Description Usage Arguments Details Value Examples
This function generates a grid of multi-dimensional uniform grids.
1 |
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. |
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} = ≤ft\{ (s_{1},s_{2},\cdots,s_{d}) \vert a_{i} ≤q s_{1} ≤q 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 ≤ft( \displaystyle ∏_{i=1}^{d} n_{i} \right) \times d matrix.
A list with d elements of Chebyshev nodes or a ≤ft( \displaystyle ∏_{i=1}^{d} n_{i} \right) \times d matrix of uniform grids
1 2 3 4 5 6 7 8 9 10 | ## 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')
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