def pop(h, vars):
h = pol(h)
vars = list(vars)
out = 0
while vars:
x = vars.pop(0)
p = vars.pop(0)
out += dop(x) * (-dop(p)(h)) + dop(p) * dop(x)(h)
return out
def pop(h,vars):
h=pol(h)
vars=list(vars)
out=0
while vars:
x=vars.pop(0)
p=vars.pop(0)
out+=dop(x)*(-dop(p)(h))+dop(p)*dop(x)(h)
return out
def acosh(y):
"""Compute ArcCosh
>>> from pol import *
>>> x,y=mkpol('x,y')
>>> acosh(cosh(1.4+x+y))
1.4 + x + y
"""
x0=pol(log(y+sqrt(y**2-1)))
for i in range(y.order):
x0=x0 + (y-cosh(x0))/sinh(x0)
return x0
def asinh(y):
"""Compute ArcSinh
>>> from pol import *
>>> x,y=mkpol('x,y')
>>> asinh(sinh(.4+x+y))
0.4 + x + y
"""
x0=pol(log(y+sqrt(y**2+1)))
for i in range(y.order):
x0=x0 + (y-sinh(x0))/cosh(x0)
return x0
def acos(y):
"""Compute ArcCos
>>> from pol import *
>>> x,y=mkpol('x,y')
>>> acos(cos(.4+x+y))
0.4 + x + y
"""
x0=pol(math.acos(y.zero()))
for i in range(y.order):
x0=x0 + -(y-cos(x0))/sin(x0)
return x0
def asin(y):
"""Compute ArcSin
>>> from pol import *
>>> x,y=mkpol('x,y')
>>> asin(sin(.4+x+y))
0.4 + x + y
"""
x0=pol(math.asin(y.zero()))
for i in range(y.order):
x0=x0 + (y-sin(x0))/cos(x0)
return x0
def _derpol(self,other):
new=pol(order=min(self.order,other.order))
new.vars=list(set(other.vars+self.vars))
for i in self.coef:
for j in other:
c=self.coef[i]*other[j]
expi=dict(zip(self.vars,i))
expj=dict(zip(other.vars,j))
newexp=tuple([-expi.get(k,0)+expj.get(k,0) for k in new.vars])
for k in self.vars:
c*=normder(expj.get(k,0), expi.get(k,0))
new[newexp]=new.get(newexp,0.)+c
return new.truncate().dropneg()
def _derpol(self, other):
new = pol(order=min(self.order, other.order))
new.vars = list(set(other.vars + self.vars))
for i in self.coef:
for j in other.coef:
c = self.coef[i] * other.coef[j]
expi = dict(zip(self.vars, i))
expj = dict(zip(other.vars, j))
newexp = tuple(
[-expi.get(k, 0) + expj.get(k, 0) for k in new.vars])
for k in self.vars:
c *= normder(expj.get(k, 0), expi.get(k, 0))
new.coef[newexp] = new.coef.get(newexp, 0.) + c
return new.truncate().dropneg()
def atan(y):
"""Compute ArcTan using Newton method
x=f(y); y=g(x)
x0=f(y0); x0=x0 +(y-g(x0))/g'(x)
>>> from pol import *
>>> p=pol('.4+x+y')
>>> print tan(atan(p))
0.4 + x + y
>>> print atan(tan(p))
0.4 + x + y
"""
x0=pol(math.atan(y.zero()))
for i in range(y.order):
x0=x0 + (y-tan(x0))*cos(x0)**2
return x0
def __init__(self,val=None,order=None,eps=1E-13,loc={},m='eval'):
self.coef={}
self.vars=[]
self.order=1000
self.eps=eps
if val!=None:
if isinstance(val,dop):
self.coef.update(val.coef)
self.vars=val.vars[:]
self.order=val.order
self.eps=val.eps
elif isinstance(val,str):
if m=='eval':
c=compile(val,'eval','eval')
l=dict( (i,dop(i,m='name')) for i in c.co_names)
l.update(loc)
dop.__init__(self,eval(c,{},l))
elif m=='name':
self.vars=[val]
self.coef[(1,)]=pol(1.)
if order is not None:
self.order=order
def __init__(self, val=None, order=None, eps=1E-13, loc={}, m='eval'):
self.coef = {}
self.vars = []
self.order = 1000
self.eps = eps
if val != None:
if isinstance(val, dop):
self.coef.update(val.coef)
self.vars = val.vars[:]
self.order = val.order
self.eps = val.eps
elif isinstance(val, str):
if m == 'eval':
c = compile(val, 'eval', 'eval')
l = dict((i, dop(i, m='name')) for i in c.co_names)
l.update(loc)
dop.__init__(self, eval(c, {}, l))
elif m == 'name':
self.vars = [val]
self.coef[(1, )] = pol(1.)
if order is not None:
self.order = order
def main(args):
""" parse command line arguments"""
tstart = time.clock()
if not args.log:
logging.basicConfig(level=args.loglevel or logging.INFO)
else:
logging.basicConfig(filename='log', filemode='w', level=logging.DEBUG)
logger = logging.getLogger(__name__)
""" read plasma parameters """
param = utils.read_param(args)
""" iterate through wavenumber """
dk = (param['kend'][0] - param['kstart'][0]) / param['ksteps'][0]
fzeta = np.empty(int(param['ksteps'][0]), dtype=complex)
wave_k = np.empty(int(param['ksteps'][0]))
zeta_guess = complex(param['omega_r'][0], param['omega_i'][0])
# eigen value and polaization iEx/Ey*(omega_r/abs(omega_r))
val = []
pol = []
for n in range(int(param['ksteps'][0])):
logger.info('%d th iteration in %d ksteps \n', n, param['ksteps'][0])
wave_k[n] = param['kstart'][0] + n * dk
""" find dispersion relation root """
data = (args, param, wave_k[n])
try:
# use parallel dsp if theta<0.1 degree
if (abs(param['theta'][0]) < 1.):
sol = root(disp.det_para,(zeta_guess.real,zeta_guess.imag), \
args=data,method='hybr',tol=param['sol_err'][0])
fzeta[n] = complex(sol.x[0], sol.x[1])
else:
sol = root(disp.det,(zeta_guess.real,zeta_guess.imag), \
args=data,method='hybr',tol=param['sol_err'][0])
fzeta[n] = complex(sol.x[0], sol.x[1])
logger.info("solution: k*di=%1.2e , omega/Omega_ci=%1.2e+%1.2ei\n",
wave_k[n], fzeta[n].real, fzeta[n].imag)
if (param['cal_pol'][0]):
import pol as p
val0, pol0 = p.pol(args, param, wave_k[n], fzeta[n])
val.append(val0)
pol.append(pol0)
if (fzeta[n].imag < 0):
param['exp'][0] = 0
except ValueError:
logger.info('ERROR in root finding: wave_k =%f', wave_k[n])
""" extrapolate previous solutions for next guess """
if (n > 3 and n < int(param['ksteps'][0]) - 1):
zeta_guess = complex(interp(wave_k[n]+dk,wave_k[n-3:n],fzeta[n-3:n].real),\
interp(wave_k[n]+dk,wave_k[n-3:n],fzeta[n-3:n].imag))
else:
zeta_guess = fzeta[n]
""" save results to output file """
param['wave_k'] = wave_k
param['fzeta'] = fzeta
if args.output:
np.save(args.output + '.npy', param)
else:
np.save('output.npy', param)
tend = time.clock()
logger.info('\n Total time lapse: %1.2f\n', tend - tstart)
return 0
