ssyequb.f −

**Functions/Subroutines**

subroutine **ssyequb** (UPLO, N, A, LDA, S, SCOND, AMAX, WORK, INFO)

SSYEQUB

**subroutine ssyequb (characterUPLO, integerN, real, dimension( lda, * )A, integerLDA, real, dimension( * )S, realSCOND, realAMAX, real, dimension( * )WORK, integerINFO)
SSYEQUB**

**Purpose:**

SSYEQUB 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.

**Parameters:**

*UPLO*

UPLO is CHARACTER*1

Specifies whether the details of the factorization are stored

as an upper or lower triangular matrix.

= ’U’: Upper triangular, form is A = U*D*U**T;

= ’L’: Lower triangular, form is A = L*D*L**T.

*N*

N is INTEGER

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

*A*

A is REAL 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*

LDA is INTEGER

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

*S*

S is REAL array, dimension (N)

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

*SCOND*

SCOND is 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*

AMAX is REAL

Absolute value of largest matrix element. If AMAX is very

close to overflow or very close to underflow, the matrix

should be scaled.

*WORK*

WORK is REAL array, dimension (3*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.

**Date:**

November 2011

**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://ruready.utah.edu/archive/papers/bin.pdf

Definition at line 136 of file ssyequb.f.

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