dlaqsp man page on Scientific

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```DLAQSP(1)	    LAPACK auxiliary routine (version 3.2)	     DLAQSP(1)

NAME
DLAQSP - equilibrates a symmetric matrix A using the scaling factors in
the vector S

SYNOPSIS
SUBROUTINE DLAQSP( UPLO, N, AP, S, SCOND, AMAX, EQUED )

CHARACTER	  EQUED, UPLO

INTEGER	  N

DOUBLE	  PRECISION AMAX, SCOND

DOUBLE	  PRECISION AP( * ), S( * )

PURPOSE
DLAQSP equilibrates a symmetric matrix A using the scaling  factors  in
the vector S.

ARGUMENTS
UPLO    (input) CHARACTER*1
Specifies  whether  the	upper  or lower triangular part of the
symmetric matrix A is stored.  = 'U':  Upper triangular
= 'L':  Lower triangular

N       (input) INTEGER
The order of the matrix A.  N >= 0.

AP      (input/output) DOUBLE PRECISION array, dimension (N*(N+1)/2)
On entry, the upper or lower triangle of the  symmetric	matrix
A,  packed  columnwise in a linear array.  The j-th column of A
is stored in the array AP as follows: if UPLO  =	 'U',  AP(i  +
(j-1)*j/2)  =  A(i,j)  for  1<=i<=j;  if	 UPLO  =  'L',	AP(i +
(j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.   On  exit,  the  equili‐
brated matrix:  diag(S) * A * diag(S), in the same storage for‐
mat as A.

S       (input) DOUBLE PRECISION array, dimension (N)
The scale factors for A.

SCOND   (input) DOUBLE PRECISION
Ratio of the smallest S(i) to the largest S(i).

AMAX    (input) DOUBLE PRECISION
Absolute value of largest matrix entry.

EQUED   (output) CHARACTER*1
Specifies whether or not equilibration was done.	  =  'N':   No
equilibration.
=  'Y':	 Equilibration	was done, i.e., A has been replaced by
diag(S) * A * diag(S).

PARAMETERS
THRESH is a threshold value used to decide if scaling  should  be  done
based  on the ratio of the scaling factors.  If SCOND < THRESH, scaling
is done.	 LARGE and SMALL are threshold values used to decide if	 scal‐
ing  should  be	done  based on the absolute size of the largest matrix
element.	 If AMAX > LARGE or AMAX < SMALL, scaling is done.

LAPACK auxiliary routine (versioNovember 2008			     DLAQSP(1)
```
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