def SF_SD(m, wavelength, dp, ndp, minAngle=0, maxAngle=180, angularResolution=0.5, space='theta', angleMeasure='radians', normalization=None):
# http://pymiescatt.readthedocs.io/en/latest/forward.html#SF_SD
_steps = int(1+(maxAngle-minAngle)/angularResolution)
ndp = coerceDType(ndp)
dp = coerceDType(dp)
SL = np.zeros(_steps)
SR = np.zeros(_steps)
SU = np.zeros(_steps)
kwargs = {'minAngle':minAngle,
'maxAngle':maxAngle,
'angularResolution':angularResolution,
'space':space,
'normalization':None}
for n,d in zip(ndp,dp):
measure,l,r,u = ScatteringFunction(m,wavelength,d,**kwargs)
SL += l*n
SR += r*n
SU += u*n
if normalization in ['n','N','number','particles']:
_n = trapz(ndp,dp)
SL /= _n
SR /= _n
SU /= _n
elif normalization in ['m','M','max','MAX']:
SL /= np.max(SL)
SR /= np.max(SR)
SU /= np.max(SU)
elif normalization in ['t','T','total','TOTAL']:
SL /= trapz(SL,measure)
SR /= trapz(SR,measure)
SU /= trapz(SU,measure)
return measure,SL,SR,SU
def update_area_pattern(self, new_pos=True):
with self.visuals_changed.hold_and_emit():
if new_pos:
# calculate average starting point y value
condition = (self.data_x >= self.area_startx - 0.1) & (self.data_x <= self.area_startx + 0.1)
section = np.extract(condition, self.data_y[:, 0])
self.avg_area_starty = np.min(section)
# calculate average ending point y value
condition = (self.data_x >= self.area_endx - 0.1) & (self.data_x <= self.area_endx + 0.1)
section = np.extract(condition, self.data_y[:, 0])
self.avg_area_endy = np.min(section)
# Calculate new bg slope
self.area_slope = (self.avg_area_starty - self.avg_area_endy) / (self.area_startx - self.area_endx)
# Get the x-values in between start and end point:
condition = (self.data_x >= self.area_startx) & (self.data_x <= self.area_endx)
section_x = np.extract(condition, self.data_x)
section_y = np.extract(condition, self.data_y)
bg_curve = (self.area_slope * (section_x - self.area_startx) + self.avg_area_starty)
#Calculate the peak area:
self.area_result = abs(trapz(section_y, x=section_x) - trapz(bg_curve, x=section_x))
# Calculate the new y-values:
self.area_pattern = (section_x, bg_curve, section_y)
def find_basis_normal(q):
"""
Finds the basis normal to the srvf
:param q1: numpy ndarray of shape (2,M) of M samples
:rtype: list of numpy ndarray
:return basis: list containing basis vectors
"""
n, T = q.shape
f1 = zeros((n, T))
f2 = zeros((n, T))
for i in range(0, T):
f1[:, i] = q[0, i] * q[:, i] / norm(q[:, i]) + array([norm(q[:, i]),
0])
f2[:, i] = q[1, i] * q[:, i] / norm(q[:, i]) + array([0,
norm(q[:, i])])
h3 = f1
h4 = f2
integrandb3 = zeros(T)
integrandb4 = zeros(T)
for i in range(0, T):
a = q[:, i].T
integrandb3[i] = a.dot(h3[:, i])
integrandb4[i] = a.dot(h4[:, i])
b3 = h3 - q * trapz(integrandb3, linspace(0, 1, T))
b4 = h4 - q * trapz(integrandb4, linspace(0, 1, T))
basis = [b3, b4]
return (basis)
def correl_swsw(self, angle, nz1, nz2, h1, h2, method='quad'):
"""Correlation coeficients between two spherical waves."""
alpha = angle * 4.85*1.e-6
R = self.pupil_diameter / 2.
R1 = (h1-self.h_profile) / h1 * R
R2 = (h2-self.h_profile) / h2 * R
zeta = alpha * self.h_profile / R1
w = R2 / R1
Lam = 2. * np.pi * R1 / self.large_scale
n1, m1 = zernike.noll2zern(nz1)
n2, m2 = zernike.noll2zern(nz2)
k1, k2 = _kvalues(n1, n2, m1, m2, nz1, nz2)
results = np.zeros(len(self.h_profile))
for idx in np.arange(len(self.h_profile)):
if method == 'quad':
result_quad = quad(_chassat_integral, 0, np.inf, args=(zeta[idx], Lam[idx], w[idx], k1, k2, n1, n2, m1, m2))
results[idx] = result_quad[0] * self.cn2[idx] * R1[idx]**(5./3.)
elif method == 'romberg':
result_quad = romberg(_modified_chassat, 1.e-26,np.pi/2., args=(zeta[idx], Lam[idx], w[idx], k1, k2, n1, n2, m1, m2), vec_func = False)
results[idx] = result_quad * self.cn2[idx] * R1[idx]**(5./3.)
if len(results) < 2:
final_integral = results / (self.cn2 * R1**(5./3.))
else:
final_integral = trapz(results, x=self.h_profile) / trapz(self.cn2 * R1**(5./3.), x=self.h_profile)
final_integral = 3.895 * (-1.)**((n1+n2-m1-m2)/2.) * np.sqrt((n1+1.)*(n2+1.)) * self.dr0**(5./3.) * final_integral
return final_integral
def calc_j(basis):
"""
Calculates Jacobian matrix from normal basis
:param basis: list of numpy ndarray of shape (2,M) of M samples basis
:rtype: numpy ndarray
:return j: Jacobian
"""
b1 = basis[0]
b2 = basis[1]
T = b1.shape[1]
integrand11 = zeros(T)
integrand12 = zeros(T)
integrand22 = zeros(T)
for i in range(0, T):
a = b1[:, i].T
b = b2[:, i].T
integrand11[i] = a.dot(b1[:, i])
integrand12[i] = a.dot(b2[:, i])
integrand22[i] = b.dot(b2[:, i])
j = zeros((2, 2))
j[0, 0] = trapz(integrand11, linspace(0, 1, T))
j[0, 1] = trapz(integrand12, linspace(0, 1, T))
j[1, 1] = trapz(integrand22, linspace(0, 1, T))
j[1, 0] = j[0, 1]
return (j)
def _ZZlk(self):
hist = np.zeros(self.result_bins)
histLB = np.zeros(self.result_bins)
self.ZZ_phist = [ np.zeros(self.prob_pts) for i in range(4) ]
for i in range(self.blocks):
pp00,pp01,pp10 = \
np.mgrid[i*self.prob_pts/self.blocks:(i+1)*self.prob_pts/self.blocks,\
0:self.prob_pts,0:self.prob_pts]/float(self.prob_pts)
plk = self.diag_likelihood(self.N_ZZ, pp00,pp01,pp10)
hist += np.histogram(pp01+pp10, bins=self.result_bins,
range=(0,1), density=False, weights=plk)[0]
histLB += np.histogram(pp01+pp10-2*np.sqrt(pp00*(1.-pp00-pp01-pp10)),
bins=self.result_bins, range=(0,1), density=False, weights=plk)[0]
for i,pp in enumerate([pp00,pp01,pp10,1.-pp00-pp01-pp10]):
self.ZZ_phist[i] += np.histogram(pp, bins=self.prob_pts,
range=(0,1), density=False, weights=plk)[0]
I = integrate.trapz(hist, dx=self.ZZ_dx)
hist /= I
ILB = integrate.trapz(histLB, dx=self.ZZ_dx)
histLB /= ILB
for h in self.ZZ_phist:
Ip = integrate.trapz(h, dx=1./self.prob_pts)
h /= Ip
return hist, histLB
def get_angular_integrated(self, psd, geometry, property_name):
if self._angular_table is None:
raise AttributeError(
"Initialize or load the table of angular-integrated " +
"quantities first."
)
psd_w = psd(self._psd_D)
def sca_xsect(geom):
return trapz(
self._angular_table["sca_xsect"][geom] * psd_w,
self._psd_D
)
if property_name == "sca_xsect":
sca_prop = sca_xsect(geometry)
elif property_name == "ext_xsect":
sca_prop = trapz(
self._angular_table["ext_xsect"][geometry] * psd_w,
self._psd_D
)
elif property_name == "asym":
sca_xsect_int = sca_xsect(geometry)
if sca_xsect_int > 0:
sca_prop = trapz(
self._angular_table["asym"][geometry] * \
self._angular_table["sca_xsect"][geometry] * psd_w,
self._psd_D
)
sca_prop /= sca_xsect_int
else:
sca_prop = 0.0
return sca_prop
def read_intensity(self, freq=[0.0], t_start=0.0, t_end=100.0):
'''
Calculates the intensity of a certain frequency in the FID. It calculates
the Fourier coefficents for that specific frequency.
Parameters
----------
freq (list, float): List of frequencies for which the intensity should be
calculated (Frequencies in MHz)
Returns
-------
intensity (1D-array, float): Array of the intensities
Notes
-----
none
'''
if len(self.fid) > 0:
fid = slice_fid(self.fid, t_start, t_end)
intensity = np.array([])
for x in freq:
cos2 = np.cos(fid[:,0]*x*1.E6*2.*np.pi)
sin2 = np.sin(fid[:,0]*x*1.E6*2.*np.pi)
a = inte.trapz(cos2*fid[:,1], fid[:,0]) / abs(fid[-1,0]) * 2.
b = inte.trapz(sin2*fid[:,1], fid[:,0]) / abs(fid[-1,0]) * 2.
intensity = np.hstack((intensity, np.sqrt(a**2 + b**2)))
return intensity
else:
return np.array([])
def computeColor(self, filtX, filtY, z=0):
"""Compute color (flux in filter X - filter Y) of SED at redshift z, return color in magnitudes
@param filtX lower wavelength filter
@param filtY higher wavelength filter
@param z redshift of SED
"""
if filtX not in self.filterDict:
emsg = "Filter " + filtX + " is not in the filter dictionary"
raise LookupError(emsg)
if filtY not in self.filterDict:
emsg = "Filter " + filtY + " is not in the filter dictionary"
raise LookupError(emsg)
if filtX == filtY:
raise ValueError("ERROR! cannot have color as difference between same filter")
# define integral limits by filter extents
aX, bX = self.filterDict[filtX].returnFilterRange()
aY, bY = self.filterDict[filtY].returnFilterRange()
# int S(lam_obs)*X(lam)*lam dlam
lam = self.filterDict[filtX].wavelengths
res = self.sed.getFlux(lam, z)*self.filterDict[filtX].getTrans(lam)*lam
integrand = interp.InterpolatedUnivariateSpline(lam, res, k=1)
if self.FAST_INTEG:
x = np.linspace(aX, bX, self.INTEG_PREC)
y = integrand(x)
int1 = integ.trapz(y,x)
else:
int1 = integ.quad(integrand, aX, bX)[0]
# int S(lam_obs)*Y(lam)*lam dlam
lam = self.filterDict[filtY].wavelengths
res = self.sed.getFlux(lam, z)*self.filterDict[filtY].getTrans(lam)*lam
integrand = interp.InterpolatedUnivariateSpline(lam, res, k=1)
if self.FAST_INTEG:
x = np.linspace(aY, bY, self.INTEG_PREC)
y = integrand(x)
int2 = integ.trapz(y,x)
else:
int2 = integ.quad(integrand, aY, bY)[0]
# Not sure about this zero-point term? But colors are totally off without it
# .integral2 = int filter(lam)/lam dlam
int3 = self.filterDict[filtX].integral2
int4 = self.filterDict[filtY].integral2
zp = -2.5*math.log10(int4/int3)
# zero observed flux in either filter so color should be infinite
if (int1==0. or int2==0.):
return float("inf")
return -2.5*math.log10(int1/int2) + zp
def readDustInfo(self):
"""
Read all column densities, min/max temperatures and min/max radii for
the species involved in the MCMax model.
Note that the self.coldens dictionary does not give real column
densities! This dict merely gives column densities in a prescribed
shell with given min and max radius, in order to compare with the H2
col density.
"""
dens = self.star.getDustDensity()
temp = self.star.getDustTemperature()
compf = os.path.join(
cc.path.mcmax, self.star.path_mcmax, "models", self.star["LAST_MCMAX_MODEL"], "composition.dat"
)
comp = DataIO.readCols(compf)
self.rad = comp.pop(0) * self.au
self.r_outer = self.rad[-1]
for species in self.star.getDustList():
# - Save the actual density profile for this dust species, as well
# - as calculating the full column density of a dust species.
self.dustfractions[species] = comp.pop(0)
self.compd[species] = self.dustfractions[species] * dens
self.fullcoldens[species] = trapz(x=self.rad, y=self.compd[species])
# - Determine the column density from 90% of the dust species formed
# - onward, based on the mass fractions!
# - Not before, because the comparison with H2 must be made,
# - and this will skew the result if not solely looking at where the
# - dust has (almost) all been formed.
# - We also save min amd max radii, for use with the H2 calculation
a_species = self.star["A_%s" % species]
maxdens = max(self.compd[species])
mindens = maxdens * 10 ** (-10)
radsel = self.rad[(self.dustfractions[species] > 0.9 * a_species) * (self.compd[species] > mindens)]
denssel = self.compd[species][
(self.dustfractions[species] > 0.9 * a_species) * (self.compd[species] > mindens)
]
self.coldens[species] = trapz(x=radsel, y=denssel)
if radsel.size:
self.r_min_cd[species] = radsel[0]
self.r_max_cd[species] = radsel[-1]
else:
print "Threshold dust mass fraction not reached for %s." % species
self.r_min_cd[species] = 0
self.r_max_cd[species] = 0
# - Determine the actual destruction radius and temperature.
# - Taken where the density reaches 1% of the maximum density
# - (not mass fraction).
self.r_des[species] = self.rad[self.compd[species] > (maxdens * 0.01)][0]
self.t_des[species] = temp[self.compd[species] > (maxdens * 0.01)][0]
# - e-10 as limit for minimum is ok, because if shell is 100000 R*
# - the mass conservation dictates ~ (10^5)^2 = 10^10 (r^2 law)
# - decrease in density. Shells this big dont occur anyway.
self.r_max[species] = self.rad[self.compd[species] > mindens][-1]
self.t_min[species] = temp[self.compd[species] > mindens][-1]
def compute_integral4D(grid, x0, x1, x2, x3):
"""
Computes norm of a 4D grid
:param grid: 4D grid to integrate
:param x0: coordinates of all points along axis=0
:param x1: coordinates of all points along axis=1
:param x2: coordinates of all points along axis=2
:param x3: coordinates of all points along axis=3
:type grid: numpy array
:type x0: numpy array
:type x1: numpy array
:type x2: numpy array
:type x3: numpy array
:rtype: float
:returns: grid norm
"""
grid_norm = si.trapz(si.trapz(si.trapz(si.trapz(grid, x=x0, axis=0),
x=x1, axis=0), x=x2, axis=0),
x=x3, axis=0)
return grid_norm
def regression_warp(beta, time, q, y, alpha):
"""
calculates optimal warping for function linear regression
:param beta: numpy ndarray of shape (M,N) of M functions with N samples
:param time: vector of size N describing the sample points
:param q: numpy ndarray of shape (M,N) of M functions with N samples
:param y: numpy ndarray of shape (1,N) of M functions with N samples
responses
:param alpha: numpy scalar
:rtype: numpy array
:return gamma_new: warping function
"""
gam_M = uf.optimum_reparam(beta, time, q)
qM = uf.warp_q_gamma(time, q, gam_M)
y_M = trapz(qM * beta, time)
gam_m = uf.optimum_reparam(-1 * beta, time, q)
qm = uf.warp_q_gamma(time, q, gam_m)
y_m = trapz(qm * beta, time)
if y > alpha + y_M:
gamma_new = gam_M
elif y < alpha + y_m:
gamma_new = gam_m
else:
gamma_new = uf.zero_crossing(y - alpha, q, beta, time, y_M, y_m,
gam_M, gam_m)
return gamma_new
def calculate_energy(alphadot, T=100, k=5):
"""
calculates energy along path
:param alphadot: numpy ndarray of shape (2,M) of M samples
:param T: Number of samples of curve (Default = 100)
:param k: number of samples along path (Default = 5)
:rtype: numpy scalar
:return E: energy
"""
integrand1 = zeros((k, T))
integrand2 = zeros(k)
for i in range(0, k):
for j in range(1, T):
tmp = alphadot[:, j, i].T
integrand1[i, j] = tmp.dot(alphadot[:, j, i])
integrand2[i] = trapz(integrand1[i, :], linspace(0, 1, T))
E = 0.5 * trapz(integrand2, linspace(0, 1, k))
return E
def draw_reabsorption(self, columns, reabsorption=1):
try:
f = plt.figure(self.graphnumber_reab)
plt.xlabel('Wavelengths, nm')
plt.ylabel('Intensity, a.u.')
Xe = self.data['Xe']
Ec = self.data['Ec']
Ec = Ec / integrate.trapz(Ec, dx=self.step_E)
Ed = self.data['Ed']
Ed = Ed / integrate.trapz(Ed, dx=self.step_E) * reabsorption
if len(Xe) > len(Ec):
Ec = np.append(Ec, np.zeros(len(Xe)-len(Ec)))
if len(Xe) > len(Ed):
Ed = np.append(Ed, np.zeros(len(Xe)-len(Ed)))
plt.plot(Xe, Ec)
plt.plot(Xe, Ed)
f.canvas.set_window_title('Reabsorption (' + str(reabsorption) + '; Xe: Ec, Ed)')
plt.title('Xe: Ec, Ed')
f.show()
self.graphnumber_reab += 1
self.logger.info('Reabsorption calculation finished')
except:
self.logger.info('No reabsortion graph could be drawn')
def kde_KL_divergence_2d(x, y, h_x, h_y, nb_bins=100, fft=True):
"""Uses Kernel Density Estimator with Gaussian kernel on two
dimensional samples x and y and returns estimated Kullback-
Leibler divergence.
@param x, y: samples, given as a (n, 2) shaped numpy array,
@param h: width of the Gaussian kernel,
@param nb_bins: number of grid points to use,
@param fft: whether to use FFT to compute convolution.
"""
min_ = np.min(np.vstack([np.min(x, axis=0), np.min(y, axis=0)]), axis=0)
max_ = np.max(np.vstack([np.max(x, axis=0), np.max(y, axis=0)]), axis=0)
bounds_ = np.vstack((min_, max_))
(x_grid, y_grid, kde_x) = gaussian_kde_2d(x, h_x, h_y,
nb_bins=nb_bins,
fft=fft,
bounds=bounds_
)
(x_grid2, y_grid2, kde_y) = gaussian_kde_2d(y, h_x, h_y,
nb_bins=nb_bins,
fft=fft,
bounds=bounds_
)
delta_x = x_grid[1] - x_grid[0]
delta_y = y_grid[1] - y_grid[0]
plogp = - kde_x * np.log((kde_x + EPSILON) / (kde_y + EPSILON))
# Integrate
div = trapz(trapz(plogp, dx=delta_x, axis=1), dx=delta_y, axis=0)
return div
def integration(self,is_quadrant=0,use_flux_per_mrad2_or_mm2=1):
if (self.X is None or self.Y is None):
raise Exception(" X and Y must be array for integration")
if self.X.shape != self.Y.shape:
raise Exception(" X and Y must have the same shape")
if len(self.X.shape)==2 :
X = np.linspace(self.X.min(), self.X.max(), self.X.shape[0])
Y = np.linspace(self.Y.min(), self.Y.max(), self.Y.shape[1])
res1=integrate.trapz(self.intensity, X)
res = integrate.trapz(res1, Y)
# res = integrate.simps(integrate.simps(self.intensity, X), Y)
# res = self.intensity.sum() * (self.X[1,0] - self.X[0,0]) * (self.Y[0,1] - self.X[0,0]) # regular grid only
else : # X and Y are 1d array
if len(self.X) == 1:
res = self.intensity[0]
else: # choix arbitraire
XY = np.zeros_like(self.X)
for i in range(1, len(self.X)):
XY[i] = XY[i-1]+np.sqrt((self.X[i] - self.X[i-1]) * 2 + (self.Y[i] - self.Y[i-1]) ** 2)
res = np.trapz(self.intensity, XY)
# Note that the value of flux is in phot/s/0.1%bw/mrad2 (or .../mm2) and
# our grid is in rad (or m), therefore we must account for this:
if use_flux_per_mrad2_or_mm2:
res *= 1e6
# in case the calculation is for a quadrant, the integral is four times the calculated value
if is_quadrant:
res *= 4
return res
def calculate_variance(beta):
"""
This function calculates variance of curve beta
:param beta: numpy ndarray of shape (2,M) of M samples
:rtype: numpy ndarray
:return variance: variance
"""
n, T = beta.shape
betadot = gradient(beta, 1. / (T - 1))
betadot = betadot[1]
normbetadot = zeros(T)
centroid = calculatecentroid(beta)
integrand = zeros((n, n, T))
t = linspace(0, 1, T)
for i in range(0, T):
normbetadot[i] = norm(betadot[:, i])
a1 = (beta[:, i] - centroid)
a1 = a1.reshape((n, 1))
integrand[:, :, i] = a1.dot(a1.T) * normbetadot[i]
l = trapz(normbetadot, t)
variance = trapz(integrand, t, axis=2)
variance /= l
return (variance)
def compute_expected_coordinates1D(grid, x0):
"""
Computes expected value and variance of a 1D grid along its (only) axis.
:param grid: 1D grid to integrate
:param x0: coordinates of all points along the integration axis
:type grid: numpy array
:type x0: numpy array
:rtype: float
:returns:
* exp_x0 : expected value
* var_x0 : variance
"""
# normalize 1D grid
grid_integral = compute_integral1D(grid, x0)
prob_x0 = grid / grid_integral
# get 1D marginals, expected values and variances
exp_x0 = si.trapz(x0*prob_x0, x=x0)
var_x0 = si.trapz((x0-exp_x0)*(x0-exp_x0)*prob_x0, x=x0)
return exp_x0, var_x0
def calculate_MOC_initial_condition(number_of_classes, U=0.177, D=0.03):
data = genfromtxt("paper_data/re6400/upstream.csv")
# Data provided are diameters in mm. We need to covert to volume
mm2m = 0.001
v_data = pi / 6 * (data[:, 0] * mm2m)**3
p_data = data[:, 1]
p_interpolated = interp1d(
v_data, p_data, kind='nearest', fill_value=0, bounds_error=False)
# From Galinat we know that phase volumetric fraction is 1.7%-3%
alpha = (0.03 + 0.017) / 2
A = pi / 4 * D**2
Vc = 1.0 * A # Assume unit height column
# Estimate the total number from total concentration
v = linspace(0, 1.2 * max(v_data), number_of_classes + 1)
dv = v[1]
p_empirical = p_interpolated(v) / trapz(p_interpolated(v), x=v)
cdf_empirical = cumsum(p_empirical) * dv # Cumulative distribution
meanVd = trapz(v * p_empirical, x=v) # Dispersed phase mean volume
N0 = alpha * Vc / meanVd # Number of drops in 1m column
# print("Total number of drops in unit column {0:0.0f}".format(N0))
# print("Particle influx will be: {0:0.2f} drops/s".format(U * N0))
# print(U * N0 * meanVd / (U * A))
return dv, clip(
N0 * (cdf_empirical[1:] - cdf_empirical[:-1]),
a_min=1e-4, a_max=None
)
def integrate(self, t0, tf, weights=None):
"""Integrates the data contained in the integrator from t0 to
tf, inclusive. Applies weights to the data according to function
weights(times - t0)
"""
if t0 < self.times[0] or tf > self.times[-1]:
return None
interp = spi.interp1d(x=np.squeeze(self.times),
y=np.squeeze(self.vals), axis=0)
# TODO Clean up using bisect
istart = next(i for i, x in enumerate(self.times) if x > t0)
ifinal = next((i for i, x in enumerate(self.times) if x > tf), -1)
times = [t0] + self.times[istart:ifinal] + [tf]
ref = [interp(t0)] + self.vals[istart:ifinal] + [interp(tf)]
times = np.array(times)
ref = np.asarray(ref)
if weights is not None:
w = weights(times - t0)
ref = ref * w
z = spt.trapz(y=w, x=times)
else:
z = 1.0
return spt.trapz(y=ref, x=times) / z
def __init__(self, waveLengths, transmission):
"""Initialise the filter transmission function
@param waveLengths
@param transmission
"""
# keep track of original range and resolution of transmission function
self.lamMin = waveLengths[0]
self.lamMax = waveLengths[-1]
self.nLam = len(waveLengths)
#this could come handy if we need to defer the construction of the interpolator
self.wavelengths = waveLengths
self.transmission = transmission
#cache these values for later reuse. Note that this will fail if the filter
#support is disconnected... need to build a safer interface?
self.integral1 = integ.trapz(transmission*waveLengths,waveLengths)
self.integral2 = integ.trapz(transmission/waveLengths,waveLengths)
self.effLambda = np.sqrt(self.integral1/self.integral2)
# check wavelength and transmission domains are valid
if (self.lamMin<0.):
raise ValueError("ERROR! wavelengths cannot be less than zero!")
if np.any(transmission<0.):
raise ValueError("ERROR! cannot have negative transmission")
if np.any(transmission>1.000001): #why not just 1.?
raise ValueError("ERROR! cannot have transmission > 1")
# filter is now represeted as an interpolation object (linear)
self.filt = interp.InterpolatedUnivariateSpline(waveLengths, transmission, k=1)
def diff_integrate(x_values, y_values):
positive_res = 0
negative_res = 0
filter_function = lambda (x, y): INTERVAL_START <= x <= INTERVAL_END
if INTERVAL_START > INTERVAL_END:
print('NOTICE: The interval start %s is bigger than the interval end %s, using all the data.' %
(INTERVAL_START, INTERVAL_END))
interval_values = zip(x_values, y_values)
else:
print('NOTICE: Calculating integrals for every value in the closed interval [%s, %s].' %
(INTERVAL_START, INTERVAL_END))
interval_values = filter(filter_function, zip(x_values, y_values))
positive_x_values = []
positive_y_values = []
negative_x_values = []
negative_y_values = []
# split positive and negative y-values
for x, y in interval_values:
if y < 0:
negative_x_values.append(x)
negative_y_values.append(y)
else:
positive_x_values.append(x)
positive_y_values.append(y)
positive_res = integrate.trapz(positive_y_values, positive_x_values)
negative_res = integrate.trapz(negative_y_values, negative_x_values)
return positive_res, negative_res
def convolve(self,filt,returnMag=True):
if not filt.type=='filter':
raise TypeError('The "filter" you specified is invalid.')
# Find the part of the spectrum where the FTC is defined
startN,stopN = np.searchsorted(self.wavelengths.value,[filt.wavelengths[0].value,filt.wavelengths[-1].value])
if startN!=0:
startN-=1
if stopN!=(len(self.wavelengths)-1):
stopN+=1
ls = self.wavelengths[startN:stopN].value
# Resample filter
newFtc = np.interp(ls,filt.wavelengths.value,filt.ftc)
num = interp1d(ls,newFtc * self.spec[startN:stopN])
denom = interp1d(ls,newFtc)
# Integrate
numerator = trapz(num(filt.wavelengths[0:-1].value),x=filt.wavelengths[0:-1].value)
denominator = trapz(denom(filt.wavelengths[0:-1].value),x=filt.wavelengths[0:-1].value)
if returnMag:
try:
ABmag = -2.5 * np.log10(numerator/denominator) - 48.60
except:
global badFilt
badFilt = filt
global badspec
badspec = self
ABmag = -2.5 * np.log10(numerator/denominator) - 48.60
if np.isnan(ABmag):
print(self.params)
return(ABmag*u.Unit('mag'))
else:
return(u.Unit('erg') * u.Unit('s')**-1 * u.Unit('cm')**-2 * u.Unit('Hz')**-1\
*numerator/denominator) # erg s−1 cm−2 Hz−1
def get_SZ(self, psd, geometry):
"""
Compute the scattering matrices for the given PSD and geometries.
Returns:
The new amplitude (S) and phase (Z) matrices.
"""
if (self._S_table is None) or (self._Z_table is None):
raise AttributeError(
"Initialize or load the scattering table first.")
if (not isinstance(psd, PSD)) or self._previous_psd != psd:
self._S_dict = {}
self._Z_dict = {}
psd_w = psd(self._psd_D)
for geom in self.geometries:
self._S_dict[geom] = \
trapz(self._S_table[geom] * psd_w, self._psd_D)
self._Z_dict[geom] = \
trapz(self._Z_table[geom] * psd_w, self._psd_D)
self._previous_psd = psd
return (self._S_dict[geometry], self._Z_dict[geometry])
def cPofZ(self, arr, zx):
## hardcoding zmax for the time being, should fix it
zmax = 1.5
Ng = len(arr)
dz = 0.001
if not hasattr(self, "cnorm"):
Nx = int(zmax / dz)
xar = np.linspace(0, zmax, Nx)
rect = np.zeros((Ng, Nx))
for i, z in enumerate(xar):
rect[:, i] = self.PofZ(arr, float(z), dz) / dz
self.cnorm = trapz(rect, xar, axis=1)
# for floats
if type(zx) == type(0.1):
Nx = int(zx / dz)
xar = np.linspace(0, zx, Nx)
rect = np.zeros((Ng, Nx))
for i, z in enumerate(xar):
rect[:, i] = self.PofZ(arr, float(z), dz) / dz
unnormC = trapz(rect, xar, axis=1)
else:
# for arrays
zxm = zx.max()
Nx = int(zxm / dz)
xar = np.linspace(0, zxm, Nx)
rect = np.zeros((Ng, Nx))
for i, z in enumerate(xar):
rect[:, i] = self.PofZ(arr, float(z), dz) / dz
rect[np.where(zx > z), i] = 0.0
unnormC = trapz(rect, xar, axis=1)
return unnormC / self.cnorm
def ps_to_xi(k,ps,r,precision='mid'):
xi = 0 * r
if precision=='low':
from scipy.integrate import trapz
from scipy import sin
for i in range(len(r)):
xi[i] = trapz((ps/k) * sin(k*r[i]) / (k*r[i]),k)
elif precision=='high':
from scipy import sin
from scipy.integrate import quad,quadrature
from scipy.interpolate import interp1d
for i in range(len(r)):
psi = interp1d(k,ps)
core = lambda k: (psi(k)/k) * sin(k*r[i]) / (k*r[i])
A = quadrature(core,min(k),2.0/r[i],tol=1e-3)
xi[i] = A[0]
else:
from scipy.integrate import trapz
from scipy import sin
from pylab import find
import numpy as np
for i in range(len(r)):
cutoff = np.min(find(k>2.0/r[i]))
kl = k[1:cutoff]
psl = ps[1:cutoff]
i1 = trapz((psl/kl) * sin(kl*r[i]) / (kl*r[i]),kl)
psh = ps[cutoff+1:len(k)]
kh = k[cutoff+1:len(k)]
i2 = trapz((psh/kh) * sin(kh*r[i]) / (kh*r[i]),kh)
xi[i] = i1+i2
return xi
def dbltrapz(f, x, y):
""" Perform a double trapezon integration of a vectorized function
f(x,y) where x is an array of x values and y is an array of y
values to perform the integral over.
Implementation taken from:
http://mail.scipy.org/pipermail/scipy-user/2011-February/028592.html
I don't really understand it, but it seems to work...
For example, if we wanted to integrate some really random function
f(x,y) = e^(-x^2*y)
from 1<x<5 and 1<y<10.
Using matheamtica, we find that the integral is ~0.09:
N[Integrate[Integrate[Exp[-(x^2*y)], {x, 1, 5}], {y, 1, 10}], 20]
Using our new function.
>>> import numpy as np
>>> f=lambda x,y: np.exp(-(x**2*y))
>>> int=dbltrapz(f, np.linspace(1,5,1000), np.linspace(1,10,1000))
>>> print np.allclose(int,0.089071862226039234609, rtol=1e-5, atol=1e-5)
True
"""
yy = y[:,np.newaxis]
xx = x[np.newaxis,:]
integrand=f(xx,yy)
return integrate.trapz(integrate.trapz(integrand, yy, axis=0), x, axis=0)
def trapez_moms(x_arg, y_arg, mom):
""" Returns numerically integrated moments """
if mom == 0:
ret = trapz(y_arg, x_arg)
else:
ret = trapz(y_arg * x_arg**mom, x_arg)
return ret
def alexpand(tau, noise_psd, freq, one2tennoise):
kern = lambda t:[ s*np.sin(np.pi*f*t)**4/(np.pi*carrier*t)**2 for s,f in zip(noise_psd,freq)]
kernFreq = lambda t:[ s*np.sin(np.pi*f*t)**4./(np.pi*f*t)**2. for s,f in zip(noise_psd,freq)]
fone2ten = np.logspace(-9,1,num=50)
alfromone2ten = 2*trapz([one2tennoise*100+.01*one2tennoise/f+.1*one2tennoise/f**2.*np.sin(np.pi*f*tau)**4./(np.pi*f*tau)**2 for f in fone2ten],fone2ten)
out = 2. *trapz(kernFreq(tau),freq)+alfromone2ten
#out = alfromone2ten
return out
def icwt(wavelet):
"""Compute the inverse continuous wavelet transform.
Parameters
----------
wavelet : Instance of the MotherWavelet class
instance of the MotherWavelet class for a particular wavelet family
Examples
--------
Use the Morlet mother wavelet to perform wavelet transform on 'data', then
use icwt to compute the inverse wavelet transform to come up with an estimate
of data ('data2'). Note that data2 is not exactly equal data.
# import matplotlib.pyplot as plt
# from scipy.signal import SDG, Morlet, cwt, icwt, fft, ifft
# import numpy as np
#
# x = np.arange(0,2*np.pi,np.pi/64)
# data = np.sin(8*x)
# scales=np.arange(0.5,17)
#
# mother_wavelet = Morlet(len_signal = len(data), scales = scales)
# wave_coefs=cwt(data, mother_wavelet)
# data2 = icwt(wave_coefs)
#
# plt.plot(data)
# plt.plot(data2)
# plt.show()
References
----------
Addison, P. S., 2002: The Illustrated Wavelet Transform Handbook. Taylor
and Francis Group, New York/London. 353 pp.
"""
from scipy.integrate import trapz
# if original wavelet was created using padding, make sure to include
# information that is missing after truncation (see self.coefs under __init__
# in class Wavelet.
if wavelet.motherwavelet.len_signal != wavelet.motherwavelet.len_wavelet:
full_wc = np.c_[wavelet.coefs,wavelet._pad_coefs]
else:
full_wc = wavelet.coefs
# get wavelet coefficients and take fft
wcf = fft(full_wc,axis=1)
# get mother wavelet coefficients and take fft
mwf = fft(wavelet.motherwavelet.coefs,axis=1)
# perform inverse continuous wavelet transform and make sure the result is the same type
# (real or complex) as the original data used in the transform
x = (1. / wavelet.motherwavelet.cg) *
trapz(fftshift(ifft(wcf * mwf,axis=1),axes=[1]) /
(wavelet.motherwavelet.scales[:,np.newaxis]**2),
dx = 1. / wavelet.motherwavelet.sampf, axis=0)
y_2 = np.zeros(shape=(len(ns), len(ls)))
A = np.zeros(shape=(len(ns), len(ls)))
A_2 = np.zeros(shape=(len(ns), len(ls)))
EL = np.zeros(len(ls))
G_l_t_dt = np.zeros(shape=(len(ls), len(thetas)))
A2_theta = np.zeros(shape=(len(ls), len(thetas)))
aiz = []
aiz = Aiz(eiz_x, eiz_z, eiz_w) # of length = len(ns)
for k, length in enumerate(ls):
sum_A = np.empty(len(ls))
sum_A_2 = np.empty(len(ls))
for j, n in enumerate(ns):
# Integral:
y[j, k] = trapz(ys(aiz[j], ts, eiz_w[j], length, n), ts, dt)
y_2[j, k] = trapz(y_2s(aiz[j], ts, eiz_w[j], length, n), ts, dt)
#print 'dt Integral y = ',i,k,j, y
#print 'dt Integral y_2 = ',i,k,j, y_2
#print '----'
#print 'N terms for A0 = ' , As(eiz_z[j],eiz_w[j],length,n,y)
#print 'N terms for A2 = ', A_2s(eiz_z[j],eiz_w[j],length,n,y_2)
#print '----'
A[j, k] = As(eiz_z[j], eiz_w[j], length, n, y[j, k])
A_2[j, k] = A_2s(eiz_z[j], eiz_w[j], length, n,
y_2[j, k]) # * np.cos(2.0*theta)
A[0] = (1. / 2) * A[0]
A_2[0] = (1. / 2) * A_2[0]
sum_A = np.sum(A, axis=0)
#print 'sum of A0 = ', k,j,sum_A
sum_A_2 = np.sum(A_2, axis=0)
def mass_MOI(self, t):
# =======================================
# this method returns mass properties of rocket
#
# INPUT: t = time
# OUTPUT: mass = total mass of rocket
# MOI = total moment of inertia wrt CG
# d_dt_MOI = MOI time rate
# CG = center of gravity location from the nose tip
# =======================================
if t >= self.Params.t_MECO:
# ---------------------------
# mass for coasting phase (m, I = const.)
# ---------------------------
# mass
mass = self.Params.m_dry
# moment of inertia
MOI = self.Params.MOI_dry
# total CG location
CG = self.Params.CG_dry
return mass, MOI, np.zeros(3), CG
else:
# ---------------------------
# mass for powered phase (m = m(t), I = I(t))
# ---------------------------
# propellant comsumption rate = (impulse consumed so far) / (total impulse)
time_so_far = np.linspace(0., t)
Impulse_so_far = integrate.trapz(
self.Params.thrust_function(time_so_far), time_so_far)
r = (1 - Impulse_so_far / self.Params.Impulse_total
) # impulse ratio
# total mass
mass = self.Params.m_dry + r * self.Params.m_prop
# total CG location
CG = (self.Params.CG_dry * self.Params.m_dry +
self.Params.CG_prop * r * self.Params.m_prop) / mass
# total MOI using parallel axis theorem
tmp = np.array([0., 1., 1.])
MOI = self.Params.MOI_dry + tmp * self.Params.m_dry * (
CG -
self.Params.CG_dry)**2. + r * self.Params.MOI_prop + tmp * (
CG - self.Params.CG_prop) * (r * self.Params.m_prop)**2.
# ---------------------------------
# finite differencing for d(MOI)/dt, dm/dt
# ---------------------------------
h = 1.E-3
Impulse_so_far = integrate.trapz(
self.Params.thrust_function(np.linspace(0., t + h)),
np.linspace(0., t + h))
r2 = (1 - Impulse_so_far / self.Params.Impulse_total
) # impulse ratio
# total mass
# mass2 = self.m_dry + r2 * self.m_prop
# total CG location
CG2 = (self.Params.CG_dry * self.Params.m_dry +
self.Params.CG_prop * r2 * self.Params.m_prop) / (
self.Params.m_dry + r2 * self.Params.m_prop)
# total MOI using parallel axis theorem
MOI2 = self.Params.MOI_dry + tmp * self.Params.m_dry * (
CG2 -
self.Params.CG_dry)**2. + r2 * self.Params.MOI_prop + tmp * (
CG2 - self.Params.CG_prop) * (r2 * self.Params.m_prop)**2.
Impulse_so_far = integrate.trapz(
self.Params.thrust_function(np.linspace(0., t - h)),
np.linspace(0., t - h))
r3 = (1 - Impulse_so_far / self.Params.Impulse_total
) # impulse ratio
# mass3 = self.m_dry + r3 * self.m_prop
CG3 = (self.Params.CG_dry * self.Params.m_dry +
self.Params.CG_prop * r3 * self.Params.m_prop) / (
self.Params.m_dry + r3 * self.Params.m_prop)
MOI3 = self.Params.MOI_dry + tmp * self.Params.m_dry * (
CG3 -
self.Params.CG_dry)**2. + r3 * self.Params.MOI_prop + tmp * (
CG3 - self.Params.CG_prop) * (r3 * self.Params.m_prop)**2.
# dm/dt and d(MOI)/dt
# d_dt_m = (mass2 - mass3) / (2*h)
d_dt_MOI = (MOI2 - MOI3) / (2 * h)
return mass, MOI, d_dt_MOI, CG
np.arange(thermo_nc.variables[theta_key][0, 0, 0, :].shape[0]) *
grid_spacing,
np.arange(thermo_nc.variables[theta_key][0, 0, :, 0].shape[0]) *
grid_spacing)
# Compute and store the horizontal mean LCL
lcl[key] = zi_nc.variables[lcl_key][t_idx, :, :].mean()
zi[key] = zi_nc.variables[zi_new_key][t_idx, :, :].mean()
# Get the mean wind speed and direction below LCL
iz_LCL = np.where(
np.abs(z_theta - lcl[key]) == np.min(np.abs(z_theta - lcl[key])))[0][0]
iz_zi = np.where(
np.abs(z_theta - zi[key]) == np.min(np.abs(z_theta - zi[key])))[0][0]
u_mean = u_nc.variables[u_key][t_idx, :iz_zi, :, :].mean(axis=(0, 2, 3))
v_mean = v_nc.variables[v_key][t_idx, :iz_zi, :, :].mean(axis=(0, 2, 3))
U_zi = integrate.trapz(x=z_theta[:iz_zi], y=u_mean) / zi[key]
V_zi = integrate.trapz(x=z_theta[:iz_zi], y=v_mean) / zi[key]
speed, wind_dir = fromComponents(u=U_zi, v=V_zi)
# Get the distance away from the island-edge of the surface warm plume.
mass_flux_xs[key]['theta_anom'] = np.nanmean(np.array([
thermo_nc.variables[theta_key][idx, 1, :, :] -
thermo_nc.variables[theta_key][idx, 1, :, :].mean() for idx in t_idx
]),
axis=0)
R_wp = 4 * R_i #np.nanmax(np.where(mass_flux_xs[key]['theta_anom'] > 0.1, np.sqrt((X-x_c)**2 + (Y-y_c)**2) - R_i, np.nan))
# Compute the rectangle and the new cartesian coordinate system
# distance travelled during time averaging period
mass_flux_xs[key]['mask'], mass_flux_xs[key]['y_prime'], mass_flux_xs[key][
'x_prime'] = downwind_rectangle(
total_i = []
findClosest = lambda a,l:min(l,key=lambda x:abs(x-a))
for scan in scan_nums:
print 'Loading scan {}'.format(scan)
flist = glob.glob(os.path.join(datadir, fprefix+'_{:04d}*.dat'.format(scan)))
flist = sorted(flist, key=lambda f: int(f.split('_')[-1].strip('.dat')))
scan_intensity = 0
for f in flist[20:]:
# print f
q, i, err, parameters = loadPrimusDatFile(f)
closest_qmin = findClosest(0.02, q)
closest_qmax = findClosest(0.1, q)
nmin = np.where(q == closest_qmin)[0][0]
nmax = np.where(q == closest_qmax)[0][0]
scan_intensity = scan_intensity + integrate.trapz(i[nmin:nmax+1], q[nmin:nmax+1])
total_i.append(scan_intensity)
plt.bar(range(1, len(total_i)+1), total_i)
plt.show()
senal[k * p:(k + 1) * p] = -sinus
#Graficamos los la senal correspondiente a los primeros 5 bits
plt.figure()
plt.plot(senal[0:5 * p])
plt.ylabel('Amplitud señal portadora')
plt.xlabel('Tiempo (ms)')
plt.title('Modulación BSPK para los primeros 5 bits del archivo "bits10k.csv"')
plt.savefig('modulacionBSPK.png')
plt.show
""" 2) Calcular la potencia promedio de la señal modulada generada.
"""
#La potencia instantánea está dada por
Pinst = senal**2
# Potencia promedio a partir de la potencia instantanea
Ps = integrate.trapz(Pinst, t) / (N * T) #W
print('La potencia promedio es: ', Ps, 'W')
#Resultado: P = 0.49 W
""" 3) Simular un canal ruidoso del tipo AWGN (ruido aditivo blanco gaussiano) con una relación
señal a ruido (SNR) desde -2 hasta 3 dB.
"""
#Se realiza el mismo procedimiento para cada SNR
# Potencia del ruido para SNR y potencia de la señal dadas
SNR0 = -2
SNR1 = -1
SNR2 = 0
SNR3 = 1
SNR4 = 2
SNR5 = 3
#######SNR = -2
energy_array = np.linspace(
energy_initial_float.value, energy_final_float.value,
energy_steps_number_float.value) * energy_step_float.unit
# ---------------------------------------------------------------------------------------------------------------------
# Calculate the fermi diff. integral:
# ---------------------------------------------------------------------------------------------------------------------
fermiDiracLeft_array = fermi_dirac_fn(energy_array, temperature_float,
chemical_potential_float)
fermiDiracRight_array = fermi_dirac_fn(energy_array + energy_bias_float,
temperature_float,
chemical_potential_float)
fermiDiracDiff_array = fermiDiracLeft_array - fermiDiracRight_array
# Use trapezoidal method to integrate:
fermi_diff_integral_value_float = integrate.trapz(fermiDiracDiff_array,
energy_array)
# ---------------------------------------------------------------------------------------------------------------------
# Plot the Fermi-Dirac curves:
# ---------------------------------------------------------------------------------------------------------------------
plt.figure(2)
plt.plot(energy_array,
fermiDiracDiff_array,
'-',
color='orange',
label='$n_{FD}^L(E) - n_{FD}^R(E)$')
plt.plot(energy_array,
fermiDiracLeft_array,
'--',
color='r',
label='$n_{FD}^L(E)$')
def CmpRealAxisBubble(filemesh, filegkr, fbubbleReal, Qlist, k_index):
def Cmp_ChiQ_real(iOm,Q,gkr,k_m_q,nkp,norb,dx_,idxl,Nd,zero_ind,k_index):
level = (iOm-1)/Nd # which linear mesh should we use?
om_idx=idxl[level] # index for the linear mesh on this level
izero= (len(om_idx)-1)/2 # zero_ind on this level
dOm = om_idx.index(zero_ind+iOm)-izero # om-Om in integer notation is i-dOm
om_idx=array(om_idx)
Qi = k_index(Q)
codeBub="""
#line 239 "Suscept.py"
using namespace std;
for (int iorb=0; iorb<norb; iorb++){
for (int jorb=0; jorb<norb; jorb++){
complex<double> csum=0.0;
for (int iom=izero; iom<izero+dOm+1; iom++){
double dom = (iom==izero || iom==izero+dOm) ? dx/2.0 : dx; // trapezoid rule has 1/2 at the last interval
complex<double> csum2=0.0;
for (int ik=0; ik<nkp; ik++){
int ikq = k_m_q(ik,Qi);
int iom1 = om_idx(iom);
int iom2 = om_idx(iom-dOm);
complex<double> irhok=(gkr(iorb,jorb,iom1,ik)-conj(gkr(jorb,iorb,iom1,ik)))/2.0; // (G_k-G_k^+)/2
complex<double> irhoq=(gkr(jorb,iorb,iom2,ikq)-conj(gkr(iorb,jorb,iom2,ikq)))/2.0;
csum2 -= irhok*irhoq; // rho_k * rho_{k+q}
}
csum += csum2*dom;
}
ImBub(iorb,jorb) = csum/(nkp*M_PI);
}
}
"""
ImBub=zeros((norb,norb),dtype=complex)
dx=float(dx_)
weave.inline(codeBub, ['ImBub','gkr','norb','dx','nkp','Qi','k_m_q','dOm','izero','om_idx'],type_converters=weave.converters.blitz, compiler='gcc')
return ImBub
#print 'Qlist=', Qlist
##########################
# Reading real axis mesh #
##########################
fm = open(filemesh, 'r')
lined = fm.next().split()
(mdelta, mmax) = map(float,lined[:2])
Nd = int(lined[2])
(oml,idxl) = LinLogMesh.LinLogMeshGen(mdelta,mmax,Nd)
#print 'Qlist=', Qlist
#######################################
# Reading real axis Green's function #
#######################################
# Reading some basic information from G_k
fg = open(filegkr,'r')
first_line = fg.next()
nkp,nsymop,nom,cixdm,norbitals = map(int,first_line.split()[1:6])
fg.close()
(gkr,omr) = ReadGk(filegkr, nkp, nsymop, nom, cixdm)
print 'shape(gkr)=', shape(gkr)
if sum(abs(omr-oml))>1e-5: print 'Mesh in '+filegkr+' and in '+filemesh+' are not compatible.'
zero_ind = oml.tolist().index(0.0)
Oml=oml[zero_ind:]
norb=cixdm
###############################
# Computing real axis Bubble #
###############################
# This is the zero frequency value
chi0r0 = zeros((len(Qlist),norb,norb), dtype=float)
#print 'Qlist=', Qlist
for iq,Q in enumerate(Qlist):
print 'Q=', Q
ImBub = zeros((norb,norb,len(Oml)),dtype=complex)
for iOm in range(1,len(Oml)):
ImBub[:,:,iOm] = Cmp_ChiQ_real(iOm,Q,gkr,k_m_q,nkp,norb,Oml[iOm]-Oml[iOm-1],idxl,Nd,zero_ind,k_index)
ImBubr = real(ImBub)
Bub = zeros((norb,norb,len(Oml)), dtype=complex)
for iorb in range(norb):
for jorb in range(norb):
tOm = hstack( (-Oml[::-1][:-1], Oml[1:]) )
ImB = hstack( (-ImBubr[iorb,jorb,::-1][:-1], ImBubr[iorb,jorb,1:]) )
Bub[iorb,jorb,0] = integrate.trapz(ImB/tOm, x=tOm)/pi
izero=len(tOm)/2
for i in range(izero,len(tOm)):
Bub[iorb,jorb,i-izero+1] = krams.kramarskronig(ImB, tOm, i) + ImB[i]*1j
chi0r0[iq,:,:] = Bub[:,:,0].real
fq = open(fbubbleReal+str(iq), 'w')
for iOm,Omx in enumerate(Oml):
print >> fq, Omx,
for iorb in range(norb):
for jorb in range(norb):
print >> fq, Bub[iorb,jorb,iOm].real, Bub[iorb,jorb,iOm].imag,
print >> fq
fq.close()
print 'Chi_q-real axis: Q point', iq, 'finished'
return chi0r0
def eiz(eiz_arg, X):
return 1. + (2. / pi) * trapz(eiz_arg, X)
a = 0
b = 1
n = 100
h = (b - a) / n
x = arange(a, b + h, h)
#print(x)
y = []
for xi in x:
y.append(f(xi))
#print(y)
I = trapz(y, x=x)
print(I)
# setting the axes at the centre
fig = plt.figure()
ax = fig.add_subplot(1, 1, 1)
ax.spines['left'].set_position('center')
ax.spines['bottom'].set_position('zero')
ax.spines['right'].set_color('none')
ax.spines['top'].set_color('none')
ax.xaxis.set_ticks_position('bottom')
ax.yaxis.set_ticks_position('left')
plt.plot(x, y, 'r')
plt.show()
def residual_area(sample_probabilities, predicted_pos_percents):
"""Compute the total area under the curve of |predicted prob - expected prob|
"""
abs_deviations = np.abs(predicted_pos_percents - sample_probabilities)
return integrate.trapz(abs_deviations, sample_probabilities)
dtype=float)) # Wavelength from dictionary appended to array
I.append(
np.array(DATA[i]['Intensity'],
dtype=float)) # Intensity from dictionary appended to array
DATA[i]['diff'] = DATA[i]['Intensity'].diff().abs(
) # Calculates the absolute value of the difference between neighboring intensity values
DATA[i] = DATA[i][
DATA[i]['diff'] <
0.002] # Descriminates large jumps in intensity out of the DATA dictionary
datacut[i] = DATA[i][(
DATA[i]['Wavelength'] > Filter
)] #& (DATA[i]['Wavelength']<600)] # Limits the wavelength between two values
intensity[i] = integrate.trapz(
datacut[i]['Intensity'],
datacut[i]['Wavelength']) # Calculates the integral of datacut
INT.append(intensity[i]) # Appends the integral to the INT array
if verbose == True: # When True
print("Length of DATA dictionary=",
len(DATA)) # Prints the number of pairs in the DATA dictionary
print(
"Length of INT dictionary=",
len(INT)) # Prints the length of the INT array. Must match DATA length
# <codecell>
### Dispose of data preceeding max ###
Cut = INT.index(
max(INT)) # Identifies the file number with the maximum intensity
Redundant = np.arange(
def J(u,y,yT,T):
t = np.linspace(0,T,len(u))
I = trapz(u**2,t)
return 0.5*(I + (y-yT)**2)
def bringData(folder,
dataFolder,
scorePosition,
lossPosition,
pickle=False,
save=False):
dir = joinPath([basePath, dataFolder, folder[0]])
f = ''
areaCompare = float('-inf')
fileName = ''
paper_fig_settings()
plt.figure(figsize=(20, 15))
for file in returnList(dir):
selectFolder = joinPath([dir, file])
selectFile = returnList(selectFolder)[[scorePosition]]
f = joinPath([selectFolder, selectFile[0]])
selectLossFile = returnList(selectFolder)[[lossPosition]]
l = joinPath([selectFolder, selectLossFile[0]])
data[file] = np.load(f, allow_pickle=pickle)
loss[file] = np.load(l, allow_pickle=pickle)
d = np.sort(data[file])
area = trapz(d)
mean = np.mean(d)
std = np.std(d)
# if areaCompare < area:
# areaCompare = area
fileName = 'focused'
try:
selectedDenseScore = data['dense']
selectedFocusedScore = data[fileName]
selectedDenseLoss = loss['dense']
selectedFocusedLoss = loss[fileName]
except:
pass
selectedFolder = folder[0]
print(
f'{folder[0]} -> {file} -> Curve Area: {area}, Mean: {mean}, std: {std}',
)
plot(d, mean, std, file)
plt.legend(data.keys())
if save:
plt.savefig('./plots/histograms/' + selectedFolder + '_histogram.png',
bbox_inches="tight")
print('selected sigma: ', fileName)
#This part will run after selecting right focused values againts dense values
# trend comparison
plt.figure(figsize=(20, 15))
paper_fig_settings()
showTrend(scores=selectedDenseScore, name=selectedFolder + ' dense')
showTrend(scores=selectedFocusedScore, name=selectedFolder + ' focused')
if save:
plt.savefig('./plots/histograms/' + selectedFolder + '-' + fileName +
'_trend.png',
bbox_inches="tight")
# loss comparison
plt.figure(figsize=(20, 15))
paper_fig_settings()
lossComparison(name=selectedFolder + ' dense', results=selectedDenseLoss)
lossComparison(name=selectedFolder + ' focused',
results=selectedFocusedLoss)
print(f'Area Under dense Curve', trapz(selectedDenseLoss))
print(f'Area Under focused Curve', trapz(selectedFocusedLoss))
if save:
plt.savefig('./plots/histograms/' + selectedFolder + '-' + fileName +
'_loss.png',
bbox_inches="tight")
# t-test will applied according to our hypotesis
# we will make an assumption according to area under curve
# and will say like this focused nn learn to solve
# the problem more fast, accurate and efficient
statistic, pvalue = ttest_ind(selectedDenseScore, selectedFocusedScore)
print('statistic: ', float(statistic))
print('pvalue: ', float(pvalue))
plt.show()
(1 - xi * xi) / (4 * np.cosh(gamma)) +
P_1 * kappa_p * kappa_p * np.sinh(kappa) *
(np.cosh(gamma * xi) / np.cosh(gamma) -
xi * np.sinh(kappa_p * xi) / np.sinh(kappa_p)) /
(2 * gamma * gamma))
uy1 = 0.5 * (kappa * P_1 * np.sinh(kappa) /
(gamma * gamma)) * (
np.sinh(kappa_p * xi) / np.sinh(kappa_p) -
np.sinh(kappa * xi) / np.sinh(kappa))
ux1 = 0.5 * ((P_1 * kappa * np.cosh(kappa) / (gamma * gamma)) *
(np.cosh(kappa * xi) / np.cosh(kappa) -
np.cosh(kappa_p * xi) / np.cosh(kappa_p)) +
(F0 * np.tanh(gamma) / (gamma)) *
(np.cosh(kappa_p * xi) / np.cosh(kappa_p) -
xi * np.sinh(gamma * xi) / np.sinh(gamma)))
ux2 -= scpi.trapz(ux2, xi) / 2 + scpi.trapz(ux1, xi) / 4
B0 = (Pe * F0 * np.tanh(gamma) /
(2 * gamma * (rho * rho - gamma * gamma))) * (
np.cosh(rho * xi) /
(rho * np.sinh(rho)) - np.cosh(gamma * xi) /
(gamma * np.sinh(gamma))) + Pe * F0 * np.tanh(
gamma) / (2 * gamma * gamma * gamma * rho * rho)
B0_deriv = (Pe * F0 * np.tanh(gamma) /
(2 * gamma * (rho * rho - gamma * gamma))) * (
np.sinh(rho * xi) / np.sinh(rho) -
np.sinh(gamma * xi) / np.sinh(gamma))
B0_deriv_deriv = (
Pe * F0 * np.tanh(gamma) /
(2 * gamma * (rho * rho - gamma * gamma))) * (
rho * np.cosh(rho * xi) / np.sinh(rho) -
def MaximumEntropy(p, tau, Gt):
beta = tau[-1]
random.seed(1) # seed for random numbers
if p.has_key('x0'):
omega = GiveTanMesh(p['x0'], p['L'], p['Nw'])
else:
omega = linspace(-p['L'], p['L'], 2 * p['Nw'] + 1)
dom = array([0.5 * (omega[1] - omega[0])] + [
0.5 * (omega[i + 1] - omega[i - 1]) for i in range(1,
len(omega) - 1)
] + [0.5 * (omega[-1] - omega[-2])])
fsg = 1
if p['statistics'] == 'fermi':
Gt = -Gt
fsg = -1
normalization = Gt[0] + Gt[-1]
Ker = me.initker_fermion(omega, dom, beta, tau)
elif p['statistics'] == 'bose':
normalization = integrate.trapz(Gt, x=tau)
Ker = me.initker_boson(omega, dom, beta, tau)
print 'beta=', beta
print 'normalization=', normalization
# Set error
if p['idg']:
sxt = ones(len(tau)) / (p['deltag']**2)
else:
sxt = Gt * p['deltag']
for i in range(len(sxt)):
if sxt[i] < 1e-5: sxt[i] = 1e-5
sxt = 1. / sxt**2
# Set model
if p['iflat'] == 0:
model = normalization * ones(len(omega)) / sum(dom)
elif p['iflat'] == 1:
model = exp(-omega**2 / p['gwidth'])
model *= normalization / dot(model, dom)
else:
dat = loadtxt('model.dat').transpose()
fm = interpolate.interp1d(dat[0], dat[1])
model = fm(omega)
model *= normalization / dot(model, dom)
#savetxt('brisi_test', vstack((tau, fsg*dot(model,Ker))).transpose())
print 'Model normalization=', dot(model, dom)
# Set starting Aw(omega)
Aw = random.rand(len(omega))
Aw = Aw * (normalization / dot(Aw, dom))
print 'Aw normalization=', dot(Aw, dom)
dlda = me.initdlda(omega, dom, Ker, sxt)
temp = 10.
rfac = 1.
alpha = p['alpha0']
for itt in range(p['Nitt']):
print itt, 'Restarting maxent with rfac=', rfac, 'alpha=', alpha
iseed = random.randint(0, maxint)
me.maxent(Aw, rfac, alpha, temp, Ker, sxt, Gt, model, dom, p['Asteps'],
iseed)
S = me.entropy(Aw, model, dom)
Trc = me.lambdac(alpha, Aw, omega, dom, dlda)
ratio = -2 * S * alpha / Trc
print 'Finished maxent with alpha=', alpha, '-2*alpha*S=', -2 * alpha * S, 'Trace=', Trc
print ' ratio=', ratio
savetxt('dos_' + str(itt), vstack((omega, Aw)).transpose())
temp = 0.001
rfac = 0.05
if abs(ratio - 1) < p['min_ratio']: break
if (abs(ratio) < 0.05):
alpha *= 0.5
else:
alpha *= (1. + 0.001 * (random.rand() - 0.5)) / ratio
for itt in range(p['Nr']):
print 'Smoothing itt ', itt
Aw = Broad(p['bwdth'], omega, Aw)
Aw *= (normalization / dot(Aw, dom)) # Normalizing Aw
savetxt('dos_' + str(p['Nitt']), vstack((omega, Aw)).transpose())
temp = 0.005
rfac = 0.005
iseed = random.randint(0, maxint)
me.maxent(Aw, rfac, alpha, temp, Ker, sxt, Gt, model, dom, p['Asteps'],
iseed)
S = me.entropy(Aw, model, dom)
Trc = me.lambdac(alpha, Aw, omega, dom, dlda)
ratio = -2 * S * alpha / Trc
print 'Finished smoothing run with alpha=', alpha, '-2*alpha*S=', -2 * alpha * S, 'Trace=', Trc
print ' ratio=', ratio
savetxt('gtn', vstack((tau, fsg * dot(Aw, Ker))).transpose())
Aw = Broad(p['bwdth'], omega, Aw)
savetxt('dos.out', vstack((omega, Aw)).transpose())
return (Aw, omega)
def gen_fine_clic(p_angles_fine,xi_r,xi_t,dt_t,rs,dr_n,s_model,model,depth,inv_f,par,tcut):
clic_theta_grid = 200
clic_theta = np.linspace(0,180,clic_theta_grid)
global clic_xi_r,clic_xi_t,clic_dt_t
clic_xi_r = np.zeros((depth,clic_theta_grid))
clic_xi_t = np.zeros((depth,clic_theta_grid))
clic_dt_t = np.zeros((depth,clic_theta_grid))
clic_rs = np.zeros((depth,clic_theta_grid))
if tcut:
cut=True
print "--- CUT ---"
else:
cut=False
for d in range(depth):
if cut:
xi_r[d,0:12] = 1.*xi_r[d,12]
xi_t[d,0:12] = 1.*xi_t[d,12]
dt_t[d,0:12] = 1.*dt_t[d,12]
rs[d,0:12] = 1.*rs[d,12]
if par=="EVEN":
xi_r[d,-9::] = 1.*xi_r[d,-10]
xi_t[d,-9::] = 1.*xi_t[d,-10]
dt_t[d,-9::] = 1.*dt_t[d,-10]
rs[d,-9::] = 1.*rs[d,-10]
clic_xi_r[d,0:100] = np.interp(clic_theta[0:100],np.linspace(0,90,100),xi_r[d,:])
clic_xi_t[d,0:100] = np.interp(clic_theta[0:100],np.linspace(0,90,100),xi_t[d,:])
clic_dt_t[d,0:100] = np.interp(clic_theta[0:100],np.linspace(0,90,100),dt_t[d,:])
clic_rs[d,0:100] = np.interp(clic_theta[0:100],np.linspace(0,90,100),rs[d,:])
for i in range(depth):
if par=="EVEN":
clic_xi_r[i,100::] = clic_xi_r[i,::-1][100::]
clic_xi_t[i,100::] = clic_xi_t[i,::-1][100::]
clic_dt_t[i,100::] = clic_dt_t[i,::-1][100::]
else:
clic_xi_r[i,100::] = -1.*clic_xi_r[i,::-1][100::]
clic_xi_t[i,100::] = -1.*clic_xi_t[i,::-1][100::]
clic_dt_t[i,100::] = -1.*clic_dt_t[i,::-1][100::]
clic_rs[i,100::] = clic_rs[i,::-1][100::]
#plt.plot(clic_theta[0:200],clic_rs[-2,0:200])
############ find the perturbed models:
# Take static ROTORC model to CLIC grid:
global s_model_c
s_model_c = np.zeros((clic_theta_grid,len(s_model[0,:])))
s_model_c[:,0] = clic_theta
for i in range(1,len(s_model[0,:])):
s_model_c[0:100,i] = np.interp(clic_theta[0:100],s_model[:,0],s_model[:,i])
s_model_c[100::,i] = s_model_c[::-1,i][100::]
G = 6.67259e-8
mass = (float((model[0]).replace("p",".")))*1.99e33
theta = np.deg2rad(s_model_c[:,0])
radius = s_model_c[:,1]*6.96e10
vrot = s_model_c[:,4]*1e5
omega = vrot/(radius*np.sin(theta))
omega = np.average(omega[50:-50])
a_r = scint.trapz(clic_dt_t[-1,:])
# inv_f = 1.
# if a_r<0:
# print "fine -T area"
# inv_f = -1.
global pmodels_fine
pert_r = np.empty((len(s_model_c[:,0]),depth))
pert_t = np.empty((len(s_model_c[:,0]),depth))
pmodels_fine = []
for i in range(depth):
#pert_r[:,i] = s_model_c[:,1]*(1.+inv_f*clic_xi_r[-i,:])
pert_r[:,i] = s_model_c[:,1]+inv_f*clic_rs[-i,:]*clic_xi_r[-i,:]
pert_t[:,i] = s_model_c[:,2]*(1.+inv_f*clic_dt_t[-i,:])
for j in range(len(pert_t[:,i])):
if pert_t[j,i]<7500.: pert_t[j,i]=7500.
g_pert = (G*mass/((pert_r[:,i]*6.96e10)**2))-((omega**2)*((pert_r[:,i]*6.96e10)*np.sin(theta)))*np.sin(theta)
for j in range(len(g_pert)):
if np.log10(g_pert[j])>4.33: g_pert[j]=10**(4.33)
tmodel = 1.*s_model_c
"""
pert_r[0:11,:] = pert_r[11,:]
pert_r[190:200,:] = pert_r[189,:]
pert_t[0:11,:] = pert_t[11,:]
pert_t[190:200,:] = pert_t[189,:]
"""
tmodel[:,1] = pert_r[:,i]
tmodel[:,2] = pert_t[:,i]
tmodel[:,3] = np.log10(g_pert)
pmodels_fine.append(tmodel)
#plt.plot(clic_dt_t[0,:])
return pmodels_fine
def MaximumEntropyTest(p, tau, Gt):
def MEStep(alpha,
rfac,
Aw,
temp,
Ker,
sxt,
Gt,
model,
f0,
Asteps,
itt,
reset=True):
if (reset):
temp = 0.001
rfac = 0.05
print 'Restarting maxent with rfac=', rfac, 'alpha=', alpha
iseed = random.randint(0, maxint)
me.maxent(Aw, rfac, alpha, temp, Ker, sxt, Gt, model, f0, Asteps,
iseed)
S = me.entropy(Aw, model, f0)
Trc = me.lambdac(alpha, Aw, omega, dlda)
ratio = -2 * S * alpha / Trc
print 'Finished maxent with alpha=', alpha, '-2*alpha*S=', -2 * alpha * S, 'Trace=', Trc
print ' ratio=', ratio
savetxt('dos_' + str(itt), vstack((omega, Aw)).transpose())
return ratio
beta = tau[-1]
random.seed(1) # seed for random numbers
omega = linspace(-p['L'], p['L'], 2 * p['Nw'] + 1)
f0, f1, f2 = me.initf0(omega)
fsg = 1
if p['statistics'] == 'fermi':
Gt = -Gt
fsg = -1
normalization = Gt[0] + Gt[-1]
Ker = me.initker_fermion(omega, beta, tau)
elif p['statistics'] == 'bose':
normalization = integrate.trapz(Gt, x=tau)
Ker = me.initker_boson(omega, beta, tau)
print 'beta=', beta
print 'normalization=', normalization
# Set error
if p['idg']:
sxt = ones(len(tau)) / (p['deltag']**2)
else:
sxt = Gt * p['deltag']
for i in range(len(sxt)):
if sxt[i] < 1e-5: sxt[i] = 1e-5
sxt = 1. / sxt**2
# Set model
if p['iflat'] == 0:
model = normalization * ones(len(omega)) / sum(f0)
elif p['iflat'] == 1:
model = exp(-omega**2 / p['gwidth'])
model *= normalization / dot(model, f0)
else:
dat = loadtxt('model.dat').transpose()
fm = interpolate.interp1d(dat[0], dat[1])
model = fm(omega)
model *= normalization / dot(model, f0)
#savetxt('brisi_test', vstack((tau, fsg*dot(model,Ker))).transpose())
print 'Model normalization=', dot(model, f0)
# Set starting Aw(omega)
Aw = random.rand(len(omega))
Aw = Aw * (normalization / dot(Aw, f0))
print 'Aw normalization=', dot(Aw, f0)
dlda = me.initdlda(omega, Ker, sxt)
temp = 10.
rfac = 1.
alpha = p['alpha0']
for itt in range(10):
ratio = MEStep(alpha, rfac, Aw, temp, Ker, sxt, Gt, model, f0,
p['Asteps'], itt, itt != 0)
if abs(ratio - 1) < p['min_ratio']: break
if (ratio < 0.05):
if ratio > 0:
alpha *= 1.1
else:
alpha /= 10.
else:
alpha *= (1. + 0.001 * (random.rand() - 0.5)) / ratio
if abs(ratio - 1) > 2 * p['min_ratio']:
alpha = 1.
p['Asteps'] *= 1.5
for itt in range(3, 6):
ratio = MEStep(alpha, rfac, Aw, temp, Ker, sxt, Gt, model, f0,
p['Asteps'], itt)
for itt in range(p['Nr']):
print 'Smoothing itt ', itt
Aw = Broad(p['bwdth'], omega, Aw)
Aw *= (normalization / dot(Aw, f0)) # Normalizing Aw
ratio = MEStep(alpha, rfac, Aw, temp, Ker, sxt, Gt, model, f0,
p['Asteps'], p['Nitt'] + itt)
savetxt('gtn', vstack((tau, fsg * dot(Aw, Ker))).transpose())
Aw = Broad(p['bwdth'], omega, Aw)
savetxt('dos.out', vstack((omega, Aw)).transpose())
return (Aw, omega)
def run_visc_pert(model,vel,mode,par,sigma,reese,force_f,minL,phase=0.,ampl=1.,tlmax=0.,tcut=False):
# Info for del dot xi calculation:------------------
# NRO Mode filename:
#modefname="MODE1"
global kind
norm_f = True
ssc = 0.02
if model[0]=="2p5": ssc = 0.01
if kind=="g":
scale = ssc
else:
scale = ssc/(sigma**2)
scale =0.001*drtempmax
depth = 10 #radial zones down from the surface
forcenro = False
#---------------------------------------------------
#clic_run = True
v = find_vel(model,vel)
folder = homedir+"ROTORCmodels/"+par+"/M"+model[0]+"_V"+v+"/"
rotorc_f = homedir+"From_Bob/Delta_Scuti_2010/"+model[0]+"Msun/"+model[0]+"Msun_V"+v+"/"
bob_bin = homedir+"From_Bob/clotho_disc10_bin/"
static_m = homedir+"ROTORCmodels/visibilities/"
#check if visibility file from pulset exits for the selected model:
#v_file = glob.glob(rotorc_f+"visibility_file")
###### FULL MODE FILE GENERATION:
temp_freqs = np.genfromtxt(folder+"temp_freqs")
tfreq = temp_freqs[mode-1]
if force_f==True:
tfreq = sigma
print sigma
#tfreq = 1.59692
#print pyNRO.run_nro(tfreq,folder,model[0],v,par,mode)
where =static_m+model[0]+'Msun/V'+v+"/MODE_"+par+"_"+str(mode)
if not os.path.exists(static_m+model[0]+'Msun/'+'V'+v):
os.makedirs(static_m+model[0]+'Msun/'+'V'+v)
if not os.path.exists(static_m+model[0]+'Msun/'+'V'+v+"/MODE_"+par+"_"+str(mode)):
os.makedirs(where)
if os.path.isfile(where+'/MODE_'+par+'_'+str(mode))==False or forcenro==True:
#check if visibility file from pulset exits for the selected model:
#v_file = glob.glob(rotorc_f+"visibility_file")
if True:
os.chdir(rotorc_f)
r_mod_name = glob.glob("*_ZAMS")
subprocess.call(["cp",r_mod_name[0],"orcmod_pulset"])
subprocess.call([bob_bin+"pulsetnonadb.exe"])
print "Generated visibility_file in "+rotorc_f
subprocess.call([bob_bin+"pulset_gammas.exe"]) #Generates Cmod with gammas
subprocess.call(["cp","Cmod",folder+"Dmod_"+model[0]+"M_V"+v])
print "Generated new Dmod"
#print(glob.glob("*_ZAMS"))
os.chdir(vis_path)
print "Dmod with GAMMAS generated!"
nro_stat = 1
idx_iter = 0
while nro_stat==1:
#RUN NRO!
nro_stat = pyNRO.run_nro(tfreq-idx_iter*1e-4,folder,model[0],v,par,mode,homedir)
idx_iter += 1
subprocess.call(['mv',folder+'MODE_'+par+'_'+str(mode),where+'/MODE_'+par+'_'+str(mode)])
print "Mode file generation complete!"
else:
print "Mode file found! Not running NRO..."
###### del_DOT_xi>
#modeloc = static_m+model[0]+'Msun/V'+vels[vel]+"/"
modeloc = where+"/"
modefname = 'MODE_'+par+'_'+str(mode)
#modefname = 'MODE13'
global s_model
s_model = np.genfromtxt(glob.glob(static_m+model[0]+'Msun/'+model[0]+'Msun_V'+v+"*")[0])
global xi_r_rot,xi_t_rot,dt_t_rot,zg_rot
global xi_r,xi_t,dt_t,zg,r,zp,cs,xi_dot_g
global xi_r_n,xi_t_n,dt_t_n,zg_n
xi_r,xi_t,dt_t,zg,r,zp,sig,cs,xi_dot_g = ddxi.calcdeldotxi(par,model,vel,modeloc,modefname)
xi_r_n,xi_t_n,dt_t_n,zg_n,dr_n = ddxi.norm_and_scale(xi_r,xi_t,dt_t,r,zg,norm_f,scale,depth,reese,sig,par)
if phase!=0:
#dt_t_n = phaser(dt_t_n,phase,1.,tlmax)
#xi_r_n = phaser(xi_r_n,0.,1.,tlmax)
dt_t_n,psi_T,psi_L,mx = phaser2(dt_t_n,phase,np.max(np.abs(dt_t[-depth])),np.max(np.abs(xi_r[-depth])))
xi_r_n = phaser(xi_r_n,0.,1.,mx+np.pi)
print "Theta L_max-----------> ",np.rad2deg(mx),"deg"
np.savetxt(modeloc+"phases.txt",[psi_T,psi_L,np.rad2deg(mx+np.pi)],header="psi_T[deg],psi_L[deg],theta_max_L[deg]")
a_r = scint.trapz(dt_t_n[-1,:])
inv_f = 1.
if a_r<0:
print "-T area"
#xi_r_n *= -1.
#xi_t_n *= -1.
#dt_t_n *= -1.
#zg_n *= -1.
inv_f = -1.
if minL==True:
inv_f *= -1.
#xi_r_rot,xi_t_rot,dt_t_rot,zg_rot = ddxi.to_rotorc(xi_r_n,xi_t_n,dt_t_n,zg_n)
if par == "EVEN":
xi_r_fine = lint.leg_interp(xi_r_n[:,:],8,"EVEN")
xi_t_fine = lint.leg_interp(xi_t_n[:,:],8,"EVEN")
dt_t_fine = lint.leg_interp(dt_t_n[:,:],8,"EVEN")
else:
xi_r_fine = lint.leg_interp(xi_r_n[:,:],8,"OE")
xi_t_fine = lint.leg_interp(xi_t_n[:,:],8,"OE")
dt_t_fine = lint.leg_interp(dt_t_n[:,:],8,"OE")
global rs_n,rs_rot
rs_n = np.empty(xi_r_fine.shape)
for d in range(depth):
rs_n[d,:] = np.interp(np.linspace(0,90,100),np.linspace(10,80,8),r[-d-1,:])
# dr_n = xi_r_fine*rs_n
# for i in range(len(dr_n[:,0])):
# imax = np.argmax(np.abs(dr_n[i,:]))
# dr_n[i,:] = dr_n[i,:]/(dr_n[i,imax]/2.28534026)
p_angles = np.empty(np.shape(xi_r_n))
p_angles_fine = np.empty(np.shape(xi_r_fine))
rot_ang = np.arange(4.5,90.,9)
xi_r_rot = np.empty((depth,len(rot_ang)))
xi_t_rot = np.empty((depth,len(rot_ang)))
dt_t_rot = np.empty((depth,len(rot_ang)))
rs_rot = np.empty((depth,len(rot_ang)))
for d in range(depth):
p_angles[d,:] = (np.linspace(10,80,8))*(1.+xi_t_n[d,:])
p_angles_fine[d,:] = (np.linspace(0,90,100))*(1.+xi_t_fine[d,:])
xi_r_rot[d,:] = np.interp(rot_ang,p_angles_fine[d,:],xi_r_fine[d,:])
xi_t_rot[d,:] = np.interp(rot_ang,p_angles_fine[d,:],xi_t_fine[d,:])
dt_t_rot[d,:] = np.interp(rot_ang,p_angles_fine[d,:],dt_t_fine[d,:])
rs_rot[d,:] = np.interp(rot_ang,p_angles_fine[d,:],rs_n[d,:])
#
# #plt.plot(p_angles_fine[2,:],xi_t_fine[2,:])
# if dr_n[0,-1]>0:
# ivrt = 1.
# else:
# ivrt = -1.
# vr = ivrt*dr_n[0,:]
# #vr = ivrt*dt_t_fine[0,:]
# #lblb = find_vel(model,vel)+" km s$^{-1}$ "+find_name(model,vel,par,mode)
# lblb = find_vel(model,vel)+" km s$^{-1}$ "
# #lblb = r"$\ell$ = "+find_name(model,vel,par,mode).split()[0]
# etsy = "-"
# if find_name(model,vel,par,mode).split()[0] == "2": etsy = "-"
# if par == "EVEN":
# #plt.plot(p_angles_fine[2,:],ivrt*lint.leg_interp(vr[:,:],8,"EVEN")[0,:],label=lblb)
# plt.plot(p_angles_fine[2,:],vr,ls=etsy,label=lblb)
#
# else:
# #plt.plot(p_angles_fine[2,:],ivrt*lint.leg_interp(vr[:,:],8,"OE")[0,:],label=lblb)
# plt.plot(p_angles_fine[2,:],vr,ls=etsy,label=lblb)
# #plt.plot(p_angles_fine[2,:],lint.leg_interp(xi_r[-depth::,:],8,"OE")[2,:],label=find_name(model,vel,par,mode))
# #plt.plot(p_angles[2,:],dt_t[-depth+2,:],"o",mfc="white",mec="k",mew=1)
# #plt.grid()
# plt.xlim(0,90)
# plt.yticks()
# plt.xlabel("Colatitude [deg]")
# plt.ylabel(r"$\delta$R [R$\odot$]")
# #plt.ylabel(r"$\delta$T/T")
# plt.legend(loc="best")
# #plt.title("Mode:" + find_name(model,vel,par,mode))
# #ax.yaxis.set_major_formatter(majorFormatter)
# plt.ticklabel_format(style='sci', axis='y', scilimits=(0,0))
# #plt.title(r"M="+model[0]+"M$_{\odot}$, V="+v+"km s$^{-1}$")
# plt.title(r"M="+model[0]+"M$_{\odot}$")
print "Generating fine clic model..."
pmodels_fine = gen_fine_clic(p_angles_fine,xi_r_fine,xi_t_fine,dt_t_fine,rs_n,dr_n,s_model,model,depth,inv_f,par,tcut)
############ find the perturbed models:
global omega
G = 6.67259e-8
mass = (float((model[0]).replace("p",".")))*1.99e33
theta = np.deg2rad(s_model[:,0])
radius = s_model[:,1]*6.96e10
vrot = s_model[:,4]*1e5
omega = vrot/(radius*np.sin(theta))
omega = np.average(omega[1:-1])
#g_r = (G*mass/(radius**2))-((omega**2)*(radius*np.sin(theta)))*np.sin(theta)
#g_theta = ((omega**2)*(radius*np.sin(theta)))*np.cos(theta)
#geff = (g_r**2 + g_theta**2)**0.5
pert_r = np.empty((len(s_model[:,0]),depth))
pert_t = np.empty((len(s_model[:,0]),depth))
pmodels = []
for i in range(depth):
pert_r[:,i] = s_model[:,1]*(1.+inv_f*xi_r_rot[-i,:])
pert_t[:,i] = s_model[:,2]*(1.+inv_f*dt_t_rot[-i,:])
g_pert = (G*mass/((pert_r[:,i]*6.96e10)**2))-((omega**2)*((pert_r[:,i]*6.96e10)*np.sin(theta)))*np.sin(theta)
for j in range(len(g_pert)):
if np.log10(g_pert[j])>4.33: g_pert[j]=10**(4.33)
tmodel = 1.*s_model
tmodel[:,1] = pert_r[:,i]
tmodel[:,2] = pert_t[:,i]
tmodel[:,3] = np.log10(g_pert)
pmodels.append(tmodel)
if par=="ODD":
pert_r = np.empty((2*len(s_model[:,0]),depth))
pert_t = np.empty((2*len(s_model[:,0]),depth))
pmodels = []
odd_angles = np.arange(4.5,180.,9)
for i in range(depth):
pert_r[0:10,i] = s_model[:,1]+inv_f*xi_r_rot[-i,:]*rs_rot[-i,:]
pert_t[0:10,i] = s_model[:,2]*(1.+inv_f*dt_t_rot[-i,:])
pert_r[10:20,i] = s_model[::-1,1]*(1.-inv_f*xi_r_rot[-i,::-1])
pert_t[10:20,i] = s_model[::-1,2]*(1.-inv_f*dt_t_rot[-i,::-1])
g_pert = (G*mass/((pert_r[:,i]*6.96e10)**2))-((omega**2)*((pert_r[:,i]*6.96e10)*np.sin(odd_angles)))*np.sin(odd_angles)
for j in range(len(g_pert)):
if np.log10(g_pert[j])>4.33: g_pert[j]=10**(4.33)
tmodel = np.empty((20,5))
tmodel[:,0] = odd_angles[:]
tmodel[:,1] = pert_r[:,i]
tmodel[:,2] = pert_t[:,i]
#tmodel[0:10,3] = s_model[:,3]
#tmodel[10:20,3] = s_model[::-1,3]
tmodel[:,3] = np.log10(g_pert)
tmodel[0:10,4] = s_model[:,4]
tmodel[10:20,4] = s_model[::-1,4]
pmodels.append(tmodel)
# plt.plot(pmodels[-1][:,0],s_model[:,1],"--",color="0.5")
#
# global old_modes
# import seaborn as sns
# sns.set(style="white",rc={"figure.figsize": (8, 8),'axes.labelsize': 16,
# 'ytick.labelsize': 12,'xtick.labelsize': 12,
# 'legend.fontsize': 16,'axes.titlesize':18,'font.size':14})
# #plt.plot(pmodels[2][0:-1,0],np.diff(pmodels[2][:,1])/(pmodels[2][1,0]-pmodels[2][0,0]),label=r"$\ell=$"+find_name(model,vel,par,mode).strip().split()[0])
# #plt.plot(pmodels[2][:,0],pmodels[2][:,1],label="old way")
# #plt.plot(pmodels_fine[2][0:-1,0],np.diff(pmodels_fine[2][:,1])/(pmodels_fine[2][1,0]-pmodels_fine[2][0,0]))
# plt.plot(pmodels_fine[2][:,0],pmodels_fine[2][:,2],"-",lw=1.5,label=r"$\ell=$"+find_name(model,vel,par,mode).strip().split()[0])
# #plt.plot(s_model[:,0],s_model[:,1],label="Static")
# #plt.vlines(90,9100,9300)
# o_lims = plt.ylim()
# #plt.vlines(90,min(pmodels_fine[2][:,2])-100,max(pmodels_fine[2][:,2])+100)
# plt.grid()
# plt.xlim(0,180)
# #plt.ylim(o_lims[0],o_lims[1])
# plt.xlabel("Colatitude [deg]")
# plt.ylabel("Radius [M$_{\odot}$]")
# #plt.ylabel("Temperature [K]")
# plt.legend(loc="best")
# #plt.title("Mode: " + find_name(model,vel,par,mode))
#plt.title(r"Perturbed T$_{\mathrm{eff}}$ - M="+model[0]+"M$_{\odot}$, V="+v+"km s$^{-1}$")
return modeloc,pmodels,pmodels_fine
def write_and_plot(sample_dict, path):
CSV_PATH, PLOT_PATH, RAW_CSV_DATA = get_output(path)
# Merge all the sample data
sample_families = list(sample_dict.keys())
composite_data = vivdict()
integral_data = []
VOLUME = 1.2
VOLUME_CALCULATED = VOLUME / (60 * 1000)
for family in sample_families:
for method, _ in sample_dict[family].items():
log.info(f"Working on {method}")
composite_data[family][method] = cd = pd.concat(
sample_dict[family][method], axis=1
).apply(lambda g: pd.Series.interpolate(g, method="cubic"))
ppm_calculated_once = cd.mul(10000 * 1.9378).droplevel(axis=1, level=1)
# Integral
ppm = pd.DataFrame(ppm_calculated_once[0:150])
ppm.reset_index(inplace=True)
ppm["Volume"] = ppm["Time"].apply(lambda x: x * VOLUME_CALCULATED)
ppm.set_index("Volume", inplace=True)
ppm = ppm.drop(columns=["Time"], errors="ignore")
row_integral = (
ppm.ewm(span=5)
.mean()
.apply(lambda g: integrate.trapz(x=g.index, y=g.values))
)
row_integral_std = row_integral.std()
integral = pd.DataFrame(
{"Integral": row_integral.mean(), "STD": row_integral_std},
index=[f"{family}_{method}"],
)
integral["lower"] = row_integral.mean() - row_integral_std
integral["upper"] = row_integral.mean() + row_integral_std
integral_data.append(integral)
# Mean Data
cd_mean = cd.mean(axis=1).reset_index()
cd_mean.columns = ["Time", "CO2"]
cd_mean.to_csv(
os.path.join(CSV_PATH, f"{family}_{method}.csv"), sep=",", index=False
)
# Mean/STD Data
source_data = pd.DataFrame()
source_data["mean"] = ppm_calculated_once.mean(axis=1)
source_data["std"] = ppm_calculated_once.std(axis=1)
source_data["lower"] = source_data["mean"] - source_data["std"]
source_data["upper"] = source_data["mean"] + source_data["std"]
# Graphing our data
output_file(os.path.join(PLOT_PATH, f"{family}-{method}.html"))
source_data = source_data.reset_index().rename(columns={"index": "Time"})
source = ColumnDataSource(source_data)
p = figure(
title=f"{family} {method}",
x_axis_label="Time",
y_axis_label="CO2 Release",
background_fill_color="#efefef",
toolbar_location=None,
)
p.line(
source=source, x="Time", y="mean",
)
band = Band(
base="Time",
lower="lower",
upper="upper",
source=source,
level="underlay",
fill_alpha=1.0,
line_width=1,
line_color="black",
)
p.add_layout(band)
p.title.text = f"{family} {method}"
p.xgrid[0].grid_line_color = None
p.ygrid[0].grid_line_alpha = 0.5
p.xaxis.axis_label = "Time"
p.yaxis.axis_label = "CO2 (PPM)"
p.y_range.start = source_data["mean"].min() - source_data["std"].max() / 6
p.y_range.end = source_data["mean"].max() + source_data["std"].max()
p.ygrid.band_fill_alpha = 0.1
p.ygrid.band_fill_color = "#C0C0C0"
p.add_tools(
HoverTool(tooltips=[("Value", "@mean"), ("STD", "@std")], mode="vline")
)
show(p)
integral_df = pd.concat(integral_data).reset_index()
groups = integral_df["index"]
output_file(os.path.join(PLOT_PATH, f"Integral Data.html"))
source = ColumnDataSource(integral_df)
p = figure(
x_range=groups,
toolbar_location=None,
title="CO2 Integral",
background_fill_color="#efefef",
y_axis_label="CO2 (mg)",
tools="tap",
)
p.circle(
x="index",
y="Integral",
color="red",
fill_alpha=0.4,
line_color="firebrick",
line_alpha=1.0,
size=10,
source=source,
selection_color="firebrick",
nonselection_fill_alpha=0.2,
nonselection_fill_color="firebrick",
nonselection_line_color="blue",
nonselection_line_alpha=1.0,
)
p.add_layout(
Whisker(
source=source, base="index", upper="upper", lower="lower", level="overlay"
)
)
p.xaxis.major_label_orientation = "vertical"
p.y_range.start = integral_df["Integral"].min() - integral_df["STD"].max() * 1.2
p.y_range.end = integral_df["Integral"].max() + integral_df["STD"].max() * 1.2
hover = HoverTool()
hover.tooltips = [("Sample", "@index"), ("Value", "@Integral"), ("STD", "@STD")]
hover.mode = "vline"
p.add_tools(hover)
show(p)
def _get_y(t, rho, gamma_eval):
if t < 0:
return 0
else:
return integrate.trapz(rho * np.exp(-t * gamma_eval), gamma_eval)
def eval_fakefeat_GZSL(it, netG, dataset, param, result):
gen_feat = np.zeros([0, param.X_dim])
for i in range(dataset.train_cls_num):
text_feat = np.tile(dataset.train_text_feature[i].astype('float32'),
(opt.nSample, 1))
text_feat = Variable(torch.from_numpy(text_feat)).cuda()
z = Variable(torch.randn(opt.nSample, param.z_dim)).cuda()
G_sample, _ = netG(z, text_feat)
gen_feat = np.vstack((gen_feat, G_sample.data.cpu().numpy()))
for i in range(dataset.test_cls_num):
text_feat = np.tile(dataset.test_text_feature[i].astype('float32'),
(opt.nSample, 1))
text_feat = Variable(torch.from_numpy(text_feat)).cuda()
z = Variable(torch.randn(opt.nSample, param.z_dim)).cuda()
G_sample, _ = netG(z, text_feat)
gen_feat = np.vstack((gen_feat, G_sample.data.cpu().numpy()))
visual_pivots = [gen_feat[i * opt.nSample:(i + 1) * opt.nSample].mean(0) \
for i in range(dataset.train_cls_num + dataset.test_cls_num)]
visual_pivots = np.vstack(visual_pivots)
"""collect points for gzsl curve"""
acc_S_T_list, acc_U_T_list = list(), list()
seen_sim = cosine_similarity(dataset.pfc_feat_data_train, visual_pivots)
unseen_sim = cosine_similarity(dataset.pfc_feat_data_test, visual_pivots)
for GZSL_lambda in np.arange(-2, 2, 0.01):
tmp_seen_sim = copy.deepcopy(seen_sim)
tmp_seen_sim[:, dataset.train_cls_num:] += GZSL_lambda
pred_lbl = np.argmax(tmp_seen_sim, axis=1)
acc_S_T_list.append(
(pred_lbl == np.asarray(dataset.labels_train)).mean())
tmp_unseen_sim = copy.deepcopy(unseen_sim)
tmp_unseen_sim[:, dataset.train_cls_num:] += GZSL_lambda
pred_lbl = np.argmax(tmp_unseen_sim, axis=1)
acc_U_T_list.append((pred_lbl == (np.asarray(dataset.labels_test) +
dataset.train_cls_num)).mean())
auc_score = integrate.trapz(y=acc_S_T_list, x=acc_U_T_list)
result.acc_list += [auc_score]
result.iter_list += [it]
result.save_model = False
if auc_score > result.best_acc:
result.best_acc = auc_score
result.best_iter = it
result.save_model = True
log_text = "AUC Score is {:.4}".format(auc_score)
print(log_text)
exp_info = 'NAB_EASY' if opt.splitmode == 'easy' else 'NAB_HARD'
exp_params = 'Eu{}_Rls{}_RWz{}'.format(opt.CENT_LAMBDA, opt.REG_W_LAMBDA,
opt.REG_Wz_LAMBDA)
out_subdir = 'out_' + str(opt.epsilon) + '/{:s}/{:s}'.format(
exp_info, exp_params)
log_dir = out_subdir + '/log_{:s}.txt'.format(exp_info)
with open(log_dir, 'a') as f:
f.write(log_text + '\n')
def bremsstrahlung_thin_target(photon_energies, ele_dist_type='bkpl', ele_dist_params=None, efd=True):
"""
Computes the thin-target bremsstrahlung x-ray/gamma-ray spectrum from an isotropic electron
distribution function provided in `broken_powerlaw`. The units of the computed flux is photons
per second per keV per square centimeter.
The electron flux distribution function is a double power law in electron energy with a
low-energy cutoff and a high-energy cutoff.
Parameters
----------
photon_energies : `numpy.array`
Array of photon energies to evaluate flux at
ele_dist_type: str
name of the electron distribution function
- "bkpl": broken powerlaw
- "kappa": kappa distribution
- "discrete": discrete distribution given by an array of electron energy "E_ele"
and differential electron distribution "dn/dE"
ele_dist_params: ele_dist_params of the specific distribution
- for powerlaw 'pl', params = (p, eelow, eehigh) (see below)
- for broken powerlaw 'bkpl', params = (p, q, eelow, eebrk, eehigh)
p : float
Slope below the break energy
q : float
Slope above the break energy
eelow : float
Low energy electron cut off
eebrk : float
Break energy
eehigh : float
High energy electron cut off
- for kappa, params (not implemented yet)
- for discrete, params = (electron_energy, electron_dist)
electron_energy: np.array of electron energies. Unit: keV
electron_dist: np.array of differential electron distribution at the given electron energy.
efd : `bool`
True (default) - input electron distribution is electron flux density distribution
(unit electrons cm^-2 s^-1 keV^-1),
False - input electron distribution is electron density distribution.
(unit electrons cm^-3 keV^-1),
This input is not used in the main routine, but is passed to brm2_dmlin and Brm2_Fthin
Returns
-------
flux: `numpy.array`
Multiplying the output of Brm2_ThinTarget by a0 gives an array of
photon fluxes in photons s^-1 keV^-1 cm^-2, corresponding to the photon energies in the
input array eph. The detector is assumed to be 1 AU rom the source. The coefficient a0 is
calculated as a0 = nth * V * nnth, where nth: plasma density; cm^-3) V:
volume of source; cm^3) nnth: Integrated nonthermal electron flux density (cm^-2 s^-1), if
efd = True, or Integrated electron number density (cm^-3), if efd = False
Notes
-----
If you want to plot the derivative of the flux, or the spectral index of the photon spectrum as
a function of photon energy, you should set RERR to 1.d-6, because it is more sensitive to RERR
than the flux.
Adapted from SSW `Brm2_ThinTarget
<https://hesperia.gsfc.nasa.gov/ssw/packages/xray/idl/brm2/brm2_thintarget.pro>`_
"""
mc2 = const.get_constant('mc2')
clight = const.get_constant('clight')
au = const.get_constant('au')
# Numerical coefficient for photo flux
fcoeff = (clight / (4 * np.pi * au ** 2)) / mc2 ** 2.
if ele_dist_type == 'bkpl':
p = ele_dist_params[0]
q = ele_dist_params[1]
eelow = ele_dist_params[2]
eebrk = ele_dist_params[3]
eehigh = ele_dist_params[4]
# Max number of points
maxfcn = 2048
# Average atomic number
z = 1.2
# Relative error
rerr = 1e-4
# Create arrays for the photon flux and error flags.
flux = np.zeros_like(photon_energies, dtype=np.float64)
iergq = np.zeros_like(photon_energies, dtype=np.float64)
if eelow >= eehigh:
raise ValueError('eehigh must be larger than eelow!')
l, = np.where((photon_energies < eehigh) & (photon_energies > 0))
if l.size > 0:
flux[l], iergq[l] = split_and_integrate(model='thin-target',
photon_energies=photon_energies[l], maxfcn=maxfcn,
rerr=rerr, eelow=eelow, eebrk=eebrk, eehigh=eehigh,
p=p, q=q, z=z, efd=efd)
flux *= fcoeff
return flux
else:
raise Warning('The photon energies are higher than the highest electron energy or not '
'greater than zero')
if ele_dist_type == 'discrete':
electron_energy = ele_dist_params[0]
electron_dist = ele_dist_params[1]
flux = np.full_like(photon_energies, 0., dtype=np.float64)
for i, eph in enumerate(photon_energies):
# only electrons with energy above E_photon can contribute to the photon flux
l, = np.where((electron_energy > eph))
if l.size > 0:
# calculate integrand
gamma = (electron_energy[l] / mc2) + 1.0
pc = np.sqrt(electron_energy[l] * (electron_energy[l] + 2.0 * mc2))
brem_cross = bremsstrahlung_cross_section(electron_energy[l], eph)
# calculate photon flux per electron energy bin
if efd:
# if electron flux distribution is assumed (default)
flux_diff = electron_dist[l] * brem_cross * (mc2 / clight)
else:
# if electron density distribution is assumed
flux_diff = electron_dist[l] * brem_cross * pc / gamma # that is n_e * sigma * mc2 * (v / c)
# now integrate the differential photon_flux with electron energy
flux[i] = fcoeff * integrate.trapz(flux_diff, electron_energy[l])
return flux
def psd(x,
fs=1.0,
window='hanning',
nperseg=None,
noverlap=None,
nfft=None,
detrend='constant',
show=True,
ax=None,
scales='linear',
xlim=None,
units='V'):
"""Estimate power spectral density characteristcs using Welch's method.
This function is just a wrap of the scipy.signal.welch function with
estimation of some frequency characteristcs and a plot. For completeness,
most of the help from scipy.signal.welch function is pasted here.
Welch's method [1]_ computes an estimate of the power spectral density
by dividing the data into overlapping segments, computing a modified
periodogram for each segment and averaging the periodograms.
Parameters
----------
x : array_like
Time series of measurement values
fs : float, optional
Sampling frequency of the `x` time series in units of Hz. Defaults
to 1.0.
window : str or tuple or array_like, optional
Desired window to use. See `get_window` for a list of windows and
required parameters. If `window` is array_like it will be used
directly as the window and its length will be used for nperseg.
Defaults to 'hanning'.
nperseg : int, optional
Length of each segment. Defaults to half of `x` length.
noverlap: int, optional
Number of points to overlap between segments. If None,
``noverlap = nperseg / 2``. Defaults to None.
nfft : int, optional
Length of the FFT used, if a zero padded FFT is desired. If None,
the FFT length is `nperseg`. Defaults to None.
detrend : str or function, optional
Specifies how to detrend each segment. If `detrend` is a string,
it is passed as the ``type`` argument to `detrend`. If it is a
function, it takes a segment and returns a detrended segment.
Defaults to 'constant'.
show : bool, optional (default = False)
True (1) plots data in a matplotlib figure.
False (0) to not plot.
ax : a matplotlib.axes.Axes instance (default = None)
scales : str, optional
Specifies the type of scale for the plot; default is 'linear' which
makes a plot with linear scaling on both the x and y axis.
Use 'semilogy' to plot with log scaling only on the y axis, 'semilogx'
to plot with log scaling only on the x axis, and 'loglog' to plot with
log scaling on both the x and y axis.
xlim : float, optional
Specifies the limit for the `x` axis; use as [xmin, xmax].
The defaukt is `None` which sets xlim to [0, Fniquist].
units : str, optional
Specifies the units of `x`; default is 'V'.
Returns
-------
Fpcntile : 1D array
frequency percentiles of the power spectral density
For example, Fpcntile[50] gives the median power frequency in Hz.
mpf : float
Mean power frequency in Hz.
fmax : float
Maximum power frequency in Hz.
Ptotal : float
Total power in `units` squared.
f : 1D array
Array of sample frequencies in Hz.
P : 1D array
Power spectral density or power spectrum of x.
See Also
--------
scipy.signal.welch
Notes
-----
An appropriate amount of overlap will depend on the choice of window
and on your requirements. For the default 'hanning' window an
overlap of 50% is a reasonable trade off between accurately estimating
the signal power, while not over counting any of the data. Narrower
windows may require a larger overlap.
If `noverlap` is 0, this method is equivalent to Bartlett's method [2]_.
References
----------
.. [1] P. Welch, "The use of the fast Fourier transform for the
estimation of power spectra: A method based on time averaging
over short, modified periodograms", IEEE Trans. Audio
Electroacoust. vol. 15, pp. 70-73, 1967.
.. [2] M.S. Bartlett, "Periodogram Analysis and Continuous Spectra",
Biometrika, vol. 37, pp. 1-16, 1950.
Examples (also from scipy.signal.welch)
--------
>>> import numpy as np
>>> from psd import psd
#Generate a test signal, a 2 Vrms sine wave at 1234 Hz, corrupted by
# 0.001 V**2/Hz of white noise sampled at 10 kHz and calculate the PSD:
>>> fs = 10e3
>>> N = 1e5
>>> amp = 2*np.sqrt(2)
>>> freq = 1234.0
>>> noise_power = 0.001 * fs / 2
>>> time = np.arange(N) / fs
>>> x = amp*np.sin(2*np.pi*freq*time)
>>> x += np.random.normal(scale=np.sqrt(noise_power), size=time.shape)
>>> psd(x, fs=freq);
"""
from scipy import signal, integrate
if not nperseg:
nperseg = np.ceil(len(x) / 2)
f, P = signal.welch(x, fs, window, nperseg, noverlap, nfft, detrend)
Area = integrate.cumtrapz(P, f, initial=0)
Ptotal = Area[-1]
mpf = integrate.trapz(f * P, f) / Ptotal # mean power frequency
fmax = f[np.argmax(P)]
# frequency percentiles
inds = [0]
Area = 100 * Area / Ptotal # + 10 * np.finfo(np.float).eps
for i in range(1, 101):
inds.append(np.argmax(Area[inds[-1]:] >= i) + inds[-1])
fpcntile = f[inds]
if show:
_plot(x, fs, f, P, mpf, fmax, fpcntile, scales, xlim, units, ax)
return fpcntile, mpf, fmax, Ptotal, f, P
def spike_train_timescale(binned_spiketrain, max_tau):
r"""
Calculates the auto-correlation time of a binned spike train; uses the
definition of the auto-correlation time proposed in
:cite:`correlation-Wieland2015_040901` (Eq. 6):
.. math::
\tau_\mathrm{corr} = \int_{-\tau_\mathrm{max}}^{\tau_\mathrm{max}}\
\left[ \frac{\hat{C}(\tau)}{\hat{C}(0)} \right]^2 d\tau
where :math:`\hat{C}(\tau) = C(\tau)-\nu\delta(\tau)` denotes
the auto-correlation function excluding the Dirac delta at zero timelag.
Parameters
----------
binned_spiketrain : elephant.conversion.BinnedSpikeTrain
A binned spike train containing the spike train to be evaluated.
max_tau : pq.Quantity
Maximal integration time :math:`\tau_{max}` of the auto-correlation
function. It needs to be a multiple of the `bin_size` of
`binned_spiketrain`.
Returns
-------
timescale : pq.Quantity
The auto-correlation time of the binned spiketrain with the same units
as in the input. If `binned_spiketrain` has less than 2 spikes, a
warning is raised and `np.nan` is returned.
Notes
-----
* :math:`\tau_\mathrm{max}` is a critical parameter: numerical estimates
of the auto-correlation functions are inherently noisy. Due to the
square in the definition above, this noise is integrated. Thus, it is
necessary to introduce a cutoff for the numerical integration - this
cutoff should be neither smaller than the true auto-correlation time
nor much bigger.
* The bin size of `binned_spiketrain` is another critical parameter as it
defines the discretization of the integral :math:`d\tau`. If it is too
big, the numerical approximation of the integral is inaccurate.
Examples
--------
>>> import neo
>>> import numpy as np
>>> import quantities as pq
>>> from elephant.spike_train_correlation import spike_train_timescale
>>> from elephant.conversion import BinnedSpikeTrain
>>> spiketrain = neo.SpikeTrain([1, 5, 7, 8], units='ms', t_stop=10*pq.ms)
>>> bst = BinnedSpikeTrain(spiketrain, bin_size=1 * pq.ms)
>>> spike_train_timescale(bst, max_tau=5 * pq.ms)
array(14.11111111) * ms
"""
if binned_spiketrain.get_num_of_spikes() < 2:
warnings.warn("Spike train contains less than 2 spikes! "
"np.nan will be returned.")
return np.nan
bin_size = binned_spiketrain._bin_size
try:
max_tau = max_tau.rescale(binned_spiketrain.units).item()
except (AttributeError, ValueError):
raise ValueError("max_tau needs units of time")
# safe casting of max_tau/bin_size to integer
max_tau_bins = int(round(max_tau / bin_size))
if not np.isclose(max_tau, max_tau_bins * bin_size):
raise ValueError("max_tau has to be a multiple of the bin_size")
cch_window = [-max_tau_bins, max_tau_bins]
corrfct, bin_ids = cross_correlation_histogram(
binned_spiketrain,
binned_spiketrain,
window=cch_window,
cross_correlation_coefficient=True)
# Take only t > 0 values, in particular neglecting the delta peak.
start_id = corrfct.time_index((bin_size / 2) * binned_spiketrain.units)
corrfct = corrfct.magnitude.squeeze()[start_id:]
# Calculate the timescale using trapezoidal integration
integr = (corrfct / corrfct[0])**2
timescale = 2 * integrate.trapz(integr, dx=bin_size)
return pq.Quantity(timescale, units=binned_spiketrain.units, copy=False)
#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Mon Mar 20 13:40:00 2017
@author: ewen
"""
import numpy as np
import scipy.integrate as sci
def fct(x):
return (np.cos(x)-np.sin(x))*np.exp(-x)
x = np.arange(0,3*np.pi/2,1e-3)
valeur = -np.exp(-3*np.pi/2)
print("\r\n Calculs d'integrales de mes 2")
print(" SCIPY.trapz")
print("_"*48+'\r\n')
print("Valeur theorique :",-np.exp(-3*np.pi/2))
print("_"*48+'\r\n')
nValue = sci.trapz(fct(x),x)
print("Erreur de",abs(nValue-valeur))
print("_"*48+'\r\n')
os.remove(sepFileName)
os.remove(sortedFileName)
# Evaluating AUC
statsList = [
] # For each method: [AUC,AUC_10%,SENS_10%,SPEC_10%,AUC_M1,SENS_M1,SPEC_M1,AUC_M2,SENS_M2,SPEC_M2,...]
statsListPr = [] # For each method: [AUPR]
for i in range(0, len(dataXList)):
# Initialization
vec = []
vecPr = []
# Evaluating regular AUC
vec.append(auc(dataXList[i], dataYList[i]))
vecPr.append(abs(trapz(dataRcList[i], dataPrList[i])))
# Evaluating 10% FPR AUC
fprVecX = []
fprVecY = []
for j in range(0, len(dataXList[i])):
if (dataXList[i][j] > fpr_auc): break
fprVecX.append(dataXList[i][j])
fprVecY.append(dataYList[i][j])
fprVecX.append(fpr_auc)
fprVecY.append(fprVecY[-1])
vec.append(auc(standardize(fprVecX), fprVecY))
vec.append(fprVecY[-1])
vec.append(1.0 - fprVecX[-1])
# Evaluating 1% FPR AUC
from __future__ import division, print_function # python 2 to 3 compatibility
from numpy import linspace, copy
import matplotlib.pyplot as plt
from scipy.integrate import trapz
if __name__ == "__main__":
# Create some test data to integrate over
x = linspace(0, 10, 10)
y = copy(x)
fig, ax = plt.subplots()
ax.plot(x, y)
print(trapz(y, x))
plt.show()
def doConvolution(x_in, y_in, x_out, widths, factor=5, oversampling=1):
'''
Perform convolution on lists with a Gaussian filter.
Reduce the input grid to the target grid by integration.
@param x_in: The input x-values
@type x_in: array
@param y_in: The input y-values
@type y_in: array
@param x_out: The target x-grid
@type x_out: array
@param widths: The full width/half maximum spectral resolution as a
function of wavelength, i.e. the fwhm of the gaussian
@type widths: array
@keyword factor: the sigma factor for determining the window pushed through
the gaussian filter. This avoids having to convolve the
whole input grid, which takes a lot of time. Beyond
sigma*factor the contribution of the y values is assumed
to be negligible.
(default: 5)
@type factor: int
@keyword oversampling: oversampling factor of the target x-grid with
respect to the given spectral resolution.
(default: 1)
@type oversampling: int
@return: The resulting y-values
@rtype: list
'''
x_in, y_in, x_out, widths = array(x_in), array(y_in), array(x_out), array(
widths)
y_out = []
print 'Convolving for x_out between %.2f micron and %.2f micron with oversampling %i.' \
%(x_out[0],x_out[-1],int(oversampling))
#- Convert FWHM's to sigma for the gaussians
sigma = [fwhm / (2. * sqrt(2. * log(2.))) for fwhm in widths]
#- Define the binsizes of the bins that will be integrated, i.e. the
#- apparent resolution of x_out
binsize = [w / oversampling for w in widths]
for delta_bin, sigi, xi_out in zip(binsize, sigma, x_out):
yi_in = y_in[abs(x_in - xi_out) <= factor * sigi]
#- if not empty: continue, else add 0
if list(yi_in) and set(yi_in) != set([0.0]):
#- all relevant xi's for the bin around xi_out, ie in this bin the
#- y-values will be integrated
xi_in = x_in[abs(x_in - xi_out) <= delta_bin]
#- The window for the convolution itself, outside this window the
#- data are assumed to be negligible, ie for a gaussian
window = x_in[abs(x_in - xi_out) <= factor * sigi]
convolution = convolveArray(window, yi_in, sigi)
#- if one value in the bin, out of the window selection: add value
if len(list(convolution[abs(window - xi_out) <= delta_bin])) == 1:
y_out.append(convolution[abs(window - xi_out) <= delta_bin][0])
print 'Convolution has a window of only one element at xi_out %f.' % xi_out
#- If more than one value: integrate
elif list(convolution[abs(window - xi_out) <= delta_bin]):
y_out.append(
trapz(y=convolution[abs(window - xi_out) <= delta_bin],
x=xi_in) / (xi_in[-1] - xi_in[0]))
#- If no values in the bin from the window: add average of the window
#- This should not occur ideally!
else:
print 'Convolution has a window of no elements at x_out ' + \
'%f. Careful! Average is taken of '%(xi_out) + \
'sigma*factor window! This should not be happening...'
y_out.append(sum(convolution) / float(len(convolution)))
else:
y_out.append(0.0)
return y_out
def compute_relief_force_x57(inputs, y_vector, chord_vector, wing_mass, fuel_mass, point_mass=True):
# Recuperating the data necessary for the computation
if point_mass:
eng_mass_vec = [6.8, 6.8, 6.8, 6.8, 6.8, 6.8, 53.1]
tot_lg_mass = inputs["data:weight:airframe:landing_gear:main:mass"]
else:
eng_mass_vec = [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
tot_lg_mass = 0.0
z_cg = inputs["data:weight:aircraft_empty:CG:z"]
lg_height = inputs["data:geometry:landing_gear:height"]
lg_type = inputs["data:geometry:landing_gear:type"]
engine_config = inputs["data:geometry:propulsion:layout"]
engine_count = inputs["data:geometry:propulsion:count"]
nacelle_width = inputs["data:geometry:propulsion:nacelle:width"]
semi_span = inputs["data:geometry:wing:span"] / 2.0
y_ratio_vec = [0.1863354, 0.30310559, 0.42236025, 0.54161491, 0.66086957, 0.79710145, 0.99171843]
g = 9.81
single_lg_mass = tot_lg_mass / 2.0 # We assume 2 MLG
# Before computing the continued weight distribution we first take care of the point masses and modify the
# y_vector accordingly
# We create the array that will store the "point mass" which we chose to represent as distributed mass over a
# small finite interval
point_mass_array = np.zeros(len(y_vector))
# Adding the motor weight
if engine_config == 1.0:
for i in range(len(y_ratio_vec)):
y_ratio = y_ratio_vec[i]
eng_mass = eng_mass_vec[i]
y_eng = y_ratio * semi_span
y_vector, chord_vector, point_mass_array = AerostructuralLoadX57.add_point_mass(
y_vector, chord_vector, point_mass_array, y_eng, eng_mass, inputs)
test = 1.0
# Computing and adding the lg weight
# Overturn angle set as a fixed value, it is recommended to take over 25° and check that we can fit both LG in
# the fuselage
phi_ot = 35. * np.pi / 180.
y_lg_1 = math.tan(phi_ot) * z_cg
y_lg = max(y_lg_1, lg_height)
y_vector, chord_vector, point_mass_array = AerostructuralLoadX57.add_point_mass(
y_vector, chord_vector, point_mass_array, y_lg, single_lg_mass, inputs)
# We can now choose what type of mass distribution we want for the mass and the fuel
distribution_type = 0.0
if distribution_type == 1.0:
Y = y_vector / semi_span
struct_weight_distribution = 4. / np.pi * np.sqrt(1. - Y ** 2.0)
else:
Y = y_vector / semi_span
struct_weight_distribution = chord_vector / max(chord_vector)
reajust_struct = trapz(struct_weight_distribution, y_vector)
if distribution_type == 1.0:
Y = y_vector / semi_span
fuel_weight_distribution = 4. / np.pi * np.sqrt(1. - Y ** 2.0)
else:
Y = y_vector / semi_span
fuel_weight_distribution = chord_vector / max(chord_vector)
if lg_type == 1.0:
for i in np.where(y_vector < y_lg):
# For now 80% size reduction in the fuel tank capacity due to the landing gear
fuel_weight_distribution[i] = fuel_weight_distribution[i] * 0.2
if engine_config == 1.0:
for i in np.where(abs(y_vector - y_eng) <= nacelle_width / 2.):
# For now 50% size reduction in the fuel tank capacity due to the engine
fuel_weight_distribution[i] = fuel_weight_distribution[i] * 0.5
reajust_fuel = trapz(fuel_weight_distribution, y_vector)
wing_mass_array = wing_mass * struct_weight_distribution / (2. * reajust_struct)
fuel_mass_array = fuel_mass * fuel_weight_distribution / (2. * reajust_fuel)
mass_array = wing_mass_array + fuel_mass_array + point_mass_array
weight_array = - mass_array * g
return y_vector, weight_array
from scipy import integrate, interpolate
hours = ["{0:02d}".format(h) for h in xrange(0, 24, 3)]
base_path = '/nerc/n02/n02/xb899100/CloudTrail/Control/'
mv_key = u'STASH_m01s00i391'
rho_key = u'STASH_m01s00i389'
for hour in hours:
mr_nc = Dataset(base_path + 'mr_' + hour + '.nc', 'r')
fluxes_nc = Dataset(base_path + 'fluxes_' + hour + '.nc', 'r')
if hour == '00':
z_theta = mr_nc.variables['thlev_zsea_theta'][:]
z_rho = fluxes_nc.variables['rholev_zsea_rho'][:]
CIWV = integrate.trapz(
y=mr_nc.variables[mv_key][:] *
interpolate.interp1d(x=z_rho,
y=fluxes_nc.variables[rho_key][:],
fill_value='extrapolate',
axis=1)(z_theta),
x=z_theta,
axis=1)
times = mr_nc.variables['min10_0'][:]
else:
CIWV = np.concatenate(
(CIWV,
integrate.trapz(
y=mr_nc.variables[mv_key][:] *
interpolate.interp1d(x=z_rho,
y=fluxes_nc.variables[rho_key][:],
fill_value='extrapolate',
axis=1)(z_theta),
x=z_theta,
axis=1)),