README

qpw - version 0.0

Paul Constantine - ICME
paul.constantine@stanford.edu

The utility qpw (for quadrature points and weights) computes the 
quadrature points and weights for Gauss-Legendre and Clenshaw-Curtis
quadrature rules with multivariate extensions to both tensor product
grids and Smolyak-type sparse grids. Its usage is the following:

[shell]$ qpw ptype gtype dimension level

Parameters:
ptype: gauss, cc
gtype: tensor, sparse
dimension: an integer greater than 0
level: For one-dimensional rules and tensor grids, this is the number
	of points in each direction. For sparse grids, this is the standard
	level parameter. 
	
Note that gtype is meaningless if dimension=1.

Output:
qpw will write separate text files for the points and the weights. Each 
multidimensinal point will occupy one line of the points file, and the
corresponding line in the weights file contains the appropriate weight.
The files will be labeled with the input parameters.

A note on memory management:
qpw will display a warning if it is about to allocate over 200M for the
points and weights. This version is currently not optimized for the 
sparse grids, meaning that it allocates the largest tensor grid necessary 
to construct the sparse grid. Therefore, you want to stick to relatively
low levels and dimensions. 

Questions? Email Paul at paul.constantine@stanford.edu

For a comprehensive list of quadrature software, go to John Burkhardt's 
page at:
http://people.scs.fsu.edu/~burkardt/

For recent literature on quadrature for random PDEs, see
F. Nobile, R. Tempone, and C.G. Webster. A Sparse Grid Stochastic 
Collocation Method for Partial Differential Equations with Random Input
Data. SINUM, May 2008.