def annotate(image_in):
image = filter_colors(image_in)
gray = grayscale(image)
blur_gray = gaussian(gray , c1.kernel_size)
edges = canny(blur_gray, c1.low_threshold, c1.high_threshold)
imshape = image.shape
vertices = np.array([[\
((imshape[1] * (1 - c1.trap_bottom_width)) // 2, imshape[0]),\
((imshape[1] * (1 - c1.trap_top_width)) // 2, imshape[0] - imshape[0] * c1.trap_height),\
(imshape[1] - (imshape[1] * (1 - c1.trap_top_width)) // 2, imshape[0] - imshape[0] * c1.trap_height),\
(imshape[1] - (imshape[1] * (1 - c1.trap_bottom_width)) // 2, imshape[0])]]\
, dtype=np.int32)
masked_edges = roi(edges, vertices)
line_image = hough(masked_edges, c1.rho, c1.theta, c1.threshold, c1.min_line_length, c1.max_line_gap)
initial_image = image_in.astype('uint8')
annotated_image = weighted_img(line_image, initial_image)
return annotated_image
def fit_gaussian(xs,ys,guess=[],x0_range=50.):
'''Fits a Guassian profile on top of a background'''
#import matplotlib.pyplot as plt
fit_func = lambda p: ys - functions.gaussian(xs,p[0:3])- p[3]
solution = leastsq(fit_func,guess)
if solution[1] not in [1,2,3,4]:
raise Error
else:
params = solution[0]
print(params)
return params
def gaussian_kernel(**kwargs):
s = kwargs.get('size', 2)
mu = kwargs.get('mu', 0.0)
sigma = kwargs.get('sigma', 1.0)
integer = kwargs.get('integer', False)
x = array(range(-s,s+1))
g = gaussian(x, mu=mu, sigma=sigma)
m = outer(g,g)
if integer:
gi = (m/m[0,0]).astype(int)
return gi, npsum(gi)
else:
return m, npsum(m)
# ax_res_y2.set_yticks((ax_res.get_yticks() / 100) * yNorm)
for xticklabel in ax.get_xticklabels():
xticklabel.set_visible(False)
for xticklabel in axy2.get_xticklabels():
xticklabel.set_visible(False)
ax.get_yticklabels()[0].set_visible(False)
axy2.get_yticklabels()[0].set_visible(False)
ax_res.get_yticklabels()[-1].set_visible(False)
ax_res_y2.get_yticklabels()[-1].set_visible(False)
if legend:
ax.legend(loc='best')
ax_res.set_xlabel(xlabel)
ax.set_ylabel(ylabel)
return fig, [ax, axy2, ax_res, ax_res_y2]
if __name__ == '__main__':
from functions import gaussian
from lmfit.models import GaussianModel
x = np.linspace(-3, 3, 200)
y = gaussian(x, sigma=0.5) * (1 + np.random.normal(0, 0.1, len(x)))
gmod = GaussianModel()
para = gmod.guess(y, x=x)
gfit = gmod.fit(y, para, x=x)
models = [gfit.init_fit, gfit.best_fit]
plt.close('all')
fig, axes = plotResidual(x, y, models, yNorm=1.0, yThresh=0.1)
axes[0].set_ylabel('relative [%]')
axes[1].set_ylabel('absolute')
axes[2].set_xlabel('xxx')
plt.show()
wf = 0.010445
k = 9.04728 # in sqrt(amu)*ang
sigma = 0.225 # broadening
t = 100 # K
zpl = 2.70845 # eV
es = 1.0
ed = 3.0
ne = 400 # energy grid
kb = 8.6173303e-5 # eV/K
# initialize
t = t * kb
f = fcf_decimal(ni, nf, wi, wf, k)
f = f**2
z = sum(exp(-i * wi / t) for i in range(100)) # partition
e = np.linspace(es, ed, ne)
pl = np.zeros(ne)
#
for ie in range(ne):
for i in range(ni):
ei = i * wi
bz = exp(-ei / t) / z
for j in range(nf):
ef = j * wf
pl[ie] += bz * e[ie]**3 * f[i, j] * gaussian(
e[ie], zpl + ei - ef, sigma)
tmp = np.vstack((e, pl))
np.savetxt('pl.dat', tmp.T)
plt.plot(e, pl)
plt.show()
'Student/Staff Ratio',
'Average Salary',
'Academic Services Expenditure per Student',
'Facilities Expenditure per Student']
bc_inds = list(df.index)
bc_inds.insert(0, 'None')
bc_col1, bc_col2 = st.beta_columns(2)
metric = bc_col1.selectbox('Select Metric', bc_cols, index=0)
institution = bc_col2.selectbox('Select Institution (Optional)', bc_inds, index=0)
if metric != 'None':
fig, ax = plt.subplots(figsize=(10,8))
if institution != 'None':
x, gauss, std, mean, xpoint, ypoint, length= gaussian(df, metric, institution)
ax.arrow(xpoint, ypoint, dx=0, dy=-length, width=std/30, head_length=length/6, length_includes_head=True)
else:
x, gauss, std, mean = gaussian(df, metric)
ax.plot(x, gauss)
ax.axes.yaxis.set_ticklabels([])
ax.set_axisbelow(True)
ax.grid(True)
ax.set_xlabel(f'{metric}')
ax.set_title(f'{metric}\nMean = {round(mean,2)}, Standard Deviation = {round(std,2)}')
st.pyplot(fig)
wij = 6e-4 # <0|dPsi/dQ> unit 1/Q
# constants
kb = 8.6173303e-5 # eV/K
hbar = 6.582119514e-16 # eV.s/rad
h = 4.135667662e-15 # eV.s
ev = 1.6021766208e-19 # J
amu = 1.660539040e-27 # kg
ang = 1.0e-10 # m
fr = ev / amu / ang**2
# initialize
t = t * kb
f = fcf_decimal(ni, nf, wi, wf, q)
z = sum(exp(-i * wi / t) for i in range(200)) # partition
beta = sqrt(wi * fr / (wi / hbar)**2 / 2) # hbar/omega unit Q^2
#
rate = 0.0
for i in range(ni - 1):
ei = i * wi
bz = exp(-ei / t) / z
for j in range(nf):
ef = j * wf
if i < 1:
rate += 2*pi*beta**2*bz*(sqrt(i+1)*f[i+1,j])**2*zpl**2*wij**2* \
gaussian(zpl+ei,ef,sigma)
else:
rate += 2*pi*beta**2*bz*(sqrt(i+1)*f[i+1,j]+sqrt(i)*f[i-1,j])**2* \
zpl**2*wij**2*gaussian(zpl+ei,ef,sigma)
print rate / h # Hz
#Initialisierung der DATEN p_d = 0.99 #Detektionsrate lambda_c = 0.3 #Clutter Intensität V = 5 #Cluttering Volume T = 0.001 #Abtastzeit F = np.array([[1, T], [0, 1]]) #Systemmatrix H = np.array([1, 0]) #Ausgangsmatrix n = 2 #Anzahl Objekte variance_motion = 0.25 variance_measurement = 0.2 variance_prior = 0.36 init_x1 = 0 init_x2 = 10 init_values = np.array([[init_x1, init_x2], [0, 0]]) x = np.arange(-20, 20, 0.1) init_prior_x1 = gaussian(x, init_x1, variance_prior) init_prior_x2 = gaussian(x, init_x2, variance_prior) number_states = len(F) # Zuständezahl estimate = np.zeros((number_states, n)) # Zustände geschätz estimate[0:number_states, 0:n] = init_values #Anfangswerte hinzufügen P = np.zeros((number_states, n * number_states)) 'nullmatrix wirklich sinnvolll??? -> die Varianz des Schätzfehlers wird mit 0 also nicht vorhanden initialisiert großer wert wäre sinnvoller' #Initialisierung KALMANFILTER Pini = np.diag([.01, .009]) Q = np.array([[.1, 0], [0, .1]]) R = np.array([[10]]) #KF = KalmanFilter(dim_x=2, dim_z=1) #KF.x = np.array([0,1]) # pos, velo init
rate = 0.0
for i in range(ni-4):
ei = i*wi - 30*lam**2*beta**6/wi*(i**2+i+11./30)
bz = exp(-ei/t)/z
for j in range(nf):
ef = j*wf
if i < 1:
ff[i,j] = beta*sqrt(i+1)*f[i+1,j] + lam*beta**4/3/wi* \
(-9*(2*i+1)*f[i,j]-2*(5*i+6)*sqrt((i+1)*(i+2))*f[i+2,j] - \
sqrt((i+1)*(i+2)*(i+3)*(i+4))*f[i+4,j])
elif i >= 1 and i < 2:
ff[i,j] = beta*(sqrt(i+1)*f[i+1,j] + sqrt(i)*f[i-1,j]) + lam*beta**4/3/wi* \
(-9*(2*i+1)*f[i,j]-2*(5*i+6)*sqrt((i+1)*(i+2))*f[i+2,j] - \
sqrt((i+1)*(i+2)*(i+3)*(i+4))*f[i+4,j])
elif i >= 2 and i < 4:
ff[i,j] = beta*(sqrt(i+1)*f[i+1,j] + sqrt(i)*f[i-1,j]) + lam*beta**4/3/wi* \
(2*(5*i-1)*sqrt(i*(i-1))*f[i-2,j]-9*(2*i+1)*f[i,j] - \
2*(5*i+6)*sqrt((i+1)*(i+2))*f[i+2,j] - \
sqrt((i+1)*(i+2)*(i+3)*(i+4))*f[i+4,j])
else:
ff[i,j] = beta*(sqrt(i+1)*f[i+1,j] + sqrt(i)*f[i-1,j]) + lam*beta**4/3/wi* \
(sqrt(i*(i-1)*(i-2)*(i-3))*f[i-4,j] + \
2*(5*i-1)*sqrt(i*(i-1))*f[i-2,j]-9*(2*i+1)*f[i,j] - \
2*(5*i+6)*sqrt((i+1)*(i+2))*f[i+2,j] - \
sqrt((i+1)*(i+2)*(i+3)*(i+4))*f[i+4,j])
rate += 2*pi*bz*ff[i,j]**2*zpl**2*wij**2*gaussian(zpl+ei,ef,sigma)
print rate/h # Hz
k = 8.71 # in sqrt(amu)*ang
sigma = 0.2665 # broadening
t = 175 # K
zpl = 2.74142 # eV
es = 1.0
ed = 4.0
ne = 1000 # energy grid
eps = 3.28
kb = 8.6173303e-5 # eV/K
eh = 27.211385 # eV
tau = 2.418884e-17 # hbar/Eh
# initialize
t = t * kb
f = fcf_decimal(ni, nf, wi, wf, k)
f = f**2
z = sum(exp(-i * wi / t) for i in range(200)) # partition
e = np.linspace(es, ed, ne)
a = sqrt(eps) / 3 / pi / 137**3 / tau
pl = np.zeros(ne)
#
for ie in range(ne):
for i in range(ni):
ei = i * wi
bz = exp(-ei / t) / z
for j in range(nf):
ef = j * wf
pl[ie] += a * bz * (e[ie] / eh)**3 * f[i, j] * gaussian(
e[ie], zpl + ei - ef, sigma)
print sum(pl) * (e[1] - e[0])