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
M_OPS function block (FB)
PIVOT operation by taking the ξ
vector from the
IorM-th column of its
input, and pivoting it into the
JorN-th column of its
output. In this case, the
inputs of the FB do not correspond to the indices i, j
or n in the algorithm above:
IorMinput specifies the column of the
Ainput matrix to be used as the ξ vector.
JorNinput specifies the pivot column index r in the
M_OPS FB performs the matrix inversion (
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
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 υr from the set of as-yet unpivoted columns.
If the absolute value of the maximum divisor υr
is less than the tolerance specified by the FB's
Amatrix is declared to be singular and the inversion operation terminates gracefully with an appropriate