"""
Function manipulation
=====================
"""

# %%
#
# In this example we are going to exhibit some of the generic function services such as:
#
# - to ask the dimension of its input and output vectors
# - to evaluate itself, its gradient and hessian
# - to set a finite difference method for the evaluation of the gradient or the hessian
# - to evaluate the number of times the function or its gradient or its hessian have been evaluated
# - to disable or enable (enabled by default) the history mechanism
# - to disable or enable the cache mechanism
# - to get all the values evaluated by the function and the associated inputs with the methods
# - to clear the history
# - to ask the description of its input and output vectors
# - to extract output components
# - to get a graphical representation

# %%
import openturns as ot
import openturns.viewer as otv


# %%
# Create a vectorial function R ^n --> R^p
# for example R^2 --> R^2
f = ot.SymbolicFunction(["x1", "x2"], ["1+2*x1+x2", "2+x1+2*x2"])

# Create a scalar function R --> R
func1 = ot.SymbolicFunction(["x"], ["x^2"])

# Create another function R^2 --> R
func2 = ot.SymbolicFunction(["x", "y"], ["x*y"])

# Create a vectorial function R ^3 --> R^2
func3 = ot.SymbolicFunction(
    ["x1", "x2", "x3"], ["1+2*x1+x2+x3^3", "2+sin(x1+2*x2)-sin(x3) * x3^4"]
)

# Create a second vectorial function R ^n --> R^p
# for example R^2 --> R^2
g = ot.SymbolicFunction(["x1", "x2"], ["x1+x2", "x1^2+2*x2^2"])


def python_eval(X):
    a, b = X
    y = a + b
    return [y]


func4 = ot.PythonFunction(2, 1, python_eval)

# %%
# Ask for the dimension of the input and output vectors
print(f.getInputDimension())
print(f.getOutputDimension())

# %%
# Enable the history mechanism
f = ot.MemoizeFunction(f)

# %%
# Evaluate the function at a particular point
x = [1.0] * f.getInputDimension()
y = f(x)
print("x=", x, "y=", y)

# %%
# Get the history
samplex = f.getInputHistory()
sampley = f.getOutputHistory()
print("evaluation history = ", samplex, sampley)

# %%
# Clear the history mechanism
f.clearHistory()

# %%
# Disable the history mechanism
f.disableHistory()

# %%
# Enable the cache mechanism
f4 = ot.MemoizeFunction(func4)
f4.enableCache()
for i in range(10):
    f4(x)

# %%
# Get the number of times cached values are reused
f4.getCacheHits()

# %%
# Evaluate the gradient of the function at a particular point
gradientMatrix = f.gradient(x)
gradientMatrix

# %%
# Evaluate the hessian of the function at a particular point
hessianMatrix = f.hessian(x)
hessianMatrix

# %%
# Change the gradient method to a non centered finite difference method
step = [1e-7] * f.getInputDimension()
gradient = ot.NonCenteredFiniteDifferenceGradient(step, f.getEvaluation())
f.setGradient(gradient)
gradient

# %%
# Change the hessian method to a centered finite difference method
step = [1e-7] * f.getInputDimension()
hessian = ot.CenteredFiniteDifferenceHessian(step, f.getEvaluation())
f.setHessian(hessian)
hessian

# %%
# Get the number of times the function has been evaluated
f.getEvaluationCallsNumber()

# %%
# Get the number of times the gradient has been evaluated
f.getGradientCallsNumber()

# %%
# Get the number of times the hessian has been evaluated
f.getHessianCallsNumber()

# %%
# Get the component i
f.getMarginal(1)

# %%
# Compose two functions : h = f o g
ot.ComposedFunction(f, g)

# %%
# Get the valid symbolic constants
ot.SymbolicFunction.GetValidConstants()

# %%
# Graph 1 : z -->  f_2(x_0,y_0,z)
# for z in [-1.5, 1.5] and y_0 = 2. and z_0 = 2.5
# Specify the input component that varies
# Care : numerotation begins at 0
inputMarg = 2
# Give its variation intervall
zMin = -1.5
zMax = 1.5
# Give the coordinates of the fixed input components
centralPt = [1.0, 2.0, 2.5]
# Specify the output marginal function
# Care : numerotation begins at 0
outputMarg = 1
# Specify the point number of the final curve
ptNb = 101
# Draw the curve!
graph = func3.draw(inputMarg, outputMarg, centralPt, zMin, zMax, ptNb)
view = otv.View(graph)

# %%
# Graph 2 : (x,z) -->  f_1(x,y_0,z)
# for x in [-1.5, 1.5], z in [-2.5, 2.5]
# and y_0 = 2.5
# Specify the input components that vary
firstInputMarg = 0
secondInputMarg = 2
# Give their variation interval
inputMin2 = [-1.5, -2.5]
inputMax2 = [1.5, 2.5]
# Give the coordinates of the fixed input components
centralPt = [0.0, 2.0, 2.5]
# Specify the output marginal function
outputMarg = 1
# Specify the point number of the final curve
ptNb = [101, 101]
graph = func3.draw(
    firstInputMarg, secondInputMarg, outputMarg, centralPt, inputMin2, inputMax2, ptNb
)
view = otv.View(graph)

# %%
# Graph 3 : simplified method for x -->  func1(x)
# for x in [-1.5, 1.5]
# Give the variation interval
xMin3 = -1.5
xMax3 = 1.5
# Specify the point number of the final curve
ptNb = 101
# Draw the curve!
graph = func1.draw(xMin3, xMax3, ptNb)
view = otv.View(graph)

# %%
# Graph 4 : (x,y) -->  func2(x,y)
# for x in [-1.5, 1.5], y in [-2.5, 2.5]
# Give their variation interval
inputMin4 = [-1.5, -2.5]
inputMax4 = [1.5, 2.5]
# Give the coordinates of the fixed input components
centralPt = [0.0, 2.0, 2.5]
# Specify the output marginal function
outputMarg = 1
# Specify the point number of the final curve
ptNb = [101, 101]
graph = func2.draw(inputMin4, inputMax4, ptNb)
view = otv.View(graph)

# %%
# Display all figures
otv.View.ShowAll()