cheequb.f

Section: LAPACK (3)
Updated: Tue Nov 14 2017
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NAME

cheequb.f  

SYNOPSIS


 

Functions/Subroutines


subroutine cheequb (UPLO, N, A, LDA, S, SCOND, AMAX, WORK, INFO)
CHEEQUB  

Function/Subroutine Documentation

 

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

CHEEQUB

Purpose:

 CHEEQUB 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.


 

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 array, dimension (LDA,N)
          The N-by-N Hermitian 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 COMPLEX 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:

April 2012

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 cheequb.f.  

Author

Generated automatically by Doxygen for LAPACK from the source code.


 

Index

NAME
SYNOPSIS
Functions/Subroutines
Function/Subroutine Documentation
subroutine cheequb (character UPLO, integer N, complex, dimension( lda, * ) A, integer LDA, real, dimension( * ) S, real SCOND, real AMAX, complex, dimension( * ) WORK, integer INFO)
Author
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