3. dataList¶
dataList contain a list of dataArray for several datasets.
- list subclass as lists of dataArrays (allowing variable sizes).
- basic list routines as read/save, appending, selection, filter, sort, prune, interpolate, spline…
- multidimensional least square fit that uses the attributes of the dataArray elements.
- read/write in human readable ASCII text of multiple files in one run (gzip possible).
dataList creation can be from read ASCII files or ndarrays as js.dL(‘filename.dat’).
A file may contain several datasets.
See dataList
for details.
Example:
p=js.grace()
dlist2=js.dL()
x=np.r_[0:10:0.5]
D,A,q=0.45,0.99,1.2
for q in np.r_[0.1:2:0.2]:
dlist2.append(js.dA(np.vstack([x,np.exp(-q**2*D*x),np.random.rand(len(x))*0.05])) )
dlist2[-1].q=q
p.clear()
p.plot(dlist2,legend='Q=$q')
p.legend()
dlist2.save('test.dat.gz')
The dataarray module can be run standalone in a new project.
3.1. Attributes¶
dataList.attr |
Returns all attribute names (including commonAttr of elements) of the dataList. |
dataList.commonAttr |
Returns list of attribute names existing in elements. |
dataList.dtype |
return dtype of elements |
dataList.names |
List of element names. |
dataList.whoHasAttributes |
Lists which attribute is found in which element. |
dataList.showattr ([maxlength, exclude]) |
Show data specific attributes for all elements. |
3.2. Fitting¶
dataList.fit (model[, freepar, fixpar, …]) |
Least square fit of model that minimizes chi**2 (uses scipy.optimize.leastsq). |
dataList.modelValues (**kwargs) |
Calculates modelValues of model after a fit. |
dataList.setlimit (**kwargs) |
Set upper and lower limits for parameters in least square fit. |
dataList.has_limit |
Return existing limits |
dataList.makeErrPlot ([title, showfixpar]) |
Creates a GracePlot for intermediate output from fit with residuals. |
dataList.makeNewErrPlot (**kwargs) |
Creates a NEW ErrPlot without destroying the last. |
dataList.detachErrPlot () |
Detaches ErrPlot without killing it and returns a reference to it. |
dataList.killErrPlot ([filename]) |
Kills ErrPlot |
dataList.showlastErrPlot ([title, modelValues]) |
Shows last ErrPlot as created by makeErrPlot with last fit result. |
dataList.errPlot (*args, **kwargs) |
Plot into an existing ErrPlot. |
dataList.savelastErrPlot (filename[, format, …]) |
Saves errplot to file with filename. |
dataList.interpolate ([func, invfunc, deg]) |
Interpolates Y at given attribute values for X values. |
dataList.polyfit ([func, invfunc, xfunc, …]) |
Inter/Extrapolated values along attribut for all given X values using a polyfit. |
dataList.extrapolate ([func, invfunc, xfunc, …]) |
Inter/Extrapolated values along attribut for all given X values using a polyfit. |
dataList.bispline ([func, invfunc, tx, ta, …]) |
Weighted least-squares bivariate spline approximation for interpolation of Y at given attribute values for X values. |
3.3. Housekeeping¶
dataList.setColumnIndex (*arg, **kwargs) |
Set the columnIndex where to find X,Y,Z, eY, eX, eZ….. |
dataList.append ([objekt, index, usecols, …]) |
Reads/creates new dataArrays and appends to dataList. |
dataList.extend ([objekt, index, usecols, …]) |
Reads/creates new dataArrays and appends to dataList. |
dataList.insert (i[, objekt, index, usecols, …]) |
Reads/creates new dataArrays and inserts in dataList. |
dataList.prune (*args, **kwargs) |
Reduce number of values between upper and lower limits. |
dataList.savetxt ([name, exclude, fmt]) |
Saves dataList as ASCII text file, optional compressed (gzip). |
dataList.sort ([key, reverse]) |
Sort dataList -> INPLACE!!! |
dataList.reverse () |
Reverse dataList -> INPLACE!!! |
dataList.delete (index) |
Delete element at index |
dataList.extractAttribut (parName[, func, …]) |
Extract a simpler attribute from a complex attribute in each element of dataList. |
dataList.filter (filterfunction) |
Filter elements according to filterfunction. |
dataList.index (value[, start, stop]) |
original doc from list |
dataList.merge (indices[, isort]) |
Merges elements of dataList. |
dataList.mergeAttribut (parName[, limit, …]) |
Merges elements of dataList if attribute values are closer than limit (in place). |
dataList.pop ([i]) |
original doc from list |
dataList.copyattr2elements ([maxndim, exclude]) |
Copy dataList specific attributes to all elements. |
dataList.getfromcomment (attrname) |
Extract a non number parameter from comment with attrname in front |
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class
jscatter.dataarray.
dataList
(objekt=None, block=None, usecols=None, delimiter=None, takeline=None, index=slice(None, None, None), replace=None, skiplines=None, ignore='#', XYeYeX=(0, 1, 2), lines2parameter=None)[source]¶ Bases:
jscatter.dataarray.dataListBase
A list of dataArrays with attributes for analysis, fitting and plotting.
- Allows reading, appending, selection, filter, sort, prune, least square fitting, ….
- Saves to human readable ASCII text format (possibly gziped). For file format see dataArray.
- The dataList allows simulteneous fit of all dataArrays dependent on attributes.
- and with different parameters for the dataArrays (see fit).
- dataList creation parameters (below) mainly determine how a file is read from file.
Parameters: objekt : strings, list of array or dataArray
Objects or filename(s) to read.Filenames with extension ‘.gz’ are decompressed (gzip).Accepts filenames with asterisk like exda=dataList(objekt=’aa12*’) as input for multiple file input.usecols : list of integer
Use only given columns and ignore others.
skiplines : boolean function, list of string or single string
Skip line if line meets condition. Function gets the list of words in a line. Examples:
- lambda words: any(w in words for w in [‘’,’ ‘,’NAN’,’‘*]) #with exact match
- lambda words: any(float(w)>3.1411 for w in words)
- lambda words: len(words)==1
If a list is given, the lambda function is generated automatically as in above example. If single string is given, it is tested if string is a substring of a word ( ‘abc’ in ‘12 3abc4 56’)
block : None,list int, string
block separates parts of a fileIf block is found a new dataArray is created from a part and appended.block can be something like “#next”or the first parameter name of a new block as block=’Temp’block=slice(2,100,3) slices the lines in file as lines[i:j:k]index : integer, slice list of integer, default is a slice for all.
Which datablock to use from single read file if multiple blocks are found. Can be integer , list of integer or slice notation.
XYeYeX : list integers, default=[0,1,2,None,None,None]
Columns for X, Y, eY, eX, Z, eZ. Change later by: data.setColumnIndex(3,5,-1).
delimiter : string, default any whitespace
Separator between words (data fields) in a line. E.g. ‘ ‘ tabulator
ignore : string, default ‘#’
Ignore lines starting with string e.g. ‘#’. For more complex lines to ignore use skiplines.
replace : dictionary of string:string
String replacement in read lines as {‘old’:’new’,…}. String pairs in this dictionary are replaced in each line. This is done prior to determining line type and can be used to convert strings to number or ‘,’:’.’.
takeline : string
takeline string is first word in a line with data. E.g. if dataline start with ‘atom’ in PDB files takeline=’atom’ to select specific lines
lines2parameter : list of integer
List of lines i which to prepend with ‘line_i’ to be found as parameter line_i. Used to mark lines with parameters without name (only numbers in a line as in .pdh files in the header). E.g. to skip the first lines.
Returns: dataList : list of dataArray
Notes
- Attribute access as atlist
- Attributes of the dataArray elements can be accessed like in dataArrays by .name notation. The difference is that a dataList returns atlist -a subclass of list- with some additional methods as the list of attributes in the dataList elements. This is necessary as it is allowed that dataList elements miss an attribute (indicated as None) or have different type. An numpy ndarray can be retrieved by the array property (as .name.array).
- Global attributes
- We have to discriminate attributes stored individual in each dataArray and in the dataList as a kind of global attribute. dataArray attributes belong to a dataArray and are saved with the dataArray, while global dataList attributes are only saved with the whole dataList at the beginning of a file. If dataArrays are saved as single files global attributes are lost.
Examples
import jscatter as js ex=js.dL('aa12*') #read aa files ex.extend('bb12*') #extend with other bb files ex.sort(...) #sort by attribute "q" ex.prune(number=100) # reduce number of points; default is to calc the mean in an intervall ex.filter(lambda a:a.Temperature>273) to filter for an attribute "Temperature" or .X.mean() value # do linear fit ex.fit(model=lambda a,b,t:a*t+b,freepar={'a':1,'b':0},mapNames={'t':'X'}) # fit using parameters in example the Temperature stored as parameter. ex.fit(model=lambda Temperature,b,x:Temperature*x+b,freepar={'b':0},mapNames={'x':'X'})
more Examples
import jscatter as js import numpy as np t=np.r_[1:100:5];D=0.05;amp=1 # using list comprehension creating a numpy array i5=js.dL([np.c_[t,amp*np.exp(-q*q*D*t),np.ones_like(t)*0.05].T for q in np.r_[0.2:2:0.4]]) # calling a function returning dataArrays i5=js.dL([js.dynamic.simpleDiffusion(q,t,amp,D) for q in np.r_[0.2:2:0.4]]) # define a function and add dataArrays to dataList ff=lambda q,D,t,amp:np.c_[t,amp*np.exp(-q*q*D*t),np.ones_like(t)*0.05].T i5=js.dL() # empty list for q in np.r_[0.2:2:0.4]: i5.append(ff(q,D,t,amp))
Get elements of dataList with specific attribute values.
i5=js.dL([js.dynamic.simpleDiffusion(q,t,amp,D) for q in np.r_[0.2:2:0.4]]) # get q=0.6 i5[i5.q.array==0.6] # get q > 0.5 i5[i5.q.array > 0.5]
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append
(objekt=None, index=slice(None, None, None), usecols=None, skiplines=None, replace=None, ignore='#', delimiter=None, takeline=None, lines2parameter=None)¶ Reads/creates new dataArrays and appends to dataList.
See dataList for description of all keywords. If objekt is dataArray or dataList all options are ignored.
original doc from list L.append(object) – append object to end
-
aslist
¶ Return as simple list.
-
attr
¶ Returns all attribute names (including commonAttr of elements) of the dataList.
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bispline
(func=None, invfunc=None, tx=None, ta=None, deg=[3, 3], eps=None, addErr=False, **kwargs)¶ Weighted least-squares bivariate spline approximation for interpolation of Y at given attribute values for X values.
Uses scipy.interpolate.LSQBivariateSpline eY values are used as weights (1/eY**2) if present.
Parameters: kwargs :
Keyword arguments The first keyword argument found as attribute is used for interpolation. E.g. conc=0.12 defines the attribute ‘conc’ to be interpolated to 0.12 Special kwargs see below.
X : array
List of X values were to evaluate. If X not given the .X of first element are used as default.
func : numpy ufunction or lambda
Simple function to be used on Y values before interpolation. see dataArray.polyfit
invfunc : numpy ufunction or lambda
To invert func after extrapolation again.
tx,ta : array like, None, int
Strictly ordered 1-D sequences of knots coordinates for X and attribute. If None the X or attribute values are used. If integer<len(X or attribute) the respective number of equidistante points in the interval between min and max are used.
deg : [int,int], optional
Degrees of the bivariate spline for X and attribute. Default is 3. If single integer given this is used for both.
eps : float, optional
A threshold for determining the effective rank of an over-determined linear system of equations. eps should have a value between 0 and 1, the default is 1e-16.
addErr : bool
If errors are present spline the error colum and add it to the result.
Returns: dataArray
Notes
- The spline interpolation results in a good approximation if the data are narrow. Around peaks values are underestimated if the data are not dense enough as the flank values are included in the spline between the maxima. See Examples.
- Without peaks there should be no artefacts.
- To estimate new errors for the splined data use .setColimnIndex(iy=ii,iey=None) with ii as index of errors. Then spline the errors and add these as new column.
- Interpolation can not be as good as fitting with a prior known model and use this for extrapolating.
Examples
import jscatter as js import numpy as np import matplotlib.pyplot as plt from mpl_toolkits.mplot3d import Axes3D fig = plt.figure() ax1 = fig.add_subplot(211, projection='3d') ax2 = fig.add_subplot(212, projection='3d') i5=js.dL([js.formel.gauss(np.r_[-50:50:5],mean,10) for mean in np.r_[-15:15.1:3]]) i5b=i5.bispline(mean=np.r_[-15:15:1],X=np.r_[-25:25:1],tx=10,ta=5) fig.suptitle('Spline comparison with different spacing of data') ax1.set_title("Narrow spacing result in good interpolation") ax1.scatter3D(i5.X.flatten, np.repeat(i5.mean,[x.shape[0] for x in i5.X]), i5.Y.flatten,s=20,c='red') ax1.scatter3D(i5b.X.flatten,np.repeat(i5b.mean,[x.shape[0] for x in i5b.X]), i5b.Y.flatten,s=2) ax1.tricontour(i5b.X.flatten,np.repeat(i5b.mean,[x.shape[0] for x in i5b.X]), i5b.Y.flatten,s=2) i5=js.dL([js.formel.gauss(np.r_[-50:50:5],mean,10) for mean in np.r_[-15:15.1:15]]) i5b=i5.bispline(mean=np.r_[-15:15:1],X=np.r_[-25:25:1]) ax2.set_title("Wide spacing result in artefacts between peaks") ax2.scatter3D(i5.X.flatten, np.repeat(i5.mean,[x.shape[0] for x in i5.X]), i5.Y.flatten,s=20,c='red') ax2.scatter3D(i5b.X.flatten,np.repeat(i5b.mean,[x.shape[0] for x in i5b.X]), i5b.Y.flatten,s=2) ax2.tricontour(i5b.X.flatten,np.repeat(i5b.mean,[x.shape[0] for x in i5b.X]), i5b.Y.flatten,s=2) plt.show(block=False)
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commonAttr
¶ Returns list of attribute names existing in elements.
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copy
()¶ Deepcopy of dataList
To make a normal shallow copy use copy.copy
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copyattr2elements
(maxndim=1, exclude=['comment'])¶ Copy dataList specific attributes to all elements.
Parameters: exclude : list of str
list of attr names to exclude from show
maxndim : int, default 2
maximum dimension e.g. to prevent copy of 2d arrays like covariance matrix
Notes
Main use is for copying fit parameters
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count
(value) → integer -- return number of occurrences of value¶
-
delete
(index)¶ Delete element at index
-
dtype
¶ return dtype of elements
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extend
(objekt=None, index=slice(None, None, None), usecols=None, skiplines=None, replace=None, ignore='#', delimiter=None, takeline=None, lines2parameter=None)¶ Reads/creates new dataArrays and appends to dataList.
See dataList for description of all keywords. If objekt is dataArray or dataList all options are ignored.
original doc from list L.append(object) – append object to end
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extractAttribut
(parName, func=None, newParName=None)¶ Extract a simpler attribute from a complex attribute in each element of dataList.
eg. extract the mean value from a list in an attribute
Parameters: parName : string
name of the parameter to process
func : function or lambda
a function (eg lambda ) that creates a new content for the parameter from the original content eg lambda a:np.mean(a)*5.123 the function gets the content of parameter whatever it is
newParName :string
if None old parameter is overwritten, otherwise this is the new parname
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extrapolate
(func=None, invfunc=None, xfunc=None, invxfunc=None, exfunc=None, **kwargs)¶ Inter/Extrapolated values along attribut for all given X values using a polyfit.
To extrapolate along an attribute using twice a polyfit (first along X then along attribute). E.g. from a concentration series to extrapolate to concentration zero.
Parameters: **kwargs :
Keyword arguments The first keyword argument found as attribute is used for extrapolation e.g. q=0.01 attribute with values where to extrapolate to Special kwargs see below.
X : arraylike
list of X values were to evaluate
funct : function or lambda
Function to be used in Y values before extrapolating. See Notes.
invfunc : function or lambda
To invert function after extrapolation again.
xfunct : function or lambda
Function to be used for X values before interpolating along X.
invxfunc : function or lambda
To invert xfunction again.
exfunc : function or lambda
Weigth for extrapol along X
degx,degy : integer default degx=0, degy=1
polynom degree for extrapolation in x,y If degx=0 (default) no extrapolation for X is done and values are linear interpolated.
Returns: dataArray
Notes
- funct is used to transfer the data to a simpler smoother or polynominal form.
- Think about data describing diffusion like I~exp(-q**2*D*t) and we want to interpolate along attribute q. If funct is np.log we interpolate on a simpler parabolic q**2 and linear in t.
- Same can be done with X axis thin in above case about subdiffusion t**a with a < 1.
Examples
Task: Extrapolate to zero q for 3 X values for an exp decaying function. Here first log(Y) is used (problem linearized), then linear extrapolate and and exp function used for the result. This is like lin extapolation of the exponent:
i5.polyfit(q=0,X=[0,1,11],func=lambda y:np.log(y),invfunc=lambda y:np.exp(y),deg=1)
concentration data with conc and extrapoleate to conc=0
data.polyfit(conc=0,X=data[0].X,deg=1)
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filter
(filterfunction)¶ Filter elements according to filterfunction.
Parameters: filterfunction : function or lambda function returning boolean
Return those items of sequence for which function(item) is true.
Examples
i5=js.dL('exampleData/iqt_1hho.dat') i1=i5.filter(lambda a:a.q>0.1) i1=i5.filter(lambda a:(a.q>0.1) ) i5.filter(lambda a:(a.q>0.1) & (a.average[0]>1)).average i5.filter(lambda a:(max(a.q*a.X)>0.1) & (a.average[0]>1))
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fit
(model, freepar={}, fixpar={}, mapNames={}, method='leastsq', xslice=slice(None, None, None), condition=None, output=True, **kw)¶ Least square fit of model that minimizes chi**2 (uses scipy.optimize.leastsq).
- A least square fit of the .Y values dependent on X (, Z) and attributes (multidimensional fitting).
- Data attributes are used automatically in model if they have the same name as a parameter.
- Resulting parameter errors are 1-sigma errors, if the data errors are 1-sigma errors.
- Results can be simulated with changed parameters in .modelValues or .showlastErrPlot.
Parameters: model : function or lambda
- Model function, should accept arrays as input (use numpy ufunctions in model).
-example: diffusion=lambda A,D,t,wavevector:A * np.exp(-wavevector**2*D*t) - Return value should be dataArray (.Y is used) or only Y values. - Errors in model should return negative integer.
freepar : dictionary
- Fit parameter names with startvalues.
- {‘D’:2.56,..} one common value for all
- {‘D’:[1,2.3,4.5,…],..} individual parameters for independent fit.
- [..] is extended with missing values equal to last given value. [1] -> [1,1,1,1,1,1]
fixpar : dictionary
Fixed parameters, overwrites data attributes. (see freepar for syntax)
mapNames : dictionary
Map parameter names from model to attribute names in data e.g. {‘t’:’X’,’wavevector’:’q’,}
method : default ‘leastsq’, ‘differential_evolution’, ‘BFGS’, ‘Nelder-Mead’ or from scipy.optimize.minimize
- Type of solver for minimization, for options see scipy.optimize. See last example for a comparison.
- Only ‘leastsq’ and ‘BFGS’ return errors for the fit parameters.
- ‘leastsq’ is fastest. ‘leastsq’ is a wrapper around MINPACK’s lmdif and lmder algorithms which are
- a modification of the Levenberg-Marquardt algorithm.
- All use bounds set in setlimits to allow bounds as described there.
- ‘differential_evolution’ uses automatic bounds as (x0/10**0.5,x0*10**0.5) if no explicit limits are set for a freepar. x0 is start value from freepar.
- For some methods the Jacobian is required.
xslice : slice object
- Use selected X values by slicing.
- xslice=slice(2,-3,2) To skip first 2,last 3 and take each second
condition : function or lambda
- A lambda function to determine which datapoints to include.
- The function should evaluate to boolean with dataArray as input and combines with xslice used on full set (first xslice then the condition is used)
- local operation on numpy arrays as “&”(and), “|”(or), “^”(xor)
- lambda a:(a.X>1) & (a.Y<1)
- lambda a:(a.X>1) & (a.X<100)
- lambda a: a.X>a.q * a.X
output : None,’last’
- !=None returns best parameters and erros
- None Returns string
- ‘last’ returns lastfit
debug : 1,2
debug modus returns:1 Free and fixed parameters but not mappedNAmes.2 Parameters in modelValues as dict to call model as model(**kwargs) with mappedNames.>2 Prints parameters sent to model and returns the output of model without fitting.kw : additional keyword arguments
Forwarded to minimizer as given in method.
Returns: dependent on output parameter
- Final results with errors is in .lastfit
- Fitparameters are additional in dataList object as .parname and corresponding errors as .parname_err.
Notes
The concept is to use data attributes as fixed parameters for the fit (multidimesional fit). This is realized by using data attribute with same name as fixed parameters if not given in freepar or fixpar.
Fit parameters can be set equal for all elements ‘par’:1 or independent ‘par’:[1] just by writing the start value as a single float or as a list of float. The same is for fixed parameters.
Change the fit is easy done by moving ‘par’:[1] between freepar and fixpar.
Limits for parameters can be set prior to the fit as .setlimit(D=[1,4,0,10]). The first two numbers (min,max) are softlimits (increase chi2) and second are hardlimits to avoid extreme values (hard set to these values if outside interval and increasing chi2).
If errors exist (.eY) and are not zero, weighted chi**2 is minimized. Without error or with single errors equal zero an unweighted chi**2 is minimized (equal weights).
The change of parameters can be simulated by .modelValues(D=3) which overides attributes and fit parameters.
.makeErrPlot creates an errorplot with residuals prior to the fit for intermediate output.
The last errPlot can be recreated after the fit with showlastErrPlot.
The simulated data can be shown in errPlot with .showlastErrPlot(D=3).
Each dataArray in a dataList can be fit individually (same model function) like this
# see Examples for dataList creation for dat in datlist: dat.fit(model,freepar,fixpar,.....)
Additinal kwargs for ‘leastsq’
all additional optional arguments passed to leastsq (see scipy.optimize.leastsq) col_deriv default 0 ftol default 1.49012e-08 xtol default 1.49012e-08 gtol default 0.0 maxfev default 200*(N+1). epsfcn default 0.0 factor default 100 diag default None
Parameter result by name in lastfit
exda.D eg freepar 'D' with errors; same for fixpar but no error use exda.lastfit.attr to see attributes of model exda.lastfit[i].D parameter D result of best fit exda.lastfit[i].D_err parameter D error as 1-sigma error, if errors of data have also 1-sigma errors in .eY exda.lastfit.chi2 sum((y-model(x,best))**2)/dof;should be around 1 if 1-sigma errors in .eY exda.lastfit.cov hessian**-1 * chi2 exda.lastfit.dof degrees of freedom len(y)-len(best) exda.lastfit.func_name name of used model exda.lastfit.func_code where to find code of used model exda.lastfit.X X values in fit exda.lastfit.Y Y values in fit exda.lastfit.eY Yerrors in fit
If intermediate output is desired (calculation of modeValues in errorplot) use exda.makeErrPlot() to create an output plot and parameter output inside
- How to construct a model:
- The model function gets .X (.Z, .eY, eX, eZ) as ndarray and parameters (from attributes) as scalar input. It should return an ndarray as output (as Y values) or dataArray (.Y is used). Therefore it is advised to use numpy ufunctions in the model because these use them automatically in the correct way. Instead of math.sin use numpy.sin, which is achieved by import numpy as np and use np.sin see http://docs.scipy.org/doc/numpy/reference/ufuncs.html
A bunch of models as templates can be found in formel.py, formfactor.py, stucturefactor.py.
Examples
Basic examples with synthetic data. Usually data are loaded from a file.
An error plot with residuals can be created for intermediate output
data=js.dL('exampleData/iqt_1hho.dat') diffusion=lambda t,wavevector,A,D,b:A*np.exp(-wavevector**2*D*t)+b data.setlimit(D=(0,2)) # set a limit for diffusion values data.makeErrPlot() # create errorplot which is updated data.fit(model=diffusion , freepar={'D':0.1, # one value for all (as a first try) 'A':[1,2,3]}, # extended to [1,2,3,3,3,3,...3] independent parameters fixpar={'b':0.} , # fixed parameters here, [1,2,3] possible mapNames= {'t':'X', # maps time t of the model as .X column for the fit. 'wavevector':'q'}, # and map model parameter 'wavevector' to data attribute .q condition=lambda a:(a.Y>0.1) ) # set a condition
Fit sine to simulated data
import jscatter as js import numpy as np x=np.r_[0:10:0.1] data=js.dA(np.c_[x,np.sin(x)+0.2*np.random.randn(len(x)),x*0+0.2].T) # simulate data with error data.fit(lambda x,A,a,B:A*np.sin(a*x)+B,{'A':1.2,'a':1.2,'B':0},{},{'x':'X'}) # fit data data.showlastErrPlot() # show fit print( data.A,data.A_err) # access A and error
Fit sine to simulated data using an attribute in data with same name
x=np.r_[0:10:0.1] data=js.dA(np.c_[x,1.234*np.sin(x)+0.1*np.random.randn(len(x)),x*0+0.1].T) # create data data.A=1.234 # add attribute data.makeErrPlot() # makes erroplot prior to fit data.fit(lambda x,A,a,B:A*np.sin(a*x)+B,{'a':1.2,'B':0},{},{'x':'X'}) # fit using .A
Fit sine to simulated data using an attribute in data with different name and fixed B
x=np.r_[0:10:0.1] data=js.dA(np.c_[x,1.234*np.sin(x)+0.1*np.random.randn(len(x)),x*0+0.1].T) # create data data.dd=1.234 # add attribute data.fit(lambda x,A,a,B:A*np.sin(a*x)+B,{'a':1.2,},{'B':0},{'x':'X','A':'dd'}) # fit data data.showlastErrPlot() # show fit
Fit sine to simulated dataList using an attribute in data with different name and fixed B from data. first one common parameter then as parameter list in [].
x=np.r_[0:10:0.1] data=js.dL() ef=0.1 # increase this to increase error bars of final result for ff in [0.001,0.4,0.8,1.2,1.6]: # create data data.append( js.dA(np.c_[x,(1.234+ff)*np.sin(x+ff)+ef*ff*np.random.randn(len(x)),x*0+ef*ff].T) ) data[-1].B=0.2*ff/2 # add attributes # fit with a single parameter for all data, obviously wrong result data.fit(lambda x,A,a,B,p:A*np.sin(a*x+p)+B,{'a':1.2,'p':0,'A':1.2},{},{'x':'X'}) data.showlastErrPlot() # show fit # now allowing multiple p,A,B as indicated by the list starting value data.fit(lambda x,A,a,B,p:A*np.sin(a*x+p)+B,{'a':1.2,'p':[0],'B':[0,0.1],'A':[1]},{},{'x':'X'}) # plot p against A , just as demonstration p=js.grace() p.plot(data.A,data.p,data.p_err)
2D fit data with an X,Z grid data and Y values For 3D fit we calc Y values from X,Z coordinates (only for scalar Y data). For fitting we need data in X,Z,Y column format.
import matplotlib.pyplot as plt from mpl_toolkits.mplot3d import Axes3D from matplotlib import cm # # create 3D data with X,Z axes and Y values as Y=f(X,Z) x,z=np.mgrid[-5:5:0.25,-5:5:0.25] xyz=js.dA(np.c_[x.flatten(),z.flatten(),0.3*np.sin(x*z/np.pi).flatten()+0.01*np.random.randn(len(x.flatten())),0.01*np.ones_like(x).flatten() ].T) # set columns where to find X,Y,Z ) xyz.setColumnIndex(ix=0,iz=1,iy=2,iey=3) # ff=lambda x,z,a,b:a*np.sin(b*x*z) xyz.fit(ff,{'a':1,'b':1/3.},{},{'x':'X','z':'Z'}) # fig = plt.figure() ax = fig.add_subplot(111, projection='3d') ax.scatter(xyz.X,xyz.Z,xyz.Y) ax.tricontour(xyz.lastfit.X,xyz.lastfit.Z,xyz.lastfit.Y, cmap=cm.coolwarm,linewidth=0, antialiased=False) plt.show(block=False)
Comparison of fit methods
import numpy as np import jscatter as js diffusion=lambda A,D,t,elastic,wavevector=0:A*np.exp(-wavevector**2*D*t)+elastic i5=js.dL(js.examples.datapath+'/iqt_1hho.dat') i5.makeErrPlot(title='diffusion model residual plot') i5.fit(model=diffusion,freepar={'D':0.2,'A':1}, fixpar={'elastic':0.0}, mapNames= {'t':'X','wavevector':'q'}, condition=lambda a:a.X>0.01 ) # 22 evaluations; error YES -> 'leastsq' #with D=[0.2] 130 evaluations i5.fit(model=diffusion,freepar={'D':0.2,'A':1}, fixpar={'elastic':0.0}, mapNames= {'t':'X','wavevector':'q'}, condition=lambda a:a.X>0.01 ,method='BFGS' ) # 52 evaluations, error YES i5.fit(model=diffusion,freepar={'D':0.2,'A':1}, fixpar={'elastic':0.0}, mapNames= {'t':'X','wavevector':'q'}, condition=lambda a:a.X>0.01 ,method='differential_evolution' ) # 498 evaluations, error NO ; needs >20000 evaluations using D=[0.2]; use only with low number of parameters i5.fit(model=diffusion,freepar={'D':0.2,'A':1}, fixpar={'elastic':0.0}, mapNames= {'t':'X','wavevector':'q'}, condition=lambda a:a.X>0.01 ,method='Powell' ) # 121 evaluations; error NO i5.fit(model=diffusion,freepar={'D':0.2,'A':1}, fixpar={'elastic':0.0}, mapNames= {'t':'X','wavevector':'q'}, condition=lambda a:a.X>0.01 ,method='SLSQP' ) # 37 evaluations, error NO i5.fit(model=diffusion,freepar={'D':0.2,'A':1}, fixpar={'elastic':0.0}, mapNames= {'t':'X','wavevector':'q'}, condition=lambda a:a.X>0.01 ,method='COBYLA' ) # 308 evaluations, error NO
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getfromcomment
(attrname)¶ Extract a non number parameter from comment with attrname in front
If multiple names start with parname first one is used. Used comment line is deleted from comments
Parameters: attrname : string
name of the parameter in first place
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has_limit
¶ Return existing limits
without limits returns None
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index
(value, start=0, stop=-1)¶ original doc from list L.index(value, [start, [stop]]) -> integer – return first index of value. Raises ValueError if the value is not present.
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insert
(i, objekt=None, index=0, usecols=None, skiplines=None, replace=None, ignore='#', delimiter=None, takeline=None, lines2parameter=None)¶ Reads/creates new dataArrays and inserts in dataList.
If objekt is dataArray or dataList all options are ignored.
Parameters: i : int, default 0
Position where to insert.
- objekt,index,usecols,skiplines,replace,ignore,delimiter,takeline,lines2parameter : options
See dataArray or dataList
original doc from list
L.insert(index, object) – insert object before index
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interpolate
(func=None, invfunc=None, deg=1, **kwargs)¶ Interpolates Y at given attribute values for X values.
Uses twice a linear interpolation (first along X then along attribute). If X and attributes are equal to existing these datapoints are returned.
Parameters: **kwargs :
Keyword arguments as float or array-like the first keyword argument found as attribute is used for interpolation. E.g. conc=0.12 defines the attribute ‘conc’ to be interpolated to 0.12 Special kwargs see below.
X : array
List of X values were to evaluate (linear interpolation). If X < or > self.X the corresbonding min/max border is used. If X not given the .X of first element are used as default.
func : function or lambda
Function to be used on Y values before interpolation. See dataArray.polyfit.
invfunc : function or lambda
To invert func after extrapolation again.
deg : integer, default =1
Polynom degree for interpolation along attribute. Outliers result in Nan.
Returns: dataArray
Notes
- This interpolation results in a good approximation if the data are narrow. Around peaks values are underestimated if the data are not dense enough. See Examples.
- To estimate new errors for the splined data use .setColumnIndex(iy=ii,iey=None) with ii as index of errors. Then spline the errors and add these as new column.
- Interpolation can not be as good as fitting with a prior known model and use this for extrapolating.
Examples
import jscatter as js import numpy as np import matplotlib.pyplot as plt from mpl_toolkits.mplot3d import Axes3D fig = plt.figure() ax1 = fig.add_subplot(211, projection='3d') ax2 = fig.add_subplot(212, projection='3d') # try different kinds of polynaminal degree deg=2 i5=js.dL([js.formel.gauss(np.r_[-50:50:5],mean,10) for mean in np.r_[-15:15.1:3]]) i5b=i5.interpolate(mean=np.r_[-15:15:1],X=np.r_[-25:25:1],deg=deg) fig.suptitle('Interpolation comparison with different spacing of data') ax1.set_title("Narrow spacing result in good interpolation") ax1.scatter3D(i5.X.flatten, np.repeat(i5.mean,[x.shape[0] for x in i5.X]), i5.Y.flatten,s=20,c='red') ax1.scatter3D(i5b.X.flatten,np.repeat(i5b.mean,[x.shape[0] for x in i5b.X]), i5b.Y.flatten,s=2) ax1.tricontour(i5b.X.flatten,np.repeat(i5b.mean,[x.shape[0] for x in i5b.X]), i5b.Y.flatten,s=2) i5=js.dL([js.formel.gauss(np.r_[-50:50:5],mean,10) for mean in np.r_[-15:15.1:15]]) i5b=i5.interpolate(mean=np.r_[-15:15:1],X=np.r_[-25:25:1],deg=deg) ax2.set_title("Wide spacing result in artefacts between peaks") ax2.scatter3D(i5.X.flatten, np.repeat(i5.mean,[x.shape[0] for x in i5.X]), i5.Y.flatten,s=20,c='red') ax2.scatter3D(i5b.X.flatten,np.repeat(i5b.mean,[x.shape[0] for x in i5b.X]), i5b.Y.flatten,s=2) ax2.tricontour(i5b.X.flatten,np.repeat(i5b.mean,[x.shape[0] for x in i5b.X]), i5b.Y.flatten,s=2) plt.show(block=False)
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makeErrPlot
(title=None, showfixpar=True, **kwargs)[source]¶ Creates a GracePlot for intermediate output from fit with residuals.
ErrPlot is updated only if consecutive steps need more than 2 seconds.
Parameters: title : string
title of plot
residuals : string
plot type of residuals ‘absolut’ or ‘a’ absolute residuals ‘relative’ or ‘r’ relative =res/y
showfixpar : boolean (None,False,0 or True,Yes,1)
show the fixed parameters in errplot
yscale,xscale : ‘n’,’l’ for ‘normal’, ‘logarithmic’
y scale, log or normal (linear)
fitlinecolor : int, [int,int,int]
Color for fit lines (or line style as in plot). if not given same color as data.
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makeNewErrPlot
(**kwargs)[source]¶ Creates a NEW ErrPlot without destroying the last. See makeErrPlot for details.
Parameters: **kwargs
keyword arguments passed to makeErrPlot
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merge
(indices, isort=None)¶ Merges elements of dataList.
The merged dataArray is stored in the lowest indices. Others are removed.
Parameters: indices : integer,’all’
list of indices to merge ‘all’ merges all elements into one.
isort : integer
argsort after merge along column eg isort=’X’, ‘Y’, or 0,1,2 None is no sorting as default
Notes
Attributes are copied as lists in the merged dataArray.
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mergeAttribut
(parName, limit=None, isort=None, func=<function mean>)¶ Merges elements of dataList if attribute values are closer than limit (in place).
If attribute is list the average is taken for comparison. For special needs create new parameter and merge along this.
Parameters: parName : string
name of a parameter
limit : float
The relative limit value. If limit is None limit is determined as standardeviation of sorted differences as limit=np.std(np.array(data.q[:-1])-np.array(data.q[1:]))/np.mean(np.array(self.q)
isort : ‘X’, ‘Y’ or 0,1,2…, None, default None
Column for isort. None is no sorting
func : function or lambda, default np.mean
a function to create a new value for parameter see extractAttribut stored as .parName+str(func.func_name)
Examples
i5=js.dL('exampleData/iqt_1hho.dat') i5.mergeAttribut('q',0.1) # use qmean instead of q or calc the new value print( i5.qmean)
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modelValues
(**kwargs)¶ Calculates modelValues of model after a fit.
Model parameters are used from dataArray attributes or last fit parameters. Given arguments overwrite parameters and attributes to simulate modelValues e.g. to extend X range.
Parameters: **kwargs : parname=value
Overwrite parname with value in the dataList attributes or fit results e.g. to extend the parameter range or simulate changed parameters.
debug : internal usage documented for completes
dictionary passed to model to allow calling model as model(**kwargs) for debugging
Returns: dataList of modelValues with parameters as attributes.
Notes
Example: extend time range
data=js.dL('iqt_1hho.dat') diffusion=lambda A,D,t,wavevector: A*np.exp(-wavevector**2*D*t) data.fit(diffusion,{'D':[2],'amplitude':[1]},{},{'t':'X'}) # do fit # overwritte t to extend range newmodelvalues=data.modelValues(t=numpy.r_[0:100]) #with more t
Example: 1-sigma interval for D
data=js.dL('exampleData/iqt_1hho.dat') diffusion=lambda A,D,t,q: A*np.exp(-q**2*D*t) data.fit(diffusion,{'D':[0.1],'A':[1]},{},{'t':'X'}) # do fit # add errors of D for confidence limits upper=data.modelValues(D=data.D+data.D_err) lower=data.modelValues(D=data.D-data.D_err) data.showlastErrPlot() data.errPlot(upper,sy=0,li=[2,1,1]) data.errPlot(lower,sy=0,li=[2,1,1])
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nakedcopy
()¶ Returns copy without attributes, thus only the data.
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names
¶ List of element names.
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polyfit
(func=None, invfunc=None, xfunc=None, invxfunc=None, exfunc=None, **kwargs)¶ Inter/Extrapolated values along attribut for all given X values using a polyfit.
To extrapolate along an attribute using twice a polyfit (first along X then along attribute). E.g. from a concentration series to extrapolate to concentration zero.
Parameters: **kwargs :
Keyword arguments The first keyword argument found as attribute is used for extrapolation e.g. q=0.01 attribute with values where to extrapolate to Special kwargs see below.
X : arraylike
list of X values were to evaluate
funct : function or lambda
Function to be used in Y values before extrapolating. See Notes.
invfunc : function or lambda
To invert function after extrapolation again.
xfunct : function or lambda
Function to be used for X values before interpolating along X.
invxfunc : function or lambda
To invert xfunction again.
exfunc : function or lambda
Weigth for extrapol along X
degx,degy : integer default degx=0, degy=1
polynom degree for extrapolation in x,y If degx=0 (default) no extrapolation for X is done and values are linear interpolated.
Returns: dataArray
Notes
- funct is used to transfer the data to a simpler smoother or polynominal form.
- Think about data describing diffusion like I~exp(-q**2*D*t) and we want to interpolate along attribute q. If funct is np.log we interpolate on a simpler parabolic q**2 and linear in t.
- Same can be done with X axis thin in above case about subdiffusion t**a with a < 1.
Examples
Task: Extrapolate to zero q for 3 X values for an exp decaying function. Here first log(Y) is used (problem linearized), then linear extrapolate and and exp function used for the result. This is like lin extapolation of the exponent:
i5.polyfit(q=0,X=[0,1,11],func=lambda y:np.log(y),invfunc=lambda y:np.exp(y),deg=1)
concentration data with conc and extrapoleate to conc=0
data.polyfit(conc=0,X=data[0].X,deg=1)
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pop
(i=-1)¶ original doc from list L.pop([index]) -> item – remove and return item at index (default last). Raises IndexError if list is empty or index is out of range.
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prune
(*args, **kwargs)¶ Reduce number of values between upper and lower limits.
Prune reduces a dataset to reduced number of data points in an interval between lower and upper by selection or by averaging including errors.
Parameters: *args,**kwargs :
arguments and keyword arguments see below
lower : float
lower bound min is min of data
upper : float
upper bound max is max of data
number : int
number of values in result
kind : {‘log’,’lin’} default ‘lin’
type of the new point distrubution‘log’ closest values in log distribution with number points in [lower,upper]‘lin’ closest values in lin distribution with number points in [lower,upper]if number==None all points between min,max are usedtype : {None,’mean’,’error’,’mean+error’} default ‘mean’
how to determine the value for a pointNone original Y value of X closest to new X value‘mean’ mean values in interval between 2 X points;weight==None -> equal weightif weight!=None with weight=1/col[weight]**2weight column will get values according to error propagation‘mean+std’ calcs mean and adds error columns with standard deviation from intervalscan be used if no errors are presentfor single values the error is interpolated from neighbouring values! for less pruned data error may be bad defined if only a few points are averagedcol : ‘X’,’Y’….., or int, default ‘X’
column to prune along X,Y,Z or index of column
weight : None, ‘eX’, ‘eY’ or int
column for weight as 1/err**2 in ‘mean’ calculation, None is equal weightweight columne gets new error sqrt(1/sum_i(1/err_i**2))if None or not existing equal weights are usedkeep : list of int
list of indices to keep in any case
Returns: dataArray with values pruned to number of values
Notes
Attention !!!!dependent on the distribution of original data a lower number of points can be the resulteg think of noisy data between 4 and 5 and a lin distribution from 1 to 10 of 9 pointsas there are no data between 5 and 10 these will all result in 5 and be set to 5 to be uniqueExamples
i5.prune(number=13,col='X',type='mean',weight='eY') i5.prune(number=13)
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remove
()¶ L.remove(value) – remove first occurrence of value. Raises ValueError if the value is not present.
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reverse
()¶ Reverse dataList -> INPLACE!!! original doc from list L.reverse() – reverse IN PLACE
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sCI
(*arg, **kwargs)¶ Set the columnIndex where to find X,Y,Z, eY, eX, eZ…..
Default is ix=0,iy=1,iey=2,iz=None,iex=None,iez=None as it is the most used. There is no limitation and each dataArray can have different ones.
Parameters: ix,iy,iey,iz,iex,iez: integer, None; default ix=0,iy=1,iey=2,iz=None,iex=None,iez=None
usability wins iey=2!!if columnIndex differs in dataArrays set them individuallyNotes
A list of all X in the dataArray is dataArray.Xinteger column index as 0,1,2,-1 , should be in rangeNone as not used eg iex=None -> no errors for xanything else does not changeShortcut sCI
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save
(name=None, exclude=['comment', 'lastfit'], fmt='%.5e')¶ Saves dataList as ASCII text file, optional compressed (gzip).
Saves dataList with attributes to one file that can be reread. Dynamic created attributes as e.g. X, Y, eY, are not saved. If name extension is ‘.gz’ the file is compressed (gzip).
Parameters: name : string
filename
exclude : list of str, default [‘comment’,’lastfit’]
List of dataList attribut names to exclude from being saved.
fmt : string, default ‘%.5e’
Format specifier for writing float as e.g. ‘%.5e’ is exponential with 5 digits precision.
Notes
Saves a sequence of the dataArray elements.
Format rules:
Dataset consists of tabulated data with optional attributes and comments. Datasets are separated by empty lines, attributes and comments come before data.
- First two strings decide for a line:
- string + value -> attribute as attribute name + list of values
- string + string -> comment line
- value + value -> data (line of an array; in sequence without break)
- single words -> are appended to comments
- optional:
- string + @name -> as attribute but links to other dataArray with .name=”name” stored in the same file after this dataset.
- internal parameters starting with underscore (‘_’) are ignored for writing, also X,Y,Z,eX,eY,eZ,
- only ndarray content is stored; no dictionaries in parameters.
- @name is used as identifier or filename can be accessed as name.
- attributes of dataList are saved as common attributes marked with a line “@name header_of_common_parameters”
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savelastErrPlot
(filename, format='agr', size=(1012, 760), dpi=300, **kwargs)[source]¶ Saves errplot to file with filename.
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savetext
(name=None, exclude=['comment', 'lastfit'], fmt='%.5e')¶ Saves dataList as ASCII text file, optional compressed (gzip).
Saves dataList with attributes to one file that can be reread. Dynamic created attributes as e.g. X, Y, eY, are not saved. If name extension is ‘.gz’ the file is compressed (gzip).
Parameters: name : string
filename
exclude : list of str, default [‘comment’,’lastfit’]
List of dataList attribut names to exclude from being saved.
fmt : string, default ‘%.5e’
Format specifier for writing float as e.g. ‘%.5e’ is exponential with 5 digits precision.
Notes
Saves a sequence of the dataArray elements.
Format rules:
Dataset consists of tabulated data with optional attributes and comments. Datasets are separated by empty lines, attributes and comments come before data.
- First two strings decide for a line:
- string + value -> attribute as attribute name + list of values
- string + string -> comment line
- value + value -> data (line of an array; in sequence without break)
- single words -> are appended to comments
- optional:
- string + @name -> as attribute but links to other dataArray with .name=”name” stored in the same file after this dataset.
- internal parameters starting with underscore (‘_’) are ignored for writing, also X,Y,Z,eX,eY,eZ,
- only ndarray content is stored; no dictionaries in parameters.
- @name is used as identifier or filename can be accessed as name.
- attributes of dataList are saved as common attributes marked with a line “@name header_of_common_parameters”
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savetxt
(name=None, exclude=['comment', 'lastfit'], fmt='%.5e')¶ Saves dataList as ASCII text file, optional compressed (gzip).
Saves dataList with attributes to one file that can be reread. Dynamic created attributes as e.g. X, Y, eY, are not saved. If name extension is ‘.gz’ the file is compressed (gzip).
Parameters: name : string
filename
exclude : list of str, default [‘comment’,’lastfit’]
List of dataList attribut names to exclude from being saved.
fmt : string, default ‘%.5e’
Format specifier for writing float as e.g. ‘%.5e’ is exponential with 5 digits precision.
Notes
Saves a sequence of the dataArray elements.
Format rules:
Dataset consists of tabulated data with optional attributes and comments. Datasets are separated by empty lines, attributes and comments come before data.
- First two strings decide for a line:
- string + value -> attribute as attribute name + list of values
- string + string -> comment line
- value + value -> data (line of an array; in sequence without break)
- single words -> are appended to comments
- optional:
- string + @name -> as attribute but links to other dataArray with .name=”name” stored in the same file after this dataset.
- internal parameters starting with underscore (‘_’) are ignored for writing, also X,Y,Z,eX,eY,eZ,
- only ndarray content is stored; no dictionaries in parameters.
- @name is used as identifier or filename can be accessed as name.
- attributes of dataList are saved as common attributes marked with a line “@name header_of_common_parameters”
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setColumnIndex
(*arg, **kwargs)¶ Set the columnIndex where to find X,Y,Z, eY, eX, eZ…..
Default is ix=0,iy=1,iey=2,iz=None,iex=None,iez=None as it is the most used. There is no limitation and each dataArray can have different ones.
Parameters: ix,iy,iey,iz,iex,iez: integer, None; default ix=0,iy=1,iey=2,iz=None,iex=None,iez=None
usability wins iey=2!!if columnIndex differs in dataArrays set them individuallyNotes
A list of all X in the dataArray is dataArray.Xinteger column index as 0,1,2,-1 , should be in rangeNone as not used eg iex=None -> no errors for xanything else does not changeShortcut sCI
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setlimit
(**kwargs)¶ Set upper and lower limits for parameters in least square fit.
Parameters: parname : [value x 4] , list of 4 x (float/None), default None
Use as setlimit(parname=(lowerlimit, upperlimit,lowerhardlimit, upperhardlimit)) - lowerlimit, upperlimit : float, default None
soft limit: chi2 increased with distance from limit, nonfloat resets limit
- lowerhardlimit, upperhardlimit: hardlimit float, None values are set to border , chi2 is increased strongly
Notes
Penalty methods are a certain class of algorithms for solving constrained optimization problems. Here the penalty function increases chi2 by a factor chi*f_conststrain - no limit overrun : 1 - softlimits : + 1+abs(val-limit)*10 per limit - hardlimits : +10+abs(val-limit)*10 per limit
Examples
- setlimit(D=(1,100),A=(0.2,0.8,0.0001)) to set lower=1 and upper=100
- A with a hard limit to avoid zero
setlimit(D=(None,100)) to reset lower and set upper=100 setlimit(D=(1,’thisisnotfloat’,’‘,)) to set lower=1 and reset upper
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shape
¶ Tuple with shapes of dataList elements.
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showattr
(maxlength=75, exclude=['comment', 'lastfit'])¶ Show data specific attributes for all elements.
Parameters: maxlength : integer
truncate string representation
exclude : list of str
list of attribute names to exclude from show
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showlastErrPlot
(title=None, modelValues=None, **kwargs)[source]¶ Shows last ErrPlot as created by makeErrPlot with last fit result.
Same arguments as in makeErrPlot.
Additional keyword arguments are passed as in modelValues and simulate changes in the parameters. Without parameters the last fit is retrieved.
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sort
(key=None, reverse=False)¶ Sort dataList -> INPLACE!!!
Parameters: key : function
A function that is applied to all elements and the output is used for sorting. e.g. ‘Temp’ or lambda a:a.Temp convenience: If key is attribut name this attribute is used
reverse : True, False
Normal or reverse order.
Examples
dlist.sort('q',True) dlist.sort(key=lambda ee:ee.X.mean() ) dlist.sort(key=lambda ee:ee.temperatur ) dlist.sort(key=lambda ee:ee.Y.mean() ) dlist.sort(key=lambda ee:ee[:,0].sum() ) dlist.sort(key=lambda ee:getattr(ee,parname)) dlist.sort(key='parname')
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whoHasAttributes
¶ Lists which attribute is found in which element.
Returns: dictionary of attributes names: list of indices
keys are the attribute names values are indices of dataList where attr is existent