def contour_2dfit(x, y, data, fit=None, par=None, nfig=None, interp=True):
""" Create a figure with the fit shown as contours
:param x: input xaxis coordinates - array
:param y: input yaxis coordinates - array (should have the same dim as x)
:param data: input data points (should have the same dim as x)
:param interp: interpolation used or not (Default is True)
:param par: parameters of the fit - Default is None. Only used if interpolation (interp=True) is used
:param fit: fitted points (should have the same dim as x)
:returns: Nothing
"""
from pygme.binning.voronoibinning import derive_unbinned_field, guess_regular_grid
from matplotlib.mlab import griddata
from pygme.mgefunctions import convert_xy_to_polar
from pygme.fitting.fitn2dgauss_mpfit import n_centred_twodgaussian_I
if nfig is None:
fig = plt.gcf()
else:
fig = plt.figure(nfig)
fig.clf()
## If interpolation is requested
if interp:
if fit is None:
print "ERROR: you did not provide 'fit' data"
return
xu, yu = guess_regular_grid(x, y)
du = griddata(x, y, data, xu, yu, interp="nn")
## if par is provided, then we compute the real MGE function
if par is None:
fu = griddata(x, y, fit, xu, yu, interp="nn")
else:
r, t = convert_xy_to_polar(xu, yu)
fu = n_centred_twodgaussian_I(pars=par)(r, t)
fu = fu.reshape(xu.shape)
## Otherwise we just use the nearest neighbour
else:
xu, yu, du = derive_unbinned_field(x, y, data)
xu, yu, fu = derive_unbinned_field(x, y, fit)
CS = plt.contour(xu, yu, np.log10(du), colors="k", label="Data")
CSfit = plt.contour(xu, yu, np.log10(fu), levels=CS.levels, colors="r", label="MGE Fit")
plt.axes().set_aspect("equal")
plt.legend()
def multi_2dgauss_lmfit(xax, yax, data, ngauss=1, err=None, params=None, paramsPSF=None,
fixed=None, limitedmin=None, limitedmax=None, minpars=None,
maxpars=None, force_Sigma_bounds=True, factor_Chi2=1.01, iprint=50, lmfit_method='leastsq',
verbose=True, veryverbose=False, linear_method="nnls", default_q=0.3, default_PA=0.0,
samePA=True, sameQ=False, minSigma=None, maxSigma=None, lmfit_iprint=lmfit_iprint(), **fcnargs):
"""
An improvement on gaussfit. Lets you fit multiple 2D gaussians.
Inputs:
xax - x axis
yax - y axis
data - count axis
ngauss - How many gaussians to fit? Default 1
err - error corresponding to data
These parameters need to have the same length.
It should by default be 3*ngauss.
If ngauss > 1 and length = 3, they will be replicated ngauss times,
otherwise they will be reset to defaults:
params - Fit parameters: [width, axis ratio, pa] * 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
force_Sigma_bounds: force the Sigmas to be within the radii range with some margin
default to True
factor_Chi2 : if one Gaussian contribute less than (factor-1) to the Chi2, we remove it
If set to 1, it means only zero Gaussians will be removed
If set to default=1.01, it means any Gaussian contributing to less than 1% will be
removed
minSigma, maxSigma: default to None but can be set for bounds for Sigma
samePA : by default set to True. In that case, only one PA value is used as a free parameter
(all Gaussians will share the same PA)
sameQ: by default set to False. In that case, only one Axis ratio value is used as a free parameter
(all Gaussians will share the same axis ratio)
lmfit_method : method to pass on to lmfit ('leastsq', 'lbfgsb', 'anneal')
Default is leastsq (most efficient for the problem)
linearmethod: Method used to solve the linear part of the problem
Two methods are implemented:
"nnls" -> NNLS (default, included in scipy)
"bvls" -> LLSP/BVLS in openopt (only if available)
The variable Exist_OpenOpt is (internally) set to True if available
**fcnargs - dictionary which will be passed to LMFIT, you can for example use:
xtol , gtol, ftol, etc
iprint - if > 0, print every iprint iterations of lmfit. default is 50
verbose - self-explanatory
veryverbose - self-explanatory
Returns:
Fit parameters
Model
Fit errors
chi2
"""
import copy
## Default values
lmfit_methods = ['leastsq', 'lbfgsb', 'anneal']
## Method check
if lmfit_method not in lmfit_methods :
print "ERROR: method must be one of the three following methods : ", lmfit_methods
## Setting up epsfcn if not forced by the user
## Removing epsfcn to get the default machine precision
## if "epsfcn" not in fcnargs.keys() : fcnargs["epsfcn"] = 0.01
if "xtol" not in fcnargs.keys() : fcnargs["xtol"] = 1.e-7
if "gtol" not in fcnargs.keys() : fcnargs["gtol"] = 1.e-7
if "ftol" not in fcnargs.keys() : fcnargs["ftol"] = 1.e-7
## Checking the method used for the linear part
if linear_method == "bvls" and not Exist_OpenOpt :
print "WARNING: you selected BVLS, but OpenOpt is not installed"
print "WARNING: we will therefore use NNLS instead"
linear_method == "nnls"
## Checking if the linear_method is implemented
if linear_method.lower() not in dic_linear_methods.keys():
print "ERROR: you should use one of the following linear_method: ", dic_linear_methods.keys()
return 0, 0, 0
f_Get_Iamp = dic_linear_methods[linear_method.lower()]
## If no coordinates is given, create them
if xax is None:
xax = np.arange(len(data))
if yax is None:
yax = np.arange(len(data))
if not isinstance(xax,np.ndarray):
xax = np.asarray(xax)
if not isinstance(yax,np.ndarray):
yax = np.asarray(yax)
if not isinstance(data,np.ndarray):
data = np.asarray(data)
xax = xax.ravel()
yax = yax.ravel()
datashape = data.shape
data = data.ravel()
## Polar coordinates
r, theta = convert_xy_to_polar(xax, yax)
selxy = (xax != 0) & (yax != 0)
rin = sqrt(xax[selxy]**2+yax[selxy]**2)
if minSigma is None : minSigma = np.min(rin)
if maxSigma is None : maxSigma = np.max(rin) / sqrt(SLOPE_outer)
lminSigma = np.log10(minSigma)
lmaxSigma = np.log10(maxSigma)
DlSigma = 0.5 * (lmaxSigma - lminSigma) / ngauss
if isinstance(params,np.ndarray): params=params.tolist()
if params is not None :
if len(params) != ngauss and (len(params) / 3) > ngauss:
ngauss = len(params) / 3
if verbose :
print "WARNING: Your input parameters do not fit the Number of input Gaussians"
print "WARNING: the new number of input Gaussians is: ", ngauss
## Extracting the parameters for the PSF and normalising the Imax for integral = 1
if paramsPSF is None :
paramsPSF = _default_parPSF
paramsPSF = norm_PSFParam(paramsPSF)
## if no input parameters are given, we set up the guess as a log spaced sigma between min and max
default_params = np.concatenate((np.log10(np.logspace(lminSigma + DlSigma, lmaxSigma - DlSigma, ngauss)), \
np.array([default_q]*ngauss), np.array([default_PA]*ngauss))).reshape(3,ngauss).transpose().ravel()
newdefault_minpars = copy.copy(default_minpars)
newdefault_maxpars = copy.copy(default_maxpars)
if force_Sigma_bounds :
newdefault_minpars[0] = lminSigma
newdefault_maxpars[0] = lmaxSigma
else :
newdefault_minpars[0] = lminSigma - np.log10(2.)
newdefault_maxpars[0] = lmaxSigma + np.log10(2.)
## Set up the default parameters if needed
params = set_parameters_and_default(params, default_params, ngauss)
fixed = set_parameters_and_default(fixed, default_fixed, ngauss)
limitedmin = set_parameters_and_default(limitedmin, default_limitedmin, ngauss)
limitedmax = set_parameters_and_default(limitedmax, default_limitedmax, ngauss)
minpars = set_parameters_and_default(minpars, newdefault_minpars, ngauss)
maxpars = set_parameters_and_default(maxpars, newdefault_maxpars, ngauss)
class input_residuals() :
def __init__(self, iprint, verbose) :
self.iprint = iprint
self.verbose = verbose
self.aprint = 0
## -----------------------------------------------------------------------------------------
## lmfit function which returns the residual from the best fit N 2D Gaussians
## Parameters are just sigma,q,pa - the amplitudes are optimised at each step
## -----------------------------------------------------------------------------------------
def opt_lmfit(pars, parPSF, myinput=None, r=None, theta=None, err=None, data=None, f_Get_Iamp=None):
""" Provide the residuals for the lmfit minimiser
for a Multi 1D gaussian
"""
# We retrieve the parameters
pars_array = extract_mult2dG_params(pars)
## Derive the Normalised Gaussians for this set of parameters
nGnorm, Iamp = f_Get_Iamp(pars_array, parPSF, r, theta, data)
if err is None :
res = fitn2dgauss_residuals1(nGnorm, Iamp)
else :
res = fitn2dgauss_residuals_err1(err, nGnorm, Iamp)
# newp = (np.vstack((Iamp, pars_array.transpose()))).transpose()
# if err is None :
# res = fitn2dgauss_residuals(newp, parPSF, r, theta, data)
# else :
# res = fitn2dgauss_residuals_err(newp, parPSF, r, theta, data, err)
lmfit_iprint(res, myinput, pars)
return res
## -----------------------------------------------------------------------------------------
## Information about the parameters
nameParam = ['logSigma', 'Q', 'PA']
Lparams = Parameters()
if verbose :
print "--------------------------------------"
print "GUESS: Sig Q PA"
print "--------------------------------------"
for i in xrange(ngauss) :
print "GAUSS %02d: %8.3e %8.3f %8.3f"%(i+1, 10**(params[3*i]), params[3*i+1], params[3*i+2])
print "--------------------------------------"
for i in xrange(ngauss) :
Lparams.add(nameParam[0]+"%02d"%(i+1), value=params[3*i], min=minpars[3*i], max=maxpars[3*i], vary= not fixed[3*i])
Lparams.add(nameParam[1]+"%02d"%(i+1), value=params[3*i+1], min=minpars[3*i+1], max=maxpars[3*i+1], vary= not fixed[3*i+1])
Lparams.add(nameParam[2]+"%02d"%(i+1), value=params[3*i+2], min=minpars[3*i+2], max=maxpars[3*i+2], vary= not fixed[3*i+2])
## Adding indices to follow up the Gaussians we may remove
Lparams.ind = range(ngauss)
## Setting the samePA option if True
## For this we set up the first PA to the default and
## then use "expr" to say that all other PA are equal to the first one
if samePA:
Lparams = Set_SamePA_params(Lparams, ngauss, params[2], minpars[2], maxpars[2], not fixed[2])
if veryverbose :
for i in xrange(ngauss) :
print "GAUSS %02d: %8.3e %8.3f %8.3f"%(i+1, 10**(params[3*i]), params[3*i+1], params[3*i+2])
if samePA:
print "WARNING: All PAs will be forced to one single value"
print "--------------------------------------"
## Setting up the printing option
myinput = input_residuals(iprint, verbose)
####################################
## Doing the minimisation with lmfit
####################################
if verbose:
print "------ Starting the minimisation -------"
result = minimize(opt_lmfit, Lparams, method=lmfit_method, args=(paramsPSF, myinput, r, theta, err, data, f_Get_Iamp), **fcnargs)
## Remove the Null Gaussians
result.params.ind = range(ngauss)
ngauss, Ind_ZGauss = Remove_Zero_2DGaussians(ngauss, nameParam, result, paramsPSF, r, theta, data, err, factor_Chi2,
f_Get_Iamp, niter=1, verbose=veryverbose, samePA=samePA)
## Recall the Minimizer function for a second iteration to get the new chi2 etc
newresult = minimize(opt_lmfit, result.params, method=lmfit_method, args=(paramsPSF, myinput, r, theta, err, data, f_Get_Iamp), **fcnargs)
## Remove the Null Gaussians
newresult.params.ind = result.params.ind
ngauss, Ind_ZGauss = Remove_Zero_2DGaussians(ngauss, nameParam, newresult, paramsPSF, r, theta, data, err, factor_Chi2,
f_Get_Iamp, niter=2, verbose=veryverbose, samePA=samePA)
## We add the Amplitudes to the array and renormalise them
bestfit_params = extract_mult2dG_params(newresult.params)
nGnorm, Iamp = f_Get_Iamp(bestfit_params, paramsPSF, r, theta, data)
Ibestfit_params = (np.vstack((Iamp, bestfit_params.transpose()))).transpose()
## Changing the parameters back to Sigma
Ibestfit_params[:,1] = 10**(Ibestfit_params[:,1])
Ibestfit_params[:,0] /= (2.0 * Ibestfit_params[:,1]**2 * Ibestfit_params[:,2] * pi)
## And we sort them with Sigma
Ibestfit_params = Ibestfit_params[Ibestfit_params[:,1].argsort()]
if verbose :
print "=================================================="
print "FIT: Imax Sig Q PA"
print "=================================================="
for i in xrange(ngauss) :
print "GAUSS %02d: %8.3e %8.3f %8.3f %8.3f"%(i+1, Ibestfit_params[i,0], Ibestfit_params[i,1], Ibestfit_params[i,2], Ibestfit_params[i,3])
print "Chi2: ",newresult.chisqr," Reduced Chi2: ",newresult.redchi
return Ibestfit_params, newresult, n_centred_twodgaussian_Imax(pars=Ibestfit_params, parPSF=paramsPSF)(r, theta).reshape(datashape)
def multi_2dgauss_mpfit(xax, yax, data, ngauss=1, err=None, params=None, paramsPSF=None,
fixed=None, limitedmin=None, limitedmax=None, minpars=None,
maxpars=None, force_Sigma_bounds=True, factor_Chi2=1.01, verbose=True, veryverbose=False,
linear_method="nnls", default_q=0.3, default_PA=0.0, samePA=True, minSigma=None, maxSigma=None,
mpfitprint=_mpfitprint(), **fcnargs):
"""
An improvement on gaussfit. Lets you fit multiple 2D gaussians.
Inputs:
xax - x axis
yax - y axis
data - count axis
ngauss - How many gaussians to fit? Default 1
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: [width, axis ratio, pa] * 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
force_Sigma_bounds: force the Sigmas to be within the radii range with some margin
default to True
factor_Chi2 : if one Gaussian contribute less than (factor-1) to the Chi2, we remove it
If set to 1, it means only zero Gaussians will be removed
If set to default=1.01, it means any Gaussian contributing to less than 1% will be
removed
minSigma, maxSigma: default to None but can be set for bounds for Sigma
linearmethod: Method used to solve the linear part of the problem
Two methods are implemented:
"nnls" -> NNLS (default, included in scipy)
"bvls" -> LLSP/BVLS in openopt (only if available)
The variable Exist_OpenOpt is (internally) set to True if available
**fcnargs - Will be passed to MPFIT, you can for example use:
xtol, gtol, ftol, quiet
verbose - self-explanatory
veryverbose - self-explanatory
Returns:
Fit parameters
Model
Fit errors
chi2
"""
import copy
## Set up some default parameters for mpfit
if "xtol" not in fcnargs.keys() : fcnargs["xtol"] = 1.e-7
if "gtol" not in fcnargs.keys() : fcnargs["gtol"] = 1.e-7
if "ftol" not in fcnargs.keys() : fcnargs["ftol"] = 1.e-7
if "quiet" not in fcnargs.keys() : fcnargs["quiet"] = True
## Checking the method used for the linear part
if linear_method == "bvls" and not Exist_OpenOpt :
print "WARNING: you selected BVLS, but OpenOpt is not installed"
print "WARNING: we will therefore use NNLS instead"
linear_method == "nnls"
## Checking if the linear_method is implemented
if linear_method.lower() not in dic_linear_methods.keys():
print "ERROR: you should use one of the following linear_method: ", dic_linear_methods.keys()
return 0, 0, 0, 0
f_Get_Iamp = dic_linear_methods[linear_method.lower()]
## If no coordinates is given, create them
if xax is None:
xax = np.arange(len(data))
if yax is None:
yax = np.arange(len(data))
if not isinstance(xax,np.ndarray):
xax = np.asarray(xax)
if not isinstance(yax,np.ndarray):
yax = np.asarray(yax)
if not isinstance(data,np.ndarray):
data = np.asarray(data)
xax = xax.ravel()
yax = yax.ravel()
datashape = data.shape
data = data.ravel()
## Polar coordinates
r, theta = convert_xy_to_polar(xax, yax)
selxy = (xax != 0) & (yax != 0)
rin = sqrt(xax[selxy]**2+yax[selxy]**2)
if minSigma is None : minSigma = np.min(rin)
if maxSigma is None : maxSigma = np.max(rin) / sqrt(SLOPE_outer)
lminSigma = np.log10(minSigma)
lmaxSigma = np.log10(maxSigma)
DlSigma = 0.5 * (lmaxSigma - lminSigma) / ngauss
if isinstance(params,np.ndarray): params=params.tolist()
if params is not None :
if len(params) != ngauss and (len(params) / 3) > ngauss:
ngauss = len(params) / 3
if verbose :
print "WARNING: Your input parameters do not fit the Number of input Gaussians"
print "WARNING: the new number of input Gaussians is: ", ngauss
## Extracting the parameters for the PSF and normalising the Imax for integral = 1
if paramsPSF is None :
paramsPSF = _default_parPSF
paramsPSF = norm_PSFParam(paramsPSF)
## if no input parameters are given, we set up the guess as a log spaced sigma between min and max
default_params = np.concatenate((np.log10(np.logspace(lminSigma + DlSigma, lmaxSigma - DlSigma, ngauss)), \
np.array([default_q]*ngauss), np.array([default_PA]*ngauss))).reshape(3,ngauss).transpose().ravel()
newdefault_minpars = copy.copy(default_minpars)
newdefault_maxpars = copy.copy(default_maxpars)
if force_Sigma_bounds :
newdefault_minpars[0] = lminSigma
newdefault_maxpars[0] = lmaxSigma
else :
newdefault_minpars[0] = lminSigma - np.log10(2.)
newdefault_maxpars[0] = lmaxSigma + np.log10(2.)
## Set up the default parameters if needed
params = set_parameters_and_default(params, default_params, ngauss)
fixed = set_parameters_and_default(fixed, default_fixed, ngauss)
limitedmin = set_parameters_and_default(limitedmin, default_limitedmin, ngauss)
limitedmax = set_parameters_and_default(limitedmax, default_limitedmax, ngauss)
minpars = set_parameters_and_default(minpars, newdefault_minpars, ngauss)
maxpars = set_parameters_and_default(maxpars, newdefault_maxpars, ngauss)
## -------------------------------------------------------------------------------------
## mpfit function which returns the residual from the best fit N 2D Gaussians
## Parameters are just sigma,q,pa - the amplitudes are optimised at each step
## Two versions are available depending on whether BVLS or NNLS is used (and available)
## -------------------------------------------------------------------------------------
def mpfitfun(p, parPSF, fjac=None, r=None, theta=None, err=None, data=None, f_Get_Iamp=None, samePA=False):
if samePA : p = regrow_PA(p)
nGnorm, Iamp = f_Get_Iamp(p, parPSF, r, theta, data)
if err is None :
return [0,fitn2dgauss_residuals1(nGnorm, Iamp)]
else :
return [0,fitn2dgauss_residuals_err1(err, nGnorm, Iamp)]
# newp = (np.vstack((Iamp, p.reshape(ngauss,3).transpose()))).transpose()
# if err is None :
# return [0,fitn2dgauss_residuals(newp, parPSF, r, theta, data)]
# else :
# return [0,fitn2dgauss_residuals_err(newp, parPSF, r, theta, data, err)]
## -------------------------------------------------------------------------------------
## Information about the parameters
if verbose :
print "--------------------------------------"
print "GUESS: Sig Q PA"
print "--------------------------------------"
for i in xrange(ngauss) :
print "GAUSS %02d: %8.3e %8.3f %8.3f"%(i+1, 10**(params[3*i]), params[3*i+1], params[3*i+2])
print "--------------------------------------"
## Information about the parameters
parnames = {0:"LOGSIGMA",1:"AXIS RATIO",2:"POSITION ANGLE"}
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+1)} for ii in xrange(len(params)) ]
## If samePA we remove all PA parameters except the last one
## We could use the 'tied' approach but we prefer setting up just one parameter
if samePA : parinfo = shrink_PA(parinfo)
## Fit with mpfit of q, sigma, pa on xax, yax, and data (+err)
fa = {'parPSF':paramsPSF, 'r': r, 'theta': theta, 'data': data, 'err':err, 'f_Get_Iamp':f_Get_Iamp, 'samePA':samePA}
result = mpfit(mpfitfun, functkw=fa, iterfunct=mpfitprint, nprint=10, parinfo=parinfo, **fcnargs)
## Getting these best fit values into the dictionnary
if samePA : result.params = regrow_PA(result.params)
bestparinfo = [ {'n':ii, 'value':result.params[ii], 'limits':[minpars[ii],maxpars[ii]],
'limited':[limitedmin[ii],limitedmax[ii]], 'fixed':fixed[ii],
'parname':parnames[ii%3]+str(ii/3)} for ii in xrange(len(result.params)) ]
## Recompute the best amplitudes to output the right parameters
## And renormalising them
nGnorm, Iamp = f_Get_Iamp(result.params, paramsPSF, r, theta, data)
# Ibestpar_array = (np.vstack((Iamp, result.params.reshape(ngauss,3).transpose()))).transpose()
bestpar_array = result.params.reshape(ngauss,3)
## Getting rid of the non-relevant Gaussians
## If parameters factor_Chi2 is set we use it as a threshold to remove gaussians
## Otherwise we just remove the zeros
if err is None : nerr = np.ones_like(data)
else : nerr = err
## First get the Chi2 from this round
# bestChi2 = fitn2dgauss_chi2_err(Ibestpar_array, paramsPSF, r, theta, data, nerr)
bestChi2 = np.sum(fitn2dgauss_residuals1(nGnorm, Iamp)**2)
result.ind = range(ngauss)
k = 0
Removed_Gaussians = []
for i in xrange(ngauss) :
## Derive the Chi2 WITHOUT the ith Gaussian
new_nGnorm, new_Iamp = f_Get_Iamp(np.delete(bestpar_array, i, 0), paramsPSF, r, theta, data)
newChi2 = np.sum(fitn2dgauss_residuals1(new_nGnorm, new_Iamp)**2)
# newChi2 = fitn2dgauss_chi2_err(np.delete(Ibestpar_array, i, 0), paramsPSF, r, theta, data, nerr)
## If this Chi2 is smaller than factor_Chi2 times the best value, then remove
## It just means that Gaussian is not an important contributor
if newChi2 <= factor_Chi2 * bestChi2 :
val = bestparinfo.pop(3*k)
val = bestparinfo.pop(3*k)
val = bestparinfo.pop(3*k)
result.ind.pop(k)
Removed_Gaussians.append(i+1)
else : k += 1
if veryverbose :
if len(Removed_Gaussians) != 0 :
print "WARNING Removed Gaussians ", Removed_Gaussians
print "WARNING: (not contributing enough to the fit)"
ngauss = len(result.ind)
## New minimisation after removing all the non relevant Gaussians
if samePA : bestparinfo = shrink_PA(bestparinfo)
newresult = mpfit(mpfitfun, functkw=fa, iterfunct=mpfitprint, nprint=10, parinfo=bestparinfo, **fcnargs)
newresult.ind = range(ngauss)
if samePA : newresult.params = regrow_PA(newresult.params)
bestfit_params = newresult.params.reshape(ngauss, 3)
## We add the Amplitudes to the array and renormalise them
nGnorm, Iamp = f_Get_Iamp(bestfit_params, paramsPSF, r, theta, data)
Ibestfit_params = (np.vstack((Iamp, bestfit_params.transpose()))).transpose()
## Going back to sigma from logsigma
Ibestfit_params[:,1] = 10**(Ibestfit_params[:,1])
Ibestfit_params[:,0] /= (2.0 * Ibestfit_params[:,1]**2 * Ibestfit_params[:,2] * pi)
## And we sort them with Sigma
Ibestfit_params = Ibestfit_params[Ibestfit_params[:,1].argsort()]
if newresult.status == 0:
raise Exception(newresult.errmsg)
if verbose :
print "=================================================="
print "FIT: Imax Sig Q PA"
print "=================================================="
for i in xrange(ngauss) :
print "GAUSS %02d: %8.3e %8.3f %8.3f %8.3f"%(i+1, Ibestfit_params[i,0], Ibestfit_params[i,1], Ibestfit_params[i,2], Ibestfit_params[i,3])
print "Chi2: ",newresult.fnorm," Reduced Chi2: ",newresult.fnorm/len(data)
return Ibestfit_params, newresult, n_centred_twodgaussian_Imax(pars=Ibestfit_params, parPSF=paramsPSF)(r, theta).reshape(datashape)
def plot_2dfit_residuals(x, y, data, fit, PAmin=0.0, PAmax=360.0, nSectors=8, WedgeFactor=1.0, nfig=None, legend=False):
""" Create a figure with the residuals and fit
:param x: input xaxis coordinates - array
:param y: input yaxis coordinates - array (should have the same dim as x)
:param data: input data points (should have the same dim as x)
:param fit: fitted points (should have the same dim as x)
:returns: Nothing
"""
if nfig is None:
fig = plt.gcf()
else:
fig = plt.figure(nfig)
fig.clf()
## Making the arrays as 1D
x_rav = x.ravel()
y_rav = y.ravel()
d_rav = data.ravel()
f_rav = fit.ravel()
lx = len(x_rav)
ly = len(y_rav)
ld = len(d_rav)
lf = len(f_rav)
## checking that the dimensions are correct
if (lx != ld) or (lx != lf) or (lx != ly):
print "ERROR: dimensions for x, y, data, and fit are not the same"
print " (respectively: %d %d %d and %d)" % (lx, ly, ld, lf)
return
## Polar coordinates
r, theta = convert_xy_to_polar(x_rav, y_rav)
theta = np.degrees(theta)
## Selecting the points with respect to their sectors
## And sorting them out
Sample_Theta = np.linspace(PAmin, PAmax, nSectors + 1)
Step_Theta = Sample_Theta[1] - Sample_Theta[0]
Min_Theta = Sample_Theta[:-1] - Step_Theta / WedgeFactor
Max_Theta = Sample_Theta[:-1] + Step_Theta / WedgeFactor
Sel_Theta = []
for i in xrange(nSectors):
newsel = np.argwhere((theta >= Min_Theta[i]) & (theta < Max_Theta[i]))
Sel_Theta.append(newsel)
xmin = np.min(np.abs(r[r > 0.0]))
xmax = np.max(np.abs(r))
plt.ioff()
## Plotting the results using matplotlib
ax01 = fig.add_subplot(nSectors, 2, 1)
ax02 = fig.add_subplot(nSectors, 2, 2)
_plot_1dfit(
ax01,
ax02,
r[Sel_Theta[0]],
d_rav[Sel_Theta[0]],
f_rav[Sel_Theta[0]],
xmin=xmin,
xmax=xmax,
labelx=False,
legend=legend,
)
for i in xrange(1, nSectors - 1):
ax1 = fig.add_subplot(nSectors, 2, 2 * i + 1, sharex=ax01)
ax2 = fig.add_subplot(nSectors, 2, 2 * i + 2, sharex=ax02)
_plot_1dfit(
ax1,
ax2,
r[Sel_Theta[i]],
d_rav[Sel_Theta[i]],
f_rav[Sel_Theta[i]],
xmin=xmin,
xmax=xmax,
labelx=False,
legend=legend,
)
ax1 = fig.add_subplot(nSectors, 2, 2 * nSectors - 1, sharex=ax01)
ax2 = fig.add_subplot(nSectors, 2, 2 * nSectors, sharex=ax02)
_plot_1dfit(
ax1,
ax2,
r[Sel_Theta[i]],
d_rav[Sel_Theta[i]],
f_rav[Sel_Theta[i]],
xmin=xmin,
xmax=xmax,
labelx=True,
legend=legend,
)
plt.ion()
plt.subplots_adjust(hspace=0, bottom=0.08, right=0.98, left=0.1, top=0.98, wspace=0.3)
def bin_to_sectors(x, y, data, **kwargs) :
"""
This routine will bin your data (x, y, data) into sectors defined by
the number (between 0 and 90 degrees) and their width.
Ellipticity : ellipticity (scalar) which will be used for defining the rings
Center : 2 numbers giving the center in X and Y (default is [0.,0.])
PA : position angle measured from top (counter-clockwise, default is -90.0 meaning the X is
already along the abscissa)
NSectors : number of sectors. Default is 19 (to cover 0-90 degrees with 5 degrees sectors)
FactorRadius : factor for sampling the radius. Default is 1.1, which provides about 24 points per decade.
WidthAngle : total Width in degrees of each sector (default is 5)
SymQuad: by default to True. Will thus derive the sectors only from 0 to 90. If set to False, it will
compute the binning in sectors between 0 and 360 degrees.
MinLevel : minimum level for the data to be taken into account (default is -999.0)
MinBinLevel : minimum Binned level for the data to be taken into account (default is 0.)
Gain : in case we need the Poissonian Error to be computed
verbose : default to 0
Return:
xout, yout, dataout, sigmaout
Where xout, yout are the cartesian coordinates of the bins
dataout is the binned value of that bin
sigmaout is the estimated standard deviation
"""
Ellipticity = kwargs.get('Ellipticity', 0.0)
Center = kwargs.get('Center', [0.0,0.0])
MinLevel = kwargs.get('MinLevel', -999.0)
MinBinLevel = kwargs.get('MinBinLevel', 0.0)
PA = kwargs.get('PA', -90.0)
NSectors = kwargs.get('NSectors', 19)
WidthAngle = kwargs.get('WidthAngle', 5.0)
SymQuad = kwargs.get('SymQuad', True)
Gain = kwargs.get('Gain', 1.0)
verbose = kwargs.get('verbose', 0)
## This provides a factor of 1.1 per range
FactorRadius = kwargs.get('FactorRadius', 1.1)
Nradii_per_decade = 1. / np.log10(1.1)
## First check that the sizes of the input coordinates + data are the same
if (np.size(x) != np.size(y)) | (np.size(x) != np.size(data)) :
print "ERROR : please check the sizes of your input arrays -> they should be the same!"
return [0.], [0.], [0.]
## Then selecting the good points
seldata = data > MinLevel
x = x[seldata].ravel()
y = y[seldata].ravel()
data = data[seldata].ravel()
## Checking if all is ok
if np.size(data) == 0 :
print "ERROR : after selecting points above MinLevel (%f), the array is empty!"%(MinLevel)
return [0.], [0.], [0.]
## Then check that the ellipticity is 0 <= eps < 1
if (Ellipticity < 0) | (Ellipticity >= 1) :
print "ERROR : please check your input Ellipticity (%f) as it should be in [0,1[ !"%(Ellipticity)
return [0.], [0.], [0.]
## We first recenter the data
PARadian = np.radians(PA)
rcx, rcy = rotxyC(x, y, cx=Center[0], cy=Center[1], angle=PARadian + np.pi/2.)
## We then convert to polar coordinates with x axis along as abscissa
## If the symmetry is forced we use the absolute values
if SymQuad :
radii, theta = convert_xy_to_polar(np.abs(rcx), np.abs(rcy))
else :
radii, theta = convert_xy_to_polar(rcx, rcy)
## We do the same but using the ellipticity now
qaxis = 1. - Ellipticity
radii_ell, theta_ell = convert_xy_to_polar(rcx, rcy / qaxis)
## ## And getting a log spaced sample
## sample_rell = np.logspace(np.log10(minr_ell), np.log10(maxr_ell), Nradii_per_decade * np.log10(maxr_ell/minr_ell))
## ## Adding the central points with a negative radii
## sample_rell = np.concatenate(([-1.0], sample_rell))
## Now we sample the radii - First getting the minimum and maximum radii
minr_ell, maxr_ell = np.min(radii_ell[np.nonzero(radii_ell)]), np.max(radii_ell)
## We go from minimum to max * 1.1
sampleR = np.logspace(np.log10(minr_ell), np.log10(maxr_ell),
Nradii_per_decade * np.log10(maxr_ell/minr_ell) + 1)
## And add the centre
sampleR = np.concatenate(([-1.0], sampleR))
Nradii = len(sampleR)
## Now we sample the Angles - All following angles in Radian
if SymQuad :
center_Angles = np.linspace(0., np.pi/2., NSectors)
else :
center_Angles = np.linspace(-np.pi / 2., 3. * np.pi / 2., NSectors)
stepAngle = (center_Angles[1] - center_Angles[0]) / 2.
low_Angles = center_Angles - stepAngle
sampleT = np.concatenate((low_Angles, [center_Angles[-1] + stepAngle]))
## Creating the output Angle array by duplicating center_Angles Nradii-1 times
thetaout = np.repeat(center_Angles[np.newaxis,:], Nradii-1, 0)
## Now we select for each sector the right points and compute the new binned data and errors
radout = np.zeros_like(thetaout)
dataout = np.zeros_like(radout) - 999.0
sigmaout = np.zeros_like(radout)
## ################ OLD - SLOW #################################################################################
## def ChoiceMean(x) :
## lx = len(x)
## if lx > 10 : return robust_mean(x)
## elif lx > 0 : return x.mean()
## else : return -999.0
##
## def ChoiceStd(x) :
## lx = len(x)
## if lx > 10 : return robust_mean(x)
## elif lx > 0 : return np.sqrt(Gain * x.sum()) / lx
## else : return -999.0
##
## def ChoiceRadii(x) :
## lx = len(x)
## return np.average(x[:lx/2], weights=x[lx/2:])
##
## if OPTION_Scipy :
## if verbose : print "Using Scipy Version (as scipy 0.11.0 or later is available)"
## dradii_ell = np.concatenate((radii_ell, radii_ell))
## dtheta = np.concatenate((theta, theta))
## ddata = np.concatenate((radii_ell, data))
## dataout = binned_statistic_2d(radii_ell, theta, data, bins=[sampleR, sampleT], statistic=ChoiceMean)[0]
## sigmaout = binned_statistic_2d(radii_ell, theta, data, bins=[sampleR, sampleT], statistic=ChoiceStd)[0]
## radout = binned_statistic_2d(dradii_ell, dtheta, ddata, bins=[sampleR, sampleT], statistic=ChoiceRadii)[0]
## ################ OLD - SLOW #################################################################################
## Counting the number of points per bin
histBins = np.histogram2d(radii_ell, theta, bins=[sampleR, sampleT])[0]
## We use the elliptical radius, but the circular angle
## We now get which bins each point gets into
digitR = np.digitize(radii_ell, sampleR)
digitT = np.digitize(theta, sampleT)
## And we loop over the Sectors
for j in xrange(NSectors) :
if verbose :
print "Section %02d starting"%(j+1)
## We select the bins within that sector
selJ = (digitT == j+1)
dataJ = data[selJ]
radiiJ = radii[selJ]
digitRJ = digitR[selJ]
## We select the bins which have >0 and >10 within that sector
selH0 = np.where((histBins[:,j] > 0) & (histBins[:,j] <= 10))[0]
selH10 = np.where(histBins[:,j] > 10)[0]
## Then we make the calculation for the two species
## The ones which have more than 10 points and the ones which have at
## least one point.
for i in selH0 :
spoints = (digitRJ == i+1)
dataS = dataJ[spoints]
radout[i, j] = np.average(radiiJ[spoints], weights=dataS)
dataout[i,j] = dataS.mean()
sigmaout[i,j] = np.sqrt(Gain * dataS.sum()) / histBins[i,j]
for i in selH10 :
spoints = (digitRJ == i+1)
dataS = dataJ[spoints]
radout[i, j] = np.average(radiiJ[spoints], weights=dataS)
dataout[i,j] = robust_mean(dataS)
sigmaout[i,j] = robust_sigma(dataS)
## Final selection without the negative points
selfinal = (dataout > -999) & (dataout > MinBinLevel)
## Finally converting it back to x, y
xout, yout = convert_polar_to_xy(radout[selfinal], thetaout[selfinal] + np.pi/2. + PARadian)
return xout, yout, dataout[selfinal], sigmaout[selfinal]