SG++-Doxygen-Documentation
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

 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


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

 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


Referenced by python.uq.operations.discretization.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

 def python.uq.operations.discretization.discretizeFunction ( f, bounds, level = 2, hasBorder = False, args, kws )
 def python.uq.operations.discretization.estimateDiscreteL2Error ( grid, alpha, f, n = 1000 )
 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().