2.1 Minterms and matlab calculations  (Page 5/6)

The procedure mincalc

The procedure mincalc performs calculations as in the preceding examples. The refinements consist of determining consistency and computability of various individual minterm probabilities and target probilities. The consistency checkis principally for negative minterm probabilities. The computability tests are tests for linear independence by means of calculation of ranks of variousmatrices. The procedure picks out the computable minterm probabilities and the computable target probabilities and calculates them.

To utilize the procedure, the problem must be formulated appropriately and precisely, as follows:

1. Use the MATLAB program minvecq to set minterm vectors for each of q basic events.
2. Data consist of Boolean combinations of the basic events and the respective probabilities of these combinations. These are organized intotwo matrices:
   • The data vector matrix $DV$ has the data Boolean combinations– one on each row. MATLAB translates each row into the minterm vector for the corresponding Boolean combination.The first entry (on the first row) is A $|$ Ac (for $A\bigvee A^c$ ), which is the whole space. Its minterm vector consists of a row of ones.
   • The data probability matrix $DP$ is a row matrix of the data probabilities. The first entry is one, the probability of the whole space.
3. The objective is to determine the probability of various target Boolean combinations. These are put into the target vector matrix $TV$ , one on each row. MATLAB produces the minterm vector for each corresponding target Boolean combination.

Computational note . In mincalc, it is necessary to turn the arrays DV and TV consisting of zero-one patterns into zero-one matrices. This is accomplished for DV by theoperation DV = ones(size(DV)).*DV . and similarly for TV. Both the original and the transformed matrices have the same zero-one pattern, but MATLAB interprets them differently.

Usual case

Ṡuppose the data minterm vectors are linearly independent and the target vectors are each linearly dependent on the data minterm vectors. Then each targetminterm vector is expressible as a linear combination of data minterm vectors. Thus, there is a matrix $CT$ such that $TV=CT*DV$ . MATLAB solves this with the command $CT=TV/DV$ . The target probabilities are the same linear combinations of the data probabilities . These are obtained by the MATLAB operation $tp=DP*C{T}^{\text{'}}$ .