Compute the transformation matrix for a projection to the left and right half-interval of Legendre polynomials for the given maximal number of modes.
Note: The transformation matrices to each subinterval are triangular, and the diagonal entries are the same. To save memory both matrices are stored in a single 2 dimensional array of size (nModes, nModes).
This matrix only needs to be computed once for a sufficiently high order, as submatices out of it can by used to perform the transformation for any lower polynomial degree.
The upper triangular matrix is created for the right subinterval, while the lower triangular matrix is used to store the rotated version for the left subinterval. For the right interval we interpret the first index as row index and the second as column. For the left interval this is reverted and we interpret the first index as columns of the matrix.
Note
Why is this a function? The reasoning for making this a function is that we need to return exactly one thing (the split matrix). It is then quite natural to refer to this by ply_split_legendre_matrix. A subroutine on the other hand usually describes something that should be done. Thus the name for a subroutine would then be ply_split_legendre_compute_matrix (describing the action performed by the subroutine). When using OpenMP it sometimes is better to use subroutines, even though it would be more natural to use a function. However, here we do not expect this to be the case, as this is expected to be called only once.
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| integer, | intent(in) | :: | nModes |
The maximal number of modes to compute the transformation for. The resulting matrix v will be max_modes x max_modes large and can be used for the transformation of all polynomials with up to this many modes. |