예제 #1
0
    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)
예제 #2
0
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()
예제 #3
0
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()
예제 #4
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    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)