The PRINCOMP Procedure

Computational Resources

Let

$\displaystyle  n  $
$\displaystyle  =  $
$\displaystyle  \mr {number~  of~  observations}  $
$\displaystyle v  $
$\displaystyle  =  $
$\displaystyle  \mr {number~  of~  VAR~  variables}  $
$\displaystyle p  $
$\displaystyle  =  $
$\displaystyle  \mr {number~  of~  PARTIAL~  variables}  $
$\displaystyle c  $
$\displaystyle  =  $
$\displaystyle  \mr {number~  of~  components}  $

  • The minimum allocated memory required (in bytes) is

    \[  232v+120p+48c+\max (8cv,8vp+4(v+p)(v+p+1))  \]
  • The time required to compute the correlation matrix is roughly proportional to

    \[  n(v+p)^2 + \frac{p}{2}(v+p)(v+p+1)  \]
  • The time required to compute eigenvalues is roughly proportional to $v^3$.

  • The time required to compute eigenvectors is roughly proportional to $cv^2$.