dsyequb.f(3) LAPACK dsyequb.f(3)
NAME
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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Version 3.4.2 Tue Sep 25 2012 dsyequb.f(3)