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

# cppequ(3lapack)

computes row and column scalings intended to equilibrate a Hermitian positive definite matrix A in packed storage and reduce its condition number (with respect to the two-norm)

## NAME

CPPEQU - computes row and column scalings intended to equilibrate a Hermitian positive definite matrix A in packed storage and reduce its condition number (with respect to the two-norm)

## SYNOPSIS

- SUBROUTINE CPPEQU(

  UPLO, N, AP, S, SCOND, AMAX, INFO )

- CHARACTER

  UPLO

- INTEGER

  INFO, N

- REAL

  AMAX, SCOND

- REAL

  S( \* )

- COMPLEX

  AP( \* )

## PURPOSE

CPPEQU computes row and column scalings intended to equilibrate a Hermitian positive definite matrix A in packed storage 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

- UPLO (input) CHARACTER\*1

  \= 'U':  Upper triangle of A is stored;\
   \= 'L':  Lower triangle of A is stored.

- N (input) INTEGER

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

- AP (input) COMPLEX array, dimension (N\*(N+1)/2)

  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.

- 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.