def plotProb(var, label, suffix, bestFit):
# Compute the probability distribution
# (not the probability density function)
(prob, bins) = matplotlib.mlab.hist(var, bins=40, normed=False)
prob = array(prob, dtype=float) / prob.sum() # normalize
# Calculate the peak of the probability distribution
# and the confidence intervals from the 1D Probs.
sid = (prob.argsort())[::-1] # indices for a reverse sort
probSort = prob[sid]
peakPix = sid[0]
peakVal = bins[peakPix]
peakProb = prob[peakPix]
# Make a cumulative distribution function starting from the
# highest pixel value. This way we can find the level above
# which 68% of the trials will fall.
cdf = cumsum(probSort)
# Determine point at which we reach XX confidence
idx1 = (where(cdf > 0.6827))[0] # 1 sigma
idx2 = (where(cdf > 0.9545))[0] # 2 sigma
idx3 = (where(cdf > 0.9973))[0] # 3 sigma
if ((len(idx1) < 2) or (len(idx2) < 2) or (len(idx3) < 2)):
clf()
hist(var)
print 'Min, Max = ', var.min(), var.max()
print idx1
print idx2
print idx3
level1 = probSort[idx1[0]]
level2 = probSort[idx2[0]]
level3 = probSort[idx3[0]]
# Find the range of values
idx1 = (where((prob > level1)))[0]
idx2 = (where((prob > level2)))[0]
idx3 = (where((prob > level3)))[0]
# Parameter Range:
range1 = array([ bins[idx1[0]], bins[idx1[-1]] ])
range2 = array([ bins[idx2[0]], bins[idx2[-1]] ])
range3 = array([ bins[idx3[0]], bins[idx3[-1]] ])
# Plus/Minus Errors:
pmErr1 = abs(range1 - peakVal)
pmErr2 = abs(range2 - peakVal)
pmErr3 = abs(range3 - peakVal)
pmErr1_best = abs(range1 - bestFit)
pmErr2_best = abs(range2 - bestFit)
pmErr3_best = abs(range3 - bestFit)
# Find the min and max values for each confidence
print ''
print 'Best Fit vs. Peak of Prob. Dist. for the %s' % label
print ' %6s = %f vs. %f' % (suffix, bestFit, peakVal)
print '1, 2, 3 Sigma Confidence Intervals for the %s' % label
print ' 68.27%% = [%10.4f -- %10.4f] or -/+ [%10.4f, %10.4f] [%10.4f, %10.4f]' % \
(range1[0], range1[1], pmErr1_best[0], pmErr1_best[1], pmErr1[0], pmErr1[1])
print ' 95.45%% = [%10.4f -- %10.4f] or -/+ [%10.4f, %10.4f] [%10.4f, %10.4f]' % \
(range2[0], range2[1], pmErr2_best[0], pmErr2_best[1], pmErr2[0], pmErr2[1])
print ' 99.73%% = [%10.4f -- %10.4f] or -/+ [%10.4f, %10.4f] [%10.4f, %10.4f]' % \
(range3[0], range3[1], pmErr3_best[0], pmErr3_best[1], pmErr3[0], pmErr3[1])
# Write in an output file:
_out.write('%6s %10.4f %10.4f ' % (suffix, bestFit, peakVal))
_out.write('%10.4f %10.4f %10.4f %10.4f ' % \
(range1[0], range1[1], pmErr1[0], pmErr1[1]))
_out.write('%10.4f %10.4f %10.4f %10.4f ' % \
(range2[0], range2[1], pmErr2[0], pmErr2[1]))
_out.write('%10.4f %10.4f %10.4f %10.4f\n' % \
(range3[0], range3[1], pmErr3[0], pmErr3[1]))
clf()
(pbins, pprob) = histNofill.convertForPlot(bins, prob)
plot(pbins, pprob, color='black')
xlabel(label)
ylabel('Probability')
# Plot the best-fit value
#quiver([bestFit], [peakProb * 1.1], [0], [-peakProb*0.1])
if (suffix == 't0'):
gca().get_xaxis().set_major_formatter(FormatStrFormatter('%.2f'))
savefig('plotParamsProb_' + suffix + '.png')
savefig('plotParamsProb_' + suffix + '.eps')
return (pbins, pprob)
def klfYoung():
dbfile = '/u/jlu/data/gc/database/stars.sqlite'
# Create a connection to the database file
connection = sqlite.connect(dbfile)
# Create a cursor object
cur = connection.cursor()
# Get info on the stars
cur.execute('select * from stars where young = "T" and cuspPaper = "T"')
rows = cur.fetchall()
starCnt = len(rows)
starName = []
x = []
y = []
kp = []
Ak = []
starInField = []
# Loop through each star and pull out the relevant information
for ss in range(starCnt):
record = rows[ss]
name = record[0]
# Check that we observed this star and what field it was in.
cur.execute('select field from spectra where name = "%s"' % (name))
row = cur.fetchone()
if row != None:
starInField.append(row[0])
starName.append(name)
kp.append(record[4])
x.append(record[7])
y.append(record[9])
Ak.append(record[24])
else:
#print 'We do not have data on this star???'
#starInField.append('C')
continue
starCnt = len(starName)
starName = np.array(starName)
starInField = np.array(starInField)
x = np.array(x)
y = np.array(y)
kp = np.array(kp)
Ak = np.array(Ak)
# Now get the completeness corrections for each field.
completenessFile = '/u/jlu/work/gc/imf/klf/2010_04_02/'
completenessFile += 'completeness_extinct_correct.txt'
completeness = asciidata.open(completenessFile)
fields = ['C', 'E', 'SE', 'S', 'W', 'N', 'NE', 'SW', 'NW']
compKp = completeness[0].tonumpy()
comp = {}
for ff in range(len(fields)):
field = fields[ff]
comp[field] = completeness[1 + ff].tonumpy()
# Load up the areas for each field
masksDir = '/u/jlu/work/gc/imf/klf/2010_04_02/osiris_fov/masks/'
area = {}
area['C'] = pyfits.getdata(masksDir + 'central.fits').sum() * 0.01**2
area['E'] = pyfits.getdata(masksDir + 'east.fits').sum() * 0.01**2
area['SE'] = pyfits.getdata(masksDir + 'southeast.fits').sum() * 0.01**2
area['S'] = pyfits.getdata(masksDir + 'south.fits').sum() * 0.01**2
area['W'] = pyfits.getdata(masksDir + 'west.fits').sum() * 0.01**2
area['N'] = pyfits.getdata(masksDir + 'north.fits').sum() * 0.01**2
area['NE'] = pyfits.getdata(masksDir + 'northeast.fits').sum() * 0.01**2
area['SW'] = pyfits.getdata(masksDir + 'southwest.fits').sum() * 0.01**2
area['NW'] = pyfits.getdata(masksDir + 'northwest.fits').sum() * 0.01**2
KLFs = np.zeros((len(fields), len(compKp)), dtype=float)
KLFs_ext = np.zeros((len(fields), len(compKp)), dtype=float)
KLFs_ext_cmp = np.zeros((len(fields), len(compKp)), dtype=float)
eKLFs_ext_cmp = np.zeros((len(fields), len(compKp)), dtype=float)
kp_ext = kp - Ak + 3.0
for ff in range(len(fields)):
field = fields[ff]
# Pull out all the stars in the field
sdx = np.where(starInField == field)[0]
kpInField = kp[sdx]
AkInField = Ak[sdx]
nameInField = starName[sdx]
# Set all stars to Ak = 3
kpInField_ext = kpInField - AkInField + 3.0
# Make a binned luminosity function
binSizeKp = compKp[1] - compKp[0]
perAsec2Mag = area[field] * binSizeKp
for kk in range(len(compKp)):
kp_lo = compKp[kk]
kp_hi = compKp[kk] + binSizeKp
idx1 = np.where((kpInField >= kp_lo) & (kpInField < kp_hi))[0]
KLFs[ff, kk] = len(idx1) / perAsec2Mag
idx2 = np.where((kpInField_ext >= kp_lo)
& (kpInField_ext < kp_hi))[0]
KLFs_ext[ff, kk] = len(idx2) / perAsec2Mag
KLFs_ext_cmp[ff, kk] = KLFs_ext[ff, kk] / comp[field][kk]
eKLFs_ext_cmp[ff, kk] = math.sqrt(len(idx2))
eKLFs_ext_cmp[ff, kk] /= perAsec2Mag * comp[field][kk]
idx = np.where(np.isnan(KLFs_ext_cmp[ff]) == True)[0]
for ii in idx:
KLFs_ext_cmp[ff, ii] = 0.0
# ==========
# Plot the KLF
# ==========
outputDir = '/u/jlu/work/gc/imf/klf/2010_04_02/plots/'
py.clf()
colors = [
'blue', 'green', 'red', 'cyan', 'magenta', 'yellow', 'purple',
'orange', 'brown'
]
legendItems = []
for ff in range(len(fields)):
plt = py.plot(compKp, KLFs_ext_cmp[ff], 'k-', color=colors[ff])
py.plot(compKp, KLFs_ext[ff], 'k--', color=colors[ff])
#py.plot(compKp, KLFs[ff], 'k-.', color=colors[ff])
legendItems.append(plt)
print 'KLF for field ' + fields[ff]
py.xlabel('Kp magnitude (A_Kp = 3)')
py.ylabel('N_stars / (arcsec^2 mag)')
py.legend(legendItems, fields, loc='upper left')
py.savefig(outputDir + 'klf_young_fields_all.png')
# Make a global KLF
KLFall = KLFs_ext_cmp.sum(axis=0)
KLFouter = KLFs_ext_cmp[1:, :].sum(axis=0)
KLFinner = KLFs_ext_cmp[0, :]
eKLFall = np.sqrt((eKLFs_ext_cmp**2).sum(axis=0))
eKLFouter = np.sqrt((eKLFs_ext_cmp[1:, :]**2).sum(axis=0))
eKLFinner = eKLFs_ext_cmp[0, :]
p_compKp, p_KLFall = histNofill.convertForPlot(compKp, KLFall)
p_compKp, p_KLFouter = histNofill.convertForPlot(compKp, KLFouter)
p_compKp, p_KLFinner = histNofill.convertForPlot(compKp, KLFinner)
py.clf()
fig = py.figure(1)
py.subplots_adjust(top=0.95, right=0.95)
grid = AxesGrid(fig,
111,
nrows_ncols=(3, 1),
axes_pad=0.12,
add_all=True,
share_all=True,
aspect=False)
grid[2].plot(p_compKp, p_KLFall, 'k-', linewidth=2)
grid[2].errorbar(compKp + 0.25, KLFall, yerr=eKLFall, fmt='k.')
grid[2].text(9.25, 25, 'KLF all')
grid[2].set_xlabel('Kp magnitude (A_Kp = 3)')
grid[1].plot(p_compKp, p_KLFouter, 'k-', linewidth=2)
grid[1].errorbar(compKp + 0.25, KLFouter, yerr=eKLFouter, fmt='k.')
grid[1].set_ylabel('N_stars / (arcsec^2 mag)')
grid[1].text(9.25, 25, 'KLF outer')
grid[0].plot(p_compKp, p_KLFinner, 'k-', linewidth=2)
grid[0].errorbar(compKp + 0.25, KLFinner, yerr=eKLFinner, fmt='k.')
grid[0].text(9.25, 25, 'KLF central')
grid[0].set_xlim(9, 16)
grid[0].set_ylim(0, 12)
grid[1].set_ylim(0, 12)
grid[2].set_ylim(0, 12)
py.savefig(outputDir + 'klf_young_fields.png')
py.clf()
py.subplots_adjust(top=0.95, right=0.95)
p1 = py.plot(p_compKp, p_KLFinner, 'k-', linewidth=2)
py.errorbar(compKp + 0.25, KLFinner, yerr=eKLFinner, fmt='k.')
p2 = py.plot(p_compKp, p_KLFouter, 'b-', linewidth=2)
py.errorbar(compKp + 0.25, KLFouter, yerr=eKLFouter, fmt='b.')
py.xlabel('Kp magnitude (A_Kp = 3)')
py.ylabel('N_stars / (arcsec^2 mag)')
py.legend((p1, p2), ('Inner', 'Outer'))
py.xlim(9, 16)
py.ylim(0, 12)
py.savefig(outputDir + 'klf_young_fields_inout.png')
# ==========
# Convert to masses
# Assume solar metallicity, A_K=3, distance = 8 kpc, age = 6 Myr
# ==========
genevaFile = '/u/jlu/work/models/geneva/iso/020/c/'
genevaFile += 'iso_c020_0680.UBVRIJHKLM'
model = asciidata.open(genevaFile)
modMass = model[1].tonumpy()
modV = model[6].tonumpy()
modVK = model[11].tonumpy()
modHK = model[15].tonumpy()
modK = modV - modVK
modH = modK + modHK
# Convert from K to Kp (Wainscoat and Cowie 1992)
modKp = modK + 0.22 * (modH - modK)
dist = 8000.0
distMod = -5.0 + 5.0 * math.log10(dist)
# Convert our observed magnitudes to absolute magnitudes.
# Use the differential extinction corrected individual magnitudes.
# Also use the diff. ex. corrected and completeness corrected KLF.
absKp = kp_ext - 3.0 - distMod
absKpKLF = compKp - 3.0 - distMod
p_absKpKLF = p_compKp - 3.0 - distMod
# First, calculate the indvidiual masses
modMassStar = np.zeros(len(absKp), dtype=float)
modKpStar = np.zeros(len(absKp), dtype=float)
for ii in range(len(absKp)):
idx = abs(absKp[ii] - modKp).argmin()
modMassStar[ii] = modMass[idx]
modKpStar[ii] = modKp[idx]
# Calculate the mass function
modMassIMF = np.zeros(len(absKpKLF), dtype=float)
modKpIMF = np.zeros(len(absKpKLF), dtype=float)
for ii in range(len(absKpKLF)):
idx = abs(absKpKLF[ii] - modKp).argmin()
modMassIMF[ii] = modMass[idx]
modKpIMF[ii] = modKp[idx]
# Calculate the mass function we can plot
p_modMassIMF = np.zeros(len(p_absKpKLF), dtype=float)
p_modKpIMF = np.zeros(len(p_absKpKLF), dtype=float)
for ii in range(len(p_absKpKLF)):
idx = abs(p_absKpKLF[ii] - modKp).argmin()
p_modMassIMF[ii] = modMass[idx]
p_modKpIMF[ii] = modKp[idx]
# ==========
# Plot the masses and mass functions
# ==========
py.clf()
py.plot(modMassStar, absKp, 'rs')
py.plot(modMassStar, modKpStar, 'b.')
py.xlabel('Mass (Msun)')
py.ylabel('Kp (mag)')
py.legend(('Observed Absolute', 'Model Absolute'))
py.savefig(outputDir + 'pdmf_young_indiv.png')
py.clf()
py.plot(modMassIMF, KLFall, 'ks')
py.plot(p_modMassIMF, p_KLFall, 'k-')
py.xlabel('Mass (Msun)')
py.ylabel('N')
# Completeness correction (polynomial fits)
comp = {
'C': [44.6449, -14.4162, 1.75114, -0.0923230, 0.00177092],
'E': [228.967, -71.9702, 8.43935, -0.435115, 0.00830836],
'SE': [527.679, -172.892, 21.1500, -1.14200, 0.0229464],
'S': [-293.901, 90.8734, -10.4823, 0.537018, -0.0103230],
'W': [2476.22, -795.154, 95.1204, -5.02096, 0.0986629],
'N': [334.286, -107.820, 12.8997, -0.676552, 0.0131203],
'NE': [-686.107, 224.631, -27.3240, 1.46633, -0.0293125],
'all':
[-142.858, 58.5277, -9.49619, 0.768180, -0.0309478, 0.000495177]
}
# Make a mass function
massEdges = 10**np.arange(1, 1.5, 0.05)
massBins = massEdges[:-1] + ((massEdges[1:] - massEdges[:-1]) / 2.0)
massHist = np.zeros(len(massBins), dtype=float)
p_massBins = np.zeros(len(massBins) * 2, dtype=float)
p_massHist = np.zeros(len(massBins) * 2, dtype=float)
for mm in range(len(massBins)):
m_lo = massEdges[mm]
m_hi = massEdges[mm + 1]
idx = np.where((modMassStar > m_lo) & (modMassStar <= m_hi))[0]
# Find the completeness factor for this mass bin
kpInBin = kp_ext[idx].mean()
cmpCorr = comp['all'][0] + comp['all'][1]*kpInBin + \
comp['all'][2]*kpInBin**2 + comp['all'][3]*kpInBin**3 +\
comp['all'][4]*kpInBin**4 + comp['all'][5]*kpInBin**5
print m_lo, m_hi, cmpCorr, len(idx), kpInBin
massHist[mm] = len(idx) # / cmpCorr
p_massBins[2 * mm] = m_lo
p_massBins[2 * mm + 1] = m_hi
p_massHist[2 * mm] = len(idx) # / cmpCorr
p_massHist[2 * mm + 1] = len(idx) # / cmpCorr
py.clf()
py.plot(p_massBins, p_massHist, 'k-')
py.plot(massBins, massHist, 'ks')
py.show()
def klfYoung():
dbfile = '/u/jlu/data/gc/database/stars.sqlite'
# Create a connection to the database file
connection = sqlite.connect(dbfile)
# Create a cursor object
cur = connection.cursor()
# Get info on the stars
cur.execute('select * from stars where young = "T" and cuspPaper = "T"')
rows = cur.fetchall()
starCnt = len(rows)
starName = []
x = []
y = []
kp = []
Ak = []
starInField = []
# Loop through each star and pull out the relevant information
for ss in range(starCnt):
record = rows[ss]
name = record[0]
# Check that we observed this star and what field it was in.
cur.execute('select field from spectra where name = "%s"' %
(name))
row = cur.fetchone()
if row != None:
starInField.append(row[0])
starName.append(name)
kp.append(record[4])
x.append(record[7])
y.append(record[9])
Ak.append(record[24])
else:
#print 'We do not have data on this star???'
#starInField.append('C')
continue
starCnt = len(starName)
starName = np.array(starName)
starInField = np.array(starInField)
x = np.array(x)
y = np.array(y)
kp = np.array(kp)
Ak = np.array(Ak)
# Now get the completeness corrections for each field.
completenessFile = '/u/jlu/work/gc/imf/klf/2010_04_02/'
completenessFile += 'completeness_extinct_correct.txt'
completeness = asciidata.open(completenessFile)
fields = ['C', 'E', 'SE', 'S', 'W', 'N', 'NE', 'SW', 'NW']
compKp = completeness[0].tonumpy()
comp = {}
for ff in range(len(fields)):
field = fields[ff]
comp[field] = completeness[1+ff].tonumpy()
# Load up the areas for each field
masksDir = '/u/jlu/work/gc/imf/klf/2010_04_02/osiris_fov/masks/'
area = {}
area['C'] = pyfits.getdata(masksDir + 'central.fits').sum() * 0.01**2
area['E'] = pyfits.getdata(masksDir + 'east.fits').sum() * 0.01**2
area['SE'] = pyfits.getdata(masksDir + 'southeast.fits').sum() * 0.01**2
area['S'] = pyfits.getdata(masksDir + 'south.fits').sum() * 0.01**2
area['W'] = pyfits.getdata(masksDir + 'west.fits').sum() * 0.01**2
area['N'] = pyfits.getdata(masksDir + 'north.fits').sum() * 0.01**2
area['NE'] = pyfits.getdata(masksDir + 'northeast.fits').sum() * 0.01**2
area['SW'] = pyfits.getdata(masksDir + 'southwest.fits').sum() * 0.01**2
area['NW'] = pyfits.getdata(masksDir + 'northwest.fits').sum() * 0.01**2
KLFs = np.zeros((len(fields), len(compKp)), dtype=float)
KLFs_ext = np.zeros((len(fields), len(compKp)), dtype=float)
KLFs_ext_cmp = np.zeros((len(fields), len(compKp)), dtype=float)
eKLFs_ext_cmp = np.zeros((len(fields), len(compKp)), dtype=float)
kp_ext = kp - Ak + 3.0
for ff in range(len(fields)):
field = fields[ff]
# Pull out all the stars in the field
sdx = np.where(starInField == field)[0]
kpInField = kp[sdx]
AkInField = Ak[sdx]
nameInField = starName[sdx]
# Set all stars to Ak = 3
kpInField_ext = kpInField - AkInField + 3.0
# Make a binned luminosity function
binSizeKp = compKp[1] - compKp[0]
perAsec2Mag = area[field] * binSizeKp
for kk in range(len(compKp)):
kp_lo = compKp[kk]
kp_hi = compKp[kk] + binSizeKp
idx1 = np.where((kpInField >= kp_lo) & (kpInField < kp_hi))[0]
KLFs[ff,kk] = len(idx1) / perAsec2Mag
idx2 = np.where((kpInField_ext >= kp_lo) & (kpInField_ext < kp_hi))[0]
KLFs_ext[ff,kk] = len(idx2) / perAsec2Mag
KLFs_ext_cmp[ff,kk] = KLFs_ext[ff,kk] / comp[field][kk]
eKLFs_ext_cmp[ff,kk] = math.sqrt(len(idx2))
eKLFs_ext_cmp[ff,kk] /= perAsec2Mag * comp[field][kk]
idx = np.where(np.isnan(KLFs_ext_cmp[ff]) == True)[0]
for ii in idx:
KLFs_ext_cmp[ff,ii] = 0.0
# ==========
# Plot the KLF
# ==========
outputDir = '/u/jlu/work/gc/imf/klf/2010_04_02/plots/'
py.clf()
colors = ['blue', 'green', 'red', 'cyan', 'magenta', 'yellow',
'purple', 'orange', 'brown']
legendItems = []
for ff in range(len(fields)):
plt = py.plot(compKp, KLFs_ext_cmp[ff], 'k-', color=colors[ff])
py.plot(compKp, KLFs_ext[ff], 'k--', color=colors[ff])
#py.plot(compKp, KLFs[ff], 'k-.', color=colors[ff])
legendItems.append(plt)
print 'KLF for field ' + fields[ff]
py.xlabel('Kp magnitude (A_Kp = 3)')
py.ylabel('N_stars / (arcsec^2 mag)')
py.legend(legendItems, fields, loc='upper left')
py.savefig(outputDir + 'klf_young_fields_all.png')
# Make a global KLF
KLFall = KLFs_ext_cmp.sum(axis=0)
KLFouter = KLFs_ext_cmp[1:,:].sum(axis=0)
KLFinner = KLFs_ext_cmp[0,:]
eKLFall = np.sqrt((eKLFs_ext_cmp**2).sum(axis=0))
eKLFouter = np.sqrt((eKLFs_ext_cmp[1:,:]**2).sum(axis=0))
eKLFinner = eKLFs_ext_cmp[0,:]
p_compKp, p_KLFall = histNofill.convertForPlot(compKp, KLFall)
p_compKp, p_KLFouter = histNofill.convertForPlot(compKp, KLFouter)
p_compKp, p_KLFinner = histNofill.convertForPlot(compKp, KLFinner)
py.clf()
fig = py.figure(1)
py.subplots_adjust(top=0.95, right=0.95)
grid = AxesGrid(fig, 111, nrows_ncols=(3,1), axes_pad=0.12, add_all=True,
share_all=True, aspect=False)
grid[2].plot(p_compKp, p_KLFall, 'k-', linewidth=2)
grid[2].errorbar(compKp+0.25, KLFall, yerr=eKLFall, fmt='k.')
grid[2].text(9.25, 25, 'KLF all')
grid[2].set_xlabel('Kp magnitude (A_Kp = 3)')
grid[1].plot(p_compKp, p_KLFouter, 'k-', linewidth=2)
grid[1].errorbar(compKp+0.25, KLFouter, yerr=eKLFouter, fmt='k.')
grid[1].set_ylabel('N_stars / (arcsec^2 mag)')
grid[1].text(9.25, 25, 'KLF outer')
grid[0].plot(p_compKp, p_KLFinner, 'k-', linewidth=2)
grid[0].errorbar(compKp+0.25, KLFinner, yerr=eKLFinner, fmt='k.')
grid[0].text(9.25, 25, 'KLF central')
grid[0].set_xlim(9, 16)
grid[0].set_ylim(0, 12)
grid[1].set_ylim(0, 12)
grid[2].set_ylim(0, 12)
py.savefig(outputDir + 'klf_young_fields.png')
py.clf()
py.subplots_adjust(top=0.95, right=0.95)
p1 = py.plot(p_compKp, p_KLFinner, 'k-', linewidth=2)
py.errorbar(compKp+0.25, KLFinner, yerr=eKLFinner, fmt='k.')
p2 = py.plot(p_compKp, p_KLFouter, 'b-', linewidth=2)
py.errorbar(compKp+0.25, KLFouter, yerr=eKLFouter, fmt='b.')
py.xlabel('Kp magnitude (A_Kp = 3)')
py.ylabel('N_stars / (arcsec^2 mag)')
py.legend((p1, p2), ('Inner', 'Outer'))
py.xlim(9, 16)
py.ylim(0, 12)
py.savefig(outputDir + 'klf_young_fields_inout.png')
# ==========
# Convert to masses
# Assume solar metallicity, A_K=3, distance = 8 kpc, age = 6 Myr
# ==========
genevaFile = '/u/jlu/work/models/geneva/iso/020/c/'
genevaFile += 'iso_c020_0680.UBVRIJHKLM'
model = asciidata.open(genevaFile)
modMass = model[1].tonumpy()
modV = model[6].tonumpy()
modVK = model[11].tonumpy()
modHK = model[15].tonumpy()
modK = modV - modVK
modH = modK + modHK
# Convert from K to Kp (Wainscoat and Cowie 1992)
modKp = modK + 0.22 * (modH - modK)
dist = 8000.0
distMod = -5.0 + 5.0 * math.log10(dist)
# Convert our observed magnitudes to absolute magnitudes.
# Use the differential extinction corrected individual magnitudes.
# Also use the diff. ex. corrected and completeness corrected KLF.
absKp = kp_ext - 3.0 - distMod
absKpKLF = compKp - 3.0 - distMod
p_absKpKLF = p_compKp - 3.0 - distMod
# First, calculate the indvidiual masses
modMassStar = np.zeros(len(absKp), dtype=float)
modKpStar = np.zeros(len(absKp), dtype=float)
for ii in range(len(absKp)):
idx = abs(absKp[ii] - modKp).argmin()
modMassStar[ii] = modMass[idx]
modKpStar[ii] = modKp[idx]
# Calculate the mass function
modMassIMF = np.zeros(len(absKpKLF), dtype=float)
modKpIMF = np.zeros(len(absKpKLF), dtype=float)
for ii in range(len(absKpKLF)):
idx = abs(absKpKLF[ii] - modKp).argmin()
modMassIMF[ii] = modMass[idx]
modKpIMF[ii] = modKp[idx]
# Calculate the mass function we can plot
p_modMassIMF = np.zeros(len(p_absKpKLF), dtype=float)
p_modKpIMF = np.zeros(len(p_absKpKLF), dtype=float)
for ii in range(len(p_absKpKLF)):
idx = abs(p_absKpKLF[ii] - modKp).argmin()
p_modMassIMF[ii] = modMass[idx]
p_modKpIMF[ii] = modKp[idx]
# ==========
# Plot the masses and mass functions
# ==========
py.clf()
py.plot(modMassStar, absKp, 'rs')
py.plot(modMassStar, modKpStar, 'b.')
py.xlabel('Mass (Msun)')
py.ylabel('Kp (mag)')
py.legend(('Observed Absolute', 'Model Absolute'))
py.savefig(outputDir + 'pdmf_young_indiv.png')
py.clf()
py.plot(modMassIMF, KLFall, 'ks')
py.plot(p_modMassIMF, p_KLFall, 'k-')
py.xlabel('Mass (Msun)')
py.ylabel('N')
# Completeness correction (polynomial fits)
comp = {'C': [44.6449, -14.4162, 1.75114, -0.0923230, 0.00177092],
'E': [228.967, -71.9702, 8.43935, -0.435115, 0.00830836],
'SE': [527.679, -172.892, 21.1500, -1.14200, 0.0229464],
'S': [-293.901, 90.8734, -10.4823, 0.537018, -0.0103230],
'W': [2476.22, -795.154, 95.1204, -5.02096, 0.0986629],
'N': [334.286, -107.820, 12.8997, -0.676552, 0.0131203],
'NE': [-686.107, 224.631, -27.3240, 1.46633, -0.0293125],
'all': [-142.858, 58.5277, -9.49619, 0.768180, -0.0309478, 0.000495177]}
# Make a mass function
massEdges = 10**np.arange(1, 1.5, 0.05)
massBins = massEdges[:-1] + ((massEdges[1:] - massEdges[:-1]) / 2.0)
massHist = np.zeros(len(massBins), dtype=float)
p_massBins = np.zeros(len(massBins)*2, dtype=float)
p_massHist = np.zeros(len(massBins)*2, dtype=float)
for mm in range(len(massBins)):
m_lo = massEdges[mm]
m_hi = massEdges[mm+1]
idx = np.where((modMassStar > m_lo) & (modMassStar <= m_hi))[0]
# Find the completeness factor for this mass bin
kpInBin = kp_ext[idx].mean()
cmpCorr = comp['all'][0] + comp['all'][1]*kpInBin + \
comp['all'][2]*kpInBin**2 + comp['all'][3]*kpInBin**3 +\
comp['all'][4]*kpInBin**4 + comp['all'][5]*kpInBin**5
print m_lo, m_hi, cmpCorr, len(idx), kpInBin
massHist[mm] = len(idx)# / cmpCorr
p_massBins[2*mm] = m_lo
p_massBins[2*mm + 1] = m_hi
p_massHist[2*mm] = len(idx)# / cmpCorr
p_massHist[2*mm+1] = len(idx)# / cmpCorr
py.clf()
py.plot(p_massBins, p_massHist, 'k-')
py.plot(massBins, massHist, 'ks')
py.show()
def plotProb(var, label, suffix, bestFit):
# Compute the probability distribution
# (not the probability density function)
(prob, bins) = matplotlib.mlab.hist(var, bins=40, normed=False)
prob = array(prob, dtype=float) / prob.sum() # normalize
# Calculate the peak of the probability distribution
# and the confidence intervals from the 1D Probs.
sid = (prob.argsort())[::-1] # indices for a reverse sort
probSort = prob[sid]
peakPix = sid[0]
peakVal = bins[peakPix]
peakProb = prob[peakPix]
# Make a cumulative distribution function starting from the
# highest pixel value. This way we can find the level above
# which 68% of the trials will fall.
cdf = cumsum(probSort)
# Determine point at which we reach XX confidence
idx1 = (where(cdf > 0.6827))[0] # 1 sigma
idx2 = (where(cdf > 0.9545))[0] # 2 sigma
idx3 = (where(cdf > 0.9973))[0] # 3 sigma
if ((len(idx1) < 2) or (len(idx2) < 2) or (len(idx3) < 2)):
clf()
hist(var)
print 'Min, Max = ', var.min(), var.max()
print idx1
print idx2
print idx3
level1 = probSort[idx1[0]]
level2 = probSort[idx2[0]]
level3 = probSort[idx3[0]]
# Find the range of values
idx1 = (where((prob > level1)))[0]
idx2 = (where((prob > level2)))[0]
idx3 = (where((prob > level3)))[0]
# Parameter Range:
range1 = array([bins[idx1[0]], bins[idx1[-1]]])
range2 = array([bins[idx2[0]], bins[idx2[-1]]])
range3 = array([bins[idx3[0]], bins[idx3[-1]]])
# Plus/Minus Errors:
pmErr1 = abs(range1 - peakVal)
pmErr2 = abs(range2 - peakVal)
pmErr3 = abs(range3 - peakVal)
pmErr1_best = abs(range1 - bestFit)
pmErr2_best = abs(range2 - bestFit)
pmErr3_best = abs(range3 - bestFit)
# Find the min and max values for each confidence
print ''
print 'Best Fit vs. Peak of Prob. Dist. for the %s' % label
print ' %6s = %f vs. %f' % (suffix, bestFit, peakVal)
print '1, 2, 3 Sigma Confidence Intervals for the %s' % label
print ' 68.27%% = [%10.4f -- %10.4f] or -/+ [%10.4f, %10.4f] [%10.4f, %10.4f]' % \
(range1[0], range1[1], pmErr1_best[0], pmErr1_best[1], pmErr1[0], pmErr1[1])
print ' 95.45%% = [%10.4f -- %10.4f] or -/+ [%10.4f, %10.4f] [%10.4f, %10.4f]' % \
(range2[0], range2[1], pmErr2_best[0], pmErr2_best[1], pmErr2[0], pmErr2[1])
print ' 99.73%% = [%10.4f -- %10.4f] or -/+ [%10.4f, %10.4f] [%10.4f, %10.4f]' % \
(range3[0], range3[1], pmErr3_best[0], pmErr3_best[1], pmErr3[0], pmErr3[1])
# Write in an output file:
_out.write('%6s %10.4f %10.4f ' % (suffix, bestFit, peakVal))
_out.write('%10.4f %10.4f %10.4f %10.4f ' % \
(range1[0], range1[1], pmErr1[0], pmErr1[1]))
_out.write('%10.4f %10.4f %10.4f %10.4f ' % \
(range2[0], range2[1], pmErr2[0], pmErr2[1]))
_out.write('%10.4f %10.4f %10.4f %10.4f\n' % \
(range3[0], range3[1], pmErr3[0], pmErr3[1]))
clf()
(pbins, pprob) = histNofill.convertForPlot(bins, prob)
plot(pbins, pprob, color='black')
xlabel(label)
ylabel('Probability')
# Plot the best-fit value
#quiver([bestFit], [peakProb * 1.1], [0], [-peakProb*0.1])
if (suffix == 't0'):
gca().get_xaxis().set_major_formatter(FormatStrFormatter('%.2f'))
savefig('plotParamsProb_' + suffix + '.png')
savefig('plotParamsProb_' + suffix + '.eps')
return (pbins, pprob)
