#! /usr/bin/env python

import openturns as ot

# Time grid creation and White Noise
Tmin = 0.0
deltaT = 0.1
steps = 11

# Initialization of the TimeGrid timeGrid
timeGrid = ot.RegularGrid(Tmin, deltaT, steps)

# Creation of the Antecedent
myARMAProcess = ot.ARMA()
myARMAProcess.setTimeGrid(timeGrid)
print("myAntecedentProcess = ", myARMAProcess)

# Creation of a function
f = ot.SymbolicFunction(["t", "x"], ["t+0.1*x^2"])

# We build a dynamical function
myFieldFunction = ot.FieldFunction(ot.VertexValueFunction(f, timeGrid))

# finally we get the compsite process
myCompositeProcess = ot.CompositeProcess(myFieldFunction, myARMAProcess)
print("myCompositeProcess = ", repr(myCompositeProcess))

# Test realization
print("One realization= ")
print(myCompositeProcess.getRealization())

# future
print("future=", myCompositeProcess.getFuture(5))

#
# Create a spatial  dynamical function
# Create the function g : R^2 --> R^2
#               (x1,x2) --> (x1^2, x1+x2)
g = ot.SymbolicFunction(["x1", "x2"], ["x1^2", "x1+x2"])

# Convert g : R --> R into a spatial function
myDynFunc = ot.ValueFunction(g, ot.Mesh(2))

# Then g acts on processes X: Omega * R^nSpat --> R^2


#
# Create a trend function fTrend: R^n --> R^q
# for example for  myXtProcess of dimension 2
# defined on a bidimensional mesh
# fTrend : R^2 --> R^2
#          (t1, t2) --> (1+2t1, 1+3t2)
fTrend = ot.SymbolicFunction(["t1", "t2"], ["1+2*t1", "1+3*t2"])


#
# Create a Gaussian process of dimension 2
# which mesh is of box of dimension 2

myIndices = ot.Indices([80, 40])
myMesher = ot.IntervalMesher(myIndices)
lowerBound = [0.0, 0.0]
upperBound = [2.0, 1.0]
myInterval = ot.Interval(lowerBound, upperBound)
myMesh = myMesher.build(myInterval)

# Define a bidimensional temporal Gaussian process on the mesh
# with independent components
amplitude = [1.0, 1.0]
scale = [0.2, 0.3]
myCovModel = ot.ExponentialModel(scale, amplitude)

myXtProcess_temp = ot.GaussianProcess(myCovModel, myMesh)

# Non linear transformation of myXtProcess
# to get a positive process
g2 = ot.SymbolicFunction(["x1", "x2"], ["x1^2", "abs(x2)"])
myDynTransform = ot.ValueFunction(g2, ot.Mesh(2))
myXtProcess = ot.CompositeProcess(myDynTransform, myXtProcess_temp)

# Create the  image Y
myYtProcess = ot.CompositeProcess(myDynFunc, myXtProcess)

# Get the antecedent : myXtProcess
print("My antecedent process = ", myYtProcess.getAntecedent())

# Get the dynamical function
# which performs the transformation
print("My dynamical function = ", myYtProcess.getFunction())