f0 = log10(x*( sin((1-a)*b*pi/(2+2*b)) / sin((1-a)*pi/(2+2*b)) )**(1/(1-a)))
de = de * y/havriliak_negami(x, f0, de, a, b)
return f0, de, a, b
def peak(f0, de, a, b):
fmax = 10**f0 * ( sin((1-a)*pi/(2+2*b)) / sin((1-a)*b*pi/(2+2*b)) )**(1/(1-a))
emax = havriliak_negami(fmax, f0, de, a, b)
return fmax, emax
def horiz(x, f0, de, a, b):
if (a+x)*b > 1:
return None
fmax, emax = peak(f0, de, a, b)
return move(fmax, emax, f0, de, a-x, b)
def vert(x, f0, de, a, b):
if a*(b+x) > 1:
return None
fmax, emax = peak(f0, de, a, b)
return move(fmax, emax, f0, de, a, b+x)
havriliak_negami.move = move
havriliak_negami.horiz = horiz
havriliak_negami.vert = vert
cole_cole = special_case(havriliak_negami, 'Dielectric/Cole-Cole (deriv)', b='1')
kwwapprox = special_case(havriliak_negami, 'Dielectric/KWW-approx (deriv)', b='1-.812*a**.387')
functions = [havriliak_negami, cole_cole, kwwapprox]
f0 = log10(x*( sin((1-a)*b*pi/(2+2*b)) / sin((1-a)*pi/(2+2*b)) )**(1/(1-a)))
de = de * y/havriliak_negami(x, f0, de, a, b, real)
return f0, de, a, b, real
def peak(f0, de, a, b):
fmax = 10**f0 * ( sin((1-a)*pi/(2+2*b)) / sin((1-a)*b*pi/(2+2*b)) )**(1/(1-a))
emax = havriliak_negami(fmax, f0, de, a, b, real)
return fmax, emax
def horiz(x, f0, de, a, b):
if (a+x)*b > 1:
return None
fmax, emax = peak(f0, de, a, b)
return move(fmax, emax, f0, de, a-x, b, real)
def vert(x, f0, de, a, b):
if a*(b+x) > 1:
return None
fmax, emax = peak(f0, de, a, b)
return move(fmax, emax, f0, de, a, b+x, real)
havriliak_negami.move = move
havriliak_negami.horiz = horiz
havriliak_negami.vert = vert
cole_cole = special_case(havriliak_negami, 'Dielectric/Cole-Cole (complex)', b='1')
kwwapprox = special_case(havriliak_negami, 'Dielectric/KWW-approx (complex)', b='1-.812*a**.387')
hnhn2 = special_case(havriliak_negami, 'HnHn2', real='-1')
functions = [havriliak_negami, cole_cole, kwwapprox, hnhn2]
if (a + x) * b <= 1:
fmax, emax = peak(f0, de, a, b)
return move(fmax, emax, f0, de, a - x, b)
def vert(x, f0, de, a, b):
if a * (b + x) <= 1:
fmax, emax = peak(f0, de, a, b)
return move(fmax, emax, f0, de, a, b + x)
havriliak_negami.move = move
havriliak_negami.horiz = horiz
havriliak_negami.vert = vert
havriliak_negami.extra = {
'fmax':
'f0 + log10(( sin((1-a)*pi/(2+2*b)) / sin((1-a)*b*pi/(2+2*b)))**(1/(1-a)))'
}
cole_cole = special_case(havriliak_negami, 'Dielectric/Cole-Cole', b='1')
kwwapprox = special_case(havriliak_negami,
'Dielectric/KWW-approx',
b='1-.812*a**.387')
kwwapprox.extra = {
'fmax':
'f0 + log10(( sin((1-a)*pi/(2+2*(1-.812*a**.387))) / sin((1-a)*(1-.812*a**.387)*pi/(2+2*(1-.812*a**.387))))**(1/(1-a)))',
'bkww': '((1-a)*(1-.812*a**.387))**(1/1.23)'
}
functions = [havriliak_negami, cole_cole, kwwapprox]
