python.uq.operations.discretization Namespace Reference

Functions
def	computeCoefficients (jgrid, grid, alpha, f)
def	computeErrors (jgrid, jalpha, grid, alpha, f, n=200)
def	discretize (grid, alpha, f, epsilon=0., refnums=0, pointsNum=10, level=0, deg=1, useDiscreteL2Error=True)
def	discretizeFunction (f, bounds, level=2, hasBorder=False, args, kws)
def	estimateDiscreteL2Error (grid, alpha, f, n=1000)
def	estimateL2error (grid1, grid2, alpha2)

Function Documentation

computeCoefficients()

def python.uq.operations.discretization.computeCoefficients	(		jgrid,
			grid,
			alpha,
			f
	)

Interpolate function f, which depends on some sparse grid function
(grid, alpha) on jgrid
@param jgrid: Grid, new discretization
@param grid: Grid, old discretization
@param alpha: DataVector, surpluses for grid
@param f: function, to be interpolated
@return: DataVector, surpluses for jgrid

References python.uq.operations.sparse_grid.evalSGFunctionMulti(), python.statsfileInfo.f, and python.uq.operations.sparse_grid.hierarchize().

Referenced by python.uq.operations.discretization.discretize().

computeErrors()

def python.uq.operations.discretization.computeErrors	(		jgrid,
			jalpha,
			grid,
			alpha,
			f,
			n = 200
	)

Compute some errors to estimate the quality of the
interpolation.
@param jgrid: Grid, new discretization
@param jalpha: DataVector, new surpluses
@param grid: Grid, old discretization
@param alpha: DataVector, old surpluses
@param f: function, to be interpolated
@param n: int, number of Monte Carlo estimates for error estimation
@return: tuple(<float>, <float>), maxdrift, l2norm

References python.uq.operations.sparse_grid.evalSGFunctionMulti(), and python.statsfileInfo.f.

Referenced by python.uq.operations.discretization.discretize().

discretize()

def python.uq.operations.discretization.discretize	(		grid,
			alpha,
			f,
			epsilon = 0.,
			refnums = 0,
			pointsNum = 10,
			level = 0,
			deg = 1,
			useDiscreteL2Error = True
	)

discretize f with a sparse grid

@param grid: Grid
@param alpha: surplus vector
@param f: function
@param epsilon: float, error tolerance
@param refnums: int, number of refinment steps
@param pointsNum: int, number of points to be refined per step
@param level: int, initial grid level
@param deg: int, degree of lagrange basis

References python.uq.operations.discretization.computeCoefficients(), python.uq.operations.discretization.computeErrors(), python.uq.operations.sparse_grid.copyGrid(), and python.uq.operations.discretization.estimateL2error().

Referenced by python.uq.quadrature.bilinearform.bilinear_form_admissible_set.computeBF(), python.uq.quadrature.bilinearform.bilinear_form.computeBilinearForm(), python.uq.quadrature.bilinearform.SparseGridQuadratureStrategy.SparseGridQuadratureStrategy.computeBilinearFormEntry(), python.uq.operations.discretization.discretizeFunction(), python.uq.estimators.PiecewiseConstantIntegralStrategy.PiecewiseConstantIntegralStrategy.estimate(), and python.uq.estimators.MarginalIntegralStrategy.MarginalIntegralStrategy.estimate().

discretizeFunction()

def python.uq.operations.discretization.discretizeFunction	(		f,
			bounds,
			level = 2,
			hasBorder = False,
			args,
			kws
	)

References python.uq.operations.discretization.discretize(), python.uq.operations.discretization.estimateDiscreteL2Error(), python.statsfileInfo.f, and python.uq.operations.sparse_grid.hierarchize().

Referenced by python.uq.dists.J.J.discretize().

estimateDiscreteL2Error()

def python.uq.operations.discretization.estimateDiscreteL2Error	(		grid,
			alpha,
			f,
			n = 1000
	)

References python.uq.operations.sparse_grid.evalSGFunctionMulti(), and python.statsfileInfo.f.

Referenced by python.uq.operations.discretization.discretizeFunction().

estimateL2error()

def python.uq.operations.discretization.estimateL2error	(		grid1,
			grid2,
			alpha2
	)

find those grid points which are in grid2 but not in grid1. The L2
error of the new sparse grid function is then reduced with respect
to

|L2(g1) - L2(g2)|^2 ~ \sum_{i = 1}^N |v_i|

@param grid1: Grid, old grid
@param grid2: Grid, new grid
@param alpha2: DataVector, new surpluses

Referenced by python.uq.operations.discretization.discretize().