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# zlaqsy

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

SYNOPSIS
SUBROUTINE ZLAQSY( UPLO, N, A, LDA, S, SCOND, AMAX, EQUED )

CHARACTER      EQUED, UPLO

INTEGER        LDA, N

DOUBLE         PRECISION AMAX, SCOND

DOUBLE         PRECISION S( * )

COMPLEX*16     A( LDA, * )

PURPOSE
ZLAQSY 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.

A       (input/output) COMPLEX*16 array, dimension (LDA,N)
On entry, the symmetric matrix A.  If UPLO = 'U',
the leading n by n upper triangular part of A con-
tains the upper triangular part of the matrix A, and
the strictly lower triangular part of A is not
referenced.  If UPLO = 'L', the leading n by n lower
triangular part of A contains the lower triangular
part of the matrix A, and the strictly upper tri-
angular part of A is not referenced.

On exit, if EQUED = 'Y', the equilibrated matrix:
diag(S) * A * diag(S).

LDA     (input) INTEGER
The leading dimension of the array A.  LDA >=
max(N,1).

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= 'Y':  Equilibration was done, i.e., A has been
replaced by diag(S) * A * diag(S).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