def weighted_wiener_lemma1_entries(ks,s=1.,t=0.):
from numpy import sign as sgn
ks = _np.array(ks,dtype='int')
ks = ks.ravel()
entries = _np.zeros([ks.size,6],dtype='complex128')
al = -1/2.
be = s-3/2.
kcount = 0
i = 1j
for k in ks:
n = _np.abs(k)-1
ka = _np.abs(k)
tempab = 2*n+al+be
temp = -i*s/2/(tempab+2)*_np.sqrt((n+al+1)*(n+be+1)/((tempab+1)*(tempab+3)))
entries[kcount,0] = temp*\
(_np.sqrt(n+al+be+1)*sgn(k)+_np.sqrt(n))*(sgn(k)*_np.sqrt(n+1) + _np.sqrt(n+al+be+2))
entries[kcount,1] = temp*\
(_np.sqrt(n+al+be+1)*sgn(k)-_np.sqrt(n))*(sgn(k)*_np.sqrt(n+1) + _np.sqrt(n+al+be+2))
entries[kcount,2] = -i*s/2*((be-al)*(al+be+1)/((tempab+2)*(tempab+4))+1)
entries[kcount,3] = -i*s/2*(al-be)/((tempab+2)*(tempab+4))*(1+sgn(k)*2*_np.sqrt((n+1)*(n+al+be+2)))
temp = -i*s/(2*(tempab+4))*_np.sqrt((n+al+2)*(n+be+2)/((tempab+3)*(tempab+5)))
entries[kcount,4] = temp*\
(sgn(k)*_np.sqrt(n+2)-_np.sqrt(n+al+be+3))*(sgn(k)*_np.sqrt(n+al+be+2)- _np.sqrt(n+1))
entries[kcount,5] = temp*\
(sgn(k)*_np.sqrt(n+2)+_np.sqrt(n+al+be+3))*(sgn(k)*_np.sqrt(n+al+be+2)- _np.sqrt(n+1))
kcount+=1
return entries
def weighted_wiener_stiff_entries(ks,s=1.,t=0.,scale=1.):
from numpy import sign as sgn
from numpy import sqrt
ks = _np.array(ks,dtype='int')
ks = ks.ravel()
entries = _np.zeros([ks.size,6],dtype='complex128')
al = -1/2.
be = s-3/2.
kcount = 0
i = 1j
for k in ks:
n = _np.abs(k)-1
ka = _np.abs(k)
tempab = 2*n+al+be
# Special expression if k=0
if k==0:
entries[kcount,2] = -i*(s-1/2.)
entries[kcount,4] = -i/2*sqrt(s-1/2.)*(1-sqrt(s))/sqrt(1+s)
entries[kcount,5] = -i/2*sqrt(s-1/2.)*(1+sqrt(s))/sqrt(1+s)
else:
# Special expression if |k|=1
if n==0:
entries[kcount,0] = i/_np.sqrt(2)*_np.sqrt((al+1)*(be+1)/((al+be+3)))*(sgn(k)*\
_np.sqrt((al+be+2)) - 1)
else:
entries[kcount,0] = i/2*_np.sqrt((n+al+1)*(n+be+1)/((tempab+1)*(tempab+3)))*\
(sgn(k)*(_np.sqrt((n+al+be+1)*(n+al+be+2)) + _np.sqrt(n*(n+1))) -\
(al+be+2)/(tempab+2)*(_np.sqrt((n+1)*(n+al+be+1)) + _np.sqrt(n*(n+al+be+2))))
entries[kcount,1] = i/2*_np.sqrt((n+al+1)*(n+be+1)/((tempab+1)*(tempab+3)))*\
(sgn(k)*(_np.sqrt((n+al+be+1)*(n+al+be+2)) - _np.sqrt(n*(n+1))) -\
(al+be+2)/(tempab+2)*(_np.sqrt((n+1)*(n+al+be+1)) - _np.sqrt(n*(n+al+be+2))))
entries[kcount,2] = i*sgn(k)*_np.sqrt((n+1)*(n+al+be+2)) - \
i*s*(be-al)*(al+be+1)/(2*(tempab+2)*(tempab+4)) - i*s/2
entries[kcount,3] = -s/2*i*(al-be)/((tempab+2)*(tempab+4))
entries[kcount,4] = i/2*_np.sqrt((n+be+2)*(n+al+2)/((tempab+3)*(tempab+5))) *\
(-s/(tempab+4)*(_np.sqrt((n+2)*(n+al+be+2)) + _np.sqrt((n+1)*(n+al+be+3))) +\
sgn(k)*(_np.sqrt((n+al+be+2)*(n+al+be+3)) + _np.sqrt((n+1)*(n+2))))
entries[kcount,5] = i/2*_np.sqrt((n+be+2)*(n+al+2)/((tempab+3)*(tempab+5))) *\
(-s/(tempab+4)*(_np.sqrt((n+2)*(n+al+be+2)) - _np.sqrt((n+1)*(n+al+be+3))) +\
sgn(k)*(-_np.sqrt((n+al+be+2)*(n+al+be+3)) + _np.sqrt((n+1)*(n+2))))
kcount += 1
return entries/scale
def wiener_stiff_entries(ks,s=1.,t=0.):
import spyctral.opoly1d.jacobi as jac
from numpy import sign as sgn
ks = _np.array(ks,dtype='int')
ks = ks.ravel()
entries = _np.zeros([ks.size,6],dtype='complex128')
al = -1/2.
be = s-3/2.
kcount = 0
for k in ks:
n = _np.abs(k)-1
ka = _np.abs(k)
tempab = 2*n+al+be
#zeta = jac.zetan(ka,al,be)
#factor = (n+al+be+2)*_np.sqrt(2*(n+al+1)*(n+al+be+2)/((tempab+2)*(tempab+3)))
#factorp1 = (n+1)*_np.sqrt(2*(n+1)*(n+be+2)/((tempab+3)*(tempab+4)))
#fs = _np.array([factor,factorp1])
#gammasn = jac.gamman(n,be+1,al)
#gammasnp1 = jac.gamman(n+1,be+1,al)
#[a_s,b_s] = jac.recurrence_ns([ka-1,ka],al+1,be+1)
# kvee, -kvee, k, -k, kwedge, -kwedge
#entries[kcount,0] = (fs[0]*gammasn[0]+zeta*_np.sqrt(b_s[0]))
entries[kcount,0] = (n+al+be+2)*_np.sqrt((n+al+1)*(n+be+1)/((tempab+1)*(tempab+2)**2*(tempab+3)))* \
(_np.sqrt((n+al+be+1)*(n+al+be+2)) + _np.sqrt(n*(n+1)))
#entries[kcount,1] = (fs[0]*gammasn[0]-zeta*_np.sqrt(b_s[0]))
entries[kcount,1] = (n+al+be+2)*_np.sqrt((n+al+1)*(n+be+1)/((tempab+1)*(tempab+2)**2*(tempab+3)))* \
(_np.sqrt((n+al+be+2)*(n+al+be+1)) - _np.sqrt(n*(n+1)))
#entries[kcount,2] = (fs[0]*gammasn[1]+fs[1]*gammasnp1[0]+zeta*(a_s[0]+1))
entries[kcount,2] = _np.sqrt((n+1)*(n+al+be+2))
#entries[kcount,3] = (fs[0]*gammasn[1]+fs[1]*gammasnp1[0]-zeta*(a_s[0]+1))
entries[kcount,3] = (al+be+2)*(al-be)/((tempab+2)*(tempab+4))*\
_np.sqrt((n+1)*(n+al+be+2))
#entries[kcount,4] = (fs[1]*gammasnp1[1]+zeta*_np.sqrt(b_s[1]))
entries[kcount,4] = (n+1)*_np.sqrt((n+be+2)*(n+al+2)/((tempab+3)*(tempab+4)**2*(tempab+5)))* \
(_np.sqrt((n+1)*(n+2)) + _np.sqrt((n+al+be+2)*(n+al+be+3)))
#entries[kcount,5] = (fs[1]*gammasnp1[1]-zeta*_np.sqrt(b_s[1]))
entries[kcount,5] = (n+1)*_np.sqrt((n+be+2)*(n+al+2)/((tempab+3)*(tempab+4)**2*(tempab+5)))* \
(_np.sqrt((n+1)*(n+2)) - _np.sqrt((n+al+be+2)*(n+al+be+3)))
entries[kcount,:] *= 1j*sgn(k)
kcount += 1
return entries
def trnsFnc(self, entrada, zm1):
self.preintval = -arry(sgn(self.integral - entrada) * self.gain) * arry(
power(abs(self.integral - entrada), potencia(self.orden))) + zm1
def sin_recurrence(ks,g,d):
from numpy import zeros, abs,sqrt
from numpy import sign as sgn
from spyctral.opoly1d.jacobi import etan, epsilonn
coeffs = zeros([ks.size,6])
al = d-1/2.
be = g-1/2.
ks0 = (ks==0)
ks1 = (abs(ks)==1)
ks2 = ~(ks0 | ks1)
n = abs(ks)
N = _np.max(n)
eta = etan(range(N+2),al,be)
eps = epsilonn(range(N+2),al+1,be+1)
# 0 = -kwedge
# 1 = -k
# 2 = -kvee
# 3 = kvee
# 4 = k
# 5 = kwedge
if any(ks0):
coeffs[ks0,0] = -1/sqrt(2)*eta[0,2]
coeffs[ks0,5] = 1/sqrt(2)*eta[0,2]
if any(ks1):
coeffs[ks1,0] = sgn(ks[ks1])/2.*(-eta[1,2]-eps[0,2])
coeffs[ks1,1] = sgn(ks[ks1])/2.*(-eta[1,1]-eps[0,1])
coeffs[ks1,3] = sgn(ks[ks1])/-sqrt(2)*eps[0,0]
coeffs[ks1,4] = sgn(ks[ks1])/2.*(eta[1,1]-eps[0,1])
coeffs[ks1,5] = sgn(ks[ks1])/2.*(eta[1,2]-eps[0,2])
if any(ks2):
n = n[ks2]
coeffs[ks2,0] = sgn(ks[ks2])/2.*(-eta[n,2]-eps[n-1,2])
coeffs[ks2,1] = sgn(ks[ks2])/2.*(-eta[n,1]-eps[n-1,1])
coeffs[ks2,2] = sgn(ks[ks2])/2.*(-eta[n,0]-eps[n-1,0])
coeffs[ks2,3] = sgn(ks[ks2])/2.*(eta[n,0]-eps[n-1,0])
coeffs[ks2,4] = sgn(ks[ks2])/2.*(eta[n,1]-eps[n-1,1])
coeffs[ks2,5] = sgn(ks[ks2])/2.*(eta[n,2]-eps[n-1,2])
return coeffs.squeeze()
def activation_dev2(output):
return np.sgn(output)
def trnsFnc(self,entrada,zm1): self.preintval=-arry(sgn(self.integral-entrada)*self.gain)*arry(power(abs(self.integral-entrada),potencia(self.orden)))+zm1
def sign(a):
"""Return the sign of a in (1, -1, 0)"""
return matrix(sgn(array(a)))