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
(max_modes, max_modes).

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.

Arguments

Type

Intent

Optional

Attributes

Name

integer,

intent(in)

::

max_modes

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.

real(kind=rk),

intent(out),

allocatable

::

v(:,:)

The transformation matrix.

Upper triangular matrix is created for shifting and lower triangular
for (-1) * shifting.
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.

Nodes of different colours represent the following:

Solid arrows point from a procedure to one which it calls. Dashed
arrows point from an interface to procedures which implement that interface.
This could include the module procedures in a generic interface or the
implementation in a submodule of an interface in a parent module.

Nodes of different colours represent the following:

Solid arrows point from a procedure to one which it calls. Dashed
arrows point from an interface to procedures which implement that interface.
This could include the module procedures in a generic interface or the
implementation in a submodule of an interface in a parent module.