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

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

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 


Download CHEEQUB + dependencies [TGZ] [ZIP] [TXT]
 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
          UPLO is CHARACTER*1
          = 'U':  Upper triangles of A and B are stored;
          = 'L':  Lower triangles of A and B are stored.
          N is INTEGER
          The order of the matrix A.  N >= 0.
          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.
          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N).
          S is REAL array, dimension (N)
          If INFO = 0, S contains the scale factors for A.
          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 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.
          WORK is COMPLEX array, dimension (3*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
NAG Ltd.
April 2012

Definition at line 127 of file cheequb.f.

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