zpoequb()

subroutine zpoequb	(	integer	n,
		complex*16, dimension( lda, * )	a,
		integer	lda,
		double precision, dimension( * )	s,
		double precision	scond,
		double precision	amax,
		integer	info )

ZPOEQUB

Download ZPOEQUB + dependencies [TGZ] [ZIP] [TXT]

Purpose:

!>
!> ZPOEQUB computes row and column scalings intended to equilibrate a
!> Hermitian positive definite 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.
!>
!> This routine differs from ZPOEQU by restricting the scaling factors
!> to a power of the radix.  Barring over- and underflow, scaling by
!> these factors introduces no additional rounding errors.  However, the
!> scaled diagonal entries are no longer approximately 1 but lie
!> between sqrt(radix) and 1/sqrt(radix).
!> 

Parameters

[in]	N	!> N is INTEGER !> The order of the matrix A. N >= 0. !>
[in]	A	!> A is COMPLEX*16 array, dimension (LDA,N) !> The N-by-N Hermitian positive definite 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 DOUBLE PRECISION array, dimension (N) !> If INFO = 0, S contains the scale factors for A. !>
[out]	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. !>
[out]	AMAX	!> AMAX is DOUBLE PRECISION !> Absolute value of largest matrix element. If AMAX is very !> close to overflow or very close to underflow, the matrix !> should be scaled. !>
[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.

Definition at line 116 of file zpoequb.f.

*
*  -- LAPACK computational routine --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
*     .. Scalar Arguments ..
      INTEGER            INFO, LDA, N
      DOUBLE PRECISION   AMAX, SCOND
*     ..
*     .. Array Arguments ..
      COMPLEX*16         A( LDA, * )
      DOUBLE PRECISION   S( * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ZERO, ONE
      parameter( zero = 0.0d+0, one = 1.0d+0 )
*     ..
*     .. Local Scalars ..
      INTEGER            I
      DOUBLE PRECISION   SMIN, BASE, TMP
*     ..
*     .. External Functions ..
      DOUBLE PRECISION   DLAMCH
      EXTERNAL           dlamch
*     ..
*     .. External Subroutines ..
      EXTERNAL           xerbla
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          max, min, sqrt, log, int, real, dimag
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
*     Positive definite only performs 1 pass of equilibration.
*
      info = 0
      IF( n.LT.0 ) THEN
         info = -1
      ELSE IF( lda.LT.max( 1, n ) ) THEN
         info = -3
      END IF
      IF( info.NE.0 ) THEN
         CALL xerbla( 'ZPOEQUB', -info )
         RETURN
      END IF
*
*     Quick return if possible.
*
      IF( n.EQ.0 ) THEN
         scond = one
         amax = zero
         RETURN
      END IF
 
      base = dlamch( 'B' )
      tmp = -0.5d+0 / log( base )
*
*     Find the minimum and maximum diagonal elements.
*
      s( 1 ) = dble( a( 1, 1 ) )
      smin = s( 1 )
      amax = s( 1 )
      DO 10 i = 2, n
         s( i ) = dble( a( i, i ) )
         smin = min( smin, s( i ) )
         amax = max( amax, s( i ) )
   10 CONTINUE
*
      IF( smin.LE.zero ) THEN
*
*        Find the first non-positive diagonal element and return.
*
         DO 20 i = 1, n
            IF( s( i ).LE.zero ) THEN
               info = i
               RETURN
            END IF
   20    CONTINUE
      ELSE
*
*        Set the scale factors to the reciprocals
*        of the diagonal elements.
*
         DO 30 i = 1, n
            s( i ) = base ** int( tmp * log( s( i ) ) )
   30    CONTINUE
*
*        Compute SCOND = min(S(I)) / max(S(I)).
*
         scond = sqrt( smin ) / sqrt( amax )
      END IF
*
      RETURN
*
*     End of ZPOEQUB
*

Here is the call graph for this function:

Here is the caller graph for this function: