def delay(omegaV, free):
E_0 = -1.1591
E_m = [-0.8502, -0.3278, -0.1665]
T = 3/0.02419
delta_m = np.zeros(np.size(E_m))
for j in (0, 1, 2):
delta_m[j] = E_m[j] - E_0
optSize = np.size(omegaV)
alpha1f = np.zeros(optSize, 'complex')
alpha3f = np.zeros(optSize, 'complex')
realFactor = np.zeros(optSize, 'complex')
imagFactor = np.zeros(optSize, 'complex')
T = 3 / 0.02419
for i in range(0, np.size(defs.omega_dip)-1):
alpha1f[i] = dipole.constructDipole(omegaV[i], defsDipole.wf1)
alpha3f[i] = dipole.constructDipole(omegaV[i], defsDipole.wf3)
dawsArg1st = T*(delta_m[0] - omegaV)
dawsArg3rd = T*(delta_m[1] - omegaV)
realFactor = np.real((alpha1f * np.exp(-free*np.power(dawsArg1st,2.0)))\
+ (alpha3f * np.exp(-np.sqrt(free)*np.power(dawsArg3rd, 2.0))))
imagFactor = (alpha1f * ((-2 * cmath.sqrt(-1))\
/ (np.sqrt(np.pi))) * spcl.dawsn(free*dawsArg1st))\
+ (alpha3f * ((-2 * cmath.sqrt(-1))\
/ (np.sqrt(np.pi))) * spcl.dawsn(np.sqrt(free)*dawsArg3rd))
dE = np.gradient(omegaV)
dIm = np.gradient(imagFactor, dE)
dRe = np.gradient(realFactor, dE)
derivFactor = (realFactor * dIm) - (np.imag(imagFactor * dRe))
zSquared = realFactor*realFactor + np.imag(imagFactor)*np.imag(imagFactor)
ans = (realFactor * np.imag(dIm) - np.imag(imagFactor * dRe)) / zSquared
return ans
def getEnergy(self, normalized=True, mask=None):
"""
Returns the current energy.
Parameters:
normalized: Flag to return the normalized energy (that is, divided
by the total density)
"""
if self.gpu:
psi = self.psi.get()
V = self.Vdt.get() / self.dt
else:
psi = self.psi
V = self.Vdt.get() / self.dt
density = np.absolute(psi) ** 2
gradx = np.gradient(psi)[0]
normFactor = density.sum() if normalized else 1.0
return (
np.ma.array(
-(
0.25 * np.gradient(np.gradient(density)[0])[0]
- 0.5 * np.absolute(gradx) ** 2
- (self.g_C * density + V) * density
),
mask=mask,
).sum()
/ normFactor
)
def _filter_small_slopes(hgt, dx, min_slope=0):
"""Masks out slopes with NaN until the slope if all valid points is at
least min_slope (in degrees).
"""
min_slope = np.deg2rad(min_slope)
slope = np.arctan(-np.gradient(hgt, dx)) # beware the minus sign
# slope at the end always OK
slope[-1] = min_slope
# Find the locs where it doesn't work and expand till we got everything
slope_mask = np.where(slope >= min_slope, slope, np.NaN)
r, nr = label(~np.isfinite(slope_mask))
for objs in find_objects(r):
obj = objs[0]
i = 0
while True:
i += 1
i0 = objs[0].start-i
if i0 < 0:
break
ngap = obj.stop - i0 - 1
nhgt = hgt[[i0, obj.stop]]
current_slope = np.arctan(-np.gradient(nhgt, ngap * dx))
if i0 <= 0 or current_slope[0] >= min_slope:
break
slope_mask[i0:obj.stop] = np.NaN
out = hgt.copy()
out[~np.isfinite(slope_mask)] = np.NaN
return out
def test_1d_gaussian_slope_error(self):
mirror_length=200.0
step=1.0
rms_slopes=1.3e-7
rms_heights = 1e-7
correlation_length = 10.0
x, f = simulate_profile_1D_gaussian(step=step, \
mirror_length=mirror_length, \
rms_heights=rms_heights, \
correlation_length=correlation_length,\
renormalize_to_slopes_sd=None)
slopes = numpy.gradient(f, x[1]-x[0])
print("test_1d_gaussian: test function: %s, Stdev (not normalized): HEIGHTS=%g.SLOPES=%g"%("test_1d_gaussian_slope_error",f.std(),slopes.std()))
x, f = simulate_profile_1D_gaussian(step=step, \
mirror_length=mirror_length, \
rms_heights=rms_heights, \
correlation_length=correlation_length,\
renormalize_to_slopes_sd=rms_slopes)
slopes = numpy.gradient(f, x[1]-x[0])
print("test_1d_gaussian: test function: %s, SLOPES Stdev (normalized to %g)=%g"%("test_1d_gaussian_slope_error",rms_slopes,slopes.std()))
assert numpy.abs( rms_slopes - slopes.std() ) < 0.01 * numpy.abs(rms_slopes)
if do_plot:
from srxraylib.plot.gol import plot
plot(x,slopes,title="test_1d_gaussian_slope_error",xtitle="Y",ytitle="slopes Z'")
def get_beta_deff(savepath, filename):
filepath = os.path.join(savepath,filename)
with open(filepath,'r') as f1:
#col1 = [] #typically mean x-position
#col2 = [] #typically mean (x-position)^2
col3 = [] #typically MSD-x as calculated from the above quantities
for line in f1:
ls = line.split()
#Analytical data output is currently set at 3 cols.
#Make sure you are using the correct data.
#col1 += [float(ls[0])]
#col2 += [float(ls[1])]
col3 += [float(ls[2])]
times = np.array(range(1, len(col3) + 1)) #create an array of times
msd_x = np.array(col3) #create an array of msd_x
#For effective diffusion:
deff = np.true_divide(msd_x, 2*times)
#For beta(t) plot.
log_times = np.log10(times)
log_msd_x = np.log10(msd_x)
dt = np.gradient(log_times)
dd = np.gradient(log_msd_x, dt)
return times, deff, log_times, dd, msd_x
def _method_df2(nu, op, alpha=1.0, beta=0.5, nmin_filter=10, log=True):
"""
Cost function: Use normalized first order derivative
Parameters:
-----------
- nu [ndarray]: photon group boundaries
- op [ndarray]: spectra
- alpha [float]: in [0.0, 2.0], default 1.0
alpha < 1: low sensitivity to gradients in the spectra
alpha > 1: high sensitivity to gradients in the spectra
"""
from scipy.ndimage.filters import minimum_filter1d
if log:
err = np.abs(np.gradient(np.gradient(np.log10(op))))
else:
err = np.abs(np.gradient(np.gradient(op)))
err /= err.max() # normalising to 1 so pow gives predictive results
err = err**alpha
if not log:
err /= minimum_filter1d(op, nmin_filter)
err /= err.sum()
err_f = (err*(1-beta)+beta/len(op))
err_f /= err_f.sum()
return err_f
def spline_do(x, y, ax, k=3, s=7, n=1, diff=True, plot=True, error=False):
'''
Finds spline with degree k and smoothing factor s for x and y.
Returns ys,d_ys: the y values of the spline and the derivative.
'''
# xs = np.array(x).astype(float)
s = UnivariateSpline(x, y, k=k, s=s)
xs = np.linspace(x.values.min(), x.values.max(), len(x))
ys = s(xs)
if plot:
if not error:
ax.plot(x, norm(y), '.', label='Data')
ax.plot(xs, norm(ys), label='Spline fit')
if error:
ax.errorbar(x, norm(y), yerr=np.sqrt(norm(y)))
d_ys = np.gradient(ys)
dd_ys = np.gradient(d_ys)
if diff:
if plot:
ax.plot(xs, norm(d_ys), '-.', label='1st derivative')
#ax.plot(xs, norm(dd_ys),'--',label='2nd derivative')
ax.plot(xs, norm(smooth(dd_ys, 81)),
'--', label='2nd derivative (smothed)')
if plot:
ax.legend(loc=0)
return xs, ys, d_ys, dd_ys
def main(args):
fig = plt.figure()
axU = fig.add_subplot(211)
axR = fig.add_subplot(212)
wall = createobstacle(args.diameter[0],111)
lat = lb_D2Q9.lattice(wall.shape,[0.,0.],args.tau[0])
lat.ux[:,0]=anSolution(5e-8,111,lat.nu) #set intel macroscopic eq vel
lat.fd = lat.eqdistributions()#New equilibrium
lat.setWalls(wall)
finlet = np.copy( lat.fd[:,:,:1]) #get inlet macroscopic vel
lat.updateMacroVariables()
for i in range(400000):
if i%50 == 0:
axU.cla()
axU.imshow(np.sqrt(lat.ux**2+lat.uy**2),vmin=0,vmax=0.2)
fname = '%08d.png'%i
dyUy,dxUy=np.gradient(lat.uy)
dyUx,dxUx=np.gradient(lat.ux)
vort=np.abs(dxUy-dyUx)
axR.cla()
axR.imshow(vort,vmin=0,vmax=0.1)
fig.savefig('tot'+fname)
lat.collision()
lat.streamming()
lat.onWallBBNS_BC(wall)
lat.fd[:,:,-1]=np.copy(lat.fd[:,:,-2]) #gradient to cero on outlet
lat.fd[:,:,:1]=np.copy(finlet)
lat.updateMacroVariables()
np.savez('out.npz',lat.ux,lat.uy,lat.rho,wall)
def airfoil(self):
"""Biconvex airfoil"""
L = self.L
N = self.N
R = 210
theta_arc = np.arcsin(L/2 / R) * 2
pi = np.pi
theta_up = np.linspace((pi+theta_arc) / 2,
+(pi-theta_arc) / 2, N)
#theta_up = theta[::-1]
theta_down =np.linspace((3*pi-theta_arc) / 2,
+(3*pi+theta_arc) / 2, N)
X_up = R * np.cos(theta_up)
Y_up = R * np.sin(theta_up)
X_down = R * np.cos(theta_down)
Y_down = R * np.sin(theta_down)
shift_r = X_up[0]
X_up -= shift_r
X_down -= shift_r
shift_up = Y_up[0]
shift_down = Y_down[0]
Y_up = Y_up - shift_up
Y_down = Y_down - shift_down
X = np.concatenate((X_up, X_down))
Y = np.concatenate((Y_up, Y_down))
slope_up = np.gradient(Y_up,1)/np.gradient(X_up,1)
slope_down = np.gradient(Y_down,1)/np.gradient(X_down,1)
angle = np.arctan(np.concatenate((slope_up, slope_down)))
return X, Y, angle
def __init__(self, sigReaders):
self.sigReaders = sigReaders
sigsTimeValues = [sr.getSignal() for sr in self.sigReaders]
sigsValues = [values for times, values in sigsTimeValues]
self.sigsRanges = [(min(values), max(values), min(np.gradient(values)), max(np.gradient(values))) for values in
sigsValues]
def vorticity(x, y, u, v, coord_type='geographic'):
"""
USAGE
-----
zeta = vorticity(x, y, u, v, coord_type='geographic')
Calculates the vertical component 'zeta' (dv/dx - du/dy, in 1/s) of the
relative vorticity vector from the 'u' and 'v' velocity arrays (in m/s)
specified in spherical coordinates by the 'lon' and 'lat' 2D meshgrid-type
arrays (in degrees).
"""
x, y, u, v = map(np.array, (x, y, u, v))
if coord_type=='geographic':
dx, dy = deg2m_dist(lon, lat)
elif coord_type=='cartesian':
dy, _ = np.gradient(y)
_, dx = np.gradient(x)
elif coord_type=='dxdy':
dx, dy = x, y
pass
duy, _ = np.gradient(u)
_, dvx = np.gradient(v)
dvdx = dvx/dx
dudy = duy/dy
vrt = dvdx - dudy # [1/s]
return vrt
def kalman_smooth_dataframe(df, arena=None, smooth=True):
if arena:
fsx = arena.scale_x
fsy = arena.scale_y
else:
fsx = fsy = lambda _v: _v
#we need dt in seconds to calculate velocity. numpy returns nanoseconds here
#because this is an array of type datetime64[ns] and I guess it retains the
#nano part when casting
dt = np.gradient(df.index.values.astype('float64')/SECOND_TO_NANOSEC)
if smooth:
print "\tsmoothing (%r)" % arena
#smooth the positions, and recalculate the velocitys based on this.
kf = Kalman()
smoothed = kf.smooth(df['x'].values, df['y'].values)
_x = fsx(smoothed[:,0])
_y = fsy(smoothed[:,1])
else:
_x = fsx(df['x'].values)
_y = fsy(df['y'].values)
_vx = np.gradient(_x) / dt
_vy = np.gradient(_y) / dt
_v = np.sqrt( (_vx**2) + (_vy**2) )
df['x'] = _x
df['y'] = _y
df['vx'] = _vx
df['vy'] = _vy
df['v'] = _v
return dt
def read_HRRS_data(ff):
"""
Read in a .dat file from SPARC high-res radiosonde data
Input ff is a string pointing to the full path of the desired file.
"""
# here is a dict that gives bad values for different columns
# alert: this is still incomplete
badvals = {'Temp':['999.0'],'Alt':['99.0','99999.0'],'Lat':['999.000'],'Lon':['9999.000']}
D= pd.read_csv(ff,skiprows=13,error_bad_lines=False,delim_whitespace=True,na_values=badvals)
colnames=list(D.columns.values)
# kick out the first two rows - they hold units and symbols
D.drop(D.index[[0,1]], inplace=True)
# also make sure that lat, lon, pressure, altitude, and temp are numerics
vars_to_float = ['Press','Temp','Lat','Lon','Alt']
D[vars_to_float] = D[vars_to_float].astype(float)
# compute the vertical gradient of potential temp and, from that, buoyancy frequency
P0=1000.0
Rd = 286.9968933 # Gas constant for dry air J/degree/kg
g = 9.80616 # Acceleration due to gravity m/s^2
cp = 1005.0 # heat capacity at constant pressure m^2/s^2*K
theta=(D['Temp']+273.15)*(P0/D['Press'])**(Rd/cp) # note that this includes conversion of Celsius to Kelvin
dZ = np.gradient(D['Alt'])
dthetadZ = np.gradient(theta,dZ)
D["N2"]=(g/theta)*dthetadZ
return(D)
def wrf_pv( U, V, F, THETA, PRES, MAPFAC_M, dx ):
"""Calculate the potential vorticity given the U and V vector components in m/s,
the Coriolis sine latitude term (F) in s^-1, THETA potential temperature in degrees
Kelvin, PRES pressure in hPa or mb, the map scale factor on mass grid and the gridspacing
dx in meters. U, V, F, THETA, and PRES must be 4D arrays.
---------------------
U (numpy.ndarray): ndarray of U vector values in m/s
V (numpy.ndarray): ndarray of V vector values in m/s
F (numpy.ndarray): ndarray of Coriolis sine latitude values in s^-1
THETA (numpy.ndarray): ndarray of potential temperature in degrees Kelvin
PRES (numpy.ndarray): ndarray of pressure in hPa or mb same shape as THETA
MAPFAC_M (numpy.ndarray): 2D of map scale factor on mass grid.
dx (float or int): float or integer of U and V grispacing in meters
---------------------
returns:
numpy.ndarray of potential vorticity values in ( K * m^2 * kg^-1 * s^-1 ) * 10^6
( or 1 PVU * 10^6).
"""
assert U.shape == V.shape == THETA.shape == PRES.shape, 'Arrays are different shapes. They must be the same shape.'
## pres in hPa needs to convert to Pa
PRES = PRES * 100
dx = dx * MAPFAC_M
dy = dx
grav = 9.8
dVt,dVp,dVy,dVx = numpy.gradient( V )
dUt,dUp,dUy,dUx = numpy.gradient( U )
dTt,dTp,dTy,dTx = numpy.gradient( THETA )
dPt,dp,dPy,dPx = numpy.gradient( PRES )
return ( -grav * ( -dVp/dp * dTx/dx + dUp/dp * dTy/dy + ( dVx/dx - dUy/dy + F ) * dTp/dp ) ) * pow(10, 6)
def extractAllDescriptors(signal):
"""
Extracts the descriptors expected for the analysis of a given audio file.
"""
described = {}
described['Silence'] = _silence = silence(signal)
signal = signal[config.hopSize * _silence[0]:config.hopSize * _silence[1]] / np.max(
signal) # Tomo solo la parte con sonido y promedio para que todas las señales sean parejas.
described['mfcc'] = mfccs(signal)
described['Inharmonicity'] = inharmonicity_tesis(signal)
described['Energy'] = energy(signal)
described['LogAttackTime'] = log_attack_time(signal)
described['Standard-Dev'] = standard_dev(signal)
described['Variance'] = variance(signal)
described['Skewness'] = skewness(signal)
described['kurtosis'] = kurtosis(signal)
# described['mfcc-1st'] = np.gradient(described['mfcc'])[1]
# described['mfcc-2nd'] = np.gradient(described['mfcc-1st'])[1]
described['Inharmonicity-1st'] = np.gradient(described['Inharmonicity'])
described['Inharmonicity-2nd'] = np.gradient(described['Inharmonicity-1st'])
described['mfcc-Std-f'], described['mfcc-Var-f'], described['mfcc-Skew-f'], described['mfcc-Kurt-f']\
= mfcc_std_frequency(described)
return described
def calculate_single_weight(self, angle):
"""Finds the strongest gradient in the image"""
obj = ShearTool(self.img)
corrected = obj.shear(angle)
p = BinaryProjection(corrected, Projection.TYPE_HORIZONTAL)
# p.debug()
return max(np.gradient(p.get_projection())) + abs(min(np.gradient(p.get_projection())))
def march(x,u_e,nu):
dx = numpy.diff(x)
du_e = numpy.gradient(u_e,numpy.gradient(x))
delta = numpy.full_like(x,0.)
lam = numpy.full_like(x,lam0)
# Initial conditions must be a stagnation point. If u_e[0]>0
# assume stagnation is at x=0 and integrate from x=0..x[0].
if u_e[0]<0.01: # stagnation point
delta[0] = numpy.sqrt(lam0*nu/du_e[0])
elif x[0]>0: # just downstream
delta[0] = numpy.sqrt(lam0*nu*x[0]/u_e[0])
delta[0] += 0.5*x[0]*g_pohl(delta[0],0,u_e,du_e,nu)
lam[0] = delta[0]**2*du_e[0]/nu
else:
raise ValueError('x=0 must be stagnation point')
# march!
for i in range(len(x)-1):
delta[i+1] = heun(g_pohl,delta[i],i,dx[i],
u_e,du_e,nu) # ...additional arguments
lam[i+1] = delta[i+1]**2*du_e[i+1]/nu
if lam[i+1] < -12: i-=1; break # separation condition
return delta,lam,i+1 # return with separation index
def hessian_matrix(image, sigma=1, mode="constant", cval=0):
"""Compute Hessian matrix.
The Hessian matrix is defined as::
H = [Hxx Hxy]
[Hxy Hyy]
which is computed by convolving the image with the second derivatives
of the Gaussian kernel in the respective x- and y-directions.
Parameters
----------
image : ndarray
Input image.
sigma : float
Standard deviation used for the Gaussian kernel, which is used as
weighting function for the auto-correlation matrix.
mode : {'constant', 'reflect', 'wrap', 'nearest', 'mirror'}, optional
How to handle values outside the image borders.
cval : float, optional
Used in conjunction with mode 'constant', the value outside
the image boundaries.
Returns
-------
Hxx : ndarray
Element of the Hessian matrix for each pixel in the input image.
Hxy : ndarray
Element of the Hessian matrix for each pixel in the input image.
Hyy : ndarray
Element of the Hessian matrix for each pixel in the input image.
Examples
--------
>>> from skimage.feature import hessian_matrix
>>> square = np.zeros((5, 5))
>>> square[2, 2] = 4
>>> Hxx, Hxy, Hyy = hessian_matrix(square, sigma=0.1)
>>> Hxy
array([[ 0., 0., 0., 0., 0.],
[ 0., 1., 0., -1., 0.],
[ 0., 0., 0., 0., 0.],
[ 0., -1., 0., 1., 0.],
[ 0., 0., 0., 0., 0.]])
"""
image = img_as_float(image)
gaussian_filtered = ndi.gaussian_filter(image, sigma=sigma, mode=mode, cval=cval)
gradients = np.gradient(gaussian_filtered)
axes = range(image.ndim)
H_elems = [np.gradient(gradients[ax0], axis=ax1) for ax0, ax1 in combinations_with_replacement(axes, 2)]
if image.ndim == 2:
# The legacy 2D code followed (x, y) convention, so we swap the axis
# order to maintain compatibility with old code
H_elems.reverse()
return H_elems
def getInflectionPoints(a, smoonum=4,sign='negative'):
"""
Returns all of the negative or positive inflection points in a plot by first
smoothing it 4 times with a running mean and then looking for points where
the second gradient is zero and the first gradient is either postive or negative.
Inputs:
a - an array of numbers
Key-Word Arguments (kwargs):
smoonum = 4 - number of times to smooth the array to remove noise. Default
set to 4.
sign = 'negative' - specifies whether to look for positive or negative
inflection points.
"""
smoo = a.copy()
for i in range(smoonum):
smoo = smoothed(smoo)
concav = 10*np.gradient(np.gradient(smoo))
Zx,Zy = getZeroes(concav)
aberr = np.gradient(concav)
retX,retY = [],[]
for x in Zx:
if sign=='negative':
if aberr[x]<0:
retX.append(x)
retY.append(a[x])
elif sign=='positive':
if aberr[x]>0:
retX.append(x)
retY.append(a[x])
else:
retX.append(x)
retY.append(a[x])
return retX,retY
def draw(x, y, x_, x_fit, y_interp, group, samplenum, result):
#
#start to draw the figs
y_df = np.gradient(y)
y_df2 = np.gradient(y_df)
fig = plt.figure(figsize=(20, 10), dpi=50, facecolor='white')
fig.suptitle(samplenum)
ax = fig.add_subplot(121)
ax.plot(np.log10(x), y)
ax.plot(np.log10(x), y_df)
ax.plot(np.log10(x), y_df2)
#ax.set_xscale('log')
#ax.set_xlim(0.1, 1000)
ax1 = fig.add_subplot(122)
ax1.scatter(x, y, c='red')
#ax1.plot(10**x_fit, y_interp)
ax1.plot(x_, func(x_fit, result.params))
ax1.set_xscale('log')
ax1.set_xlim(0.1, 10**3)
ax1.set_ylim(0, y.max()*1.2)
for i in np.arange(group):
p = 'p'+str(i)
a = 'a'+str(i)
b = 'b'+str(i)
para = [result.params[p].value, result.params[a].value, result.params[b].value]
ax1.plot(x_,single(x_fit, para))
#ax1.plot(10**x_fit, y_-sum(y_test))
return fig
def setupdetectorresponse(\
BSgridA, BSgridB, BSgridC, BSgridD,
nxi, nyi, dnx, dny):
# These are rules for interpolating the response functions
Arule = scipy.interpolate.interp2d(nxi, nyi, BSgridA.T, kind='linear')
Brule = scipy.interpolate.interp2d(nxi, nyi, BSgridB.T, kind='linear')
Crule = scipy.interpolate.interp2d(nxi, nyi, BSgridC.T, kind='linear')
Drule = scipy.interpolate.interp2d(nxi, nyi, BSgridD.T, kind='linear')
# Calculating the gradients of the response functions
KAx, KAy = np.gradient(BSgridA); KAy=KAy/dny; KAx = KAx/dnx
KBx, KBy = np.gradient(BSgridB); KBy=KBy/dny; KBx = KBx/dnx
KCx, KCy = np.gradient(BSgridC); KCy=KCy/dny; KCx = KCx/dnx
KDx, KDy = np.gradient(BSgridD); KDy=KDy/dny; KDx = KDx/dnx
# These are rules for interpolating the response functions
KAxrule = scipy.interpolate.interp2d(nxi, nyi, KAx.T, kind='linear')
KAyrule = scipy.interpolate.interp2d(nxi, nyi, KAy.T, kind='linear')
KBxrule = scipy.interpolate.interp2d(nxi, nyi, KBx.T, kind='linear')
KByrule = scipy.interpolate.interp2d(nxi, nyi, KBy.T, kind='linear')
KCxrule = scipy.interpolate.interp2d(nxi, nyi, KCx.T, kind='linear')
KCyrule = scipy.interpolate.interp2d(nxi, nyi, KCy.T, kind='linear')
KDxrule = scipy.interpolate.interp2d(nxi, nyi, KDx.T, kind='linear')
KDyrule = scipy.interpolate.interp2d(nxi, nyi, KDy.T, kind='linear')
return \
Arule, Brule, Crule, Drule,\
KAxrule, KAyrule, KBxrule, KByrule, KCxrule, KCyrule, KDxrule, KDyrule
def PlotTSUMU():
import matplotlib.pyplot as plt
domain = history[:, 0]
plot_deriv = True
if plot_deriv:
# plot derivative of norm...
deriv = np.gradient(history[:,3])
deriv2 = np.gradient(deriv)
# plt.plot(domain, history[:, 3], color='blue') # Norm of S0
plt.plot(cjr_data, color='black')
# plt.plot(domain, deriv2, color='red')
plt.plot(cjr_detections, np.ones(len(cjr_detections)), marker='o', color='r', ls='')
# from scipy.interpolate import Rbf, InterpolatedUnivariateSpline
# rbf = Rbf(domain, deriv)
# plt.show()
# return
plt.plot(domain, history[:, 1], color='red') # Minimum of first window
plt.plot(domain, history[:, 2], color='green') # Maximum of second window
plt.plot(domain, history[:, 3], color='blue') # Norm of S0
# Plot the detections.
plt.plot(detections, np.ones(len(detections)) * 500, marker='o', color='r', ls='')
# Plot the thresholds.
plt.plot(domain, np.ones(len(domain)) * T1, color='#aadddd') # Minimum must be lower
plt.plot(domain, np.ones(len(domain)) * T2, color='#ddaadd') # Maximum must be higher
plt.show()
def exportGradientImage(sigma=3.0): x, y = 5000, 3500 size = 2000 topleft = (x, y) bottomright = (x+size, y+size) image = getImageByName(imagefilename='../resources/images/registered-to-2008-07-24-09_55.tif', topleft=topleft, bottomright=bottomright) smooth = vigra.filters.gaussianSmoothing(image, sigma) smoothswap = smooth.swapaxes(0, 1) m, n = vigra.Image((2000,2000)), vigra.Image((2000,2000)) for i in range(size): grad = np.gradient(smooth[i]) for j in range(len(grad)): m[i][j] = grad[j] for i in range(size): grad = np.gradient(smoothswap[i]) for j in range(len(grad)): n[j][i] = grad[j] out = m + n vigra.impex.writeImage(vigra.colors.linearRangeMapping(out), '/home/max/Desktop/out.png') vigra.impex.writeImage(vigra.colors.linearRangeMapping(m), '/home/max/Desktop/m.png') vigra.impex.writeImage(vigra.colors.linearRangeMapping(n), '/home/max/Desktop/n.png') return smooth
def rect_guess(self, data, x=None, **kwargs):
if x is None:
return
ymin, ymax = min(data), max(data)
xmin, xmax = min(x), max(x)
ntest = min(2, len(data)/5)
step_up = (data[:ntest].mean() > data[-ntest:].mean())
dydx = savitzky_golay(np.gradient(data)/np.gradient(x), 5, 2)
cen1 = x[np.where(dydx==dydx.max())][0]
cen2 = x[np.where(dydx==dydx.min())][0]
if step_up:
center1 = cen1 # + (xmax+xmin)/4.0)/2.
center2 = cen2 # + 3*(xmax+xmin)/4.0)/2.
else:
center1 = cen2 # + (xmax+xmin)/4.0)/2.0
center2 = cen1 # + 3*(xmax+xmin)/4.0)/2.0
pars = self.make_params(amplitude=(ymax-ymin),
center1=center1, center2=center2)
pars['%ssigma1' % self.prefix].set(value=(xmax-xmin)/5.0, min=0.0)
pars['%ssigma2' % self.prefix].set(value=(xmax-xmin)/5.0, min=0.0)
return update_param_vals(pars, self.prefix, **kwargs)
def _optimize_num_overlap_pixels(data):
"""
"""
num_projection, num_slices, num_pixels = data.shape
if num_projection % 2 != 0: # if odd
img_first_half = np.squeeze(data[1:num_projection/2 + 1, num_slices/2, :])
img_second_half = np.squeeze(data[num_projection/2:num_projection - 1, num_slices/2, :])
else:
img_first_half = np.squeeze(data[1:num_projection/2 + 1, num_slices/2, :])
img_second_half = np.squeeze(data[num_projection/2:num_projection, num_slices/2, :])
ind = range(0, num_pixels)[::-1]
img_second_half = img_second_half[:, ind]
img_first_half = ndimage.filters.gaussian_filter(img_first_half, sigma=2)
img_second_half = ndimage.filters.gaussian_filter(img_second_half, sigma=2)
gx1, gy1 = np.gradient(img_first_half)
gx2, gy2 = np.gradient(img_second_half)
img_first_half = np.power(gx1, 2) + np.power(gy1, 2)
img_second_half = np.power(gx2, 2) + np.power(gy2, 2)
img1 = np.fft.fft(img_first_half)
img2 = np.fft.fft(img_second_half)
tmp = np.real(np.fft.ifft(np.multiply(np.conj(img2), img1)))
return np.argmax(np.sum(np.abs(tmp), axis=0))
def deblurImage(blurImg,iteration,mode=0):
niter=0
edge=getEdge(blurImg*255,mode)
stDesv=np.std(edge)
grady, gradx=np.gradient((blurImg*255))
deblurImg=np.copy(blurImg)
normalizar=False
#print "Gradiente antes", np.sum(gradx+grady)
desv=np.std(deblurImg)
extraGain=1.0
while(niter<iteration):
desv=np.std(deblurImg)
#Dprint "Desviacion estandar borrosa", desv
for j in range(deblurImg.shape[0]-1):
for k in range(deblurImg.shape[1]-1):
gain=gradx[j,k]*stDesv+grady[j,k]*stDesv
if(gain<extraGain):
extraGain=gain
deblurImg[j,k]=deblurImg[j,k]+gain
if(deblurImg[j,k]<0.0 or deblurImg[j,k]>255.0):
normalizar=True
deblurImg=extraGain/10.0+deblurImg
if normalizar:
normalize(deblurImg)
edge=getEdge(deblurImg,mode)
stDesv=np.std(edge)
niter=niter+1
gradx2, grady2=np.gradient(deblurImg)
return deblurImg
def propagate_tie(mu, delta, pixel_size, dist):
"""
Propagate emitting x-ray wave based on Transport of Intensity.
Parameters
----------
mu : ndarray, optional
3D tomographic data for attenuation.
delta : ndarray
3D tomographic data for refractive index.
pixel_size : float
Detector pixel size in cm.
dist : float
Propagation distance of the wavefront in cm.
Returns
-------
ndarray
3D propagated tomographic intensity.
"""
i1 = np.exp(-mu)
i2 = np.zeros(delta.shape)
for m in range(delta.shape[0]):
dx, dy = np.gradient(delta[m], pixel_size)
d2x, _ = np.gradient(i1[m] * dx, pixel_size)
_, d2y = np.gradient(i1[m] * dy, pixel_size)
i2[m] = i1[m] + dist * (d2x + d2y)
return i2
def _threshold_gradient(im):
"""Indicate pixel locations with gradient below the bottom 10th percentile
Parameters
----------
im : array
The mean intensity images for each channel.
Size: (num_channels, num_rows, num_columns).
Returns
-------
array
Binary values indicating whether the magnitude of the gradient is below
the 10th percentile. Same size as im.
"""
if im.shape[0] > 1:
# Calculate directional relative derivatives
_, g_x, g_y = np.gradient(np.log(im))
else:
# Calculate directional relative derivatives
g_x, g_y = np.gradient(np.log(im[0]))
g_x = g_x.reshape([1, g_x.shape[0], g_x.shape[1]])
g_y = g_y.reshape([1, g_y.shape[0], g_y.shape[1]])
gradient_magnitudes = np.sqrt((g_x ** 2) + (g_y ** 2))
below_threshold = []
for chan in gradient_magnitudes:
threshold = mquantiles(chan[np.isfinite(chan)].flatten(), [0.1])[0]
below_threshold.append(chan < threshold)
return np.array(below_threshold)
def get_quantum_driving_parameters(self):
"""Return the adapted parameters (eps_prime, delta, theta_prime) to
obtain adiabatic dynamics for arbitrary length.
"""
eps, delta = self.get_cycle_parameters()
eps_dot, delta_dot = [np.gradient(x, self.dt) for x in eps, delta]
mixing_angle_dot = 2.*np.abs(self.B0)*(delta*eps_dot-delta_dot*eps)
mixing_angle_dot /= (delta**2 + 4.*np.abs(self.B0)**2*eps**2)
self.mixing_angle_dot = mixing_angle_dot
self.mixing_angle = np.arctan(2.*np.abs(self.B0)*eps/delta)
self.mixing_angle_dot_alt = np.gradient(self.mixing_angle, self.dt)
theta_prime = -2.*np.arctan2(mixing_angle_dot, (2*np.abs(self.B0)*eps))
B_prime = (-1j * (np.exp(1j*theta_prime) + 1.) * np.pi**2 /
self.W**3 / np.sqrt(self.k0*self.k1))
eps_prime = np.sqrt(4.*np.abs(self.B0)**2*eps**2 + mixing_angle_dot**2)
eps_prime /= 2.*np.abs(B_prime)
# avoid divergencies
for n in (0, -1):
eps_prime[n] = 0.0
self.eps_prime = eps_prime
self.delta_prime = delta
self.theta_prime = theta_prime
return eps_prime, delta, theta_prime
def V(U):
""" Spatial Viscous Fluxes at cell centres """
rho, momx, momy, E = rollaxis(U, U.ndim-1) # shape to (neq,nx,ny)
rho = rho.copy() # GASMODEL needs contiguous arrays
u = momx/rho
v = momy/rho
e = E/rho - 0.5*(u**2+v**2) # Gas internal energy (J/kg)
T,Xi = GASMODEL.decode_conserved(rho, e)
mu = 8.6412e-6*(T/288.16)**1.5*(398.16)/(T+110) # Sutherland viscosity law
k = mu*14320.0/0.70 # This thing is important and hard to calculate
dudx,dudy = gradient(u,dx,dy)
dvdx,dvdy = gradient(v,dx,dy)
dTdx,dTdy = gradient(T,dx,dy)
tauxx = 2.0/3.0*mu*(2*dudx-dvdy)
tauxy = mu*(dudy + dvdx)
qx = -k*dTdx
nx,ny,neq = U.shape
C = zeros((nx,ny,neq)) # Input is cells, output is faces
Q = rollaxis(C,C.ndim-1) # View of C with nicer indexing
Q[1] = -tauxx
Q[2] = -tauxy
Q[3] = -u*tauxx -v*tauxy + qx
return C
def test_calc_lwc_gradient():
from cloudnetpy.utils import l2norm
ERROR_OBJ.lwc = np.ma.array([[0.1, 0.2, 0.3],
[0.1, 0.3, 0.6]])
expected = l2norm(*np.gradient(ERROR_OBJ.lwc))
assert_array_almost_equal(ERROR_OBJ._calc_lwc_gradient(), expected)
def Velocity(P_deg, framerate):
ret = copy(P_deg)
# Gradient in deg/sec or px/sec
for k in ret:
ret[k] = np.gradient(ret[k]) * framerate
return ret
#lon = lon[-1,:,:]
#lat = lat[-1,:,:]
#latin = lat[:25,:,:]
#longin = lon[:25,:,:]
#x = np.linspace(-grid_spacing*(xdim-1)/2,grid_spacing*(xdim-1)/2,xdim)
x = np.linspace(0,grid_spacing*(xdim-1),xdim)
dx = x[1]-x[0]
#y = np.linspace(-grid_spacing*(ydim-1)/2,grid_spacing*(ydim-1)/2,ydim)
y = np.linspace(0,grid_spacing*(ydim-1),ydim)
dy = y[1]-y[0]
x, y = np.meshgrid(x,y)
dudy,dudx = np.gradient(u,dy,dx)
dvdy,dvdx = np.gradient(v,dy,dx)
s1 = np.ma.empty([ydim,xdim])
s2 = np.ma.empty([ydim,xdim])
J = np.array([[0, 1], [-1, 0]])
for i in range(ydim):
for j in range(xdim):
if (dudx[i,j] and dudy[i,j] and dvdx[i,j] and dvdy[i,j] and u[i,j] and v[i,j]) is not np.ma.masked:
Utemp = np.array([u[i, j], v[i, j]])
Grad = np.array([[dudx[i, j], dudy[i, j]], [dvdx[i, j], dvdy[i, j]]])
S = 0.5*(Grad + np.transpose(Grad))
s1[i,j] = 3600*np.min(np.linalg.eig(S)[0])
s2[i,j] = 3600*np.max(np.linalg.eig(S)[0])
def plot_score_slvol(self, ens_scr):
#import analyse_timeseries as at; reload(at)
#import glob
#ts_path_names = os.path.join(cf.resultpath,cf.pism_file_name.replace(str(cf.fillnum),str("*")))
#ensemble_members = glob.glob(ts_path_names)
#ts_data = at.Ensemble_TimeSeries(ensemble_members)
#print ens_scr # dict of ensemble members and individual score(s)
#fig24, [ax24a,ax24b] = plt.subplots(2, 1,figsize=(7, 6),num=24) #sharex='col', sharey='row'
fig24, ax24b = plt.subplots(1, 1, figsize=(9, 4),
num=24) #sharex='col', sharey='row'
ax24a = ax24b.twinx()
#ax24a.grid('on')
plotgradient = False
plottopresent = False
if self.grvol:
plt.title("grounded ice volume anomaly")
ax24a.set_ylabel("(PD obs - mod) in mio km3")
volunit = "mio. km3"
volscale = 1.0e15
varname = "ice_volume_glacierized_grounded"
printname = self.printname.replace("placeholder", "grvolall")
slvol0 = 26.2914 #16km
varmax = 10
else:
#plt.title("equivalent global-mean sea-level contribution (ESL)")
if plottopresent:
ax24a.set_ylabel("(PD - ESL) in m sea-level equivalent")
else:
#ax24a.set_ylabel("(PD obs - ESL) in m sea-level equivalent")
ax24a.set_ylabel("sea-level anomaly in m")
ax24b.set_ylabel("sea-level relevant volume in m")
volunit = "m SLE"
volscale = 1.0
varname = "slvol"
printname = self.printname.replace("placeholder", "slvolall")
slvol0 = self.slvol0
varmax = 20
ax24a.plot([-125, 0], [0, 0],
color="k",
linewidth=1,
linestyle="dashed")
#ax24a.axvline(-14.35,color="k",linewidth=1,linestyle="dotted")
#ax24a.set_xlabel("time [kyr]")
ax24a.set_xlabel("time in kyr")
#x24a.axis([-125,0,-varmax,varmax])
ax24a.axis([-125, 0, -varmax / 2, varmax])
ax24a.set_xticks(np.arange(-120, varmax, varmax))
if True: #include penultimate glacial cycle
ax24a.plot([-210, 0], [0, 0],
color="k",
linewidth=1,
linestyle="dashed")
#ax24a.axis([-210,0,-varmax,varmax])
ax24a.axis([-210, 0, -varmax / 2, varmax])
ax24a.set_xticks(np.arange(-200, 25, 25))
#print cf.start_from_file
if True: #show deglaciation period
#ax24a.plot([-15,0],[0,0],color="k",linewidth=1,linestyle="dashed")
#ax24b.plot([-15,0],[slvol0,slvol0],color="k",linewidth=1,linestyle="dashed")
#ax24a.axis([-15,0,-varmax/2,varmax])
ax24b.axis([-15, 0, -varmax / 2 + slvol0, varmax + slvol0])
#ax24a.set_xticks(np.arange(-14,2,2))
ax24b.set_xticks(np.arange(-14, 2, 2))
if plotgradient:
ax24a.axis([-15, 0, -0.02, 0.02])
#ax24a.yaxis.grid(True)
#ax24a.grid(True, which='both')
ax24b.set_ylim([-varmax / 2 + slvol0, varmax + slvol0])
for i in [2529, 2533, 2534, 2535]:
#initfile='/p/tmp/albrecht/pism18/pismOut/forcing/'
#initfile='/p/projects/pism/albrecht/pism_paleo_ensemble/ensemble_2400-2540/'
#TODO
initfile = cf.resultpath2 + 'forcing' + str(
i) + '_TPSO/results/ts_forcing_' + str(
cf.resolution) + 'km_' + str(cf.runtime) + 'yrs.nc'
if os.path.exists(initfile):
tsdata = nc.Dataset(initfile, 'r')
slvol = np.squeeze(tsdata.variables[varname][:]) / volscale
sltime = np.squeeze(
tsdata.variables["time"][:]) / cf.seconds_per_year * 1e-3
tsdata.close()
if plottopresent:
slvol0 = slvol[-1]
if plotgradient:
ax24a.plot(sltime,
np.gradient(slvol),
color=cf.colorscheme[1],
linewidth=1,
zorder=2,
alpha=0.8)
else:
#ax24a.plot(sltime,slvol0-slvol,color=cf.colorscheme[1],linewidth=1,zorder=0,alpha=0.8)
ax24a.plot(sltime[0:85000],
slvol[0:85000] - slvol0,
color=cf.colorscheme[1],
linewidth=1,
zorder=2,
alpha=0.8)
#print i,sltime[-5000],slvol[-5000]
### aggreagated score normalized to probability sum(P)=1
agg_score = {k: v[0] for k, v in ens_scr.iteritems()}
agg_score_prop = {
k: v / sum(agg_score.values())
for k, v in agg_score.iteritems()
}
#best_score = np.nanmax(agg_score.values(),axis=0)
best_score_mem = self.best_scores[0]
best_score = agg_score[best_score_mem]
worst_score = agg_score[self.best_scores[-1]]
sl_data = {}
#loop over ensemble members/scores
for l, (enum, scores) in enumerate(sorted(ens_scr.items())):
### read each netcdf timeseries file ###############
ts_file_name = cf.pism_file_name.replace(str(cf.fillnum),
str(enum))
tsfile = os.path.join(cf.resultpath, ts_file_name)
tsfile = tsfile.replace('paleo.nc',
'timeseries.nc') #'timeseries-slvol.nc'
if os.path.exists(tsfile):
tsdata = nc.Dataset(tsfile, 'r')
slvol = np.squeeze(tsdata.variables[varname][:]) / volscale
sltime = np.squeeze(
tsdata.variables["time"][:]) / cf.seconds_per_year * 1e-3
tsdata.close()
sl_data[enum] = slvol
if plottopresent:
slvol0 = slvol[-1]
### plot sl-curve with alpha according to score
alphamin = 0.03
alphamax = 0.9
alphaval = alphamax + (
(alphamax - alphamin) *
(scores[0] - best_score)) / (best_score - worst_score)
if plotgradient:
ax24a.plot(sltime,
np.gradient(slvol),
color="k",
linewidth=0.5,
alpha=alphaval,
zorder=1)
else:
#ax24a.plot(sltime,slvol0-slvol,color="k",linewidth=0.5,alpha=alphaval,zorder=1)
ax24a.plot(sltime[::10],
slvol[::10] - slvol0,
color="k",
linewidth=0.5,
alpha=alphaval,
zorder=1)
### best/reference run #############################
#if enum=='1170':#reference
if enum == best_score_mem:
#if enum in self.best_scores[0:3]:
if plotgradient:
ax24a.plot(sltime,
np.gradient(slvol),
color=cf.colorscheme[3],
linewidth=2,
zorder=3,
label="best")
else:
ax24a.plot(sltime,
slvol - slvol0,
color=cf.colorscheme[3],
linewidth=1.5,
zorder=3,
label="best")
#ax24a.plot(sltime,slvol0-slvol,color=cf.colorscheme[3],linewidth=1.5,zorder=3,label="best")
### ensemble mean ###################################
if l == 0:
ensemble_mean_slvol = slvol * agg_score_prop[enum]
tslen = len(slvol)
sltime0 = sltime
ensemble_stddev_slvol = np.zeros_like(slvol)
else:
ensemble_mean_slvol += slvol[-tslen:] * agg_score_prop[enum]
if not plotgradient:
if plottopresent:
slvol0 = ensemble_mean_slvol[-1]
ax24a.plot(sltime0,
ensemble_mean_slvol - slvol0,
color=cf.colorscheme[2],
linewidth=2.0,
zorder=2,
label="mean")
#ax24a.plot(sltime0,slvol0-ensemble_mean_slvol,color=cf.colorscheme[2],linewidth=2.0,zorder=2,label="mean")
### ensemble standard deviation ########################
for l, (enum, sl) in enumerate(sorted(sl_data.items())):
ensemble_stddev_slvol += (ensemble_mean_slvol -
sl[-tslen:])**2 * agg_score_prop[enum]
ensemble_stddev_slvol = np.sqrt(ensemble_stddev_slvol)
#stnd_upper = slvol0-ensemble_mean_slvol+ensemble_stddev_slvol
#stnd_lower = slvol0-ensemble_mean_slvol-ensemble_stddev_slvol
stnd_upper = ensemble_mean_slvol - slvol0 + ensemble_stddev_slvol
stnd_lower = ensemble_mean_slvol - slvol0 - ensemble_stddev_slvol
if not plotgradient:
ax24a.fill_between(sltime0[::10],
stnd_upper[::10],
stnd_lower[::10],
color=cf.colorscheme[2],
zorder=0,
alpha=0.4,
label="stdev")
#ax24a.plot(sltime0,stnd_upper,color=cf.colorscheme[2],linewidth=2,zorder=2,linestyle="dotted",label="stdev")
#ax24a.plot(sltime0,stnd_lower,color=cf.colorscheme[2],linewidth=2,zorder=2,linestyle="dotted")
legend24 = ax24a.legend(loc="lower left", shadow=False, fontsize=11)
rcParams['legend.frameon'] = 'False'
### min and max values ##################################
pm = str(r"$\pm$")
pd_mean_sl = ensemble_mean_slvol[-1]
#pd_span = str(np.around(stnd_lower[-1],decimals=1))
#pd_span += " - "+str(np.around(stnd_upper[-1],decimals=1))+" \n "+volunit
pd_span = str(np.around(pd_mean_sl - slvol0, decimals=1)) + pm
pd_span += str(np.around(ensemble_stddev_slvol[-1],
decimals=1)) #+" \n "+volunit
lgm_mean_sl = np.max(ensemble_mean_slvol)
lgm_mean_k = np.argmax(ensemble_mean_slvol)
lgm_mean_k2 = np.argmin((sltime0 + 15)**2)
lgm_mean_t = sltime0[lgm_mean_k]
#lgm_span = str(np.around(stnd_lower[lgm_mean_k2],decimals=1))
#lgm_span += " - "+str(np.around(stnd_upper[lgm_mean_k2],decimals=1))+" \n "+volunit
lgm_span = str(
np.around(ensemble_mean_slvol[lgm_mean_k2] - slvol0,
decimals=1)) + pm
lgm_span += str(
np.around(ensemble_stddev_slvol[lgm_mean_k2],
decimals=1)) #+" \n "+volunit
eeam_mean_sl = np.min(ensemble_mean_slvol[-tslen:-tslen / 2])
eeam_mean_k = np.argmin(ensemble_mean_slvol[-tslen:-tslen / 2])
eeam_mean_k2 = np.argmin((sltime0 + 120)**2)
eeam_mean_t = sltime0[eeam_mean_k]
#eeam_span = str(np.around(stnd_lower[eeam_mean_k2],decimals=1))
#eeam_span += " - "+str(np.around(stnd_upper[eeam_mean_k2],decimals=1))+" \n "+volunit
eeam_span = str(
np.around(ensemble_mean_slvol[eeam_mean_k2] - slvol0,
decimals=1)) + pm
eeam_span += str(
np.around(ensemble_stddev_slvol[eeam_mean_k2],
decimals=1)) #+" \n "+volunit
degl_mean_k10 = np.argmin((sltime0 + 10)**2)
degl_mean_k5 = np.argmin((sltime0 + 5)**2)
#print pd_mean_sl,lgm_mean_sl,lgm_mean_t,eeam_mean_sl,eeam_span,eeam_mean_t
#print slvol0,ensemble_mean_slvol[-1],ensemble_stddev_slvol[-1]
print "Reconstructions of sea-level contributions:"
print "period", "mean sl", "std sl", "time", "mean anomaly"
print "\nPD:", pd_mean_sl, ensemble_stddev_slvol[-1], sltime0[
-1], pd_mean_sl - slvol0
print "LGM:", lgm_mean_sl, ensemble_stddev_slvol[
lgm_mean_k], lgm_mean_t, lgm_mean_sl - slvol0
print "LIG:", eeam_mean_sl, ensemble_stddev_slvol[
eeam_mean_k], eeam_mean_t, eeam_mean_sl - slvol0, "\n"
print "LGM2:", ensemble_mean_slvol[lgm_mean_k2], ensemble_stddev_slvol[
lgm_mean_k2], sltime0[
lgm_mean_k2], ensemble_mean_slvol[lgm_mean_k2] - slvol0
print "LIG2:", ensemble_mean_slvol[
eeam_mean_k2], ensemble_stddev_slvol[eeam_mean_k2], sltime0[
eeam_mean_k2], ensemble_mean_slvol[eeam_mean_k2] - slvol0, "\n"
print "DEG10:", ensemble_mean_slvol[
degl_mean_k10], ensemble_stddev_slvol[degl_mean_k10], sltime0[
degl_mean_k10], ensemble_mean_slvol[degl_mean_k10] - slvol0
print "DEG5:", ensemble_mean_slvol[
degl_mean_k5], ensemble_stddev_slvol[degl_mean_k5], sltime0[
degl_mean_k5], ensemble_mean_slvol[degl_mean_k5] - slvol0, "\n"
#ax24a.text(eeam_mean_t,6.0*varmax/8.0,eeam_span,color=cf.colorscheme[2],zorder=3,fontsize=10)
#ax24a.text(-35,varmax/2.0,lgm_span,color=cf.colorscheme[2],zorder=3,fontsize=10)
#ax24a.text(-20,3.0*varmax/4.0,pd_span,color=cf.colorscheme[2],zorder=3,fontsize=10)
ax24a.text(eeam_mean_t,
-3.0 * varmax / 8.0,
eeam_span,
color=cf.colorscheme[2],
zorder=3,
fontsize=11)
ax24a.text(-30,
7.0 * varmax / 8.0,
lgm_span,
color=cf.colorscheme[2],
zorder=3,
fontsize=11)
ax24a.text(-21,
-3.0 * varmax / 8.0,
pd_span,
color=cf.colorscheme[2],
zorder=3,
fontsize=11)
if self.printtopdf:
#printname = self.printname.replace("placeholder","slvolall")
plt.savefig(printname, format='pdf')
plt.savefig(printname.replace(".pdf", ".png"),
format='png',
dpi=300)
points = 500
cmap = elphmod.plot.colormap(
(0, elphmod.plot.Color(255, 255, 255)),
(1, elphmod.plot.Color(0, 0, 0)),
)
el = elphmod.el.Model('data/NbSe2')
e = elphmod.dispersion.dispersion_full(el.H, nk)[:, :, 0] - mu
kxmax, kymax, kx, ky, e = elphmod.plot.toBZ(e,
points=points,
return_k=True,
outside=np.nan)
dedky, dedkx = np.gradient(e, ky, kx)
dedk = np.sqrt(dedkx**2 + dedky**2)
image = elphmod.plot.color(dedk, cmap)
if comm.rank == 0:
elphmod.plot.save('fermi_velocity.png', image)
info('Min./max./mean number of k-points for meV resolution:')
FS = np.where(np.logical_and(~np.isnan(dedk), abs(e) < 0.1))
for v in dedk[FS].min(), dedk[FS].max(), np.average(dedk[FS]):
info(int(round(2 * kymax * v / 1e-3)))
fs_solutions = []
normvalue = np.inf
l = 0
while normvalue > TOL and l < numTimeSteps:
# solve non-localized system
lod = lod_wave.LodWave(b_coef, world, np.inf, IPatchGenerator, a_coef,
prev_fs_sol, ms_basis)
lod.solve_fs_system()
# store sparse solution
prev_fs_sol = sparse.csc_matrix(np.array(np.column_stack(lod.fs_list)))
fs_solutions.append(prev_fs_sol)
normvalue = np.sqrt(
np.dot(np.gradient(prev_fs_sol.toarray()[:, N / 2]),
np.gradient(prev_fs_sol.toarray()[:, N / 2])))
l += 1
print 'N = %d, l = %d' % (N, l)
'''
Compute v^n and w^n
'''
# initial value
Uo = xpCoarse * (1 - xpCoarse)
# coarse v^(-1) and v^0
V = [Uo]
V.append(Uo)
def do_boxcar(image, psf, outwave, boxwidth=2.5, nspec=500):
"""Extracts spectra row by row, given the centroids
Args:
image : desispec.image object
psf: desispec.psf.PSF like object
Or do we just parse the traces here and write a separate wrapper to handle this? Leaving psf in the input argument now.
outwave: wavelength array for the final spectra output
boxwidth: HW box size in pixels
Returns desispec.frame.Frame object
"""
import math
from desispec.frame import Frame
#wavelength=psf.wavelength() # (nspec,npix_y)
wmin = psf.wmin
wmax = psf.wmax
waves = np.arange(wmin, wmax, 0.25)
xs = psf.x(None, waves) #- xtraces # doing the full image here.
ys = psf.y(None, waves) #- ytraces
camera = image.camera
spectrograph = int(camera[1:]) #- first char is "r", "b", or "z"
mask = np.zeros(image.pix.T.shape)
maxx, maxy = mask.shape
maxx = maxx - 1
maxy = maxy - 1
ranges = np.zeros((mask.shape[1], xs.shape[0] + 1), dtype=int)
for bin in xrange(0, len(waves)):
ixmaxold = 0
for spec in xrange(0, xs.shape[0]):
xpos = xs[spec][bin]
ypos = int(ys[spec][bin])
if xpos < 0 or xpos > maxx or ypos < 0 or ypos > maxy:
continue
xmin = xpos - boxwidth
xmax = xpos + boxwidth
ixmin = int(math.floor(xmin))
ixmax = int(math.floor(xmax))
if ixmin <= ixmaxold:
print "Error Box width overlaps,", xpos, ypos, ixmin, ixmaxold
return None, None
ixmaxold = ixmax
if mask[int(xpos)][ypos] > 0:
continue
# boxing in x vals
if ixmin < 0: #int value is less than 0
ixmin = 0
rxmin = 1.0
else: # take part of the bin depending on real xmin
rxmin = 1.0 - xmin + ixmin
if ixmax > maxx: # xmax is bigger than the image
ixmax = maxx
rxmax = 1.0
else: # take the part of the bin depending on real xmax
rxmax = xmax - ixmax
ranges[ypos][spec + 1] = math.ceil(xmax) #end at next column
if ranges[ypos][spec] == 0:
ranges[ypos][spec] = ixmin
mask[ixmin][ypos] = rxmin
for x in xrange(ixmin + 1, ixmax):
mask[x][ypos] = 1.0
mask[ixmax][ypos] = rxmax
for ypos in xrange(ranges.shape[0]):
lastval = ranges[ypos][0]
for sp in xrange(1, ranges.shape[1]):
if ranges[ypos][sp] == 0:
ranges[ypos][sp] = lastval
lastval = ranges[ypos][sp]
maskedimg = (image.pix * mask.T)
flux = np.zeros((maskedimg.shape[0], ranges.shape[1] - 1))
for r in xrange(flux.shape[0]):
row = np.add.reduceat(maskedimg[r], ranges[r])[:-1]
flux[r] = row
from desispec.interpolation import resample_flux
wtarget = outwave
#- limit nspec to psf.nspec max
if nspec > psf.nspec:
nspec = psf.nspec
print "Warning! Extracting only %s spectra" % psf.nspec
fflux = np.zeros((nspec, len(wtarget)))
ivar = np.zeros((nspec, len(wtarget)))
resolution = np.zeros(
(nspec, 21, len(wtarget)
)) #- placeholder for online case. Offline should be usable
#TODO get the approximate resolution matrix for online purpose or don't need them? How to perform fiberflat, sky subtraction etc or should have different version of them for online?
#- convert to per angstrom first and then resample to desired wave length grid.
for spec in xrange(nspec):
ww = psf.wavelength(spec)
dwave = np.gradient(ww)
flux[:, spec] /= dwave
fflux[spec, :] = resample_flux(wtarget, ww, flux[:, spec])
#- image.readnoise is no more a scalar but a full CCD pixel size array
#- TODO Using median readnoise here for now. Need to propagate per-pixel readnoise from top.
readnoise = np.median(image.readnoise)
ivar[spec, :] = 1. / (
fflux[spec, :].clip(0.0) + 2 * boxwidth * readnoise**2
) #- 2*half width=boxsize
return fflux, ivar, resolution
def InitialConditions(x, rho, v, Pressure, args, p):
N = args.n
dx = np.gradient(x) # Cell Sizes (UNIFORM GRID ONLY)
M = (rho * dx).sum() # Total Mass (UNIFORM GRID ONLY)
# Particle Parameters
mp = M / N # Particle Mass, Total Mass divided by total particles
p['mp'] = mp
# Final number of particles per cell, and total
Np = np.floor((rho * dx) / mp +
np.random.uniform(size=rho.size)).astype(int)
NP = Np.sum()
p['NP'] = NP
# Particle Diameter
Dmax = (dx / Np).min()
D = 1e-4 * Dmax
D = 0
p['D'] = D
#Initialize Velocities
s = np.sqrt(Pressure / rho)
# bin and effbin sizes
# velocities
effbins = np.array([])
bins = np.array([])
effbins = []
bins = []
vels = []
for j in range(len(dx)):
effbins.append(np.ones(Np[j]) * (dx[j] / Np[j] - D))
bins.append(np.ones(Np[j]) * dx[j] / Np[j])
vels.append(np.random.randn(Np[j]) * s[j] + v[j])
#effbins = np.array(effbins)
#bins = np.array(bins)
#pos_in_bin = effbins*np.random.uniform(size=effbins.size)
effbins = np.concatenate(effbins)
bins = np.concatenate(bins)
vels = np.concatenate(vels)
uniforms = np.random.random(Np.sum())
# Computing particle dx's
if args.b == 0: #Periodic Boundary Conditions
Pdx = np.roll(effbins * uniforms, -1) - effbins * uniforms + bins
v0 = vels[0]
P0 = uniforms[0] * effbins[0] + D / 2
vels = np.roll(vels, -1) - vels
P = np.concatenate(([P0], P0 + np.cumsum(Pdx[:-1])))
elif args.b == 1: #Reflective Boundary Conditions #NEED TO FIX VELOCITY
Pdx = effbins[1:] * uniforms[
1:] - effbins[:-1] * uniforms[:-1] + bins[:-1]
vels = np.roll(vels, -1) - vels
P0 = uniforms[0] * effbins[0] + D / 2
Pdx = np.append(np.array([P0]), Pdx)
P = np.cumsum(Pdx)
#MP = mp*np.arange(1,Np.sum())
#rhoP = mp/Pdx
return P, Pdx, vels, P0, p
fid.write('%f %f\n' % (x_target[j], gr_new[j]))
fid.close()
#test the fit
F_fit(gr_target, gr_new)
#add a boltzman to the potential to get the next potential
V_new = []
for j in range(len(x_target)):
try:
boltz = .2 * T * math.log(gr_new[j] / gr_target[j])
if math.isnan(boltz):
V_new.append(V[j])
elif math.isinf(boltz):
V_new.append(V[j])
else:
V_new.append(V[j] +
alpha[j] * T * math.log(gr_new[j] / gr_target[j]))
except:
print 'error', gr_new[j], gr_target[j]
V_new.append(V[j])
#Smooth Out V
V = Smooth(V_new)
F_new = -np.gradient(V, x_target[1] - x_target[0])
#write new potential table
pot = open('potential/potential%i.dat' % i, 'w')
pot.write('#r V F\n')
for j in range(len(x_target)):
pot.write('%f %f %f\n' % (x_target[j], V[j], F_new[j]))
pot.close()
table.set_from_file('A', 'A', filename='potential/potential%i.dat' % i)
def average_energy(read_Z_data=True,
generate_Z_data=False,
Z_file_name=None,
plot_energy=True,
save_plot_E=True,
show_plot_E=True,
E_plot_name=None,
temp_min=1. / 10,
temp_max=1 / 2.,
N_temp=10,
save_Z_csv=True,
relevant_info_Z=None,
print_Z_data=True,
x_max=7.,
nx=201,
N_iter=7,
potential=harmonic_potential,
potential_string='harmonic_potential',
print_steps=False,
save_pi_x_data=False,
pi_x_file_name=None,
relevant_info_pi_x=None,
plot_pi_x=False,
save_plot_pi_x=False,
show_plot_pi_x=False):
"""
"""
if read_Z_data:
Z_file_read = pd.read_csv(Z_file_name, index_col=0, comment='#')
elif generate_Z_data:
t_0 = time()
Z_data = Z_several_values(
temp_min, temp_max, N_temp, save_Z_csv, Z_file_name,
relevant_info_Z, print_Z_data, x_max, nx, N_iter, potential,
potential_string, print_steps, save_pi_x_data, pi_x_file_name,
relevant_info_pi_x, plot_pi_x, save_plot_pi_x, show_plot_pi_x)
t_1 = time()
print(
'--------------------------------------------------------------------------\n'
+ '%d values of Z(beta) generated --> %.3f sec.' %
(N_temp, t_1 - t_0))
Z_file_read = Z_data
else:
print(
'Elegir si se generan o se leen los datos para la función partición, Z.\n'
+
'Estas opciones son mutuamente exluyentes. Si se seleccionan las dos, el'
+ 'algoritmo escoge leer los datos.')
# READ DATA IS OK
beta_read = Z_file_read['beta']
temp_read = Z_file_read['temperature']
Z_read = Z_file_read['Z']
E_avg = np.gradient(-np.log(Z_read), beta_read)
if plot_energy:
plt.figure(figsize=(8, 5))
plt.plot(
temp_read,
E_avg,
label=u'$\langle E \\rangle$ via path integral\nnaive sampling')
plt.plot(temp_read,
E_QHO_avg_theo(beta_read),
label=u'$\langle E \\rangle$ teórico')
plt.legend(loc='best')
plt.xlabel(u'$T$')
plt.ylabel(u'$\langle E \\rangle$')
if save_plot_E:
if E_plot_name is None:
script_dir = os.path.dirname(os.path.abspath(__file__))
E_plot_name='E-ms-plot-%s-beta_max_%.3f-'%(potential_string,1./temp_min) +\
'beta_min_%.3f-N_temp_%d-x_max_%.3f-'%(1./temp_max,N_temp,x_max) +\
'nx_%d-N_iter_%d.eps'%(nx, N_iter)
E_plot_name = script_dir + '/' + E_plot_name
plt.savefig(E_plot_name)
if show_plot_E:
plt.show()
plt.close()
return E_avg, beta_read.to_numpy()
def add_cyclic(data):
# Add Cyclic point around 360 degrees longitude:
lons = data.getLongitude()[:]
dx = np.gradient(lons)[-1]
data2 = data(longitude=(0, dx + np.max(lons)), squeeze=True)
return data2
potential_string = 'harmonic_potential', print_steps=False,
save_pi_x_data=False, pi_x_file_name=None, relevant_info_pi_x=None,
plot=False, save_plot=False, show_plot=False )
t_1= time()
print('<E(beta)> --> %.3f sec.'%(t_1-t_0))
# READ DATA IS OK
Z_file_name = script_dir+'/'+'partition-function-test-2.csv'
Z_file_read = pd.read_csv(Z_file_name, index_col=0, comment='#')
beta_read = Z_file_read['beta']
beta_read = beta_read.to_numpy()
temp_read = Z_file_read['temperature']
temp_read = temp_read.to_numpy()
Z_read = Z_file_read['Z']
Z_read = Z_read.to_numpy()
E_avg = np.gradient(-np.log(Z_read),beta_read)
def Z_QHO(beta):
return 0.5/np.sinh(beta/2)
def E_QHO_avg_theo(beta):
return 0.5/np.tanh(0.5*beta)
plt.figure()
plt.plot(temp_read,E_avg,label=u'$< E > Path Integral$')
plt.plot(temp_read,E_QHO_avg_theo(beta_read),label=u'$< E > theory$')
plt.plot(temp_read,Z_read,'v-',label=u'$ Z(T) $')
plt.legend(loc='best')
plt.xlabel(u'$T$')
plt.ylabel(u'$< E >$ or $Z(T)$')
plt.show()
plt.close()
import numpy as np
import matplotlib.pyplot as plt
from scipy.optimize import brentq
from solver import I1, I1andI2
t = np.linspace(0., 1, 10000 - 1)
u = np.cos(1. * 2. * np.pi * t)
print(I1andI2(u))
def F(x):
u[int(u.size / 2)] = x
return I1(u)
u[int(u.size / 2)] = brentq(F, -1.5902, -1.5901, xtol=1e-14)
print(I1andI2(u))
plt.title("Numerically exact solution")
plt.subplot(121)
plt.title("function")
plt.plot(t, u, '-')
plt.subplot(122)
plt.title("derivatives")
plt.plot(t, np.gradient(u), '-')
plt.show()
def Pressure(x, y, u, v, x_body, y_body, step=1, rho=1, nu=128 / 150):
"""
Calculates the pressure field from the velocity field. To avoid problems
with the velocity inside the body, the integration is carried out always
only up to the body.
Parameters
----------
x : 2D-Array
x-Coordinates.
y : 2D-Array
x-Coordinates.
u : 2D-Array
Velocity x-component.
v : 2D-Array
Velocity x-component.
x_body : 1D-Array
x-coordinates of body.
y_body : 1D-Array
y-coordinates of body.
step : int, optional
Step size on grid. The default is 1.
rho : float, optional
Density. The default is 1.
nu : float, optional
Viscosity. The default is 128/150.
Returns
-------
p : 2D-Array
Pressure field.
"""
dudx = np.gradient(u, step, axis=1)
dudy = np.gradient(u, step, axis=0)
dpdx = -(rho * (u * dudx + v * dudy) + nu *
(np.gradient(dudx, step, axis=1)) +
np.gradient(dudy, step, axis=0))
dvdx = np.gradient(v, step, axis=1)
dvdy = np.gradient(v, step, axis=0)
dpdy = -(
rho * (u * dvdx + v * dvdy) + nu *
(np.gradient(dvdx, step, axis=1) + np.gradient(dvdy, step, axis=0)))
p = np.empty_like(x)
p[:, 0] = step * dpdx[:, 0]
i = 1
while (x[0, i] < np.min(x_body)) and i < len(x):
p[:, i] = p[:, i - 1] + step * dpdx[:, i]
i += 1
for k in range(i, len(x)):
p[0, k] = p[0, k - 1] + step * dpdx[0, k]
p[-1, k] = p[-1, k - 1] + step * dpdx[-1, k]
k = 1
while (y[k, 0] < np.min(y_body)) and k < len(x):
p[k, :] = p[k - 1, :] + step * dpdy[k, :]
k += 1
l = len(x) - 2
while (y[l, 0] > np.max(y_body)) and l > 0:
p[l, :] = p[l + 1, :] - step * dpdy[l, :]
l -= 1
while x[0, i] <= np.max(x_body):
yl = np.interp(x[0, i], x_body, y_body)
ind = abs(yl - y[:, 0]).argmin()
for m in range(k, ind):
p[m, i] = p[m - 1, i] + step * dpdy[k, i]
for m in range(l - ind):
p[l - m, i] = p[l - m + 1, i] - step * dpdy[l - m, i]
i += 1
yl = np.interp(x[0, i], x_body, y_body)
ind = abs(yl - y[:, 0]).argmin()
for m in range(k, ind):
p[m, i] = p[m - 1, i] + step * dpdy[k, i]
for m in range(l - ind):
p[l - m, i] = p[l - m + 1, i] - step * dpdy[l - m, i]
i += 1
for m in range(k, l + 1):
p[m, i:] = p[m - 1, i:] + step * dpdy[m, i:]
return p
def Main(p, q, r):
###緯度経度メッシュ作成
###緯度経度メッシュ->直交座標メッシュ
X, Y = Convert(LON, LAT, theta, point[0], point[1])
###Python_mesh output
with open('xy_py2ft.txt', 'w') as f:
for i in range(N):
plot = "{:.7f}\t{:.7f}\n".format(X[i], Y[i])
f.write(plot)
###Fortran_calculate
Fortran(r)
###Fortran_result_input
with open('result_ft2py.csv', 'r') as f:
df = np.loadtxt(f, delimiter=",", skiprows=0)
###Reshaping
UX = df[:, 0]
UY = df[:, 1]
UZ = df[:, 2]
# UZX=df[:,3]
# UZY=df[:,4]
# UZZ=df[:,5]
UX_pyplot = UX.reshape((yscale, xscale))
UY_pyplot = UY.reshape((yscale, xscale))
UZ_pyplot = UZ.reshape((yscale, xscale))
# UZX_pyplot=UZX.reshape((yscale,xscale))
# UZY_pyplot=UZY.reshape((yscale,xscale))
# UZZ_pyplot=UZZ.reshape((yscale,xscale))
FP = Rectangleplot(AL1, AL2, AW1, AW2, point[0], point[1], theta)
###溶岩層の傾斜について
###2019/1/24 とりあえず,np.gradientのため、真ん中あたりの間隔[m]を求める
Xkankaku = (X[xscale * int(yscale / 2) + 1] -
X[xscale * int(yscale / 2 + 1) + 1]) * 1000
Ykankaku = (Y[int(yscale / 2)] - Y[int(yscale / 2) - 1]) * 1000
UZX, UZY = np.gradient(UZ_pyplot, Xkankaku, Ykankaku)
UZY = -UZY
UZX = -UZX
THETA_pyplot = np.rad2deg(np.arccos(np.sqrt(1 / (1 + UZX**2 + UZY**2))))
#DIREC=np.rad2deg(np.arctan2(UZX,UZY))
#GRAD_pyplot=GRAD.reshape((yscale,xscale))
#THETA_pyplot=THETA.reshape((yscale,xscale))
THETA = THETA_pyplot.reshape(N, 1)
UZX = UZX.reshape(N, 1)
UZY = UZY.reshape(N, 1)
###GMT output
if p == 1:
import time
#別に速くならなかった
'''
LON_g=np.reshape(LON, (LON.shape[0], 1))
LAT_g=np.reshape(LAT, (LAT.shape[0], 1))
UZ_g=np.reshape(UZ, (UZ.shape[0], 1))
np.savetxt('GMT_py2gmt.txt',np.concatenate([LON_g,LAT_g,UZ_g],axis=1), fmt="%.7f")
'''
with open('断層重ね合わせ/B/UZ_%s.txt' % str(i_main), 'w') as f_plot:
for i in range(0, N):
u = "{:.7f}\t{:.7f}\t{:.7f}\n".format(LON[i], LAT[i], UZ[i])
f_plot.write(u)
with open('断層重ね合わせ/B/UX_%s.txt' % str(i_main), 'w') as f_plot:
for i in range(0, N):
u = "{:.7f}\t{:.7f}\t{:.7f}\n".format(LON[i], LAT[i], UX[i])
f_plot.write(u)
with open('断層重ね合わせ/B/UY_%s.txt' % str(i_main), 'w') as f_plot:
for i in range(0, N):
u = "{:.7f}\t{:.7f}\t{:.7f}\n".format(LON[i], LAT[i], UY[i])
f_plot.write(u)
'''
with open('GMT_py2gmt-2.txt', 'w') as f_plot:
for i in range(4):
edge= "{:.7f}\t{:.7f}\n".format(FP[i][0],FP[i][1])
f_plot.write(edge)
'''
'''
with open('GMT_py2gmt-3slope.txt', 'w') as f_plot:
for i in range(0,N):
u = "{:.7f}\t{:.7f}\t{:.7f}\n".format(LON[i], LAT[i], float(THETA[i]))
f_plot.write(u)
with open('GMT_py2gmt-uzx.txt', 'w') as f_plot:
for i in range(0,N):
u = "{:.7f}\t{:.7f}\t{:.7f}\n".format(LON[i], LAT[i], float(UZX[i]))
f_plot.write(u)
with open('GMT_py2gmt-uzy.txt', 'w') as f_plot:
for i in range(0,N):
u = "{:.7f}\t{:.7f}\t{:.7f}\n".format(LON[i], LAT[i], float(UZY[i]))
f_plot.write(u)
'''
print('GMTdata sucessfully outputed.')
if q == 1:
###python plot
KEIDO_plot, IDO_plot = np.meshgrid(KEIDO, IDO)
print(FP)
fig = plt.figure()
ax = plt.axes()
pz = ax.pcolor(KEIDO_plot, IDO_plot, THETA_pyplot, cmap='coolwarm')
cz = ax.contour(KEIDO_plot,
IDO_plot,
THETA_pyplot,
colors=['black'],
linewidths=1,
linestyles='dashed')
ax.clabel(cz, fontsize=8)
#ax.quiver(X,Y,DX,DY)
plt.show()
fig, axes = plt.subplots(1, 3, figsize=(13, 4))
px = axes[0].pcolor(KEIDO_plot, IDO_plot, UX_pyplot, cmap='coolwarm')
py = axes[1].pcolor(KEIDO_plot, IDO_plot, UY_pyplot, cmap='coolwarm')
pz = axes[2].pcolor(KEIDO_plot, IDO_plot, UZ_pyplot, cmap='coolwarm')
cx = axes[0].contour(KEIDO_plot,
IDO_plot,
UX_pyplot,
colors=['black'],
linewidths=1,
linestyles='dashed')
cy = axes[1].contour(KEIDO_plot,
IDO_plot,
UY_pyplot,
colors=['black'],
linewidths=1,
linestyles='dashed')
cz = axes[2].contour(KEIDO_plot,
IDO_plot,
UZ_pyplot,
colors=['black'],
linewidths=1,
linestyles='dashed')
axes[0].clabel(cx, fontsize=8)
axes[1].clabel(cy, fontsize=8)
axes[2].clabel(cz, fontsize=8)
for i in range(3):
fault = plt.Polygon(((FP[0], FP[1], FP[2], FP[3])),
fc="#770000",
alpha=0.5)
axes[i].add_patch(fault)
# axes[i].set_xlabel('longitude', fontsize=14)
# axes[i].set_ylabel('latitude', fontsize=14)
axes[0].set_title('X-Displacement[m]')
axes[1].set_title('Y-Displacement[m]')
axes[2].set_title('Z-Displacement[m]')
#plt.gca().xaxis.set_major_formatter(plt.FormatStrFormatter('%.2f'))
#plt.gca().yaxis.set_major_formatter(plt.FormatStrFormatter('%.2f'))
#plt.gca().xaxis.get_major_formatter().set_useOffset(False)
#plt.gca().yaxis.get_major_formatter().set_useOffset(False)
#fig.colorbar(px)
#fig.colorbar(py)
#fig.colorbar(pz)
plt.show()
import numpy as np
import yaml
import matplotlib.pyplot as plt
if __name__ == "__main__":
CONFIG = 'config.yaml'
with open(CONFIG) as f:
path = yaml.load(f)
J1_PATH = path['robotCalibration'] + 'goal/j1.yaml'
with open(J1_PATH) as f:
J1p = yaml.load(f)
J1v = np.gradient(J1p)
plt.figure()
plt.plot(J1p, 'r.')
plt.figure()
plt.plot(J1v)
plt.show()
def Ze(diameters,
psd,
wavelength,
properties,
ref_index=None,
temperature=None,
mass=None,
theta=0.0,
bck=None,
K2=None):
"""radar reflectivity
Compute radar reflectivity directly from hydrometeor parameters
Parameters
----------
diameters : array(Nparticles) - double
spectrum of diameters of the particles [meters]
psd : callable
size distribution of the particle
concentration [meters^-1 meters^-3]
wavelength : scalar - double
electromagnetic wavelength to be passed to the snowScatt
properties calculator
properties : string
name of the snowflake properties to call from the snowLibrary
ref_index : scalar - complex (default to None)
complex refractive index of ice to be passed to the snowScatt
properties calculator
temperature : scalar - double
absolute temperature, alternative formulation of ref_index when
ref_index is None to be passed to the snowScatt properties
calculator
mass : array(Nparticles) - double (default to None)
mass of the snowflakes to be passed to the snowScatt properties
calculator if left None the mass is derived by the snowLibrary
properties
theta : scalar - double - (default to 0.0 vertical pointing)
zenith incident angle of the electromagnetic radiation, to be passed
to the snowScatt properties calculator
bck : array(Nparticles) - double (default to None)
radar backscattering cross-section [meters**2] override calculation of
bck using particle parameters
K2 : scalar - double
Rayleigh dielectric factor K^2 (dimensionless)
K = (n^2 - 1)/(n^2 + 2) for the Clausius Mossotti relation
override calculation of K2 from dielectric properties (useful for
multirequency radar cross-calibration)
Returns
-------
Z : scalar - double
Radar reflectivity in logaritmic units [dBZ]
"""
freq = _c / wavelength
if bck is None: # compute only if not precalculated
bck = backscatter(diameters, wavelength, properties, ref_index,
temperature, mass, theta)
if K2 is None: # compute only if not precalculated
eps = refractiveIndex.water.eps(temperature, freq, 'Turner')
K2 = refractiveIndex.utilities.K2(eps)
z = specific_reflectivity(wavelength, bck, K2)
Z = dB(np.sum(z * psd * np.gradient(diameters), axis=-1))
return Z
def peak_response(self, T, dr):
"""
RESPONSE SPECTRUM
Computes the peak dynamic response of a single-degree-of-freedom systems
(mass-spring-dashpot) using the Newmark Method for linear systems
Inputs
- a : input accelorgram (in ms-2)
- T : fundametal period (in s)
- dr : damping ratio = damping coeficient / critical damping coefficient
Outputs
- maxA : peak acceleration response
- maxV : peak velocity response
- maxD : peak displacement response
"""
if not self.velocity.size:
print("Reading velocity traces")
veloc = self.read_seismo(filter_s=True)
else:
veloc = self.velocity
# Integrate the velocities to get acceleration
accel = np.gradient(veloc, self.dt, axis=0)
if isinstance(T, (int, float, list, tuple)):
T = np.array(T)
l = T.size
a = np.zeros((l, *accel.shape))
v = np.zeros((l, *accel.shape))
d = np.zeros((l, *accel.shape))
# Parameters defined for the average acceleration method (Page 177 of Chopra's bok')
gamma = 0.5
beta = 0.25
# Properties of the SDOF
w = 2 * np.pi / T # Angular frequency
w = w[:, np.newaxis]
m = 1 # Mass
k = m * w**2 # stifness
dc = 2.0 * dr * m * w
# Initial calculations
a[:, 0, :] = ((-1 * m * accel[0, :]) - (dc * v[:, 0, :]) -
(k * d[:, 0, :])) / m
kk = k + ((gamma * dc) / (beta * self.dt)) + (m / (beta * self.dt**2))
var_a = (m / (beta / self.dt)) + ((gamma * dc) / beta)
var_b = (m / (2.0 * beta)) + (self.dt * dc * ((gamma /
(2 * beta)) - 1))
# Iteration
for j in range(1, accel.shape[0]):
dp = (-1 * m * ( accel[j,:] - accel[j-1,:]) ) + (var_a * v[:,j-1,:]) \
+ (var_b * a[:,j-1,:])
du = dp / kk
dv = ( (gamma * du) / (beta / self.dt) ) - ( gamma * v[:,j-1,:] / beta ) + \
( self.dt * a[:,j-1,:] * ( 1 - (gamma/(2.0 * beta)) ) )
da = (du /
(beta * self.dt**2)) - (v[:, j - 1, :] /
(beta * self.dt)) - (a[:, j - 1, :] /
(2.0 * beta))
d[:, j, :] = d[:, j - 1, :] + du
v[:, j, :] = v[:, j - 1, :] + dv
a[:, j, :] = a[:, j - 1, :] + da
self.maxA = np.max(np.abs(a + accel), axis=1)
self.maxV = np.max(np.abs(v), axis=1)
self.maxD = np.max(np.abs(d), axis=1)
return self.maxA
def get_normal(depth_refine, fx=-1, fy=-1, cx=-1, cy=-1, for_vis=True):
res_y = depth_refine.shape[0]
res_x = depth_refine.shape[1]
# inpainting
scaleOri = np.amax(depth_refine)
print(scaleOri)
inPaiMa = np.where(depth_refine == 0.0, 255, 0)
inPaiMa = inPaiMa.astype(np.uint8)
inPaiDia = 5.0
depth_refine = depth_refine.astype(np.float32)
depPaint = cv2.inpaint(depth_refine, inPaiMa, inPaiDia, cv2.INPAINT_NS)
depNorm = depPaint - np.amin(depPaint)
rangeD = np.amax(depNorm)
depNorm = np.divide(depNorm, rangeD)
depth_refine = np.multiply(depNorm, scaleOri)
depth_inp = copy.deepcopy(depth_refine)
centerX = cx
centerY = cy
constant = 1 / fx
uv_table = np.zeros((res_y, res_x, 2), dtype=np.int16)
column = np.arange(0, res_y)
uv_table[:, :, 1] = np.arange(0, res_x) - centerX # x-c_x (u)
uv_table[:, :, 0] = column[:, np.newaxis] - centerY # y-c_y (v)
uv_table_sign = np.copy(uv_table)
uv_table = np.abs(uv_table)
# kernel = np.ones((5, 5), np.uint8)
# depth_refine = cv2.dilate(depth_refine, kernel, iterations=1)
# depth_refine = cv2.medianBlur(depth_refine, 5 )
depth_refine = ndimage.gaussian_filter(depth_refine, 2) # sigma=3)
# depth_refine = ndimage.uniform_filter(depth_refine, size=11)
# very_blurred = ndimage.gaussian_filter(face, sigma=5)
v_x = np.zeros((res_y, res_x, 3))
v_y = np.zeros((res_y, res_x, 3))
normals = np.zeros((res_y, res_x, 3))
dig = np.gradient(depth_refine, 2, edge_order=2)
v_y[:, :, 0] = uv_table_sign[:, :, 1] * constant * dig[0]
v_y[:, :, 1] = depth_refine * constant + (uv_table_sign[:, :, 0] *
constant) * dig[0]
v_y[:, :, 2] = dig[0]
v_x[:, :,
0] = depth_refine * constant + uv_table_sign[:, :,
1] * constant * dig[1]
v_x[:, :, 1] = uv_table_sign[:, :, 0] * constant * dig[1]
v_x[:, :, 2] = dig[1]
cross = np.cross(v_x.reshape(-1, 3), v_y.reshape(-1, 3))
norm = np.expand_dims(np.linalg.norm(cross, axis=1), axis=1)
# norm[norm == 0] = 1
cross = cross / norm
cross = cross.reshape(res_y, res_x, 3)
cross = np.abs(cross)
cross = np.nan_to_num(cross)
#cross[depth_refine <= 200] = 0 # 0 and near range cut
cross[depth_refine > depthCut] = 0 # far range cut
if not for_vis:
scaDep = 1.0 / np.nanmax(depth_refine)
depth_refine = np.multiply(depth_refine, scaDep)
cross[:, :, 0] = cross[:, :, 0] * (1 - (depth_refine - 0.5)
) # nearer has higher intensity
cross[:, :, 1] = cross[:, :, 1] * (1 - (depth_refine - 0.5))
cross[:, :, 2] = cross[:, :, 2] * (1 - (depth_refine - 0.5))
scaCro = 255.0 / np.nanmax(cross)
cross = np.multiply(cross, scaCro)
cross = cross.astype(np.uint8)
return cross, depth_refine, depth_inp
def plot_generated_toy_batch(X_real,
generator_model,
discriminator_model,
noise_dim,
gen_iter,
noise_scale=0.5):
# Generate images
X_gen = sample_noise(noise_scale, 10000, noise_dim)
X_gen = generator_model.predict(X_gen)
# Get some toy data to plot KDE of real data
data = load_toy(pts_per_mixture=200)
x = data[:, 0]
y = data[:, 1]
xmin, xmax = -1.5, 1.5
ymin, ymax = -1.5, 1.5
# Peform the kernel density estimate
xx, yy = np.mgrid[xmin:xmax:100j, ymin:ymax:100j]
positions = np.vstack([xx.ravel(), yy.ravel()])
values = np.vstack([x, y])
kernel = stats.gaussian_kde(values)
f = np.reshape(kernel(positions).T, xx.shape)
# Plot the contour
fig = plt.figure(figsize=(10, 10))
plt.suptitle("Generator iteration %s" % gen_iter,
fontweight="bold",
fontsize=22)
ax = fig.gca()
ax.contourf(xx,
yy,
f,
cmap='Blues',
vmin=np.percentile(f, 80),
vmax=np.max(f),
levels=np.linspace(0.25, 0.85, 30))
# Also plot the contour of the discriminator
delta = 0.025
xmin, xmax = -1.5, 1.5
ymin, ymax = -1.5, 1.5
# Create mesh
XX, YY = np.meshgrid(np.arange(xmin, xmax, delta),
np.arange(ymin, ymax, delta))
arr_pos = np.vstack((np.ravel(XX), np.ravel(YY))).T
# Get Z = predictions
ZZ = discriminator_model.predict(arr_pos)
ZZ = ZZ.reshape(XX.shape)
# Plot contour
ax.contour(XX, YY, ZZ, cmap="Blues", levels=np.linspace(0.25, 0.85, 10))
dy, dx = np.gradient(ZZ)
# Add streamlines
# plt.streamplot(XX, YY, dx, dy, linewidth=0.5, cmap="magma", density=1, arrowsize=1)
# Scatter generated data
plt.scatter(X_gen[:1000, 0],
X_gen[:1000, 1],
s=20,
color="coral",
marker="o")
l_gen = plt.Line2D((0, 1), (0, 0),
color='coral',
marker='o',
linestyle='',
markersize=20)
l_D = plt.Line2D((0, 1), (0, 0), color='steelblue', linewidth=3)
l_real = plt.Rectangle((0, 0), 1, 1, fc="steelblue")
# Create legend from custom artist/label lists
# bbox_to_anchor = (0.4, 1)
ax.legend([l_real, l_D, l_gen],
['Real data KDE', 'Discriminator contour', 'Generated data'],
fontsize=18,
loc="upper left")
ax.set_xlim(xmin, xmax)
ax.set_ylim(ymin, ymax + 0.8)
plt.savefig("../../figures/toy_dataset_iter%s.jpg" % gen_iter)
plt.clf()
plt.close()
ax.legend(loc='lower center')
plt.show()
# %%
# %%
# loss of normalization, or integral of antiderivative...
bayesian_denominator_nonpw = 1 - norm(evolution.T[NPLOTPOINTS - 1])**2
# %%
fig, ax = plt.subplots(figsize=(12, 8))
ax.set_xlabel('t')
ax.set_ylabel('Detection probability density')
ax.plot(times, -np.gradient(norms**2, times), c='b', linewidth=2)
# %%
labels = PROB_LABELS
colors = ["#cc1111", "#33aa33", "#1111cc"]
fig, ax = plt.subplots(figsize=(22, 3))
ax.stackplot(times_extended,
np.abs(evolution_extended[0])**2,
np.abs(evolution_extended[1])**2,
np.abs(evolution_extended[2])**2,
labels=labels,
colors=colors)
ax.legend(loc='upper right')
def imageProcessing2(imagename, filtertype, filterval):
#main image processing function
path2file = os.path.join('./static', imagename + '.jpg')
im = plt.imread(path2file)
im.dtype = 'uint8' #just in case frce 0, 255 channels
x, y, z = im.shape
imgray = im.mean(axis=-1, keepdims=1)
cmap_type = 'bwr'
filterval = float(filterval)
if request.method == "GET":
if filtertype == 'grayscale':
# already computed above
processed_im = imgray[:, :, 0] #im.mean(axis=-1,keepdims=1)
cmap_type = 'gray'
if filtertype == 'lowpass':
# use gaussian convolution with a provided standard deviation
processed_im = ndimage.gaussian_filter(input=im, sigma=filterval)
if filtertype == 'dx':
#gradient in x direction along each x 1D array
processed_im = np.zeros(im.shape)
for i in list(range(0, y)):
processed_im[:, i, 0] = np.gradient(imgray[:, i, 0], 0.1)
processed_im = processed_im[:, :, 0]
if filtertype == 'dy':
#gradient in y dir, along each 1d array
processed_im = np.zeros(im.shape)
for i in list(range(0, x)):
processed_im[i, :, 0] = np.gradient(imgray[i, :, 0], 0.1)
processed_im = processed_im[:, :, 0]
if filtertype == 'rotate':
# rotation in degrees
processed_im = ndimage.rotate(im, filterval)
processed_im = processed_im[:, :, 0]
# stash image in memory rather than writing to disk
# use PIL and IO encoding
proc_im_pil = Image.fromarray(processed_im).convert('RGB')
data = io.BytesIO()
proc_im_pil.save(data, "JPEG")
encoded_img_data = base64.b64encode(data.getvalue())
## pseudo refresh page - > option to reset results with new query-> then render filter
if request.method == "POST":
picname = request.form['imagename']
filtertype = request.form['filtertype']
filterval = request.form['filterval']
return redirect(
url_for("imageProcessing2",
imagename=picname,
filtertype=filtertype,
filterval=filterval))
# return full_filename image to server
return render_template('imageproc.html',
img_data=encoded_img_data.decode('utf-8'),
data=meta_list)
plt.plot(e3d_t, e3d_dat, label=e3d_lab)
plt.xlabel(xlab)
plt.ylabel(ylab)
plt.legend(prop={"family": "serif", "size": 11})
plt.savefig(outfile, bbox_inches="tight")
plt.close()
FILEPATH_iSVV = "/media/yorgos/HardDrive2/TGV/iSVV/time_evol.dat"
iSVV_t, iSVV_enst, iSVV_ke = read_stats_second(FILEPATH_iSVV)
FILEPATH_SS = "/media/yorgos/HardDrive2/TGV/SS/time_evol.dat"
SS_t, SS_enst, SS_ke = read_stats_first(FILEPATH_SS)
SS_enst2 = -np.gradient(SS_ke, SS_t)
FILEPATH_Reference = "/media/yorgos/HardDrive2/TGV/DNS_reference/TGV_Re10000.dat"
A = np.genfromtxt(FILEPATH_Reference, skip_header=47, delimiter='')
Ref_t = A[:, 0]
Ref_ke = A[:, 1]
Ref_enst = A[:, 2]
fig = plt.figure(1, figsize=(10, 4), edgecolor='none')
plt.subplots_adjust(left=None,
bottom=None,
right=None,
top=None,
wspace=0.25,
hspace=None)
ax1 = fig.add_subplot(121)
m = Basemap(
llcrnrlon=lon_min,
llcrnrlat=lat_min,
urcrnrlon=lon_max,
urcrnrlat=lat_max,
projection='merc',
resolution='h',
area_thresh=1000.,
)
parallels = np.arange(round(lat_min, 0), lat_max + 2, 2)
meridians = np.arange(round(lon_max, 0), lon_min - 2, -2)
s1 = np.ma.empty(u.shape) #[ydim,xdim])
for t in range(u.shape[0]):
dudy, dudx = np.gradient(u[t, :, :], dy, dx)
dvdy, dvdx = np.gradient(v[t, :, :], dy, dx)
#s1 = np.ma.empty([ydim,xdim])
J = np.array([[0, 1], [-1, 0]])
for i in range(ydim):
for j in range(xdim):
if (dudx[i, j] and dudy[i, j] and dvdx[i, j] and dvdy[i, j]
and u[t, i, j] and v[t, i, j]) is not np.ma.masked:
Utemp = np.array([u[t, i, j], v[t, i, j]])
Grad = np.array([[dudx[i, j], dudy[i, j]],
[dvdx[i, j], dvdy[i, j]]])
S = 0.5 * (Grad + np.transpose(Grad))
s1[t, i, j] = -3600 * np.min(np.linalg.eig(S)[0])
else:
s1[t, i, j] = np.ma.masked
delta_alpha = 1.
# Factor of refinement of the strain rate increase
delta_alpha_factor = 50.
# Limit of the refinement: Minimum normalized strain rate increase
delta_alpha_min = .001
# Limit of the Temperature decrease
delta_T_min = 1 # K
# Iteration indicator
n = 0
# Indicator of the latest flame still burning
n_last_burning = 0
# List of peak temperatures
T_max = [np.max(f.T)]
# List of maximum axial velocity gradients
a_max = [np.max(np.abs(np.gradient(f.velocity) / np.gradient(f.grid)))]
# Simulate counterflow flames at increasing strain rates until the flame is
# extinguished. To achieve a fast simulation, an initial coarse strain rate
# increase is set. This increase is reduced after an extinction event and
# the simulation is again started based on the last burning solution.
# The extinction point is considered to be reached if the abortion criteria
# on strain rate increase and peak temperature decrease are fulfilled.
while True:
n += 1
# Update relative strain rates
alpha.append(alpha[n_last_burning] + delta_alpha)
strain_factor = alpha[-1] / alpha[n_last_burning]
# Create an initial guess based on the previous solution
# Update grid
# Note that grid scaling changes the diffusion flame width
def Seaangles_mod(numviews, thresholdimg):
'''
From Seaangles_mod.m
Takes an image and extracts its Opening Angle Map
Returns shorelines and shallowsea????
'''
Sx, Sy = np.gradient(thresholdimg)
G = np.sqrt(Sx**2 + Sy**2)
edges = (G > 0) & (thresholdimg > 0)
bordermap = np.pad(np.zeros_like(edges), 1, 'edge')
bordermap[:-2, 1:-1] = edges
bordermap[0, :] = 1
points = np.fliplr(np.array(np.where(edges > 0)).T)
hull = ConvexHull(points, qhull_options='Qc')
sea = np.fliplr(np.array(np.where(thresholdimg > 0.5)).T)
points_to_test = [Point(i[0], i[1]) for i in sea]
polygon = Polygon(points[hull.vertices]).buffer(0.01)
In = np.array(map(lambda pt: polygon.contains(pt), points_to_test))
Shallowsea_ = sea[In]
seamap = np.zeros(bordermap.shape)
flat_indices = map(lambda x: np.ravel_multi_index(x, seamap.shape),
np.fliplr(Shallowsea_))
seamap.flat[flat_indices] = 1
seamap[:3, :] = 0
Deepsea_ = sea[~In]
Deepsea = np.zeros((7, len(Deepsea_)))
Deepsea[:2, :] = np.flipud(Deepsea_.T)
Deepsea[-1, :] = 200. # where does this 200 come from?
Shallowsea = np.array(np.where(seamap > 0.5))
shoreandborder = np.array(np.where(bordermap > 0.5))
c1 = len(Shallowsea[0])
c2 = len(shoreandborder[0])
maxtheta = np.zeros((numviews, c1))
for i in range(c1):
diff = shoreandborder - Shallowsea[:, i, np.newaxis]
x = diff[0]
y = diff[1]
angles = np.arctan2(x, y)
angles = np.sort(angles) * 180. / np.pi
dangles = angles[1:] - angles[:-1]
dangles = np.concatenate(
(dangles, [360 - (angles.max() - angles.min())]))
dangles = np.sort(dangles)
maxtheta[:, i] = dangles[-numviews:]
allshore = np.array(np.where(edges > 0))
c3 = len(allshore[0])
maxthetashore = np.zeros((numviews, c3))
for i in range(c3):
diff = shoreandborder - allshore[:, i, np.newaxis]
x = diff[0]
y = diff[1]
angles = np.arctan2(x, y)
angles = np.sort(angles) * 180. / np.pi
dangles = angles[1:] - angles[:-1]
dangles = np.concatenate(
(dangles, [360 - (angles.max() - angles.min())]))
dangles = np.sort(dangles)
maxthetashore[:, i] = dangles[-numviews:]
waves1 = np.vstack([
np.hstack([Shallowsea, Deepsea[:2, :]]),
np.hstack([maxtheta.sum(axis=0), Deepsea[-1, :]])
])
waves1s = sparse.csr_matrix((waves1[2, :], (waves1[0, :], waves1[1, :])),
shape=thresholdimg.shape)
shoreline = np.vstack([allshore, maxthetashore.sum(axis=0)])
picshore = sparse.csr_matrix(
(shoreline[2, :], (shoreline[0, :], shoreline[1, :])),
shape=thresholdimg.shape)
shoreangles = np.vstack([allshore, maxthetashore])
seaangles = np.hstack([np.vstack([Shallowsea, maxtheta]), Deepsea])
return shoreangles, waves1s, seaangles, picshore
for row in np.arange(Nx):
for col in np.arange(Ny):
x = [xc[row], yc[col], zc[sl]]
if (xc[row]**2 + yc[col]**2 + zc[sl]**2) <= r**2:
phantom[row, col, sl] = reconstruct_phantom(obj, x, dpc)
'''plt.figure()
extent = [-r/2.0, r/2.0, -r/2.0, r/2.0]
res = plt.imshow((phantom[:,:,0]), cmap=plt.cm.gray, extent=extent, \
interpolation='none')
plt.title('Phantom')
plt.colorbar()
plt.show() '''
# compute gradient of refraction index decrement
# centered derivatives
gradPhantom = array(np.gradient(phantom, dx, dy, dz))
if dpc:
obj1 = phantom
else:
obj1 = phantom
# source point
P = 0.1
s = array([0])
sp = array([R * np.cos(s), R * np.sin(s), P / (2.0 * np.pi) * s],
dtype=TYPE)
projection = siddon_cone_beam_projection(obj1, sp, s, shift_detector,
alpha, w, Nr, Nc, r, D, Nx, Ny,
Nz, dx, dy, dz, bx, by, bz, dpc)
print projection
def simulate(self, track):
# Calculate the first and second derivative of the points
dX = np.gradient(self.xyz, axis=0)
ddX = np.gradient(dX, axis=0)
s = mag(dX) #distance between points
# magnitude of curvature
k = mag(np.cross(dX, ddX))/mag(dX)**3
T = dX / s[:,None] #unit tangent (direction of travel)
B = np.cross(dX, ddX) #binormal
B = B / mag(B)[:,None] #unit binormal
N = np.cross(B, T) #unit normal vector
# direction of curvature (normal vector with magnitude 1/R)
Nk = N * k[:,None]
# car and track share tangent vector. We're not flying
Tt = T
#Rotate Tt 90deg CW in xy-plane
Bt = Tt[:,[1, 0, 2]]
Bt[:,1] *= -1
Bt[:,2] = self.slope #align Bt with the track and normalize
Bt = Bt / mag(Bt)[:,None]
Nt = np.cross(Bt, Tt)
proj_car_axis = lambda v: np.c_[dot(v, Tt), dot(v, Bt), dot(v, Nt)]
k_car = proj_car_axis(Nk) #curvature projected in car axis [lon, lat, z]
g_car = proj_car_axis(np.array([0, 0, g])[None,:]) #direction of gravity in car axis [lon, lat, z]
# k = kt[:,1]
# g_lat = gt[:,1]
#
v_max = ((acc_grip_max - g_car[:,1]) / abs(k_car[:,1]).clip(1e-3))**0.5
i = len(v_max)
v_a = np.zeros(i) #simulated speed maximum acceleration
v_b = np.zeros(i) #simulated speed maximum braking
for i in range(-800,i): #negative index to simulate running start....
j = i-1 #index to previous timestep
## max possible speed accelerating out of corners
if v_a[j] < v_max[j]: #check if previous speed was lower than max
acc_lat = v_a[j]**2 * k_car[j,1] + g_car[j,1] #calc lateral acceleration based on
acc_lon = acc_lon_max / acc_grip_max * (acc_grip_max**2 - acc_lat**2)**0.5 #grip circle (no downforce accounted for)
acc_lon -= v_a[j]**2 * c_drag #aerodynamic drag +
acc_lon -= v_a[j] * c_roll #rolling resistance +
if v_a[j]>27:
print()
acc_lon -= g_car[j,0] #gravity up/down hill
v_a[i] = min( (v_a[j]**2 + 2*acc_lon * s[j])**0.5 , v_max[i])
else:
#acc_lon = 0
v_a[i] = min( v_a[j] , v_max[i])
## max possible speed braking into corners (backwards lap)
if v_b[j] < v_max[-i]:
acc_lat = v_b[j]**2 * k_car[-i,1] + g_car[-i,1]
acc_lon = acc_lon_min / acc_grip_max * (acc_grip_max**2 - acc_lat**2)**0.5
acc_lon += v_b[j]**2 * c_drag
acc_lon += v_b[j] * c_roll
# acc_lon += g_car[j,0]
v_b[i] = min( (v_b[j]**2 + 2*acc_lon * s[::-1][j])**0.5 , v_max[::-1][i])
else:
#acc_lon = 0
v_b[i] = min( v_b[j] , v_max[::-1][i])
v_b = v_b[::-1] #flip te matrix
self.speed = np.fmin(v_a, v_b)
self.a_lat = self.speed**2 * Nk[:,1]
self.a_lon = np.gradient(self.speed, s.cumsum())*self.speed
# self.Nk = Nk
# self.Nt = Nt
self.Bt = Bt
self.s = s
self.laptime = sum(s) / self.speed.mean()
return self.laptime
def calculate_thermal_electronic_contribution(dos,
t0=0,
t1=2000,
td=5,
xdn=-100,
xup=100,
ndosmx=10001,
dope=0.0,
natom=1,
gaussian=1000):
"""
Calculate thermal electronic contribution from pymatgen Dos objects
Parameters
----------
dos : pymatgen.electronic_structure.dos.Dos
DOS object
t0 : float
Start temperature
t1 : float
Final temperature
td : float
Temperature step size
xdn : float
Minimum energy of the DOS to consider
xup : float
Maximum energy of the DOS to consider
ndosmx : int
Size of grid to interpolate the DOS on
dope : float
Doping level
natom : int
Number of atoms in the cell
gaussian : int
Number of grid points in the Gaussian mesh near the Fermi energy
Returns
-------
"""
n_electrons, fermi_shift, e, dos = getdos(dos, xdn, xup, dope, ndosmx,
gaussian)
# for all temperatures
nT = int(np.round((t1 - t0) / td + 1.0))
T = np.arange(t0, t1 + td, td)
chemical_potential = np.zeros(nT)
gmu0 = 0.0
beta = 1.0 / (T * k_B)
beta[0] = 1.0e30
for i, t in enumerate(T):
chemical_potential[i] = brentq(gfind,
gmu0 - 10.0,
gmu0 + 10.0,
args=(e, dos, n_electrons, beta[i]),
maxiter=10000)
U_el = calculate_internal_energy(chemical_potential[:, np.newaxis],
e[np.newaxis, :], dos[np.newaxis, :],
beta[:, np.newaxis])
S_el = calculate_entropy(chemical_potential[:,
np.newaxis], e[np.newaxis, :],
dos[np.newaxis, :], beta[:, np.newaxis])
C_el = np.gradient(U_el, td, edge_order=2)
C_el[0] = 0
# construct a dictionary of results
results = {
'temperature': T,
'internal_energy': U_el / natom,
'free_energy': (U_el - T * S_el - U_el[0]) / natom,
'entropy': S_el / natom,
'heat_capacity': C_el / natom,
'chemical_potential': chemical_potential,
'n_electrons': n_electrons,
}
return results
def siddon_cone_beam_projection_flat_detector(objFileName,
sp,
s,
u,
w,
Nr,
Nc,
r,
R,
D,
H,
Nx,
Ny,
Nz,
dx,
dy,
dz,
bx,
by,
bz,
dpc=False):
'''
Computes 2D projection for cone beam x-ray source
Input: obj - phantom (voxel values = attenuation coef., absorbtion) or
phantom (voxel values = refraction ind. decrement, DPC)
sp - array of source point position(s)
s - array of angular parameters for source point position(s)
u, w - pixel coordinates for flat detector
Nr/Nc - number of detector rows/ columns
r - radius of the ROI
D - curved detector's radius
Nx, Ny, Nz - number of voxels
dx, dy, dz - dimensions of voxels
bx, by, bz - intersection of first x, y and z planes
delta - shift between source point projection and center of
detector
dpc - use attenuation coefficient (if False) or
use refraction index decrement (if True) to compute x-ray
transform
Output: Df - 2d projection measurments collected at particular source point
position
'''
Np = len(s) # number of projections
Df = np.zeros((Np, Nr, Nc), dtype=TYPE)
for p in range(Np):
print p
# detector coordinate system
eu = array([-sin(s[p]), cos(s[p]), 0], dtype=TYPE)
ev = array([-cos(s[p]), -sin(s[p]), 0], dtype=TYPE)
ez = array([0, 0, 1.0], dtype=TYPE)
# partially load phantom data and compute gradient
Nkmin, Nkmax = slice_range(sp[2, p], Nz, H, D, R, r)
#load object data
phantomf = h5py.File(objFileName, 'r')
obj = phantomf['phantom'][:, :, range(int(Nkmin), int(Nkmax) + 1)]
phantomf.close()
# compute gradient of object
if dpc:
gradobj = np.array(np.gradient(obj, dx, dy, dz))
refv = [0, 0, 0]
for i in range(Nr):
for j in range(Nc):
theta = ray_flat_detector(D, u[j], w[i], eu, ev, ez)
dp = theta + sp[:, p]
if dpc:
# gradient projection onto vector which is perpendicular
# to ray direction (theta) and gradient line direction (ez)
# refv - vector pointing towards x-ray refraction
# - equal to np.cross(theta, ez)
theta = theta / sqrt(sum(theta**2))
refv = np.zeros_like(theta)
refv[0] = theta[1]
refv[1] = -theta[0]
#print refv
Df[p, Nr - 1 - i,
j] = siddon_xray_transform(gradobj, dp, sp[:, p], r, D,
Nx, Ny, Nkmax, dx, dy, dz,
bx, by, bz, Nkmin, refv, dpc)
else:
Df[p, Nr - 1 - i,
j] = siddon_xray_transform(obj, dp, sp[:, p], r, D, Nx,
Ny, Nkmax, dx, dy, dz, bx,
by, bz, Nkmin, refv, dpc)
return Df