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:

(17–143)

where:

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

= the jth solution vector of solution 2. For the case of the .unv file, it can be a displacement or an acceleration vector of solution 2. (Solution 2 is read from 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 ( Option = ABSTOLN and/or RELTOLN > 0 on the MACOPT command). k = 2 if nodes are mapped and solution 1 is interpolated ( Option = NODMAP on the MACOPT command).

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

(17–144)

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 or for non-structural degrees of freedom), the modal assurance criterion is not weighted with the mass; that is, the mass is assumed to be equal at all degrees of freedom.

The dot product of the solution vectors is calculated: