---
name: "zlaqsy"
section: "3lapack"
platform: "linux"
package: "liblapack-doc"
version: "3.2.1-8"
release: "Debian 6.0 (Squeeze)"
platforms: ["linux"]
url: "https://new.carta.tech/zlaqsy/3lapack"
---

# zlaqsy(3lapack)

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

## NAME

ZLAQSY - equilibrates 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 contains 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 triangular 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   \= 'Y':  Equilibration was done, i.e., A has been replaced by diag(S) \* A \* diag(S).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 scaling should be done based on the absolute size of the largest matrix element. If AMAX \> LARGE or AMAX \< SMALL, scaling is done.