def addAbsorber(self, qp, data=None, **kwargs):
# todo? absorber type (mpArray) -> type(Stateoq) ?
if data != None and qp == 'q':
if self.__dummy[0]:
self.absorber[0] = mpArray(self.dim)
self.__dummy[0] = False
self.absorber[0] += data
if True in (numpy.abs(self.absorber[0]) > 1.0):
self.absorber[0] = self.absorber[0]/self.absorber[0].real.max()
x = State(self.scaleinfo, self.absorber[0])
x.savetxt("absorber_q.dat")
elif qp =='p':
if self.__dummy[1]:
self.absorber[1] = mpArray(self.dim)
self.__dummy[1] = False
self.absorber[1] += data
if True in (numpy.abs(self.absorber[1]) > 1.0):
self.absorber[1] = self.absorber[1]/self.absorber[1].real.max()
x = State(self.scaleinfo, self.absorber[1])
x.savetxt("absorber_p.dat",qp="p")
elif qp == 'cs':
index = len(self.absorber)
self.absorber.append(mpArray(self.dim))
self.absorber[index] = data
x = State(self.scaleinfo, mpArray.ones(self.dim) - self.absorber[index])
x.savetxt("absorber_cs_%d.dat" % (index - 2))
def op0(self, x, isShift=False):
if isShift:
sub_x = numpy.fft.fftshift(x)
func = self.map.ifunc0(sub_x)
self.operator[0] = mpArray([ mpmath.exp(mpmath.mpc("0", -twopi*func[i]*self.tau/self.h*mpmath.mpf("0.5"))) for i in range(self.dim) ])
else:
func = self.map.ifunc0(x)
self.operator[0] = mpArray([ mpmath.exp(mpmath.mpc("0", -twopi*func[i]*self.tau/self.h*mpmath.mpf("0.5"))) for i in range(self.dim) ])
def op1(self, x, isShift=True):
if isShift:
sub_x = numpy.fft.fftshift(x)
func = self.map.ifunc1(sub_x)
self.operator[1] = mpArray([ mpmath.exp(mpmath.mpc("0", -twopi*func[i]*self.tau/self.h)) for i in range(self.dim) ])
else:
func = self.map.ifunc1(x)
self.operator[1] = mpArray([ mpmath.exp(mpmath.mpc("0", -twopi*func[i]*self.tau/self.h)) for i in range(self.dim) ])
def hole_operate(self, invec=None, queue=None, verbose=False):
self._operate(invec, None, False) # = self.operate
sum1 = mpArray(self.dim)
for i in range(2,len(self.absorber)):
sum0 = mpmath.fsum(self.absorber[i].conj()*mpArray(self.stateOut))
sum1 += self.absorber[i]*sum0*mpmath.mpf("0.5")*self.gamma[i-2]
self.stateOut = self.stateOut - State(self.scaleinfo, sum1)
if queue !=None:
queue.put(self.stateOut)
def _expotanh(self, x, x1, x2, **kwargs):
if 'alpha' in kwargs:
alpha=kwargs['alpha']
else:
alpha=mpmath.mpf("1e10")
z1 = x - x1
z2 = x - x2
y1 = mpArray([ mpmath.mpf("0.5")*(mpmath.mpf("1") - mpmath.tanh(x*alpha)) for x in z1 ])
y2 = mpArray([ mpmath.mpf("0.5")*(mpmath.mpf("1") + mpmath.tanh(x*alpha)) for x in z2 ])
return -(z1*z1*y1 + z2*z2*y2)
def operate(self, invec=None, queue=None, verbose=False):
if invec != None:
if isinstance(invec, mpArray):
self.setIn(invec)
elif isinstance(invec, list) and self.dim==len(invec):
self.setIn(mpArray(invec))
qvec = self.operator[0]*self.stateIn
pvec = mpArray(mpfft.fft(qvec))#, inverse=False, verbose=verbose))
pvec = self.operator[1]*pvec
self.stateOut = mpArray(mpfft.ifft(pvec))#, inverse=True, verbose=verbose))
if queue !=None:
queue.put(self.stateOut)
def operate(self, invec=None, queue=None, verbose=False):
if invec != None:
self.setIn(invec)
## tood: 一度だけしか呼びたくない
if self._isShift():
self.absorber[1] = self.absorber[1].fftshift()
qvec = self.absorber[0]*self.operator[0]*self.stateIn
pvec = mpArray(mpfft.fft(qvec))#, inverse=False, verbose=verbose))
pvec = self.absorber[1]*self.operator[1]*pvec
qvec = self.absorber[0]*mpArray(mpfft.ifft(pvec))#, inverse=True, verbose=verbose))
self.stateOut = State(self.scaleinfo, qvec)
if queue !=None:
queue.put(self.stateOut)
def setMatrix(self, fft=True, core=2, verbose=False,**kwargs):
from utility import parallel
self.setOperator(fft)
matrix = mpMatrix(self.dim)
orth_basis = [mpArray(self.dim) for i in range(self.dim)]
for i in range(self.dim):
orth_basis[i][i] = mpmath.mpc("1","0")
start = time.time()
if core > 1:
#data = [orth_basis[i] for i in range(self.dim)]
multi = parallel.MultiProcessing(self.operate, orth_basis, core=core)
multi.run()
res = multi.getResults()
for i in range(self.dim):
matrix[i,:] = res[i]
elif core == 1:
for i in range(self.dim):
self.setIn(orth_basis[i])
self.operate()
matrix[i,:] = self.stateOut[:] #mpmath.matrix(self.stateOut.data).T
t = time.time() -start
self.matrix = matrix.T
if verbose :
print("Making matrix of size" , self.dim, "in", t, "sec.", "using core", core)
def coherent(self, q_c, p_c, x=None):
if not isinstance(q_c, mpmath.mpf) and not isinstance(p_c, mpmath.mpf):
raise ValueError("q_c, p_c must be mpmath.mpf")
if x == None:
x = self.scaleinfo.x[0]
re = -(x - q_c)*(x - q_c)*mpmath.pi/(self.scaleinfo.h)
im = (x - q_c)*p_c*twopi/self.scaleinfo.h
res = mpArray([mpmath.exp(mpmath.mpc(re[i], im[i])) for i in range(len(x))])
return res.normalize()
def cs(self, q_c, p_c):
self.__raiseTypeError(q_c)
self.__raiseTypeError(p_c)
qrange = self.scaleinfo.domain[0]
d = qrange[1] - qrange[0]
lqmin, lqmax = qrange[0] - 2*d, qrange[1] + 2*d
long_q = mpArray.linspace(lqmin, lqmax, 5*self.dim, endpoint=False)
coh_state = self.coherent(q_c, p_c, long_q)
vec = mpArray(self.dim)
m = len(coh_state)/self.dim
coh_state = coh_state.reshape(m,self.dim)
for i in range(m):
vec += coh_state[i][::1]
return State(self.scaleinfo, vec.normalize())
def setOperator(self, fft=True):
self.operator = [mpArray(self.dim) for i in range(2)]
self.op0(self.scaleinfo.x[0], False)
self.op1(self.scaleinfo.x[1], self._isShift())
def tanh(self, x, x1, x2, **kwargs):
if not 'beta' in kwargs: raise ValueError("excepted kwargs: 'beta'")
beta = kwargs['beta']
z1 = (x - x1)*beta
z2 = (x - x2)*beta
return mpArray( [ mpmath.mpf("0.5")*(mpmath.tanh(z1[i]) - mpmath.tanh(z2[i])) for i in range(len(x)) ])
def tompArray(self):
return mpArray(self)
def exp(self, x, x1,x2,**kwargs):
if not 'beta' in kwargs: raise ValueError("excepted kwargs: 'beta'")
beta = kwargs['beta']
expo = self._expotanh(x, x1, x2, **kwargs)
return mpArray([mpmath.exp(expo[i]/(twopi)*beta) for i in range(len(x))])
def set(self,x):
if len(x) != self.scaleinfo.dim:
raise TypeError("len(x) != dim")
return State(self.scaleinfo, data = mpArray(x))
def expcs(self, q_c,p_c, gamma):
cs = self.cs(q_c,p_c)
expcs=mpArray([mpmath.exp(-mpmath.mpf("0.5")*gamma*x) for x in cs])
return State(self.scaleinfo,expcs)
def __init__(self,dim, domain):
HilbertSpace.__init__(self, dim)
self.scaleinfo = ScaleInfo(dim, domain)
self.stateIn = mpArray(dim)
self.stateOut = mpArray(dim)
def getEnergy(self,**kwargs):
evals, evecs = self.getEigen(**kwargs)
energy = mpArray([1.j*self.qmap.h*mpmath.log(val)/self.qmap.tau for val in evals])
return energy
def __setDomain(self, r):
self.__setQdomain(r[0][0], r[0][1])
self.__setPdomain(r[1][0], r[1][1])
x = [mpArray(mpmath.linspace(self.domain[i][0], self.domain[i][1], self.dim, endpoint=False)) for i in range(2) ]
self.__x = (x[0], x[1])
