The Product Form of the Inverse (PFI) is based on the fact that, if we already have the inverse B of an n×n matrix C, we can obtain the inverse B ^{*} of a new matrix C ^{*} , formed by replacing column r of C by a vector ξ, by evaluating the matrix product υ = Bξ and then performing a pivot operation expressed by the formulae
An M_OPS
function block (FB)
performs the PIVOT
operation by taking the ξ
vector from the IorM
th column of its A
MATRIX
input, and pivoting it into the JorN
th column of its B
output. In this case, the IorM
and JorN
inputs of the FB do not correspond to the indices i, j
or n in the algorithm above:

The
IorM
input specifies the column of theA
input matrix to be used as the ξ vector. 
The
JorN
input specifies the pivot column index r in theB
matrix output.
An M_OPS
FB performs the matrix inversion (INV
)
function by initializing the B
matrix output to an
identity matrix of the same order as the A
matrix input,
and then pivoting the columns of A
into B
one at a time.
 A maximum pivot divisor strategy is used to provide the highest accuracy of the inverse. That is, at each iteration, the index r of the pivot column is chosen to maximize the absolute value of the divisor υ_{r} from the set of asyet unpivoted columns.

If the absolute value of the maximum divisor υ_{r}
is less than the tolerance specified by the FB's
X
input, theA
matrix is declared to be singular and the inversion operation terminates gracefully with an appropriateSTATUS
output code.