subroutine zheequb (UPLO, N, A, LDA, S, SCOND, AMAX, WORK, INFO)
subroutine zheequb (character UPLO, integer N, complex*16, dimension( lda, * ) A, integer LDA, double precision, dimension( * ) S, double precision SCOND, double precision AMAX, complex*16, dimension( * ) WORK, integer INFO)
ZHEEQUB computes row and column scalings intended to equilibrate a Hermitian matrix A (with respect to the Euclidean norm) and reduce its condition number. The scale factors S are computed by the BIN algorithm (see references) so that the scaled matrix B with elements B(i,j) = S(i)*A(i,j)*S(j) has a condition number within a factor N of the smallest possible condition number over all possible diagonal scalings.
UPLO is CHARACTER*1 = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored.
N is INTEGER The order of the matrix A. N >= 0.
A is COMPLEX*16 array, dimension (LDA,N) The N-by-N Hermitian matrix whose scaling factors are to be computed.
LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).
S is DOUBLE PRECISION array, dimension (N) If INFO = 0, S contains the scale factors for A.
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 is DOUBLE PRECISION Largest absolute value of any matrix element. If AMAX is very close to overflow or very close to underflow, the matrix should be scaled.
WORK is COMPLEX*16 array, dimension (2*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: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.3.1679
Definition at line 134 of file zheequb.f.
Generated automatically by Doxygen for LAPACK from the source code.
The man page zheequb(3) is an alias of zheequb.f(3).