def plotNewtonStats(movelens, its, functionValues, max_vals, max_names,
difs, numOfIts):
i = []
for s in range(its.shape[0]):
if not functionValues[s] == 0:
i.append(int(its[s]))
#print("movelens:")
#print(movelens)
plt.plot(i,
np.split(movelens, [len(i), movelens.shape[0] - len(i)])[0])
plt.title("movelens")
plt.show()
plt.plot(
i,
np.split(functionValues, [len(i), movelens.shape[0] - len(i)])[0])
plt.title("funtion values")
plt.show()
plt.plot(i,
np.split(max_vals, [len(i), movelens.shape[0] - len(i)])[0])
plt.title("maxvals")
plt.show()
#print("names:")
#print(max_names)
#print("difs:")
#print(difs)
plt.plot(i, np.split(difs, [len(i), movelens.shape[0] - len(i)])[0])
plt.title("difs")
plt.show()
def spindens(self,lrgm_out):
from scipy import split,pi,complex128,zeros,repeat
number_of_lattice_points = self.canvas.shape[0]*self.canvas.shape[1]
number_of_nodes = len(self.tuple_canvas_coordinates)
if number_of_nodes == number_of_lattice_points:
if self.order == 'even':
Gup, Gdown = split(lrgm_out.reshape(self.canvas.shape[0],self.canvas.shape[1]*2),2,axis=1)
if self.order == 'odd':
Gup, Gdown = split(lrgm_out.reshape(-1,2),2,axis=1)
Gup, Gdown = Gup.reshape(self.canvas.shape), Gdown.reshape(self.canvas.shape)
else:
print "Please specify order of Nodes, i.e 'even' for allspinup-allspindown per sclice or odd for spinup-spindown-spinup-..."
Sz = self.p.upar.hbar/(4*pi*1j*self.p.upar.a**2)*(Gup-Gdown)
elif number_of_nodes < number_of_lattice_points:
Sz= zeros(self.canvas.shape,dtype=complex128)
print 'calculating spin density for sparse structure'
lrgm_out = self.p.hbar/(4*pi*1j*self.p.upar.a**2)*lrgm_out
expanded_array_of_coords = repeat(self.tuple_canvas_coordinates,2,axis=0)
for index,node_name in enumerate(self.nodelist):
if node_name % 2 == 0:
sign = 1
else:
sign = -1
Sz[tuple(expanded_array_of_coords[node_name])] += sign * lrgm_out[index]
else:
print 'Number of nodes larger than canvas, something is wrong!'
print 'max Spin Split: ', Sz.real.max()-Sz.real.min()
#Realteil scheint wahrscheinlicher, imag oszilliert wie bloed
return Sz.real
def splitTargetChunk(self):
## create mosaic data-structure + list of 'pointers' to the tiles in
## this structure
self.mosaic = scipy.zeros((self.sliceDim[1]*self.Tiles[1]/self.NPlacers,
self.sliceDim[0]*self.Tiles[0], 3), dtype='i')
VertSplitFinalArrs = scipy.split(self.mosaic, self.Tiles[0], axis=1)
for VertSplitFinalArr in VertSplitFinalArrs:
SplitFinalArrs = scipy.split(VertSplitFinalArr,
self.Tiles[1]/self.NPlacers, axis=0)
for SplitFinalArr in SplitFinalArrs:
self.mosaicTiles.append(SplitFinalArr)
def getTargetChunk(self):
#print "P{} > listening".format(self.rank)
NodeArr = self.comm.recv(source=0, tag=1, status=self.status)
#print "P{} < listening".format(self.rank)
#%% Divide the NodeArr into tiles
#print "P{} > dividing".format(self.rank)
VertSplitArrs = scipy.split(NodeArr, self.Tiles[0], axis=1)
for VertSplitArr in VertSplitArrs:
SplitArrs = scipy.split(VertSplitArr,self.Tiles[1]/self.NPlacers,
axis=0)
for splitArr in SplitArrs:
self.targetPieces.append(splitArr)
def detect_signals():
vector, label = weeklydataset_sg_ndata(
"/media/4AC0AB31C0AB21E5/Documents and Settings/Claudio/Documenti/Thesis/Workloads/MSClaudio/ews/access_log-20110805.csv",
[],
)
x, target = aggregatebymins_sg_ndata(vector[1])
starttime = time.time()
y = array(target)
t = array(x)
thr = max(y) * 2 / 3
print thr
I = pylab.find(y > thr)
# print I
# pylab.plot(t,y, 'b',label='signal')
# pylab.plot(t[I], y[I],'ro',label='detections')
# pylab.plot([0, t[len(t)-1]], [thr,thr], 'g--')
J = pylab.find(diff(I) > 1)
argpeak = []
targetpeak = []
for K in split(I, J + 1):
ytag = y[K]
peak = pylab.find(ytag == max(ytag))
# pylab.plot(peak+K[0],ytag[peak],'sg',ms=7)
argpeak.append(peak + K[0])
targetpeak.append(ytag[peak])
eta = time.time() - starttime
print "time elapsed %f" % eta
return list(itertools.chain(*argpeak)), list(itertools.chain(*targetpeak))
def get_HRRR_data(filename):
grbs = pygrib.open(filename)
msgs = [str(grb) for grb in grbs]
string = 'Geopotential Height:gpm'
temp = [
msg for msg in msgs
if msg.find(string) > -1 and msg.find('isobaricInhPa') > -1
]
pressure_levels_Pa = s.array([int(s.split(' ')[3]) for s in temp])
geo_pot_height_grbs = grbs.select(name = 'Geopotential Height', \
typeOfLevel='isobaricInhPa', level=lambda l: l > 0)
temperature_grbs = grbs.select(name = 'Temperature', \
typeOfLevel='isobaricInhPa', level=lambda l: l > 0)
rh_grbs = grbs.select(name = 'Relative humidity', \
typeOfLevel='isobaricInhPa', level=lambda l: l > 0)
lat, lon = geo_pot_height_grbs[0].latlons()
geo_pot_height = s.stack([grb.values for grb in geo_pot_height_grbs])
temperature = s.stack([grb.values for grb in temperature_grbs])
rh = s.stack([grb.values for grb in rh_grbs])
return lat, lon, geo_pot_height, temperature, rh, pressure_levels_Pa
def crossvalidation(self, fold, v, k):
error = 0
data = Data(k, 0, 0)
data.importDataFromMat()
data.normalize()
n = data.train_cat.shape[1]
all_indices = sp.arange(n)
data.shuffleData()
sq = SquaredErrorLinearClassifier(v,k)
dataset_indices = sp.split(all_indices, fold)
for i in range(fold):
set_without_D_i_indices = sp.concatenate(dataset_indices[0:i]+dataset_indices[i+1:fold])
#print "-"*30+"train"+"-"*30
sq.train(data.train_left[:,set_without_D_i_indices], data.train_right[:,set_without_D_i_indices], data.train_cat[:,set_without_D_i_indices])
#print "-"*30+"classify"+"-"*30
results, classes = sq.classify(data.train_left[:,dataset_indices[i]], data.train_right[:,dataset_indices[i]])
#print "-"*30+"error"+"-"*30
err, _ = sq.error(results, data.train_cat[:,dataset_indices[i]].T)
error += fold/(n*1.0)*err
error = error / fold
with open("results/crossvalidation.txt", "a") as myfile:
toWrite = "v="+str(v)+" error="+str(error)
myfile.write(toWrite)
def Merge_pores(network, pores, Neighbor,Cordinate, trimradius, labels=['merged']):
# Assert that `pores` is list of lists
try:
len(pores[0])
except (TypeError, IndexError):
pores = [pores]
N = len(pores)
NBs, XYZs = [], []
for Ps in pores:
NBs.append(Neighbor)
XYZs.append(Cordinate)
op.topotools.extend(network, pore_coords=XYZs, labels=labels)
Pnew = network.Ps[-N::]
pores_set = [set(items) for items in pores]
NBs_set = [set(items) for items in NBs]
ps1, ps2 = [], []
from itertools import combinations
for i, j in combinations(range(N), 2):
if not NBs_set[i].isdisjoint(pores_set[j]):
ps1.append([network.Ps[-N+i]])
ps2.append([network.Ps[-N+j]])
# Add (possible) connections between the new pores
op.topotools.connect_pores(network, pores1=ps1, pores2=ps2, labels=labels)
# Add connections between the new pores and the rest of the network
op.topotools.connect_pores(network, pores2=sp.split(Pnew, N), pores1=NBs, labels=labels)
# Trim merged pores from the network
op.topotools.trim(network=network, pores=sp.concatenate(pores))
Ps = network.find_nearby_pores(pores=network.Ps[-len(pores)::], r=trimradius, flatten=True)
op.topotools.trim(network=network, pores=Ps)
def chunk(A, n_chunks=10):
""" split A into n chunks, ignore overhaning samples """
chunk_size = sp.floor(A.shape[0] / n_chunks)
drop = int(A.shape[0] % chunk_size)
if drop != 0:
A = A[:-drop]
A_chunks = sp.split(A, n_chunks)
return A_chunks
def weights(self, new_weights):
sections = shapesToSections(self.shapes)
syn_wo, inter_ws, syn_wi, wi, wo = split(new_weights.copy(), sections)
shapes = self.shapes
self.syn_wo = syn_wo.reshape(shapes['syn_wo'])
self.inter_ws = inter_ws
self.syn_wi = syn_wi.reshape(shapes['syn_wi'])
self.wi = wi.reshape(shapes['wi'])
self.wo = wo.reshape(shapes['wo'])
def weights(self, new_weights):
sections = shapesToSections(self.shapes)
syn_wo, inter_ws, syn_wi, wi, wo = split(new_weights.copy(), sections)
shapes = self.shapes
self.syn_wo = syn_wo.reshape(shapes['syn_wo'])
self.inter_ws = inter_ws
self.syn_wi = syn_wi.reshape(shapes['syn_wi'])
self.wi = wi.reshape(shapes['wi'])
self.wo = wo.reshape(shapes['wo'])
def animate(frame):
updated = [Sun.point, Sun.patch] #sun doesnt move
for planet in LargeList[1:]: #large bodies after sun
planet.pos = planet.orbitPos(times[frame])
updated.extend(planet.update())
Demo2.pos, Demo2.vel = sp.split(path.sol(times[frame]), 2)# x, y, v_x, v_y
updated.extend(Demo2.update())
focus(ax2, Demo2)
return tuple(updated)
def fastKineticsCrop(self, rawArray, n):
"""in fast kinetic picture we have one large array and then need to crop it into n equal arrays vertically.
Uses scipy split function which returns a python list of the arrays
returned list has the order of first picture taken --> last picture taken. i.e. [atomsImage,lightImage]"""
try:
return scipy.split(rawArray, n, axis=0)
except ValueError as e:
logger.error(
"fastKinetics crop couldn't equally divide the image into n=%s. This will fail. You must crop the image to a divisble size first."
% n)
raise e
def edens(self, lrgm_out):
from scipy import split, pi, asarray, sum
# TODO implement sparse and noncoliear structure mapping
number_of_lattice_points = self.canvas.shape[0] * self.canvas.shape[1]
number_of_nodes = len(self.tuple_canvas_coordinates)
if number_of_nodes == number_of_lattice_points:
print 'Using stride bases reshape, Attention !!! Probably not what you want!'
if self.p.multi == 1:
edensity = lrgm_out.reshape(asarray(self.canvas.shape) +
[0, 0]) * 2 / (2 * pi * self.p.upar.a**
2) #times 2 for spin
if self.p.multi == 2:
if self.order == 'even':
Gup, Gdown = split(lrgm_out.reshape(self.canvas.shape[0],
self.canvas.shape[1] * 2),
2,
axis=1)
edensity = 1 / (2 * pi * self.upar.p.a**2) * (Gup + Gdown)
if self.order == 'odd':
edensity = 1 / (2 * pi * self.p.upar.a**2) * sum(
lrgm_out.reshape(-1, 2), axis=1).reshape(self.canvas.shape)
else:
print "Please specify order of Nodes, i.e 'even' for allspinup-allspindown per sclice or odd for spinup-spindown-spinup-..."
elif number_of_nodes < number_of_lattice_points:
from scipy import zeros, complex128, repeat
edensity_spin_up = zeros(self.canvas.shape, dtype=complex128)
edensity_spin_down = zeros(self.canvas.shape, dtype=complex128)
if self.p.multi == 1:
print 'calculating electron density without SO'
lrgm_out = lrgm_out * 2 / (2 * pi * self.p.upar.a**2)
for index, node_name in enumerate(self.nodelist):
edensity_spin_up[
self.tuple_canvas_coordinates[node_name]] = lrgm_out[index]
if self.p.multi == 2:
print 'calculating electron density with SO'
lrgm_out = lrgm_out * 1 / (2 * pi * self.p.upar.a**2)
expanded_array_of_coords = repeat(self.tuple_canvas_coordinates,
2,
axis=0)
for index, node_name in enumerate(self.nodelist):
if node_name % 2 == 0:
edensity_spin_up[tuple(
expanded_array_of_coords[node_name])] = lrgm_out[index]
else:
edensity_spin_down[tuple(
expanded_array_of_coords[node_name])] = lrgm_out[index]
edensity = edensity_spin_up + edensity_spin_down
edensity = (edensity.real, edensity_spin_up.real,
edensity_spin_down.real)
else:
print 'Number of nodes larger than canvas, something is wrong!'
# print 'max Electron Density: ', edensity.max()
return edensity
def Grafica(x, y, vx, vy, Np):
x1 = sp.zeros(Np // 2)
x2 = sp.zeros(Np // 2)
vx1 = sp.zeros(Np // 2)
vx2 = sp.zeros(Np // 2)
y1 = sp.zeros(Np // 2)
y2 = sp.zeros(Np // 2)
vy1 = sp.zeros(Np // 2)
vy2 = sp.zeros(Np // 2)
x1, x2 = sp.split(x, 2)
vx1, vx2 = sp.split(vx, 2)
[y1, y2] = sp.split(y, 2)
[vy1, vy2] = sp.split(vy, 2)
plt.figure('Malla')
plt.plot(x, y, '.', markersize=1)
plt.figure('Velocidades x')
plt.plot(x1, vx1, '.', markersize=1, c='m')
plt.plot(x2, vx2, '.', markersize=1, c='c')
plt.figure('Velocidades y')
plt.plot(y1, vy1, '.', markersize=1, c='m')
plt.plot(y2, vy2, '.', markersize=1, c='c')
def spindens(self, lrgm_out):
from scipy import split, pi, complex128, zeros, repeat
number_of_lattice_points = self.canvas.shape[0] * self.canvas.shape[1]
number_of_nodes = len(self.tuple_canvas_coordinates)
if number_of_nodes == number_of_lattice_points:
if self.order == 'even':
Gup, Gdown = split(lrgm_out.reshape(self.canvas.shape[0],
self.canvas.shape[1] * 2),
2,
axis=1)
if self.order == 'odd':
Gup, Gdown = split(lrgm_out.reshape(-1, 2), 2, axis=1)
Gup, Gdown = Gup.reshape(self.canvas.shape), Gdown.reshape(
self.canvas.shape)
else:
print "Please specify order of Nodes, i.e 'even' for allspinup-allspindown per sclice or odd for spinup-spindown-spinup-..."
Sz = self.p.upar.hbar / (4 * pi * 1j * self.p.upar.a**2) * (Gup -
Gdown)
elif number_of_nodes < number_of_lattice_points:
Sz = zeros(self.canvas.shape, dtype=complex128)
print 'calculating spin density for sparse structure'
lrgm_out = self.p.hbar / (4 * pi * 1j * self.p.upar.a**2) * lrgm_out
expanded_array_of_coords = repeat(self.tuple_canvas_coordinates,
2,
axis=0)
for index, node_name in enumerate(self.nodelist):
if node_name % 2 == 0:
sign = 1
else:
sign = -1
Sz[tuple(
expanded_array_of_coords[node_name])] += sign * lrgm_out[index]
else:
print 'Number of nodes larger than canvas, something is wrong!'
print 'max Spin Split: ', Sz.real.max() - Sz.real.min()
#Realteil scheint wahrscheinlicher, imag oszilliert wie bloed
return Sz.real
def fastKineticsCrop(self, rawArray, n):
"""in fast kinetic picture we have one large array and then need to crop it into n equal arrays vertically.
Uses scipy split function which returns a python list of the arrays
returned list has the order of first picture taken --> last picture taken. i.e. [atomsImage,lightImage]"""
if self.cut_white_line:
# split the image, but remove some lines, which are usually very bright, we are not quite sure about the reason
cut1 = 509
padding = 3
pic1, pic2 = rawArray[:cut1], rawArray[cut1 + padding:2 * cut1 +
padding]
return pic1, pic2
else:
try:
return scipy.split(rawArray, n, axis=0)
except ValueError as e:
print "Kinetics crop did not work"
def shred_data_run_pnc():
iplist=sorted(glob.glob('*matrix.txt'))
pheno=pd.read_csv('phenotypes_info.csv')
df_filter=pheno[['SUBJID','pmat_cr']]
df_filter=df_filter.dropna()
subs_mats=[i.split('_')[0] for i in iplist]
subs_pheno=list(map(str,df_filter.SUBJID.unique()))
subs_pheno=[sp.split('.')[0] for sp in subs_pheno]
substouse=sorted(list(set(subs_mats) & set(subs_pheno)))
iplist=[ip for ip in iplist if any([s in ip for s in substouse])]
mats=[pd.read_csv(m,sep='\t',header=None).dropna(axis=1).values for m in iplist]
ipmats=np.stack(mats,axis=2)
pmatvals=df_filter.sort_values('SUBJID').pmat_cr.values
return ipmats,pmatvals,substouse
def animate(frame):
updated = [Sun.point, Sun.patch] #sun doesnt move
for planet in LargeList[1:]: #large bodies after sun
planet.pos = planet.orbitPos(t[frame])
updated.extend(planet.update())
Demo2.pos, Demo2.vel = sp.split(path.sol(t[frame]), 2)#x, y, v_x, v_y
# vel_text.set_text('velocity = %.1f' % Demo2.vel) #¢€€€€€
updated.extend(Demo2.update())
#updated.extend(vel_text)
#ax2.title(vel_text)
#plt.title(vel_text)
ax2.legend(["velocty = %.1f" %(mag(Demo2.vel[0] , Demo2.vel[1])) ])
# ax2.title("test")
#updated.extend(vel_text)
focus(Earth)
return tuple(updated)
def edens(self,lrgm_out):
from scipy import split,pi,asarray,sum
# TODO implement sparse and noncoliear structure mapping
number_of_lattice_points = self.canvas.shape[0]*self.canvas.shape[1]
number_of_nodes = len(self.tuple_canvas_coordinates)
if number_of_nodes == number_of_lattice_points:
print 'Using stride bases reshape, Attention !!! Probably not what you want!'
if self.p.multi ==1:
edensity = lrgm_out.reshape(asarray(self.canvas.shape)+[0,0])*2/(2*pi*self.p.upar.a**2) #times 2 for spin
if self.p.multi ==2:
if self.order == 'even':
Gup, Gdown = split(lrgm_out.reshape(self.canvas.shape[0],self.canvas.shape[1]*2),2,axis=1)
edensity = 1/(2*pi*self.upar.p.a**2)*(Gup+Gdown)
if self.order == 'odd':
edensity = 1/(2*pi*self.p.upar.a**2)*sum(lrgm_out.reshape(-1,2), axis=1).reshape(self.canvas.shape)
else:
print "Please specify order of Nodes, i.e 'even' for allspinup-allspindown per sclice or odd for spinup-spindown-spinup-..."
elif number_of_nodes < number_of_lattice_points:
from scipy import zeros,complex128,repeat
edensity_spin_up = zeros(self.canvas.shape,dtype=complex128)
edensity_spin_down = zeros(self.canvas.shape,dtype=complex128)
if self.p.multi ==1:
print 'calculating electron density without SO'
lrgm_out = lrgm_out *2/(2*pi*self.p.upar.a**2)
for index,node_name in enumerate(self.nodelist):
edensity_spin_up[self.tuple_canvas_coordinates[node_name]]= lrgm_out[index]
if self.p.multi ==2:
print 'calculating electron density with SO'
lrgm_out = lrgm_out*1/(2*pi*self.p.upar.a**2)
expanded_array_of_coords = repeat(self.tuple_canvas_coordinates,2,axis=0)
for index,node_name in enumerate(self.nodelist):
if node_name % 2 ==0:
edensity_spin_up[tuple(expanded_array_of_coords[node_name])] = lrgm_out[index]
else:
edensity_spin_down[tuple(expanded_array_of_coords[node_name])] = lrgm_out[index]
edensity = edensity_spin_up + edensity_spin_down
edensity = (edensity.real, edensity_spin_up.real , edensity_spin_down.real)
else:
print 'Number of nodes larger than canvas, something is wrong!'
# print 'max Electron Density: ', edensity.max()
return edensity
def gen(kf,upper,lower,r=25):
X=sp.matrix(sp.ndarray([0,2]))
xv=sp.linspace(lower[0],upper[0],r)
yv=sp.linspace(lower[1],upper[1],r)
for y in yv:
for x in xv:
p=sp.matrix([[x,y]])
X=sp.vstack([X,p])
K= sp.array(buildKsym(kf,X))
m=sp.zeros([K.shape[0]])
zv = sp.random.multivariate_normal(m,K)
f=spi.interp2d(xv,yv,sp.vstack(sp.split(zv,r)))
g = lambda x:f(x[0,0],x[0,1])[0]
return g
def transfersigma(self, ind_contact, E):
from scipy.linalg import eig, inv
from scipy.sparse import lil_matrix
from aux import SparseBlocks
from scipy import argsort, dot, eye, hstack, vstack, zeros, complex128, asarray, split
E = E + self.zplus
Ndim = len(self.p.tuple_canvas_coordinates)
block = ind_contact.length
Hblock = SparseBlocks(self.H, self.block_sizes)
self.Hblock = Hblock
I = eye(block * self.p.multi)
Zeros = zeros((block * self.p.multi, block * self.p.multi))
#if ind_contact.SO is False:
# H00 = 4*self.t0*eye(block) -self.t0*eye(block,k=1) -self.t0*eye(block,k=-1)
# Hhop = -self.t0*I #no Bfield as of now
# inv_Hhop = -1/self.t0*I #no Bfield as of now
if ind_contact.index == 0:
H00 = asarray(Hblock[0, 0].todense())
#H10 = asarray(Hblock[1,0].todense())
H01 = asarray(Hblock[0, 1].todense())
inv_H01 = inv(H01)
if ind_contact.index == 1:
H00 = asarray(Hblock[-1, -1].todense())
#H10 = asarray(Hblock[-1,-2].todense())
H01 = asarray(Hblock[-2, -1].todense())
"""indices switch because hopping matrices go the other
direction x --> -x, better results this way altough not much difference"""
inv_H01 = inv(H01)
TransMatrix = vstack((hstack(
(dot(inv_H01, E * I - H00), dot(-inv_H01,
H01.conj().T))), hstack(
(I, Zeros))))
v, S = eig(TransMatrix)
ndx = argsort(abs(v))
S = S[:, ndx]
v = v[ndx]
self.S = S
self.v = v
Sleft, Sright = split(S, 2, axis=1)
S4, S3 = split(Sright, 2, axis=0)
S2, S1 = split(Sleft, 2, axis=0)
#S2 =S[:block*self.p.multi,:block*self.p.multi]
#S1= S[block*self.p.multi:,:block*self.p.multi]
self.S2 = S2
self.S1 = S1
self.S4 = S4
self.S3 = S3
print 'S1 shape: ', S1.shape
print 'S2 shape: ', S2.shape
if ind_contact.index == 0:
dotted = dot(S2, inv(S1))
if ind_contact.index == 1:
dotted = dot(S3, inv(S4))
invBracket = inv(E * I - H00 - dot(H01, dotted))
SigmaRet = self.t0**2 * invBracket
if ind_contact.index == 0:
self.SigmaRet1 = SigmaRet
#temp = zeros((60,60),dtype=complex128)
#temp[30:60,30:60] =SigmaRet[:30,:30]
#SigmaRet=temp
else:
self.SigmaRet2 = SigmaRet
print 'SigaRet shape: ', SigmaRet.shape
sigma = lil_matrix((self.p.multi * Ndim, self.p.multi * Ndim),
dtype=complex128)
print 'sigma shape: ', sigma.shape
if ind_contact.index == 0:
sigma[0:SigmaRet.shape[0], 0:SigmaRet.shape[1]] = SigmaRet
self.sigma1 = sigma
elif ind_contact.index == 1:
sigma[-SigmaRet.shape[0]:, -SigmaRet.shape[1]:] = SigmaRet
self.sigma2 = sigma
import pudb
pudb.set_trace()
return sigma
arrival_times, service_times = getRandomArrivalServiceTimes(n_process, arrival_rate, service_rate)
server_prob = array([0.2, 0.2, 0.2, 0.2, 0.2])
n_server = server_prob.size
# maps kth process to ith server
server_address_table = digitize(uniform.rvs(size = n_process), cumsum(server_prob))
server_arrival_times = [arrival_times[server_address_table == i] for i in range(n_server)]
server_service_times = [service_times[server_address_table == i] for i in range(n_server)]
results = map(mm1, server_arrival_times, server_service_times)
print "Mean Wait(1)", array([mean(result['wait_times']) for result in results])
print "Mean QueueSize(1)", array([mean(result['queue_size']) for result in results])
server_prob_matrix = array([[ 0.2, 0.2, 0.2, 0.2, 0.2],
[ 0.2, 0.2, 0.2, 0.2, 0.2],
[ 0.2, 0.2, 0.2, 0.2, 0.2],
[ 0.2, 0.2, 0.2, 0.2, 0.2],
[ 0.2, 0.2, 0.2, 0.2, 0.2]])
server_prob_matrix_cumsumed = cumsum(server_prob_matrix, axis = 1)
server_address_tables = [
digitize(uniform.rvs(size = len(server_arrival_times[i])), server_prob_matrix_cumsumed[i])
for i in range(n_server)
]
server_arrival_times = [
sort(concatenate([results[i]['completion_times'][server_address_tables[i] == k]
for i in range(n_server)]))
for k in range(n_server)
]
new_service_times = getRandomArrivalServiceTimes(n_process, arrival_rate, service_rate)[1]
server_service_times = split(new_service_times, cumsum([x.size for x in server_arrival_times]))[:-1]
results2 = map(mm1, server_arrival_times, server_service_times)
print "Mean Wait(2)", array([mean(result['wait_times']) for result in results2])
print "Mean QueueSize(2)", array([mean(result['queue_size']) for result in results2])
output_hdulist.writeto(progenitor_image_name.replace("coadd", "fakestars1_" + str(h) + "_" + str(g)))
# Call Source Extractor in two-image mode for both sky apertures and weight
# apertures.
make_sex_cat_fake_stars(progenitor_image_name.replace("coadd", "fakestars1_" + str(h) + "_" + str(g)),
progenitor_image_name, weight_image_name, aperture_size)
make_sex_cat_fake_stars_no_weight(
progenitor_image_name.replace("coadd", "fakestars1_" + str(h) + "_" + str(g)), weight_image_name,
aperture_size)
# Delete the fakestars image, we don't need it anymore.
system("rm " + progenitor_image_name.replace("coadd", "fakestars1_" + str(h) + "_" + str(g)))
# Read the SEX catalogs into data lists. The format of the sex_file is:
# ra, dec, inst_mag, e_inst_mag, flags, fwhm, signal, noise
temp_array = loadtxt(file(progenitor_image_name.replace(".fits", ".sex")))
aperture_data = append(aperture_data, temp_array)
aperture_data = split(aperture_data, len(aperture_data)/8)
flux_array = append(flux_array, (temp_array[:,6]))
temp_array = loadtxt(file(weight_image_name.replace(".fits", ".sex")))
weight_aperture_data = append(weight_aperture_data, temp_array)
weight_aperture_data = split(weight_aperture_data, len(weight_aperture_data)/8)
for g in range(order):
for h in range(order):
fake_star_data = zeros([height,width])
for i in range(int(width/aperture_size/order)-1):
for j in range(int(height/aperture_size/order)-1):
fake_star_data[int((j+1-1./(order*2))*spacing+aperture_size*h)][int((i+1-1./(order*2))*spacing+aperture_size*g)] = peak
blurred_fake_star_data = zeros([height,width])
gaussian_filter(fake_star_data*weight_mask_expanded, 0.7,
def generate_sigma(self):
import networkx as nx
from scipy.linalg import inv,schur,eig
from scipy.sparse import lil_matrix
from numpy import asarray_chkfinite,isfinite,inf
from aux import SparseBlocks, eigenvector_from_eigenvalue, all_elements_are_unique
from scipy import argsort,dot,eye,hstack,vstack,zeros,complex128,split,asarray,diag,array
# should be able to turn zplus off, but then i need better eigenvalue comparison
E= self.p.E+self.p.zplus
Ndim = len(self.p.tuple_canvas_coordinates)
block=self.graph.order()/2
I=eye(block)
Zeros = zeros((block,block))
Hlead = nx.to_numpy_matrix(self.graph,nodelist=self.nodelist,dtype=complex128)
self.Hlead = Hlead
#import pudb; pudb.set_trace()
# add 4*self.t0 because the matrix from graph lacks diagonal (no self-loops)
try:
H00 = asarray_chkfinite(Hlead[:block,:block])+4*self.p.t0 * I
self.H00 = H00
except ValueError:
print 'H00 contains infs or NaNs'
import pudb; pudb.set_trace()
try:
H01 = asarray_chkfinite(Hlead[:block,block:])
self.H01 = H01
except ValueError:
print 'H01 contains infs or NaNs'
import pudb; pudb.set_trace()
inv_H01 = inv(H01)
while not isfinite(inv_H01).all():
print 'inv_H01 contains infs or NaNs, repeating'
inv_H01 = inv(H01)
#import pudb; pudb.set_trace()
self.inv_H01 = inv_H01
CompanionMatrix_array =vstack((hstack((Zeros,I)),hstack((dot(-inv_H01,H01.conj().T),dot(inv_H01,E*I-H00)))))
if not isfinite(CompanionMatrix_array).all():
print 'CompanionMatrix contains infs or NaNs'
import pudb; pudb.set_trace()
#CompanionMatrix_array =vstack((hstack((dot(inv_H01,E*I-H00),dot(-inv_H01,H01.conj().T))),hstack((I,Zeros))))
# the following 'complex' might be superfluous and only for real input matrices.
T,Z,number_sorted= schur(CompanionMatrix_array,sort='iuc')
eigenvalues = diag(T)
# propagating_eigenvalues = []
# propagating_eigenvectors = []
# for eigenvalue in eigenvalues:
# if abs(abs(eigenvalue)-1) < 0.01:
# propagating_eigenvalues.append(eigenvalue)
# eigenvector = eigenvector_from_eigenvalue(CompanionMatrix_array, eigenvalue)
# propagating_eigenvectors.append(eigenvector)
# prop_eig_array = array(propagating_eigenvectors).T
if not all_elements_are_unique(eigenvalues):
print "--------------WARNING!!!!!---------------"
print "One or more eigenvalues are identical, please rotate eigenvectors, I don't know how to do that"
#v,d = eig(CompanionMatrix_array)
#ndx = argsort(v)
#S=d[:,ndx]
#v=v[ndx]
#Sleft,Sright = split(S,2,axis=1)
#S4,S3 = split(Sright,2,axis=0)
#S2,S1 = split(Sleft,2,axis=0)
#S2 =S[:block*self.p.multi,:block*self.p.multi]
#S1= S[block*self.p.multi:,:block*self.p.multi]
#self.S2 = S2
#self.S1 = S1
#self.S4 = S4
#self.S3 = S3
#print 'S1 shape: ',S1.shape
#print 'S2 shape: ',S2.shape
# sort eigenvalues and Z according to acending abs(eigenvalue), TODO: do better sorting, now it
# depends on luck. sort using the calulated eigenvectors above
# sorting_indices = abs(eigenvalues).argsort()
#T = T[:,sorting_indices][sorting_indices,:]
#Z = Z[:,sorting_indices][sorting_indices,:]
Zleft,Zright = split(Z,2,axis=1)
#S4,S3 = split(Sright,2,axis=0)
Z11,Z21 = split(Zleft,2,axis=0)
self.Z11 = Z11
self.Z21 = Z21
if self.index == 0:
SigmaRet = dot(H01,dot(Z21,inv(Z11)))
else:
SigmaRet = dot(H01.conj(),dot(Z21,inv(Z11)))
self.SigmaRet = SigmaRet
print '- SimgaRet (',self.index,') shape: ',SigmaRet.shape
sigma = lil_matrix((self.p.multi*Ndim,self.p.multi*Ndim), dtype=complex128)
print '- sigma shape: ',sigma.shape
#implement polarization like (for spin up) reshape(-1,2) --> [:,1] = 0 --> reshape(shape(SigmaRet))
if self.index == 0:
if 'up' in self.current:
print 'Up polarized input'
SigmaRet.reshape(-1,2)[:,1] = 0
elif 'down' in self.current:
print 'Down polarized input'
SigmaRet.reshape(-1,2)[:,0] = 0
sigma[0:SigmaRet.shape[0], 0:SigmaRet.shape[1]] = SigmaRet
elif self.index == 1:
sigma[-SigmaRet.shape[0]:, -SigmaRet.shape[1]:] = SigmaRet
self.sigma=sigma
return sigma
def solve(self, wls):
"""Anisotropic solver.
INPUT
wls = wavelengths to scan (any asarray-able object).
OUTPUT
self.DEO1, self.DEE1, self.DEO3, self.DEE3 = power reflected
and transmitted.
"""
self.wls = S.atleast_1d(wls)
LAMBDA = self.LAMBDA
n = self.n
multilayer = self.multilayer
alpha = self.alpha
delta = self.delta
psi = self.psi
phi = self.phi
nlayers = len(multilayer)
i = S.arange(-n, n + 1)
nood = 2 * n + 1
hmax = nood - 1
DEO1 = S.zeros((nood, self.wls.size))
DEO3 = S.zeros_like(DEO1)
DEE1 = S.zeros_like(DEO1)
DEE3 = S.zeros_like(DEO1)
c1 = S.array([1., 0., 0.])
c3 = S.array([1., 0., 0.])
# grating on the xy plane
K = 2 * pi / LAMBDA * \
S.array([S.sin(phi), 0., S.cos(phi)], dtype=complex)
dirk1 = S.array([S.sin(alpha) * S.cos(delta),
S.sin(alpha) * S.sin(delta),
S.cos(alpha)])
# D polarization vector
u = S.array([S.cos(psi) * S.cos(alpha) * S.cos(delta) - S.sin(psi) * S.sin(delta),
S.cos(psi) * S.cos(alpha) * S.sin(delta) +
S.sin(psi) * S.cos(delta),
-S.cos(psi) * S.sin(alpha)])
kO1i = S.zeros((3, i.size), dtype=complex)
kE1i = S.zeros_like(kO1i)
kO3i = S.zeros_like(kO1i)
kE3i = S.zeros_like(kO1i)
Mp = S.zeros((4 * nood, 4 * nood, nlayers), dtype=complex)
M = S.zeros((4 * nood, 4 * nood, nlayers), dtype=complex)
dlt = (i == 0).astype(int)
for iwl, wl in enumerate(self.wls):
nO1 = nE1 = multilayer[0].mat.n(wl).item()
nO3 = nE3 = multilayer[-1].mat.n(wl).item()
# wavevectors
k = 2 * pi / wl
eps1 = S.diag(S.asarray([nE1, nO1, nO1]) ** 2)
eps3 = S.diag(S.asarray([nE3, nO3, nO3]) ** 2)
# ordinary wave
abskO1 = k * nO1
# abskO3 = k * nO3
# extraordinary wave
# abskE1 = k * nO1 *nE1 / S.sqrt(nO1**2 + (nE1**2 - nO1**2) * S.dot(-c1, dirk1)**2)
# abskE3 = k * nO3 *nE3 / S.sqrt(nO3**2 + (nE3**2 - nO3**2) * S.dot(-c3, dirk1)**2)
k1 = abskO1 * dirk1
kO1i[0, :] = k1[0] - i * K[0]
kO1i[1, :] = k1[1] * S.ones_like(i)
kO1i[2, :] = - \
dispersion_relation_ordinary(kO1i[0, :], kO1i[1, :], k, nO1)
kE1i[0, :] = kO1i[0, :]
kE1i[1, :] = kO1i[1, :]
kE1i[2,
:] = -dispersion_relation_extraordinary(kE1i[0,
:],
kE1i[1,
:],
k,
nO1,
nE1,
c1)
kO3i[0, :] = kO1i[0, :]
kO3i[1, :] = kO1i[1, :]
kO3i[
2, :] = dispersion_relation_ordinary(
kO3i[
0, :], kO3i[
1, :], k, nO3)
kE3i[0, :] = kO1i[0, :]
kE3i[1, :] = kO1i[1, :]
kE3i[
2, :] = dispersion_relation_extraordinary(
kE3i[
0, :], kE3i[
1, :], k, nO3, nE3, c3)
# k2i = S.r_[[k1[0] - i * K[0]], [k1[1] - i * K[1]], [k1[2] - i * K[2]]]
k2i = S.r_[[k1[0] - i * K[0]], [k1[1] - i * K[1]], [- i * K[2]]]
# aliases for constant wavevectors
kx = kO1i[0, :] # o kE1i(1,;), tanto e' lo stesso
ky = k1[1]
# matrices
I = S.eye(nood, dtype=complex)
ZERO = S.zeros((nood, nood), dtype=complex)
Kx = S.diag(kx / k)
Ky = ky / k * I
Kz = S.diag(k2i[2, :] / k)
KO1z = S.diag(kO1i[2, :] / k)
KE1z = S.diag(kE1i[2, :] / k)
KO3z = S.diag(kO3i[2, :] / k)
KE3z = S.diag(kE3i[2, :] / k)
ARO = Kx * eps1[0, 0] + Ky * eps1[1, 0] + KO1z * eps1[2, 0]
BRO = Kx * eps1[0, 1] + Ky * eps1[1, 1] + KO1z * eps1[2, 1]
CRO_1 = inv(Kx * eps1[0, 2] + Ky * eps1[1, 2] + KO1z * eps1[2, 2])
ARE = Kx * eps1[0, 0] + Ky * eps1[1, 0] + KE1z * eps1[2, 0]
BRE = Kx * eps1[0, 1] + Ky * eps1[1, 1] + KE1z * eps1[2, 1]
CRE_1 = inv(Kx * eps1[0, 2] + Ky * eps1[1, 2] + KE1z * eps1[2, 2])
ATO = Kx * eps3[0, 0] + Ky * eps3[1, 0] + KO3z * eps3[2, 0]
BTO = Kx * eps3[0, 1] + Ky * eps3[1, 1] + KO3z * eps3[2, 1]
CTO_1 = inv(Kx * eps3[0, 2] + Ky * eps3[1, 2] + KO3z * eps3[2, 2])
ATE = Kx * eps3[0, 0] + Ky * eps3[1, 0] + KE3z * eps3[2, 0]
BTE = Kx * eps3[0, 1] + Ky * eps3[1, 1] + KE3z * eps3[2, 1]
CTE_1 = inv(Kx * eps3[0, 2] + Ky * eps3[1, 2] + KE3z * eps3[2, 2])
DRE = c1[1] * KE1z - c1[2] * Ky
ERE = c1[2] * Kx - c1[0] * KE1z
FRE = c1[0] * Ky - c1[1] * Kx
DTE = c3[1] * KE3z - c3[2] * Ky
ETE = c3[2] * Kx - c3[0] * KE3z
FTE = c3[0] * Ky - c3[1] * Kx
b = S.r_[u[0] * dlt, u[1] * dlt, (k1[1] / k * u[2] - k1[2] / k * u[1]) * dlt, (
k1[2] / k * u[0] - k1[0] / k * u[2]) * dlt]
Ky_CRO_1 = ky / k * CRO_1
Ky_CRE_1 = ky / k * CRE_1
Kx_CRO_1 = kx[:, S.newaxis] / k * CRO_1
Kx_CRE_1 = kx[:, S.newaxis] / k * CRE_1
MR31 = -S.dot(Ky_CRO_1, ARO)
MR32 = -S.dot(Ky_CRO_1, BRO) - KO1z
MR33 = -S.dot(Ky_CRE_1, ARE)
MR34 = -S.dot(Ky_CRE_1, BRE) - KE1z
MR41 = S.dot(Kx_CRO_1, ARO) + KO1z
MR42 = S.dot(Kx_CRO_1, BRO)
MR43 = S.dot(Kx_CRE_1, ARE) + KE1z
MR44 = S.dot(Kx_CRE_1, BRE)
MR = S.asarray(S.bmat([[I, ZERO, I, ZERO],
[ZERO, I, ZERO, I],
[MR31, MR32, MR33, MR34],
[MR41, MR42, MR43, MR44]]))
Ky_CTO_1 = ky / k * CTO_1
Ky_CTE_1 = ky / k * CTE_1
Kx_CTO_1 = kx[:, S.newaxis] / k * CTO_1
Kx_CTE_1 = kx[:, S.newaxis] / k * CTE_1
MT31 = -S.dot(Ky_CTO_1, ATO)
MT32 = -S.dot(Ky_CTO_1, BTO) - KO3z
MT33 = -S.dot(Ky_CTE_1, ATE)
MT34 = -S.dot(Ky_CTE_1, BTE) - KE3z
MT41 = S.dot(Kx_CTO_1, ATO) + KO3z
MT42 = S.dot(Kx_CTO_1, BTO)
MT43 = S.dot(Kx_CTE_1, ATE) + KE3z
MT44 = S.dot(Kx_CTE_1, BTE)
MT = S.asarray(S.bmat([[I, ZERO, I, ZERO],
[ZERO, I, ZERO, I],
[MT31, MT32, MT33, MT34],
[MT41, MT42, MT43, MT44]]))
Mp.fill(0.0)
M.fill(0.0)
for nlayer in range(nlayers - 2, 0, -1): # internal layers
layer = multilayer[nlayer]
thickness = layer.thickness
EPS2, EPS21 = layer.getEPSFourierCoeffs(
wl, n, anisotropic=True)
# Exx = S.squeeze(EPS2[0, 0, :])
# Exx = toeplitz(S.flipud(Exx[0:hmax + 1]), Exx[hmax:])
Exy = S.squeeze(EPS2[0, 1, :])
Exy = toeplitz(S.flipud(Exy[0:hmax + 1]), Exy[hmax:])
Exz = S.squeeze(EPS2[0, 2, :])
Exz = toeplitz(S.flipud(Exz[0:hmax + 1]), Exz[hmax:])
Eyx = S.squeeze(EPS2[1, 0, :])
Eyx = toeplitz(S.flipud(Eyx[0:hmax + 1]), Eyx[hmax:])
Eyy = S.squeeze(EPS2[1, 1, :])
Eyy = toeplitz(S.flipud(Eyy[0:hmax + 1]), Eyy[hmax:])
Eyz = S.squeeze(EPS2[1, 2, :])
Eyz = toeplitz(S.flipud(Eyz[0:hmax + 1]), Eyz[hmax:])
Ezx = S.squeeze(EPS2[2, 0, :])
Ezx = toeplitz(S.flipud(Ezx[0:hmax + 1]), Ezx[hmax:])
Ezy = S.squeeze(EPS2[2, 1, :])
Ezy = toeplitz(S.flipud(Ezy[0:hmax + 1]), Ezy[hmax:])
Ezz = S.squeeze(EPS2[2, 2, :])
Ezz = toeplitz(S.flipud(Ezz[0:hmax + 1]), Ezz[hmax:])
Exx_1 = S.squeeze(EPS21[0, 0, :])
Exx_1 = toeplitz(S.flipud(Exx_1[0:hmax + 1]), Exx_1[hmax:])
Exx_1_1 = inv(Exx_1)
# lalanne
Ezz_1 = inv(Ezz)
Ky_Ezz_1 = ky / k * Ezz_1
Kx_Ezz_1 = kx[:, S.newaxis] / k * Ezz_1
Exz_Ezz_1 = S.dot(Exz, Ezz_1)
Eyz_Ezz_1 = S.dot(Eyz, Ezz_1)
H11 = 1j * S.dot(Ky_Ezz_1, Ezy)
H12 = 1j * S.dot(Ky_Ezz_1, Ezx)
H13 = S.dot(Ky_Ezz_1, Kx)
H14 = I - S.dot(Ky_Ezz_1, Ky)
H21 = 1j * S.dot(Kx_Ezz_1, Ezy)
H22 = 1j * S.dot(Kx_Ezz_1, Ezx)
H23 = S.dot(Kx_Ezz_1, Kx) - I
H24 = -S.dot(Kx_Ezz_1, Ky)
H31 = S.dot(Kx, Ky) + Exy - S.dot(Exz_Ezz_1, Ezy)
H32 = Exx_1_1 - S.dot(Ky, Ky) - S.dot(Exz_Ezz_1, Ezx)
H33 = 1j * S.dot(Exz_Ezz_1, Kx)
H34 = -1j * S.dot(Exz_Ezz_1, Ky)
H41 = S.dot(Kx, Kx) - Eyy + S.dot(Eyz_Ezz_1, Ezy)
H42 = -S.dot(Kx, Ky) - Eyx + S.dot(Eyz_Ezz_1, Ezx)
H43 = -1j * S.dot(Eyz_Ezz_1, Kx)
H44 = 1j * S.dot(Eyz_Ezz_1, Ky)
H = 1j * S.diag(S.repeat(S.diag(Kz), 4)) + \
S.asarray(S.bmat([[H11, H12, H13, H14],
[H21, H22, H23, H24],
[H31, H32, H33, H34],
[H41, H42, H43, H44]]))
q, W = eig(H)
W1, W2, W3, W4 = S.split(W, 4)
#
# boundary conditions
#
# x = [R T]
# R = [ROx ROy REx REy]
# T = [TOx TOy TEx TEy]
# b + MR.R = M1p.c
# M1.c = M2p.c
# ...
# ML.c = MT.T
# therefore: b + MR.R = (M1p.M1^-1.M2p.M2^-1. ...).MT.T
# missing equations from (46)..(49) in glytsis_rigorous
# [b] = [-MR Mtot.MT] [R]
# [0] [...........] [T]
z = S.zeros_like(q)
z[S.where(q.real > 0)] = -thickness
D = S.exp(k * q * z)
Sy0 = W1 * D[S.newaxis, :]
Sx0 = W2 * D[S.newaxis, :]
Uy0 = W3 * D[S.newaxis, :]
Ux0 = W4 * D[S.newaxis, :]
z = thickness * S.ones_like(q)
z[S.where(q.real > 0)] = 0
D = S.exp(k * q * z)
D1 = S.exp(-1j * k2i[2, :] * thickness)
Syd = D1[:, S.newaxis] * W1 * D[S.newaxis, :]
Sxd = D1[:, S.newaxis] * W2 * D[S.newaxis, :]
Uyd = D1[:, S.newaxis] * W3 * D[S.newaxis, :]
Uxd = D1[:, S.newaxis] * W4 * D[S.newaxis, :]
Mp[:, :, nlayer] = S.r_[Sx0, Sy0, -1j * Ux0, -1j * Uy0]
M[:, :, nlayer] = S.r_[Sxd, Syd, -1j * Uxd, -1j * Uyd]
Mtot = S.eye(4 * nood, dtype=complex)
for nlayer in range(1, nlayers - 1):
Mtot = S.dot(
S.dot(Mtot, Mp[:, :, nlayer]), inv(M[:, :, nlayer]))
BC_b = S.r_[b, S.zeros_like(b)]
BC_A1 = S.c_[-MR, S.dot(Mtot, MT)]
BC_A2 = S.asarray(S.bmat(
[[(c1[0] * I - c1[2] * S.dot(CRO_1, ARO)), (c1[1] * I - c1[2] * S.dot(CRO_1, BRO)), ZERO, ZERO, ZERO,
ZERO, ZERO, ZERO],
[ZERO, ZERO, (DRE - S.dot(S.dot(FRE, CRE_1), ARE)), (ERE - S.dot(S.dot(FRE, CRE_1), BRE)), ZERO, ZERO,
ZERO, ZERO],
[ZERO, ZERO, ZERO, ZERO, (c3[0] * I - c3[2] * S.dot(CTO_1, ATO)),
(c3[1] * I - c3[2] * S.dot(CTO_1, BTO)), ZERO, ZERO],
[ZERO, ZERO, ZERO, ZERO, ZERO, ZERO, (DTE - S.dot(S.dot(FTE, CTE_1), ATE)),
(ETE - S.dot(S.dot(FTE, CTE_1), BTE))]]))
BC_A = S.r_[BC_A1, BC_A2]
x = linsolve(BC_A, BC_b)
ROx, ROy, REx, REy, TOx, TOy, TEx, TEy = S.split(x, 8)
ROz = -S.dot(CRO_1, (S.dot(ARO, ROx) + S.dot(BRO, ROy)))
REz = -S.dot(CRE_1, (S.dot(ARE, REx) + S.dot(BRE, REy)))
TOz = -S.dot(CTO_1, (S.dot(ATO, TOx) + S.dot(BTO, TOy)))
TEz = -S.dot(CTE_1, (S.dot(ATE, TEx) + S.dot(BTE, TEy)))
denom = (k1[2] - S.dot(u, k1) * u[2]).real
DEO1[:, iwl] = -((S.absolute(ROx) ** 2 + S.absolute(ROy) ** 2 + S.absolute(ROz) ** 2) * S.conj(kO1i[2, :]) -
(ROx * kO1i[0, :] + ROy * kO1i[1, :] + ROz * kO1i[2, :]) * S.conj(ROz)).real / denom
DEE1[:, iwl] = -((S.absolute(REx) ** 2 + S.absolute(REy) ** 2 + S.absolute(REz) ** 2) * S.conj(kE1i[2, :]) -
(REx * kE1i[0, :] + REy * kE1i[1, :] + REz * kE1i[2, :]) * S.conj(REz)).real / denom
DEO3[:, iwl] = ((S.absolute(TOx) ** 2 + S.absolute(TOy) ** 2 + S.absolute(TOz) ** 2) * S.conj(kO3i[2, :]) -
(TOx * kO3i[0, :] + TOy * kO3i[1, :] + TOz * kO3i[2, :]) * S.conj(TOz)).real / denom
DEE3[:, iwl] = ((S.absolute(TEx) ** 2 + S.absolute(TEy) ** 2 + S.absolute(TEz) ** 2) * S.conj(kE3i[2, :]) -
(TEx * kE3i[0, :] + TEy * kE3i[1, :] + TEz * kE3i[2, :]) * S.conj(TEz)).real / denom
# save the results
self.DEO1 = DEO1
self.DEE1 = DEE1
self.DEO3 = DEO3
self.DEE3 = DEE3
return self
TilesHor = (TargetSize[0]*PixPerTile[1]*TilesVert)/(TargetSize[1]*PixPerTile[0])
Tiles = scipy.array((TilesHor, TilesVert), dtype=int)
TilesPerNode = scipy.array((TilesHor, TilesVert/NPlacers), dtype=int)
TotalTilesPerNode = scipy.prod(TilesPerNode)
Pixels = Tiles*PixPerTile
UnscaledWidth = (TargetSize[1]*Tiles[0])/Tiles[1]# the width of the original size image to yield the correct aspect ratio
CropMargin = (TargetSize[0] - UnscaledWidth)/2
#TargetImg.crop((0,0,))
#TargetImg.resize(Pixels)
CroppedImg = TargetImg.transform((UnscaledWidth,TargetSize[1]), Image.EXTENT, (CropMargin,0, CropMargin+UnscaledWidth,TargetImg.size[1]))
CroppedArr = scipy.array(CroppedImg)
#%% reduce CroppedArr to NPlacers NodeArrs
NodeHeightInCroppedArr = float(TargetSize[1])/NPlacers
sections = scipy.array(scipy.arange(NodeHeightInCroppedArr, TargetSize[1], NodeHeightInCroppedArr), dtype=int)
NodeArrs = scipy.split(CroppedArr, sections, axis=0) # each tile in the image
#%% reduce NodeArr to TilesPerNode TileArrs
NodeArr = NodeArrs.pop(0)
pm = photo_match.photoMatch()
TileArrs = [] # each tile in the image
TileCompacts = [] # each tile in the image
whichSources = scipy.zeros((TotalTilesPerNode), dtype=int)
Distances = scipy.ones((TotalTilesPerNode))*scipy.Inf # the quality of the current fit for each tile (put at infinity to start with)
TileWidthInCroppedArr = float(UnscaledWidth)/Tiles[0]
vertSections = scipy.array(scipy.arange(TileWidthInCroppedArr, UnscaledWidth-.5*TileWidthInCroppedArr, TileWidthInCroppedArr), dtype=int)
VertSplitArrs = scipy.split(NodeArr, vertSections, axis=1)
for VertSplitArr in VertSplitArrs:
TileHeightInCroppedArr = float(VertSplitArr.shape[0])/Tiles[1]*NPlacers
def solve(self, wls):
"""Isotropic solver.
INPUT
wls = wavelengths to scan (any asarray-able object).
OUTPUT
self.DE1, self.DE3 = power reflected and transmitted.
NOTE
see:
Moharam, "Formulation for stable and efficient implementation
of the rigorous coupled-wave analysis of binary gratings",
JOSA A, 12(5), 1995
Lalanne, "Highly improved convergence of the coupled-wave
method for TM polarization", JOSA A, 13(4), 1996
Moharam, "Stable implementation of the rigorous coupled-wave
analysis for surface-relief gratings: enhanced trasmittance
matrix approach", JOSA A, 12(5), 1995
"""
self.wls = S.atleast_1d(wls)
LAMBDA = self.LAMBDA
n = self.n
multilayer = self.multilayer
alpha = self.alpha
delta = self.delta
psi = self.psi
phi = self.phi
nlayers = len(multilayer)
i = S.arange(-n, n + 1)
nood = 2 * n + 1
hmax = nood - 1
# grating vector (on the xz plane)
# grating on the xy plane
K = 2 * pi / LAMBDA * np.array(
[S.sin(phi), 0., S.cos(phi)], dtype=complex)
DE1 = S.zeros((nood, self.wls.size))
DE3 = S.zeros_like(DE1)
dirk1 = np.array([
S.sin(alpha) * S.cos(delta),
S.sin(alpha) * S.sin(delta),
S.cos(alpha)
])
# usefull matrices
I = S.eye(i.size)
I2 = S.eye(i.size * 2)
ZERO = S.zeros_like(I)
X = S.zeros((2 * nood, 2 * nood, nlayers), dtype=complex)
MTp1 = S.zeros((2 * nood, 2 * nood, nlayers), dtype=complex)
MTp2 = S.zeros_like(MTp1)
EPS2 = S.zeros(2 * hmax + 1, dtype=complex)
EPS21 = S.zeros_like(EPS2)
dlt = (i == 0).astype(int)
for iwl, wl in enumerate(self.wls):
# free space wavevector
k = 2 * pi / wl
n1 = multilayer[0].mat.n(wl).item()
n3 = multilayer[-1].mat.n(wl).item()
# incident plane wave wavevector
k1 = k * n1 * dirk1
# all the other wavevectors
tmp_x = k1[0] - i * K[0]
tmp_y = k1[1] * S.ones_like(i)
tmp_z = dispersion_relation_ordinary(tmp_x, tmp_y, k, n1)
k1i = S.r_[[tmp_x], [tmp_y], [tmp_z]]
# k2i = S.r_[[k1[0] - i*K[0]], [k1[1] - i * K[1]], [-i * K[2]]]
tmp_z = dispersion_relation_ordinary(tmp_x, tmp_y, k, n3)
k3i = S.r_[[k1i[0, :]], [k1i[1, :]], [tmp_z]]
# aliases for constant wavevectors
kx = k1i[0, :]
ky = k1[1]
# angles of reflection
# phi_i = S.arctan2(ky,kx)
phi_i = S.arctan2(ky, kx.real) # OKKIO
Kx = S.diag(kx / k)
Ky = ky / k * I
Z1 = S.diag(k1i[2, :] / (k * n1**2))
Y1 = S.diag(k1i[2, :] / k)
Z3 = S.diag(k3i[2, :] / (k * n3**2))
Y3 = S.diag(k3i[2, :] / k)
# Fc = S.diag(S.cos(phi_i))
fc = S.cos(phi_i)
# Fs = S.diag(S.sin(phi_i))
fs = S.sin(phi_i)
MR = S.asarray(
S.bmat([[I, ZERO], [-1j * Y1, ZERO], [ZERO, I],
[ZERO, -1j * Z1]]))
MT = S.asarray(
S.bmat([[I, ZERO], [1j * Y3, ZERO], [ZERO, I], [ZERO,
1j * Z3]]))
# internal layers (grating or layer)
X.fill(0.0)
MTp1.fill(0.0)
MTp2.fill(0.0)
for nlayer in range(nlayers - 2, 0, -1): # internal layers
layer = multilayer[nlayer]
d = layer.thickness
EPS2, EPS21 = layer.getEPSFourierCoeffs(wl,
n,
anisotropic=False)
E = toeplitz(EPS2[hmax::-1], EPS2[hmax:])
E1 = toeplitz(EPS21[hmax::-1], EPS21[hmax:])
E11 = inv(E1)
# B = S.dot(Kx, linsolve(E,Kx)) - I
B = kx[:, S.newaxis] / k * linsolve(E, Kx) - I
# A = S.dot(Kx, Kx) - E
A = S.diag((kx / k)**2) - E
# Note: solution bug alfredo
# randomizzo Kx un po' a caso finche' cond(A) e' piccolo (<1e10)
# soluzione sporca... :-(
# per certi kx, l'operatore di helmholtz ha 2 autovalori nulli e A, B
# non sono invertibili --> cambio leggermente i kx... ma dovrei invece
# trattare separatamente (analiticamente) questi casi
if cond(A) > 1e10:
warning("BAD CONDITIONING: randomization of kx")
while cond(A) > 1e10:
Kx = Kx * (1 + 1e-9 * S.rand())
B = kx[:, S.newaxis] / k * linsolve(E, Kx) - I
A = S.diag((kx / k)**2) - E
if S.absolute(K[2] / k) > 1e-10:
raise ValueError(
"First Order Helmholtz Operator not implemented, yet!")
elif ky == 0 or S.allclose(S.diag(Ky / ky * k), 1):
# lalanne
# H_U_reduced = S.dot(Ky, Ky) + A
H_U_reduced = (ky / k)**2 * I + A
# H_S_reduced = S.dot(Ky, Ky) + S.dot(Kx, linsolve(E, S.dot(Kx, E11))) - E11
H_S_reduced = ((ky / k)**2 * I + kx[:, S.newaxis] / k *
linsolve(E, kx[:, S.newaxis] / k * E11) -
E11)
q1, W1 = eig(H_U_reduced)
q1 = S.sqrt(q1)
q2, W2 = eig(H_S_reduced)
q2 = S.sqrt(q2)
# boundary conditions
# V11 = S.dot(linsolve(A, W1), S.diag(q1))
V11 = linsolve(A, W1) * q1[S.newaxis, :]
V12 = (ky / k) * S.dot(linsolve(A, Kx), W2)
V21 = (ky / k) * S.dot(linsolve(B, Kx), linsolve(E, W1))
# V22 = S.dot(linsolve(B, W2), S.diag(q2))
V22 = linsolve(B, W2) * q2[S.newaxis, :]
# Vss = S.dot(Fc, V11)
Vss = fc[:, S.newaxis] * V11
# Wss = S.dot(Fc, W1) + S.dot(Fs, V21)
Wss = fc[:, S.newaxis] * W1 + fs[:, S.newaxis] * V21
# Vsp = S.dot(Fc, V12) - S.dot(Fs, W2)
Vsp = fc[:, S.newaxis] * V12 - fs[:, S.newaxis] * W2
# Wsp = S.dot(Fs, V22)
Wsp = fs[:, S.newaxis] * V22
# Wpp = S.dot(Fc, V22)
Wpp = fc[:, S.newaxis] * V22
# Vpp = S.dot(Fc, W2) + S.dot(Fs, V12)
Vpp = fc[:, S.newaxis] * W2 + fs[:, S.newaxis] * V12
# Wps = S.dot(Fc, V21) - S.dot(Fs, W1)
Wps = fc[:, S.newaxis] * V21 - fs[:, S.newaxis] * W1
# Vps = S.dot(Fs, V11)
Vps = fs[:, S.newaxis] * V11
Mc2bar = S.asarray(
S.bmat([
[Vss, Vsp, Vss, Vsp],
[Wss, Wsp, -Wss, -Wsp],
[Wps, Wpp, -Wps, -Wpp],
[Vps, Vpp, Vps, Vpp],
]))
x = S.r_[S.exp(-k * q1 * d), S.exp(-k * q2 * d)]
# Mc1 = S.dot(Mc2bar, S.diag(S.r_[S.ones_like(x), x]))
xx = S.r_[S.ones_like(x), x]
Mc1 = Mc2bar * xx[S.newaxis, :]
X[:, :, nlayer] = S.diag(x)
MTp = linsolve(Mc2bar, MT)
MTp1[:, :, nlayer] = MTp[0:2 * nood, :]
MTp2 = MTp[2 * nood:, :]
MT = S.dot(
Mc1,
S.r_[I2,
S.
dot(MTp2,
linsolve(MTp1[:, :, nlayer], X[:, :,
nlayer])), ],
)
else:
ValueError(
"Second Order Helmholtz Operator not implemented, yet!"
)
# M = S.asarray(S.bmat([-MR, MT]))
M = S.c_[-MR, MT]
b = S.r_[S.sin(psi) * dlt,
1j * S.sin(psi) * n1 * S.cos(alpha) * dlt,
-1j * S.cos(psi) * n1 * dlt,
S.cos(psi) * S.cos(alpha) * dlt, ]
x = linsolve(M, b)
R, T = S.split(x, 2)
Rs, Rp = S.split(R, 2)
for ii in range(1, nlayers - 1):
T = S.dot(linsolve(MTp1[:, :, ii], X[:, :, ii]), T)
Ts, Tp = S.split(T, 2)
DE1[:, iwl] = (k1i[2, :] / (k1[2])).real * S.absolute(Rs)**2 + (
k1i[2, :] / (k1[2] * n1**2)).real * S.absolute(Rp)**2
DE3[:, iwl] = (k3i[2, :] / (k1[2])).real * S.absolute(Ts)**2 + (
k3i[2, :] / (k1[2] * n3**2)).real * S.absolute(Tp)**2
# save the results
self.DE1 = DE1
self.DE3 = DE3
return self
def process(pars, data=None):
#%% load the parameters that CAN be specified from the command line
NPlacers = pars['NPlacers']
NScrapers = pars['NScrapers']
iters = pars['iters']
MaxTilesVert = pars['MaxTilesVert']
per_page = pars['per_page']
fidelity = pars['fidelity']
poolSize = pars['poolSize']
if (data != None):
tags = data['search'].split(', ')
else:
#tags = ('Minimalism',)
tags = ('Face','Leuven','Belgium','Computer')
#tags = ('Bussum','Football','PSV','Minimalism','urbex')
#%% MPI stuff
comm = MPI.COMM_WORLD
rank = comm.Get_rank()
size = comm.Get_size()
status = MPI.Status()
#%% initiate plogger
#execfile('../mosaic_gui/daemon/params.par')
logger = plogger.PLogger(rank, host_url=LOGGER_HOST)
#%% print the values of those parameters that CAN be specified via the command line
#for key, value in pars.iteritems():
#print "M{}: {} is now {}".format(rank, key, value)
#%% identify oneself
#print "Master, process {} out of {}".format(rank, size)
#print "M{}: > init".format(rank)
logger.write('Initializing', status=plogger.INIT)
#%% initialize the photo matcher
pmPars = {'fidelity': fidelity}
pm = photo_match.photoMatch(pmPars)
# create empty save-path
if not pars['useDB']:
if (os.path.exists(pars['savepath'])):
shutil.rmtree(pars['savepath'], ignore_errors=True)
os.mkdir(pars['savepath'])
#%% call the scrapers right at the beginning, as it is probably the slowest
PixPerTile = scipy.array((75,75))
ComparePixPerTile = scipy.array((fidelity,fidelity))
scraperPars = {'pm': pm, 'tags': tags, 'PixPerTile': PixPerTile, 'poolSize': poolSize}
for scraper in range(1,1+NScrapers):
comm.send(scraperPars, dest=scraper, tag=0)
TilesVert = int(MaxTilesVert/NPlacers) * NPlacers
TargetImg = Image.open('./output/doesnotmatter.jpg')
#TargetImg = Image.open('./Matilda.JPG')
#TargetImg = Image.open('./rainbow_flag_by_kelly.jpg')
#TargetImg = Image.open('./korneel_test.jpg')
TargetSize = TargetImg.size
TilesHor = (TargetSize[0]*PixPerTile[1]*TilesVert)/(TargetSize[1]*PixPerTile[0])
Tiles = scipy.array((TilesHor, TilesVert), dtype=int)
TilesPerNode = scipy.array((TilesHor, TilesVert/NPlacers), dtype=int)
Pixels = Tiles*PixPerTile
ratio = 2.0 / 3.0
TargetChunkPixels = Tiles*scipy.int_(PixPerTile*ratio)
ComparePixels = Tiles*scipy.int_(ComparePixPerTile*ratio)
#%% adjust the image to have the correct shape (aspect ratio) for turning it into a mosaic
UnscaledWidth = (TargetSize[1]*Tiles[0])/Tiles[1]# the width of the original size image to yield the correct aspect ratio
CropMargin = (TargetSize[0] - UnscaledWidth)/2
#TargetImg.crop((0,0,))
#TargetImg.resize(Pixels)
CroppedImg = TargetImg.transform((ComparePixels[0],ComparePixels[1]), Image.EXTENT, (CropMargin,0, CropMargin+UnscaledWidth,TargetImg.size[1]))
CroppedArr = color.rgb2lab(scipy.array(CroppedImg))
#%% send each placer some parameters
placerPars = {'TilesPerNode': TilesPerNode, 'UnscaledWidth': UnscaledWidth,
'Tiles': Tiles, 'pm': pm, 'iters': iters, 'PixPerTile': PixPerTile, 'ComparePixPerTile' : ComparePixPerTile}
for placer in range(NPlacers):
comm.send(placerPars, dest=1+NScrapers+placer, tag=0)
#print "M{}: < init".format(rank)
#print "M{}: > dividing image".format(rank)
#%% reduce CroppedArr to NPlacers NodeArrs
NodeArrs = scipy.split(CroppedArr, NPlacers, axis=0)
#%% send each of the placers its piece of the picture
for placer in range(NPlacers):
comm.send(NodeArrs[placer], dest=1+NScrapers+placer, tag=1)
#%% create the final image and divide it into pieces for the placers to FinalArr = CroppedArr.copy()
# now the division has to be accurate!
FinalArr = scipy.zeros((TargetChunkPixels[1], TargetChunkPixels[0], 3), dtype='i')
# FinalArr = scipy.zeros((Tiles[1]*PixPerTile[1], Tiles[0]*PixPerTile[0], 3), dtype='i')
NodeFinalArrs = scipy.split(FinalArr, NPlacers, axis=0)
#print "M{}: < dividing image".format(rank)
#%% listen to the placers' intermediate results
tempNodeFinalArr = NodeFinalArrs[0].copy() # for receiving the data, before it is known whence it came
for it in range(iters):
#print "M{}: > not listening to the placer to scraper broadcast".format(rank)
dummy_arrs = scipy.zeros((per_page, PixPerTile[1], PixPerTile[0], 3), dtype=scipy.uint8)
for scraper in range(1, 1+NScrapers):
#print "M{}: not listening to scraper {}".format(rank, scraper)
comm.Bcast(dummy_arrs, root=scraper)
#print "M{}: < not listening to the placer to scraper broadcast".format(rank)
#print "M{}: now listening for placer results at iter {} out of {}".format(rank, it, iters)
#print "M{}: > listening for results".format(rank)
logger.write('Listening for placers', status=plogger.RECEIVING)
for p in range(NPlacers): # listen for the placers
#print "M{}: NodeFinalArrs[{}] has shape ".format(rank, placer), NodeFinalArrs[placer].shape
#print "M{}: NodeFinalArrs[{}] has type ".format(rank, placer), type(NodeFinalArrs[placer][0,0,0])
comm.Recv([tempNodeFinalArr, MPI.INT], source=MPI.ANY_SOURCE, tag=4, status=status)
placer = status.Get_source()
NodeFinalArrs[placer-(1+NScrapers)][:,:,:] = tempNodeFinalArr
#print "M{}: < listening for results".format(rank)
#print "M{}: > writing image".format(rank)
partial_filename = 'output/mosaic_{}.png'.format(it)
FinalImg = Image.fromarray(scipy.array(FinalArr, dtype=scipy.uint8), 'RGB')
FinalImg.save(partial_filename) # for fewer output images
# Notify gui
logger.emit_partial(partial_filename)
#print "M{}: < writing image at iter {}".format(rank, it)
writepars = pars.copy()
del(writepars['savepath'])
strrep = '_'.join(['{}{:d}'.format(item, value) for item, value in sorted(writepars.items())])
final_filename = 'output/final{}_{}.png'.format(strrep, int(time.time()))
FinalImg.save(final_filename)
os.chmod(final_filename, 0744)
print "M{}: Final image saved".format(rank)
shutil.copy('log', 'output/log_'+strrep)
# email result
if (data != None):
msg = MIMEMultipart()
msg['Subject'] = "KU Leuven openbedrijvendag - uw mozaiek"
msg['From'] = "SuperPi <*****@*****.**>"
msg['To'] = data['email']
fp = open(final_filename, 'rb')
img = MIMEImage(fp.read())
fp.close()
msg.attach(img)
s = smtplib.SMTP('mail4.cs.kuleuven.be')
s.sendmail('*****@*****.**', [msg['To']], msg.as_string())
s.quit()
logger.emit_finished(final_filename)
#%% signal completion
logger.write('Finished', status=plogger.FINISHED)
comm.barrier()
def solve(self, wls):
"""Isotropic solver.
INPUT
wls = wavelengths to scan (any asarray-able object).
OUTPUT
self.DE1, self.DE3 = power reflected and transmitted.
NOTE
see:
Moharam, "Formulation for stable and efficient implementation
of the rigorous coupled-wave analysis of binary gratings",
JOSA A, 12(5), 1995
Lalanne, "Highly improved convergence of the coupled-wave
method for TM polarization", JOSA A, 13(4), 1996
Moharam, "Stable implementation of the rigorous coupled-wave
analysis for surface-relief gratings: enhanced trasmittance
matrix approach", JOSA A, 12(5), 1995
"""
self.wls = S.atleast_1d(wls)
LAMBDA = self.LAMBDA
n = self.n
multilayer = self.multilayer
alpha = self.alpha
delta = self.delta
psi = self.psi
phi = self.phi
nlayers = len(multilayer)
i = S.arange(-n, n + 1)
nood = 2 * n + 1
hmax = nood - 1
# grating vector (on the xz plane)
# grating on the xy plane
K = 2 * pi / LAMBDA * \
S.array([S.sin(phi), 0., S.cos(phi)], dtype=complex)
DE1 = S.zeros((nood, self.wls.size))
DE3 = S.zeros_like(DE1)
dirk1 = S.array([S.sin(alpha) * S.cos(delta),
S.sin(alpha) * S.sin(delta),
S.cos(alpha)])
# usefull matrices
I = S.eye(i.size)
I2 = S.eye(i.size * 2)
ZERO = S.zeros_like(I)
X = S.zeros((2 * nood, 2 * nood, nlayers), dtype=complex)
MTp1 = S.zeros((2 * nood, 2 * nood, nlayers), dtype=complex)
MTp2 = S.zeros_like(MTp1)
EPS2 = S.zeros(2 * hmax + 1, dtype=complex)
EPS21 = S.zeros_like(EPS2)
dlt = (i == 0).astype(int)
for iwl, wl in enumerate(self.wls):
# free space wavevector
k = 2 * pi / wl
n1 = multilayer[0].mat.n(wl).item()
n3 = multilayer[-1].mat.n(wl).item()
# incident plane wave wavevector
k1 = k * n1 * dirk1
# all the other wavevectors
tmp_x = k1[0] - i * K[0]
tmp_y = k1[1] * S.ones_like(i)
tmp_z = dispersion_relation_ordinary(tmp_x, tmp_y, k, n1)
k1i = S.r_[[tmp_x], [tmp_y], [tmp_z]]
# k2i = S.r_[[k1[0] - i*K[0]], [k1[1] - i * K[1]], [-i * K[2]]]
tmp_z = dispersion_relation_ordinary(tmp_x, tmp_y, k, n3)
k3i = S.r_[[k1i[0, :]], [k1i[1, :]], [tmp_z]]
# aliases for constant wavevectors
kx = k1i[0, :]
ky = k1[1]
# angles of reflection
# phi_i = S.arctan2(ky,kx)
phi_i = S.arctan2(ky, kx.real) # OKKIO
Kx = S.diag(kx / k)
Ky = ky / k * I
Z1 = S.diag(k1i[2, :] / (k * n1 ** 2))
Y1 = S.diag(k1i[2, :] / k)
Z3 = S.diag(k3i[2, :] / (k * n3 ** 2))
Y3 = S.diag(k3i[2, :] / k)
# Fc = S.diag(S.cos(phi_i))
fc = S.cos(phi_i)
# Fs = S.diag(S.sin(phi_i))
fs = S.sin(phi_i)
MR = S.asarray(S.bmat([[I, ZERO],
[-1j * Y1, ZERO],
[ZERO, I],
[ZERO, -1j * Z1]]))
MT = S.asarray(S.bmat([[I, ZERO],
[1j * Y3, ZERO],
[ZERO, I],
[ZERO, 1j * Z3]]))
# internal layers (grating or layer)
X.fill(0.0)
MTp1.fill(0.0)
MTp2.fill(0.0)
for nlayer in range(nlayers - 2, 0, -1): # internal layers
layer = multilayer[nlayer]
d = layer.thickness
EPS2, EPS21 = layer.getEPSFourierCoeffs(
wl, n, anisotropic=False)
E = toeplitz(EPS2[hmax::-1], EPS2[hmax:])
E1 = toeplitz(EPS21[hmax::-1], EPS21[hmax:])
E11 = inv(E1)
# B = S.dot(Kx, linsolve(E,Kx)) - I
B = kx[:, S.newaxis] / k * linsolve(E, Kx) - I
# A = S.dot(Kx, Kx) - E
A = S.diag((kx / k) ** 2) - E
# Note: solution bug alfredo
# randomizzo Kx un po' a caso finche' cond(A) e' piccolo (<1e10)
# soluzione sporca... :-(
# per certi kx, l'operatore di helmholtz ha 2 autovalori nulli e A, B
# non sono invertibili --> cambio leggermente i kx... ma dovrei invece
# trattare separatamente (analiticamente) questi casi
if cond(A) > 1e10:
warning('BAD CONDITIONING: randomization of kx')
while cond(A) > 1e10:
Kx = Kx * (1 + 1e-9 * S.rand())
B = kx[:, S.newaxis] / k * linsolve(E, Kx) - I
A = S.diag((kx / k) ** 2) - E
if S.absolute(K[2] / k) > 1e-10:
raise ValueError(
'First Order Helmholtz Operator not implemented, yet!')
elif ky == 0 or S.allclose(S.diag(Ky / ky * k), 1):
# lalanne
# H_U_reduced = S.dot(Ky, Ky) + A
H_U_reduced = (ky / k) ** 2 * I + A
# H_S_reduced = S.dot(Ky, Ky) + S.dot(Kx, linsolve(E, S.dot(Kx, E11))) - E11
H_S_reduced = (ky / k) ** 2 * I + kx[:, S.newaxis] / k * linsolve(E,
kx[:, S.newaxis] / k * E11) - E11
q1, W1 = eig(H_U_reduced)
q1 = S.sqrt(q1)
q2, W2 = eig(H_S_reduced)
q2 = S.sqrt(q2)
# boundary conditions
# V11 = S.dot(linsolve(A, W1), S.diag(q1))
V11 = linsolve(A, W1) * q1[S.newaxis, :]
V12 = (ky / k) * S.dot(linsolve(A, Kx), W2)
V21 = (ky / k) * S.dot(linsolve(B, Kx), linsolve(E, W1))
# V22 = S.dot(linsolve(B, W2), S.diag(q2))
V22 = linsolve(B, W2) * q2[S.newaxis, :]
# Vss = S.dot(Fc, V11)
Vss = fc[:, S.newaxis] * V11
# Wss = S.dot(Fc, W1) + S.dot(Fs, V21)
Wss = fc[:, S.newaxis] * W1 + fs[:, S.newaxis] * V21
# Vsp = S.dot(Fc, V12) - S.dot(Fs, W2)
Vsp = fc[:, S.newaxis] * V12 - fs[:, S.newaxis] * W2
# Wsp = S.dot(Fs, V22)
Wsp = fs[:, S.newaxis] * V22
# Wpp = S.dot(Fc, V22)
Wpp = fc[:, S.newaxis] * V22
# Vpp = S.dot(Fc, W2) + S.dot(Fs, V12)
Vpp = fc[:, S.newaxis] * W2 + fs[:, S.newaxis] * V12
# Wps = S.dot(Fc, V21) - S.dot(Fs, W1)
Wps = fc[:, S.newaxis] * V21 - fs[:, S.newaxis] * W1
# Vps = S.dot(Fs, V11)
Vps = fs[:, S.newaxis] * V11
Mc2bar = S.asarray(S.bmat([[Vss, Vsp, Vss, Vsp],
[Wss, Wsp, -Wss, -Wsp],
[Wps, Wpp, -Wps, -Wpp],
[Vps, Vpp, Vps, Vpp]]))
x = S.r_[S.exp(-k * q1 * d), S.exp(-k * q2 * d)]
# Mc1 = S.dot(Mc2bar, S.diag(S.r_[S.ones_like(x), x]))
xx = S.r_[S.ones_like(x), x]
Mc1 = Mc2bar * xx[S.newaxis, :]
X[:, :, nlayer] = S.diag(x)
MTp = linsolve(Mc2bar, MT)
MTp1[:, :, nlayer] = MTp[0:2 * nood, :]
MTp2 = MTp[2 * nood:, :]
MT = S.dot(
Mc1, S.r_[
I2, S.dot(
MTp2, linsolve(
MTp1[
:, :, nlayer], X[
:, :, nlayer]))])
else:
ValueError(
'Second Order Helmholtz Operator not implemented, yet!')
# M = S.asarray(S.bmat([-MR, MT]))
M = S.c_[-MR, MT]
b = S.r_[S.sin(psi) * dlt,
1j * S.sin(psi) * n1 * S.cos(alpha) * dlt,
-1j * S.cos(psi) * n1 * dlt,
S.cos(psi) * S.cos(alpha) * dlt]
x = linsolve(M, b)
R, T = S.split(x, 2)
Rs, Rp = S.split(R, 2)
for ii in range(1, nlayers - 1):
T = S.dot(linsolve(MTp1[:, :, ii], X[:, :, ii]), T)
Ts, Tp = S.split(T, 2)
DE1[:, iwl] = (k1i[2, :] / (k1[2])).real * S.absolute(Rs) ** 2 + \
(k1i[2, :] / (k1[2] * n1 ** 2)).real * \
S.absolute(Rp) ** 2
DE3[:, iwl] = (k3i[2, :] / (k1[2])).real * S.absolute(Ts) ** 2 + \
(k3i[2, :] / (k1[2] * n3 ** 2)).real * \
S.absolute(Tp) ** 2
# save the results
self.DE1 = DE1
self.DE3 = DE3
return self
def generate_sigma(self):
import networkx as nx
from scipy.linalg import inv, schur, eig
from scipy.sparse import lil_matrix
from numpy import asarray_chkfinite, isfinite, inf
from aux import SparseBlocks, eigenvector_from_eigenvalue, all_elements_are_unique
from scipy import argsort, dot, eye, hstack, vstack, zeros, complex128, split, asarray, diag, array
# should be able to turn zplus off, but then i need better eigenvalue comparison
E = self.p.E + self.p.zplus
Ndim = len(self.p.tuple_canvas_coordinates)
block = self.graph.order() / 2
I = eye(block)
Zeros = zeros((block, block))
Hlead = nx.to_numpy_matrix(self.graph,
nodelist=self.nodelist,
dtype=complex128)
self.Hlead = Hlead
#import pudb; pudb.set_trace()
# add 4*self.t0 because the matrix from graph lacks diagonal (no self-loops)
try:
H00 = asarray_chkfinite(Hlead[:block, :block]) + 4 * self.p.t0 * I
self.H00 = H00
except ValueError:
print 'H00 contains infs or NaNs'
import pudb
pudb.set_trace()
try:
H01 = asarray_chkfinite(Hlead[:block, block:])
self.H01 = H01
except ValueError:
print 'H01 contains infs or NaNs'
import pudb
pudb.set_trace()
inv_H01 = inv(H01)
while not isfinite(inv_H01).all():
print 'inv_H01 contains infs or NaNs, repeating'
inv_H01 = inv(H01)
#import pudb; pudb.set_trace()
self.inv_H01 = inv_H01
CompanionMatrix_array = vstack(
(hstack((Zeros, I)),
hstack((dot(-inv_H01,
H01.conj().T), dot(inv_H01, E * I - H00)))))
if not isfinite(CompanionMatrix_array).all():
print 'CompanionMatrix contains infs or NaNs'
import pudb
pudb.set_trace()
#CompanionMatrix_array =vstack((hstack((dot(inv_H01,E*I-H00),dot(-inv_H01,H01.conj().T))),hstack((I,Zeros))))
# the following 'complex' might be superfluous and only for real input matrices.
T, Z, number_sorted = schur(CompanionMatrix_array, sort='iuc')
eigenvalues = diag(T)
# propagating_eigenvalues = []
# propagating_eigenvectors = []
# for eigenvalue in eigenvalues:
# if abs(abs(eigenvalue)-1) < 0.01:
# propagating_eigenvalues.append(eigenvalue)
# eigenvector = eigenvector_from_eigenvalue(CompanionMatrix_array, eigenvalue)
# propagating_eigenvectors.append(eigenvector)
# prop_eig_array = array(propagating_eigenvectors).T
if not all_elements_are_unique(eigenvalues):
print "--------------WARNING!!!!!---------------"
print "One or more eigenvalues are identical, please rotate eigenvectors, I don't know how to do that"
#v,d = eig(CompanionMatrix_array)
#ndx = argsort(v)
#S=d[:,ndx]
#v=v[ndx]
#Sleft,Sright = split(S,2,axis=1)
#S4,S3 = split(Sright,2,axis=0)
#S2,S1 = split(Sleft,2,axis=0)
#S2 =S[:block*self.p.multi,:block*self.p.multi]
#S1= S[block*self.p.multi:,:block*self.p.multi]
#self.S2 = S2
#self.S1 = S1
#self.S4 = S4
#self.S3 = S3
#print 'S1 shape: ',S1.shape
#print 'S2 shape: ',S2.shape
# sort eigenvalues and Z according to acending abs(eigenvalue), TODO: do better sorting, now it
# depends on luck. sort using the calulated eigenvectors above
# sorting_indices = abs(eigenvalues).argsort()
#T = T[:,sorting_indices][sorting_indices,:]
#Z = Z[:,sorting_indices][sorting_indices,:]
Zleft, Zright = split(Z, 2, axis=1)
#S4,S3 = split(Sright,2,axis=0)
Z11, Z21 = split(Zleft, 2, axis=0)
self.Z11 = Z11
self.Z21 = Z21
if self.index == 0:
SigmaRet = dot(H01, dot(Z21, inv(Z11)))
else:
SigmaRet = dot(H01.conj(), dot(Z21, inv(Z11)))
self.SigmaRet = SigmaRet
print '- SimgaRet (', self.index, ') shape: ', SigmaRet.shape
sigma = lil_matrix((self.p.multi * Ndim, self.p.multi * Ndim),
dtype=complex128)
print '- sigma shape: ', sigma.shape
#implement polarization like (for spin up) reshape(-1,2) --> [:,1] = 0 --> reshape(shape(SigmaRet))
if self.index == 0:
if 'up' in self.current:
print 'Up polarized input'
SigmaRet.reshape(-1, 2)[:, 1] = 0
elif 'down' in self.current:
print 'Down polarized input'
SigmaRet.reshape(-1, 2)[:, 0] = 0
sigma[0:SigmaRet.shape[0], 0:SigmaRet.shape[1]] = SigmaRet
elif self.index == 1:
sigma[-SigmaRet.shape[0]:, -SigmaRet.shape[1]:] = SigmaRet
self.sigma = sigma
return sigma
def to_dataframe(cls, network=None, phases=[], join=False, delim=' | '):
r"""
Convert the Network (and optionally Phase) data to Pandas DataFrames.
Parameters
----------
network: OpenPNM Network Object
The network containing the data to be stored
phases : list of OpenPNM Phase Objects
The data on each supplied phase will be added to DataFrame
join : boolean
If ``False`` (default), two DataFrames are returned with *pore*
data in one, and *throat* data in the other. If ``True`` the pore
and throat data are combined into a single DataFrame. This can be
problematic as it will put NaNs into all the *pore* columns which
are shorter than the *throat* columns.
Returns
-------
Pandas ``DataFrame`` object containing property and label data in each
column. If ``join`` was False (default) the two DataFrames are
returned i a named tuple, or else a single DataFrame with pore and
throat data in the same file, despite the column length being
different.
"""
project, network, phases = cls._parse_args(network=network,
phases=phases)
# Initialize pore and throat data dictionary using Dict class
pdata = Dict.to_dict(network=network,
phases=phases,
element='pore',
interleave=True,
flatten=True,
categorize_by=['object'])
tdata = Dict.to_dict(network=network,
phases=phases,
element='throat',
interleave=True,
flatten=True,
categorize_by=['object'])
pdata = FlatDict(pdata, delimiter=delim)
tdata = FlatDict(tdata, delimiter=delim)
# Scan data and convert non-1d arrays to multiple columns
for key in list(pdata.keys()):
if sp.shape(pdata[key]) != (network[0].Np, ):
arr = pdata.pop(key)
tmp = sp.split(arr, arr.shape[1], axis=1)
cols = range(len(tmp))
pdata.update(
{key + '[' + str(i) + ']': tmp[i].squeeze()
for i in cols})
for key in list(tdata.keys()):
if sp.shape(tdata[key]) != (network[0].Nt, ):
arr = tdata.pop(key)
tmp = sp.split(arr, arr.shape[1], axis=1)
cols = range(len(tmp))
tdata.update(
{key + '[' + str(i) + ']': tmp[i].squeeze()
for i in cols})
# Convert sanitized dictionaries to DataFrames
pdata = pd.DataFrame(sanitize_dict(pdata))
tdata = pd.DataFrame(sanitize_dict(tdata))
# Prepare DataFrames to be returned
if join:
data = tdata.join(other=pdata, how='left')
else:
nt = namedtuple('dataframes', ('pore', 'throat'))
data = nt(pore=pdata, throat=tdata)
return data
def transfersigma(self,ind_contact,E):
from scipy.linalg import eig,inv
from scipy.sparse import lil_matrix
from aux import SparseBlocks
from scipy import argsort,dot,eye,hstack,vstack,zeros,complex128,asarray,split
E= E+self.zplus
Ndim = len(self.p.tuple_canvas_coordinates)
block=ind_contact.length
Hblock = SparseBlocks(self.H,self.block_sizes)
self.Hblock = Hblock
I=eye(block*self.p.multi)
Zeros = zeros((block*self.p.multi,block*self.p.multi))
#if ind_contact.SO is False:
# H00 = 4*self.t0*eye(block) -self.t0*eye(block,k=1) -self.t0*eye(block,k=-1)
# Hhop = -self.t0*I #no Bfield as of now
# inv_Hhop = -1/self.t0*I #no Bfield as of now
if ind_contact.index == 0:
H00 = asarray(Hblock[0,0].todense())
#H10 = asarray(Hblock[1,0].todense())
H01 = asarray(Hblock[0,1].todense())
inv_H01 = inv(H01)
if ind_contact.index == 1:
H00 = asarray(Hblock[-1,-1].todense())
#H10 = asarray(Hblock[-1,-2].todense())
H01 = asarray(Hblock[-2,-1].todense())
"""indices switch because hopping matrices go the other
direction x --> -x, better results this way altough not much difference"""
inv_H01 = inv(H01)
TransMatrix =vstack((hstack((dot(inv_H01,E*I-H00),dot(-inv_H01,H01.conj().T))),hstack((I,Zeros))))
v,S = eig(TransMatrix)
ndx = argsort(abs(v))
S=S[:,ndx]
v=v[ndx]
self.S=S
self.v =v
Sleft,Sright = split(S,2,axis=1)
S4,S3 = split(Sright,2,axis=0)
S2,S1 = split(Sleft,2,axis=0)
#S2 =S[:block*self.p.multi,:block*self.p.multi]
#S1= S[block*self.p.multi:,:block*self.p.multi]
self.S2 = S2
self.S1 = S1
self.S4 = S4
self.S3 = S3
print 'S1 shape: ',S1.shape
print 'S2 shape: ',S2.shape
if ind_contact.index == 0:
dotted = dot(S2,inv(S1))
if ind_contact.index == 1:
dotted = dot(S3,inv(S4))
invBracket =inv(E*I-H00-dot(H01,dotted))
SigmaRet=self.t0**2*invBracket
if ind_contact.index == 0:
self.SigmaRet1 = SigmaRet
#temp = zeros((60,60),dtype=complex128)
#temp[30:60,30:60] =SigmaRet[:30,:30]
#SigmaRet=temp
else :
self.SigmaRet2 = SigmaRet
print 'SigaRet shape: ',SigmaRet.shape
sigma = lil_matrix((self.p.multi*Ndim,self.p.multi*Ndim), dtype=complex128)
print 'sigma shape: ',sigma.shape
if ind_contact.index == 0:
sigma[0:SigmaRet.shape[0], 0:SigmaRet.shape[1]] = SigmaRet
self.sigma1=sigma
elif ind_contact.index == 1:
sigma[-SigmaRet.shape[0]:, -SigmaRet.shape[1]:] = SigmaRet
self.sigma2=sigma
import pudb; pudb.set_trace()
return sigma
def solve(self, wls):
"""Anisotropic solver.
INPUT
wls = wavelengths to scan (any asarray-able object).
OUTPUT
self.DEO1, self.DEE1, self.DEO3, self.DEE3 = power reflected
and transmitted.
"""
self.wls = S.atleast_1d(wls)
LAMBDA = self.LAMBDA
n = self.n
multilayer = self.multilayer
alpha = self.alpha
delta = self.delta
psi = self.psi
phi = self.phi
nlayers = len(multilayer)
i = S.arange(-n, n + 1)
nood = 2 * n + 1
hmax = nood - 1
DEO1 = S.zeros((nood, self.wls.size))
DEO3 = S.zeros_like(DEO1)
DEE1 = S.zeros_like(DEO1)
DEE3 = S.zeros_like(DEO1)
c1 = np.array([1., 0., 0.])
c3 = np.array([1., 0., 0.])
# grating on the xy plane
K = 2 * pi / LAMBDA * np.array(
[S.sin(phi), 0., S.cos(phi)], dtype=complex)
dirk1 = np.array([
S.sin(alpha) * S.cos(delta),
S.sin(alpha) * S.sin(delta),
S.cos(alpha)
])
# D polarization vector
u = np.array([
S.cos(psi) * S.cos(alpha) * S.cos(delta) -
S.sin(psi) * S.sin(delta),
S.cos(psi) * S.cos(alpha) * S.sin(delta) +
S.sin(psi) * S.cos(delta),
-S.cos(psi) * S.sin(alpha),
])
kO1i = S.zeros((3, i.size), dtype=complex)
kE1i = S.zeros_like(kO1i)
kO3i = S.zeros_like(kO1i)
kE3i = S.zeros_like(kO1i)
Mp = S.zeros((4 * nood, 4 * nood, nlayers), dtype=complex)
M = S.zeros((4 * nood, 4 * nood, nlayers), dtype=complex)
dlt = (i == 0).astype(int)
for iwl, wl in enumerate(self.wls):
nO1 = nE1 = multilayer[0].mat.n(wl).item()
nO3 = nE3 = multilayer[-1].mat.n(wl).item()
# wavevectors
k = 2 * pi / wl
eps1 = S.diag(S.asarray([nE1, nO1, nO1])**2)
eps3 = S.diag(S.asarray([nE3, nO3, nO3])**2)
# ordinary wave
abskO1 = k * nO1
# abskO3 = k * nO3
# extraordinary wave
# abskE1 = k * nO1 *nE1 / S.sqrt(nO1**2 + (nE1**2 - nO1**2) * S.dot(-c1, dirk1)**2)
# abskE3 = k * nO3 *nE3 / S.sqrt(nO3**2 + (nE3**2 - nO3**2) * S.dot(-c3, dirk1)**2)
k1 = abskO1 * dirk1
kO1i[0, :] = k1[0] - i * K[0]
kO1i[1, :] = k1[1] * S.ones_like(i)
kO1i[2, :] = -dispersion_relation_ordinary(kO1i[0, :], kO1i[1, :],
k, nO1)
kE1i[0, :] = kO1i[0, :]
kE1i[1, :] = kO1i[1, :]
kE1i[2, :] = -dispersion_relation_extraordinary(
kE1i[0, :], kE1i[1, :], k, nO1, nE1, c1)
kO3i[0, :] = kO1i[0, :]
kO3i[1, :] = kO1i[1, :]
kO3i[2, :] = dispersion_relation_ordinary(kO3i[0, :], kO3i[1, :],
k, nO3)
kE3i[0, :] = kO1i[0, :]
kE3i[1, :] = kO1i[1, :]
kE3i[2, :] = dispersion_relation_extraordinary(
kE3i[0, :], kE3i[1, :], k, nO3, nE3, c3)
# k2i = S.r_[[k1[0] - i * K[0]], [k1[1] - i * K[1]], [k1[2] - i * K[2]]]
k2i = S.r_[[k1[0] - i * K[0]], [k1[1] - i * K[1]], [-i * K[2]]]
# aliases for constant wavevectors
kx = kO1i[0, :] # o kE1i(1,;), tanto e' lo stesso
ky = k1[1]
# matrices
I = S.eye(nood, dtype=complex)
ZERO = S.zeros((nood, nood), dtype=complex)
Kx = S.diag(kx / k)
Ky = ky / k * I
Kz = S.diag(k2i[2, :] / k)
KO1z = S.diag(kO1i[2, :] / k)
KE1z = S.diag(kE1i[2, :] / k)
KO3z = S.diag(kO3i[2, :] / k)
KE3z = S.diag(kE3i[2, :] / k)
ARO = Kx * eps1[0, 0] + Ky * eps1[1, 0] + KO1z * eps1[2, 0]
BRO = Kx * eps1[0, 1] + Ky * eps1[1, 1] + KO1z * eps1[2, 1]
CRO_1 = inv(Kx * eps1[0, 2] + Ky * eps1[1, 2] + KO1z * eps1[2, 2])
ARE = Kx * eps1[0, 0] + Ky * eps1[1, 0] + KE1z * eps1[2, 0]
BRE = Kx * eps1[0, 1] + Ky * eps1[1, 1] + KE1z * eps1[2, 1]
CRE_1 = inv(Kx * eps1[0, 2] + Ky * eps1[1, 2] + KE1z * eps1[2, 2])
ATO = Kx * eps3[0, 0] + Ky * eps3[1, 0] + KO3z * eps3[2, 0]
BTO = Kx * eps3[0, 1] + Ky * eps3[1, 1] + KO3z * eps3[2, 1]
CTO_1 = inv(Kx * eps3[0, 2] + Ky * eps3[1, 2] + KO3z * eps3[2, 2])
ATE = Kx * eps3[0, 0] + Ky * eps3[1, 0] + KE3z * eps3[2, 0]
BTE = Kx * eps3[0, 1] + Ky * eps3[1, 1] + KE3z * eps3[2, 1]
CTE_1 = inv(Kx * eps3[0, 2] + Ky * eps3[1, 2] + KE3z * eps3[2, 2])
DRE = c1[1] * KE1z - c1[2] * Ky
ERE = c1[2] * Kx - c1[0] * KE1z
FRE = c1[0] * Ky - c1[1] * Kx
DTE = c3[1] * KE3z - c3[2] * Ky
ETE = c3[2] * Kx - c3[0] * KE3z
FTE = c3[0] * Ky - c3[1] * Kx
b = S.r_[u[0] * dlt, u[1] * dlt,
(k1[1] / k * u[2] - k1[2] / k * u[1]) * dlt,
(k1[2] / k * u[0] - k1[0] / k * u[2]) * dlt, ]
Ky_CRO_1 = ky / k * CRO_1
Ky_CRE_1 = ky / k * CRE_1
Kx_CRO_1 = kx[:, S.newaxis] / k * CRO_1
Kx_CRE_1 = kx[:, S.newaxis] / k * CRE_1
MR31 = -S.dot(Ky_CRO_1, ARO)
MR32 = -S.dot(Ky_CRO_1, BRO) - KO1z
MR33 = -S.dot(Ky_CRE_1, ARE)
MR34 = -S.dot(Ky_CRE_1, BRE) - KE1z
MR41 = S.dot(Kx_CRO_1, ARO) + KO1z
MR42 = S.dot(Kx_CRO_1, BRO)
MR43 = S.dot(Kx_CRE_1, ARE) + KE1z
MR44 = S.dot(Kx_CRE_1, BRE)
MR = S.asarray(
S.bmat([
[I, ZERO, I, ZERO],
[ZERO, I, ZERO, I],
[MR31, MR32, MR33, MR34],
[MR41, MR42, MR43, MR44],
]))
Ky_CTO_1 = ky / k * CTO_1
Ky_CTE_1 = ky / k * CTE_1
Kx_CTO_1 = kx[:, S.newaxis] / k * CTO_1
Kx_CTE_1 = kx[:, S.newaxis] / k * CTE_1
MT31 = -S.dot(Ky_CTO_1, ATO)
MT32 = -S.dot(Ky_CTO_1, BTO) - KO3z
MT33 = -S.dot(Ky_CTE_1, ATE)
MT34 = -S.dot(Ky_CTE_1, BTE) - KE3z
MT41 = S.dot(Kx_CTO_1, ATO) + KO3z
MT42 = S.dot(Kx_CTO_1, BTO)
MT43 = S.dot(Kx_CTE_1, ATE) + KE3z
MT44 = S.dot(Kx_CTE_1, BTE)
MT = S.asarray(
S.bmat([
[I, ZERO, I, ZERO],
[ZERO, I, ZERO, I],
[MT31, MT32, MT33, MT34],
[MT41, MT42, MT43, MT44],
]))
Mp.fill(0.0)
M.fill(0.0)
for nlayer in range(nlayers - 2, 0, -1): # internal layers
layer = multilayer[nlayer]
thickness = layer.thickness
EPS2, EPS21 = layer.getEPSFourierCoeffs(wl,
n,
anisotropic=True)
# Exx = S.squeeze(EPS2[0, 0, :])
# Exx = toeplitz(S.flipud(Exx[0:hmax + 1]), Exx[hmax:])
Exy = S.squeeze(EPS2[0, 1, :])
Exy = toeplitz(S.flipud(Exy[0:hmax + 1]), Exy[hmax:])
Exz = S.squeeze(EPS2[0, 2, :])
Exz = toeplitz(S.flipud(Exz[0:hmax + 1]), Exz[hmax:])
Eyx = S.squeeze(EPS2[1, 0, :])
Eyx = toeplitz(S.flipud(Eyx[0:hmax + 1]), Eyx[hmax:])
Eyy = S.squeeze(EPS2[1, 1, :])
Eyy = toeplitz(S.flipud(Eyy[0:hmax + 1]), Eyy[hmax:])
Eyz = S.squeeze(EPS2[1, 2, :])
Eyz = toeplitz(S.flipud(Eyz[0:hmax + 1]), Eyz[hmax:])
Ezx = S.squeeze(EPS2[2, 0, :])
Ezx = toeplitz(S.flipud(Ezx[0:hmax + 1]), Ezx[hmax:])
Ezy = S.squeeze(EPS2[2, 1, :])
Ezy = toeplitz(S.flipud(Ezy[0:hmax + 1]), Ezy[hmax:])
Ezz = S.squeeze(EPS2[2, 2, :])
Ezz = toeplitz(S.flipud(Ezz[0:hmax + 1]), Ezz[hmax:])
Exx_1 = S.squeeze(EPS21[0, 0, :])
Exx_1 = toeplitz(S.flipud(Exx_1[0:hmax + 1]), Exx_1[hmax:])
Exx_1_1 = inv(Exx_1)
# lalanne
Ezz_1 = inv(Ezz)
Ky_Ezz_1 = ky / k * Ezz_1
Kx_Ezz_1 = kx[:, S.newaxis] / k * Ezz_1
Exz_Ezz_1 = S.dot(Exz, Ezz_1)
Eyz_Ezz_1 = S.dot(Eyz, Ezz_1)
H11 = 1j * S.dot(Ky_Ezz_1, Ezy)
H12 = 1j * S.dot(Ky_Ezz_1, Ezx)
H13 = S.dot(Ky_Ezz_1, Kx)
H14 = I - S.dot(Ky_Ezz_1, Ky)
H21 = 1j * S.dot(Kx_Ezz_1, Ezy)
H22 = 1j * S.dot(Kx_Ezz_1, Ezx)
H23 = S.dot(Kx_Ezz_1, Kx) - I
H24 = -S.dot(Kx_Ezz_1, Ky)
H31 = S.dot(Kx, Ky) + Exy - S.dot(Exz_Ezz_1, Ezy)
H32 = Exx_1_1 - S.dot(Ky, Ky) - S.dot(Exz_Ezz_1, Ezx)
H33 = 1j * S.dot(Exz_Ezz_1, Kx)
H34 = -1j * S.dot(Exz_Ezz_1, Ky)
H41 = S.dot(Kx, Kx) - Eyy + S.dot(Eyz_Ezz_1, Ezy)
H42 = -S.dot(Kx, Ky) - Eyx + S.dot(Eyz_Ezz_1, Ezx)
H43 = -1j * S.dot(Eyz_Ezz_1, Kx)
H44 = 1j * S.dot(Eyz_Ezz_1, Ky)
H = 1j * S.diag(S.repeat(S.diag(Kz), 4)) + S.asarray(
S.bmat([
[H11, H12, H13, H14],
[H21, H22, H23, H24],
[H31, H32, H33, H34],
[H41, H42, H43, H44],
]))
q, W = eig(H)
W1, W2, W3, W4 = S.split(W, 4)
#
# boundary conditions
#
# x = [R T]
# R = [ROx ROy REx REy]
# T = [TOx TOy TEx TEy]
# b + MR.R = M1p.c
# M1.c = M2p.c
# ...
# ML.c = MT.T
# therefore: b + MR.R = (M1p.M1^-1.M2p.M2^-1. ...).MT.T
# missing equations from (46)..(49) in glytsis_rigorous
# [b] = [-MR Mtot.MT] [R]
# [0] [...........] [T]
z = S.zeros_like(q)
z[S.where(q.real > 0)] = -thickness
D = S.exp(k * q * z)
Sy0 = W1 * D[S.newaxis, :]
Sx0 = W2 * D[S.newaxis, :]
Uy0 = W3 * D[S.newaxis, :]
Ux0 = W4 * D[S.newaxis, :]
z = thickness * S.ones_like(q)
z[S.where(q.real > 0)] = 0
D = S.exp(k * q * z)
D1 = S.exp(-1j * k2i[2, :] * thickness)
Syd = D1[:, S.newaxis] * W1 * D[S.newaxis, :]
Sxd = D1[:, S.newaxis] * W2 * D[S.newaxis, :]
Uyd = D1[:, S.newaxis] * W3 * D[S.newaxis, :]
Uxd = D1[:, S.newaxis] * W4 * D[S.newaxis, :]
Mp[:, :, nlayer] = S.r_[Sx0, Sy0, -1j * Ux0, -1j * Uy0]
M[:, :, nlayer] = S.r_[Sxd, Syd, -1j * Uxd, -1j * Uyd]
Mtot = S.eye(4 * nood, dtype=complex)
for nlayer in range(1, nlayers - 1):
Mtot = S.dot(S.dot(Mtot, Mp[:, :, nlayer]), inv(M[:, :,
nlayer]))
BC_b = S.r_[b, S.zeros_like(b)]
BC_A1 = S.c_[-MR, S.dot(Mtot, MT)]
BC_A2 = S.asarray(
S.bmat([
[
(c1[0] * I - c1[2] * S.dot(CRO_1, ARO)),
(c1[1] * I - c1[2] * S.dot(CRO_1, BRO)),
ZERO,
ZERO,
ZERO,
ZERO,
ZERO,
ZERO,
],
[
ZERO,
ZERO,
(DRE - S.dot(S.dot(FRE, CRE_1), ARE)),
(ERE - S.dot(S.dot(FRE, CRE_1), BRE)),
ZERO,
ZERO,
ZERO,
ZERO,
],
[
ZERO,
ZERO,
ZERO,
ZERO,
(c3[0] * I - c3[2] * S.dot(CTO_1, ATO)),
(c3[1] * I - c3[2] * S.dot(CTO_1, BTO)),
ZERO,
ZERO,
],
[
ZERO,
ZERO,
ZERO,
ZERO,
ZERO,
ZERO,
(DTE - S.dot(S.dot(FTE, CTE_1), ATE)),
(ETE - S.dot(S.dot(FTE, CTE_1), BTE)),
],
]))
BC_A = S.r_[BC_A1, BC_A2]
x = linsolve(BC_A, BC_b)
ROx, ROy, REx, REy, TOx, TOy, TEx, TEy = S.split(x, 8)
ROz = -S.dot(CRO_1, (S.dot(ARO, ROx) + S.dot(BRO, ROy)))
REz = -S.dot(CRE_1, (S.dot(ARE, REx) + S.dot(BRE, REy)))
TOz = -S.dot(CTO_1, (S.dot(ATO, TOx) + S.dot(BTO, TOy)))
TEz = -S.dot(CTE_1, (S.dot(ATE, TEx) + S.dot(BTE, TEy)))
denom = (k1[2] - S.dot(u, k1) * u[2]).real
DEO1[:, iwl] = (-(
(S.absolute(ROx)**2 + S.absolute(ROy)**2 + S.absolute(ROz)**2)
* S.conj(kO1i[2, :]) -
(ROx * kO1i[0, :] + ROy * kO1i[1, :] + ROz * kO1i[2, :]) *
S.conj(ROz)).real / denom)
DEE1[:, iwl] = (-(
(S.absolute(REx)**2 + S.absolute(REy)**2 + S.absolute(REz)**2)
* S.conj(kE1i[2, :]) -
(REx * kE1i[0, :] + REy * kE1i[1, :] + REz * kE1i[2, :]) *
S.conj(REz)).real / denom)
DEO3[:, iwl] = (
(S.absolute(TOx)**2 + S.absolute(TOy)**2 + S.absolute(TOz)**2)
* S.conj(kO3i[2, :]) -
(TOx * kO3i[0, :] + TOy * kO3i[1, :] + TOz * kO3i[2, :]) *
S.conj(TOz)).real / denom
DEE3[:, iwl] = (
(S.absolute(TEx)**2 + S.absolute(TEy)**2 + S.absolute(TEz)**2)
* S.conj(kE3i[2, :]) -
(TEx * kE3i[0, :] + TEy * kE3i[1, :] + TEz * kE3i[2, :]) *
S.conj(TEz)).real / denom
# save the results
self.DEO1 = DEO1
self.DEE1 = DEE1
self.DEO3 = DEO3
self.DEE3 = DEE3
return self
p=8
lista=[]
for i in range(1,p+1):
lista.append(i)
k=10
Y=sy.array(y)
Y=sy.arange(Y.shape[0])
test=sy.array(sy.split(Y,len(x)/k))
medias=[]
for s in lista:
traierror=[]
for i in test:
trainingy=sy.array(y)
trainingx=sy.array(x)
trainingy=sy.delete(trainingy,i)
trainingx=sy.delete(trainingx,i)
