Analysis of Crosscutting in Early Software Development Phases Based on Traceability - Transactions on Aspect-Oriented Software Development - page 80

Based on the dependency matrix, we define some auxiliary matrices: the scattering
matrix (source x target) and the tangling matrix (target x source). For our example in
Table 4 these matrices are shown in Table 5 . These two matrices are defined as
follows:
•

In a scattering matrix, a row contains only dependency relations from source to
target elements if the source element in this row is scattered (mapped onto
multiple target elements); otherwise, the row contains just zeroes (no scattering).

• In a tangling matrix, a row contains only dependency relations from target to

source elements if the target element in this row is tangled (mapped onto multiple
source elements); otherwise, the row contains just zeroes (no tangling).

Table 5. Scattering and tangling matrices for dependency matrix in Table 4

scattering matrix

target

t[1] t[2] t[3] t[4] t[5] t[6]

s[1] 1 0 0 1 0 0

s[2] 1 0 1 0 1 1

s[3] 0 0 0 0 0 0

s[4] 0 1 1 0 0 0

s[5] 0 0 0 1 1 0

tangling matrix

source

s[1] S[2] s[3] s[4] s[5]

t[1] 1 1 1 0 0

t[2] 0 0 0 0 0

t[3] 0 1 0 1 0

t[4] 1 0 0 0 1

t[5] 0 1 0 0 1

t[6] 0 0 0 0 0

We now define the crosscutting product matrix, showing the number of
crosscutting relations. The crosscutting product matrix ccpm can be obtained through
the matrix multiplication of the scattering matrix sm and the tangling matrix tm:
ccpm = sm x tm where ccpm [i][k] = sm[i][j] x tm[j][k]. We use this matrix to derive
the final crosscutting matrix. In the crosscutting matrix, a matrix cell denotes the
occurrence of crosscutting; it abstracts from the quantity of crosscutting. The
crosscutting matrix ccm can be derived from the crosscutting product matrix ccpm
using a simple conversion: ccm[i][k] = if (ccpm[i][k] > 0) /\ ( i ≠ j) then 1 else 0.
The crosscutting product matrix for the example is given in Table 6 . From this
crosscutting product matrix we derive the crosscutting matrix shown in Table 4 .
In this example there are no cells in the crosscutting product matrix larger than
one, except on the diagonal where it denotes a crosscutting relation with itself and
which we disregard here. In the crosscutting matrix, we set the diagonal cells to zero
because, we assume that an element cannot crosscut itself.
In the crosscutting matrix in Table 4 there are now ten crosscutting relations
between the source elements. The crosscutting matrix shows again that our definition