def check(self, im_axis_fine=None):
"""Sanity check for Pade approximant
Evaluate the Pade approximant on the imaginary axis,
however not only at Matsubara frequencies, but on a
dense grid. If the approximant is good, then this
should yield a smooth interpolating curve on the Matsubara
axis. On the other hand, little 'spikes' are a hint
for pole-zero pairs close to the imaginary axis. This
is usually a result of noise and a different choice of
Matsubara frequencies may help.
Parameters
----------
im_axis_fine : numpy.ndarray, default=None
Imaginary-axis points where the approximant is
evaluated for checking. If not specified,
an array of length 500 is generated, which goes
up to twice the maximum frequency that was used
for constructing the approximant.
Returns
-------
numpy.ndarray
Values of the Pade approximant at the points
of `im_axis_fine`.
"""
if im_axis_fine is None:
self.ivcheck = np.linspace(0, 2 * np.max(self.im_axis), num=500)
else:
self.ivcheck = im_axis_fine
check = pade.C(self.ivcheck * 1j, 1j * self.im_axis, self.im_data,
self.a)
return check
def check(self,show_plot=False):
# As a check, look if Pade approximant smoothly interpolates the original data
self.ivcheck=np.linspace(0,2*np.max(self.im_axis),num=500)
self.check=pade.C(self.ivcheck*1j,1j*self.im_axis,self.im_data,self.a)
if show_plot:
f1=plt.figure()
plt.plot(ivpade,siwpade.real,marker='*',linestyle='None')
plt.plot(ivpade,siwpade.imag,marker='*',linestyle='None')
plt.plot(ivcheck,check.real)
plt.plot(ivcheck,check.imag)
f1.show()
def solve(self,show_plot=False):
# Compute the Pade approximation on the real axis
self.result=pade.C(self.re_axis,1j*self.im_axis,self.im_data,self.a)
if show_plot:
f2=plt.figure(2)
plt.plot(zr.real,result.real)
plt.plot(zr.real,result.imag)
f2.show()
# Compute the integral of the imaginary part
#self.norm=-np.trapz(self.result.imag,self.re_axis)/np.pi
#print 'norm: ',self.norm
return self.result
def check(self, show_plot=False):
# As a check, look if Pade approximant smoothly interpolates the original data
self.ivcheck = np.linspace(0, 2 * np.max(self.im_axis), num=500)
self.check = pade.C(self.ivcheck * 1j, 1j * self.im_axis, self.im_data,
self.a)
return self.check
def solve(self, show_plot=False):
# Compute the Pade approximation on the real axis
self.result = pade.C(self.re_axis, 1j * self.im_axis, self.im_data,
self.a)
return self.result