def mass_bh(lum, fwhm, a=0.660, b=0.53):
mbh = unumpy.uarray(np.zeros(len(lum)), np.zeros(len(lum)))
successful = (unumpy.nominal_values(lum) >
0) & (unumpy.nominal_values(fwhm) > 0)
try:
mbh[successful] = 10**(a + b * unumpy.log10(lum[successful] / 1e44) +
2 * unumpy.log10(fwhm[successful]))
except:
print('Runtime Error in the FWHM, no number printed')
return mbh
def phot_error(cat_name, phot_gc_dens, ch):
phot_err = np.loadtxt(cat_name, usecols=(2, ))
dens_err = unp.uarray(phot_gc_dens, phot_err)
if ch == 'l':
denslog_err = unp.log10(dens_err)
else:
denslog_err = -2.5 * unp.log10(dens_err)
error = unp.std_devs(denslog_err)
return error
def compute_distance_modulus(par_mas):
if par_mas > 0:
dist_pc = 1. / (par_mas * 1e-3)
mu = 5. * unp.log10(dist_pc) - 5
return dist_pc, mu
else:
return unp.uarray(np.nan, np.nan), unp.uarray(np.nan, np.nan)
def get_oddsratio_file(datanum, iteration):
lls, ells = scale_ll(datanum, iteration)
lls = unp.uarray(lls, ells)
# compute odd ratios
numerator, denominator = np.zeros(3), np.zeros(3)
median_ratio, sigma_ratio = np.zeros(3), np.zeros(3)
for i in range(3):
numerator[i], denominator[i] = i + 1, i
try:
log10_oddsratio = unp.log10(unp.exp(lls[i + 1] - lls[i]))
except ValueError:
log10_oddsratio = unp.uarray(-np.inf, np.nan)
median_ratio[i], sigma_ratio[i] = unp.nominal_values(log10_oddsratio), \
unp.std_devs(log10_oddsratio)
# create odds ratio files
f = open(
'Cloutier/TimeSeriesCV/oddsratio_%.4d%s.txt' % (datanum, iteration),
'w')
g = '# Number of lnL evaluations, planet model denominator, planet model numerator, mode log10(odds ratio), median log10(odds ratio), minus 2 sigma (not used), minus 1 sigma, plus 1 sigma, plus 2 sigma (not used)'
for i in range(3):
g += '\n1.6E+07,%i,%i,%.6f,%.6f,NaN,%.6f,%.6f,NaN' % (
denominator[i], numerator[i], median_ratio[i], median_ratio[i],
sigma_ratio[i], sigma_ratio[i])
g = g.replace('nan', 'NaN')
f.write(g)
f.close()
def other(g=True):
freq = unumpy.uarray([100, 500, 1000, 5000, 10000, 50000], np.array([100, 500, 1000, 5000, 10000, 50000]) * 0.01)
vin = ufloat(1.01, 0.01)
vout = unumpy.uarray([0.640, 3.02, 5.27, 9.2, 9.6, 6.4], [0.01, 0.01, 0.01, 0.1, 0.1, 0.1])
fase = unumpy.uarray([92, 108, 123, 166, 178, -125], [1, 2, 1, 1, 1, 1])
Gs = vout / vin
dB = 10 * unumpy.log10(Gs)
if not g:
return None
f = plt.figure(figsize=(8, 8))
f.suptitle("Differenziatore", fontsize=15, y=0.98)
ax = f.add_subplot(211)
ax.errorbar(x=unumpy.nominal_values(freq),
y=unumpy.nominal_values(Gs),
c='black', fmt='o-')
ax.set_xlabel('Frequenza', fontsize=14)
ax.set_ylabel('Guadagno G', fontsize=14)
ax.set_xscale('log')
#ax.set_ylim((-13, 1))
#ax.set_yticklabels(('', 2, 4, 6, 8, 10, 12))
ax.set_xticklabels(('', '100 Hz', u"1 kHz", u"10 kHz", u"100 kHz", u"1 MHz"))
ax.minorticks_on()
ax.grid(b=True, which='major', color='0.7', linestyle='-', zorder=-5)
ax.grid(b=True, which='minor', color='0.9', linestyle='-', zorder=-9)
ax.set_axisbelow(True)
ax2 = f.add_subplot(212)
ax2.errorbar(x=unumpy.nominal_values(freq),
y=unumpy.nominal_values(fase),
c='black', fmt='o-')
ax2.set_ylabel('Sfasamento [Gradi]', fontsize=14)
ax2.set_xscale('log')
#ax2.set_yticklabels(('', 25, 50, 75, 100))
ax2.set_xticklabels(('', '100 Hz', u"1 kHz", u"10 kHz", u"100 kHz"))
ax2.minorticks_on()
ax2.grid(b=True, which='major', color='0.7', linestyle='-', zorder=-5)
ax2.grid(b=True, which='minor', color='0.9', linestyle='-', zorder=-9)
ax2.set_axisbelow(True)
ax3 = ax2.twiny()
ax3.set_xticks((0, 0.333, 0.666, 1))
ax3.set_xticklabels(('', "1 kHz", u"10 kHz", u"100 kHz"))
f.subplots_adjust(top=0.93, hspace=0.25, bottom=0.07, right=0.95)
plt.savefig("../latex/diff.pdf")
plt.show()
def pH_from_R(R, temp, sal):
"""
Calculate pH from Base/Acid absorption ratio, at known temperature and salinity.
Equation 11 of Nand & Ellwood (2018, doi:10.1002/lom3.10253)
Form:
pH = pK + log10((R - e1) / (e2 - R * e3))
Parameters
----------
R : array_like
Measured Base/Acid absorption ratio.
temp : array_like
Temperature of measurement (C)
sal : array_like
Salinity in PSU
Returns
-------
array_like : Solution pH (Total Scale)
"""
e1 = 5.3259624e-3
e2 = 2.2319033
e3 = 3.19e-2
pKa = calc_pKBPB(sal)
R25 = calc_R25(R, temp)
return pKa + unp.log10((R25 - e1) / (e2 - R25 * e3))
def DTM_oxy(axs, i):
import Wiseman_data_OH
Wiseman_OH = Wiseman_data_OH.OH_abund
Wiseman_z = Wiseman_data_OH.z
Wiseman_DTM = Wiseman_data_OH.DTM_all
import De_Cia_data
Cia_OH = De_Cia_data.OH_abund
Cia_z = De_Cia_data.z
Cia_DTM = De_Cia_data.DTM_all
Cia_xuplims = De_Cia_data.xuplims
Cia_yuplims = De_Cia_data.yuplims
if(i == 0):
x = RR_2015['Oxygen']
y = RR_2015['DTM_1B']
yerror = np.abs((0.75*RR_2015['DTM_1B']))
yall = unumpy.uarray(y, yerror)
ynew = yall - unumpy.log10(1. + 10**yall)
axs.errorbar(x, unumpy.nominal_values(ynew), yerr=unumpy.std_devs(ynew), color='g',label=r'$\mathrm{Remy-Ruyer}$ $\mathrm{2015}$',fmt='o')
if(i == 2):
ok = np.where(Wiseman_z == 2)
x = Wiseman_OH[ok]
y = Wiseman_DTM[ok]
axs.errorbar(unumpy.nominal_values(x), unumpy.nominal_values(y), xerr = unumpy.std_devs(x), yerr = unumpy.std_devs(y), color='r',label=r'$\mathrm{Wiseman}$ $\mathrm{2017}$',fmt='o')
ok = np.where(Cia_z == 2)
x = Cia_OH[ok]
y = Cia_DTM[ok]
xuplims = Cia_xuplims[ok]
yuplims = Cia_yuplims[ok]
up = np.logical_and(xuplims == 0, yuplims == 0)
axs.errorbar(unumpy.nominal_values(x[up]), unumpy.nominal_values(y[up]), xerr = unumpy.std_devs(x[up]), yerr = unumpy.std_devs(y[up]), color='b',label=r'$\mathrm{De}$ $\mathrm{Cia}$ $\mathrm{2016}$',fmt='o')
axs.errorbar(unumpy.nominal_values(x[~up]), unumpy.nominal_values(y[~up]), xerr = unumpy.std_devs(x[~up]), yerr = unumpy.std_devs(y[~up]), xuplims = xuplims[~up], uplims = yuplims[~up], color='b', markerfacecolor='None', markeredgecolor = 'b', fmt='o', alpha = 0.8, elinewidth=0.5)
if(i == 3):
ok = np.where(Wiseman_z == 3)
x = Wiseman_OH[ok]
y = Wiseman_DTM[ok]
axs.errorbar(unumpy.nominal_values(x), unumpy.nominal_values(y), xerr = unumpy.std_devs(x), yerr = unumpy.std_devs(y), label=r'$\mathrm{Wiseman}$ $\mathrm{2017}$', color='r',fmt='o')
ok = np.where(Cia_z == 3)
x = Cia_OH[ok]
y = Cia_DTM[ok]
xuplims = Cia_xuplims[ok]
yuplims = Cia_yuplims[ok]
up = np.logical_and(xuplims == 0, yuplims == 0)
axs.errorbar(unumpy.nominal_values(x[up]), unumpy.nominal_values(y[up]), xerr = unumpy.std_devs(x[up]), yerr = unumpy.std_devs(y[up]), color='b',label=r'$\mathrm{De}$ $\mathrm{Cia}$ $\mathrm{2016}$',fmt='o')
axs.errorbar(unumpy.nominal_values(x[~up]), unumpy.nominal_values(y[~up]), xerr = unumpy.std_devs(x[~up]), yerr = unumpy.std_devs(y[~up]), xuplims = xuplims[~up], uplims = yuplims[~up], color='b', markerfacecolor='None', markeredgecolor = 'b', fmt='o', alpha = 0.8, elinewidth=0.5)
if(i == 4):
ok = np.where(Wiseman_z == 4)
x = Wiseman_OH[ok]
y = Wiseman_DTM[ok]
axs.errorbar(unumpy.nominal_values(x), unumpy.nominal_values(y), xerr = unumpy.std_devs(x), yerr = unumpy.std_devs(y), label=r'$\mathrm{Wiseman}$ $\mathrm{2017}$', color='r',fmt='o')
if(i == 5):
ok = np.where(Wiseman_z == 5)
x = Wiseman_OH[ok]
y = Wiseman_DTM[ok]
axs.errorbar(unumpy.nominal_values(x), unumpy.nominal_values(y), xerr = unumpy.std_devs(x), yerr = unumpy.std_devs(y), label=r'$\mathrm{Wiseman}$ $\mathrm{2017}$', color='r',fmt='o')
def O3N2(OIII5007, NII6583, Halpha, Hbeta):
''' Calculate O3N3 from Yin et al. 2007:
O3N2 = log[([O iii]λ5007/Hβ)/([N ii] λ6583/Hα)]
'''
O3N2 = unp.log10((OIII5007 / Hbeta) /
(NII6583 / Halpha))
return O3N2
def calcSFR(DMpc, logFHa, logFHa_err): Dpc = DMpc*(1E6) logFHa_arr = unumpy.uarray(logFHa,logFHa_err) F_Ha = 10**(logFHa_arr) L_Ha = F_Ha*(4*np.pi*((Dpc*(3.086E18))**2.)) logsfr = unumpy.log10(L_Ha) - 41.27 sfr = 10**(logsfr) return sfr
def DTM_stell(axs, i):
if(i == 0):
x = RR_2015['SM']
y = RR_2015['DTM_1B']
yerror = np.abs((0.75*RR_2015['DTM_1B']))
yall = unumpy.uarray(y, yerror)
ynew = yall - unumpy.log10(1. + 10**yall)
axs.errorbar(x, unumpy.nominal_values(ynew), yerr=unumpy.std_devs(ynew), color='g',label=r'$\mathrm{Remy-Ruyer}$ $\mathrm{2015}$',fmt='o')
def getLumin(self):
''' Set the sample log luminosities (and error if flux errors available)
based on given flux values and luminosity distance values
'''
if self.flux_e is not None:
ulum = unumpy.log10(4.0*np.pi*(self.DL*3.086e24)**2 * unumpy.uarray(self.flux,self.flux_e))
self.lum, self.lum_e = unumpy.nominal_values(ulum), unumpy.std_devs(ulum)
else:
self.lum = np.log10(4.0*np.pi*(self.DL*3.086e24)**2 * self.flux)
self.lum_e = None
def EBV_calzetti(HaHb):
''' Computes E(B-V) based on the method of Domínguez et al. 2012,
ArXiv 1206.1867, assuming a reddening curve from Calzetti(2000).
(NB! Explanation in Atek 2012 is good!)
With Calzetti 2000 values of k(alpha) and k(beta), we get:
E(B-V) = 1.97 log10((Ha/Hb) / 2.86)
'''
EBV = 1.97* unp.log10(HaHb / 2.86)
return EBV
def evaluate(energy, amplitude, reference, alpha, beta):
"""Evaluate the model (static function)."""
try:
xx = energy / reference
exponent = -alpha - beta * np.log10(xx)
except AttributeError:
from uncertainties.unumpy import log10
xx = energy / reference
exponent = -alpha - beta * log10(xx)
return amplitude * np.power(xx, exponent)
def config_logplots(dens, err, r):
denslog10 = unp.uarray(dens, err)
denslog10 = unp.log10(denslog10)
errlog = unp.std_devs(denslog10)
#rmin = r/60
rlog = r
#TO DO: add binsizes
return dens, errlog, rlog
def OH_from_TeO3(fluxes, Te=None):
''' Again, translated from Miguel's code.
'''
if Te is None:
Te = Te_O3(fluxes['OIII4363'], fluxes['OIII4959'],
fluxes['OIII5007'], fluxes['Hbeta'])
if not 'Te4' in Te.columns:
Te['Te4'] = Te['Te'] * 1.e4
Oplus = 7.34e-7 * (fluxes['OII3726'] + fluxes['OII3729'])/fluxes['Hbeta']\
* unp.exp(3.9/Te['Te4'])
O2plus = (1.3e-6 / Te['Te4']**0.38) * unp.exp(2.9/Te['Te4'])\
* 4.2 * fluxes['OIII4959']/fluxes['Hbeta']
return 12. + unp.log10(Oplus + O2plus)
def evaluate(energy, amplitude, reference, alpha, beta, z):
"""Evaluate the model (static function)."""
scale_factor = 1 / (1 + z)
scaled_energy = energy * scale_factor
try:
xx = (scaled_energy / reference).to("")
exponent = -alpha - beta * np.log10(xx)
except AttributeError:
from uncertainties.unumpy import log10
xx = scaled_energy / reference
exponent = -alpha - beta * log10(xx)
return amplitude * np.power(xx, exponent) * scale_factor
def hi_scalelength(self,m=0.86,m_error=0.04,c=0.79,c_error=0.02,
k=0.19,k_error=0.03): # Wang+14, Lelli+16
exists = 'R_hi' in self.__dict__
if exists is False:
m_param = uf(m,m_error)
c_param = uf(c,c_error)
k_param = uf(k,k_error)
r_d = self.R_disc
log_r_d = unp.log10(r_d)
logr_hi = m_param * log_r_d + c_param
r_hi = 10**logr_hi
self.R_hi = k_param * r_hi
return self.R_hi
def density(nbin, r, rgal, ):
import numpy as np
import uncertainties.unumpy as unp
n = len(r)
NGC = np.zeros(nbin) #number of GC in each bin
rmed = [[] for i in range(0,nbin)]
for h in range(0, nbin):
for i in range(0, n):
if (rgal[h+1] >= r[i] and r[i] > rgal[h]):
NGC[h] = NGC[h] + 1
rmed[h].append(r[i])
#median value of the bins
radius = [[] for i in range(0,nbin)]
for i in range(0,nbin):
radius[i] = np.linspace(rgal[i], rgal[i+1], 1000)
median = np.linspace(0,0,nbin)
medianGC = np.linspace(0,0,nbin)
for i in range(0,nbin):
median[i] = np.median(radius[i])
medianGC[i] = np.median(rmed[i])
area = []
for h in range(0, nbin):
area.append((np.pi*rgal[h+1]**2)-(np.pi*rgal[h]**2)) #area per bin
binsize = np.linspace(0,0,nbin)
for h in range(0,nbin):
binsize[h] = rgal[h+1]-rgal[h]
binsize = binsize/2
dens2 = np.linspace(0,0,nbin)
for h in range(0, nbin):
dens2[h] = NGC[h]/area[h]
#error in density
poi_err = (np.sqrt(NGC)/area)
dens2err = unp.uarray(dens2, poi_err)
denslog2 = -2.5*np.log10(dens2)
denslog2err = -2.5*unp.log10(dens2err)
poi_err2 = unp.std_devs(denslog2err)
return denslog2, poi_err2, area, NGC, median, rgal, binsize
def ZOH_M13(fluxtab, ext='', method='o3n2', name='ZOH', err=False):
N2F = fluxtab['flux_[NII]6583'+ext]
O3F = fluxtab['flux_[OIII]5007'+ext]
HaF = fluxtab['flux_Halpha'+ext]
HbF = fluxtab['flux_Hbeta'+ext]
if method == 'o3n2':
good = (N2F>0) & (O3F>0) & (HaF>0) & (HbF>0)
elif method == 'n2':
good = (N2F>0) & (HaF>0)
else:
raise Exception('Method {} is not recognized'.format(method))
nelt = len(N2F)
BPT = bpt_type(fluxtab, ext=ext)
if err == False:
O3N2 = np.full(nelt, np.nan)
O3N2[good] = (np.log10(O3F[good]) - np.log10(HbF[good])
- (np.log10(N2F[good]) - np.log10(HaF[good])))
N2 = np.full(nelt, np.nan)
N2[good] = np.log10(N2F[good]) - np.log10(HaF[good])
else:
try:
from uncertainties import ufloat
import uncertainties.unumpy as unp
except:
print('uncertainties package required for err=True')
uN2F = unp.uarray(N2F, fluxtab['e_flux_[NII]6583'+ext])
uO3F = unp.uarray(O3F, fluxtab['e_flux_[OIII]5007'+ext])
uHaF = unp.uarray(HaF, fluxtab['e_flux_Halpha'+ext])
uHbF = unp.uarray(HbF, fluxtab['e_flux_Hbeta'+ext])
O3N2 = unp.uarray(np.full(nelt, np.nan),np.full(nelt, np.nan))
O3N2[good] = (unp.log10(uO3F[good]) - unp.log10(uHbF[good])
- (unp.log10(uN2F[good]) - unp.log10(uHaF[good])))
N2 = unp.uarray(np.full(nelt, np.nan),np.full(nelt, np.nan))
N2[good] = unp.log10(uN2F[good]) - unp.log10(uHaF[good])
if method == 'o3n2':
ZOH_M13 = 8.533 - 0.214 * O3N2 # Eq(2) from Marino+2013
else:
ZOH_M13 = 8.743 + 0.462 * N2 # Eq(4) from Marino+2013
desc = '12+log(O/H) using {} method in Marino+13'.format(method)
if err == False:
ZOH_M13[BPT != -1] = np.nan
return Column(ZOH_M13, name=name, unit='dex', dtype='f4', description=desc)
else:
ZOH_M13[BPT != -1] = ufloat(np.nan, np.nan)
return (Column(unp.nominal_values(ZOH_M13), name=name, dtype='f4',
unit='dex', description=desc),
Column(unp.std_devs(ZOH_M13), name='e_'+name, dtype='f4',
unit='dex', description='error in '+desc))
def R_halo(self):
exists = 'R200' in self.__dict__
exists = False
# unit converter
cf = (1 * u.Msun)**(1 / 3) * (1 * u.kg)**(-1 / 3) * (1 * u.m)
cf = cf.to(u.kpc).value
if exists is False:
h = 0.7
K = 3 / (4 * np.pi * 200 * self.rho_crit.value)
M200 = self.M_halo()
logc200 = (0.905 - 0.101 * unp.log10(M200 / (10**12 * h**(-1))))
c200 = 10**logc200
self.R200 = (K * (M200))**(1 / 3) * cf
self.a_h = self.R200 / c200
return self.a_h, self.R200
def doPlotWithUnc(self):
#plot absolute and phase along with uncertainties
f=1
uabs=unumpy.uarray(self.getFAbs(),self.getFAbsUnc())
#scale the uncertainty for the 20*log10 plot
uabs=20*unumpy.log10(uabs)
u_a=unumpy.nominal_values(uabs)
u_s=unumpy.std_devs(uabs)
py.figure('FD-ABS-UNC-Plot')
py.plot(self.getfreqsGHz(),u_a)
py.plot(self.getfreqsGHz(),u_a+u_s,'--',self.getfreqsGHz(),u_a-u_s,'--')
py.figure('FD-PH-UNC-Plot')
py.plot(self.getfreqsGHz(),self.getFPh())
py.plot(self.getfreqsGHz(),self.getFPh()+f*self.getFPhUnc(),'--',self.getfreqsGHz(),self.getFPh()-self.getFPhUnc(),'--')
def mag(lc: LightCurve) -> LightCurve:
"""
Converts and normalizes a LighCurve object to magnitudes.
:param lc: lightcurve object
:return: reduced light curve object
"""
lc = lc.remove_nans()
flux = lc.flux + (np.abs(2 * np.amin(lc.flux)) if np.amin(lc.flux) < 0 else 100)
flux = unp.uarray(flux, lc.flux_err)
flux = -2.5 * unp.log10(flux)
flux = flux[~unp.isnan(flux)]
flux -= np.median(flux)
lc.flux = unp.nominal_values(flux) * u.mag
lc.flux_err = unp.std_devs(flux) * u.mag
return lc
def config_pne(N, area, r):
area = area / 3600
denslog = N / area
#denslog = np.log10(density)
errlog = np.sqrt(N) / area
#errlog = err/(2.3*(density))
#errlog = np.log10(err)
denslog10 = unp.uarray(denslog, errlog)
denslog10 = unp.log10(denslog10)
errlog = unp.std_devs(denslog10)
rmin = r / 60
rlog = rmin
#TO DO: add binsizes
return denslog, errlog, rlog
def mjy(lognu, ll, dist, llerr=None):
"""
Converts log(nu/Hz), log(nu Lnu [erg/s]), error in log(nuLnu) to
log(lambda/micron), log(Fnu/mJy), error in log(Fnu).
The input units are CGS.
Usage:
If you have errors in the flux:
>>> lamb,fnu,ferr=mjy(xdata,ydata,dist,yerr)
If you do not have errors in the flux:
>>> lamb,fnu=mjy(xdata,ydata,dist)
:param dist: distance in Mpc
"""
import uncertainties.unumpy as unumpy
c = 29979245800. # speed of light in CGS
dist = dist * 3.085677581e24 # Mpc -> cm
nu = 10**lognu
lamb = c / nu * 1e4 # cm -> micron
if llerr != None:
lllerr = unumpy.uarray(ll, llerr)
else:
lllerr = ll
lnuerr = 10**lllerr / nu
fluxerr = lnuerr / (1e-26 * 4. * numpy.pi * dist**2
) # Lnu (erg/s/Hz) -> Fnu (mJy)
if llerr != None:
fluxerr = unumpy.log10(fluxerr)
return numpy.log10(lamb), unumpy.nominal_values(
fluxerr), unumpy.std_devs(fluxerr)
else:
return numpy.log10(lamb), numpy.log10(fluxerr)
from math import *
import matplotlib.pyplot as plt
import numpy as np
from uncertainties import ufloat, unumpy
# 20 dB
data20 = np.genfromtxt(open("../dati/banda_20.csv"), delimiter=",", skip_header=1)
freq20 = data20[:,0]
vout20 = unumpy.uarray(data20[:,1] / 2.0, 10*np.ones(len(freq20)))
phase20 = data20[:,2]
dphase20 = data20[:,3]
vin20 = ufloat(50, 0.5)
db20 = 20.0 * unumpy.log10(vout20/vin20)
m3db = db20[0].nominal_value - 3.0
p3db = None
for f1, db1, f2, db2 in zip(freq20[:-1], db20[:-1], freq20[1:], db20[1:]):
if db1 > m3db and db2 < m3db:
p3db = f1 + (f2 - f1) * (m3db - db1) / (db2 - db1)
print(p3db)
# 40 dB
data40 = np.genfromtxt(open("../dati/banda_40.csv"), delimiter=",", skip_header=1)
freq40 = data40[:,0]
vout40 = unumpy.uarray(data40[:,1] / 2.0, data40[:,3]) * 1000
phase40 = data40[:,2]
pylab.savefig("bode.png",
dpi=None,
facecolor='w',
edgecolor='w',
orientation='portrait',
papertype=None,
format=None,
transparent=False,
bbox_inches=None,
pad_inches=0.1,
frameon=None)
print(covm)
logF = unumpy.log10(F)
logf = unumpy.nominal_values(logF)
dlogf = unumpy.std_devs(logF)
pylab.figure(num=None, figsize=(12, 6), dpi=80, facecolor='w', edgecolor='k')
pylab.errorbar(logf, phi, dphi, dlogf, linestyle='', marker='')
#pylab.xscale("log")
#pylab.xlim(400, 3200)
pylab.legend(numpoints=1, loc='upper right')
pylab.xlabel('log(f/1kHz)', size="16")
pylab.ylabel(' $\phi$ [$\pi$ rad]', size="16")
#pylab.xlim(0,2000)
pylab.title('Sfasamento', fontsize="18")
pylab.grid()
#Fare attenzione che gli errori devono essere sempre sommati con le stesse unita di misura,
retaMax = [InterceptMax, InterceptMax + (Txmax * Esp)]
retaMin = [InterceptMin, InterceptMin + (Txmin * Esp)]
#retaMax=[IdadeB,IdadeB+(Txmax*IdadeA)]
#retaMin=[IdadeB,IdadeB+(Txmin*IdadeA)]
plt.figure('taxa Sed')
plt.plot([0, Esp], [IdadeB, IdadeA], 'ro')
plt.errorbar([0, Esp], [IdadeB, IdadeA], yerr=[ErroB, ErroA], zorder=10)
plt.errorbar([0, Esp], [IdadeB, IdadeA], zorder=11)
plt.plot([0, Esp], retaMax, 'w--')
plt.plot([0, Esp], retaMin, 'w--')
plt.fill_between([0, Esp],
retaMax,
retaMin,
color='tomato',
alpha=0.2,
label='erro taxa')
plt.title(f'Simulação taxa sedimentação\ntaxa={TaxaSed} m/mil anos')
plt.xlabel('distância estratigráfica (m)')
plt.ylabel('idade (mil anos)')
plt.legend(loc='upper left')
plt.savefig('Erro_taxa.png')
Zeta = (UArr[0]**UArr[1]) / (unumpy.log10(UArr[2] - unumpy.log10(UArr[3])))
print(Zeta)
#plt.show()
def pH_from_F(F, K):
return -log10(K / F)
def _trapz_loglog(self, y, x, axis=-1, intervals=False):
"""
Integrate along the given axis using the composite trapezoidal rule in
loglog space. Integrate y(x) along given axis in loglog space. This follows
the script in the Naima package.
Parameters
----------
- y (array_like): Input array to integrate.
- x (array_like): optional. Independent variable to integrate over.
- axis (int): Specify the axis.
- intervals (bool): Return array of shape x not the total integral, default: False
Returns
-------
trapz (float): Definite integral as approximated by trapezoidal rule in loglog space.
"""
log10 = np.log10
#----- Check for units
try:
y_unit = y.unit
y = y.value
except AttributeError:
y_unit = 1.0
try:
x_unit = x.unit
x = x.value
except AttributeError:
x_unit = 1.0
y = np.asanyarray(y)
x = np.asanyarray(x)
#----- Define the slices
slice1 = [slice(None)] * y.ndim
slice2 = [slice(None)] * y.ndim
slice1[axis] = slice(None, -1)
slice2[axis] = slice(1, None)
slice1, slice2 = tuple(slice1), tuple(slice2)
#----- arrays with uncertainties contain objects, remove tiny elements
if y.dtype == "O":
from uncertainties.unumpy import log10
# uncertainties.unumpy.log10 can't deal with tiny values see
# https://github.com/gammapy/gammapy/issues/687, so we filter out the values
# here. As the values are so small it doesn't affect the final result.
# the sqrt is taken to create a margin, because of the later division
# y[slice2] / y[slice1]
valid = y > np.sqrt(np.finfo(float).tiny)
x, y = x[valid], y[valid]
#----- reshaping x
if x.ndim == 1:
shape = [1] * y.ndim
shape[axis] = x.shape[0]
x = x.reshape(shape)
#-----
with np.errstate(invalid="ignore", divide="ignore"):
# Compute the power law indices in each integration bin
b = log10(y[slice2] / y[slice1]) / log10(x[slice2] / x[slice1])
# if local powerlaw index is -1, use \int 1/x = log(x); otherwise use normal
# powerlaw integration
trapzs = np.where(
np.abs(b + 1.0) > 1e-10,
(y[slice1] * (x[slice2] *
(x[slice2] / x[slice1])**b - x[slice1])) /
(b + 1), x[slice1] * y[slice1] * np.log(x[slice2] / x[slice1]))
tozero = (y[slice1] == 0.0) + (y[slice2] == 0.0) + (x[slice1]
== x[slice2])
trapzs[tozero] = 0.0
if intervals:
return trapzs * x_unit * y_unit
ret = np.add.reduce(trapzs, axis) * x_unit * y_unit
return ret
T_OIII = 0.8254 - 0.0002415*ROIII + (47.77/ROIII)
RSII = SII_6716_Flux / SII_6730_Flux
a_0 = 2.21 - 1.3/T_OIII - 1.25*T_OIII + 0.23*T_OIII**2
a_1 = -3.35 + 1.94/T_OIII + 1.93*T_OIII - 0.36*T_OIII**2
b_0 = -4.33 + 2.33/T_OIII + 2.72*T_OIII - 0.57*T_OIII**2
b_1 = 1.84 - 1.0/T_OIII - 1.14*T_OIII + 0.24*T_OIII**2
n_SII = (10.0**3)*(RSII*a_0 + a_1)/(RSII*b_0 + b_1)
if n_SII > 0.0:
T_OII = (1.2 + 0.002*n_SII + 4.2/n_SII)/(1/T_OIII + 0.08 + 0.003*n_SII + 2.5/n_SII)
logOII_logHII = -12 + unumpy.log10(OII_7319_Flux/HBeta_Flux) + 6.895 + 2.44/T_OII -0.58*unumpy.log10(T_OII) - unumpy.log10(1.0 + 0.0047*n_SII)
logOIII_logHII = -12 + unumpy.log10((OIII_4959_Flux+OIII_5007_Flux)/HBeta_Flux) + 6.144 + 1.251/T_OIII - 0.55*unumpy.log10(T_OII)
OII_HII = 10**(logOII_logHII)
OIII_HII = 10**(logOIII_logHII)
OI_HI = OII_HII + OIII_HII
O_Abundances.append(OI_HI)
else:
if (n_SII < None):
Error_Message = "Aritmetic error: n_SII < 0"
Comments.append(Error_Message)
INPUT = "/home/federico/Laboratorio3/relazione4/datiBode.txt"
OUTPUT = "/home/federico/Laboratorio3/relazione4/datiBode.txt"
Vout, dVout, f, df = pylab.loadtxt(INPUT, unpack=True)
#Nelle visualizzazioni devo introdurre gli errori
F = unumpy.uarray(f, df)
VOUT = unumpy.uarray(Vout, dVout)
VOUT3 = unumpy.uarray(Vout, (dVout**2 + (0.03*Vout)**2))
VIN = ufloat(1.00, 0.01)
VIN3 = ufloat(1.00, ((0.01)**2+(0.03*1.00)**2)**0.5)
#Per la visualizzazione inserisco il 3%
A = VOUT3/VIN3
dB = 20*unumpy.log10(A)
logF = unumpy.log10(F)
pylab.title('A vs logf')
pylab.xlim(-6, 1)
pylab.ylim(-5, 25)
pylab.xlabel('log(f/1MHz)')
pylab.ylabel('A (dB)')
pylab.grid(color = "gray")
pylab.errorbar(unumpy.nominal_values(logF), unumpy.nominal_values(dB),
unumpy.std_devs(dB), unumpy.std_devs(logF), "o", color="black")
pylab.show()
mT = unumpy.matrix(XHB) filename = "resXHB.csv" numpy.savetxt(filename, mT, fmt='%r', delimiter='\n') concH = (0.0000169) * (1 + XB) / (XHB) mT = unumpy.matrix(concH) filename = "resconcH.csv" numpy.savetxt(filename, mT, fmt='%r', delimiter='\n') FI = 0.5 * (XB * 4 * 0.0000169 + XHB * 0.0000169 + 2 * conc) mT = unumpy.matrix(FI) filename = "resFI.csv" numpy.savetxt(filename, mT, fmt='%r', delimiter='\n') pkc = -(unumpy.log10(0.0000169 * XB * (1 + XB) / (1 - XB))) mT = unumpy.matrix(pkc) filename = "respkc.csv" numpy.savetxt(filename, mT, fmt='%r', delimiter='\n') sqI = unumpy.sqrt(FI) fi = (sqI) / (1 + 2.3 * sqI) mT = unumpy.matrix(fi) filename = "resfi.csv" numpy.savetxt(filename, mT, fmt='%r', delimiter='\n') #http://docs.scipy.org/doc/numpy/reference/generated/numpy.savetxt.html
import uncertainties from uncertainties import ufloat import math import numpy import numpy import pylab from scipy.optimize import curve_fit import math import scipy.stats import uncertainties from uncertainties import unumpy V_IN = ufloat(0.340, 0.002) V_OUT = ufloat(13.00, 0.2) A = 20.0 * unumpy.log10(V_OUT / V_IN) Amis = A - 3.0 V_OUT_mis = V_IN * 10**(Amis / 20) print(V_OUT_mis)
freq_low = data_low[:,0]
va_low = unumpy.uarray(data_low[:,1] / 2.0, data_low[:,3])
vout_low = unumpy.uarray(data_low[:,2] / 2.0, data_low[:,4])
G_low = 1001 * vout_low / va_low
data_high = np.genfromtxt(open("../dati/guadagno_alta_freq_sum.csv"), delimiter=",", skip_header=1)
freq_high = data_high[:,0] * 1000
va_high = unumpy.uarray(data_high[:,1] / 2.0, data_high[:,3])
vout_high = unumpy.uarray(data_high[:,2] / 2.0, data_high[:,4])
G_high = vout_high / va_high
print(G_low, G_high)
print(20*unumpy.log10(G_low), 20*unumpy.log10(G_high))
f1 = plt.figure()
ax1 = f1.add_subplot(111)
ax1.set_xscale('log')
ax1.set_yscale('log')
p1 = ax1.errorbar(x=freq_low, y=unumpy.nominal_values(G_low), yerr=unumpy.std_devs(G_low), fmt="o", c="black")
p2 = ax1.errorbar(x=freq_high, y=unumpy.nominal_values(G_high), yerr=unumpy.std_devs(G_high), fmt="o", c="gray")
ax1.set_title("Guadagno di un opamp in funzione della frequenza")
ax1.set_xlabel("Frequenza [Hz]")
ax1.set_ylabel("Amplificazione")
ax1.set_xlim((1, 3e6))
ax1.set_ylim((1e-1, 1e6))
ax1.grid(True)
Errors[n] = Valid_EmLines[n][5]
np_HBeta[n] = HBeta_Flux
np_HBeta_error[n] = HBeta_Error
#Calculation gradient:
x = np.zeros(NumberRecombinationRatios)
y = np.zeros(NumberRecombinationRatios)
FluxEL_and_error = unumpy.uarray([Flux_EL], [Errors])
HBeta_and_Error = unumpy.uarray([np_HBeta], [np_HBeta_error])
for o in range(NumberRecombinationRatios):
x[o] = f_lambda[o] - f_Beta
y[o] = math.log10(TheoRatio[o]/ObsRatio[o])
y_and_error = unumpy.log10(TheoRatio / (FluxEL_and_error/HBeta_and_Error))
y_err=unumpy.std_devs(y_and_error)
y_err = y_err[0]
#Old method
A = np.vstack([x, np.ones(len(x))]).T
cHBeta_Old, n_Old = np.linalg.lstsq(A, y)[0]
TrendLine = Axis1.plot(x, cHBeta_Old*x+n_Old, color=Colors[2][1], label='Fitted line')
#New method
Regression_Fit, Uncertainty_Matrix, Red_Chi_Sq, Residuals = linfit(x, y, y_err, cov=True, relsigma=False, chisq=True, residuals=True)
m_n_error = [np.sqrt(Uncertainty_Matrix[t,t]) for t in range(2)]
R_Factor = Uncertainty_Matrix[0,1]/(m_n_error[0]*m_n_error[1])
cHbeta, cHbeta_error = Regression_Fit[0], m_n_error[0]
wfc_g102_file = input_path + 'sgas1723_1Dsum_'+item+'_G102_wcontMWdr_meth2.fitdf'
wfc_g102_file = cr.deredden(wfc_g102_file, 0.3, 0.02, niter=int(1e5), constant=1e-17, dered=True, change_ID=True, change_errors=True,
SNR_thresh=0.014, readcsv=True) # to deredden WFC3 spectra and re-write the file
wfc_g141_file = input_path + 'sgas1723_1Dsum_'+item+'_G141_wcontMWdr_meth2.fitdf'
wfc_g141_file = cr.deredden(wfc_g141_file, 0.3, 0.02, niter=int(1e5), constant=1e-17, dered=True, change_ID=True, change_errors=True,
SNR_thresh=0.014, readcsv=True) # to deredden WFC3 spectra and re-write the file
g102 = pd.read_table(wfc_g102_file, delim_whitespace=True, comment='#')
g141 = pd.read_table(wfc_g141_file, delim_whitespace=True, comment='#')
H_g102 = unp.uarray(cr.getf(g102, g102_hlist), cr.gete(g102, g102_hlist))
H_g141 = unp.uarray(cr.getf(g141, g141_hlist), cr.gete(g141, g141_hlist))
ratio_obs = [H_g141[0] / H_g141[1], H_g141[0] / H_g102[0], H_g102[0] / H_g102[1],
H_g102[0] / H_g102[2]] # , H_g102[0]/H_g102[3], H_g102[0]/(H_esi[0]*esi_to_mmt_scale), H_esi[0]/H_esi[1]]
Eb_v = (2.5 / delta_k) * unp.log10(ratio_obs / ratio_theoretical)
print '\nMean E(B-V) =', np.mean(Eb_v)
edf = pd.concat([edf, pd.DataFrame(np.transpose(np.vstack([ratio_labels, spec_labels, ['%.2F' % x.n for x in Eb_v], ['%.2F' % x.s for x in Eb_v], ['%.2F' % x.n for x in ratio_obs], ['%.2F' % x.s for x in ratio_obs]])),
columns=['Line ratio', 'Grism(s)', 'E(B-V)', r'E(B-V)$_u$', 'Observed ratio', 'Observed ratio uncert'])])
# ------to plot the E(B-V) values for visual comparison-----
col_ar = ['r', 'g', 'b', 'orange']
for ii in range(len(Eb_v)):
ax.scatter(index + ii*0.1, Eb_v[ii].n, s=40, color=col_ar[ii], lw=0, label=ratio_labels[ii]+' '+spec_labels[ii] if not index else None)
ax.errorbar(index + ii*0.1, Eb_v[ii].n, yerr=Eb_v[ii].s, color=col_ar[ii])
fs = 15 # plot label fontsize
plt.legend(loc='lower left', fontsize=fs)
ax.set_xticks(np.arange(len(filenames)))
ax.set_xticklabels(filenames, rotation=50, fontsize=fs, ha='right', va='top')
plt.ylim(-0.6,0.8)
plt.ylabel('E(B-V)', fontsize=fs)
mT = unumpy.matrix(XHB) filename = "resXHB.csv" numpy.savetxt(filename, mT, fmt='%r', delimiter='\n') concH = (0.0000169)*(1+ XB)/(XHB) mT = unumpy.matrix(concH) filename = "resconcH.csv" numpy.savetxt(filename, mT, fmt='%r', delimiter='\n') FI = 0.5*(XB*4*0.0000169+XHB*0.0000169+2*conc) mT = unumpy.matrix(FI) filename = "resFI.csv" numpy.savetxt(filename, mT, fmt='%r', delimiter='\n') pkc = -(unumpy.log10(0.0000169*XB*(1+XB)/(1-XB))) mT = unumpy.matrix(pkc) filename = "respkc.csv" numpy.savetxt(filename, mT, fmt='%r', delimiter='\n') sqI = unumpy.sqrt(FI) fi = (sqI)/(1+2.3 * sqI) mT = unumpy.matrix(fi) filename = "resfi.csv" numpy.savetxt(filename, mT, fmt='%r', delimiter='\n') #http://docs.scipy.org/doc/numpy/reference/generated/numpy.savetxt.html
validity_entry = catalogue_df.loc[objName, element + '_valid']
element_abundance_key = '{}I_HI_emis2nd'.format(element)
element_abundance_check = isnull(catalogue_df.loc[objName, element_abundance_key])
print objName, element, element_abundance_check
if element_abundance_check is False:
if (validity_entry not in ['ignored', 'NO_excess', 'Wide Component']):
regressions_employed.append(element)
else:
print 'Fallo', objName, element
name_superscript = r'\textsuperscript{{{regrens}}}'.format(regrens = ', '.join(regressions_employed))
entry_name = r'{text}{expo}'.format(text=catalogue_df.loc[objName].quick_index, expo=name_superscript)
objData = catalogue_df.loc[objName]
abundValues = objData[metals_list].values
objData[metals_list] = 12.0 + unumpy.log10(abundValues)
HeI_HI_entry = dz.format_for_table(catalogue_df.loc[objName, 'HeII_HII_from_O' + ext_data], rounddig=3, rounddig_er=2)
Ymass_O_entry = dz.format_for_table(catalogue_df.loc[objName, 'Ymass_O' + ext_data], rounddig=3, rounddig_er=2)
Ymass_S_entry = dz.format_for_table(catalogue_df.loc[objName, 'Ymass_S' + ext_data], rounddig=3, rounddig_er=2)
print objName, objData[['OI_HI' + ext_data]].values, objData[['OI_HI' + ext_data]].isnull().values.any(), regressions_employed
row = [entry_name] + [HeI_HI_entry, Ymass_O_entry, Ymass_S_entry]
row += list(objData[['OI_HI' + ext_data, 'NI_HI' + ext_data, 'SI_HI' + ext_data]].values)
dz.addTableRow(row, last_row = False if catalogue_df.index[-1] != objName else True, rounddig=3, rounddig_er=1)
# dz.generate_pdf()
dz.generate_pdf(output_address=pdf_address)
def X_H(F, M_H):
#A = unumpy.uarray([-0.02], [0.1])
#B = unumpy.uarray([-0.15], [0.09])
A = unumpy.uarray([-0.145], [0.051])
B = unumpy.uarray([-0.225], [0.053])
return A + B * (F - 0.598) + M_H
#return A + B*(F-0.598)
data = np.genfromtxt('./Obs_data/Wiseman_data_2017.txt', delimiter=',')
F, Ferr, M_H, M_Herror, z, DTM, DTMerr = data[:,
0], data[:,
1], data[:,
2], data[:,
3], data[:,
4], data[:,
5], data[:,
6]
F_all = unumpy.uarray(F, Ferr)
M_H_all = unumpy.uarray(M_H, M_Herror)
DTM_all = unumpy.log10(unumpy.uarray(DTM, DTMerr) * 0.464)
depl = X_H(F_all, M_H_all)
OH_abund = depl + 8.69
z = np.round(z, 0)
def plot_lines_and_other_points_NII():
# PLOT LINES
plt.figure('BPT_NII')
# y1: log([OIII]5007/Hbeta) = 0.61 / (log([NII]6584/Halpha) - 0.05) + 1.3 (curve of Kauffmann+03 line)
# y2: log([OIII]5007/Hbeta) = 0.61 / (log([NII]6584/Halpha) - 0.47) + 1.19 (curve of Kewley+01 line)
x1 = np.arange(-2, 0.02, 0.01)
y1 = 0.61 / (x1 - 0.05) + 1.3
x2 = np.arange(-2, 0.44, 0.01)
y2 = 0.61 / (x2 - 0.47) + 1.19
plt.plot(x1, y1, 'k--')
plt.plot(x2, y2, 'k--')
# AREA LABELS
plt.text(-1.25, -0.5, r'Photoionization', fontsize=12)
plt.text(0.05, 0.55, r'Shocks', fontsize=12)
# plt.text(-1, -0.8, r'Starburst', fontsize=12)
# plt.text(-0.22, -0.75, r'Transition', fontsize=12)
# plt.text(-0.18, -0.9, r'Objects', fontsize=12)
# plt.text(0.16, -0.5, r'LINERs', fontsize=12)
# plt.text(0.05, 0.55, r'Seyferts', fontsize=12)
# plt.text(-1.46, 1.1, r'Extreme Starburst Line', fontsize=12)
# OTHER POINTS FROM PAPER
# Olave et al., 2015 (regions of NGC6845)
hBetaAbs = [
0.025, 0.033, 0.007, 0.084, 0.632, 0.075, 0.015, 0.082, 0.013, 0.038,
0.078, 0.055, 0.008, 0.021, 0.894, 0.408, 0.052, 0.009, 0.024, 0.007,
0.012
]
hBetaErr = [
0.011, 0.027, 0.003, 0.019, 0.03, 0.022, 0.009, 0.017, 0.004, 0.017,
0.019, 0.016, 0.006, 0.013, 0.08, 0.026, 0.014, 0.004, 0.014, 0.003,
0.008
]
oIII5007Abs = [
0.035, 0.092, 0.036, 0.473, 4.651, 0.134, 0.021, 0.183, 0.02, 0.068,
0.135, 0.082, 0.018, 0.014, 0.672, 0.503, 0.038, 0.008, 0.036, 0.013,
0.028
]
oIII5007Err = [
0.012, 0.025, 0.029, 0.247, 0.698, 0.027, 0.013, 0.015, 0.007, 0.018,
0.023, 0.018, 0.007, 0.008, 0.072, 0.028, 0.006, 0.004, 0.014, 0.007,
0.016
]
hAlphaAbs = [
0.069, 0.102, 0.032, 0.377, 3.011, 0.224, 0.05, 0.256, 0.046, 0.111,
0.246, 0.172, 0.027, 0.062, 3.3, 1.66, 0.161, 0.013, 0.062, 0.015,
0.035
]
hAlphaErr = [
0.01, 0.025, 0.011, 0.029, 0.452, 0.032, 0.015, 0.034, 0.019, 0.024,
0.035, 0.027, 0.013, 0.019, 0.204, 0.14, 0.02, 0.01, 0.017, 0.008,
0.012
]
nII6584Abs = [
0.011, 0.014, 0.007, 0.04, 0.227, 0.036, 0.009, 0.033, 0.01, 0.022,
0.041, 0.036, 0.006, 0.021, 1.064, 0.48, 0.056, 0.003, 0.011, 0.003,
0.004
]
nII6584Err = [
0.005, 0.009, 0.006, 0.016, 0.024, 0.017, 0.007, 0.013, 0.004, 0.011,
0.016, 0.012, 0.003, 0.012, 0.062, 0.033, 0.014, 0.002, 0.007, 0.003,
0.003
]
hBeta = (unumpy.uarray(hBetaAbs, hBetaErr))
oIII5007 = unumpy.uarray(oIII5007Abs, oIII5007Err)
hAlpha = unumpy.uarray(hAlphaAbs, hAlphaErr)
nII6584 = unumpy.uarray(nII6584Abs, nII6584Err)
ratioNII = unumpy.log10(nII6584 / hAlpha)
ratioOIII = unumpy.log10(oIII5007 / hBeta)
x = unumpy.nominal_values(ratioNII)
xErr = unumpy.std_devs(ratioNII)
y = unumpy.nominal_values(ratioOIII)
yErr = unumpy.std_devs(ratioOIII)
plt.scatter(x,
y,
marker='s',
color='grey',
alpha=0.3,
label="Olave et al. 2015")
plt.errorbar(x,
y,
xerr=xErr,
yerr=yErr,
color='grey',
ecolor='grey',
elinewidth=0.5,
fmt='none',
alpha=0.3)
def _trapz_loglog(y, x, axis=-1, intervals=False):
"""
Integrate along the given axis using the composite trapezoidal rule in
loglog space.
Integrate `y` (`x`) along given axis in loglog space.
Parameters
----------
y : array_like
Input array to integrate.
x : array_like, optional
Independent variable to integrate over.
axis : int, optional
Specify the axis.
intervals : bool, optional
Return array of shape x not the total integral, default: False
Returns
-------
trapz : float
Definite integral as approximated by trapezoidal rule in loglog space.
"""
log10 = np.log10
try:
y_unit = y.unit
y = y.value
except AttributeError:
y_unit = 1.0
try:
x_unit = x.unit
x = x.value
except AttributeError:
x_unit = 1.0
y = np.asanyarray(y)
x = np.asanyarray(x)
slice1 = [slice(None)] * y.ndim
slice2 = [slice(None)] * y.ndim
slice1[axis] = slice(None, -1)
slice2[axis] = slice(1, None)
slice1, slice2 = tuple(slice1), tuple(slice2)
# arrays with uncertainties contain objects
if y.dtype == "O":
from uncertainties.unumpy import log10
# uncertainties.unumpy.log10 can't deal with tiny values see
# https://github.com/gammapy/gammapy/issues/687, so we filter out the values
# here. As the values are so small it doesn't affect the final result.
# the sqrt is taken to create a margin, because of the later division
# y[slice2] / y[slice1]
valid = y > np.sqrt(np.finfo(float).tiny)
x, y = x[valid], y[valid]
if x.ndim == 1:
shape = [1] * y.ndim
shape[axis] = x.shape[0]
x = x.reshape(shape)
with np.errstate(invalid="ignore", divide="ignore"):
# Compute the power law indices in each integration bin
b = log10(y[slice2] / y[slice1]) / log10(x[slice2] / x[slice1])
# if local powerlaw index is -1, use \int 1/x = log(x); otherwise use normal
# powerlaw integration
trapzs = np.where(
np.abs(b + 1.0) > 1e-10,
(y[slice1] * (x[slice2] * (x[slice2] / x[slice1]) ** b - x[slice1]))
/ (b + 1),
x[slice1] * y[slice1] * np.log(x[slice2] / x[slice1]),
)
tozero = (y[slice1] == 0.0) + (y[slice2] == 0.0) + (x[slice1] == x[slice2])
trapzs[tozero] = 0.0
if intervals:
return trapzs * x_unit * y_unit
ret = np.add.reduce(trapzs, axis) * x_unit * y_unit
return ret
def _trapz_loglog(y, x, axis=-1, intervals=False, ulog10=False):
"""
Integrate along the given axis using the composite trapezoidal rule in
loglog space.
Integrate `y` (`x`) along given axis in loglog space.
Parameters
----------
y : array_like
Input array to integrate.
x : array_like, optional
Independent variable to integrate over.
axis : int, optional
Specify the axis.
intervals : bool, optional
Return array of shape x not the total integral, default: False
ulog10 : bool, optional
Use `~uncertainties.unumpy.log10` to allow uarrays for y and do error
propagation for the integral value.
Returns
-------
trapz : float
Definite integral as approximated by trapezoidal rule in loglog space.
"""
log10 = np.log10
if ulog10:
from uncertainties.unumpy import log10
try:
y_unit = y.unit
y = y.value
except AttributeError:
y_unit = 1.
try:
x_unit = x.unit
x = x.value
except AttributeError:
x_unit = 1.
y = np.asanyarray(y)
x = np.asanyarray(x)
slice1 = [slice(None)] * y.ndim
slice2 = [slice(None)] * y.ndim
slice1[axis] = slice(None, -1)
slice2[axis] = slice(1, None)
if x.ndim == 1:
shape = [1] * y.ndim
shape[axis] = x.shape[0]
x = x.reshape(shape)
with np.errstate(invalid='ignore', divide='ignore'):
# Compute the power law indices in each integration bin
b = log10(y[slice2] / y[slice1]) / log10(x[slice2] / x[slice1])
# if local powerlaw index is -1, use \int 1/x = log(x); otherwise use normal
# powerlaw integration
trapzs = np.where(
np.abs(b + 1.) > 1e-10, (y[slice1] * (
x[slice2] * (x[slice2] / x[slice1]) ** b - x[slice1])) / (b + 1),
x[slice1] * y[slice1] * np.log(x[slice2] / x[slice1]))
tozero = (y[slice1] == 0.) + (y[slice2] == 0.) + (x[slice1] == x[slice2])
trapzs[tozero] = 0.
if intervals:
return trapzs * x_unit * y_unit
ret = np.add.reduce(trapzs, axis) * x_unit * y_unit
return ret