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# slaqsp

```
NAME
SLAQSP - equilibrate a symmetric matrix A using the scaling
factors in the vector S

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

CHARACTER      EQUED, UPLO

INTEGER        N

REAL           AMAX, SCOND

REAL           AP( * ), S( * )

PURPOSE
SLAQSP 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) REAL array, dimension (N*(N+1)/2)
On entry, the upper or lower triangle of the sym-
metric 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 equilibrated matrix:  diag(S) * A *
diag(S), in the same storage format as A.

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

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

AMAX    (input) REAL
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= 'Y':  Equilibration was done, i.e., A has been
replaced by diag(S) * A * diag(S).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.
```