ssyequb.f man page

ssyequb.f —

Synopsis

Functions/Subroutines

subroutine ssyequb (UPLO, N, A, LDA, S, SCOND, AMAX, WORK, INFO)
SSYEQUB

Function/Subroutine Documentation

subroutine ssyequb (character UPLO, integer N, real, dimension( lda, * ) A, integer LDA, real, dimension( * ) S, real SCOND, real AMAX, real, dimension( * ) WORK, integer INFO)

SSYEQUB  

Purpose:

 SSYEQUB 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 REAL 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 REAL array, dimension (N)
          If INFO = 0, S contains the scale factors for A.

SCOND

          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

          AMAX is REAL
          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 REAL 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:

December 2016

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 133 of file ssyequb.f.

Author

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Referenced By

The man page ssyequb(3) is an alias of ssyequb.f(3).

Sat Jun 24 2017 Version 3.7.1 LAPACK