subroutine zsyequb (UPLO, N, A, LDA, S, SCOND, AMAX, WORK, INFO)
subroutine zsyequb (characterUPLO, integerN, complex*16, dimension( lda, * )A, integerLDA, double precision, dimension( * )S, double precisionSCOND, double precisionAMAX, complex*16, dimension( * )WORK, integerINFO)ZSYEQUB Purpose:
ZSYEQUB 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.
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 COMPLEX*16 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 COMPLEX*16 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.
Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd.Date:
Livne, O.E. and Golub, G.H., 'Scaling by Binormalization',Definition at line 137 of file zsyequb.f.
Numerical Algorithms, vol. 35, no. 1, pp. 97-120, January 2004.
Tech report version: http://ruready.utah.edu/archive/papers/bin.pdf