def PadeTest(om, Gm, x, gamma, Norder):
from scipy import poly1d
zn = om[:Norder] * 1j
gn = Gm[:Norder]
an = me.padecof(gn, zn)
print 'zn=', zn
print 'an=', an
Aq_0 = poly1d([0])
Aq_1 = poly1d([an[0]])
Bq_0 = poly1d([1.])
Bq_1 = poly1d([1.])
for i in range(Norder - 1):
Aq_2 = Aq_1 + poly1d([1, -zn[i]]) * an[i + 1] * Aq_0
Aq_0 = Aq_1
Aq_1 = Aq_2
Bq_2 = Bq_1 + poly1d([1, -zn[i]]) * an[i + 1] * Bq_0
Bq_0 = Bq_1
Bq_1 = Bq_2
poles = sorted(roots(Bq_2), key=real)
ezeros = sorted(roots(Aq_2), key=real)
Bqp = poly1d(poles, r=True)
Cbq = Bq_2(0.0) / Bqp(0.0)
print 'ratio=', Cbq
wgh = []
print 'poles='
for i in range(len(poles)):
Rq = poly1d(poles[:i] + poles[i + 1:], r=True)
wi = Aq_2(poles[i]) / (Cbq * Rq(poles[i]))
wgh.append(wi)
if (poles[i].imag < 0): used = 'Yes'
else: used = 'No'
print "%2d %12.4g %12.4g %12.4g %12.4g used=%s" % (
i + 1, poles[i].real, poles[i].imag, wi.real, wi.imag, used)
wgh = array(wgh)
#print 'zeros='
#for i in range(len(ezeros)):
# print i+1, ezeros[i]
#print 'weights=', wgh
yt = zeros(len(om), dtype=complex)
for i in range(len(poles)):
if (poles[i].imag < 0):
yt += real(wgh[i]) / (om * 1j - poles[i])
normy = sum(real(yt))
normg = sum(real(Gm))
if normy > 1e-6:
print 'Warning: norm mismatch: ratio=', normg / normy
print 'Renormalizing'
wgh *= (normg / normy)
else:
print 'Warning: Not enough poles. Bailing out'
yt = zeros(len(om), dtype=complex)
for i in range(len(poles)):
if (poles[i].imag < 0):
yt += real(wgh[i]) / (om * 1j - poles[i])
yr = zeros(len(x), dtype=complex)
for i in range(len(poles)):
if (poles[i].imag < 0):
yr += real(wgh[i]) / (x - poles[i] + gamma * 1j)
savetxt('pade.corrected', vstack((x, real(yr), imag(yr))).transpose())
G0 = Aq_2(zn) / Bq_2(zn)
print 'G0=', G0
plot(om, real(Gm), 'o')
plot(om, real(yt), ':')
show()
plot(x, imag(yr))
#xlim([0,2.4])
#ylim([0,0.6])
show()
Gx = array([me.padeg(w + gamma * 1j, zn, an) for w in x])
return Gx
def Pade(om, Gm, x, gamma, Norder):
zn = om[:Norder] * 1j
gn = Gm[:Norder]
Pt = me.padecof(gn, zn)
Gx = array([me.padeg(w + gamma * 1j, zn, Pt) for w in x])
return Gx