Rather than describing the distribution of each individual
vector and matrix directly, the PLAPACK infrastructure requires
the distribution of (imaginary)
*template* vectors and
matrices to
be described. Vector and matrix distribution is
given by indicating alignment with respect to these template vectors and matrices.

Imagine an infinite length vector *t* , which is
partitioned like

with all of uniform length , the
distribution blocking size (see Figure 2.1).
Sub-vectors are assigned to the logical two-dimensional
mesh corresponding to the communicator (mentioned above)
by wrapping in
column-major order:
is assigned to
,
as illustrated in Figure 2.1.
Here *r* and *c* denote the row and column dimension
of the mesh of nodes encoded in the PLAPACK base communicator.
We will call this the
**template vector**.
In our discussion, we will start our indexing at zero, as is
customary in C.
PLAPACK allows one to specify whether
to start counting at one, as is customary in FORTRAN, or zero.

A distributed vector is
**aligned** to this template vector
by indicating the element of the template vector with which
the first element of the vector to be distributed is aligned,
as illustrated in Figure 2.1.
The distribution of the elements of the vector to be distributed
is
then dictated by the distribution of corresponding elements
of the template vector.
Thus, if the first element of the vector is aligned with
element *i* of the template vector,
the *j* th element of the vector to be distributed is
assigned to the same node as the *i*+*j* th element
of the template vector.

The distribution of matrices is now induced by this template vector.
More specifically, let *T* be an infinite matrix,
partitioned like

where are sub-matrices.
Then this
**template matrix**
is distributed to
nodes as induced by the template vector, *t* ,
as illustrated
in Figure .
A given matrix to be distributed is now
aligned to
this template by indicating the element of *T* with
which the top-left element of the matrix to be distributed
is aligned, as illustrated in Figure 2.2.