The CANCORR Procedure

Computational Resources

Notation

Let

$\displaystyle  n  $
$\displaystyle  =  $
$\displaystyle  \mbox{number of observations}  $
$\displaystyle v  $
$\displaystyle  =  $
$\displaystyle  \mbox{number of variables}  $
$\displaystyle w  $
$\displaystyle  =  $
$\displaystyle  \mbox{number of WITH variables}  $
$\displaystyle p  $
$\displaystyle  =  $
$\displaystyle  \max (v,w)  $
$\displaystyle q  $
$\displaystyle  =  $
$\displaystyle  \min (v,w)  $
$\displaystyle b  $
$\displaystyle  =  $
$\displaystyle  v + w  $
$\displaystyle t  $
$\displaystyle  =  $
$\displaystyle  \mbox{total number of variables (VAR, WITH, and PARTIAL)}  $

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.