def example5():
## First, we want to configure which grid points to use in which dimension.
## We use Chebyshev points in the 0th dimension. To make them nested, we have to use at least \f$n
## = 3^l\f$ points at level \f$l\f$. This is why this method contains the prefix exp.
## CombiHierarchies provides some matching configurations for grid points. If you nevertheless
## need your own configuration or you want to know which growth strategy and ordering fit to which
## point distribution, look up the implementation details in CombiHierarchies, it is not
## difficult to implement your own configuration.
grids = pysgpp.AbstractPointHierarchyVector()
grids.push_back(pysgpp.CombiHierarchies.expChebyshev())
## Our next set of grid points are Leja points with linear growth (\f$n = 1 + 3l\f$).
## For the last dimension, we use equidistant points with boundary. These are suited for linear
## interpolation. To make them nested, again the slowest possible exponential growth is selected
## by the CombiHierarchies class.
grids.push_back(pysgpp.CombiHierarchies.linearLeja(3))
grids.push_back(pysgpp.CombiHierarchies.expUniformBoundary())
## The next thing we have to configure is the linear operation that is performed in those
## directions. We will use polynomial interpolation in the 0th dimension, quadrature in the 1st
## dimension and linear interpolation in the 2nd dimension.
## Roughly spoken, this means that a quadrature is performed on the 1D function that is the
## interpolated function with two fixed parameters. But since those operators "commute", the
## result is invariant under the order that the operations are applied in.
## The CombiEvaluators class also provides analogous methods and typedefs for the multi-evaluation
## case.
evaluators = pysgpp.FloatScalarAbstractLinearEvaluatorVector()
evaluators.push_back(pysgpp.CombiEvaluators.polynomialInterpolation())
evaluators.push_back(pysgpp.CombiEvaluators.quadrature())
evaluators.push_back(pysgpp.CombiEvaluators.linearInterpolation())
## To create a CombigridOperation object with our own configuration, we have to provide a
## LevelManager as well:
levelManager = pysgpp.WeightedRatioLevelManager()
operation = pysgpp.CombigridOperation(grids, evaluators, levelManager,
func)
## The two interpolations need a parameter \f$(x, z)\f$. If \f$\tilde{f}\f$ is the interpolated
## function, the operation approximates the result of \f$\int_0^1 \tilde{f}(x, y, z) \,dy\f$.
parameters = pysgpp.DataVector([0.777, 0.14159])
result = operation.evaluate(2, parameters)
print("Result: " + str(result))
def example6():
## To create a CombigridOperation, we currently have to use the longer way as in example 5.
grids = pysgpp.AbstractPointHierarchyVector(
d, pysgpp.CombiHierarchies.expUniformBoundary())
evaluators = pysgpp.FloatScalarAbstractLinearEvaluatorVector(
d, pysgpp.CombiEvaluators.cubicSplineInterpolation())
levelManager = pysgpp.WeightedRatioLevelManager()
## We have to specify if the function always produces the same value for the same grid points.
## This can make the storage smaller if the grid points are nested. In this implementation, this
## is true. However, it would be false in the PDE case, so we set it to false here.
exploitNesting = False
## Now create an operation as usual and evaluate the interpolation with a test parameter.
operation = pysgpp.CombigridOperation(grids, evaluators, levelManager,
pysgpp.gridFunc(gf), exploitNesting)
parameter = pysgpp.DataVector([0.1, 0.2, 0.3])
result = operation.evaluate(4, parameter)
print("Target function value: " + str(func(parameter)))
print("Numerical result: " + str(result))
marginal = Uniform(0, 1)
elif args.marginalType == "beta":
marginal = Beta(5, 10)
else:
marginal = Normal(0.5, 0.1, 0, 1)
# plot pdf
dist = J([marginal] * numDims)
fig = plt.figure()
plotDensity2d(dist)
savefig(fig, "/tmp/%s" % (args.marginalType, ))
plt.close(fig)
w = pysgpp.singleFunc(marginal.pdf)
grids = pysgpp.AbstractPointHierarchyVector()
grids.push_back(pysgpp.CombiHierarchies.linearLeja(w))
grids.push_back(pysgpp.CombiHierarchies.linearLeja(w))
evaluators = pysgpp.FloatScalarAbstractLinearEvaluatorVector()
evaluators.push_back(pysgpp.CombiEvaluators.polynomialInterpolation())
evaluators.push_back(pysgpp.CombiEvaluators.polynomialInterpolation())
# To create a CombigridOperation object with our own configuration, we have to provide a
# LevelManager as well:
levelManager = pysgpp.WeightedRatioLevelManager()
operation = pysgpp.CombigridOperation(grids, evaluators, levelManager,
func)
# We can add regular levels like before:
levelManager.addRegularLevels(args.level)