def __init__(self, op_char='m', label=r'modes', color='b',
operator=np.array(None), pickled=None):
if not TRC.init:
print "WARNING: class Transmission Rows Container not initialized"
return None
self.op_char = op_char
self.label = label
self.color = color
if not operator.any() and not pickled:
self.operator = np.identity(TRC.refmodes, dtype="complex")
self.eigvec = scat.inflate_small_mat(np.identity(TRC.refmodes, dtype="complex"), TRC.modes)
self.Leigvec = scat.inflate_small_mat(np.identity(TRC.refmodes, dtype="complex"), TRC.modes)
elif not operator.any() and pickled:
self.operator = np.identity(TRC.refmodes, dtype="complex")
self.eigvec, self.Leigvec = trans.unpickle_states(pickled, modes, refmodes)
else:
self.operator = operator
self.eigval, self.eigvec, self.Leigvec = trans.calc_eigensystem(self.operator, TRC.modes)
self.times, self.tisdv = trans.calc_qexpvals(self.eigvec, TRC.q, TRC.qLeigbas,
TRC.modes, TRC.refmodes, TRC.Nk)
self.vectransmit, self.vecLtransmit = trans.calc_transmitted_states(TRC.t, TRC.tinv, self.eigvec, self.Leigvec,
TRC.modes, TRC.refmodes, TRC.refpos, TRC.Nk)
self.mu = trans.calc_mu(self.vectransmit, self.vecLtransmit, TRC.refmodes, TRC.Nk)
def calc_eigensystem(a, modes):
'''
Calculcate eigenvalues, right eigenvectors and left eigenvectors of matrix a.
Eigenvectors are store column-wise and inflated by appending zeros
to size modes x modes.
'''
aeigval, aeigvec = ut.sort_eig(a)
aeigvec = aeigvec.transpose()
aLeigvec = np.linalg.inv(aeigvec).transpose()
aeigvec = scat.inflate_small_mat(aeigvec, modes)
aLeigvec = scat.inflate_small_mat(aLeigvec, modes)
return aeigval, aeigvec, aLeigvec
def calc_eigensystem(a, modes):
'''
Calculcate eigenvalues, right eigenvectors and left eigenvectors of matrix a.
Eigenvectors are store column-wise and inflated by appending zeros
to size modes x modes.
'''
aeigval, aeigvec = ut.sort_eig(a)
aeigvec = aeigvec.transpose()
aLeigvec = np.linalg.inv(aeigvec).transpose()
aeigvec = scat.inflate_small_mat(aeigvec, modes)
aLeigvec = scat.inflate_small_mat(aLeigvec, modes)
return aeigval, aeigvec, aLeigvec
def __init__(self,
op_char='m',
label=r'modes',
color='b',
operator=np.array(None),
pickled=None):
if not TRC.init:
print "WARNING: class Transmission Rows Container not initialized"
return None
self.op_char = op_char
self.label = label
self.color = color
if not operator.any() and not pickled:
self.operator = np.identity(TRC.refmodes, dtype="complex")
self.eigvec = scat.inflate_small_mat(
np.identity(TRC.refmodes, dtype="complex"), TRC.modes)
self.Leigvec = scat.inflate_small_mat(
np.identity(TRC.refmodes, dtype="complex"), TRC.modes)
elif not operator.any() and pickled:
self.operator = np.identity(TRC.refmodes, dtype="complex")
self.eigvec, self.Leigvec = trans.unpickle_states(
pickled, modes, refmodes)
else:
self.operator = operator
self.eigval, self.eigvec, self.Leigvec = trans.calc_eigensystem(
self.operator, TRC.modes)
self.times, self.tisdv = trans.calc_qexpvals(self.eigvec, TRC.q,
TRC.qLeigbas, TRC.modes,
TRC.refmodes, TRC.Nk)
self.vectransmit, self.vecLtransmit = trans.calc_transmitted_states(
TRC.t, TRC.tinv, self.eigvec, self.Leigvec, TRC.modes,
TRC.refmodes, TRC.refpos, TRC.Nk)
self.mu = trans.calc_mu(self.vectransmit, self.vecLtransmit,
TRC.refmodes, TRC.Nk)
def unpickle_states(filestr, modes, refmodes):
'''
Loads states from pickled files, calculates left states
and inflates both.
'''
try:
(vec, Lvec) = pickle.load(open(filestr, 'rb'))
n, m = np.shape(vec)
eigvec = np.identity(refmodes, dtype="complex")
Leigvec = np.identity(refmodes, dtype="complex")
eigvec[:n, :m] = vec
Leigvec[:n, :m] = Lvec
eigvec = scat.inflate_small_mat(eigvec, modes)
Leigvec = scat.inflate_small_mat(Leigvec, modes)
except:
print "WARNING: unable to load pickled states"
eigvec = np.identity(refmodes, dtype="complex")
Leigvec = np.identity(refmodes, dtype="complex")
eigvec = scat.inflate_small_mat(eigvec, modes)
Leigvec = scat.inflate_small_mat(Leigvec, modes)
return eigvec, Leigvec
def unpickle_states(filestr, modes, refmodes):
'''
Loads states from pickled files, calculates left states
and inflates both.
'''
try:
(vec, Lvec) = pickle.load(open(filestr, 'rb'))
n,m = np.shape(vec)
eigvec = np.identity(refmodes, dtype="complex")
Leigvec = np.identity(refmodes, dtype="complex")
eigvec[:n,:m] = vec
Leigvec[:n,:m] = Lvec
eigvec = scat.inflate_small_mat(eigvec, modes)
Leigvec = scat.inflate_small_mat(Leigvec, modes)
except:
print "WARNING: unable to load pickled states"
eigvec = np.identity(refmodes, dtype="complex")
Leigvec = np.identity(refmodes, dtype="complex")
eigvec = scat.inflate_small_mat(eigvec, modes)
Leigvec = scat.inflate_small_mat(Leigvec, modes)
return eigvec, Leigvec
def calc_transmitted_states(t, tinv, vec, Lvec, modes, refmodes, refpos, Nk):
'''
Calculate transmitted right vector at each frequency and transmitted
left vector only at reference frequency. Transmitted right vector is
normalized, transmitted left vector is normalized such that inner
product of the two transmitted vectors is equal to one if vectors
are aligned w.r.t. the considered modes and scattering into modes
that are not considered is zero.
'''
vectransmit = np.zeros((Nk, refmodes, modes), dtype="complex")
for i in range(Nk):
t_inf = scat.inflate_small_mat(t[3 * i + 1], modes)
for j in range(refmodes):
vectransmit[i][j] = np.dot(t_inf, vec[j]) /\
np.linalg.norm(np.dot(t_inf, vec[j]))
vecLtransmit = np.zeros((refmodes, modes), dtype="complex")
tfull_ref_inf = scat.inflate_small_mat(t[3 * refpos], modes)
tinv_inf = scat.inflate_small_mat(tinv, modes)
for j in range(refmodes):
vecLtransmit[j] = np.dot(Lvec[j], tinv_inf) *\
np.linalg.norm(np.dot(tfull_ref_inf, vec[j]))
return vectransmit, vecLtransmit
def calc_transmitted_states(t, tinv, vec, Lvec, modes, refmodes, refpos, Nk):
'''
Calculate transmitted right vector at each frequency and transmitted
left vector only at reference frequency. Transmitted right vector is
normalized, transmitted left vector is normalized such that inner
product of the two transmitted vectors is equal to one if vectors
are aligned w.r.t. the considered modes and scattering into modes
that are not considered is zero.
'''
vectransmit = np.zeros((Nk,refmodes,modes), dtype="complex")
for i in range(Nk):
t_inf = scat.inflate_small_mat(t[3*i+1], modes)
for j in range(refmodes):
vectransmit[i][j] = np.dot(t_inf, vec[j]) /\
np.linalg.norm(np.dot(t_inf, vec[j]))
vecLtransmit = np.zeros((refmodes,modes), dtype="complex")
tfull_ref_inf = scat.inflate_small_mat(t[3*refpos], modes)
tinv_inf = scat.inflate_small_mat(tinv, modes)
for j in range(refmodes):
vecLtransmit[j] = np.dot(Lvec[j], tinv_inf) *\
np.linalg.norm(np.dot(tfull_ref_inf, vec[j]))
return vectransmit, vecLtransmit
def calc_qexpvals(eigvec, q, qLeigbas, modes, refmodes, Nk):
'''
Calculate proper expectation value of q using its left eigenbasis
and standard deviations for vectors 'eigvec' at each frequency.
'''
times = np.empty((refmodes, Nk), dtype="complex")
tisdv = np.empty((refmodes, Nk), dtype="complex")
for w in range(Nk):
for state in range(refmodes):
vec = scat.inflate_vec(eigvec[state], modes)
vecL = 1./np.linalg.norm(np.dot(qLeigbas[w], vec))**2 *\
np.dot(qLeigbas[w].transpose(), np.dot(qLeigbas[w].conj(), vec.conj()))
A = scat.inflate_small_mat(q[w], modes)
times[state][w] = np.dot(vecL, np.dot(A, vec))
tisqr = np.dot(vecL, np.dot(A, np.dot(A, vec)))
tisdv[state][w] = sqrt(tisqr - times[state][w]**2)
return times, tisdv
def calc_qexpvals(eigvec, q, qLeigbas, modes, refmodes, Nk):
'''
Calculate proper expectation value of q using its left eigenbasis
and standard deviations for vectors 'eigvec' at each frequency.
'''
times = np.empty((refmodes,Nk), dtype="complex")
tisdv = np.empty((refmodes,Nk), dtype="complex")
for w in range(Nk):
for state in range(refmodes):
vec = scat.inflate_vec(eigvec[state], modes)
vecL = 1./np.linalg.norm(np.dot(qLeigbas[w], vec))**2 *\
np.dot(qLeigbas[w].transpose(), np.dot(qLeigbas[w].conj(), vec.conj()))
A = scat.inflate_small_mat(q[w], modes)
times[state][w] = np.dot(vecL, np.dot(A, vec))
tisqr = np.dot(vecL, np.dot(A, np.dot(A, vec)))
tisdv[state][w] = sqrt(tisqr - times[state][w]**2)
return times, tisdv
self.times, self.tisdv = trans.calc_qexpvals(self.eigvec, TRC.q, TRC.qLeigbas,
TRC.modes, TRC.refmodes, TRC.Nk)
self.vectransmit, self.vecLtransmit = trans.calc_transmitted_states(TRC.t, TRC.tinv, self.eigvec, self.Leigvec,
TRC.modes, TRC.refmodes, TRC.refpos, TRC.Nk)
qeigval, qeigvec, qLeigvec = trans.calc_eigensystem(qref, modes)
teigval, teigvec, tLeigvec = trans.calc_eigensystem(tref, modes)
modesvec = scat.inflate_small_mat(np.identity(refmodes, dtype="complex"), modes)
qyeigvec, qyLeigvec = trans.unpickle_states(pic_direc+'qpeaks.1.p', modes, refmodes)
#trans.print_freq_indep(qeigval, kmin, kmax, Dk)
eigvec = (qeigvec, teigvec, modesvec, qyeigvec)
Leigvec = (qLeigvec, tLeigvec, modesvec, qyLeigvec)
qeigbas, qLeigbas = trans.calc_qeigbas(q, Nk, modes, refmodes)
Nop = np.shape(eigvec)[0]
times = np.empty((Nop,refmodes,Nk), dtype="complex")
tisdv = np.empty((Nop,refmodes,Nk), dtype="complex")
for i in range(Nop):
times[i], tisdv[i] = trans.calc_qexpvals(
eigvec[i], q, qLeigbas, modes, refmodes, Nk)
teigval = ut.sort_eig(t_q[3*(refpos)+0])[0] np.savetxt(direc+"teigvals."+filen+".dat", np.array([range(np.shape(teigval)[0]), teigval.real, teigval.imag]).transpose()) qeigvec = ut.sort_eig(qref)[1].transpose() teigvec = ut.sort_eig(tref)[1].transpose() #teigvec = np.linalg.eig(tref)[1].transpose() modesvec = np.identity(refmodes, dtype="complex") # left eigenvectors are to be calculated before inflating qLeigvec = np.linalg.inv(qeigvec).transpose() tLeigvec = np.linalg.inv(teigvec).transpose() ### inflate eigenvectors to maximum size and number by appending zeros ### qeigvec = scat.inflate_small_mat(qeigvec, modes) teigvec = scat.inflate_small_mat(teigvec, modes) modesvec = scat.inflate_small_mat(modesvec, modes) qLeigvec = scat.inflate_small_mat(qLeigvec, modes) tLeigvec = scat.inflate_small_mat(tLeigvec, modes) eigvec = (qeigvec, teigvec, modesvec) taumin = np.min( qeigval.real ) taumax = np.max( qeigval.real ) Dk = (kmax-kmin)/(Nk-1) print print 'estimate for smallest frequency-independence' print 'wmin =', kmin, 'wmax =', kmax, 'dw =', Dk
def write_states(states,
nr,
n_states,
nin_Max,
energ,
filen,
append=0,
state_sort=''):
'''
write states to file in proper format for Flo's code
parameters:
states: ndarray, float
matrix containing row-wise states to write
nr: int
number of different energies = number of data sets
n_states: int
number of states to be propagated by Flo's code
nin_Max: int
actual number of open modes
energ: ndarray, float
scattering energy (k**2/2)
filen: str
namestring of calculation
append: int
whether coeffs should be appended to existing file
state_sort: str (optional)
string containing information which kind of
states are calculated and to be propagated
'''
if (state_sort == ''):
if (append):
f = open('coeff.'+filen+'.dat', 'a')
f.write('\n')
elif(not append):
f = open('coeff.'+filen+'.dat', 'w')
f.write('%i -1\n' % nr)
f.write('1.0 0.5\n')
else:
if (append):
f = open('coeff.'+filen+'.'+state_sort+'.dat', 'a')
f.write('\n')
elif(not append):
f = open('coeff.'+filen+'.'+state_sort+'.dat', 'w')
f.write('%i -1\n' % nr)
f.write('1.0 0.5\n')
states = scat.inflate_small_mat(states, nin_Max)
# append zeros to make number and size of vectors match
# nin_Max = actual number of open modes in system
f.write(str(energ)+' '+str(nin_Max)+'\n')
for i in range(nin_Max):
f.write('\n')
if (i < n_states):
f.write('1.0\n')
else:
f.write('2.0\n')
for j in range(nin_Max):
f.write('(' + str(states[i,j].real)
+ ', ' + str(states[i,j].imag) + ')\n')
return
qeigval, qeigvec = ut.sort_eig(qref) teigval, teigvec = ut.sort_eig(tref) qeigvec = qeigvec.transpose() teigvec = teigvec.transpose() modesvec = np.identity(refmodes, dtype="complex") teigval = ut.sort_eig(t_q[3*(refpos)+1])[0] np.savetxt(data_direc+"teigvals."+filen+".dat", np.array([range(np.shape(teigval)[0]), teigval.real, teigval.imag]).transpose()) # left eigenvectors are to be calculated before inflating, needed for measure \mu qLeigvec = np.linalg.inv(qeigvec).transpose() tLeigvec = np.linalg.inv(teigvec).transpose() ### inflate eigenvectors to maximum size and number by appending zeros ### qeigvec = scat.inflate_small_mat(qeigvec, modes) teigvec = scat.inflate_small_mat(teigvec, modes) modesvec = scat.inflate_small_mat(modesvec, modes) qLeigvec = scat.inflate_small_mat(qLeigvec, modes) tLeigvec = scat.inflate_small_mat(tLeigvec, modes) # taumin = np.min( qeigval.real ) # taumax = np.max( qeigval.real ) # Dk = (kmax-kmin)/(Nk-1) # print # print 'estimate for smallest frequency-independence' # print 'wmin =', kmin, 'wmax =', kmax, 'dw =', Dk # print 'tau_min =', taumin # print 'tau_max =', taumax
