def GetResult(self):
print "fit list: ", self.fit_list
#Propagate any value changes through all tied parameters
for i in range(len(self.fit_list)):
group = self._paramGroupList[i]
print "group: ", group
for param in group:
#This will change the values in the matrices
param.value = self.fit_list[i]
monteCarloMats = []
#Used later for spinwave calculation
jnums = []
jmats = []
print "matrices[0]: ", self._matrices[0].tolist()
for i in range(len(self._matrices)):
j11 = self._matrices[i][0][0].value
j12 = self._matrices[i][0][1].value
j13 = self._matrices[i][0][2].value
j21 = self._matrices[i][1][0].value
j22 = self._matrices[i][1][1].value
j23 = self._matrices[i][1][2].value
j31 = self._matrices[i][2][0].value
j32 = self._matrices[i][2][1].value
j33 = self._matrices[i][2][2].value
monteCarloMats.append(numpy.array([[j11,j12,j13],
[j21,j22,j23],
[j31,j32,j33]]))
#Used later for spinwave calculation
jij=sympy.matrices.Matrix([[j11,j12,j13],
[j21,j22,j23],
[j31,j32,j33]])
jnums.append(i)
jmats.append(jij)
#Run the monteCarlo simulation
#temporary (bad) method of picking tMin/tMax
# jAvg = 0
# for mat in monteCarloMats:
# jSum = 0
# for i in range(3):
# for j in range(3):
# val = abs(mat[i][j])
# jSum += val
# jAvg += jSum/9
#
# self._tMax = jAvg*12
# self._tMin = jAvg/10000
# self._tMax = 10
# self._tMin = 1E-6
print "\n\n\nmonte Carlo Mats:\n", monteCarloMats
if self._runMCeveryTime or self._run == 0:
#self._handle.write("\n\n\n\n\n------------Get Ground State---------------\n\n")
self.spins = get_ground_state(self._k, self._tMax, self._tMin, self._tFactor,
self._simpleAtoms, monteCarloMats)
else:
#self._handle.write("\n\n\n\n\n------------Opt Aux---------------\n\n")
self.spins = opt_aux(self._simpleAtoms, monteCarloMats, self.spins)
#self.spins = opt_aux(self._simpleAtoms, monteCarloMats, self.spins)
#print "\nspins:\n", self.spins
#self._handle.write("\n\n\n\nparam:\n\n")
#self._handle.write(str(self.fit_list))
#self._handle.write("\n\nSpins After:\n\n")
#self._handle.write(str(self.spins))
#self._handle.flush()
def inUnitCell(atom):
"""Returns true of the atom is in the unit cell at Na, Nb, Nc, where
those are the dimensions of the interaction cell. That cell is being
used to ensure that it is completely surrounded and no interactions
are left out. Handles simpleAtom type"""
if atom.pos[0] >= self._interactionCellDimensions[0] and atom.pos[0] < (self._interactionCellDimensions[0] + 1):
if atom.pos[1] >= self._interactionCellDimensions[1] and atom.pos[1] < (self._interactionCellDimensions[1] + 1):
if atom.pos[2] >= self._interactionCellDimensions[2] and atom.pos[2] < (self._interactionCellDimensions[2] + 1):
return True
return False
def inInteractionCell(atoms, atom):
"""Handles simpleAtom type."""
#First check if the atom is in the first crystallographic cell
# if atom.pos[0] < 1.0 and atom.pos[1] < 1.0 and atom.pos[2] < 1.0:
# return True
#Now the crystallographic unit cell being used is at Na, Nb, Nc, not 0,0,0
if inUnitCell(atom):
return True
#If not, check if it bonds to an atom that is
for i in range(len(atom.interactions)):
if inUnitCell(atoms[atom.interactions[i][0]]):
return True
return False
#Do the spinwave calculation
spinwave_atoms = []
first_cell_atoms = 0
for i in range(len(self._simpleAtoms)):
atom = self._simpleAtoms[i]
if inInteractionCell(self._simpleAtoms, atom):
Dx = atom.anisotropy[0]
Dy = atom.anisotropy[1]
Dz = atom.anisotropy[2]
spinwave_atom = SpinwaveAtom(pos=atom.pos, Dx=Dx,Dy=Dy,Dz=Dz,
orig_Index = i)
rmat = findmat(self.spins[i])#indices match up
spinwave_atom.spinRmatrix = rmat
for interaction in atom.interactions:
spinwave_atom.neighbors.append(interaction[0])
spinwave_atom.interactions.append(interaction[1])
spinwave_atoms.append(spinwave_atom)
#x,y,z = spinwave_atom.pos
#if x<1 and y<1 and z<1:
# first_cell_atoms +=1
#Find atoms in desired cell and organize list so they come first
tmp = []
for i in range(len(spinwave_atoms)):
if inUnitCell(spinwave_atoms[i]):
first_cell_atoms += 1
tmp.append(spinwave_atoms.pop(i))
for a in spinwave_atoms:
tmp.append(a)
spinwave_atoms = tmp
#change interaction indices to match indices in new list
for a in spinwave_atoms:
neighborList = a.neighbors
i = 0
while i < len(neighborList):
neighbor_index = neighborList[i]
for atom_index in range(len(spinwave_atoms)):
atom = spinwave_atoms[atom_index]
if atom.origIndex == neighbor_index:
a.neighbors[i] = atom_index
i +=1
break
else:#This neighbor index is not in the interaction cell
neighborList.pop(i)
a.interactions.pop(i)
N_atoms=len(spinwave_atoms)
Hsave=calculate_dispersion(spinwave_atoms,first_cell_atoms,N_atoms,jmats
,showEigs=False)
qrange = []
wrange = []
q = 0
for point in self.spinwave_domain:
#print "point:", point
wrange.append(calc_eigs(Hsave,point[0], point[1], point[2]))
qrange.append(q)
q += 1
wrange=numpy.real(wrange)
wrange=numpy.array(wrange)
wrange=numpy.real(wrange.T)
#for wrange1 in wrange:
# pylab.plot(qrange,wrange1,'s')
#pylab.show()
self._run+=1
#self._handle.write("\n\ndispersion:\n\n")
#self._handle.write(str(wrange[0]))
return wrange[0]#for now just one set
def eval_cross_section(interactionfile,
spinfile,
lattice,
arg,
tau_list,
h_list,
k_list,
l_list,
w_vect_list,
direction,
temperature,
kmin,
kmax,
steps,
eief,
efixed=14.7):
"""
Calculates the cross_section given the following parameters:
interactionfile, spinfile - files to get atom data
lattice - Lattice object from tripleaxisproject
arg - reduced list of operator combinations
tau_list - list of tau position
w_list - list of w's probed
direction - direction of scan
temp - temperature
kmin - minimum value of k to scan
kmax - maximum value of k to scan
steps - number of steps between kmin, kmax
eief - True if the energy scheme is Ei - Ef, False if it is Ef - Ei
efixed - value of the fixed energy, either Ei or Ef
"""
# Read files, get atom_list and such
atom_list, jnums, jmats, N_atoms_uc = readFiles(interactionfile, spinfile)
N_atoms = len(atom_list)
N = N_atoms
# TEMPORARY TO OVERRIDE ATOM_LIST ABOVE
# atom1 = atom(pos = [0.00,0,0], neighbors = [1], interactions = [0], int_cell = [0],
# atomicNum = 26, valence = 3, spinRmatrix=spm.Matrix([[1, 0, 0],[0, 1, 0],[0, 0, 1]]))
# atom2 = atom(pos = [0.25,0,0], neighbors = [0,2], interactions = [0], int_cell = [0],
# atomicNum = 26, valence = 3, spinRmatrix=spm.Matrix([[1, 0, 0],[0, 1, 0],[0, 0, 1]]))
# atom3 = atom(pos = [0.50,0,0], neighbors = [1,3], interactions = [0], int_cell = [0],
# atomicNum = 26, valence = 3, spinRmatrix=spm.Matrix([[1, 0, 0],[0, 1, 0],[0, 0, 1]]))
# atom4 = atom(pos = [0.75,0,0], neighbors = [2], interactions = [0], int_cell = [0],
# atomicNum = 26, valence = 3, spinRmatrix=spm.Matrix([[1, 0, 0],[0, 1, 0],[0, 0, 1]]))
# atom_list,N_atoms_uc = ([atom1, atom2, atom3, atom4],1)
N_atoms = len(atom_list)
# Get Hsave to calculate its eigenvalues
(Hsave, charpoly, eigs) = calculate_dispersion(atom_list,
N_atoms_uc,
N_atoms,
jmats,
showEigs=True)
print "Calculated: Dispersion Relation"
# Generate kappa's from (h,k,l)
kaprange = []
kapvect = []
if len(h_list) == len(k_list) == len(l_list):
for i in range(len(h_list)):
kappa = lattice.modvec(h_list[i], k_list[i], l_list[i],
'latticestar')
kaprange.append(kappa[0])
kapvect.append(np.array([h_list[i], k_list[i], l_list[i]]))
# kapvect.append(np.array([h_list[i]/kappa,k_list[i]/kappa,l_list[i]/kappa]))
else:
raise Exception('h,k,l not same lengths')
# Generate q's from kappa and tau
pqrange = []
mqrange = []
for tau in tau_list:
ptemp = []
mtemp = []
for kap in kapvect:
#tau = lattice.modvec(tau[0],tau[1],tau[2], 'latticestar')
ptemp.append(kap - tau)
mtemp.append(tau - kap)
pqrange.append(ptemp)
mqrange.append(mtemp)
# Calculate w_q's using q
qrange = []
# krange = []
wrange = []
if 1: # Change this later
for set in pqrange:
temp = []
temp1 = []
for q in set:
eigs = calc_eigs(Hsave, q[0] * direction['kx'],
q[1] * direction['ky'],
q[2] * direction['kz'])
# Take only one set of eigs. Should probably have a flag here.
temp.append(eigs[0])
# krange.append(np.array([q*direction['kx'], q*direction['ky'], q*direction['kz']]))
temp1.append(q)
wrange.append(temp)
qrange.append(temp1)
print "Calculated: Eigenvalues"
wrange = np.array(np.real(wrange))
qrange = np.array(np.real(qrange))
kaprange = np.array(np.real(kaprange))
print qrange.shape
print wrange.shape
print kaprange.shape
# Calculate w (not _q) as well as kp/k
w_calc = []
kpk = []
if eief == True:
for tau in tau_list:
temp = []
temp1 = []
for om in w_vect_list:
temp.append(om - efixed)
temp1.append(np.sqrt(om / efixed))
w_calc.append(temp)
kpk.append(temp1)
else:
for tau in tau_list:
temp = []
temp1 = []
for om in w_vect_list:
temp.append(-(om - efixed))
temp1.append(np.sqrt(efixed / om))
w_calc.append(temp)
kpk.append(temp1)
w_calc = np.array(np.real(w_calc))
# Grab Form Factors
ff_list = []
s = sp.Symbol('s')
for i in range(N_atoms):
el = elements[atom_list[i].atomicNum]
val = atom_list[i].valence
if val != None:
Mq = el.magnetic_ff[val].M_Q(kaprange)
else:
Mq = el.magnetic_ff[0].M_Q(kaprange)
ff_list.append(Mq)
print "Calculated: Form Factors"
# Other Constants
gamr0 = 2 * 0.2695 * 10**(-12) #sp.Symbol('gamma', commutative = True)
hbar = 1.0 # 1.05457148*10**(-34) #sp.Symbol('hbar', commutative = True)
g = 2. #sp.Symbol('g', commutative = True)
# Kappa vector
kap = sp.Symbol(
'kappa', real=True
) #spm.Matrix([sp.Symbol('kapx',real = True),sp.Symbol('kapy',real = True),sp.Symbol('kapz',real = True)])
t = sp.Symbol('t', real=True)
w = sp.Symbol('w', real=True)
W = sp.Symbol('W', real=True)
tau = sp.Symbol('tau', real=True)
q = sp.Symbol('q', real=True)
L = sp.Symbol('L', real=True)
boltz = 1. #1.3806503*10**(-23)
# Wilds for sub_in method
A = sp.Wild('A', exclude=[0, t])
B = sp.Wild('B', exclude=[0, t])
C = sp.Wild('C')
D = sp.Wild('D')
K = sp.Wild('K')
# First the exponentials are turned into delta functions:
for i in range(len(arg)):
for j in range(N):
print '1', arg[i][j]
arg[i][j] = sp.powsimp(
arg[i]
[j]) #sp.powsimp(arg[i][j], deep = True, combine = 'all')
arg[i][j] = (
arg[i][j] * exp(-I * w * t) * exp(I * kap * L)).expand(
) # * exp(I*inner_prod(spm.Matrix(atom_list[j].pos).T,kap))
arg[i][j] = sp.powsimp(
arg[i]
[j]) #sp.powsimp(arg[i][j], deep = True, combine = 'all')
# print '2', arg[i][j]
arg[i][j] = sub_in(
arg[i][j], exp(I * t * A + I * t * B + I * C + I * D + I * K),
sp.DiracDelta(A * t + B * t + C + D + K)) #*sp.DiracDelta(C))
# print '3', arg[i][j]
arg[i][j] = sub_in(
arg[i][j],
sp.DiracDelta(A * t + B * t + C * L + D * L + K * L),
sp.DiracDelta(A * hbar + B * hbar) *
sp.simplify(sp.DiracDelta(C + D + K + tau)))
# print '4', arg[i][j]
arg[i][j] = sub_in(arg[i][j],
sp.DiracDelta(-A - B) * sp.DiracDelta(C),
sp.DiracDelta(A + B) * sp.DiracDelta(C))
print '5', arg[i][j]
print "Applied: Delta Function Conversion"
# Grabs the unit vectors from the back of the lists.
unit_vect = []
kapxhat = sp.Symbol('kapxhat', commutative=False)
kapyhat = sp.Symbol('kapyhat', commutative=False)
kapzhat = sp.Symbol('kapzhat', commutative=False)
for i in range(len(arg)):
unit_vect.append(arg[i].pop())
# Subs the actual values for kx,ky,kz, omega_q and n_q into the operator combos
# The result is basically a nested list:
#
# csdata = [ op combos ]
# op combos = [ one combo per atom ]
# 1 per atom = [ evaluated exp ]
#
csdata = []
for i in range(len(arg)):
temp1 = []
for j in range(len(arg[i])):
temp2 = []
for k in range(len(tau_list)):
temp3 = []
print i, j, k
for g in range(len(qrange[k])):
pvalue = tau_list[k] + kapvect[g] + qrange[k][g]
mvalue = tau_list[k] + kapvect[g] - qrange[k][g]
if pvalue[0] == 0 and pvalue[1] == 0 and pvalue[2] == 0:
arg[i][j] = arg[i][j].subs(
sp.DiracDelta(kap + tau + q), sp.DiracDelta(0))
else:
arg[i][j] = arg[i][j].subs(
sp.DiracDelta(kap + tau + q), 0)
if mvalue[0] == 0 and mvalue[1] == 0 and mvalue[2] == 0:
arg[i][j] = arg[i][j].subs(
sp.DiracDelta(kap + tau - q), sp.DiracDelta(0))
else:
arg[i][j] = arg[i][j].subs(
sp.DiracDelta(kap + tau - q), 0)
wq = sp.Symbol('wq', real=True)
nq = sp.Symbol('n%i' % (k, ), commutative=False)
arg[i][j] = arg[i][j].subs(wq, wrange[k][g])
arg[i][j] = arg[i][j].subs(w, w_calc[k][g])
n = sp.Pow(
sp.exp(hbar * wrange[k][g] / boltz * temperature) - 1,
-1)
arg[i][j] = arg[i][j].subs(nq, n)
temp3.append(arg[i][j])
temp2.append(temp3)
temp1.append(temp2)
csdata.append(temp1)
## print arg[i][j]
# for g in range(len(kaprange)):
# arg[i][j] = arg[i][j].subs(kap, kaprange[g])
# for g in range(len(krange)):
## print 'calculating'
# temp3 = []
# wg = sp.Symbol('w%i'%(g,), real = True)
# ng = sp.Symbol('n%i'%(g,), commutative = False)
## kx = sp.Symbol('kx', real = True, commutative = True)
## ky = sp.Symbol('ky', real = True, commutative = True)
## kz = sp.Symbol('kz', real = True, commutative = True)
## arg[i][j] = arg[i][j].subs(kx,krange[g][0])
## arg[i][j] = arg[i][j].subs(ky,krange[g][1])
## arg[i][j] = arg[i][j].subs(kz,krange[g][2])
# arg[i][j] = arg[i][j].subs(wg,wrange[g])
# arg[i][j] = arg[i][j].subs(w,w_calc[g])
# nq = sp.Pow( sp.exp(hbar*wrange[g]/boltz*temp) - 1 ,-1)
# arg[i][j] = arg[i][j].subs(ng,nq)
## arg[i][j] = arg[i][j].subs(tau,tau_list[0])
#
# temp3.append(arg[i][j])
## print arg[i][j]
# temp2.append(temp3)
## print arg[i][j]
# csdata.append(temp2)
print csdata
# Front constants and stuff for the cross-section
front_constant = 1.0 # (gamr0)**2/(2*pi*hbar)
front_func = (1. / 2.) * g #*F(k)
vanderwaals = 1. #exp(-2*W)
csrange = []
if 1:
temp1 = []
temp2 = []
for q in range(len(qrange)):
print 'calculating'
for ii in range(len(csdata)):
for jj in range(len(csdata[ii])):
temp1.append(csdata[ii][jj])
# Put on gamr0, 2pi hbar, form factor, kp/k, vanderwaals first
dif = front_func**2 * front_constant # * kpk[q][0] * vanderwaals * ff_list[0][q]
# for vect in unit_vect:
# vect.subs(kapxhat,kapvect[q][0][0])
# vect.subs(kapyhat,kapvect[q][1][0])
# vect.subs(kapzhat,kapvect[q][2][0])
print 'diff', dif
print 'temp1', temp1
print sum(temp1)
dif = (dif * sum(temp1)) # * sum(unit_vect))#.expand()
csrange.append(dif)
print "Calculated: Cross-section"
csrange = np.real(csrange)
csrange = np.array(csrange)
xi = qrange
yi = wrange
zi = csrange
Z = np.zeros((xi.shape[0], yi.shape[0]))
Z[range(len(xi)), range(len(yi))] = zi
pylab.contourf(xi, yi, Z)
pylab.colorbar()
pylab.show()
def GetResult(self):
print "fit list: ", self.fit_list
#Propagate any value changes through all tied parameters
for i in range(len(self.fit_list)):
group = self._paramGroupList[i]
print "group: ", group
for param in group:
#This will change the values in the matrices
param.value = self.fit_list[i]
monteCarloMats = []
#Used later for spinwave calculation
jnums = []
jmats = []
print "matrices[0]: ", self._matrices[0].tolist()
for i in range(len(self._matrices)):
j11 = self._matrices[i][0][0].value
j12 = self._matrices[i][0][1].value
j13 = self._matrices[i][0][2].value
j21 = self._matrices[i][1][0].value
j22 = self._matrices[i][1][1].value
j23 = self._matrices[i][1][2].value
j31 = self._matrices[i][2][0].value
j32 = self._matrices[i][2][1].value
j33 = self._matrices[i][2][2].value
monteCarloMats.append(numpy.array([[j11,j12,j13],
[j21,j22,j23],
[j31,j32,j33]]))
#Used later for spinwave calculation
jij=sympy.matrices.Matrix([[j11,j12,j13],
[j21,j22,j23],
[j31,j32,j33]])
jnums.append(i)
jmats.append(jij)
#Run the monteCarlo simulation
#temporary (bad) method of picking tMin/tMax
# jAvg = 0
# for mat in monteCarloMats:
# jSum = 0
# for i in range(3):
# for j in range(3):
# val = abs(mat[i][j])
# jSum += val
# jAvg += jSum/9
#
# self._tMax = jAvg*12
# self._tMin = jAvg/10000
# self._tMax = 10
# self._tMin = 1E-6
print "\n\n\nmonte Carlo Mats:\n", monteCarloMats
if self._runMCeveryTime or self._run == 0:
#self._handle.write("\n\n\n\n\n------------Get Ground State---------------\n\n")
self.spins = get_ground_state(self._k, self._tMax, self._tMin, self._tFactor,
self._simpleAtoms, monteCarloMats)
else:
#self._handle.write("\n\n\n\n\n------------Opt Aux---------------\n\n")
self.spins = opt_aux(self._simpleAtoms, monteCarloMats, self.spins)
#self.spins = opt_aux(self._simpleAtoms, monteCarloMats, self.spins)
#print "\nspins:\n", self.spins
#self._handle.write("\n\n\n\nparam:\n\n")
#self._handle.write(str(self.fit_list))
#self._handle.write("\n\nSpins After:\n\n")
#self._handle.write(str(self.spins))
#self._handle.flush()
def inUnitCell(atom):
"""Returns true of the atom is in the unit cell at Na, Nb, Nc, where
those are the dimensions of the interaction cell. That cell is being
used to ensure that it is completely surrounded and no interactions
are left out. Handles simpleAtom type"""
if atom.pos[0] >= self._interactionCellDimensions[0] and atom.pos[0] < (self._interactionCellDimensions[0] + 1):
if atom.pos[1] >= self._interactionCellDimensions[1] and atom.pos[1] < (self._interactionCellDimensions[1] + 1):
if atom.pos[2] >= self._interactionCellDimensions[2] and atom.pos[2] < (self._interactionCellDimensions[2] + 1):
return True
return False
def inInteractionCell(atoms, atom):
"""Handles simpleAtom type."""
#First check if the atom is in the first crystallographic cell
# if atom.pos[0] < 1.0 and atom.pos[1] < 1.0 and atom.pos[2] < 1.0:
# return True
#Now the crystallographic unit cell being used is at Na, Nb, Nc, not 0,0,0
if inUnitCell(atom):
return True
#If not, check if it bonds to an atom that is
for i in range(len(atom.interactions)):
if inUnitCell(atoms[atom.interactions[i][0]]):
return True
return False
#Do the spinwave calculation
spinwave_atoms = []
first_cell_atoms = 0
for i in range(len(self._simpleAtoms)):
atom = self._simpleAtoms[i]
if inInteractionCell(self._simpleAtoms, atom):
Dx = atom.anisotropy[0]
Dy = atom.anisotropy[1]
Dz = atom.anisotropy[2]
spinwave_atom = SpinwaveAtom(pos=atom.pos, Dx=Dx,Dy=Dy,Dz=Dz,
orig_Index = i)
rmat = findmat(self.spins[i])#indices match up
spinwave_atom.spinRmatrix = rmat
for interaction in atom.interactions:
spinwave_atom.neighbors.append(interaction[0])
spinwave_atom.interactions.append(interaction[1])
spinwave_atoms.append(spinwave_atom)
#x,y,z = spinwave_atom.pos
#if x<1 and y<1 and z<1:
# first_cell_atoms +=1
#Find atoms in desired cell and organize list so they come first
tmp = []
for i in range(len(spinwave_atoms)):
if inUnitCell(spinwave_atoms[i]):
first_cell_atoms += 1
tmp.append(spinwave_atoms.pop(i))
for a in spinwave_atoms:
tmp.append(a)
spinwave_atoms = tmp
#change interaction indices to match indices in new list
for a in spinwave_atoms:
neighborList = a.neighbors
i = 0
while i < len(neighborList):
neighbor_index = neighborList[i]
for atom_index in range(len(spinwave_atoms)):
atom = spinwave_atoms[atom_index]
if atom.origIndex == neighbor_index:
a.neighbors[i] = atom_index
i +=1
break
else:#This neighbor index is not in the interaction cell
neighborList.pop(i)
a.interactions.pop(i)
N_atoms=len(spinwave_atoms)
Hsave=calculate_dispersion(spinwave_atoms,first_cell_atoms,N_atoms,jmats
,showEigs=False)
qrange = []
wrange = []
q = 0
for point in self.spinwave_domain:
#print "point:", point
wrange.append(calc_eigs(Hsave,point[0], point[1], point[2]))
qrange.append(q)
q += 1
wrange=numpy.real(wrange)
wrange=numpy.array(wrange)
wrange=numpy.real(wrange.T)
#for wrange1 in wrange:
# pylab.plot(qrange,wrange1,'s')
#pylab.show()
self._run+=1
#self._handle.write("\n\ndispersion:\n\n")
#self._handle.write(str(wrange[0]))
return wrange[0]#for now just one set
def eval_cross_section(interactionfile, spinfile, lattice, arg,
tau_list, h_list, k_list, l_list, w_vect_list,
direction, temperature, kmin, kmax, steps, eief, efixed = 14.7):
"""
Calculates the cross_section given the following parameters:
interactionfile, spinfile - files to get atom data
lattice - Lattice object from tripleaxisproject
arg - reduced list of operator combinations
tau_list - list of tau position
w_list - list of w's probed
direction - direction of scan
temp - temperature
kmin - minimum value of k to scan
kmax - maximum value of k to scan
steps - number of steps between kmin, kmax
eief - True if the energy scheme is Ei - Ef, False if it is Ef - Ei
efixed - value of the fixed energy, either Ei or Ef
"""
# Read files, get atom_list and such
atom_list, jnums, jmats,N_atoms_uc=readFiles(interactionfile,spinfile)
N_atoms = len(atom_list)
N = N_atoms
# TEMPORARY TO OVERRIDE ATOM_LIST ABOVE
# atom1 = atom(pos = [0.00,0,0], neighbors = [1], interactions = [0], int_cell = [0],
# atomicNum = 26, valence = 3, spinRmatrix=spm.Matrix([[1, 0, 0],[0, 1, 0],[0, 0, 1]]))
# atom2 = atom(pos = [0.25,0,0], neighbors = [0,2], interactions = [0], int_cell = [0],
# atomicNum = 26, valence = 3, spinRmatrix=spm.Matrix([[1, 0, 0],[0, 1, 0],[0, 0, 1]]))
# atom3 = atom(pos = [0.50,0,0], neighbors = [1,3], interactions = [0], int_cell = [0],
# atomicNum = 26, valence = 3, spinRmatrix=spm.Matrix([[1, 0, 0],[0, 1, 0],[0, 0, 1]]))
# atom4 = atom(pos = [0.75,0,0], neighbors = [2], interactions = [0], int_cell = [0],
# atomicNum = 26, valence = 3, spinRmatrix=spm.Matrix([[1, 0, 0],[0, 1, 0],[0, 0, 1]]))
# atom_list,N_atoms_uc = ([atom1, atom2, atom3, atom4],1)
N_atoms = len(atom_list)
# Get Hsave to calculate its eigenvalues
(Hsave, charpoly, eigs) = calculate_dispersion(atom_list,N_atoms_uc,N_atoms,jmats,showEigs=True)
print "Calculated: Dispersion Relation"
# Generate kappa's from (h,k,l)
kaprange = []
kapvect = []
if len(h_list) == len(k_list) == len(l_list):
for i in range(len(h_list)):
kappa = lattice.modvec(h_list[i],k_list[i],l_list[i], 'latticestar')
kaprange.append(kappa[0])
kapvect.append(np.array([h_list[i],k_list[i],l_list[i]]))
# kapvect.append(np.array([h_list[i]/kappa,k_list[i]/kappa,l_list[i]/kappa]))
else:
raise Exception('h,k,l not same lengths')
# Generate q's from kappa and tau
pqrange = []
mqrange = []
for tau in tau_list:
ptemp = []
mtemp = []
for kap in kapvect:
#tau = lattice.modvec(tau[0],tau[1],tau[2], 'latticestar')
ptemp.append(kap - tau)
mtemp.append(tau - kap)
pqrange.append(ptemp)
mqrange.append(mtemp)
# Calculate w_q's using q
qrange = []
# krange = []
wrange = []
if 1: # Change this later
for set in pqrange:
temp = []
temp1 = []
for q in set:
eigs = calc_eigs(Hsave,q[0]*direction['kx'], q[1]*direction['ky'], q[2]*direction['kz'])
# Take only one set of eigs. Should probably have a flag here.
temp.append(eigs[0])
# krange.append(np.array([q*direction['kx'], q*direction['ky'], q*direction['kz']]))
temp1.append(q)
wrange.append(temp)
qrange.append(temp1)
print "Calculated: Eigenvalues"
wrange=np.array(np.real(wrange))
qrange=np.array(np.real(qrange))
kaprange=np.array(np.real(kaprange))
print qrange.shape
print wrange.shape
print kaprange.shape
# Calculate w (not _q) as well as kp/k
w_calc = []
kpk = []
if eief == True:
for tau in tau_list:
temp = []
temp1 = []
for om in w_vect_list:
temp.append(om - efixed)
temp1.append(np.sqrt(om/efixed))
w_calc.append(temp)
kpk.append(temp1)
else:
for tau in tau_list:
temp = []
temp1 = []
for om in w_vect_list:
temp.append(-(om - efixed))
temp1.append(np.sqrt(efixed/om))
w_calc.append(temp)
kpk.append(temp1)
w_calc = np.array(np.real(w_calc))
# Grab Form Factors
ff_list = []
s = sp.Symbol('s')
for i in range(N_atoms):
el = elements[atom_list[i].atomicNum]
val = atom_list[i].valence
if val != None:
Mq = el.magnetic_ff[val].M_Q(kaprange)
else:
Mq = el.magnetic_ff[0].M_Q(kaprange)
ff_list.append(Mq)
print "Calculated: Form Factors"
# Other Constants
gamr0 = 2*0.2695*10**(-12) #sp.Symbol('gamma', commutative = True)
hbar = 1.0 # 1.05457148*10**(-34) #sp.Symbol('hbar', commutative = True)
g = 2.#sp.Symbol('g', commutative = True)
# Kappa vector
kap = sp.Symbol('kappa', real = True)#spm.Matrix([sp.Symbol('kapx',real = True),sp.Symbol('kapy',real = True),sp.Symbol('kapz',real = True)])
t = sp.Symbol('t', real = True)
w = sp.Symbol('w', real = True)
W = sp.Symbol('W', real = True)
tau = sp.Symbol('tau', real = True)
q = sp.Symbol('q', real = True)
L = sp.Symbol('L', real = True)
boltz = 1.#1.3806503*10**(-23)
# Wilds for sub_in method
A = sp.Wild('A',exclude = [0,t])
B = sp.Wild('B',exclude = [0,t])
C = sp.Wild('C')
D = sp.Wild('D')
K = sp.Wild('K')
# First the exponentials are turned into delta functions:
for i in range(len(arg)):
for j in range(N):
print '1', arg[i][j]
arg[i][j] = sp.powsimp(arg[i][j])#sp.powsimp(arg[i][j], deep = True, combine = 'all')
arg[i][j] = (arg[i][j] * exp(-I*w*t) * exp(I*kap*L)).expand()# * exp(I*inner_prod(spm.Matrix(atom_list[j].pos).T,kap))
arg[i][j] = sp.powsimp(arg[i][j])#sp.powsimp(arg[i][j], deep = True, combine = 'all')
# print '2', arg[i][j]
arg[i][j] = sub_in(arg[i][j],exp(I*t*A + I*t*B + I*C + I*D + I*K),sp.DiracDelta(A*t + B*t + C + D + K))#*sp.DiracDelta(C))
# print '3', arg[i][j]
arg[i][j] = sub_in(arg[i][j],sp.DiracDelta(A*t + B*t + C*L + D*L + K*L),sp.DiracDelta(A*hbar + B*hbar)*sp.simplify(sp.DiracDelta(C + D + K + tau)))
# print '4', arg[i][j]
arg[i][j] = sub_in(arg[i][j],sp.DiracDelta(-A - B)*sp.DiracDelta(C),sp.DiracDelta(A + B)*sp.DiracDelta(C))
print '5', arg[i][j]
print "Applied: Delta Function Conversion"
# Grabs the unit vectors from the back of the lists.
unit_vect = []
kapxhat = sp.Symbol('kapxhat',commutative = False)
kapyhat = sp.Symbol('kapyhat',commutative = False)
kapzhat = sp.Symbol('kapzhat',commutative = False)
for i in range(len(arg)):
unit_vect.append(arg[i].pop())
# Subs the actual values for kx,ky,kz, omega_q and n_q into the operator combos
# The result is basically a nested list:
#
# csdata = [ op combos ]
# op combos = [ one combo per atom ]
# 1 per atom = [ evaluated exp ]
#
csdata = []
for i in range(len(arg)):
temp1 = []
for j in range(len(arg[i])):
temp2 = []
for k in range(len(tau_list)):
temp3 = []
print i,j,k
for g in range(len(qrange[k])):
pvalue = tau_list[k] + kapvect[g] + qrange[k][g]
mvalue = tau_list[k] + kapvect[g] - qrange[k][g]
if pvalue[0] == 0 and pvalue[1] == 0 and pvalue[2] == 0:
arg[i][j] = arg[i][j].subs(sp.DiracDelta(kap+tau+q),sp.DiracDelta(0))
else: arg[i][j] = arg[i][j].subs(sp.DiracDelta(kap+tau+q),0)
if mvalue[0] == 0 and mvalue[1] == 0 and mvalue[2] == 0:
arg[i][j] = arg[i][j].subs(sp.DiracDelta(kap+tau-q),sp.DiracDelta(0))
else: arg[i][j] = arg[i][j].subs(sp.DiracDelta(kap+tau-q),0)
wq = sp.Symbol('wq', real = True)
nq = sp.Symbol('n%i'%(k,), commutative = False)
arg[i][j] = arg[i][j].subs(wq,wrange[k][g])
arg[i][j] = arg[i][j].subs(w,w_calc[k][g])
n = sp.Pow( sp.exp(hbar*wrange[k][g]/boltz*temperature) - 1 ,-1)
arg[i][j] = arg[i][j].subs(nq,n)
temp3.append(arg[i][j])
temp2.append(temp3)
temp1.append(temp2)
csdata.append(temp1)
## print arg[i][j]
# for g in range(len(kaprange)):
# arg[i][j] = arg[i][j].subs(kap, kaprange[g])
# for g in range(len(krange)):
## print 'calculating'
# temp3 = []
# wg = sp.Symbol('w%i'%(g,), real = True)
# ng = sp.Symbol('n%i'%(g,), commutative = False)
## kx = sp.Symbol('kx', real = True, commutative = True)
## ky = sp.Symbol('ky', real = True, commutative = True)
## kz = sp.Symbol('kz', real = True, commutative = True)
## arg[i][j] = arg[i][j].subs(kx,krange[g][0])
## arg[i][j] = arg[i][j].subs(ky,krange[g][1])
## arg[i][j] = arg[i][j].subs(kz,krange[g][2])
# arg[i][j] = arg[i][j].subs(wg,wrange[g])
# arg[i][j] = arg[i][j].subs(w,w_calc[g])
# nq = sp.Pow( sp.exp(hbar*wrange[g]/boltz*temp) - 1 ,-1)
# arg[i][j] = arg[i][j].subs(ng,nq)
## arg[i][j] = arg[i][j].subs(tau,tau_list[0])
#
# temp3.append(arg[i][j])
## print arg[i][j]
# temp2.append(temp3)
## print arg[i][j]
# csdata.append(temp2)
print csdata
# Front constants and stuff for the cross-section
front_constant = 1.0 # (gamr0)**2/(2*pi*hbar)
front_func = (1./2.)*g#*F(k)
vanderwaals = 1. #exp(-2*W)
csrange = []
if 1:
temp1 = []
temp2 = []
for q in range(len(qrange)):
print 'calculating'
for ii in range(len(csdata)):
for jj in range(len(csdata[ii])):
temp1.append(csdata[ii][jj])
# Put on gamr0, 2pi hbar, form factor, kp/k, vanderwaals first
dif = front_func**2 * front_constant# * kpk[q][0] * vanderwaals * ff_list[0][q]
# for vect in unit_vect:
# vect.subs(kapxhat,kapvect[q][0][0])
# vect.subs(kapyhat,kapvect[q][1][0])
# vect.subs(kapzhat,kapvect[q][2][0])
print 'diff',dif
print 'temp1',temp1
print sum(temp1)
dif = (dif * sum(temp1))# * sum(unit_vect))#.expand()
csrange.append(dif)
print "Calculated: Cross-section"
csrange=np.real(csrange)
csrange=np.array(csrange)
xi=qrange
yi=wrange
zi=csrange
Z=np.zeros((xi.shape[0],yi.shape[0]))
Z[range(len(xi)),range(len(yi))]=zi
pylab.contourf(xi,yi,Z)
pylab.colorbar()
pylab.show()