err
return Q
return val, err
return val
def _get_best_estimate(self, k, Q0, Q1, Q2):
@staticmethod
def _get_best_estimate(k, q0, q1, q2):
if k >= 5:
Qv = np.hstack((Q0[k], Q1[k], Q2[k]))
Qw = np.hstack((Q0[k - 1], Q1[k - 1], Q2[k - 1]))
qv = np.hstack((q0[k], q1[k], q2[k]))
qw = np.hstack((q0[k - 1], q1[k - 1], q2[k - 1]))
elif k >= 3:
Qv = np.hstack((Q0[k], Q1[k]))
Qw = np.hstack((Q0[k - 1], Q1[k - 1]))
qv = np.hstack((q0[k], q1[k]))
qw = np.hstack((q0[k - 1], q1[k - 1]))
else:
Qv = np.atleast_1d(Q0[k])
Qw = Q0[k - 1]
errors = np.atleast_1d(abs(Qv - Qw))
qv = np.atleast_1d(q0[k])
qw = q0[k - 1]
errors = np.atleast_1d(abs(qv - qw))
j = np.nanargmin(errors)
return Qv[j], errors[j]
return qv[j], errors[j]
def _extrapolate(self, k, Q0, Q1, Q2):
def _extrapolate(self, k, q0, q1, q2):
if k >= 4:
Q1[k], _err1 = dea3(Q0[k - 2], Q0[k - 1], Q0[k])
Q2[k], _err2 = dea3(Q1[k - 2], Q1[k - 1], Q1[k])
q1[k], _err1 = dea3(q0[k - 2], q0[k - 1], q0[k])
q2[k], _err2 = dea3(q1[k - 2], q1[k - 1], q1[k])
elif k >= 2:
Q1[k], _err1 = dea3(Q0[k - 2], Q0[k - 1], Q0[k])
q1[k], _err1 = dea3(q0[k - 2], q0[k - 1], q0[k])
# # Richardson extrapolation
# if k >= 4:
# Q1[k] = richardson(Q0, k)
# Q2[k] = richardson(Q1, k)
# q1[k] = richardson(q0, k)
# q2[k] = richardson(q1, k)
# elif k >= 2:
# Q1[k] = richardson(Q0, k)
Q, err = self._get_best_estimate(k, Q0, Q1, Q2)
return Q, err
# q1[k] = richardson(q0, k)
q, err = self._get_best_estimate(k, q0, q1, q2)
return q, err
def _quad_osc(self, f, g, dg, a, b, omega, *args, **kwds):
if a == b:
@ -355,7 +361,8 @@ class AdaptiveLevin(object):
self.endpoints = endpoints
self.full_output = full_output
def aLevinTQ(self, omega, ff, gg, dgg, x, s, basis, *args, **kwds):
@staticmethod
def aLevinTQ(omega, ff, gg, dgg, x, s, basis, *args, **kwds):
def Psi(t, k):
return dgg(t, *args, **kwds) * basis(t, k)
@ -439,7 +446,8 @@ class AdaptiveLevin(object):
return val, info
return val
def _get_num_points(self, s, prec, betam):
@staticmethod
def _get_num_points(s, prec, betam):
return 1 if s > 1 else int(prec / max(np.log10(betam + 1), 1) + 1)
def _QaL(self, s, a, b, omega, *args, **kwds):

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