VPEI
VPEI is a graphical tool based on the PEI theory, that generates
PEI equations from geometrical domain transformations.
The user is given the ability to create geometrical domains
that contains its input values, put in particular points of
the domain. Typically, coefficients of an (NxN) matrix will be
drawn in a ZxZ space, in the range 1<=i,j<=N. This domain of values
equipped with this particular drawing is called a data field.
Any created data field can be manipulated using any of the 3
functions
- Routing (or geometrical) function that moves the set of values
within the data field. (It can be thought in terms of communications)
- Computing (or functional) function that apply a calculus on
the whole set of values within the data field.
- Change of basis function that changes the drawing of the data field.
Values from distinct data fields have often to be combined to
compute results, as in the basic example of adding matrix A and
B. In this case, A and B values have to be superimposed so that
the calculus a(i,j)+b(i,j) can take place. PEI provides a superimposition
operator (a set operator) to enable several data fields to interact :
The result of a set operation like C = A /&/ B is data field C
whose values are sequences of values (a;b), given A and B had the same
drawing and values in all their components. We can now complete
the matrix addition example by writing that the application
of the add function on all pairs (a(i,j);b(i,j)) gives c(i,j)
in data field C, which is
C = add |> ( A/&/ B)
VPEI allows an operational step-by-step construction of the program,
writing at every transformation (function application) the
corresponding PEI equations in a dedicated text editor. A major
advantage of VPEI resides in the vizualisation of transformations
made on geometrical domains.
An example of VPEI session (matrix product).
Stephane Genaud
An example of VPEI session (matrix product).