def square(anti = False):
ats = [rf.atom() for i in range(5)]
spin = rf.findmat(N.array([0,0,1]))
# Positions
# 0 1 2 3 4
pstn = [[0,0,0],[0,1,0],[1,0,0],[0,-1,0],[-1,0,0]]
# Neighbors
# 0 1 2 3 4
nbrs = [[1,2,3,4],[0],[0],[0],[0]]
# Interactions
# 0 1 2 3 4
ints = [[0,1,2,3],[0],[1],[2],[3]]
for i in range(len(ats)):
ats[i].pos = N.array(pstn[i])
ats[i].neighbors = nbrs[i]
ats[i].interactions = ints[i]
ats[i].spinRmatrix = spin
ats[i].spinMagnitude = 1
if anti == True:
spin = rf.findmat(N.array([0,0,-1]))
ats[0].spinMagnitude = 1
ats[0].spinRmatrix = spin
return ats
def square(anti=False):
ats = [rf.atom() for i in range(5)]
spin = rf.findmat(N.array([0, 0, 1]))
# Positions
# 0 1 2 3 4
pstn = [[0, 0, 0], [0, 1, 0], [1, 0, 0], [0, -1, 0], [-1, 0, 0]]
# Neighbors
# 0 1 2 3 4
nbrs = [[1, 2, 3, 4], [0], [0], [0], [0]]
# Interactions
# 0 1 2 3 4
ints = [[0, 1, 2, 3], [0], [1], [2], [3]]
for i in range(len(ats)):
ats[i].pos = N.array(pstn[i])
ats[i].neighbors = nbrs[i]
ats[i].interactions = ints[i]
ats[i].spinRmatrix = spin
ats[i].spinMagnitude = 1
if anti == True:
spin = rf.findmat(N.array([0, 0, -1]))
ats[0].spinMagnitude = 1
ats[0].spinRmatrix = spin
return ats
def gen_chain(num, anti = False):
ats = [rf.atom(pos = [i,0,0]) for i in range(num)]
spin = rf.findmat(N.array([0,0,1]))
if num == 2:
ints = [[0],[0]]
nbrs = [[1],[0]]
for i in range(num):
ats[i].interactions = ints[i]
ats[i].neighbors = nbrs[i]
ats[i].spinRmatrix = spin
ats[i].spinMagnitude = 1
elif num == 3:
ints = [[0],[0,1],[1]]
nbrs = [[1],[0,2],[1]]
for i in range(num):
ats[i].interactions = ints[i]
ats[i].neighbors = nbrs[i]
ats[i].spinRmatrix = spin
ats[i].spinMagnitude = 1
if anti == True:
spin = rf.findmat(N.array([0,0,-1]))
for i in range(1,num,2):
ats[i].spinRmatrix = spin
ats[i].spinMagnitude = 1
for i in range(len(ats)):
print ats[i].spinRmatrix
return ats
def gen_chain(num, anti=False):
ats = [rf.atom(pos=[i, 0, 0]) for i in range(num)]
spin = rf.findmat(N.array([0, 0, 1]))
if num == 2:
ints = [[0], [0]]
nbrs = [[1], [0]]
for i in range(num):
ats[i].interactions = ints[i]
ats[i].neighbors = nbrs[i]
ats[i].spinRmatrix = spin
ats[i].spinMagnitude = 1
elif num == 3:
ints = [[0], [0, 1], [1]]
nbrs = [[1], [0, 2], [1]]
for i in range(num):
ats[i].interactions = ints[i]
ats[i].neighbors = nbrs[i]
ats[i].spinRmatrix = spin
ats[i].spinMagnitude = 1
if anti == True:
spin = rf.findmat(N.array([0, 0, -1]))
for i in range(1, num, 2):
ats[i].spinRmatrix = spin
ats[i].spinMagnitude = 1
for i in range(len(ats)):
print ats[i].spinRmatrix
return ats
def testChain(self, num = 3, num_uc = 1):
ats = [rf.atom(pos = [i,0,0]) for i in range(num)]
spin = rf.findmat(N.array([0,0,1]))
ints = [[0],[0,1],[1]]
nbrs = [[1],[0,2],[1]]
for i in range(num):
ats[i].interactions = ints[i]
ats[i].neighbors = nbrs[i]
ats[i].spinRmatrix = spin
inters = [item for atom in ats for item in atom.interactions]
max_inter = max(inters)
J = sp.Symbol('J', real = True)
Jij = [N.matrix([[J,0,0],[0,J,0],[0,0,J]]) for i in range(max_inter+1)]
(Hsave, charpoly, eigs) = calculate_dispersion(ats, num_uc, num, Jij, showEigs = True)
eigs = eigs.keys()
for item in eigs:
item = item.expand(mul = True, multinomial=True)
testeig = (-8.0*self.J**2*self.S**2*sp.cos(self.kx) + 4.0*self.J**2*self.S**2 + 4.0*self.J**2*self.S**2*sp.cos(self.kx)**2)**(0.5)
self.assertAlmostEqual(Hsave.shape[0],2,4, 'H wrong shape')
self.assertAlmostEqual(Hsave.shape[1],2,4, 'H wrong shape')
self.assert_(len(eigs[0].args)==len(testeig.args), 'Eig.arg lengths are different sizes')
f = sp.simplify(eigs[0].args[0].expand())
f = f.subs([(self.J,1),(self.S,2),(self.kx,3),(self.ky,4),(self.kz,5)])
g = sp.simplify(testeig.args[0].expand())
g = g.subs([(self.J,1),(self.S,2),(self.kx,3),(self.ky,4),(self.kz,5)])
myFlag = f-g
self.assertAlmostEqual(myFlag,0,7, 'Eigs are wrong')
def testSquare(self, num=5, num_uc=1):
ats = [rf.atom() for i in range(num)]
spin = rf.findmat(N.array([0, 0, 1]))
# Positions
# 0 1 2 3 4
pstn = [[0, 0, 0], [0, 1, 0], [1, 0, 0], [0, -1, 0], [-1, 0, 0]]
# Neighbors
# 0 1 2 3 4
nbrs = [[1, 2, 3, 4], [0], [0], [0], [0]]
# Interactions
# 0 1 2 3 4
ints = [[0, 1, 2, 3], [0], [1], [2], [3]]
for i in range(len(ats)):
ats[i].pos = N.array(pstn[i])
ats[i].neighbors = nbrs[i]
ats[i].interactions = ints[i]
ats[i].spinRmatrix = spin
ats[i].spinMagnitude = 1
inters = [item for atom in ats for item in atom.interactions]
max_inter = max(inters)
J = sp.Symbol('J', real=True)
Jij = [
N.matrix([[J, 0, 0], [0, J, 0], [0, 0, J]])
for i in range(max_inter + 1)
]
(Hsave, charpoly, eigs) = calculate_dispersion(ats,
num_uc,
num,
Jij,
showEigs=True)
eigs = eigs.keys()
for item in eigs:
item = item.expand(mul=True, multinomial=True)
testeig = (
-64.0 * self.J**2 * self.S**2 * sp.cos(self.kx) -
64.0 * self.J**2 * self.S**2 * sp.cos(self.ky) +
32.0 * self.J**2 * self.S**2 * sp.cos(self.kx) * sp.cos(self.ky) +
64.0 * self.J**2 * self.S**2 +
16.0 * self.J**2 * self.S**2 * sp.cos(self.kx)**2 +
16.0 * self.J**2 * self.S**2 * sp.cos(self.ky)**2)**(0.5)
self.assertAlmostEqual(Hsave.shape[0], 2, 4, 'H wrong shape')
self.assertAlmostEqual(Hsave.shape[1], 2, 4, 'H wrong shape')
self.assert_(
len(eigs[1].args) == len(testeig.args),
'Eig.arg lengths are different sizes')
f = sp.simplify(eigs[1].args[0].expand())
f = f.subs([(self.J, 1), (self.S, 2), (self.kx, 3), (self.ky, 4),
(self.kz, 5)])
g = sp.simplify(testeig.args[0].expand())
g = g.subs([(self.J, 1), (self.S, 2), (self.kx, 3), (self.ky, 4),
(self.kz, 5)])
myFlag = f - g
self.assertAlmostEqual(myFlag, 0, 7, 'Eigs are wrong')
def testFCC(self, num = 13, num_uc = 1):
ats = [rf.atom() for i in range(num)]
spin = rf.findmat(N.array([0,0,1]))
aspin = rf.findmat(N.array([0,0,-1]))
# Positions
# 0 1 2 3 4
pstn = [[0,0,0], [0.5,0,0.5], [-0.5,0,0.5], [0.5,0,-0.5], [-0.5,0,-0.5],
# 5 6 7 8 9
[0,0.5,0.5], [0,-0.5,0.5], [0,0.5,-0.5], [0,-0.5,-0.5], [0.5,0.5,0],
# 10 11 12
[-0.5,0.5,0], [0.5,-0.5,0], [-0.5,-0.5,0]]
# Neighbors
# 0 1 2 3 4
nbrs = [[1,2,3,4,5,6,7,8,9,10,11,12], [], [], [], [],
# 5 6 7 8 9
[], [], [], [], [],
# 10 11 12
[], [], []]
# Interactions
# 0 1 2 3 4
ints = [[0,1,2,3,4,5,6,7,8,9,10,11], [], [], [], [],
# 5 6 7 8 9
[], [], [], [], [],
# 10 11 12
[], [], []]
for i in range(len(ats)):
ats[i].pos = N.array(pstn[i])
ats[i].neighbors = nbrs[i]
ats[i].interactions = ints[i]
ats[i].spinRmatrix = spin
ats[i].spinMagnitude = 1
ats[0].spinMagnitude = 1
ats[0].spinRmatrix = aspin
inters = [item for atom in ats for item in atom.interactions]
max_inter = max(inters)
J = sp.Symbol('J', real = True)
Jij = [N.matrix([[J,0,0],[0,J,0],[0,0,J]]) for i in range(max_inter+1)]
(Hsave, charpoly, eigs) = calculate_dispersion(ats, num_uc, num, Jij, showEigs = True)
eigs = eigs.keys()
for item in eigs:
item = item.expand(mul = True, multinomial=True)
testeig = (-128.0*self.J**2*self.S**2*sp.cos(0.5*self.kx)**2*sp.cos(0.5*self.ky)*sp.cos(0.5*self.kz) - 128.0*self.J**2*self.S**2*sp.cos(0.5*self.ky)**2*sp.cos(0.5*self.kx)*sp.cos(0.5*self.kz) - 128.0*self.J**2*self.S**2*sp.cos(0.5*self.kz)**2*sp.cos(0.5*self.kx)*sp.cos(0.5*self.ky) + 576.0*self.J**2*self.S**2 - 64.0*self.J**2*self.S**2*sp.cos(0.5*self.kx)**2*sp.cos(0.5*self.ky)**2 - 64.0*self.J**2*self.S**2*sp.cos(0.5*self.kx)**2*sp.cos(0.5*self.kz)**2 - 64.0*self.J**2*self.S**2*sp.cos(0.5*self.ky)**2*sp.cos(0.5*self.kz)**2)**(0.5)
self.assertAlmostEqual(Hsave.shape[0],2,4, 'H wrong shape')
self.assertAlmostEqual(Hsave.shape[1],2,4, 'H wrong shape')
self.assert_(len(eigs[1].args)==len(testeig.args), 'Eig.arg lengths are different sizes')
f = sp.simplify(eigs[1].args[0].expand())
f = f.subs([(self.J,1),(self.S,2),(self.kx,3),(self.ky,4),(self.kz,5)])
g = sp.simplify(testeig.args[0].expand())
g = g.subs([(self.J,1),(self.S,2),(self.kx,3),(self.ky,4),(self.kz,5)])
myFlag = f-g
self.assertAlmostEqual(myFlag,0,7, 'Eigs are wrong')
def testChain(self, num=3, num_uc=1):
ats = [rf.atom(pos=[i, 0, 0]) for i in range(num)]
spin = rf.findmat(N.array([0, 0, 1]))
aspin = rf.findmat(N.array([0, 0, -1]))
ints = [[0], [0, 1], [1]]
nbrs = [[1], [0, 2], [1]]
for i in range(num):
ats[i].interactions = ints[i]
ats[i].neighbors = nbrs[i]
ats[i].spinRmatrix = spin
ats[i].spinMagnitude = 1
for i in range(1, num, 2):
ats[i].spinRmatrix = aspin
ats[i].spinMagnitude = 1
inters = [item for atom in ats for item in atom.interactions]
max_inter = max(inters)
J = sp.Symbol('J', real=True)
Jij = [
N.matrix([[J, 0, 0], [0, J, 0], [0, 0, J]])
for i in range(max_inter + 1)
]
(Hsave, charpoly, eigs) = calculate_dispersion(ats,
num_uc,
num,
Jij,
showEigs=True)
eigs = eigs.keys()
for item in eigs:
item = item.expand(mul=True, multinomial=True)
testeig = (4 * self.J**2 * self.S**2 -
4.0 * self.J**2 * self.S**2 * sp.cos(self.kx)**2)**(0.5)
self.assertAlmostEqual(Hsave.shape[0], 2, 4, 'H wrong shape')
self.assertAlmostEqual(Hsave.shape[1], 2, 4, 'H wrong shape')
self.assert_(
len(eigs[0].args) == len(testeig.args),
'Eig.arg lengths are different sizes')
f = sp.simplify(eigs[0].args[0].expand())
f = f.subs([(self.J, 1), (self.S, 2), (self.kx, 3), (self.ky, 4),
(self.kz, 5)])
g = sp.simplify(testeig.args[0].expand())
g = g.subs([(self.J, 1), (self.S, 2), (self.kx, 3), (self.ky, 4),
(self.kz, 5)])
myFlag = f - g
self.assertAlmostEqual(myFlag, 0, 7, 'Eigs are wrong')
def create_matrix(atom_list, jnums, jmats, numCutOff, magCellSize, q):
"""Using hte Saenz technique. The matrix indeices, i and j refer to atoms in the magnetic
unit cell, so M will be an N*N matrix, where N is the number of atoms in the magnetic cell.
However, the l_vector is still in cyrstallographic unit cell units.
-numCutOff is the number of atoms in the cutoff/interaction (or really magnetic, but we
are assuming htey are the same) cell.
-magCellSize is a length 3 np.array of the size of the magnetic cell in terms of crystallographic
unit cells. ie. (1,1,1) for simple ferromagnet or (2,1,1) for simple antiferromagnetic chain along
x direction.
-q should also be a 3 element numpy array
-atom_list, jums, and jmats come from readfiles. atom_list must contain all atoms in the
interaction/magnetic cell as well as atoms that they bond to. Atoms in the magnetic cell
should appear first in the list.
"""
min_diff = 1e-8 #he threshold for equality between floats(positions of atoms)
#spin component to use:
spin_comp = 2 #use z component of spins (assume they are aligned along z)
#Loop through the atoms in the cutoff cell?
natoms = numCutOff #We really want the magnetic cell, but we are assuming thats the same as the interaction cell.
#natoms = N_atoms_uc
if 0: #Hardcoded ferro and anit-ferro test cases
#I'm hardcoding in this test case
atom_list = []
#Ferro-magnet
natoms = 1
jnums = [0]
jmats = [np.array([[1, 0, 0], [0, 1, 0], [0, 0, 1]])]
atom_list.append(
atom(pos=np.array([0, 0, 0]), spin=np.array([0, 0, 1])))
atom_list.append(
atom(pos=np.array([1, 0, 0]), spin=np.array([0, 0, 1])))
#Add the ferro interaction
atom_list[0].neighbors = [1]
atom_list[0].interactions = [0]
atom_list[1].neighbors = [0]
atom_list[1].interactions = [0]
#Adding interactions outside of the magnetic cell
atom_list.append(
atom(pos=np.array([-1, 0, 0]), spin=np.array([0, 0, 1])))
# atom_list.append(atom(pos = np.array([2,0,0]), spin = np.array([0,0,1])))
atom_list[0].neighbors = [1, 2]
atom_list[0].interactions = [0, 0]
#These are not necessary
# atom_list[1].neighbors = [0,3]
# atom_list[1].interactions = [0,0]
magCellSize = np.array([1.0, 1.0, 1.0])
#anti-ferro
if 0:
atom_list = []
magCellSize = np.array([2, 1, 1], dtype=np.float64)
natoms = 2
jnums = [0]
jmats = [np.array([[-1, 0, 0], [0, -1, 0], [0, 0, -1]])]
#Here the magnetic cell is the cut-off cell. This should be all I need.
atom_list.append(
atom(pos=np.array([0, 0, 0]), spin=np.array([0, 0, 1])))
atom_list.append(
atom(pos=np.array([1, 0, 0]), spin=np.array([0, 0, -1])))
#These two are not in the magnetic cell
atom_list.append(
atom(pos=np.array([-1, 0, 0]), spin=np.array([0, 0, -1])))
atom_list.append(
atom(pos=np.array([2, 0, 0]), spin=np.array([0, 0, 1])))
atom_list[0].neighbors = [1, 2]
atom_list[0].interactions = [0, 0]
atom_list[1].neighbors = [0, 3]
atom_list[1].interactions = [0, 0]
Mij = np.zeros((natoms, natoms), dtype=np.complex)
#print "atoms in cell:"
#for a in atom_list:
# print a.pos
#Choose a unit cell to use as a reference point for the l vector
#firstCellPos = atom_list[0].pos.astype(int)
#print "first cell position: " , firstCellPos
for i in range(natoms):
for j in range(natoms):
term_ij = 0.0 + 0j
#print "i: ", i, " j: ", j
#print "atom_i pos: ", atom_list[i].pos
if i == j: #delta_ij term (diaginal elements only)
for lk in range(len(atom_list[i].neighbors)):
#assuming Jij matrix is diagonal, take one of the diagonal terms:
J = (get_Jij(jnums, jmats,
atom_list[i].interactions[lk]))[1][1]
spin_k = atom_list[
atom_list[i].neighbors[lk]].spin[spin_comp]
term_ij += 2 * J * spin_k #*sigma_k*S_k
S_i = np.abs(atom_list[i].spin[spin_comp])
spin_j = atom_list[j].spin[spin_comp]
sigma_j = spin_j / np.abs(spin_j)
S_j = np.abs(spin_j)
#now for each atom correspondingto atom j in cell l sum J * exp(i*Q.l)
#I'll loop through all the interactions, but only pick out those that bond
#corresponding atoms in different(or the same) cells, ie. their positions - any integer
#component are the same.
atom_j = atom_list[j]
for l in range(len(atom_list[i].neighbors)):
atom_l = atom_list[atom_list[i].neighbors[l]]
#Use unit cell lengtsh to construct l vecter
l_pos = atom_l.pos
#print "l_pos: ", l_pos
#First we assumed it had to be a vector with integer components:
#l_vec = l_pos.astype(int)-(atom_list[i].pos).astype(int)#firstCellPos
#However, that ^ often produced imaginary numbers in the matrix
l_vec = l_pos - atom_list[i].pos
#use magnetic cell lengths to determine if atom_l is has the same position
l_pos = l_pos / magCellSize
l_pos = l_pos - l_pos.astype(int) #translate to first cell
#in case l_pos is negative:
l_pos = np.ceil(-l_pos) + l_pos
#same for j_pos
j_pos = atom_j.pos / magCellSize
j_pos = j_pos - j_pos.astype(int)
j_pos = np.ceil(-j_pos) + j_pos
pos_diff = (l_pos) - (j_pos) #converted to magcell pos
if ((np.abs(pos_diff) < min_diff).all()):
#print "l_vec: ", l_vec
J = (get_Jij(jnums, jmats, atom_list[i].interactions[l])
)[1][1] #taking a value from diagonal matrix
#print "sinusoidal comp: ", 2*sigma_j*np.sqrt(S_i*S_j)*J*np.exp(1j*np.dot(q,l_vec))
term_ij -= 2 * sigma_j * np.sqrt(S_i * S_j) * J * np.exp(
1j * np.dot(q, l_vec))
#print "term[",i,"][",j,"]: ", term_ij
# elif (i != j):
#for testing:
# print ""
#print "\n\n\nOMG!!! I shouldn't be here for the simple ferro/antiferro cases!\n\n\n"
#print "term_ij: ", term_ij
Mij[i][j] = term_ij
#print "Mij: ", Mij
#print "Q: ", q
#print "M:\n", Mij
#this creates eigenvalues that are different from ours by a factor of 2. For now I'll
#I'll just divide that out.
return Mij / 2.0
def gen_cube(body = False, face = False, anti = False):
ats = []
spin = rf.findmat(N.array([0,0,1]))
# Cubic
if not body and not face:
ats = [rf.atom() for i in range(7)]
# # Positions
# # 0 1 2 3 4 5 6
# pstn = [[0,0,0], [1,0,0], [-1,0,0], [0,1,0], [0,-1,0], [0,0,1], [0,0,-1]]
#
# # Neighbors
# # 0 1 2 3 4 5 6
# nbrs = [[1,2,3,4,5,6], [0], [0], [0], [0], [0], [0]]
#
# # Interactions
# # 0 1 2 3 4 5 6
# ints = [[0,1,2,3,4,5], [0], [1], [2], [3], [4], [5]]
# Positions
# 0 1 2 3 4 5 6
pstn = [[0,0,0], [1,0,0], [-1,0,0], [0,1,0], [0,-1,0], [0,0,1], [0,0,-1]]
# Neighbors
# 0 1 2 3 4 5 6
nbrs = [[1,2,3,4,5,6], [0], [0], [0], [0], [0], [0]]
# Interactions
# 0 1 2 3 4 5 6
ints = [[0,0,0,0,0,0], [1], [2], [3], [4], [5], [6]]
# Plug in values for positions and neighbors
for i in range(len(ats)):
ats[i].pos = N.array(pstn[i])
ats[i].neighbors = nbrs[i]
ats[i].interactions = ints[i]
ats[i].spinRmatrix = spin
ats[i].spinMagnitude = 1
# BCC - Body Centered Cubic
elif body and not face:
# Positions
# 0 1 2 3 4
pstn = [[0,0,0], [-0.5,0.5,-0.5], [0.5,0.5,-0.5], [0.5,0.5,0.5], [-0.5,0.5,0.5],
# 5 6 7 8
[-0.5,-0.5,-0.5], [0.5,-0.5,-0.5], [0.5,-0.5,0.5], [-0.5,-0.5,0.5]]
# Neighbors
# 0 1 2 3 4
nbrs = [[1,2,3,4,5,6,7,8], [], [], [], [],
# 5 6 7 8
[], [], [], []]
# Interactions
# 0 1 2 3 4
ints = [[0,1,2,3,4,5,6,7], [], [], [], [],
# 5 6 7 8
[], [], [], []]
ats = [rf.atom() for i in range(len(pstn))]
for i in range(len(ats)):
ats[i].pos = N.array(pstn[i])
ats[i].neighbors = nbrs[i]
ats[i].interactions = ints[i]
ats[i].spinRmatrix = spin
ats[i].spinMagnitude = 1
# FCC - Face Centered Cubic
elif face and not body:
# Positions
# 0 1 2 3 4
pstn = [[0,0,0], [0.5,0,0.5], [-0.5,0,0.5], [0.5,0,-0.5], [-0.5,0,-0.5],
# 5 6 7 8 9
[0,0.5,0.5], [0,-0.5,0.5], [0,0.5,-0.5], [0,-0.5,-0.5], [0.5,0.5,0],
# 10 11 12
[-0.5,0.5,0], [0.5,-0.5,0], [-0.5,-0.5,0]]
# Neighbors
# 0 1 2 3 4
nbrs = [[1,2,3,4,5,6,7,8,9,10,11,12], [], [], [], [],
# 5 6 7 8 9
[], [], [], [], [],
# 10 11 12
[], [], []]
# Interactions
# 0 1 2 3 4
ints = [[0,1,2,3,4,5,6,7,8,9,10,11], [], [], [], [],
# 5 6 7 8 9
[], [], [], [], [],
# 10 11 12
[], [], []]
ats = [rf.atom() for i in range(len(pstn))]
for i in range(len(ats)):
ats[i].pos = N.array(pstn[i])
ats[i].neighbors = nbrs[i]
ats[i].interactions = ints[i]
ats[i].spinRmatrix = spin
ats[i].spinMagnitude = 1
if anti == True:
spin = rf.findmat(N.array([0,0,-1]))
ats[0].spinMagnitude = 1
ats[0].spinRmatrix = spin
return ats
def run_cross_section(interactionfile, spinfile):
start = clock()
# Generate Inputs
atom_list, jnums, jmats, N_atoms_uc = readFiles(interactionfile, spinfile)
atom1 = atom(pos=[0.00, 0, 0],
neighbors=[1],
interactions=[0],
int_cell=[0],
atomicNum=26,
valence=3)
atom2 = atom(pos=[0.25, 0, 0],
neighbors=[0, 2],
interactions=[0],
int_cell=[0],
atomicNum=26,
valence=3)
atom3 = atom(pos=[0.50, 0, 0],
neighbors=[1, 3],
interactions=[0],
int_cell=[0],
atomicNum=26,
valence=3)
atom4 = atom(pos=[0.75, 0, 0],
neighbors=[2],
interactions=[0],
int_cell=[0],
atomicNum=26,
valence=3)
# atom_list,N_atoms_uc = ([atom1, atom2, atom3, atom4],1)
N_atoms = len(atom_list)
print N_atoms
if 1:
kx = sp.Symbol('kx', real=True, commutative=True)
ky = sp.Symbol('ky', real=True, commutative=True)
kz = sp.Symbol('kz', real=True, commutative=True)
k = spm.Matrix([kx, ky, kz])
(b, bd) = generate_b_bd_operators(atom_list)
# list_print(b)
(a, ad) = generate_a_ad_operators(atom_list, k, b, bd)
list_print(a)
(Sp, Sm) = generate_Sp_Sm_operators(atom_list, a, ad)
list_print(Sp)
(Sa, Sb, Sn) = generate_Sa_Sb_Sn_operators(atom_list, Sp, Sm)
# list_print(Sa)
(Sx, Sy, Sz) = generate_Sx_Sy_Sz_operators(atom_list, Sa, Sb, Sn)
list_print(Sx)
print ''
#Ham = generate_Hamiltonian(N_atoms, atom_list, b, bd)
ops = generate_possible_combinations(atom_list, [Sx, Sy, Sz])
# list_print(ops)
ops = holstein(atom_list, ops)
# list_print(ops)
ops = apply_commutation(atom_list, ops)
# list_print(ops)
ops = replace_bdb(atom_list, ops)
# list_print(ops)
ops = reduce_options(atom_list, ops)
list_print(ops)
# Old Method
#cross_sect = generate_cross_section(atom_list, ops, 1, real, recip)
#print '\n', cross_sect
if 1:
aa = bb = cc = np.array([2.0 * np.pi], 'Float64')
alpha = beta = gamma = np.array([np.pi / 2.0], 'Float64')
vect1 = np.array([[1, 0, 0]])
vect2 = np.array([[0, 0, 1]])
lattice = Lattice(aa, bb, cc, alpha, beta, gamma,
Orientation(vect1, vect2))
data = {}
data['kx'] = 1.
data['ky'] = 0.
data['kz'] = 0.
direction = data
temperature = 100.0
min = 0
max = 2 * sp.pi
steps = 25
tau_list = []
for i in range(1):
tau_list.append(np.array([0, 0, 0], 'Float64'))
h_list = np.linspace(0, 2, 100)
k_list = np.zeros(h_list.shape)
l_list = np.zeros(h_list.shape)
w_list = np.linspace(-4, 4, 100)
efixed = 14.7 #meV
eief = True
eval_cross_section(interactionfile, spinfile, lattice, ops, tau_list,
h_list, k_list, l_list, w_list, data, temperature,
min, max, steps, eief, efixed)
end = clock()
print "\nFinished %i atoms in %.2f seconds" % (N_atoms, end - start)
def mcQueeny_case(interactionfile, spinfile, tau_list, temperature,
direction={'kx':1,'ky':0,'kz':0}, hkl_interval=[1e-3,2*np.pi,100],
omega_interval=[0,5,100], eig_eps = 0.001):
initial_time = time.clock()
#to plot eigenvector components
# q1 = []
# q2 = []
#to plot w's
#w1_list = []
#w2_list = []
#w3_list = []
#w4_list = []
#w5_list = []
#w6_list = []
#w7_list = []
#w8_list = []
# w_output_list = []
#plot the structure factor to compare with lovesey (In McQueeny Paper)
# strfac_sums = []
# strfac1 = []
# strfac2 = []
atom_list, jnums, jmats, N_atoms_uc, numCutOff, magCellSize = readFiles(interactionfile,spinfile, rtn_cutOffInfo = True)
#Hardcoding body-center cubic
if 0:
atom_list = []
jnums = [0]
N_atom_uc = 1
numCutOff = 7
magCellSize = np.array([1,1,1])
jmats = [np.array([[-1,0,0],[0,-1,0],[0,0,-1]])]
atom_list.append(atom(pos = np.array([0.5,0.5,0.5]),
spin = np.array([0,0,1]),
interactions = [0,0,0,0,0,0],
neighbors = [1,2,3,4,5,6]))
atom_list.append(atom(pos = np.array([0.,0.,0.]),
spin = np.array([0,0,-1]),
interactions = [0],
neighbors = [0]))
atom_list.append(atom(pos = np.array([1.,0.,0.]),
spin = np.array([0,0,-1]),
interactions = [0],
neighbors = [0]))
atom_list.append(atom(pos = np.array([1.,1.,0.]),
spin = np.array([0,0,-1]),
interactions = [0],
neighbors = [0]))
atom_list.append(atom(pos = np.array([1.,0.,1.]),
spin = np.array([0,0,-1]),
interactions = [0],
neighbors = [0]))
atom_list.append(atom(pos = np.array([1.,1.,1.]),
spin = np.array([0,0,-1]),
interactions = [0],
neighbors = [0]))
atom_list.append(atom(pos = np.array([0.,1.,0.]),
spin = np.array([0,0,-1]),
interactions = [0],
neighbors = [0]))
atom_list.append(atom(pos = np.array([0.,0.,1.]),
spin = np.array([0,0,-1]),
interactions = [0],
neighbors = [0]))
atom_list.append(atom(pos = np.array([0.,1.,1.]),
spin = np.array([0,0,-1]),
interactions = [0],
neighbors = [0]))
h_list, k_list, l_list = generate_hkl(hkl_interval, direction)
e = generate_wt(omega_interval)
ff_list = generate_form_factors(N_atoms_uc, atom_list, hkl_interval)
s = []
basis = []
for a in atom_list:
s.append(a.spin[2])#z component of spin (assume aligned with z)
#basis.append(a.pos)
basis.append(a.pos - magCellSize) #translate back to 0,0,0
#normalize? NO!
#basis.append([a.pos[0] - int(a.pos[0]), a.pos[1]-int(a.pos[1]), a.pos[2] - int(a.pos[2])])
#print "\n\nbasis vectors:\n"
#mess with basis vectors and spin
#basis[0] = [0.25,0,0]
#basis[0] = [1.0,0,0]
#tmp = s[0]
#s[0] = s[1]
#s[1] = tmp
#for pos in basis:
# print pos
#print "\n\nspins:\n"
#for spin in s:
# print spin
mesh = np.zeros((len(h_list), len(e)))
#output q, w, and eigenvectors before and after normalization to compare with McQueeny's
# f = open("/home/tom/Desktop/Python_Eigs.txt", 'w')
# f.write("q w eigVec_before_norm T\n\n")
# f2 = open("/home/tom/Desktop/Values.txt", 'w')
# f2.write("Q w wvec (wvec norm) e^(-i*Q.d_i)\n\n")
#create the T_ni matricies (eigenvector matrices)
#This algorithm uses a differnt matrix:
#evecs, mats = calc_eig_mats_numerically(Hsave, h_list,k_list,l_list)
#eigvals = calc_eigs_numerically(Hsave, h_list, k_list, l_list)#This is innefficient, eigs already calculated and thrown away in calc_eig_mats_..
#w_list = gen_eigs_with_sign(Hsave, h_list, k_list, l_list, 0.001)
for Qindex in range(len(h_list)):
Q = (np.array([h_list,k_list,l_list]).transpose())[Qindex]
# f2.write(str(Q))
#CALL SPINWAVE(q,w,evec) - get w, evec for given q
M = create_matrix(atom_list, jnums, jmats, numCutOff, magCellSize, Q-np.array(tau_list))
w, evec = np.linalg.eig(M)
# f2.write(" " + str(w))
# f2.write(" " + str(evec.flatten()))
# evec = evecs[Qindex]
# w = w_list[Qindex]
# print "\nw = ", w
#w1_list.append(w[0])
#w2_list.append(w[1])
#w3_list.append(w[1])
#w4_list.append(w[1])
#w5_list.append(w[1])
#w6_list.append(w[1])
#w7_list.append(w[1])
#w8_list.append(w[1])
# w_output_list.append(w)
ff = ff_list[Qindex]
#Get number of atoms
numAtoms = numCutOff
#numAtoms = np.sqrt(evec.size)#This should be the number of atoms that I need to loop through.
#if int(numAtoms) != numAtoms:#I beleive t_mat should always be square, but lets check
# raise Exception("t_mat not square!")
#Normalize evec to get T_ni
#for i in range(0, numAtoms):
# normi = 0
# for j in range(0, numAtoms):
# sigma_j = s[j]/np.abs(s[j])
# normi += sigma_j * np.abs(evec[j][i])**2
# for j in range(0, numAtoms):
# evec[i][j] = evec[j][i]/np.sqrt(np.abs(normi))
evec2 = evec.copy()
#I'm going to write this from scratch
# print "evec before = ", evec
T = evec
sigma = []
for i in range(numAtoms):
sigma.append(s[i]/np.abs(s[i]))
for n in range(numAtoms):
norm = 0
for i in range(numAtoms):
norm += sigma[i]*(np.abs(evec2[n][i])**2)
for i in range(numAtoms):
# print "norm : ", norm
# print "w sign: ", np.sign(w[n])
#T[n][i] = T[n][i]*np.sqrt((w[n]/np.abs(w[n]))/norm + 0j)
T[n][i] = evec2[n][i]/np.sqrt(np.abs(norm))
evec = T
# f2.write(" " + str(T.flatten()))
#evec = evec2
# q1.append(evec[0][0])
# q2.append(evec[0][0])
#output eigs to file
# f.write(str(Q))
# f.write(" w:" + str(w))
# f.write("\nmat: " + str(M))#the matrix for which the eigs were found
# f.write("\nbefore_norm: " + str(evec2.flatten()))
# f.write("\nafterNorm: " + str(evec.flatten()) + "\n\n")
#evec = evec.transpose()
#test = 0
#for i in range(numAtoms):
# sigma_i = s[j]/np.abs(s[j])
# test += sigma_i * np.dot(evec[i],evec[i])
# print "sigma_i = ", sigma_i
#print "\n\nsum{sigma_i * |T_ni|^2} = ", test, "\n\n"
# print "evec = " , evec
# print "sigma1: ", s[0]/np.abs(s[0])
# print "sigma2: ", s[1]/np.abs(s[1])
# print "sign lambda_0: ", (s[0]/np.abs(s[0]))*(evec[0][0]**2) + (s[1]/np.abs(s[1]))*(evec[0][1]**2)
# print "sign lambda_1: ", (s[0]/np.abs(s[0]))*(evec[1][0]**2) + (s[1]/np.abs(s[1]))*(evec[1][1]**2)
#using only positive eigenvalue
#w = [w[0]]
#evec = [evec[0]]
#print "eigenvalues used: ", w
#print "eigenvectors used: ", evec
strfac = np.zeros(numAtoms)
#for testing:
ff = 1
for i in range(numAtoms):
dum = 0
for j in range(numAtoms):
dum += (s[j]/np.sqrt(np.abs(s[j]))) * ff * evec[j][i] #* np.exp(1.0j*
#(-Q[0]*basis[j][0] -Q[1]*basis[j][1] -Q[2]*basis[j][2]))
# print "\n\n\nwritting to f2:\n\n\n", np.exp(1.0j*
# (-Q[0]*basis[j][0] -Q[1]*basis[j][1] -Q[2]*basis[j][2]))
# print "j: ", j
# print "basis: ", basis[j]
# print "Q.di", (-Q[0]*basis[j][0] -Q[1]*basis[j][1] -Q[2]*basis[j][2])
exp = np.exp(1.0j*(-Q[0]*basis[j][0] -Q[1]*basis[j][1] -Q[2]*basis[j][2]))
# f2.write(" " + str(exp))
strfac[i] = np.abs(dum)**2
# print "Q: ", Q, " strfac[",i,"]: ", strfac[i]
# f2.write("\n\n")
# strfac_sums.append(0.0);
# strfac1.append(strfac[0])
# strfac2.append(strfac[1])
sqw = np.zeros(len(e))
for j in range(numAtoms):
# strfac_sums[Qindex] +=strfac[j]
for i in range(len(e)):
y = LIFETIME_VALUE/2
lorentzian = (1/np.pi)*y/((e[i]- w[j])**2+y**2)
#test
#strfac[j] = ff*1
sqw[i] = sqw[i] + strfac[j] * lorentzian #he has some 'bose' factor in here
#more test
#sqw[i] = sqw[i] + strfac[j]
mesh[Qindex] = sqw #* 0.5*(1 + Q[0]**2) #along x, Q_hat is just 1?
#f.close()
#f = open("/home/tom/Desktop/output.txt", 'w')
#for q in range(0,len(h_list)):
#for w in range(0,len(e)):
#f.write(str(h_list[q]))
#f.write(" ")
#f.write(str(e[w]))
#f.write(" ")
#f.write(str(mesh[q][w]))
#f.write("\n")
#f.close()
#f = open("/home/tom/Desktop/output2.txt", 'w')
#for q in range(0,len(h_list)):
#f.write(str(h_list[q]))
#f.write(" ")
#f.write(str(np.abs(q1[q])))
#f.write(" ")
#f.write(str(np.abs(q2[q])))
#f.write("\n")
#f.close()
#f = open("/home/tom/Desktop/output3.txt", 'w')
#for q in range(0,len(h_list)):
#f.write(str(h_list[q]))
#f.write(" ")
#f.write(str(np.real(w1_list[q])))
#f.write(" ")
#f.write(str(np.real(w2_list[q])))
#f.write(" ")
#f.write(str(np.real(w3_list[q])))
#f.write(" ")
#f.write(str(np.real(w4_list[q])))
#f.write(" ")
#f.write(str(np.real(w5_list[q])))
#f.write(" ")
#f.write(str(np.real(w6_list[q])))
#f.write(" ")
#f.write(str(np.real(w7_list[q])))
#f.write(" ")
#f.write(str(np.real(w8_list[q])))
#f.write("\n")
#f.close()
#f = open("/home/tom/Desktop/strfacs.txt", 'w')
#for q in range(0,len(h_list)):
#f.write(str(h_list[q]))
#f.write(" ")
#f.write(str(k_list[q]))
#f.write(" ")
#f.write(str(l_list[q]))
#f.write(" ")
#f.write(str(strfac1[q]))
#f.write(" ")
#f.write(str(strfac2[q]))
#f.write(" ")
#f.write(str(strfac_sums[q]))
#f.write("\n")
#f.close()
#plt.plot(w1_list)
#plt.plot(w2_list)
#plt.show()
print "Run Time: ", time.clock()-initial_time, " seconds"
def create_matrix(atom_list, jnums, jmats, numCutOff, magCellSize, q):
"""Using hte Saenz technique. The matrix indeices, i and j refer to atoms in the magnetic
unit cell, so M will be an N*N matrix, where N is the number of atoms in the magnetic cell.
However, the l_vector is still in cyrstallographic unit cell units.
-numCutOff is the number of atoms in the cutoff/interaction (or really magnetic, but we
are assuming htey are the same) cell.
-magCellSize is a length 3 np.array of the size of the magnetic cell in terms of crystallographic
unit cells. ie. (1,1,1) for simple ferromagnet or (2,1,1) for simple antiferromagnetic chain along
x direction.
-q should also be a 3 element numpy array
-atom_list, jums, and jmats come from readfiles. atom_list must contain all atoms in the
interaction/magnetic cell as well as atoms that they bond to. Atoms in the magnetic cell
should appear first in the list.
"""
min_diff = 1e-8#he threshold for equality between floats(positions of atoms)
#spin component to use:
spin_comp = 2#use z component of spins (assume they are aligned along z)
#Loop through the atoms in the cutoff cell?
natoms = numCutOff #We really want the magnetic cell, but we are assuming thats the same as the interaction cell.
#natoms = N_atoms_uc
if 0: #Hardcoded ferro and anit-ferro test cases
#I'm hardcoding in this test case
atom_list = []
#Ferro-magnet
natoms = 1
jnums = [0]
jmats = [np.array([[1,0,0],[0,1,0],[0,0,1]])]
atom_list.append(atom(pos = np.array([0,0,0]), spin = np.array([0,0,1])))
atom_list.append(atom(pos = np.array([1,0,0]), spin = np.array([0,0,1])))
#Add the ferro interaction
atom_list[0].neighbors = [1]
atom_list[0].interactions = [0]
atom_list[1].neighbors = [0]
atom_list[1].interactions = [0]
#Adding interactions outside of the magnetic cell
atom_list.append(atom(pos = np.array([-1,0,0]), spin = np.array([0,0,1])))
# atom_list.append(atom(pos = np.array([2,0,0]), spin = np.array([0,0,1])))
atom_list[0].neighbors = [1,2]
atom_list[0].interactions = [0,0]
#These are not necessary
# atom_list[1].neighbors = [0,3]
# atom_list[1].interactions = [0,0]
magCellSize = np.array([1.0,1.0,1.0])
#anti-ferro
if 0:
atom_list = []
magCellSize = np.array([2,1,1],dtype = np.float64)
natoms = 2
jnums = [0]
jmats = [np.array([[-1,0,0],[0,-1,0],[0,0,-1]])]
#Here the magnetic cell is the cut-off cell. This should be all I need.
atom_list.append(atom(pos = np.array([0,0,0]), spin = np.array([0,0,1])))
atom_list.append(atom(pos = np.array([1,0,0]), spin = np.array([0,0,-1])))
#These two are not in the magnetic cell
atom_list.append(atom(pos = np.array([-1,0,0]), spin = np.array([0,0,-1])))
atom_list.append(atom(pos = np.array([2,0,0]), spin = np.array([0,0,1])))
atom_list[0].neighbors = [1,2]
atom_list[0].interactions = [0,0]
atom_list[1].neighbors = [0,3]
atom_list[1].interactions = [0,0]
Mij = np.zeros((natoms,natoms), dtype = np.complex)
#print "atoms in cell:"
#for a in atom_list:
# print a.pos
#Choose a unit cell to use as a reference point for the l vector
#firstCellPos = atom_list[0].pos.astype(int)
#print "first cell position: " , firstCellPos
for i in range(natoms):
for j in range(natoms):
term_ij = 0.0 +0j
#print "i: ", i, " j: ", j
#print "atom_i pos: ", atom_list[i].pos
if i == j:#delta_ij term (diaginal elements only)
for lk in range(len(atom_list[i].neighbors)):
#assuming Jij matrix is diagonal, take one of the diagonal terms:
J = (get_Jij(jnums, jmats,atom_list[i].interactions[lk]))[1][1]
spin_k = atom_list[atom_list[i].neighbors[lk]].spin[spin_comp]
term_ij += 2*J*spin_k#*sigma_k*S_k
S_i = np.abs(atom_list[i].spin[spin_comp])
spin_j = atom_list[j].spin[spin_comp]
sigma_j = spin_j/np.abs(spin_j)
S_j = np.abs(spin_j)
#now for each atom correspondingto atom j in cell l sum J * exp(i*Q.l)
#I'll loop through all the interactions, but only pick out those that bond
#corresponding atoms in different(or the same) cells, ie. their positions - any integer
#component are the same.
atom_j = atom_list[j]
for l in range(len(atom_list[i].neighbors)):
atom_l = atom_list[atom_list[i].neighbors[l]]
#Use unit cell lengtsh to construct l vecter
l_pos = atom_l.pos
#print "l_pos: ", l_pos
#First we assumed it had to be a vector with integer components:
#l_vec = l_pos.astype(int)-(atom_list[i].pos).astype(int)#firstCellPos
#However, that ^ often produced imaginary numbers in the matrix
l_vec = l_pos - atom_list[i].pos
#use magnetic cell lengths to determine if atom_l is has the same position
l_pos = l_pos/magCellSize
l_pos = l_pos - l_pos.astype(int) #translate to first cell
#in case l_pos is negative:
l_pos = np.ceil(-l_pos) + l_pos
#same for j_pos
j_pos = atom_j.pos/magCellSize
j_pos = j_pos - j_pos.astype(int)
j_pos = np.ceil(-j_pos) + j_pos
pos_diff = (l_pos)-(j_pos)#converted to magcell pos
if ((np.abs(pos_diff)<min_diff).all()):
#print "l_vec: ", l_vec
J = (get_Jij(jnums, jmats, atom_list[i].interactions[l]))[1][1]#taking a value from diagonal matrix
#print "sinusoidal comp: ", 2*sigma_j*np.sqrt(S_i*S_j)*J*np.exp(1j*np.dot(q,l_vec))
term_ij -= 2*sigma_j*np.sqrt(S_i*S_j)*J*np.exp(1j*np.dot(q,l_vec))
#print "term[",i,"][",j,"]: ", term_ij
# elif (i != j):
#for testing:
# print ""
#print "\n\n\nOMG!!! I shouldn't be here for the simple ferro/antiferro cases!\n\n\n"
#print "term_ij: ", term_ij
Mij[i][j] = term_ij
#print "Mij: ", Mij
#print "Q: ", q
#print "M:\n", Mij
#this creates eigenvalues that are different from ours by a factor of 2. For now I'll
#I'll just divide that out.
return Mij/2.0
def read_files(interactionFileStr, allAtoms=False):
""" MODIFIED FROM SPINWAVE CALC FILE TO ONLY READ INTERACTION FILE"""
"""modified from read_interactions. Originally this(read_interactions) read
in the atoms from the interaction file and matched the spin rotation
matrices with the appropriate atoms based on indices. Now it takes the
interaction and spin file strings, reads in the atom information and matches
it with spin rotation matrices based on coordinates"""
#print interactionFileStr
interactionFile = open(interactionFileStr, 'r')
myFlag = True
returnline = ['']
jmats = []
jnums = []
atomlist = []
numcell = 0
Na, Nb, Nc = 0, 0, 0
while myFlag:
tokenized = get_tokenized_line(interactionFile, returnline=returnline)
if not (tokenized):
break
if tokenized == []:
break
if tokenized[0] == "#na":
tokenized = get_tokenized_line(interactionFile,
returnline=returnline)
Na = int(tokenized[0])
Nb = int(tokenized[1])
Nc = int(tokenized[2])
if tokenized[0] == '#number':
while 1:
tokenized = get_tokenized_line(interactionFile,
returnline=returnline)
#print 'intoken ',tokenized
if tokenized == []:
break
if tokenized[0] != '#atomnumber':
#print tokenized[0]
jnum = float(tokenized[0])
j11 = float(tokenized[1])
j12 = float(tokenized[2])
j13 = float(tokenized[3])
j21 = float(tokenized[4])
j22 = float(tokenized[5])
j23 = float(tokenized[6])
j31 = float(tokenized[7])
j32 = float(tokenized[8])
j33 = float(tokenized[9])
#jij=N.matrix([[j11,j12,j13],[j21,j22,j23],[j31,j32,j33]],'Float64')
jij = sp.matrices.Matrix([[j11, j12, j13], [j21, j22, j23],
[j31, j32, j33]])
jnums.append(jnum)
jmats.append(jij)
else:
currnum = 0
while 1:
tokenized = get_tokenized_line(interactionFile,
returnline=returnline)
if not (tokenized):
break
#print tokenized
atom_num = int(tokenized[0])
if tokenized[
5] == 'x' or allAtoms: #If it is in the first interaction cell
print "atom in first interaction cell"
x, y, z = float(tokenized[6]), float(
tokenized[7]), float(tokenized[8])
print x, y, z
Dx, Dy, Dz = float(tokenized[9]), float(
tokenized[10]), float(tokenized[11])
#spin0=N.matrix([[1,0,0],[0,1,0],[0,0,1]],'float64')
spinMagnitude = float(tokenized[12])
valence = int(tokenized[4])
massNum = int(tokenized[3])
label = tokenized[1].capitalize()
pos0 = [x, y, z]
atom0 = atom(spinMag=spinMagnitude,
pos=pos0,
label=label,
Dx=Dx,
Dy=Dy,
Dz=Dz,
orig_Index=atom_num,
valence=valence,
massNum=massNum)
neighbors = []
interactions = []
for i in range(13, len(tokenized), 2):
interacting_spin = int(tokenized[i])
#index number in export list not necessarily the same as index
#in list of atoms in first interacting 'cell'
interaction_matrix = int(tokenized[i + 1])
neighbors.append(interacting_spin)
interactions.append(interaction_matrix)
atom0.neighbors = neighbors
atom0.interactions = interactions
currnum = currnum + 1
atomlist.append(atom0)
interactionFile.close()
def inDesiredCell(atom):
if atom.pos[0] >= Na and atom.pos[0] < (Na + 1):
if atom.pos[1] >= Nb and atom.pos[1] < (Nb + 1):
if atom.pos[2] >= Nc and atom.pos[2] < (Nc + 1):
return True
return False
#Add atoms in desired cell to the beginning of the new list
newAtomList = []
Flag = True
i = 0
while Flag:
#for i in range(len(atomlist)):
if inDesiredCell(atomlist[i]):
numcell += 1
newAtomList.append(atomlist.pop(i))
else:
i = i + 1
if i == len(atomlist):
Flag = False
#Add remaining atoms to the new list
for i in range(len(atomlist)):
newAtomList.append(atomlist[i])
atomlist = newAtomList
for a in atomlist:
neighborList = a.neighbors
i = 0
while i < len(neighborList):
neighbor_index = neighborList[i]
for atom_index in range(len(atomlist)):
atom1 = atomlist[atom_index]
if atom1.origIndex == neighbor_index:
a.neighbors[i] = atom_index
i += 1
break
else:
neighborList.pop(i)
a.interactions.pop(i)
for atom1 in atomlist:
print atom1.pos, atom1.neighbors
return atomlist, numcell
def gen_cube(body=False, face=False, anti=False):
ats = []
spin = rf.findmat(N.array([0, 0, 1]))
# Cubic
if not body and not face:
ats = [rf.atom() for i in range(7)]
# # Positions
# # 0 1 2 3 4 5 6
# pstn = [[0,0,0], [1,0,0], [-1,0,0], [0,1,0], [0,-1,0], [0,0,1], [0,0,-1]]
#
# # Neighbors
# # 0 1 2 3 4 5 6
# nbrs = [[1,2,3,4,5,6], [0], [0], [0], [0], [0], [0]]
#
# # Interactions
# # 0 1 2 3 4 5 6
# ints = [[0,1,2,3,4,5], [0], [1], [2], [3], [4], [5]]
# Positions
# 0 1 2 3 4 5 6
pstn = [[0, 0, 0], [1, 0, 0], [-1, 0, 0], [0, 1, 0], [0, -1, 0],
[0, 0, 1], [0, 0, -1]]
# Neighbors
# 0 1 2 3 4 5 6
nbrs = [[1, 2, 3, 4, 5, 6], [0], [0], [0], [0], [0], [0]]
# Interactions
# 0 1 2 3 4 5 6
ints = [[0, 0, 0, 0, 0, 0], [1], [2], [3], [4], [5], [6]]
# Plug in values for positions and neighbors
for i in range(len(ats)):
ats[i].pos = N.array(pstn[i])
ats[i].neighbors = nbrs[i]
ats[i].interactions = ints[i]
ats[i].spinRmatrix = spin
ats[i].spinMagnitude = 1
# BCC - Body Centered Cubic
elif body and not face:
# Positions
# 0 1 2 3 4
pstn = [
[0, 0, 0],
[-0.5, 0.5, -0.5],
[0.5, 0.5, -0.5],
[0.5, 0.5, 0.5],
[-0.5, 0.5, 0.5],
# 5 6 7 8
[-0.5, -0.5, -0.5],
[0.5, -0.5, -0.5],
[0.5, -0.5, 0.5],
[-0.5, -0.5, 0.5]
]
# Neighbors
# 0 1 2 3 4
nbrs = [
[1, 2, 3, 4, 5, 6, 7, 8],
[],
[],
[],
[],
# 5 6 7 8
[],
[],
[],
[]
]
# Interactions
# 0 1 2 3 4
ints = [
[0, 1, 2, 3, 4, 5, 6, 7],
[],
[],
[],
[],
# 5 6 7 8
[],
[],
[],
[]
]
ats = [rf.atom() for i in range(len(pstn))]
for i in range(len(ats)):
ats[i].pos = N.array(pstn[i])
ats[i].neighbors = nbrs[i]
ats[i].interactions = ints[i]
ats[i].spinRmatrix = spin
ats[i].spinMagnitude = 1
# FCC - Face Centered Cubic
elif face and not body:
# Positions
# 0 1 2 3 4
pstn = [
[0, 0, 0],
[0.5, 0, 0.5],
[-0.5, 0, 0.5],
[0.5, 0, -0.5],
[-0.5, 0, -0.5],
# 5 6 7 8 9
[0, 0.5, 0.5],
[0, -0.5, 0.5],
[0, 0.5, -0.5],
[0, -0.5, -0.5],
[0.5, 0.5, 0],
# 10 11 12
[-0.5, 0.5, 0],
[0.5, -0.5, 0],
[-0.5, -0.5, 0]
]
# Neighbors
# 0 1 2 3 4
nbrs = [
[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12],
[],
[],
[],
[],
# 5 6 7 8 9
[],
[],
[],
[],
[],
# 10 11 12
[],
[],
[]
]
# Interactions
# 0 1 2 3 4
ints = [
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11],
[],
[],
[],
[],
# 5 6 7 8 9
[],
[],
[],
[],
[],
# 10 11 12
[],
[],
[]
]
ats = [rf.atom() for i in range(len(pstn))]
for i in range(len(ats)):
ats[i].pos = N.array(pstn[i])
ats[i].neighbors = nbrs[i]
ats[i].interactions = ints[i]
ats[i].spinRmatrix = spin
ats[i].spinMagnitude = 1
if anti == True:
spin = rf.findmat(N.array([0, 0, -1]))
ats[0].spinMagnitude = 1
ats[0].spinRmatrix = spin
return ats
def mcQueeny_case(interactionfile,
spinfile,
tau_list,
temperature,
direction={
'kx': 1,
'ky': 0,
'kz': 0
},
hkl_interval=[1e-3, 2 * np.pi, 100],
omega_interval=[0, 5, 100],
eig_eps=0.001):
initial_time = time.clock()
#to plot eigenvector components
# q1 = []
# q2 = []
#to plot w's
#w1_list = []
#w2_list = []
#w3_list = []
#w4_list = []
#w5_list = []
#w6_list = []
#w7_list = []
#w8_list = []
# w_output_list = []
#plot the structure factor to compare with lovesey (In McQueeny Paper)
# strfac_sums = []
# strfac1 = []
# strfac2 = []
atom_list, jnums, jmats, N_atoms_uc, numCutOff, magCellSize = readFiles(
interactionfile, spinfile, rtn_cutOffInfo=True)
#Hardcoding body-center cubic
if 0:
atom_list = []
jnums = [0]
N_atom_uc = 1
numCutOff = 7
magCellSize = np.array([1, 1, 1])
jmats = [np.array([[-1, 0, 0], [0, -1, 0], [0, 0, -1]])]
atom_list.append(
atom(pos=np.array([0.5, 0.5, 0.5]),
spin=np.array([0, 0, 1]),
interactions=[0, 0, 0, 0, 0, 0],
neighbors=[1, 2, 3, 4, 5, 6]))
atom_list.append(
atom(pos=np.array([0., 0., 0.]),
spin=np.array([0, 0, -1]),
interactions=[0],
neighbors=[0]))
atom_list.append(
atom(pos=np.array([1., 0., 0.]),
spin=np.array([0, 0, -1]),
interactions=[0],
neighbors=[0]))
atom_list.append(
atom(pos=np.array([1., 1., 0.]),
spin=np.array([0, 0, -1]),
interactions=[0],
neighbors=[0]))
atom_list.append(
atom(pos=np.array([1., 0., 1.]),
spin=np.array([0, 0, -1]),
interactions=[0],
neighbors=[0]))
atom_list.append(
atom(pos=np.array([1., 1., 1.]),
spin=np.array([0, 0, -1]),
interactions=[0],
neighbors=[0]))
atom_list.append(
atom(pos=np.array([0., 1., 0.]),
spin=np.array([0, 0, -1]),
interactions=[0],
neighbors=[0]))
atom_list.append(
atom(pos=np.array([0., 0., 1.]),
spin=np.array([0, 0, -1]),
interactions=[0],
neighbors=[0]))
atom_list.append(
atom(pos=np.array([0., 1., 1.]),
spin=np.array([0, 0, -1]),
interactions=[0],
neighbors=[0]))
h_list, k_list, l_list = generate_hkl(hkl_interval, direction)
e = generate_wt(omega_interval)
ff_list = generate_form_factors(N_atoms_uc, atom_list, hkl_interval)
s = []
basis = []
for a in atom_list:
s.append(a.spin[2]) #z component of spin (assume aligned with z)
#basis.append(a.pos)
basis.append(a.pos - magCellSize) #translate back to 0,0,0
#normalize? NO!
#basis.append([a.pos[0] - int(a.pos[0]), a.pos[1]-int(a.pos[1]), a.pos[2] - int(a.pos[2])])
#print "\n\nbasis vectors:\n"
#mess with basis vectors and spin
#basis[0] = [0.25,0,0]
#basis[0] = [1.0,0,0]
#tmp = s[0]
#s[0] = s[1]
#s[1] = tmp
#for pos in basis:
# print pos
#print "\n\nspins:\n"
#for spin in s:
# print spin
mesh = np.zeros((len(h_list), len(e)))
#output q, w, and eigenvectors before and after normalization to compare with McQueeny's
# f = open("/home/tom/Desktop/Python_Eigs.txt", 'w')
# f.write("q w eigVec_before_norm T\n\n")
# f2 = open("/home/tom/Desktop/Values.txt", 'w')
# f2.write("Q w wvec (wvec norm) e^(-i*Q.d_i)\n\n")
#create the T_ni matricies (eigenvector matrices)
#This algorithm uses a differnt matrix:
#evecs, mats = calc_eig_mats_numerically(Hsave, h_list,k_list,l_list)
#eigvals = calc_eigs_numerically(Hsave, h_list, k_list, l_list)#This is innefficient, eigs already calculated and thrown away in calc_eig_mats_..
#w_list = gen_eigs_with_sign(Hsave, h_list, k_list, l_list, 0.001)
for Qindex in range(len(h_list)):
Q = (np.array([h_list, k_list, l_list]).transpose())[Qindex]
# f2.write(str(Q))
#CALL SPINWAVE(q,w,evec) - get w, evec for given q
M = create_matrix(atom_list, jnums, jmats, numCutOff, magCellSize,
Q - np.array(tau_list))
w, evec = np.linalg.eig(M)
# f2.write(" " + str(w))
# f2.write(" " + str(evec.flatten()))
# evec = evecs[Qindex]
# w = w_list[Qindex]
# print "\nw = ", w
#w1_list.append(w[0])
#w2_list.append(w[1])
#w3_list.append(w[1])
#w4_list.append(w[1])
#w5_list.append(w[1])
#w6_list.append(w[1])
#w7_list.append(w[1])
#w8_list.append(w[1])
# w_output_list.append(w)
ff = ff_list[Qindex]
#Get number of atoms
numAtoms = numCutOff
#numAtoms = np.sqrt(evec.size)#This should be the number of atoms that I need to loop through.
#if int(numAtoms) != numAtoms:#I beleive t_mat should always be square, but lets check
# raise Exception("t_mat not square!")
#Normalize evec to get T_ni
#for i in range(0, numAtoms):
# normi = 0
# for j in range(0, numAtoms):
# sigma_j = s[j]/np.abs(s[j])
# normi += sigma_j * np.abs(evec[j][i])**2
# for j in range(0, numAtoms):
# evec[i][j] = evec[j][i]/np.sqrt(np.abs(normi))
evec2 = evec.copy()
#I'm going to write this from scratch
# print "evec before = ", evec
T = evec
sigma = []
for i in range(numAtoms):
sigma.append(s[i] / np.abs(s[i]))
for n in range(numAtoms):
norm = 0
for i in range(numAtoms):
norm += sigma[i] * (np.abs(evec2[n][i])**2)
for i in range(numAtoms):
# print "norm : ", norm
# print "w sign: ", np.sign(w[n])
#T[n][i] = T[n][i]*np.sqrt((w[n]/np.abs(w[n]))/norm + 0j)
T[n][i] = evec2[n][i] / np.sqrt(np.abs(norm))
evec = T
# f2.write(" " + str(T.flatten()))
#evec = evec2
# q1.append(evec[0][0])
# q2.append(evec[0][0])
#output eigs to file
# f.write(str(Q))
# f.write(" w:" + str(w))
# f.write("\nmat: " + str(M))#the matrix for which the eigs were found
# f.write("\nbefore_norm: " + str(evec2.flatten()))
# f.write("\nafterNorm: " + str(evec.flatten()) + "\n\n")
#evec = evec.transpose()
#test = 0
#for i in range(numAtoms):
# sigma_i = s[j]/np.abs(s[j])
# test += sigma_i * np.dot(evec[i],evec[i])
# print "sigma_i = ", sigma_i
#print "\n\nsum{sigma_i * |T_ni|^2} = ", test, "\n\n"
# print "evec = " , evec
# print "sigma1: ", s[0]/np.abs(s[0])
# print "sigma2: ", s[1]/np.abs(s[1])
# print "sign lambda_0: ", (s[0]/np.abs(s[0]))*(evec[0][0]**2) + (s[1]/np.abs(s[1]))*(evec[0][1]**2)
# print "sign lambda_1: ", (s[0]/np.abs(s[0]))*(evec[1][0]**2) + (s[1]/np.abs(s[1]))*(evec[1][1]**2)
#using only positive eigenvalue
#w = [w[0]]
#evec = [evec[0]]
#print "eigenvalues used: ", w
#print "eigenvectors used: ", evec
strfac = np.zeros(numAtoms)
#for testing:
ff = 1
for i in range(numAtoms):
dum = 0
for j in range(numAtoms):
dum += (s[j] / np.sqrt(np.abs(
s[j]))) * ff * evec[j][i] #* np.exp(1.0j*
#(-Q[0]*basis[j][0] -Q[1]*basis[j][1] -Q[2]*basis[j][2]))
# print "\n\n\nwritting to f2:\n\n\n", np.exp(1.0j*
# (-Q[0]*basis[j][0] -Q[1]*basis[j][1] -Q[2]*basis[j][2]))
# print "j: ", j
# print "basis: ", basis[j]
# print "Q.di", (-Q[0]*basis[j][0] -Q[1]*basis[j][1] -Q[2]*basis[j][2])
exp = np.exp(1.0j * (-Q[0] * basis[j][0] - Q[1] * basis[j][1] -
Q[2] * basis[j][2]))
# f2.write(" " + str(exp))
strfac[i] = np.abs(dum)**2
# print "Q: ", Q, " strfac[",i,"]: ", strfac[i]
# f2.write("\n\n")
# strfac_sums.append(0.0);
# strfac1.append(strfac[0])
# strfac2.append(strfac[1])
sqw = np.zeros(len(e))
for j in range(numAtoms):
# strfac_sums[Qindex] +=strfac[j]
for i in range(len(e)):
y = LIFETIME_VALUE / 2
lorentzian = (1 / np.pi) * y / ((e[i] - w[j])**2 + y**2)
#test
#strfac[j] = ff*1
sqw[i] = sqw[i] + strfac[
j] * lorentzian #he has some 'bose' factor in here
#more test
#sqw[i] = sqw[i] + strfac[j]
mesh[Qindex] = sqw #* 0.5*(1 + Q[0]**2) #along x, Q_hat is just 1?
#f.close()
#f = open("/home/tom/Desktop/output.txt", 'w')
#for q in range(0,len(h_list)):
#for w in range(0,len(e)):
#f.write(str(h_list[q]))
#f.write(" ")
#f.write(str(e[w]))
#f.write(" ")
#f.write(str(mesh[q][w]))
#f.write("\n")
#f.close()
#f = open("/home/tom/Desktop/output2.txt", 'w')
#for q in range(0,len(h_list)):
#f.write(str(h_list[q]))
#f.write(" ")
#f.write(str(np.abs(q1[q])))
#f.write(" ")
#f.write(str(np.abs(q2[q])))
#f.write("\n")
#f.close()
#f = open("/home/tom/Desktop/output3.txt", 'w')
#for q in range(0,len(h_list)):
#f.write(str(h_list[q]))
#f.write(" ")
#f.write(str(np.real(w1_list[q])))
#f.write(" ")
#f.write(str(np.real(w2_list[q])))
#f.write(" ")
#f.write(str(np.real(w3_list[q])))
#f.write(" ")
#f.write(str(np.real(w4_list[q])))
#f.write(" ")
#f.write(str(np.real(w5_list[q])))
#f.write(" ")
#f.write(str(np.real(w6_list[q])))
#f.write(" ")
#f.write(str(np.real(w7_list[q])))
#f.write(" ")
#f.write(str(np.real(w8_list[q])))
#f.write("\n")
#f.close()
#f = open("/home/tom/Desktop/strfacs.txt", 'w')
#for q in range(0,len(h_list)):
#f.write(str(h_list[q]))
#f.write(" ")
#f.write(str(k_list[q]))
#f.write(" ")
#f.write(str(l_list[q]))
#f.write(" ")
#f.write(str(strfac1[q]))
#f.write(" ")
#f.write(str(strfac2[q]))
#f.write(" ")
#f.write(str(strfac_sums[q]))
#f.write("\n")
#f.close()
#plt.plot(w1_list)
#plt.plot(w2_list)
#plt.show()
print "Run Time: ", time.clock() - initial_time, " seconds"
def run_cross_section(interactionfile, spinfile):
start = clock()
# Generate Inputs
atom_list, jnums, jmats,N_atoms_uc=readFiles(interactionfile,spinfile)
atom1 = atom(pos = [0.00,0,0], neighbors = [1], interactions = [0], int_cell = [0],
atomicNum = 26, valence = 3)
atom2 = atom(pos = [0.25,0,0], neighbors = [0,2], interactions = [0], int_cell = [0],
atomicNum = 26, valence = 3)
atom3 = atom(pos = [0.50,0,0], neighbors = [1,3], interactions = [0], int_cell = [0],
atomicNum = 26, valence = 3)
atom4 = atom(pos = [0.75,0,0], neighbors = [2], interactions = [0], int_cell = [0],
atomicNum = 26, valence = 3)
# atom_list,N_atoms_uc = ([atom1, atom2, atom3, atom4],1)
atom_list=atom_list[:N_atoms_uc]
N_atoms = len(atom_list)
print N_atoms
if 1:
kx = sp.Symbol('kx', real = True)
ky = sp.Symbol('ky', real = True)
kz = sp.Symbol('kz', real = True)
k = spm.Matrix([kx,ky,kz])
(b,bd) = generate_b_bd_operators(atom_list)
# list_print(b)
(a,ad) = generate_a_ad_operators(atom_list, k, b, bd)
# list_print(a)
(Sp,Sm) = generate_Sp_Sm_operators(atom_list, a, ad)
# list_print(Sp)
(Sa,Sb,Sn) = generate_Sa_Sb_Sn_operators(atom_list, Sp, Sm)
# list_print(Sa)
(Sx,Sy,Sz) = generate_Sx_Sy_Sz_operators(atom_list, Sa, Sb, Sn)
# list_print(Sx)
print ''
#Ham = generate_Hamiltonian(N_atoms, atom_list, b, bd)
ops = generate_possible_combinations(atom_list, [Sx,Sy,Sz])
# list_print(ops)
ops = holstein(atom_list, ops)
# list_print(ops)
ops = apply_commutation(atom_list, ops)
# list_print(ops)
ops = replace_bdb(atom_list, ops)
# list_print(ops)
ops = reduce_options(atom_list, ops)
list_print(ops)
# Old Method
#cross_sect = generate_cross_section(atom_list, ops, 1, real, recip)
#print '\n', cross_sect
if 1:
aa = bb = cc = np.array([2.0*np.pi], 'Float64')
alpha = beta = gamma = np.array([np.pi/2.0], 'Float64')
vect1 = np.array([[1,0,0]])
vect2 = np.array([[0,0,1]])
lattice = Lattice(aa, bb, cc, alpha, beta, gamma, Orientation(vect1, vect2))
data={}
data['kx']=1.
data['ky']=0.
data['kz']=0.
direction=data
temperature = 1.0
kmin = 0
kmax = 2*sp.pi
steps = 25
tau_list = []
for i in range(1):
tau_list.append(np.array([0,0,0], 'Float64'))
h_list = np.linspace(0.1,12.0,200)
k_list = np.zeros(h_list.shape)
l_list = np.zeros(h_list.shape)
w_list = np.linspace(0.1,10.0,200)
efixed = 14.7 #meV
eief = True
N_atoms_uc,csection,kaprange,qlist,tau_list,eig_list,kapvect,wtlist = generate_cross_section(interactionfile, spinfile, lattice, ops,
tau_list, h_list, k_list, l_list, w_list,
temperature, steps, eief, efixed)
print csection
return N_atoms_uc,csection,kaprange,qlist,tau_list,eig_list,kapvect,wtlist
end = clock()
print "\nFinished %i atoms in %.2f seconds" %(N_atoms,end-start)
pylab.show()
sys.exit()
if 0:
x,y = sp.symbols('xy')
out = x*y
print sp.latex(out)
if 0:
a = np.array([1,1,1])
b = 5
print b/a
print a/b
if 0:
at1 = atom(pos=[0,0,0], atomicNum = 26, valence = 3)
print at1.atomicNum
el = elements[at1.atomicNum]
print el
Q=np.arange(0.,1.,1./100.)
print Q
Mq = el.magnetic_ff[at1.valence].M_Q(Q)
print type(Mq)
print type(Q)
pylab.plot(Q,Mq)
pylab.show()
if 0:
x,y = sp.symbols('xy')
print (x+1)*y
pylab.show()
sys.exit()
if 0:
x, y = sp.symbols('xy')
out = x * y
print sp.latex(out)
if 0:
a = np.array([1, 1, 1])
b = 5
print b / a
print a / b
if 0:
at1 = atom(pos=[0, 0, 0], atomicNum=26, valence=3)
print at1.atomicNum
el = elements[at1.atomicNum]
print el
Q = np.arange(0., 1., 1. / 100.)
print Q
Mq = el.magnetic_ff[at1.valence].M_Q(Q)
print type(Mq)
print type(Q)
pylab.plot(Q, Mq)
pylab.show()
if 0:
x, y = sp.symbols('xy')
print(x + 1) * y
def testBCC(self, num=9, num_uc=1):
ats = [rf.atom() for i in range(num)]
spin = rf.findmat(N.array([0, 0, 1]))
# Positions
# 0 1 2 3 4
pstn = [
[0, 0, 0],
[-0.5, 0.5, -0.5],
[0.5, 0.5, -0.5],
[0.5, 0.5, 0.5],
[-0.5, 0.5, 0.5],
# 5 6 7 8
[-0.5, -0.5, -0.5],
[0.5, -0.5, -0.5],
[0.5, -0.5, 0.5],
[-0.5, -0.5, 0.5]
]
# Neighbors
# 0 1 2 3 4
nbrs = [
[1, 2, 3, 4, 5, 6, 7, 8],
[],
[],
[],
[],
# 5 6 7 8
[],
[],
[],
[]
]
# Interactions
# 0 1 2 3 4
ints = [
[0, 1, 2, 3, 4, 5, 6, 7],
[],
[],
[],
[],
# 5 6 7 8
[],
[],
[],
[]
]
for i in range(len(ats)):
ats[i].pos = N.array(pstn[i])
ats[i].neighbors = nbrs[i]
ats[i].interactions = ints[i]
ats[i].spinRmatrix = spin
ats[i].spinMagnitude = 1
inters = [item for atom in ats for item in atom.interactions]
max_inter = max(inters)
J = sp.Symbol('J', real=True)
Jij = [
N.matrix([[J, 0, 0], [0, J, 0], [0, 0, J]])
for i in range(max_inter + 1)
]
(Hsave, charpoly, eigs) = calculate_dispersion(ats,
num_uc,
num,
Jij,
showEigs=True)
eigs = eigs.keys()
for item in eigs:
item = item.expand(mul=True, multinomial=True)
testeig = (-2048.0 * self.J**2 * self.S**2 * sp.cos(0.5 * self.kx) *
sp.cos(0.5 * self.ky) * sp.cos(0.5 * self.kz) +
1024.0 * self.J**2 * self.S**2 +
1024.0 * self.J**2 * self.S**2 * sp.cos(0.5 * self.kx)**2 *
sp.cos(0.5 * self.ky)**2 * sp.cos(0.5 * self.kz)**2)**(
0.5) * 0.5
self.assertAlmostEqual(Hsave.shape[0], 2, 4, 'H wrong shape')
self.assertAlmostEqual(Hsave.shape[1], 2, 4, 'H wrong shape')
f = eigs[0].args[2].args[1].args[0].expand()
f = f.subs([(self.J, 1), (self.S, 2), (self.kx, 3), (self.ky, 4),
(self.kz, 5), (sp.I, 0)])
g = sp.simplify(testeig.args[1].args[0].expand())
g = g.subs([(self.J, 1), (self.S, 2), (self.kx, 3), (self.ky, 4),
(self.kz, 5)])
myFlag = f - g
self.assertAlmostEqual(myFlag, 0, 7, 'Eigs are wrong')
