dsyequb.f (3) Linux Manual Page

dsyequb.f –

Synopsis

Functions/Subroutines

subroutine dsyequb (UPLO, N, A, LDA, S, SCOND, AMAX, WORK, INFO)
DSYEQUB

Function/Subroutine Documentation

subroutine dsyequb (characterUPLO, integerN, double precision, dimension( lda, * )A, integerLDA, double precision, dimension( * )S, double precisionSCOND, double precisionAMAX, double precision, dimension( * )WORK, integerINFO)

DSYEQUB

Purpose:

 DSYEQUB 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 DOUBLE PRECISION 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 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

 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 DOUBLE PRECISION 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 dsyequb.f.

Author

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