unigrids {capn} | R Documentation |
Generating unifrom grids
Description
This function generates a grid of multi-dimensional uniform grids.
Usage
unigrids(nnodes, lb, ub, rtype = NULL)
Arguments
nnodes |
An array of numbers of nodes |
lb |
An array of lower bounds |
ub |
An array of upper bounds |
rtype |
A type of results; default is NULL that returns a list class; if rtype = list, returns a list class; if rtype = grid, returns a matrix class. |
Details
For the i
-th dimension of i = 1, 2, \cdots, d
, suppose a polynomial approximant
s_{i}
over a bounded interval [a_{i},b_{i}]
is defined by evenly gridded nodes. Then, a d
-dimensional
uniform grids can be defined as:
\mathbf{S} = \left\{ (s_{1},s_{2},\cdots,s_{d}) \vert a_{i} \leq s_{1} \leq b_{i}, i = 1, 2, \cdots, d \right\}
.
This is all combinations of s_{i}
. Two types of results are provided. 'rtype = list
' provides a list
of d
dimensions wherease 'rtype = grids
' creates a \left( \displaystyle \prod_{i=1}^{d} n_{i} \right) \times d
matrix.
Value
A list with d
elements of Chebyshev nodes or a \left( \displaystyle \prod_{i=1}^{d} n_{i} \right) \times d
matrix of uniform grids
Examples
## Uniform grids with two-dimension
unigrids(c(5,3), c(1,1), c(2,3))
## Returns the same results
unigrids(c(5,3), c(1,1), c(2,3), rtype='list')
## Returns a matrix grids with the same domain
unigrids(c(5,3), c(1,1), c(2,3), rtype='grid')
## Uniform grid with one-dimension
unigrids(5,1,2)
## Uniform grids with three stock
unigrids(c(3,4,5),c(1,1,1),c(2,3,4),rtype='grid')