The CANCORR Procedure

Computational Resources

Notation

Let

\begin{eqnarray*}  n &  = &  \mbox{number of observations} \\ v &  = &  \mbox{number of variables} \\ w &  = &  \mbox{number of WITH variables} \\ p &  = &  \max (v,w) \\ q &  = &  \min (v,w) \\ b &  = &  v + w \\ t &  = &  \mbox{total number of variables (VAR, WITH, and PARTIAL)} \\ \end{eqnarray*}

Time Requirements

The time required to compute the correlation matrix is roughly proportional to

\[  n(p+q)^2  \]

The time required for the canonical analysis is roughly proportional to

\[  \frac{1}{6}p^3 + p^2q + \frac{3}{2}pq^2 + 5q^3  \]

but the coefficient for $q^3$ varies depending on the number of QR iterations in the singular value decomposition.

Memory Requirements

The minimum memory required is approximately

\[  4(v^2 + w^2 + t^2)  \]

bytes. Additional memory is required if you request the VDEP or WDEP option.