  The theory of persistence modules on the commutative ladders $CL_n(\tau)$
provides an extension of persistent homology. However, an efficient algorithm
to compute the generalized persistence diagrams is still lacking. In this work,
we view a persistence module $M$ on $CL_n(\tau)$ as a morphism between zigzag
modules, which can be expressed in a block matrix form. For the representation
finite case ($n\leq 4)$, we provide an algorithm that uses certain permissible
row and column operations to compute a normal form of the block matrix. In this
form an indecomposable decomposition of $M$, and thus its persistence diagram,
is obtained.
