# zheequb.f - Man Page

SRC/zheequb.f

## Synopsis

### Functions/Subroutines

subroutine **zheequb** (uplo, n, a, lda, s, scond, amax, work, info)**ZHEEQUB**

## Function/Subroutine Documentation

### subroutine zheequb (character uplo, integer n, complex*16, dimension( lda, * ) a, integer lda, double precision, dimension( * ) s, double precision scond, double precision amax, complex*16, dimension( * ) work, integer info)

**ZHEEQUB**

**Purpose:**

ZHEEQUB computes row and column scalings intended to equilibrate a Hermitian matrix A (with respect to the Euclidean norm) and reduce its condition number. The scale factors S are computed by the BIN algorithm (see references) so that the scaled matrix B with elements B(i,j) = S(i)*A(i,j)*S(j) has a condition number within a factor N of the smallest possible condition number over all possible diagonal scalings.

**Parameters***UPLO*UPLO is CHARACTER*1 = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored.

*N*N is INTEGER The order of the matrix A. N >= 0.

*A*A is COMPLEX*16 array, dimension (LDA,N) The N-by-N Hermitian matrix whose scaling factors are to be computed.

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

*S*S is DOUBLE PRECISION array, dimension (N) If INFO = 0, S contains the scale factors for A.

*SCOND*SCOND is DOUBLE PRECISION 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*AMAX is DOUBLE PRECISION Largest absolute value of any matrix element. If AMAX is very close to overflow or very close to underflow, the matrix should be scaled.

*WORK*WORK is COMPLEX*16 array, dimension (2*N)

*INFO*INFO is 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.

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**References:**Livne, O.E. and Golub, G.H., 'Scaling by Binormalization',

Numerical Algorithms, vol. 35, no. 1, pp. 97-120, January 2004.

DOI 10.1023/B:NUMA.0000016606.32820.69

Tech report version: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.3.1679

Definition at line **131** of file **zheequb.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page zheequb(3) is an alias of zheequb.f(3).

Tue Nov 28 2023 12:08:42 Version 3.12.0 LAPACK