csyequb.f(3) LAPACK csyequb.f(3)NAME
subroutine csyequb (UPLO, N, A, LDA, S, SCOND, AMAX, WORK, INFO)
subroutine csyequb (characterUPLO, integerN, complex, dimension( lda, * )A,
integerLDA, real, dimension( * )S, realSCOND, realAMAX, complex,
dimension( * )WORK, integerINFO)
CSYEQUB 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
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 is INTEGER
The order of the matrix A. N >= 0.
A is COMPLEX array, dimension (LDA,N)
The N-by-N symmetric matrix whose scaling
factors are to be computed. Only the diagonal elements of A
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,N).
S is REAL array, dimension (N)
If INFO = 0, S contains the scale factors for A.
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 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 is COMPLEX array, dimension (3*N)
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.
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
Livne, O.E. and Golub, G.H., 'Scaling by Binormalization',
Numerical Algorithms, vol. 35, no. 1, pp. 97-120, January 2004.
Tech report version:
Definition at line 137 of file csyequb.f.
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Version 3.4.2 Tue Sep 25 2012 csyequb.f(3)