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zsyequb.f(3) LAPACK zsyequb.f(3)

NAME

zsyequb.f

SYNOPSIS

Functions/Subroutines


subroutine zsyequb (UPLO, N, A, LDA, S, SCOND, AMAX, WORK, INFO)
ZSYEQUB

Function/Subroutine Documentation

subroutine zsyequb (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)

ZSYEQUB

Purpose:


ZSYEQUB computes row and column scalings intended to equilibrate a
symmetric 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.

Parameters:

UPLO


UPLO is CHARACTER*1
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.

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.

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
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


WORK is COMPLEX*16 array, dimension (2*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 2017

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://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.3.1679

Definition at line 134 of file zsyequb.f.

Author

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