zspt03.f

Go to the documentation of this file.

*> \brief \b ZSPT03
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 
*
*  Definition:
*  ===========
*
*       SUBROUTINE ZSPT03( UPLO, N, A, AINV, WORK, LDW, RWORK, RCOND,
*                          RESID )
* 
*       .. Scalar Arguments ..
*       CHARACTER          UPLO
*       INTEGER            LDW, N
*       DOUBLE PRECISION   RCOND, RESID
*       ..
*       .. Array Arguments ..
*       DOUBLE PRECISION   RWORK( * )
*       COMPLEX*16         A( * ), AINV( * ), WORK( LDW, * )
*       ..
*  
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> ZSPT03 computes the residual for a complex symmetric packed matrix
*> times its inverse:
*>    norm( I - A*AINV ) / ( N * norm(A) * norm(AINV) * EPS ),
*> where EPS is the machine epsilon.
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] UPLO
*> \verbatim
*>          UPLO is CHARACTER*1
*>          Specifies whether the upper or lower triangular part of the
*>          complex symmetric matrix A is stored:
*>          = 'U':  Upper triangular
*>          = 'L':  Lower triangular
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>          The number of rows and columns of the matrix A.  N >= 0.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*>          A is COMPLEX*16 array, dimension (N*(N+1)/2)
*>          The original complex symmetric matrix A, stored as a packed
*>          triangular matrix.
*> \endverbatim
*>
*> \param[in] AINV
*> \verbatim
*>          AINV is COMPLEX*16 array, dimension (N*(N+1)/2)
*>          The (symmetric) inverse of the matrix A, stored as a packed
*>          triangular matrix.
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*>          WORK is COMPLEX*16 array, dimension (LDW,N)
*> \endverbatim
*>
*> \param[in] LDW
*> \verbatim
*>          LDW is INTEGER
*>          The leading dimension of the array WORK.  LDW >= max(1,N).
*> \endverbatim
*>
*> \param[out] RWORK
*> \verbatim
*>          RWORK is DOUBLE PRECISION array, dimension (N)
*> \endverbatim
*>
*> \param[out] RCOND
*> \verbatim
*>          RCOND is DOUBLE PRECISION
*>          The reciprocal of the condition number of A, computed as
*>          ( 1/norm(A) ) / norm(AINV).
*> \endverbatim
*>
*> \param[out] RESID
*> \verbatim
*>          RESID is DOUBLE PRECISION
*>          norm(I - A*AINV) / ( N * norm(A) * norm(AINV) * EPS )
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date November 2011
*
*> \ingroup complex16_lin
*
*  =====================================================================
      SUBROUTINE zspt03( UPLO, N, A, AINV, WORK, LDW, RWORK, RCOND,
     $                   resid )
*
*  -- LAPACK test routine (version 3.4.0) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     November 2011
*
*     .. Scalar Arguments ..
      CHARACTER          uplo
      INTEGER            ldw, n
      DOUBLE PRECISION   rcond, resid
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION   rwork( * )
      COMPLEX*16         a( * ), ainv( * ), work( ldw, * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   zero, one
      parameter( zero = 0.0d+0, one = 1.0d+0 )
*     ..
*     .. Local Scalars ..
      INTEGER            i, icol, j, jcol, k, kcol, nall
      DOUBLE PRECISION   ainvnm, anorm, eps
      COMPLEX*16         t
*     ..
*     .. External Functions ..
      LOGICAL            lsame
      DOUBLE PRECISION   dlamch, zlange, zlansp
      COMPLEX*16         zdotu
      EXTERNAL           lsame, dlamch, zlange, zlansp, zdotu
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          dble
*     ..
*     .. Executable Statements ..
*
*     Quick exit if N = 0.
*
      IF( n.LE.0 ) THEN
         rcond = one
         resid = zero
         return
      END IF
*
*     Exit with RESID = 1/EPS if ANORM = 0 or AINVNM = 0.
*
      eps = dlamch( 'Epsilon' )
      anorm = zlansp( '1', uplo, n, a, rwork )
      ainvnm = zlansp( '1', uplo, n, ainv, rwork )
      IF( anorm.LE.zero .OR. ainvnm.LE.zero ) THEN
         rcond = zero
         resid = one / eps
         return
      END IF
      rcond = ( one / anorm ) / ainvnm
*
*     Case where both A and AINV are upper triangular:
*     Each element of - A * AINV is computed by taking the dot product
*     of a row of A with a column of AINV.
*
      IF( lsame( uplo, 'U' ) ) THEN
         DO 70 i = 1, n
            icol = ( ( i-1 )*i ) / 2 + 1
*
*           Code when J <= I
*
            DO 30 j = 1, i
               jcol = ( ( j-1 )*j ) / 2 + 1
               t = zdotu( j, a( icol ), 1, ainv( jcol ), 1 )
               jcol = jcol + 2*j - 1
               kcol = icol - 1
               DO 10 k = j + 1, i
                  t = t + a( kcol+k )*ainv( jcol )
                  jcol = jcol + k
   10          continue
               kcol = kcol + 2*i
               DO 20 k = i + 1, n
                  t = t + a( kcol )*ainv( jcol )
                  kcol = kcol + k
                  jcol = jcol + k
   20          continue
               work( i, j ) = -t
   30       continue
*
*           Code when J > I
*
            DO 60 j = i + 1, n
               jcol = ( ( j-1 )*j ) / 2 + 1
               t = zdotu( i, a( icol ), 1, ainv( jcol ), 1 )
               jcol = jcol - 1
               kcol = icol + 2*i - 1
               DO 40 k = i + 1, j
                  t = t + a( kcol )*ainv( jcol+k )
                  kcol = kcol + k
   40          continue
               jcol = jcol + 2*j
               DO 50 k = j + 1, n
                  t = t + a( kcol )*ainv( jcol )
                  kcol = kcol + k
                  jcol = jcol + k
   50          continue
               work( i, j ) = -t
   60       continue
   70    continue
      ELSE
*
*        Case where both A and AINV are lower triangular
*
         nall = ( n*( n+1 ) ) / 2
         DO 140 i = 1, n
*
*           Code when J <= I
*
            icol = nall - ( ( n-i+1 )*( n-i+2 ) ) / 2 + 1
            DO 100 j = 1, i
               jcol = nall - ( ( n-j )*( n-j+1 ) ) / 2 - ( n-i )
               t = zdotu( n-i+1, a( icol ), 1, ainv( jcol ), 1 )
               kcol = i
               jcol = j
               DO 80 k = 1, j - 1
                  t = t + a( kcol )*ainv( jcol )
                  jcol = jcol + n - k
                  kcol = kcol + n - k
   80          continue
               jcol = jcol - j
               DO 90 k = j, i - 1
                  t = t + a( kcol )*ainv( jcol+k )
                  kcol = kcol + n - k
   90          continue
               work( i, j ) = -t
  100       continue
*
*           Code when J > I
*
            icol = nall - ( ( n-i )*( n-i+1 ) ) / 2
            DO 130 j = i + 1, n
               jcol = nall - ( ( n-j+1 )*( n-j+2 ) ) / 2 + 1
               t = zdotu( n-j+1, a( icol-n+j ), 1, ainv( jcol ), 1 )
               kcol = i
               jcol = j
               DO 110 k = 1, i - 1
                  t = t + a( kcol )*ainv( jcol )
                  jcol = jcol + n - k
                  kcol = kcol + n - k
  110          continue
               kcol = kcol - i
               DO 120 k = i, j - 1
                  t = t + a( kcol+k )*ainv( jcol )
                  jcol = jcol + n - k
  120          continue
               work( i, j ) = -t
  130       continue
  140    continue
      END IF
*
*     Add the identity matrix to WORK .
*
      DO 150 i = 1, n
         work( i, i ) = work( i, i ) + one
  150 continue
*
*     Compute norm(I - A*AINV) / (N * norm(A) * norm(AINV) * EPS)
*
      resid = zlange( '1', n, n, work, ldw, rwork )
*
      resid = ( ( resid*rcond ) / eps ) / dble( n )
*
      return
*
*     End of ZSPT03
*
      END