def powerfit(xax, data, err=None, alphaguess=-2.0, scaleguess=1.0, quiet=True):
"""
Fit a power law (a line in log-space) to data as a function of x
differs from 'plfit' because plfit fits a power law distribution,
this code simply fits a power law
"""
logdata = np.log10(data)
if err is None: err = np.ones(data.shape, dtype='float')
def mpfitfun(data, err):
def f(p, fjac=None):
return [
0,
np.ravel(
((np.log10(p[0]) + np.log10(xax) * p[1]) - data) / err)
]
return f
mp = mpfit.mpfit(mpfitfun(logdata, err),
xall=[scaleguess, alphaguess],
quiet=quiet)
fitp = mp.params
return fitp, mp
def fit_blackbody(xdata, flux, guesses=(0,0), err=None,
blackbody_function=blackbody, quiet=True, **kwargs):
"""
Parameters
----------
xdata : array
Array of the X-values (frequency, wavelength) of the data
flux : array
The fluxes corresponding to the xdata values
guesses : (Temperature,Scale) or (Temperature,Beta,Scale)
The input guesses. 3 parameters are used for greybody
fitting, two for temperature fitting.
blackbody_function: function
Must take x-axis (e.g. frequency), temperature, scale, and then
optionally beta args
quiet : bool
quiet flag passed to mpfit
Returns
-------
mp : mpfit structure
An mpfit structure. Access parameters and errors via
`mp.params` and `mp.perror`. The covariance matrix
is in mp.covar.
Examples
--------
>>> wavelength = array([20,70,160,250,350,500,850,1100])
>>> flux = modified_blackbody_wavelength(wavelength, 15, beta=1.75,
logN=22, wavelength_units='microns', normalize=False,
logscale=16)
>>> err = 0.1 * flux
>>> np.random.seed(0)
>>> flux += np.random.randn(len(wavelength)) * err
>>> tguess, bguess, nguess = 20.,2.,21.5
>>> mp = fit_blackbody(wavelength, flux, err=err,
blackbody_function=modified_blackbody_wavelength,
logscale=16, guesses=(tguess, bguess, nguess),
wavelength_units='microns')
>>> print mp.params
[ 14.99095224 1.78620237 22.05271119]
>>> # T~14.9 K, beta ~1.79, column ~10^22
"""
def mpfitfun(x,y,err):
if err is None:
def f(p,fjac=None): return [0,(y-blackbody_function(x, *p,
normalize=False, **kwargs))]
else:
def f(p,fjac=None): return [0,(y-blackbody_function(x, *p,
normalize=False, **kwargs))/err]
return f
err = err if err is not None else flux*0.0 + 1.0
mp = mpfit.mpfit(mpfitfun(xdata,flux,err), guesses, quiet=quiet)
return mp
def mpfitter(xdata, ydata, params=None, error=None, model=gaussian, quiet=True, **kwargs):
"""
Find the least-squares fit using mpfit
"""
errfunc = error_function_generator(xdata,ydata,error=error,model=model,mpfit=True)
mp = mpfit(errfunc, params, quiet=quiet, **kwargs)
return mp.params,mp.perror
def brokenpowerfit(xax, data, err=None, alphaguess1=0.0, alphaguess2=-2.0, scaleguess=1.0,
breakpoint=None, quiet=True):
"""
Fit a broken power law (a line in log-space) to data as a function of x
differs from 'plfit' because plfit fits a power law distribution,
this code simply fits a power law
This is a lot more intricate than the simple power law fit, since it involves
fitting two power laws with different slopes
Parameters:
p[0] - scale
p[1] - breakpoint
p[2] - power 1 (xax < breakpoint)
p[3] - power 2 (xax >= breakpoint)
There are 5 parameters (NOT 4) returned because there are two scales that are *NOT*
independent
returns: scale1,scale2,breakpoint,alpha1,alpha2
"""
logdata = np.log10(data)
if err is None: err = np.ones(data.shape,dtype='float')
def brokenpowerlaw(p):
lowerhalf = (np.log10(p[0]) + np.log10(xax)*p[2]) * (xax < p[1])
# find the location at which both functions must be equal
scale2loc = np.argmin(np.abs(xax - p[1]))
scale2 = np.log10(xax[scale2loc])*(p[2] - p[3]) + np.log10(p[0])
upperhalf = (scale2 + np.log10(xax)*p[3]) * (xax >= p[1])
# DEBUG print "scale1: %15g scale2: %15g xaxind: %5i xaxval: %15g lower: %15g upper: %15g" % (p[0],scale2,scale2loc,np.log10(xax[scale2loc]),lowerhalf[scale2loc-1],upperhalf[scale2loc])
return lowerhalf+upperhalf
def mpfitfun(data,err):
def f(p,fjac=None): return [0,np.ravel((brokenpowerlaw(p)-data)/err)]
return f
if breakpoint is None: breakpoint = np.median(xax)
parinfo = [{}, {'mpminstep':xax.min(),'mpmaxstep':xax.max(),'step':xax.min()}, {}, {}]
mp = mpfit.mpfit(mpfitfun(logdata,err),xall=[scaleguess,breakpoint,alphaguess1,alphaguess2],quiet=quiet,parinfo=parinfo)
fitp = mp.params
scale2loc = np.argmin(np.abs(xax - fitp[1]))
scale2 = 10**( np.log10(xax[scale2loc])*(fitp[2] - fitp[3]) + np.log10(fitp[0]) )
fitp = np.array( [fitp[0],scale2] + fitp[1:].tolist() )
return fitp,mp
def emtau(freq,flux,err=None,EMguess=1e7,Te=8500,normfac=5e-6,quiet=1):
"""
Returns emission measure & optical depth given
radio continuum data points at frequency freq with flux
density flux.
return bestEM,nu(tau=1),chi^2
"""
mp = mpfit(mpfitfun(freq,flux,err),xall=[EMguess,normfac],quiet=quiet)
mpp = mp.params
mpperr = mp.perror
chi2 = mp.fnorm
bestEM = mpp[0]
normfac = mpp[1]
nu_tau = ( Te**1.35 / bestEM / 8.235e-2 )**(-1/2.1)
return bestEM,nu_tau,normfac,chi2
def powerfit(xax,data,err=None,alphaguess=-2.0,scaleguess=1.0,quiet=True):
"""
Fit a power law (a line in log-space) to data as a function of x
differs from 'plfit' because plfit fits a power law distribution,
this code simply fits a power law
"""
logdata = np.log10(data)
if err is None: err = np.ones(data.shape,dtype='float')
def mpfitfun(data,err):
def f(p,fjac=None): return [0,np.ravel(((np.log10(p[0])+np.log10(xax)*p[1])-data)/err)]
return f
mp = mpfit.mpfit(mpfitfun(logdata,err),xall=[scaleguess,alphaguess],quiet=quiet)
fitp = mp.params
return fitp,mp
def mpfitter(xdata,
ydata,
params=None,
error=None,
model=gaussian,
quiet=True,
**kwargs):
"""
Find the least-squares fit using mpfit
"""
errfunc = error_function_generator(xdata,
ydata,
error=error,
model=model,
mpfit=True)
mp = mpfit(errfunc, params, quiet=quiet, **kwargs)
return mp.params, mp.perror
def fitspec(specsegments,
aperture=None,
modelspec=modelspec,
outpars=False,
vlsrcorr=0,
extinction=False,
parinfo=modelpars(),
quiet=1,
**kwargs):
""" fit a model spectrum
The model is defined internal to fitspec so that parameters can
be fixed based on input parameters """
specsegments = copy(specsegments) # copy.deepcopy(specsegments)
parinfo = copy(parinfo) # copy.deepcopy(parinfo)
kwargs = {'extinction': extinction}
if extinction:
parinfo = modelpars(extinction=extinction)
def fitfun(x, y, err):
return lambda (p): (y - modelspec(x, *p, **kwargs)) / err
def mpfitfun(x, y, err):
def f(p, fjac=None):
return [0, (y - modelspec(x, *p, **kwargs)) / err]
return f
if aperture is not None:
miny, maxy = aperture
fitdata = asarray([
ss['data'][miny:maxy, :].sum(axis=0) for ss in specsegments
]).ravel()
fiterr = asarray([
ss['err'][:] * sqrt(maxy - miny) for ss in specsegments
]).ravel() # since it is a summed aperture, add in quadrature
else:
fitdata = asarray([ss['data'] for ss in specsegments]).ravel()
fiterr = asarray([ss['err'] for ss in specsegments]).ravel()
fitwl = asarray([ss['wavelength'] for ss in specsegments]).ravel()
try:
parinfo = parinfo.tolist()
print "Parinfo was an array. No idea why, it was never set to one. Ever."
except:
pass
mp = mpfit(mpfitfun(fitwl, fitdata, fiterr), parinfo=parinfo, quiet=quiet)
mpp = mp.params
mpperr = mp.perror
for i, p in enumerate(mpp):
parinfo[i]['value'] = p
if parinfo[i]['parname'] == 'SHIFT':
print parinfo[i]['parname'], p + vlsrcorr, " +/- ", mpperr[i]
else:
print parinfo[i]['parname'], p, " +/- ", mpperr[i]
# print "Temperature: ",mpp[0]," Shift: ",mpp[3],mpp[3]*mean(fitwl)/3e5," Width: ",mpp[2],mpp[2]*mean(fitwl)/3e5," Ortho/Para: ",mpp[4]
# print "ERRORS: Temperature: ",mpperr[0]," Shift: ",mpperr[3],mpperr[3]*mean(fitwl)/3e5," Width: ",mpperr[2],mpperr[2]*mean(fitwl)/3e5," Ortho/Para: ",mpperr[4]
print "Chi2: ", mp.fnorm, " Reduced Chi2: ", mp.fnorm / len(
fitdata), " DOF:", len(fitdata) - len(mpp)
apfitd = {
'params': mpp,
'parerr': mpperr,
'parinfo': parinfo,
'wl': fitwl,
'data': fitdata,
'model': modelspec(fitwl, *mpp),
'err': fiterr
}
if aperture is not None:
for ss in specsegments:
ss['data'] = ss['data'][miny:maxy, :].sum(axis=0)
for ss in specsegments:
ss['model'] = modelspec(ss['wavelength'], *mpp)
if outpars: return specsegments, apfitd, parinfo
else: return specsegments, apfitd
def multigaussfit(xax, data, ngauss=1, err=None, params=[1,0,1],
fixed=[False,False,False], limitedmin=[False,False,True],
limitedmax=[False,False,False], minpars=[0,0,0], maxpars=[0,0,0],
quiet=True, shh=True, veryverbose=False):
"""
An improvement on onedgaussfit. Lets you fit multiple gaussians.
Inputs:
xax - x axis
data - y axis
ngauss - How many gaussians to fit? Default 1 (this could supersede onedgaussfit)
err - error corresponding to data
These parameters need to have length = 3*ngauss. If ngauss > 1 and length = 3, they will
be replicated ngauss times, otherwise they will be reset to defaults:
params - Fit parameters: [amplitude, offset, width] * ngauss
If len(params) % 3 == 0, ngauss will be set to len(params) / 3
fixed - Is parameter fixed?
limitedmin/minpars - set lower limits on each parameter (default: width>0)
limitedmax/maxpars - set upper limits on each parameter
quiet - should MPFIT output each iteration?
shh - output final parameters?
Returns:
Fit parameters
Model
Fit errors
chi2
"""
if len(params) != ngauss and (len(params) / 3) > ngauss:
ngauss = len(params) / 3
if isinstance(params,numpy.ndarray): params=params.tolist()
# make sure all various things are the right length; if they're not, fix them using the defaults
for parlist in (params,fixed,limitedmin,limitedmax,minpars,maxpars):
if len(parlist) != 3*ngauss:
# if you leave the defaults, or enter something that can be multiplied by 3 to get to the
# right number of gaussians, it will just replicate
if len(parlist) == 3:
parlist *= ngauss
elif parlist==params:
parlist[:] = [1,0,1] * ngauss
elif parlist==fixed or parlist==limitedmax:
parlist[:] = [False,False,False] * ngauss
elif parlist==limitedmin:
parlist[:] = [False,False,True] * ngauss
elif parlist==minpars or parlist==maxpars:
parlist[:] = [0,0,0] * ngauss
def mpfitfun(x,y,err):
if err is None:
def f(p,fjac=None): return [0,(y-n_gaussian(pars=p)(x))]
else:
def f(p,fjac=None): return [0,(y-n_gaussian(pars=p)(x))/err]
return f
if xax == None:
xax = numpy.arange(len(data))
parnames = {0:"AMPLITUDE",1:"SHIFT",2:"WIDTH"}
parinfo = [ {'n':ii, 'value':params[ii],
'limits':[minpars[ii],maxpars[ii]],
'limited':[limitedmin[ii],limitedmax[ii]], 'fixed':fixed[ii],
'parname':parnames[ii%3]+str(ii%3), 'error':ii}
for ii in xrange(len(params)) ]
if veryverbose:
print "GUESSES: "
print "\n".join(["%s: %s" % (p['parname'],p['value']) for p in parinfo])
mp = mpfit(mpfitfun(xax,data,err),parinfo=parinfo,quiet=quiet)
mpp = mp.params
mpperr = mp.perror
chi2 = mp.fnorm
if mp.status == 0:
raise Exception(mp.errmsg)
if not shh:
print "Final fit values: "
for i,p in enumerate(mpp):
parinfo[i]['value'] = p
print parinfo[i]['parname'],p," +/- ",mpperr[i]
print "Chi2: ",mp.fnorm," Reduced Chi2: ",mp.fnorm/len(data)," DOF:",len(data)-len(mpp)
return mpp,n_gaussian(pars=mpp)(xax),mpperr,chi2
def onedgaussfit(xax, data, err=None,
params=[0,1,0,1],fixed=[False,False,False,False],
limitedmin=[False,False,False,True],
limitedmax=[False,False,False,False], minpars=[0,0,0,0],
maxpars=[0,0,0,0], quiet=True, shh=True,
veryverbose=False,
vheight=True, negamp=False,
usemoments=False):
"""
Inputs:
xax - x axis
data - y axis
err - error corresponding to data
params - Fit parameters: Height of background, Amplitude, Shift, Width
fixed - Is parameter fixed?
limitedmin/minpars - set lower limits on each parameter (default: width>0)
limitedmax/maxpars - set upper limits on each parameter
quiet - should MPFIT output each iteration?
shh - output final parameters?
usemoments - replace default parameters with moments
Returns:
Fit parameters
Model
Fit errors
chi2
"""
def mpfitfun(x,y,err):
if err is None:
def f(p,fjac=None): return [0,(y-onedgaussian(x,*p))]
else:
def f(p,fjac=None): return [0,(y-onedgaussian(x,*p))/err]
return f
if xax == None:
xax = numpy.arange(len(data))
if vheight is False:
height = params[0]
fixed[0] = True
if usemoments:
params = onedmoments(xax,data,vheight=vheight,negamp=negamp, veryverbose=veryverbose)
if vheight is False: params = [height]+params
if veryverbose: print "OneD moments: h: %g a: %g c: %g w: %g" % tuple(params)
parinfo = [ {'n':0,'value':params[0],'limits':[minpars[0],maxpars[0]],'limited':[limitedmin[0],limitedmax[0]],'fixed':fixed[0],'parname':"HEIGHT",'error':0} ,
{'n':1,'value':params[1],'limits':[minpars[1],maxpars[1]],'limited':[limitedmin[1],limitedmax[1]],'fixed':fixed[1],'parname':"AMPLITUDE",'error':0},
{'n':2,'value':params[2],'limits':[minpars[2],maxpars[2]],'limited':[limitedmin[2],limitedmax[2]],'fixed':fixed[2],'parname':"SHIFT",'error':0},
{'n':3,'value':params[3],'limits':[minpars[3],maxpars[3]],'limited':[limitedmin[3],limitedmax[3]],'fixed':fixed[3],'parname':"WIDTH",'error':0}]
mp = mpfit(mpfitfun(xax,data,err),parinfo=parinfo,quiet=quiet)
mpp = mp.params
mpperr = mp.perror
chi2 = mp.fnorm
if mp.status == 0:
raise Exception(mp.errmsg)
if (not shh) or veryverbose:
print "Fit status: ",mp.status
for i,p in enumerate(mpp):
parinfo[i]['value'] = p
print parinfo[i]['parname'],p," +/- ",mpperr[i]
print "Chi2: ",mp.fnorm," Reduced Chi2: ",mp.fnorm/len(data)," DOF:",len(data)-len(mpp)
return mpp,onedgaussian(xax,*mpp),mpperr,chi2
def gaussfit(data,err=None,params=(),autoderiv=True,return_all=False,circle=False,
fixed=numpy.repeat(False,7),limitedmin=[False,False,False,False,True,True,True],
limitedmax=[False,False,False,False,False,False,True],
usemoment=numpy.array([],dtype='bool'),
minpars=numpy.repeat(0,7),maxpars=[0,0,0,0,0,0,360],
rotate=1,vheight=1,quiet=True,returnmp=False,
returnfitimage=False,**kwargs):
"""
Gaussian fitter with the ability to fit a variety of different forms of
2-dimensional gaussian.
Input Parameters:
data - 2-dimensional data array
err=None - error array with same size as data array
params=[] - initial input parameters for Gaussian function.
(height, amplitude, x, y, width_x, width_y, rota)
if not input, these will be determined from the moments of the system,
assuming no rotation
autoderiv=1 - use the autoderiv provided in the lmder.f function (the
alternative is to us an analytic derivative with lmdif.f: this method
is less robust)
return_all=0 - Default is to return only the Gaussian parameters.
1 - fit params, fit error
returnfitimage - returns (best fit params,best fit image)
returnmp - returns the full mpfit struct
circle=0 - default is an elliptical gaussian (different x, y widths),
but can reduce the input by one parameter if it's a circular gaussian
rotate=1 - default allows rotation of the gaussian ellipse. Can remove
last parameter by setting rotate=0. numpy.expects angle in DEGREES
vheight=1 - default allows a variable height-above-zero, i.e. an
additive constant for the Gaussian function. Can remove first
parameter by setting this to 0
usemoment - can choose which parameters to use a moment estimation for.
Other parameters will be taken from params. Needs to be a boolean
array.
Output:
Default output is a set of Gaussian parameters with the same shape as
the input parameters
If returnfitimage=True returns a numpy array of a guassian
contructed using the best fit parameters.
If returnmp=True returns a `mpfit` object. This object contains
a `covar` attribute which is the 7x7 covariance array
generated by the pmfit class in the `mpfit_custom.py`
module. It contains a `param` attribute that contains a
list of the best fit parameters in the same order as the
optional input parameter `params`.
Warning: Does NOT necessarily output a rotation angle between 0 and 360 degrees.
"""
usemoment=numpy.array(usemoment,dtype='bool')
params=numpy.array(params,dtype='float')
if usemoment.any() and len(params)==len(usemoment):
moment = numpy.array(moments(data,circle,rotate,vheight,**kwargs),dtype='float')
params[usemoment] = moment[usemoment]
elif params == [] or len(params)==0:
params = (moments(data,circle,rotate,vheight,**kwargs))
if vheight==0:
vheight=1
params = numpy.concatenate([[0],params])
fixed[0] = 1
# mpfit will fail if it is given a start parameter outside the allowed range:
for i in xrange(len(params)):
if params[i] > maxpars[i] and limitedmax[i]: params[i] = maxpars[i]
if params[i] < minpars[i] and limitedmin[i]: params[i] = minpars[i]
if err is None:
errorfunction = lambda p: numpy.ravel((twodgaussian(p,circle,rotate,vheight)\
(*numpy.indices(data.shape)) - data))
else:
errorfunction = lambda p: numpy.ravel((twodgaussian(p,circle,rotate,vheight)\
(*numpy.indices(data.shape)) - data)/err)
def mpfitfun(data,err):
if err is None:
def f(p,fjac=None): return [0,numpy.ravel(data-twodgaussian(p,circle,rotate,vheight)\
(*numpy.indices(data.shape)))]
else:
def f(p,fjac=None): return [0,numpy.ravel((data-twodgaussian(p,circle,rotate,vheight)\
(*numpy.indices(data.shape)))/err)]
return f
parinfo = [
{'n':1,'value':params[1],'limits':[minpars[1],maxpars[1]],'limited':[limitedmin[1],limitedmax[1]],'fixed':fixed[1],'parname':"AMPLITUDE",'error':0},
{'n':2,'value':params[2],'limits':[minpars[2],maxpars[2]],'limited':[limitedmin[2],limitedmax[2]],'fixed':fixed[2],'parname':"XSHIFT",'error':0},
{'n':3,'value':params[3],'limits':[minpars[3],maxpars[3]],'limited':[limitedmin[3],limitedmax[3]],'fixed':fixed[3],'parname':"YSHIFT",'error':0},
{'n':4,'value':params[4],'limits':[minpars[4],maxpars[4]],'limited':[limitedmin[4],limitedmax[4]],'fixed':fixed[4],'parname':"XWIDTH",'error':0} ]
if vheight == 1:
parinfo.insert(0,{'n':0,'value':params[0],'limits':[minpars[0],maxpars[0]],'limited':[limitedmin[0],limitedmax[0]],'fixed':fixed[0],'parname':"HEIGHT",'error':0})
if circle == 0:
parinfo.append({'n':5,'value':params[5],'limits':[minpars[5],maxpars[5]],'limited':[limitedmin[5],limitedmax[5]],'fixed':fixed[5],'parname':"YWIDTH",'error':0})
if rotate == 1:
parinfo.append({'n':6,'value':params[6],'limits':[minpars[6],maxpars[6]],'limited':[limitedmin[6],limitedmax[6]],'fixed':fixed[6],'parname':"ROTATION",'error':0})
if autoderiv == 0:
# the analytic derivative, while not terribly difficult, is less
# efficient and useful. I only bothered putting it here because I was
# instructed to do so for a class project - please ask if you would
# like this feature implemented
raise ValueError("I'm sorry, I haven't implemented this feature yet.")
else:
# p, cov, infodict, errmsg, success = optimize.leastsq(errorfunction,\
# params, full_output=1)
mp = mpfit(mpfitfun(data,err),parinfo=parinfo,quiet=quiet)
if returnmp:
returns = (mp)
elif return_all == 0:
returns = mp.params
elif return_all == 1:
returns = mp.params,mp.perror
if returnfitimage:
fitimage = twodgaussian(mp.params,circle,rotate,vheight)(*numpy.indices(data.shape))
returns = (returns,fitimage)
return returns
def psffit(data,
err=None,
params=[],
autoderiv=True,
return_all=False,
circle=True,
fixed=numpy.repeat(False, 7),
limitedmin=[False, False, False, False, True, True, True],
limitedmax=[False, False, False, False, False, False, True],
usemoment=numpy.array([], dtype='bool'),
minpars=numpy.repeat(0, 7),
maxpars=[0, 0, 0, 0, 0, 0, 360],
rotate=0,
vheight=1,
quiet=True,
returnmp=False,
returnfitimage=False,
psffunction=airy,
extra_pars=None,
return_parinfo=False,
**kwargs):
"""
PSF fitter with the ability to fit a variety of different forms of
2-dimensional gaussian OR an Airy.
This code is mostly directly copied from gaussfitter.py and presents
yet another argument for me turning this into a class...
Input Parameters:
data - 2-dimensional data array
err=None - error array with same size as data array
params=[] - initial input parameters for Gaussian function.
(height, amplitude, x, y, width_x, width_y, rota)
if not input, these will be determined from the moments of the system,
assuming no rotation
autoderiv=1 - use the autoderiv provided in the lmder.f function (the
alternative is to us an analytic derivative with lmdif.f: this method
is less robust)
return_all=0 - Default is to return only the Gaussian parameters.
1 - fit params, fit error
returnfitimage - returns (best fit params,best fit image)
returnmp - returns the full mpfit struct
circle=0 - default is an elliptical gaussian (different x, y widths),
but can reduce the input by one parameter if it's a circular gaussian
rotate=1 - default allows rotation of the gaussian ellipse. Can remove
last parameter by setting rotate=0. numpy.expects angle in DEGREES
vheight=1 - default allows a variable height-above-zero, i.e. an
additive constant for the Gaussian function. Can remove first
parameter by setting this to 0
usemoment - can choose which parameters to use a moment estimation for.
Other parameters will be taken from params. Needs to be a boolean
array.
extra_pars - If your psffunction requires extra parameters, pass their
parinfo dictionaries through this variable
Output:
Default output is a set of Gaussian parameters with the same shape as
the input parameters
Can also output the covariance matrix, 'infodict' that contains a lot
more detail about the fit (see scipy.optimize.leastsq), and a message
from leastsq telling what the exit status of the fitting routine was
Warning: Does NOT necessarily output a rotation angle between 0 and 360 degrees.
"""
usemoment = numpy.array(usemoment, dtype='bool')
params = numpy.array(params, dtype='float')
if usemoment.any() and len(params) == len(usemoment):
moment = numpy.array(moments(data, circle, rotate, vheight, **kwargs),
dtype='float')
params[usemoment] = moment[usemoment]
elif params == [] or len(params) == 0:
params = (moments(data, circle, rotate, vheight, **kwargs))
if vheight == 0:
vheight = 1
params = numpy.concatenate([[0], params])
fixed[0] = 1
# mpfit will fail if it is given a start parameter outside the allowed range:
for i in xrange(len(params)):
if params[i] > maxpars[i] and limitedmax[i]: params[i] = maxpars[i]
if params[i] < minpars[i] and limitedmin[i]: params[i] = minpars[i]
if err is None:
errorfunction = lambda p: numpy.ravel((psffunction(p,circle,rotate,vheight)\
(*numpy.indices(data.shape)) - data))
else:
errorfunction = lambda p: numpy.ravel((psffunction(p,circle,rotate,vheight)\
(*numpy.indices(data.shape)) - data)/err)
def mpfitfun(data, err):
if err is None:
def f(p, fjac=None): return [0,numpy.ravel(data-psffunction(p,circle,rotate,vheight)\
(*numpy.indices(data.shape)))]
else:
def f(p, fjac=None): return [0,numpy.ravel((data-psffunction(p,circle,rotate,vheight)\
(*numpy.indices(data.shape)))/err)]
return f
parinfo = []
if vheight:
parinfo.insert(
0, {
'n': 0,
'value': params[0],
'limits': [minpars[0], maxpars[0]],
'limited': [limitedmin[0], limitedmax[0]],
'fixed': fixed[0],
'parname': "HEIGHT",
'error': 0
})
ind = 1
else:
ind = 0
parinfo.append({
'n': 0 + ind,
'value': params[0 + ind],
'limits': [minpars[0 + ind], maxpars[0 + ind]],
'limited': [limitedmin[0 + ind], limitedmax[0 + ind]],
'fixed': fixed[0 + ind],
'parname': "AMPLITUDE",
'error': 0
})
parinfo.append({
'n': 1 + ind,
'value': params[1 + ind],
'limits': [minpars[1 + ind], maxpars[1 + ind]],
'limited': [limitedmin[1 + ind], limitedmax[1 + ind]],
'fixed': fixed[1 + ind],
'parname': "XSHIFT",
'error': 0
})
parinfo.append({
'n': 2 + ind,
'value': params[2 + ind],
'limits': [minpars[2 + ind], maxpars[2 + ind]],
'limited': [limitedmin[2 + ind], limitedmax[2 + ind]],
'fixed': fixed[2 + ind],
'parname': "YSHIFT",
'error': 0
})
parinfo.append({
'n': 3 + ind,
'value': params[3 + ind],
'limits': [minpars[3 + ind], maxpars[3 + ind]],
'limited': [limitedmin[3 + ind], limitedmax[3 + ind]],
'fixed': fixed[3 + ind],
'parname': "XWIDTH",
'error': 0
})
if not (circle):
parinfo.append({
'n': 4 + ind,
'value': params[4 + ind],
'limits': [minpars[4 + ind], maxpars[4 + ind]],
'limited': [limitedmin[4 + ind], limitedmax[4 + ind]],
'fixed': fixed[4 + ind],
'parname': "YWIDTH",
'error': 0
})
if rotate:
parinfo.append({
'n':
5 + ind,
'value':
params[5 + ind],
'limits': [minpars[5 + ind], maxpars[5 + ind]],
'limited': [limitedmin[5 + ind], limitedmax[5 + ind]],
'fixed':
fixed[5 + ind],
'parname':
"ROTATION",
'error':
0
})
if extra_pars:
for P in extra_pars:
parinfo.append(P)
if autoderiv is False:
# the analytic derivative, while not terribly difficult, is less
# efficient and useful. I only bothered putting it here because I was
# instructed to do so for a class project - please ask if you would
# like this feature implemented
raise NotImplementedError(
"I'm sorry, I haven't implemented this feature yet.")
else:
# p, cov, infodict, errmsg, success = optimize.leastsq(errorfunction,\
# params, full_output=1)
mp = mpfit(mpfitfun(data, err), parinfo=parinfo, quiet=quiet)
if returnmp:
returns = (mp)
elif return_parinfo:
returns = (parinfo)
elif return_all is False:
returns = mp.params
elif return_all:
returns = mp.params, mp.perror
if returnfitimage:
fitimage = psffunction(mp.params, circle, rotate,
vheight)(*numpy.indices(data.shape))
returns = (returns, fitimage)
return returns
# p[5]:Omega_bh2
# p[6]:Omega_m
# p[7]:Omega_r
# p[8]:Omega_k
# p[9]... other Cosmological parameters
# initial conditions
print 'Prepare and reading data ...'
p0 = np.array([0.141, 3.099, -19.10, -0.07, 68.34, 0.0221, 0.305, ogh2, 0],
dtype='float64')
n = len(p0)
parbase = {'value': 0., 'fixed': 0, 'limited': [0, 0], 'limits': [0., 0.]}
parinfo = []
for i in range(n):
parinfo.append(copy.deepcopy(parbase))
for i in range(n):
parinfo[i]['value'] = p0[i]
m = mpfit(residual, p0, parinfo=parinfo)
if (m.status <= 0):
print 'error message = ', m.errmsg
chisq = (residual(m.params)[1]**2).sum()
print m.params
print m.perror
def fitspec(specsegments,aperture=None,
modelspec=modelspec,
outpars=False,
vlsrcorr=0,
extinction=False,
parinfo=modelpars(),
quiet=1,
**kwargs):
""" fit a model spectrum
The model is defined internal to fitspec so that parameters can
be fixed based on input parameters """
specsegments = copy(specsegments) # copy.deepcopy(specsegments)
parinfo = copy(parinfo) # copy.deepcopy(parinfo)
kwargs = {'extinction':extinction}
if extinction:
parinfo=modelpars(extinction=extinction)
def fitfun(x,y,err):
return lambda(p): (y-modelspec(x,*p,**kwargs))/err
def mpfitfun(x,y,err):
def f(p,fjac=None): return [0,(y-modelspec(x,*p,**kwargs))/err]
return f
if aperture is not None:
miny,maxy = aperture
fitdata = asarray([ss['data'][miny:maxy,:].sum(axis=0) for ss in specsegments]).ravel()
fiterr = asarray([ss['err'][:]*sqrt(maxy-miny) for ss in specsegments]).ravel() # since it is a summed aperture, add in quadrature
else:
fitdata = asarray([ss['data'] for ss in specsegments]).ravel()
fiterr = asarray([ss['err'] for ss in specsegments]).ravel()
fitwl = asarray([ss['wavelength'] for ss in specsegments]).ravel()
try:
parinfo = parinfo.tolist()
print "Parinfo was an array. No idea why, it was never set to one. Ever."
except:
pass
mp = mpfit(mpfitfun(fitwl,fitdata,fiterr),parinfo=parinfo,quiet=quiet)
mpp = mp.params
mpperr = mp.perror
for i,p in enumerate(mpp):
parinfo[i]['value'] = p
if parinfo[i]['parname'] == 'SHIFT':
print parinfo[i]['parname'],p+vlsrcorr," +/- ",mpperr[i]
else:
print parinfo[i]['parname'],p," +/- ",mpperr[i]
# print "Temperature: ",mpp[0]," Shift: ",mpp[3],mpp[3]*mean(fitwl)/3e5," Width: ",mpp[2],mpp[2]*mean(fitwl)/3e5," Ortho/Para: ",mpp[4]
# print "ERRORS: Temperature: ",mpperr[0]," Shift: ",mpperr[3],mpperr[3]*mean(fitwl)/3e5," Width: ",mpperr[2],mpperr[2]*mean(fitwl)/3e5," Ortho/Para: ",mpperr[4]
print "Chi2: ",mp.fnorm," Reduced Chi2: ",mp.fnorm/len(fitdata)," DOF:",len(fitdata)-len(mpp)
apfitd = {
'params':mpp,
'parerr':mpperr,
'parinfo':parinfo,
'wl':fitwl,
'data':fitdata,
'model':modelspec(fitwl,*mpp),
'err':fiterr
}
if aperture is not None:
for ss in specsegments: ss['data'] = ss['data'][miny:maxy,:].sum(axis=0)
for ss in specsegments: ss['model'] = modelspec(ss['wavelength'],*mpp)
if outpars: return specsegments,apfitd,parinfo
else: return specsegments,apfitd
def brokenpowerfit(xax,
data,
err=None,
alphaguess1=0.0,
alphaguess2=-2.0,
scaleguess=1.0,
breakpoint=None,
quiet=True):
"""
Fit a broken power law (a line in log-space) to data as a function of x
differs from 'plfit' because plfit fits a power law distribution,
this code simply fits a power law
This is a lot more intricate than the simple power law fit, since it involves
fitting two power laws with different slopes
Parameters:
p[0] - scale
p[1] - breakpoint
p[2] - power 1 (xax < breakpoint)
p[3] - power 2 (xax >= breakpoint)
There are 5 parameters (NOT 4) returned because there are two scales that are *NOT*
independent
returns: scale1,scale2,breakpoint,alpha1,alpha2
"""
logdata = np.log10(data)
if err is None: err = np.ones(data.shape, dtype='float')
def brokenpowerlaw(p):
lowerhalf = (np.log10(p[0]) + np.log10(xax) * p[2]) * (xax < p[1])
# find the location at which both functions must be equal
scale2loc = np.argmin(np.abs(xax - p[1]))
scale2 = np.log10(xax[scale2loc]) * (p[2] - p[3]) + np.log10(p[0])
upperhalf = (scale2 + np.log10(xax) * p[3]) * (xax >= p[1])
# DEBUG print "scale1: %15g scale2: %15g xaxind: %5i xaxval: %15g lower: %15g upper: %15g" % (p[0],scale2,scale2loc,np.log10(xax[scale2loc]),lowerhalf[scale2loc-1],upperhalf[scale2loc])
return lowerhalf + upperhalf
def mpfitfun(data, err):
def f(p, fjac=None):
return [0, np.ravel((brokenpowerlaw(p) - data) / err)]
return f
if breakpoint is None: breakpoint = np.median(xax)
parinfo = [{}, {
'mpminstep': xax.min(),
'mpmaxstep': xax.max(),
'step': xax.min()
}, {}, {}]
mp = mpfit.mpfit(mpfitfun(logdata, err),
xall=[scaleguess, breakpoint, alphaguess1, alphaguess2],
quiet=quiet,
parinfo=parinfo)
fitp = mp.params
scale2loc = np.argmin(np.abs(xax - fitp[1]))
scale2 = 10**(np.log10(xax[scale2loc]) * (fitp[2] - fitp[3]) +
np.log10(fitp[0]))
fitp = np.array([fitp[0], scale2] + fitp[1:].tolist())
return fitp, mp
def fit_sed_mpfit_hz(xdata,
flux,
guesses=(0, 0),
err=None,
blackbody_function='blackbody',
quiet=True,
sc=1e20,
**kwargs):
"""
Parameters
----------
xdata : array
Array of the frequencies of the data
flux : array
The fluxes corresponding to the xdata values. Should be in
erg/s/cm^2/Hz
guesses : (Temperature,Column) or (Temperature,Beta,Column)
The input guesses. 3 parameters are used for modified blackbody
fitting, two for temperature fitting.
blackbody_function: str
The blackbody function to fit, either 'blackbody', 'modified', or
'modified_blackbody'
quiet : bool
quiet flag passed to mpfit
sc : float
A numerical parameter to enable the fitter to function properly.
It is unclear what values this needs to take, 1e20 seems to work
by bringing the units from erg/s/cm^2/Hz to Jy, i.e. bringing them
into the "of order 1" regime. This does NOT affect the output *units*,
though it may affect the quality of the fit.
Returns
-------
mp : mpfit structure
An mpfit structure. Access parameters and errors via
`mp.params` and `mp.perror`. The covariance matrix
is in mp.covar.
Examples
--------
>>> from astropy import units as u
>>> import numpy as np
>>> wavelengths = np.array([20,70,160,250,350,500,850,1100]) * u.um
>>> frequencies = wavelengths.to(u.Hz, u.spectral())
>>> temperature = 15 * u.K
>>> column = 1e22 * u.cm**-2
>>> flux = modified_blackbody(frequencies, temperature, beta=1.75,
... column=column)
>>> err = 0.1 * flux
>>> np.random.seed(0)
>>> noise = np.random.randn(frequencies.size) * err
>>> tguess, bguess, nguess = 20.,2.,21.5
>>> bbunit = u.erg/u.s/u.cm**2/u.Hz
>>> mp = fit_sed_mpfit_hz(frequencies.to(u.Hz).value,
... (flux+noise).to(bbunit).value, err=err.to(bbunit).value,
... blackbody_function='modified',
... guesses=(tguess, bguess, nguess))
>>> print(mp.params)
[ 14.99095224 1.78620237 22.05271119]
>>> # T~14.9 K, beta ~1.79, column ~10^22
"""
try:
from agpy import mpfit
except ImportError:
print("Cannot import mpfit: cannot use mpfit-based fitter.")
bbfd = {
'blackbody': _blackbody_hz,
'modified': _modified_blackbody_hz,
'modified_blackbody': _modified_blackbody_hz
}
bbf = bbfd[blackbody_function]
def mpfitfun(x, y, err):
if err is None:
def f(p, fjac=None):
return [0, (y * sc - bbf(x, *p, **kwargs) * sc)]
else:
def f(p, fjac=None):
return [0, (y * sc - bbf(x, *p, **kwargs) * sc) / (err * sc)]
return f
err = err if err is not None else flux * 0.0 + 1.0
mp = mpfit.mpfit(mpfitfun(xdata, flux, err), guesses, quiet=quiet)
return mp
def fit_sed_mpfit_hz(xdata, flux, guesses=(0,0), err=None,
blackbody_function='blackbody', quiet=True, sc=1e20,
**kwargs):
"""
Parameters
----------
xdata : array
Array of the frequencies of the data
flux : array
The fluxes corresponding to the xdata values. Should be in
erg/s/cm^2/Hz
guesses : (Temperature,Column) or (Temperature,Beta,Column)
The input guesses. 3 parameters are used for modified blackbody
fitting, two for temperature fitting.
blackbody_function: str
The blackbody function to fit, either 'blackbody', 'modified', or
'modified_blackbody'
quiet : bool
quiet flag passed to mpfit
sc : float
A numerical parameter to enable the fitter to function properly.
It is unclear what values this needs to take, 1e20 seems to work
by bringing the units from erg/s/cm^2/Hz to Jy, i.e. bringing them
into the "of order 1" regime. This does NOT affect the output *units*,
though it may affect the quality of the fit.
Returns
-------
mp : mpfit structure
An mpfit structure. Access parameters and errors via
`mp.params` and `mp.perror`. The covariance matrix
is in mp.covar.
Examples
--------
>>> from astropy import units as u
>>> import numpy as np
>>> wavelengths = np.array([20,70,160,250,350,500,850,1100]) * u.um
>>> frequencies = wavelengths.to(u.Hz, u.spectral())
>>> temperature = 15 * u.K
>>> column = 1e22 * u.cm**-2
>>> flux = modified_blackbody(frequencies, temperature, beta=1.75,
... column=column)
>>> err = 0.1 * flux
>>> np.random.seed(0)
>>> noise = np.random.randn(frequencies.size) * err
>>> tguess, bguess, nguess = 20.,2.,21.5
>>> bbunit = u.erg/u.s/u.cm**2/u.Hz
>>> mp = fit_sed_mpfit_hz(frequencies.to(u.Hz).value,
... (flux+noise).to(bbunit).value, err=err.to(bbunit).value,
... blackbody_function='modified',
... guesses=(tguess, bguess, nguess))
>>> print(mp.params)
[ 14.99095224 1.78620237 22.05271119]
>>> # T~14.9 K, beta ~1.79, column ~10^22
"""
try:
from agpy import mpfit
except ImportError:
print("Cannot import mpfit: cannot use mpfit-based fitter.")
bbfd = {'blackbody': _blackbody_hz,
'modified': _modified_blackbody_hz,
'modified_blackbody': _modified_blackbody_hz}
bbf = bbfd[blackbody_function]
def mpfitfun(x,y,err):
if err is None:
def f(p,fjac=None):
return [0,(y*sc-bbf(x, *p, **kwargs)*sc)]
else:
def f(p,fjac=None):
return [0,(y*sc-bbf(x, *p, **kwargs)*sc)/(err*sc)]
return f
err = err if err is not None else flux*0.0 + 1.0
mp = mpfit.mpfit(mpfitfun(xdata,flux,err), guesses, quiet=quiet)
return mp
def multigaussfit(xax,
data,
ngauss=1,
err=None,
params=[1, 0, 1],
fixed=[False, False, False],
limitedmin=[False, False, True],
limitedmax=[False, False, False],
minpars=[0, 0, 0],
maxpars=[0, 0, 0],
quiet=True,
shh=True,
veryverbose=False):
"""
An improvement on onedgaussfit. Lets you fit multiple gaussians.
Inputs:
xax - x axis
data - y axis
ngauss - How many gaussians to fit? Default 1 (this could supersede onedgaussfit)
err - error corresponding to data
These parameters need to have length = 3*ngauss. If ngauss > 1 and length = 3, they will
be replicated ngauss times, otherwise they will be reset to defaults:
params - Fit parameters: [amplitude, offset, width] * ngauss
If len(params) % 3 == 0, ngauss will be set to len(params) / 3
fixed - Is parameter fixed?
limitedmin/minpars - set lower limits on each parameter (default: width>0)
limitedmax/maxpars - set upper limits on each parameter
quiet - should MPFIT output each iteration?
shh - output final parameters?
Returns:
Fit parameters
Model
Fit errors
chi2
"""
if len(params) != ngauss and (len(params) / 3) > ngauss:
ngauss = len(params) / 3
if isinstance(params, numpy.ndarray): params = params.tolist()
# make sure all various things are the right length; if they're not, fix them using the defaults
for parlist in (params, fixed, limitedmin, limitedmax, minpars, maxpars):
if len(parlist) != 3 * ngauss:
# if you leave the defaults, or enter something that can be multiplied by 3 to get to the
# right number of gaussians, it will just replicate
if len(parlist) == 3:
parlist *= ngauss
elif parlist == params:
parlist[:] = [1, 0, 1] * ngauss
elif parlist == fixed or parlist == limitedmax:
parlist[:] = [False, False, False] * ngauss
elif parlist == limitedmin:
parlist[:] = [False, False, True] * ngauss
elif parlist == minpars or parlist == maxpars:
parlist[:] = [0, 0, 0] * ngauss
def mpfitfun(x, y, err):
if err is None:
def f(p, fjac=None):
return [0, (y - n_gaussian(pars=p)(x))]
else:
def f(p, fjac=None):
return [0, (y - n_gaussian(pars=p)(x)) / err]
return f
if xax == None:
xax = numpy.arange(len(data))
parnames = {0: "AMPLITUDE", 1: "SHIFT", 2: "WIDTH"}
parinfo = [{
'n': ii,
'value': params[ii],
'limits': [minpars[ii], maxpars[ii]],
'limited': [limitedmin[ii], limitedmax[ii]],
'fixed': fixed[ii],
'parname': parnames[ii % 3] + str(ii % 3),
'error': ii
} for ii in xrange(len(params))]
if veryverbose:
print "GUESSES: "
print "\n".join(
["%s: %s" % (p['parname'], p['value']) for p in parinfo])
mp = mpfit(mpfitfun(xax, data, err), parinfo=parinfo, quiet=quiet)
mpp = mp.params
mpperr = mp.perror
chi2 = mp.fnorm
if mp.status == 0:
raise Exception(mp.errmsg)
if not shh:
print "Final fit values: "
for i, p in enumerate(mpp):
parinfo[i]['value'] = p
print parinfo[i]['parname'], p, " +/- ", mpperr[i]
print "Chi2: ", mp.fnorm, " Reduced Chi2: ", mp.fnorm / len(
data), " DOF:", len(data) - len(mpp)
return mpp, n_gaussian(pars=mpp)(xax), mpperr, chi2
# p[9]... other Cosmological parameters
# initial conditions
print 'Prepare and reading data ...'
p0 = np.array([0.141 ,3.099 ,-19.10 ,-0.07 , 68.34 , 0.0221, 0.305,ogh2, 0],dtype='float64')
n = len(p0)
parbase={'value':0., 'fixed':0, 'limited':[0,0], 'limits':[0.,0.]}
parinfo=[]
for i in range(n):
parinfo.append(copy.deepcopy(parbase))
for i in range(n):
parinfo[i]['value']=p0[i]
m = mpfit(residual, p0, parinfo=parinfo)
if (m.status <= 0):
print 'error message = ', m.errmsg
chisq=(residual(m.params)[1]**2).sum()
print m.params
print m.perror
def psffit(data,err=None,params=[],autoderiv=True,return_all=False,circle=True,
fixed=numpy.repeat(False,7),limitedmin=[False,False,False,False,True,True,True],
limitedmax=[False,False,False,False,False,False,True],
usemoment=numpy.array([],dtype='bool'),
minpars=numpy.repeat(0,7),maxpars=[0,0,0,0,0,0,360],
rotate=0,vheight=1,quiet=True,returnmp=False,
returnfitimage=False,
psffunction=airy,
extra_pars=None,
return_parinfo=False,
**kwargs):
"""
PSF fitter with the ability to fit a variety of different forms of
2-dimensional gaussian OR an Airy.
This code is mostly directly copied from gaussfitter.py and presents
yet another argument for me turning this into a class...
Input Parameters:
data - 2-dimensional data array
err=None - error array with same size as data array
params=[] - initial input parameters for Gaussian function.
(height, amplitude, x, y, width_x, width_y, rota)
if not input, these will be determined from the moments of the system,
assuming no rotation
autoderiv=1 - use the autoderiv provided in the lmder.f function (the
alternative is to us an analytic derivative with lmdif.f: this method
is less robust)
return_all=0 - Default is to return only the Gaussian parameters.
1 - fit params, fit error
returnfitimage - returns (best fit params,best fit image)
returnmp - returns the full mpfit struct
circle=0 - default is an elliptical gaussian (different x, y widths),
but can reduce the input by one parameter if it's a circular gaussian
rotate=1 - default allows rotation of the gaussian ellipse. Can remove
last parameter by setting rotate=0. numpy.expects angle in DEGREES
vheight=1 - default allows a variable height-above-zero, i.e. an
additive constant for the Gaussian function. Can remove first
parameter by setting this to 0
usemoment - can choose which parameters to use a moment estimation for.
Other parameters will be taken from params. Needs to be a boolean
array.
extra_pars - If your psffunction requires extra parameters, pass their
parinfo dictionaries through this variable
Output:
Default output is a set of Gaussian parameters with the same shape as
the input parameters
Can also output the covariance matrix, 'infodict' that contains a lot
more detail about the fit (see scipy.optimize.leastsq), and a message
from leastsq telling what the exit status of the fitting routine was
Warning: Does NOT necessarily output a rotation angle between 0 and 360 degrees.
"""
usemoment=numpy.array(usemoment,dtype='bool')
params=numpy.array(params,dtype='float')
if usemoment.any() and len(params)==len(usemoment):
moment = numpy.array(moments(data,circle,rotate,vheight,**kwargs),dtype='float')
params[usemoment] = moment[usemoment]
elif params == [] or len(params)==0:
params = (moments(data,circle,rotate,vheight,**kwargs))
if vheight==0:
vheight=1
params = numpy.concatenate([[0],params])
fixed[0] = 1
# mpfit will fail if it is given a start parameter outside the allowed range:
for i in xrange(len(params)):
if params[i] > maxpars[i] and limitedmax[i]: params[i] = maxpars[i]
if params[i] < minpars[i] and limitedmin[i]: params[i] = minpars[i]
if err is None:
errorfunction = lambda p: numpy.ravel((psffunction(p,circle,rotate,vheight)\
(*numpy.indices(data.shape)) - data))
else:
errorfunction = lambda p: numpy.ravel((psffunction(p,circle,rotate,vheight)\
(*numpy.indices(data.shape)) - data)/err)
def mpfitfun(data,err):
if err is None:
def f(p,fjac=None): return [0,numpy.ravel(data-psffunction(p,circle,rotate,vheight)\
(*numpy.indices(data.shape)))]
else:
def f(p,fjac=None): return [0,numpy.ravel((data-psffunction(p,circle,rotate,vheight)\
(*numpy.indices(data.shape)))/err)]
return f
parinfo = [ ]
if vheight:
parinfo.insert(0,{'n':0,'value':params[0],'limits':[minpars[0],maxpars[0]],'limited':[limitedmin[0],limitedmax[0]],'fixed':fixed[0],'parname':"HEIGHT",'error':0})
ind = 1
else:
ind = 0
parinfo.append({'n':0+ind,'value':params[0+ind],'limits':[minpars[0+ind],maxpars[0+ind]],'limited':[limitedmin[0+ind],limitedmax[0+ind]],'fixed':fixed[0+ind],'parname':"AMPLITUDE",'error':0})
parinfo.append({'n':1+ind,'value':params[1+ind],'limits':[minpars[1+ind],maxpars[1+ind]],'limited':[limitedmin[1+ind],limitedmax[1+ind]],'fixed':fixed[1+ind],'parname':"XSHIFT",'error':0})
parinfo.append({'n':2+ind,'value':params[2+ind],'limits':[minpars[2+ind],maxpars[2+ind]],'limited':[limitedmin[2+ind],limitedmax[2+ind]],'fixed':fixed[2+ind],'parname':"YSHIFT",'error':0})
parinfo.append({'n':3+ind,'value':params[3+ind],'limits':[minpars[3+ind],maxpars[3+ind]],'limited':[limitedmin[3+ind],limitedmax[3+ind]],'fixed':fixed[3+ind],'parname':"XWIDTH",'error':0})
if not(circle):
parinfo.append({'n':4+ind,'value':params[4+ind],'limits':[minpars[4+ind],maxpars[4+ind]],'limited':[limitedmin[4+ind],limitedmax[4+ind]],'fixed':fixed[4+ind],'parname':"YWIDTH",'error':0})
if rotate:
parinfo.append({'n':5+ind,'value':params[5+ind],'limits':[minpars[5+ind],maxpars[5+ind]],'limited':[limitedmin[5+ind],limitedmax[5+ind]],'fixed':fixed[5+ind],'parname':"ROTATION",'error':0})
if extra_pars:
for P in extra_pars:
parinfo.append(P)
if autoderiv is False:
# the analytic derivative, while not terribly difficult, is less
# efficient and useful. I only bothered putting it here because I was
# instructed to do so for a class project - please ask if you would
# like this feature implemented
raise NotImplementedError("I'm sorry, I haven't implemented this feature yet.")
else:
# p, cov, infodict, errmsg, success = optimize.leastsq(errorfunction,\
# params, full_output=1)
mp = mpfit(mpfitfun(data,err),parinfo=parinfo,quiet=quiet)
if returnmp:
returns = (mp)
elif return_parinfo:
returns = (parinfo)
elif return_all is False:
returns = mp.params
elif return_all:
returns = mp.params,mp.perror
if returnfitimage:
fitimage = psffunction(mp.params,circle,rotate,vheight)(*numpy.indices(data.shape))
returns = (returns,fitimage)
return returns
def fit_blackbody(xdata,
flux,
guesses=(0, 0),
err=None,
blackbody_function=blackbody,
quiet=True,
**kwargs):
"""
Parameters
----------
xdata : array
Array of the X-values (frequency, wavelength) of the data
flux : array
The fluxes corresponding to the xdata values
guesses : (Temperature,Scale) or (Temperature,Beta,Scale)
The input guesses. 3 parameters are used for greybody
fitting, two for temperature fitting.
blackbody_function: function
Must take x-axis (e.g. frequency), temperature, scale, and then
optionally beta args
quiet : bool
quiet flag passed to mpfit
Returns
-------
mp : mpfit structure
An mpfit structure. Access parameters and errors via
`mp.params` and `mp.perror`. The covariance matrix
is in mp.covar.
Examples
--------
>>> wavelength = array([20,70,160,250,350,500,850,1100])
>>> flux = modified_blackbody_wavelength(wavelength, 15, beta=1.75,
logN=22, wavelength_units='microns', normalize=False,
logscale=16)
>>> err = 0.1 * flux
>>> np.random.seed(0)
>>> flux += np.random.randn(len(wavelength)) * err
>>> tguess, bguess, nguess = 20.,2.,21.5
>>> mp = fit_blackbody(wavelength, flux, err=err,
blackbody_function=modified_blackbody_wavelength,
logscale=16, guesses=(tguess, bguess, nguess),
wavelength_units='microns')
>>> print mp.params
[ 14.99095224 1.78620237 22.05271119]
>>> # T~14.9 K, beta ~1.79, column ~10^22
"""
def mpfitfun(x, y, err):
if err is None:
def f(p, fjac=None):
return [
0,
(y -
blackbody_function(x, *p, normalize=False, **kwargs))
]
else:
def f(p, fjac=None):
return [
0,
(y - blackbody_function(
x, *p, normalize=False, **kwargs)) / err
]
return f
err = err if err is not None else flux * 0.0 + 1.0
mp = mpfit.mpfit(mpfitfun(xdata, flux, err), guesses, quiet=quiet)
return mp
def onedgaussfit(xax,
data,
err=None,
params=[0, 1, 0, 1],
fixed=[False, False, False, False],
limitedmin=[False, False, False, True],
limitedmax=[False, False, False, False],
minpars=[0, 0, 0, 0],
maxpars=[0, 0, 0, 0],
quiet=True,
shh=True,
veryverbose=False,
vheight=True,
negamp=False,
usemoments=False):
"""
Inputs:
xax - x axis
data - y axis
err - error corresponding to data
params - Fit parameters: Height of background, Amplitude, Shift, Width
fixed - Is parameter fixed?
limitedmin/minpars - set lower limits on each parameter (default: width>0)
limitedmax/maxpars - set upper limits on each parameter
quiet - should MPFIT output each iteration?
shh - output final parameters?
usemoments - replace default parameters with moments
Returns:
Fit parameters
Model
Fit errors
chi2
"""
def mpfitfun(x, y, err):
if err is None:
def f(p, fjac=None):
return [0, (y - onedgaussian(x, *p))]
else:
def f(p, fjac=None):
return [0, (y - onedgaussian(x, *p)) / err]
return f
if xax == None:
xax = numpy.arange(len(data))
if vheight is False:
height = params[0]
fixed[0] = True
if usemoments:
params = onedmoments(xax,
data,
vheight=vheight,
negamp=negamp,
veryverbose=veryverbose)
if vheight is False: params = [height] + params
if veryverbose:
print "OneD moments: h: %g a: %g c: %g w: %g" % tuple(params)
parinfo = [{
'n': 0,
'value': params[0],
'limits': [minpars[0], maxpars[0]],
'limited': [limitedmin[0], limitedmax[0]],
'fixed': fixed[0],
'parname': "HEIGHT",
'error': 0
}, {
'n': 1,
'value': params[1],
'limits': [minpars[1], maxpars[1]],
'limited': [limitedmin[1], limitedmax[1]],
'fixed': fixed[1],
'parname': "AMPLITUDE",
'error': 0
}, {
'n': 2,
'value': params[2],
'limits': [minpars[2], maxpars[2]],
'limited': [limitedmin[2], limitedmax[2]],
'fixed': fixed[2],
'parname': "SHIFT",
'error': 0
}, {
'n': 3,
'value': params[3],
'limits': [minpars[3], maxpars[3]],
'limited': [limitedmin[3], limitedmax[3]],
'fixed': fixed[3],
'parname': "WIDTH",
'error': 0
}]
mp = mpfit(mpfitfun(xax, data, err), parinfo=parinfo, quiet=quiet)
mpp = mp.params
mpperr = mp.perror
chi2 = mp.fnorm
if mp.status == 0:
raise Exception(mp.errmsg)
if (not shh) or veryverbose:
print "Fit status: ", mp.status
for i, p in enumerate(mpp):
parinfo[i]['value'] = p
print parinfo[i]['parname'], p, " +/- ", mpperr[i]
print "Chi2: ", mp.fnorm, " Reduced Chi2: ", mp.fnorm / len(
data), " DOF:", len(data) - len(mpp)
return mpp, onedgaussian(xax, *mpp), mpperr, chi2
