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# LAPACK-3

## man page of LAPACK-3

### LAPACK-3: equilibrates a Hermitian matrix A using the scaling factors in the vector S

```NAME
LAPACK-3  - equilibrates a Hermitian matrix A using the scaling factors
in the vector S

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

CHARACTER      EQUED, UPLO

INTEGER        N

DOUBLE         PRECISION AMAX, SCOND

DOUBLE         PRECISION S( * )

COMPLEX*16     AP( * )

PURPOSE
ZLAQHP equilibrates a Hermitian 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
Hermitian matrix A is stored.
= 'U':  Upper triangular
= 'L':  Lower triangular

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

AP      (input/output) COMPLEX*16 array, dimension (N*(N+1)/2)
On entry, the upper or lower triangle of the Hermitian 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) 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= 'Y':  Equilibration was done, i.e., A has been replaced by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 scaling 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 (versionMarch 2011                       LAPACK-3(3)
```