def generateStatistics(varname, ens, fit, scl=None, reference=None, mode='Ratio', plot_labels=None,
nsamples=None, bootstrap_axis='bootstrap', lflatten=False, sample_axis='time',
lcrossval=True):
''' Perform K-S test and compute ratio of means; return results in formatted string. '''
# some average diagnosics
idkey = 'dataset_name' if ens.basetype is Dataset else 'name'
varlist = Ensemble(*[ds[varname] for ds in ens if ds is not None and varname in ds], idkey=idkey)
if not all(varlist[0].ndim==ndim for ndim in varlist.ndim):
new_axes = varlist[np.argmax(varlist.ndim)].axes
varlist = varlist.insertAxes(new_axes=new_axes, lcheckAxis=False)
mvars = varlist.mean() # growth rate
lratio = mode.lower() == 'ratio'
lshift = mode.lower() == 'shift'
if plot_labels is None: plot_labels = dict()
# figure out fillValue
if np.issubdtype(varlist[0].dtype, np.floating): fillValue = np.NaN
elif np.issubdtype(varlist[0].dtype, np.integer): fillValue = 0
else: raise TypeError(varlist[0].dtype)
# define reference
if isinstance(reference,(list,tuple)):
reflist0 = list(reference); reference = reference[0]
else: reflist0 = [] # dummy list
if reference is None: iref0 = 0
elif isinstance(reference,(int,np.integer)): iref0 = reference
elif isinstance(reference,str): iref0 = varlist.idkeys.index(reference)
else: raise ArgumentError
# goodness of fit, reported on plot panels
if fit:
fitlist = Ensemble(*[ds[varname] for ds in fit if ds is not None and varname in ds], idkey=idkey)
if any(fitlist.hasAxis(bootstrap_axis)): fitlist = fitlist(**{bootstrap_axis:0, 'lcheckAxis':False})
if not all(fitlist[0].ndim==ndim for ndim in fitlist.ndim):
new_axes = fitlist[np.argmax(fitlist.ndim)].axes
fitlist = fitlist.insertAxes(new_axes=new_axes, lcheckAxis=False)
# for var in fitlist:
# print [ax.name for ax in var.axes], var.shape
# assert np.all(fitlist[0][1,:] == fitlist[0][2,:])
assert not isinstance(reference,str) or iref0 == fitlist.idkeys.index(reference), reference
if any([isinstance(dist,VarRV) for dist in fitlist]) or not scl:
names = [plot_labels.get(getattr(dist,idkey),getattr(dist,idkey)) for dist in fitlist]
lnames = max([len(name) for name in names]) # allocate line space
headline = 'Sample'; lhead = len(headline) # sample/exp header
headline += ' '*max(lnames-lhead,0) # 'Exp.'+' '*max(lnames-4,0) if lnames < 8 else 'Experiment'
string = '{:s} Fit {:s}\n'.format(headline,mode.title())
namestr = '{{:>{:d}s}} {{:s}} '.format(max(lhead,lnames))
iref = iref0; reflist = reflist0[:] # copy list
for i,dist,var,name,mvar in zip(range(len(fitlist)),fitlist,varlist,names,mvars):
if isinstance(dist,VarRV) or not scl:
if isinstance(dist,VarRV):
pval = dist.fittest(var, nsamples=nsamples, asVar=False, lcrossval=lcrossval) #lflatten=lflatten, axis_idx=var.axisIndex(sample_axis, lcheck=False))
# print var.name, pval, pval.mean().__class__.__name__, '{:s}'.format(pval.mean())
# pval = '{:3.2f}'.format(float(pval.mean())) # mean is only necessary to convert to scalar
pval = '{:3.2f}'.format(float(np.median(pval))) # mean is only necessary to convert to scalar
# for some reason masked array scalars appear string-type, rather than numbers...
else: pval = ' - '
if len(reflist) > 0 and name == reflist[0]: # assign new reference
iref = i; del reflist[0] # pop element
if isinstance(mvar,np.ma.core.MaskedConstant) or isinstance(mvars[iref],np.ma.core.MaskedConstant):
string += namestr.format(name,' N/A\n')
elif lratio: string += (namestr+'{:3.2f}\n').format(name,pval,(mvar/mvars[iref]).mean())
elif lshift: string += (namestr+'{:+2.1f}\n').format(name,pval,(mvar-mvars[iref]).mean())
else: string = ''
else: raise NotImplementedError
if scl:
scllist = Ensemble(*[ds[varname] for ds in scl if ds is not None and varname in ds], idkey=idkey)
bs_axes = scllist.axisIndex(bootstrap_axis, lcheck=False) # return None, if not present
if bs_axes is None: bs_axes = [None]*len(scllist)
scllist = scllist(**{bootstrap_axis:0, 'lcheckAxis':False})
if not all(scllist[0].ndim==ndim for ndim in scllist.ndim):
new_axes = scllist[np.argmax(scllist.ndim)].axes
scllist = scllist.insertAxes(new_axes=new_axes, lcheckAxis=False)
assert not isinstance(reference,str) or iref0 == scllist.idkeys.index(reference), reference
if len(scllist) != len(varlist): raise AxisError(scllist)
# compute means
mvars = []
for svr,var in zip(scllist,varlist):
if isinstance(svr,VarRV): mvar = svr.stats(moments='mv', asVar=False)[...,0] # only first moment
else: mvar = var.mean()*svr.atts.get('loc_factor',1.)
mvars.append(mvar)
# figure out label width and prepare header
if len(varlist) > 1: # otherwise no comparison...
names = [plot_labels.get(getattr(dist,idkey),getattr(dist,idkey)) for dist in scllist]
lnames = max([len(name) for name in names]) # allocate line space
namestr = '{{:>{:d}s}} {{:s}} '.format(max(lhead,lnames))
tmphead = 'Fit to {:s}:' if scl == fit else 'Rescaled to {:s}:' # new heading
tmphead += ' '*(max(lnames-len(names[iref0]),0)+5)+'\n'
string += tmphead.format(names[iref0])
# prepare first reference sample for K-S test
scale,shape = scllist[iref0].atts.get('scale_factor', 1),scllist[iref0].atts.get('shape_factor', 1)
if not (scale is None or scale == 1) and not (shape is None or shape == 1):
raise NotImplementedError("Cannot rescale scale/variance and shape parameters of reference sample!")
refsmpl = varlist[iref0].getArray(unmask=True, fillValue=fillValue) # only once
loc0 = scllist[iref0].atts.get('loc_factor', 1)
refsmpl = _rescaleSample(refsmpl, loc0, bs_axis=bs_axes[iref0]) # apply rescaling (varies, dependign on loc-type)
# print varlist[iref0].dataset_name, [ax.name for ax in varlist[iref0].axes], refsmpl.shape,
# start loop
iref = iref0; reflist = reflist0[:] # copy list
for i,dist,varsmpl,mvar,bs_axis in zip(range(len(varlist)),scllist,varlist,mvars,bs_axes):
name = getattr(dist,idkey)
if len(reflist) > 0 and name == reflist[0]: # assign new reference
iref = i; del reflist[0] # pop element
# prepare subsequent reference sample for K-S test
scale,shape = dist.atts.get('scale_factor', 1),dist.atts.get('shape_factor', 1)
if not (scale is None or scale == 1) and not (shape is None or shape == 1):
raise NotImplementedError("Cannot rescale scale/variance and shape parameters of reference sample!")
refsmpl = varsmpl.getArray(unmask=True, fillValue=fillValue) # only once
if not varsmpl.atts.get('rescaled',False):
refsmpl = _rescaleSample(refsmpl, dist.atts.get('loc_factor', 1), bs_axis=bs_axis) # apply rescaling (varies, dependign on loc-type)
elif i != iref:
scale,shape = dist.atts.get('scale_factor', 1),dist.atts.get('shape_factor', 1)
# perform K-S test
if (scale is None or scale == 1) and (shape is None or shape == 1):
# K-S test between actual samples is more realistic, and rescaling of mean is simple
smpl = varsmpl.getArray(unmask=True, fillValue=fillValue) # only once
if not varsmpl.atts.get('rescaled',False):
smpl = _rescaleSample(smpl, dist.atts.get('loc_factor', 1), bs_axis=bs_axis) # apply rescaling (varies, dependign on loc-type)
# print varsmpl.dataset_name, [ax.name for ax in varsmpl.axes], smpl.shape
# print smpl.shape, np.nanmean(smpl), refsmpl.shape, np.nanmean(refsmpl)
# print lflatten, sample_axis
pval = ks_2samp(refsmpl, smpl, asVar=False, lflatten=lflatten,
axis_idx=varsmpl.axisIndex(sample_axis, lcheck=False))
# print dist.name, pval
# pval = '{:3.2f}'.format(float(pval.mean()))
pval = '{:3.2f}'.format(float(np.median(pval)))
else:
# no straight-forward way to rescale samples, so have to compare distribution with
# reference sample, which means more noise (since the distribution will be randomly sampled)
if isinstance(dist,VarRV): pval = '{:3.2f}'.format(float(dist.kstest(refsmpl).mean()))
else: pval = ' - '
# add column with ratio/difference of means after rescaling
if name in plot_labels: name = plot_labels[name]
if isinstance(mvar,np.ma.core.MaskedConstant) or isinstance(mvars[iref],np.ma.core.MaskedConstant):
string += namestr.format(name,' N/A\n')
elif lratio: string += (namestr+'{:3.2f}\n').format(name,pval,(mvar/mvars[iref]).mean())
elif lshift: string += (namestr+'{:+2.1f}\n').format(name,pval,(mvar-mvars[iref]).mean())
# return formatted table in string
return string
