The modal assurance criterion (MAC) can compare two real solutions or two complex solutions.

The MAC between two real solutions is computed using the equation:

(17–160)

where:

= the ith displacement vector of solution 1. (solution 1 is read on File1 and index i corresponds to Sbstep1 on the RSTMAC command).

= the jth displacement vector of solution 2. For the case of the .UNV file, it can also be an acceleration vector of solution 2. (solution 2 is read on File2 and index j corresponds to Sbstep2 on the RSTMAC command).

m (k) = diagonal of the mass matrix used in obtaining solution k. It is included in the calculation only if KeyMass is ON (default). k = 1 if nodes are matched (TolerN and/or TolerR > 0 on the RSTMAC command). k = 2 if nodes are mapped and solution 1 is interpolated (TolerN = -1 on the RSTMAC command).

The MAC between two complex solutions is computed using the equation:

(17–161)

where:

= the complex conjugate of a complex vector .

If the diagonal of the mass matrix is not available (for example on a Universal Format file), the modal assurance criterion is not weighted with the mass, i.e. the mass is assumed to be equal at all degrees of freedom.

The dot product of the displacement vectors is calculated at matched nodes if TolerN or TolerR > 0, and at mapped nodes if TolerN = -1.