Computes row and column scaling factors intended to equilibrate a symmetric (Hermitian) positive definite matrix in packed storage and reduce its condition number.
The routine computes row and column scalings intended to equilibrate a symmetric (Hermitian) positive definite matrix
Ain packed storage and reduce its condition number (with respect to the two-norm).
The output array
sreturns scale factors such that
These factors are chosen so that the scaled matrix
has diagonal elements equal to 1.
This choice of
sputs the condition number of
Bwithin a factor
nof the smallest possible condition number over all possible diagonal scalings.
?laqspauxiliary function that uses scaling factors computed by
- Must beCHARACTER*1.'U'or'L'.Indicates whether the upper or lower triangular part ofAis packed in the arrayap:If, the arrayuplo='U'apstores the upper triangular part of the matrixA.If, the arrayuplo='L'apstores the lower triangular part of the matrixA.
- The order of matrixINTEGER.A;.n≥0
- REALfor single precision flavorsDOUBLE PRECISIONfor double precision flavors.Array, size (n).If, the arrayinfo= 0scontains the scale factors forA.
- REALfor single precision flavorsDOUBLE PRECISIONfor double precision flavors.If