cget22.f

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*> \brief \b CGET22
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
*  Definition:
*  ===========
*
*       SUBROUTINE CGET22( TRANSA, TRANSE, TRANSW, N, A, LDA, E, LDE, W,
*                          WORK, RWORK, RESULT )
*
*       .. Scalar Arguments ..
*       CHARACTER          TRANSA, TRANSE, TRANSW
*       INTEGER            LDA, LDE, N
*       ..
*       .. Array Arguments ..
*       REAL               RESULT( 2 ), RWORK( * )
*       COMPLEX            A( LDA, * ), E( LDE, * ), W( * ), WORK( * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> CGET22 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 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 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 array, dimension (N)
*>          The eigenvalues of A.
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*>          WORK is COMPLEX array, dimension (N*N)
*> \endverbatim
*>
*> \param[out] RWORK
*> \verbatim
*>          RWORK is REAL array, dimension (N)
*> \endverbatim
*>
*> \param[out] RESULT
*> \verbatim
*>          RESULT is REAL 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 December 2016
*
*> \ingroup complex_eig
*
*  =====================================================================
      SUBROUTINE cget22( TRANSA, TRANSE, TRANSW, N, A, LDA, E, LDE, W,
     $                   WORK, RWORK, RESULT )
*
*  -- LAPACK test routine (version 3.7.0) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     December 2016
*
*     .. Scalar Arguments ..
      CHARACTER          TRANSA, TRANSE, TRANSW
      INTEGER            LDA, LDE, N
*     ..
*     .. Array Arguments ..
      REAL               RESULT( 2 ), RWORK( * )
      COMPLEX            A( lda, * ), E( lde, * ), W( * ), WORK( * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      REAL               ZERO, ONE
      parameter( zero = 0.0e+0, one = 1.0e+0 )
      COMPLEX            CZERO, CONE
      parameter( czero = ( 0.0e+0, 0.0e+0 ),
     $                   cone = ( 1.0e+0, 0.0e+0 ) )
*     ..
*     .. Local Scalars ..
      CHARACTER          NORMA, NORME
      INTEGER            ITRNSE, ITRNSW, J, JCOL, JOFF, JROW, JVEC
      REAL               ANORM, ENORM, ENRMAX, ENRMIN, ERRNRM, TEMP1,
     $                   ulp, unfl
      COMPLEX            WTEMP
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      REAL               CLANGE, SLAMCH
      EXTERNAL           lsame, clange, slamch
*     ..
*     .. External Subroutines ..
      EXTERNAL           cgemm, claset
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          abs, aimag, conjg, max, min, real
*     ..
*     .. Executable Statements ..
*
*     Initialize RESULT (in case N=0)
*
      result( 1 ) = zero
      result( 2 ) = zero
      IF( n.LE.0 )
     $   RETURN
*
      unfl = slamch( 'Safe minimum' )
      ulp = slamch( '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( REAL( E( J, JVEC ) ) )+
     $                 abs( aimag( 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( REAL( E( JVEC, J ) ) )+
     $                         abs( aimag( 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( clange( norma, n, n, a, lda, rwork ), unfl )
*
*     Norm of E:
*
      enorm = max( clange( norme, n, n, e, lde, rwork ), ulp )
*
*     Norm of error:
*
*     Error =  AE - EW
*
      CALL claset( 'Full', n, n, czero, czero, work, n )
*
      joff = 0
      DO 100 jcol = 1, n
         IF( itrnsw.EQ.0 ) THEN
            wtemp = w( jcol )
         ELSE
            wtemp = conjg( 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 ) = conjg( e( jcol, jrow ) )*wtemp
   90       CONTINUE
         END IF
         joff = joff + n
  100 CONTINUE
*
      CALL cgemm( transa, transe, n, n, n, cone, a, lda, e, lde, -cone,
     $            work, n )
*
      errnrm = clange( '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 ) ) /
     $              ( REAL( n )*ULP )
*
      RETURN
*
*     End of CGET22
*
      END