LAPACK  3.4.2
LAPACK: Linear Algebra PACKage
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cheequb.f File Reference

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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

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Purpose: 
 CHEEQUB computes row and column scalings intended to equilibrate a
 Hermitian 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.
Parameters:
[in]UPLO
          UPLO is CHARACTER*1
          = 'U':  Upper triangles of A and B are stored;
          = 'L':  Lower triangles of A and B are stored.
[in]N
          N is INTEGER
          The order of the matrix A.  N >= 0.
[in]A
          A is COMPLEX array, dimension (LDA,N)
          The N-by-N Hermitian matrix whose scaling
          factors are to be computed.  Only the diagonal elements of A
          are referenced.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N).
[out]S
          S is REAL array, dimension (N)
          If INFO = 0, S contains the scale factors for A.
[out]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.
[out]AMAX
          AMAX is REAL
          Absolute value of largest matrix element.  If AMAX is very
          close to overflow or very close to underflow, the matrix
          should be scaled.
[out]WORK
          WORK is COMPLEX array, dimension (3*N)
[out]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

Definition at line 127 of file cheequb.f.

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