def roots(self, use_2nd=True):
if use_2nd:
cs = flipud(chebt2(self.Ys))
roots = chebroots(cs)
reals = abs(imag(roots)) < params.interpolation.convergence.abstol
roots = real(roots[reals])
unit = (roots>-1.0) & (roots < 1.0)
roots = roots[unit]
return (roots*(self.Xs[-1]-self.Xs[0])+(self.Xs[0]+self.Xs[-1]))*0.5
else:
Ys = self.interp_at(chebspace(self.Xs[0], self.Xs[-1], self.n))
cs = flipud(chebt2(Ys))
roots = chebroots(cs)
reals = abs(imag(roots)) < params.interpolation.convergence.abstol
roots = real(roots[reals])
unit = (roots>-1.0) & (roots < 1.0)
roots = roots[unit]
return (roots*(self.Xs[-1]-self.Xs[0])+(self.Xs[0]+self.Xs[-1]))*0.5
def trim(self, abstol=None):
c = chebt2(self.Ys)
if abstol is None:
abstol = params.interpolation.convergence.abstol
while c[0] < abstol:
c = c[1:]
Ydiffvals = ichebt2(c)
Ydiffvals = flipud(Ydiffvals)
Xs, Ws = chebspace(self.a, self.b, len(Ydiffvals), returnWeights=True)
f = BarycentricInterpolator(Xs, Ydiffvals, Ws)
return f
def diff(self, use_2nd=True):
if use_2nd:
c = chebt2(self.Ys)
n = len(c);
cdiff = zeros(n + 1);
v = concatenate(([0, 0], 2 * arange(n - 1, 0, -1) * c[0:-1]));
cdiff[0::2] = cumsum(v[0::2]);
cdiff[1::2] = cumsum(v[1::2]);
cdiff[-1] = .5 * cdiff[-1];
cdiff = cdiff[2:];
Ydiffvals = ichebt2(cdiff) / ((self.Xs[-1] - self.Xs[0]) * 0.5)
Ydiffvals = flipud(Ydiffvals)
Xs, Ws = chebspace(self.Xs[0], self.Xs[-1], len(Ydiffvals), returnWeights=True)
f = BarycentricInterpolator(Xs, Ydiffvals, Ws)
return f
else:
Xs, Ws = chebspace(self.Xs[0], self.Xs[-1], len(self.Xs)+2, returnWeights=True)
Ys = self.interp_at(Xs)
return BarycentricInterpolator(Xs, Ys, Ws).diff(use_2nd=True)