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SloppyScaling.py
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SloppyScaling.py
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import scipy
import pylab
import copy
from scipy import exp
import scipy.optimize
import scipy.special
import WindowScalingInfo as WS
reload(WS)
class ScalingTheory:
"""
A ScalingTheory's job is to provide a function Y(X) that predicts
theory for an experiment, given a set of independent variables and
parameters. The independent variables are those specifying the Data
being described; the parameters describe universal critical
exponents, universal scaling functions, and analytic
and singular corrections to scaling.
The theory is represented in a string consisting of a Python command.
The variables are unpacked on the fly and the string is executed...
For application convenience, you may use the natural variables for
X and Y (say, 'S' and 'A') in the expressions, and set Xname and Yname
appropriately.
#
Example of implementation:
sizeHisto = ScalingTheory('S**(-tau)*scipy.exp((-(S*(R-Rc)**sigma)/XS)**nS)',
'tau, sigma, XS, nS, Rc', (1.5,0.5,1.0,1.0,2.0),
independentNames = 'R',
scalingX = 'S*r**sigma', scalingY = 'D*S**tau',
scalingXTeX = r'$S r^\sigma$',
scalingYTeX = r'$D S^\tau$',
title= 'Avalanche histo$'
scalingTitle= 'Avalanche histo scaling plot'
Xname = 'S', XscaledName='Ss', Yname = 'D', normalization = True)
"""
def __init__(self, Ytheory, parameterNames, initialParameterValues, \
independentNames, \
scalingX = 'X', scalingY = 'Y', scalingW = None, \
scalingXTeX = r'${\cal{X}}$', \
scalingYTeX = r'${\cal{Y}}$', \
title = 'Fit', scalingTitle = 'Scaling Collapse',
Xname='X', XscaledName = 'Xs', Yname='Y', WscaledName = 'Ws',\
heldParameterBool = False, heldParameterList = "", heldParameterPass = False,
normalization = None):
#YJC: added WscaledName = 'Ws' and scalingW =None to theory
# to make the scaling function easier to read, need to keep default none for scalingW,
#because some theories don't have this second variable
#YJC: want to make the scaling variables a list? So we can specify as many as we want
self.Ytheory = Ytheory
self.parameterNames = parameterNames
self.parameterNameList = parameterNames.split(",")
self.initialParameterValues = initialParameterValues
self.parameterNames0 = parameterNames
self.parameterNameList0 = self.parameterNameList
self.initialParameterValues0 = initialParameterValues
self.independentNames = independentNames
self.Xname = Xname
self.XscaledName = XscaledName
self.Yname = Yname
self.WscaledName = WscaledName
self.scalingX = scalingX
self.scalingY = scalingY
self.scalingW = scalingW
self.scalingXTeX = scalingXTeX
self.scalingYTeX = scalingYTeX
self.title = title
self.scalingTitle = scalingTitle
self.normalization = normalization
self.heldParameterBool = heldParameterBool
self.heldParameterPass = heldParameterPass
def Y(self, X, parameterValues, independentValues):
"""
Predicts Y as a function of X
"""
# Set values of parameters based on vector of current guess
# Set values of independent variables based on which curve is being fit
# Set up vector of independent variable from X
# Warning: local variables in subroutine must be named
# 'parameterValues', 'independentValues', and 'X'
exec(self.parameterNames + " = parameterValues")
exec(self.independentNames + " = independentValues")
if self.heldParameterBool:
for par, val in self.heldParameterList:
exec(par + " = " + str(val))
exec(self.Xname + ' = X')
if self.XscaledName:
exec(self.XscaledName +'='+ self.scalingX)
#YJC: added scalingW here
if self.scalingW:
exec(self.WscaledName +"="+ self.scalingW)
exec("Y = " + self.Ytheory)
if self.normalization:
fn = getattr(self, self.normalization)
Y = fn(X, Y, parameterValues, independentValues)
return Y
def ScaleX(self, X, parameterValues, independentValues):
"""
Rescales X according to scaling form
"""
# Set values of parameters, independent variables, and X vector
# Warning: local variables in subroutine must be named
# 'parameterValues', 'independentValues', and 'X'
exec(self.parameterNames + " = parameterValues")
exec(self.independentNames + " = independentValues")
if self.heldParameterBool:
for par, val in self.heldParameterList:
exec(par + " = " + str(val))
exec(self.Xname + " = X")
#YJC: added scalingW here too
if self.scalingW is not None:
exec(self.WscaledName + '=' +self.scalingW)
exec("XScale = " + self.scalingX)
return XScale
def ScaleY(self, X, Y, parameterValues, independentValues):
"""
Rescales Y according to form
"""
# Set values of parameters, independent variables, and X vector
# Warning: local variables in subroutine must be named
# 'parameterValues', 'independentValues', and 'X'
exec(self.parameterNames + " = parameterValues")
exec(self.independentNames + " = independentValues")
if self.heldParameterBool:
for par, val in self.heldParameterList:
exec(par + " = " + str(val))
exec(self.Xname + " = X")
#YJC: added scalingW here too
if self.scalingW is not None:
exec(self.WscaledName + '=' +self.scalingW)
if self.XscaledName:
exec(self.XscaledName + "="+self.scalingX)
exec(self.Yname + " = Y")
exec("YScale = " + self.scalingY)
return YScale
def reduceParameters(self,pNames,pValues,heldParams):
list_params = pNames.split(",")
list_initials = list(pValues)
for param_to_remove, val in heldParams:
try:
index = list_params.index(param_to_remove)
list_params.pop(index)
list_initials.pop(index)
except ValueError:
print "Warning: parameter ", param_to_remove, " NOT included in the list"
return ",".join(list_params), tuple(list_initials)
def HoldFixedParams(self, heldParameters):
"""
Sets parameters to fixed values.
heldParameters is a list of tuple(s) of the type:
[('param1', val1), ('param2', val2)]
"""
if heldParameters:
self.heldParameterBool = True
pNames, pValues = \
self.reduceParameters(self.parameterNames0, \
self.initialParameterValues0, \
heldParameters)
self.parameterNames = pNames
self.parameterNameList = pNames.split(",")
self.initialParameterValues = pValues
self.heldParameterList = heldParameters
self.heldParameterBool = True
self.heldParameterPass = True
else:
# Check if some parameters have been held before, and reset
if self.heldParameterPass:
self.parameterNames=self.parameterNames0
self.parameterNameList = self.parameterNameList0
self.initialParameterValues = self.initialParameterValues0
self.heldParameterBool = False
self.heldParameterList = None
#
# Various options for normalization
#
def NormBasic(self, X, Y, parameterValues, independentValues):
"""
Must guess at bin sizes for first and last bins
"""
norm = Y[0]*(X[1]-X[0])
norm += sum(Y[1:-1] * (X[2:]-X[:-2])/2.0)
# GF: Why not this below?
#norm += sum(Y[1:-2] * (X[2:-1]-X[:-3])/2.0)
norm += Y[-1]*(X[-1]-X[-2])
return Y/norm
def NormIntegerSum(self, X, Y, parameterValues, independentValues, \
xStart=1., xEnd=1024.):
"""
Function summed over positive integers equals one; brute force
up to xEnd
"""
x = scipy.arange(xStart, xEnd)
return Y/sum(self.Y(x, parameterValues, independentValues))
def NormLog(self,X,Y,parameterValues, independentValues):
"""
This kind of normalization is correct
if the data are uniform in log scale,
as prepared by our code toBinDistributions.py
"""
lgX = scipy.log10(X)
D = scipy.around(lgX[1] - lgX[0],2)
bins = 10**(lgX+D/2.) - 10**(lgX-D/2.)
return Y/sum(Y*bins)
class Data:
"""
A Data object contains a series of curves each for a set of independent
control parameters. For example, the X values might be avalanche sizes
(Xname = 'S'), the Y values might be percentage area covered by
avalalanches of that size (Yname = 'A'),
the sigmas the standard errors in the means, and an independent control
parameters might be the demagnetizing field (independent = 'k'). If,
as for A(S), the data plots are typically log-log set self.linlog = 'log';
for things like V(t,T) set self.linlog = 'lin'.
"""
def __init__(self, linlog = 'log'):
self.experiments = []
self.X = {}
self.Y = {}
self.linlog = linlog
self.pointType = {}
self.errorBar = {}
self.fileNames = {}
self.defaultFractionalError = {}
self.initialSkip = {}
def InstallCurve(self, independent, fileName, defaultFractionalError = 0.1,\
pointSymbol="o", pointColor="b", \
xCol=0, yCol=1, errorCol = 2, initialSkip = 0, factorError = 10.0):
"""
Curves for independent control parameters given by "independent"
loaded from "fileName". Plots use, for example, pointSymbol from
['o','^','v','<','>','s', 'p', 'h','+','x']
and pointColor from
['b','g','r','c','m','burlywood','chartreuse']
factorError is to artificially increase error bars for better fits
"""
# check if independent is a tuple
if not isinstance(independent, tuple):
print "Warning: the independent variable is not a tuple"
independent = tuple(independent)
#
self.experiments.append(independent)
self.fileNames[independent] = fileName
self.initialSkip[independent] = initialSkip
self.pointType[independent] = pointColor + pointSymbol
self.defaultFractionalError[independent] = defaultFractionalError
try:
infile = open(fileName, 'r')
lines = infile.readlines()
infile.close()
success = 1
numbers = [line.split() for line in lines]
self.X[independent] = scipy.array( \
[float(line[xCol]) for line in numbers])
self.Y[independent] = scipy.array( \
[float(line[yCol]) for line in numbers])
if not errorCol:
self.errorBar[independent] = \
scipy.array([float(line[errorCol])*factorError for line in numbers])
else:
self.errorBar[independent] = \
self.Y[independent] * defaultFractionalError
except IOError:
print "File %s not found"%fileName
success = 0
return success
class Model:
"""
A Model object unites Theory with Data. It's primary task is to
calculate the residuals (the difference between theory and data)
and the cost.
"""
def __init__(self, theory, data, name, sorting):
self.theory = theory
self.data = data
self.name = name
self.sorting = sorting
def Residual(self, parameterValues, dictResidual=False):
"""
Calculate the weighted residuals,
with the weights = 1 / errorbar
"""
if dictResidual:
residuals = {}
else:
residuals = scipy.array([])
for independentValues in self.data.experiments:
initialSkip = self.data.initialSkip[independentValues]
X = self.data.X[independentValues][initialSkip:]
Y = self.data.Y[independentValues][initialSkip:]
errorBar = self.data.errorBar[independentValues][initialSkip:]
Ytheory = self.theory.Y(X, parameterValues, independentValues)
# XXX Likely a better way to merge scipy arrays into big one
# Yes: there is
res = (Ytheory-Y)/errorBar
if dictResidual:
residuals[independentValues] = res
else:
residuals = scipy.concatenate((residuals,res))
return residuals
def Cost(self, parameterValues=None):
"""
Sum of the squares of the residuals
"""
if parameterValues is None:
parameterValues = self.theory.initialParameterValues
residuals = self.Residual(parameterValues)
return sum(residuals*residuals)
def SST(self, parameterValues=None):
"""
SST is the sum of the squares about the mean
"""
sst = 0.
if parameterValues is None:
parameterValues = self.theory.initialParameterValues
for independentValues in self.data.experiments:
initialSkip = self.data.initialSkip[independentValues]
Y = self.data.Y[independentValues][initialSkip:]
errorBar = self.data.errorBar[independentValues][initialSkip:]
sst_partial = (Y-scipy.mean(Y))/errorBar
sst += sum(sst_partial*sst_partial)
return sst
def R_square(self,parameterValues=None):
"""
Calculates the R-square = 1 - cost / SST
where SST is the sum of the squares about the mean
"""
sst = self.SST(parameterValues)
cost = self.Cost(parameterValues)
return 1.- cost/sst
def getLabel(self, names, values, withRescale = False, sigma = 0.387):
"""
Get the Labels to be plotted.
"""
#lb_name = (names[-1] == ',') and names[:-1] or names[-1]
lb = names + " = "
lb += ",".join([str(i) for i in values])
if withRescale:
for nm, val in zip(a,b):
exec(nm + "= " + str(val))
if len(values) == 2:
lb += str(1.0*k/L)
elif len(values) == 3:
lb += str((1.0*k/L)**sigma*W)[0:5]
return lb
def getAxis(self,X,Y):
"""
return the proper axis limits for the plots
"""
out = []
mM = [(min(X),max(X)),(min(Y),max(Y))]
for i,j in mM:
#YJC: checking if values are negative, if yes, return 0 and break
if j <0 or i <0:
return 0
log_i = scipy.log10(i)
d, I = scipy.modf(log_i)
if log_i < 0:
add = 0.5 *(scipy.absolute(d)<0.5)
else:
add = 0.5 *(scipy.absolute(d)>0.5)
m = scipy.floor(log_i) + add
out.append(10**m)
log_j = scipy.log10(j)
d, I = scipy.modf(log_j)
if log_j < 0:
add = - 0.5 *(scipy.absolute(d)>0.5)
else:
add = - 0.5 *(scipy.absolute(d)<0.5)
m = scipy.ceil(log_j) + add
out.append(10**m)
return tuple(out)
def PlotFunctions(self, parameterValues=None, plotCollapse = False,
fontSizeLabels = 18, fontSizeLegend=12, pylabLegendLoc=(0.,0.)):
if parameterValues is None:
parameterValues = self.theory.initialParameterValues
# XXX Having problems with pylab.ioff()
pylab.ioff()
pylab.clf()
ax0 = [1.e99,0,1.e99,0]
if self.data.linlog == 'log':
minY = 1.e99
for independentValues in self.data.experiments:
Y = self.data.Y[independentValues]
if plotCollapse:
X = self.data.X[independentValues]
Y = self.theory.ScaleY(X,Y,parameterValues,\
independentValues)
minY = min(minY,min(Y))
#pylab.plot([],label=r'$win (k/L)^{\sigma_k \zeta}$')
if self.sorting:
# preserve order of values as provided
# by Utils.get_independent
data_experiments = self.data.experiments
else:
# set sorted
data_experiments = sorted(self.data.experiments)
for independentValues in data_experiments:
X = self.data.X[independentValues]
Y = self.data.Y[independentValues]
Ytheory = self.theory.Y(X, parameterValues, independentValues)
pointType = self.data.pointType[independentValues]
errorBar = self.data.errorBar[independentValues]
if plotCollapse:
# Scaled error bars and Y need not-rescaled X
errorBar = self.theory.ScaleY(X, errorBar, parameterValues, \
independentValues)
Y = self.theory.ScaleY(X, Y, parameterValues, independentValues)
Ytheory = self.theory.ScaleY(X, Ytheory, \
parameterValues, independentValues)
# Then rescale X too
X = self.theory.ScaleX(X, parameterValues, independentValues)
# Avoid error bars crossing zero on log-log plots
if self.data.linlog == 'log':
errorBarDown = errorBar * (errorBar < Y) + (Y -minY) * (errorBar > Y)
y_error=[errorBarDown,errorBar]
else:
y_error=errorBar
# Prepare the labels
lb = self.getLabel(self.theory.independentNames, independentValues)
pylab.rcParams.update({'legend.fontsize':fontSizeLabels})
#####################
if self.data.linlog == 'log' or self.data.linlog == 'lin':
if self.data.linlog == 'log':
plot_fn = getattr(pylab,'loglog')
elif self.data.linlog == 'lin':
plot_fn = getattr(pylab,'plot')
# Plot first data with their error
plot_fn(X,Y,pointType[1])
pylab.errorbar(X,Y, yerr=y_error, fmt=pointType,label=lb)
axis_dep = self.getAxis(X,Y)
# Get the current values of the axis
# YJC: some values of binned data are negative, modified getAxis to check, and return 0 if negative values encountered
if axis_dep ==0:
print "this data set has negative values", independentValues
print "\n"
for i, Ax in enumerate(axis_dep):
ax0[i] = i%2 and max(ax0[i],Ax) or min(ax0[i],Ax)
# Plot the theory function
plot_fn(X,Ytheory,pointType[0])
else:
print "Format " + self.data.linlog + \
" not supported yet in PlotFits"
pylab.axis(tuple(ax0))
#pylab.legend(loc=pylabLegendLoc, col=2)
pylab.legend(loc=pylabLegendLoc)
if plotCollapse:
pylab.xlabel(self.theory.scalingXTeX, fontsize=fontSizeLabels)
pylab.ylabel(self.theory.scalingYTeX, fontsize=fontSizeLabels)
pylab.title(self.theory.scalingTitle)
else:
pylab.xlabel(self.theory.Xname, fontsize=fontSizeLabels)
pylab.ylabel(self.theory.Yname, fontsize=fontSizeLabels)
pylab.title(self.theory.title, fontsize=fontSizeLabels)
# XXX Turn on if ioff used pylab.ion()
pylab.ion()
pylab.show()
def PlotResiduals(self, parameterValues=None, \
fontSizeLabels = 18, pylabLegendLoc=(0.2,0.)):
if parameterValues is None:
parameterValues = self.theory.initialParameterValues
pylab.ioff()
pylab.clf()
residuals = self.Residual(parameterValues, dictResidual=True)
x0 = 0
for independentValues in sorted(residuals):
res = residuals[independentValues]
xStep = len(res)
x = range(x0,x0+xStep)
x0 += xStep
pointType = self.data.pointType[independentValues]
lb = self.getLabel(self.theory.independentNames, independentValues)
pylab.plot(x,res,pointType, label=lb)
pylab.ylabel("Weighted residuals")
pylab.axhline(y=0,color='k')
pylab.legend(loc=pylabLegendLoc)
pylab.ion()
pylab.show()
def BestFit(self,initialParameterValues = None):
if initialParameterValues is None:
initialParameterValues = self.theory.initialParameterValues
out = scipy.optimize.minpack.leastsq(self.Residual, \
initialParameterValues, full_output=1, ftol=1.e-16)
return out
def PlotBestFit(self, initialParameterValues = None, \
figFit = 1, figCollapse=2, fontSizeLabels=18, heldParams = None):
#YJC: added abilitiy to set fixedParams for this, and also modified output to match what is done in composite theory
if heldParams:
if not isinstance(heldParams, list):
heldParams=[heldParams]
#Check now if the name is correct
l_index=[]
for index, par in enumerate(heldParams):
pName, pValue = par
if pName not in self.theory.parameterNameList0:
print "%s is not a valid name. Ignored" %pName
l_index.append(index)
if l_index:
for i in l_index:
heldParams.pop(i)
# Call setHeldParams even if heldParams=None to
# check if original Names and values have to be used
self.theory.HoldFixedParams(heldParams)
if initialParameterValues is None:
initialParameterValues = self.theory.initialParameterValues
print 'initial cost = ', self.Cost(initialParameterValues)
optimizedParameterValues = self.BestFit(initialParameterValues)[0]
covar = self.BestFit(initialParameterValues)[1]
errors = [covar[i,i]**0.5 for i in range(len(covar))]
print 'optimized cost = ', self.Cost(optimizedParameterValues)
print 'R-value = ', self.R_square(optimizedParameterValues)
if heldParams:
print "====== Held Parameters ======"
for pName, pValue in heldParams:
print "%s = %2.2f" %(pName, pValue)
print "====== Fitted Parameters (with one sigma error) ======"
for name, val, error in \
zip(self.theory.parameterNameList,optimizedParameterValues, errors):
print name + "= %2.4f +/- %2.4f" %(val, error)
print "======================================================"
pylab.figure(figFit)
self.PlotFunctions(optimizedParameterValues)
pylab.figure(figCollapse)
self.PlotFunctions(optimizedParameterValues, plotCollapse = True)
#YJC: need to call these twice to show figures properly
pylab.figure(figFit)
pylab.figure(figCollapse)
return optimizedParameterValues
class CompositeModel:
"""
Class combining several Models into one
The main job of CompositeModel is to combine the parameter lists and
initial values into a single structure, and then to impose that structure
on the individual theories.
Also, plots and stuff should be delegated to the individual theories.
"""
class CompositeTheory:
def __init__(self):
self.parameterNames = ""
self.initialParameterValues = []
self.parameterNameList = []
def __init__(self, name):
self.Models = {}
self.theory = self.CompositeTheory()
self.name = name
self.heldParamsPass = False
def InstallModel(self,modelName, model):
self.Models[modelName] = model
th = self.theory
for param, init in zip(model.theory.parameterNameList, \
model.theory.initialParameterValues):
if param not in th.parameterNameList:
th.parameterNameList.append(param)
th.initialParameterValues.append(init)
else:
# Check if shared param has consistent initial value
# between models
paramCurrentIndex = th.parameterNameList.index(param)
paramCurrentInitialValue = \
th.initialParameterValues[paramCurrentIndex]
if paramCurrentInitialValue != init:
print "Initial value %f"%(init,) \
+ " for parameter " + param + " in model " + modelName \
+ " \n disagrees with value %f"%(paramCurrentInitialValue)\
+ " already stored for previous theory in " \
+ " CompositeTheory.\n Ignoring new value."
th.parameterNames = ",".join(th.parameterNameList)
#th.initialParameterValues = tuple(th.initialParameterValues)
#
# Update list of parameter names and values for all attached models
#
for currentModel in self.Models.values():
currentModel.theory.parameterNames=th.parameterNames
currentModel.theory.parameterNames0=th.parameterNames
currentModel.theory.parameterNameList=th.parameterNameList
currentModel.theory.parameterNameList0=th.parameterNameList
currentModel.theory.initialParameterValues=tuple(th.initialParameterValues)
currentModel.theory.initialParameterValues0=tuple(th.initialParameterValues)
#
# Remember original Names and values
th.initialParameterValues0 = copy.copy(th.initialParameterValues)
th.parameterNames0 = copy.copy(th.parameterNames)
th.parameterNameList0 = copy.copy(th.parameterNameList)
def reduceParameters(self,pNames,pValues,heldParams):
list_params = pNames.split(",")
list_initials = list(pValues)
for param_to_remove, val in heldParams:
try:
index = list_params.index(param_to_remove)
list_params.pop(index)
list_initials.pop(index)
except ValueError:
print "Warning: parameter ", param_to_remove, " NOT included in the list"
return ",".join(list_params), tuple(list_initials)
def HoldFixedParams(self, heldParameters):
"""
Sets parameters in fixedParamNames to their initial values,
and updates the parameter values, names of the composite model
heldParameters is a list of tuple(s) of the type: [('par1', val1)]
"""
th = self.theory
if heldParameters:
pNames, pValues = self.reduceParameters(th.parameterNames0,\
th.initialParameterValues0,\
heldParameters)
th.parameterNames = pNames
th.parameterNameList = pNames.split(",")
th.initialParameterValues = pValues
for currentModel in self.Models.values():
currentModel.theory.heldParameterBool = True
currentModel.theory.HoldFixedParams(heldParameters)
self.heldParamsPass = True
else:
if self.heldParamsPass:
th.parameterNames = th.parameterNames0
th.parameterNameList = th.parameterNameList0
th.initialParameterValues = th.initialParameterValues0
for currentModel in self.Models.values():
currentModel.theory.parameterNames=th.parameterNames0
currentModel.theory.parameterNameList=th.parameterNameList0
currentModel.theory.initialParameterValues=th.initialParameterValues0
currentModel.theory.heldParameterBool = False
currentModel.theory.heldParameterList = None
def Residual(self, parameterValues):
residuals = scipy.array([])
for model in self.Models.values():
modelResidual = model.Residual(parameterValues)
residuals = scipy.concatenate((residuals,modelResidual))
return residuals
def Cost(self, parameterValues=None):
if parameterValues is None:
parameterValues = self.theory.initialParameterValues
residuals = self.Residual(parameterValues)
return sum(residuals*residuals)
#return sum(scipy.absolute(residuals))
def SST(self, parameterValues=None):
sst = 0.
for model in self.Models.values():
sst += model.SST(parameterValues)
return sst
def R_square(self,parameterValues):
"""
Calculates the R-square = 1 - cost / SST
where SST is the sum of the squares about the mean
"""
sst = self.SST(parameterValues)
cost = self.Cost(parameterValues)
return 1.- cost/sst
def PlotFits(self, parameterValues=None, \
fontSizeLabels = 18, pylabLegendLoc=(0.2,0.), figNumStart=1):
if parameterValues is None:
parameterValues = self.theory.initialParameterValues
figNum = figNumStart-1
for model in self.Models.values():
figNum+=1
pylab.figure(figNum)
model.PlotFits(parameterValues, fontSizeLabels, pylabLegendLoc)
# Weird bug: repeating figure needed to get to show
pylab.figure(figNum)
def PlotCollapse(self, parameterValues=None, \
fontSizeLabels = 18, pylabLegendLoc=(0.2,0.), figNumStart=1):
if parameterValues is None:
parameterValues = self.theory.initialParameterValues
figNum = figNumStart-1
for model in self.Models.values():
figNum+=1
pylab.figure(figNum)
model.PlotFunctions(parameterValues, fontSizeLabels, \
pylabLegendLoc, plotCollapse = True)
pylab.figure(figNum)
def BestFit(self,initialParameterValues=None):
if initialParameterValues is None:
initialParameterValues = self.theory.initialParameterValues
out = scipy.optimize.minpack.leastsq(self.Residual, \
initialParameterValues, full_output=1, ftol = 1e-16)
return out
def PlotBestFit(self, initialParameterValues=None, \
figNumStart = 1, heldParams = None):
# Unicode characters
uniSymbol = {'tau': unichr(964), 'sigma_k': unichr(963)+"_k",\
'zeta': unichr(950)}
if heldParams:
if not isinstance(heldParams, list):
heldParams = [heldParams]
# Check now if the name is correct
l_index = []
for index, par in enumerate(heldParams):
pName, pValue = par
if pName not in self.theory.parameterNameList0:
print "%s is not a valid name. Ignored" % pName
l_index.append(index)
if l_index:
for i in l_index:
heldParams.pop(i)
# Call HoldFixedParams even if heldParams = None to check
# if original Names and values have to be used
self.HoldFixedParams(heldParams)
if initialParameterValues is None:
initialParameterValues = self.theory.initialParameterValues
print 'initial cost = ', self.Cost(initialParameterValues)
out = self.BestFit(initialParameterValues)
optimizedParameterValues = out[0]
covar = out[1]
errors = [covar[i,i]**0.5 for i in range(len(covar))]
#inv_t_student = scipy.special.stdtrit(len(errors),0.90)
#errors = inv_t_student*errors
print 'optimized cost = ', self.Cost(optimizedParameterValues)
print 'optimized SST = ', self.SST(optimizedParameterValues)
print 'R-value = ', self.R_square(optimizedParameterValues)
print
if heldParams:
print "=== Held parameters ================"
for pName,pValue in heldParams:
if pName in uniSymbol:
print "%3s = %2.2f" % (uniSymbol[pName], pValue)
else:
print "%3s = %2.2f" % (pName, pValue)
# Print parameter values
# YJC: changed printing here to print one sigma error instead of 95% confidence level
print "=== Fitting parameters (with one sigma error)=============="
for name, val, error in \
zip(self.theory.parameterNameList,optimizedParameterValues, errors):
if name in uniSymbol:
print "%3s = %2.3f +/- %2.3f" %(uniSymbol[name], val, error)
else:
print "%3s = %2.3f +/- %2.3f" %(name, val, error)
print "====================================="
#
# Print plots
#
figNum = figNumStart-1
for model in self.Models.values():
for FT in [False,True]:
figNum+=1
pylab.figure(figNum)
model.PlotFunctions(optimizedParameterValues, plotCollapse = FT)
# Weird bug: repeating figure needed to get to show
pylab.figure(figNum)
figNum+=1
pylab.figure(figNum)
model.PlotResiduals(optimizedParameterValues)
pylab.figure(figNum)
#return optimizedParameterValues
return out