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

# csyequb(3lapack)

computes row and column scalings intended to equilibrate a symmetric matrix A and reduce its condition number (with respect to the two-norm)

## NAME

CSYEQUB - computes row and column scalings intended to equilibrate a symmetric matrix A and reduce its condition number (with respect to the two-norm)

## SYNOPSIS

- SUBROUTINE CSYEQUB(

  UPLO, N, A, LDA, S, SCOND, AMAX, WORK, INFO )

- IMPLICIT

  NONE

- INTEGER

  INFO, LDA, N

- REAL

  AMAX, SCOND

- CHARACTER

  UPLO

- COMPLEX

  A( LDA, \* ), WORK( \* )

- REAL

  S( \* )

## PURPOSE

CSYEQUB computes row and column scalings intended to equilibrate a symmetric matrix A and reduce its condition number (with respect to the two-norm).  S contains the scale factors, S(i) = 1/sqrt(A(i,i)), chosen so that the scaled matrix B with elements B(i,j) = S(i)\*A(i,j)\*S(j) has ones on the diagonal.  This choice of S puts the condition number of B within a factor N of the smallest possible condition number over all possible diagonal scalings.\

## ARGUMENTS

- N (input) INTEGER

  The order of the matrix A.  N \>= 0.

- A (input) COMPLEX array, dimension (LDA,N)

  The N-by-N symmetric matrix whose scaling factors are to be computed.  Only the diagonal elements of A are referenced.

- LDA (input) INTEGER

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

- S (output) REAL array, dimension (N)

  If INFO = 0, S contains the scale factors for A.

- SCOND (output) REAL

  If INFO = 0, S contains the ratio of the smallest S(i) to the largest S(i).  If SCOND \>= 0.1 and AMAX is neither too large nor too small, it is not worth scaling by S.

- AMAX (output) REAL

  Absolute value of largest matrix element.  If AMAX is very close to overflow or very close to underflow, the matrix should be scaled. INFO    (output) INTEGER = 0:  successful exit\
   \< 0:  if INFO = -i, the i-th argument had an illegal value\
   \> 0:  if INFO = i, the i-th diagonal element is nonpositive.