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@ -116,11 +116,11 @@ def osc_weights(omega, g, dg, x, basis, ab, *args, **kwds):
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return np.asarray(w).ravel()
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return np.asarray(w).ravel()
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class QuadOsc(object):
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class _Integrator(object):
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info = namedtuple('info', ['error_estimate', 'n'])
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info = namedtuple('info', ['error_estimate', 'n'])
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def __init__(self, f, g, dg=None, a=-1, b=1, basis=chebyshev_basis, s=15,
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def __init__(self, f, g, dg=None, a=-1, b=1, basis=chebyshev_basis, s=1,
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precision=10, endpoints=False, maxiter=17, full_output=False):
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precision=10, endpoints=True, full_output=False):
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self.f = f
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self.f = f
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self.g = g
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self.g = g
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self.dg = nd.Derivative(g) if dg is None else dg
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self.dg = nd.Derivative(g) if dg is None else dg
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@ -129,10 +129,18 @@ class QuadOsc(object):
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self.b = b
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self.b = b
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self.s = s
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self.s = s
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self.endpoints = endpoints
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self.endpoints = endpoints
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self.maxiter = maxiter
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self.precision = precision
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self.precision = precision
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self.full_output = full_output
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self.full_output = full_output
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class QuadOsc(_Integrator):
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def __init__(self, f, g, dg=None, a=-1, b=1, basis=chebyshev_basis, s=15,
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precision=10, endpoints=False, full_output=False, maxiter=17):
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self.maxiter = maxiter
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super(QuadOsc, self).__init__(f, g, dg=dg, a=a, b=b, basis=basis, s=s,
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precision=precision, endpoints=endpoints,
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full_output=full_output)
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@staticmethod
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@staticmethod
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def _change_interval_to_0_1(f, g, dg, a, b):
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def _change_interval_to_0_1(f, g, dg, a, b):
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def f1(t, *args, **kwds):
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def f1(t, *args, **kwds):
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@ -344,22 +352,8 @@ def chebyshev_roots(M, delta=None):
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return x
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return x
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class AdaptiveLevin(object):
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class AdaptiveLevin(_Integrator):
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'''Return integral for the Levin-type and adaptive Levin-type methods'''
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'''Return integral for the Levin-type and adaptive Levin-type methods'''
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info = namedtuple('info', ['error_estimate', 'n'])
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def __init__(self, f, g, dg=None, a=-1, b=1, basis=chebyshev_basis, s=1,
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precision=10, endpoints=True, full_output=False):
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self.f = f
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self.g = g
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self.dg = nd.Derivative(g) if dg is None else dg
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self.basis = basis
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self.a = a
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self.b = b
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self.s = s
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self.precision = precision
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self.endpoints = endpoints
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self.full_output = full_output
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@staticmethod
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@staticmethod
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def aLevinTQ(omega, ff, gg, dgg, x, s, basis, *args, **kwds):
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def aLevinTQ(omega, ff, gg, dgg, x, s, basis, *args, **kwds):
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@ -510,16 +504,10 @@ class EvansWebster(AdaptiveLevin):
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def __init__(self, f, g, dg=None, a=-1, b=1, basis=chebyshev_basis, s=8,
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def __init__(self, f, g, dg=None, a=-1, b=1, basis=chebyshev_basis, s=8,
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precision=10, endpoints=False, full_output=False):
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precision=10, endpoints=False, full_output=False):
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self.f = f
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super(EvansWebster,
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self.g = g
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self).__init__(f, g, dg=dg, a=a, b=b, basis=basis, s=s,
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self.dg = nd.Derivative(g) if dg is None else dg
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precision=precision, endpoints=endpoints,
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self.basis = basis
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full_output=full_output)
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self.a = a
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self.b = b
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self.s = s
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self.endpoints = endpoints
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self.precision = precision
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self.full_output = full_output
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def aLevinTQ(self, omega, ff, gg, dgg, x, s, basis, *args, **kwds):
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def aLevinTQ(self, omega, ff, gg, dgg, x, s, basis, *args, **kwds):
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w = evans_webster_weights(omega, gg, dgg, x, basis, *args, **kwds)
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w = evans_webster_weights(omega, gg, dgg, x, basis, *args, **kwds)
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@ -531,55 +519,6 @@ class EvansWebster(AdaptiveLevin):
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def _get_num_points(self, s, prec, betam):
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def _get_num_points(self, s, prec, betam):
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return 8 if s > 1 else int(prec / max(np.log10(betam + 1), 1) + 1)
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return 8 if s > 1 else int(prec / max(np.log10(betam + 1), 1) + 1)
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# def _QaL(self, s, a, b, omega, *args, **kwds):
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# '''if s>1,the integral is computed by Q_s^L'''
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# scale = (b - a) / 2
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# offset = (a + b) / 2
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# prec = self.precision # desired precision
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#
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# def ff(t, *args, **kwds):
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# return scale * self.f(scale * t + offset, *args, **kwds)
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#
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# def gg(t, *args, **kwds):
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# return self.g(scale * t + offset, *args, **kwds)
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#
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# def dgg(t, *args, **kwds):
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# return scale * self.dg(scale * t + offset, *args, **kwds)
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# dg_a = abs(omega * dgg(-1, *args, **kwds))
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# dg_b = abs(omega * dgg(1, *args, **kwds))
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# g_a = abs(omega * gg(-1, *args, **kwds))
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# g_b = abs(omega * gg(1, *args, **kwds))
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# delta, alpha = min(dg_a, dg_b), min(g_a, g_b)
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#
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# betam = delta # * scale
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# if self.endpoints:
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# if (delta < 10 or alpha <= 10 or s > 1):
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# points = chebyshev_extrema
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# else:
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# points = adaptive_levin_points
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# elif (delta < 10 or alpha <= 10 or s > 1):
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# points = chebyshev_roots
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# else:
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# points = tanh_sinh_open_nodes
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#
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# m = 8 if s > 1 else int(prec / max(np.log10(betam + 1), 1) + 1)
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# abseps = 10*10.0**-prec
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# num_collocation_point_list = 2*m*np.arange(1, 6, 2)
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# # range(num_points, num_points+3, 2)
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# basis = self.basis
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# Q = 1e+300
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# n = 0
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# for num_collocation_points in num_collocation_point_list:
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# Q_old = Q
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# x = points(num_collocation_points-1, betam)
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# Q = self.aLevinTQ(omega, ff, gg, dgg, x, s, basis, *args, **kwds)
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# n += num_collocation_points
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# err = np.abs(Q-Q_old)
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# if err <= abseps:
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# break
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# info = self.info(err, n)
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# return Q, info
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if __name__ == '__main__':
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if __name__ == '__main__':
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tanh_sinh_nodes(16)
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tanh_sinh_nodes(16)
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