zget22.f

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*> \brief \b ZGET22
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 
*
*  Definition:
*  ===========
*
*       SUBROUTINE ZGET22( TRANSA, TRANSE, TRANSW, N, A, LDA, E, LDE, W,
*                          WORK, RWORK, RESULT )
* 
*       .. Scalar Arguments ..
*       CHARACTER          TRANSA, TRANSE, TRANSW
*       INTEGER            LDA, LDE, N
*       ..
*       .. Array Arguments ..
*       DOUBLE PRECISION   RESULT( 2 ), RWORK( * )
*       COMPLEX*16         A( LDA, * ), E( LDE, * ), W( * ), WORK( * )
*       ..
*  
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> ZGET22 does an eigenvector check.
*>
*> The basic test is:
*>
*>    RESULT(1) = | A E  -  E W | / ( |A| |E| ulp )
*>
*> using the 1-norm.  It also tests the normalization of E:
*>
*>    RESULT(2) = max | m-norm(E(j)) - 1 | / ( n ulp )
*>                 j
*>
*> where E(j) is the j-th eigenvector, and m-norm is the max-norm of a
*> vector.  The max-norm of a complex n-vector x in this case is the
*> maximum of |re(x(i)| + |im(x(i)| over i = 1, ..., n.
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] TRANSA
*> \verbatim
*>          TRANSA is CHARACTER*1
*>          Specifies whether or not A is transposed.
*>          = 'N':  No transpose
*>          = 'T':  Transpose
*>          = 'C':  Conjugate transpose
*> \endverbatim
*>
*> \param[in] TRANSE
*> \verbatim
*>          TRANSE is CHARACTER*1
*>          Specifies whether or not E is transposed.
*>          = 'N':  No transpose, eigenvectors are in columns of E
*>          = 'T':  Transpose, eigenvectors are in rows of E
*>          = 'C':  Conjugate transpose, eigenvectors are in rows of E
*> \endverbatim
*>
*> \param[in] TRANSW
*> \verbatim
*>          TRANSW is CHARACTER*1
*>          Specifies whether or not W is transposed.
*>          = 'N':  No transpose
*>          = 'T':  Transpose, same as TRANSW = 'N'
*>          = 'C':  Conjugate transpose, use -WI(j) instead of WI(j)
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>          The order of the matrix A.  N >= 0.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*>          A is COMPLEX*16 array, dimension (LDA,N)
*>          The matrix whose eigenvectors are in E.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*>          LDA is INTEGER
*>          The leading dimension of the array A.  LDA >= max(1,N).
*> \endverbatim
*>
*> \param[in] E
*> \verbatim
*>          E is COMPLEX*16 array, dimension (LDE,N)
*>          The matrix of eigenvectors. If TRANSE = 'N', the eigenvectors
*>          are stored in the columns of E, if TRANSE = 'T' or 'C', the
*>          eigenvectors are stored in the rows of E.
*> \endverbatim
*>
*> \param[in] LDE
*> \verbatim
*>          LDE is INTEGER
*>          The leading dimension of the array E.  LDE >= max(1,N).
*> \endverbatim
*>
*> \param[in] W
*> \verbatim
*>          W is COMPLEX*16 array, dimension (N)
*>          The eigenvalues of A.
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*>          WORK is COMPLEX*16 array, dimension (N*N)
*> \endverbatim
*>
*> \param[out] RWORK
*> \verbatim
*>          RWORK is DOUBLE PRECISION array, dimension (N)
*> \endverbatim
*>
*> \param[out] RESULT
*> \verbatim
*>          RESULT is DOUBLE PRECISION array, dimension (2)
*>          RESULT(1) = | A E  -  E W | / ( |A| |E| ulp )
*>          RESULT(2) = max | m-norm(E(j)) - 1 | / ( n ulp )
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date November 2011
*
*> \ingroup complex16_eig
*
*  =====================================================================
      SUBROUTINE zget22( TRANSA, TRANSE, TRANSW, N, A, LDA, E, LDE, W,
     $                   work, rwork, result )
*
*  -- 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          transa, transe, transw
      INTEGER            lda, lde, n
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION   result( 2 ), rwork( * )
      COMPLEX*16         a( lda, * ), e( lde, * ), w( * ), work( * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   zero, one
      parameter( zero = 0.0d+0, one = 1.0d+0 )
      COMPLEX*16         czero, cone
      parameter( czero = ( 0.0d+0, 0.0d+0 ),
     $                   cone = ( 1.0d+0, 0.0d+0 ) )
*     ..
*     .. Local Scalars ..
      CHARACTER          norma, norme
      INTEGER            itrnse, itrnsw, j, jcol, joff, jrow, jvec
      DOUBLE PRECISION   anorm, enorm, enrmax, enrmin, errnrm, temp1,
     $                   ulp, unfl
      COMPLEX*16         wtemp
*     ..
*     .. External Functions ..
      LOGICAL            lsame
      DOUBLE PRECISION   dlamch, zlange
      EXTERNAL           lsame, dlamch, zlange
*     ..
*     .. External Subroutines ..
      EXTERNAL           zgemm, zlaset
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          abs, dble, dconjg, dimag, max, min
*     ..
*     .. Executable Statements ..
*
*     Initialize RESULT (in case N=0)
*
      result( 1 ) = zero
      result( 2 ) = zero
      IF( n.LE.0 )
     $   return
*
      unfl = dlamch( 'Safe minimum' )
      ulp = dlamch( 'Precision' )
*
      itrnse = 0
      itrnsw = 0
      norma = 'O'
      norme = 'O'
*
      IF( lsame( transa, 'T' ) .OR. lsame( transa, 'C' ) ) THEN
         norma = 'I'
      END IF
*
      IF( lsame( transe, 'T' ) ) THEN
         itrnse = 1
         norme = 'I'
      ELSE IF( lsame( transe, 'C' ) ) THEN
         itrnse = 2
         norme = 'I'
      END IF
*
      IF( lsame( transw, 'C' ) ) THEN
         itrnsw = 1
      END IF
*
*     Normalization of E:
*
      enrmin = one / ulp
      enrmax = zero
      IF( itrnse.EQ.0 ) THEN
         DO 20 jvec = 1, n
            temp1 = zero
            DO 10 j = 1, n
               temp1 = max( temp1, abs( dble( e( j, jvec ) ) )+
     $                 abs( dimag( e( j, jvec ) ) ) )
   10       continue
            enrmin = min( enrmin, temp1 )
            enrmax = max( enrmax, temp1 )
   20    continue
      ELSE
         DO 30 jvec = 1, n
            rwork( jvec ) = zero
   30    continue
*
         DO 50 j = 1, n
            DO 40 jvec = 1, n
               rwork( jvec ) = max( rwork( jvec ),
     $                         abs( dble( e( jvec, j ) ) )+
     $                         abs( dimag( e( jvec, j ) ) ) )
   40       continue
   50    continue
*
         DO 60 jvec = 1, n
            enrmin = min( enrmin, rwork( jvec ) )
            enrmax = max( enrmax, rwork( jvec ) )
   60    continue
      END IF
*
*     Norm of A:
*
      anorm = max( zlange( norma, n, n, a, lda, rwork ), unfl )
*
*     Norm of E:
*
      enorm = max( zlange( norme, n, n, e, lde, rwork ), ulp )
*
*     Norm of error:
*
*     Error =  AE - EW
*
      CALL zlaset( 'Full', n, n, czero, czero, work, n )
*
      joff = 0
      DO 100 jcol = 1, n
         IF( itrnsw.EQ.0 ) THEN
            wtemp = w( jcol )
         ELSE
            wtemp = dconjg( w( jcol ) )
         END IF
*
         IF( itrnse.EQ.0 ) THEN
            DO 70 jrow = 1, n
               work( joff+jrow ) = e( jrow, jcol )*wtemp
   70       continue
         ELSE IF( itrnse.EQ.1 ) THEN
            DO 80 jrow = 1, n
               work( joff+jrow ) = e( jcol, jrow )*wtemp
   80       continue
         ELSE
            DO 90 jrow = 1, n
               work( joff+jrow ) = dconjg( e( jcol, jrow ) )*wtemp
   90       continue
         END IF
         joff = joff + n
  100 continue
*
      CALL zgemm( transa, transe, n, n, n, cone, a, lda, e, lde, -cone,
     $            work, n )
*
      errnrm = zlange( 'One', n, n, work, n, rwork ) / enorm
*
*     Compute RESULT(1) (avoiding under/overflow)
*
      IF( anorm.GT.errnrm ) THEN
         result( 1 ) = ( errnrm / anorm ) / ulp
      ELSE
         IF( anorm.LT.one ) THEN
            result( 1 ) = ( min( errnrm, anorm ) / anorm ) / ulp
         ELSE
            result( 1 ) = min( errnrm / anorm, one ) / ulp
         END IF
      END IF
*
*     Compute RESULT(2) : the normalization error in E.
*
      result( 2 ) = max( abs( enrmax-one ), abs( enrmin-one ) ) /
     $              ( dble( n )*ulp )
*
      return
*
*     End of ZGET22
*
      END