def computeBoxCox(factors, valuesInit, shift):
# if no affine trend is considered
graph = ot.Graph()
myBoxCoxFactory = ot.BoxCoxFactory()
myModelTransform = myBoxCoxFactory.build(valuesInit, [shift], graph)
lambdaBoxCox = myModelTransform.getLambda()[0]
# if an affine trend is considered (more computing time required)
# works only in 1D
# myBoxCoxFactory = LinearBoxCoxFactory()
# myModelTransform, graph = myBoxCoxFactory.build(factors, valuesInit)
# lambdaBoxCox = myModelTransform.getLambda()[0]
return lambdaBoxCox, graph
# Transform myXproc to make its variance depend on the vertex (s,t)
# and to get a positive process
# thanks to the spatial function g
# myXtProcess R --> R
g = ot.SymbolicFunction(['x1'], ['exp(x1)'])
myDynTransform = ot.ValueFunction(g, 2)
myXtProcess = ot.CompositeProcess(myDynTransform, myXproc)
myField = myXtProcess.getRealization()
graphMarginal1 = ot.KernelSmoothing().build(myField.getValues()).drawPDF()
graphMarginal1.setTitle("")
graphMarginal1.setXTitle("X")
graphMarginal1.setLegendPosition("")
# Initiate a BoxCoxFactory
myBoxCoxFactory = ot.BoxCoxFactory()
graph = ot.Graph()
shift = [0.0]
# We estimate the lambda parameter from the field myField
# All values of the field are positive
myModelTransform = myBoxCoxFactory.build(myField, shift, graph)
graphMarginal2 = ot.KernelSmoothing().build(
myModelTransform(myField).getValues()).drawPDF()
graphMarginal2.setTitle("")
graphMarginal2.setXTitle("T_lambda(X)")
graphMarginal2.setLegendPosition("")
graph.setLegendPosition("bottomright")
scale = [0.2, 0.2] myCovModel = ot.ExponentialModel(scale, amplitude) myXproc = ot.GaussianProcess(myCovModel, myMesh) g = ot.SymbolicFunction(['x1'], ['exp(x1)']) myDynTransform = ot.ValueFunction(g, myMesh) myXtProcess = ot.CompositeProcess(myDynTransform, myXproc) # %% # Draw a field field = myXtProcess.getRealization() graph = field.drawMarginal(0) view = viewer.View(graph) # %% # Draw values marginal = ot.HistogramFactory().build(field.getValues()) graph = marginal.drawPDF() view = viewer.View(graph) # %% # Build the transformed field through Box-Cox myModelTransform = ot.BoxCoxFactory().build(field) myStabilizedField = myModelTransform(field) # %% # Draw values marginal = ot.HistogramFactory().build(myStabilizedField.getValues()) graph = marginal.drawPDF() view = viewer.View(graph) plt.show()