numeric-linalg

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*> \brief \b DGET36
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
*  Definition:
*  ===========
*
*       SUBROUTINE DGET36( RMAX, LMAX, NINFO, KNT, NIN )
*
*       .. Scalar Arguments ..
*       INTEGER            KNT, LMAX, NIN
*       DOUBLE PRECISION   RMAX
*       ..
*       .. Array Arguments ..
*       INTEGER            NINFO( 3 )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> DGET36 tests DTREXC, a routine for moving blocks (either 1 by 1 or
*> 2 by 2) on the diagonal of a matrix in real Schur form.  Thus, DLAEXC
*> computes an orthogonal matrix Q such that
*>
*>    Q' * T1 * Q  = T2
*>
*> and where one of the diagonal blocks of T1 (the one at row IFST) has
*> been moved to position ILST.
*>
*> The test code verifies that the residual Q'*T1*Q-T2 is small, that T2
*> is in Schur form, and that the final position of the IFST block is
*> ILST (within +-1).
*>
*> The test matrices are read from a file with logical unit number NIN.
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[out] RMAX
*> \verbatim
*>          RMAX is DOUBLE PRECISION
*>          Value of the largest test ratio.
*> \endverbatim
*>
*> \param[out] LMAX
*> \verbatim
*>          LMAX is INTEGER
*>          Example number where largest test ratio achieved.
*> \endverbatim
*>
*> \param[out] NINFO
*> \verbatim
*>          NINFO is INTEGER array, dimension (3)
*>          NINFO(J) is the number of examples where INFO=J.
*> \endverbatim
*>
*> \param[out] KNT
*> \verbatim
*>          KNT is INTEGER
*>          Total number of examples tested.
*> \endverbatim
*>
*> \param[in] NIN
*> \verbatim
*>          NIN is INTEGER
*>          Input logical unit number.
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup double_eig
*
*  =====================================================================
      SUBROUTINE DGET36( RMAX, LMAX, NINFO, KNT, NIN )
*
*  -- LAPACK test 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            KNT, LMAX, NIN
      DOUBLE PRECISION   RMAX
*     ..
*     .. Array Arguments ..
      INTEGER            NINFO( 3 )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ZERO, ONE
      PARAMETER          ( ZERO = 0.0D0, ONE = 1.0D0 )
      INTEGER            LDT, LWORK
      PARAMETER          ( LDT = 10, LWORK = 2*LDT*LDT )
*     ..
*     .. Local Scalars ..
      INTEGER            I, IFST, IFST1, IFST2, IFSTSV, ILST, ILST1,
     $                   ILST2, ILSTSV, INFO1, INFO2, J, LOC, N
      DOUBLE PRECISION   EPS, RES
*     ..
*     .. Local Arrays ..
      DOUBLE PRECISION   Q( LDT, LDT ), RESULT( 2 ), T1( LDT, LDT ),
     $                   T2( LDT, LDT ), TMP( LDT, LDT ), WORK( LWORK )
*     ..
*     .. External Functions ..
      DOUBLE PRECISION   DLAMCH
      EXTERNAL           DLAMCH
*     ..
*     .. External Subroutines ..
      EXTERNAL           DHST01, DLACPY, DLASET, DTREXC
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          ABS, SIGN
*     ..
*     .. Executable Statements ..
*
      EPS = DLAMCH( 'P' )
      RMAX = ZERO
      LMAX = 0
      KNT = 0
      NINFO( 1 ) = 0
      NINFO( 2 ) = 0
      NINFO( 3 ) = 0
*
*     Read input data until N=0
*
   10 CONTINUE
      READ( NIN, FMT = * )N, IFST, ILST
      IF( N.EQ.0 )
     $   RETURN
      KNT = KNT + 1
      DO 20 I = 1, N
         READ( NIN, FMT = * )( TMP( I, J ), J = 1, N )
   20 CONTINUE
      CALL DLACPY( 'F', N, N, TMP, LDT, T1, LDT )
      CALL DLACPY( 'F', N, N, TMP, LDT, T2, LDT )
      IFSTSV = IFST
      ILSTSV = ILST
      IFST1 = IFST
      ILST1 = ILST
      IFST2 = IFST
      ILST2 = ILST
      RES = ZERO
*
*     Test without accumulating Q
*
      CALL DLASET( 'Full', N, N, ZERO, ONE, Q, LDT )
      CALL DTREXC( 'N', N, T1, LDT, Q, LDT, IFST1, ILST1, WORK, INFO1 )
      DO 40 I = 1, N
         DO 30 J = 1, N
            IF( I.EQ.J .AND. Q( I, J ).NE.ONE )
     $         RES = RES + ONE / EPS
            IF( I.NE.J .AND. Q( I, J ).NE.ZERO )
     $         RES = RES + ONE / EPS
   30    CONTINUE
   40 CONTINUE
*
*     Test with accumulating Q
*
      CALL DLASET( 'Full', N, N, ZERO, ONE, Q, LDT )
      CALL DTREXC( 'V', N, T2, LDT, Q, LDT, IFST2, ILST2, WORK, INFO2 )
*
*     Compare T1 with T2
*
      DO 60 I = 1, N
         DO 50 J = 1, N
            IF( T1( I, J ).NE.T2( I, J ) )
     $         RES = RES + ONE / EPS
   50    CONTINUE
   60 CONTINUE
      IF( IFST1.NE.IFST2 )
     $   RES = RES + ONE / EPS
      IF( ILST1.NE.ILST2 )
     $   RES = RES + ONE / EPS
      IF( INFO1.NE.INFO2 )
     $   RES = RES + ONE / EPS
*
*     Test for successful reordering of T2
*
      IF( INFO2.NE.0 ) THEN
         NINFO( INFO2 ) = NINFO( INFO2 ) + 1
      ELSE
         IF( ABS( IFST2-IFSTSV ).GT.1 )
     $      RES = RES + ONE / EPS
         IF( ABS( ILST2-ILSTSV ).GT.1 )
     $      RES = RES + ONE / EPS
      END IF
*
*     Test for small residual, and orthogonality of Q
*
      CALL DHST01( N, 1, N, TMP, LDT, T2, LDT, Q, LDT, WORK, LWORK,
     $             RESULT )
      RES = RES + RESULT( 1 ) + RESULT( 2 )
*
*     Test for T2 being in Schur form
*
      LOC = 1
   70 CONTINUE
      IF( T2( LOC+1, LOC ).NE.ZERO ) THEN
*
*        2 by 2 block
*
         IF( T2( LOC, LOC+1 ).EQ.ZERO .OR. T2( LOC, LOC ).NE.
     $       T2( LOC+1, LOC+1 ) .OR. SIGN( ONE, T2( LOC, LOC+1 ) ).EQ.
     $       SIGN( ONE, T2( LOC+1, LOC ) ) )RES = RES + ONE / EPS
         DO 80 I = LOC + 2, N
            IF( T2( I, LOC ).NE.ZERO )
     $         RES = RES + ONE / RES
            IF( T2( I, LOC+1 ).NE.ZERO )
     $         RES = RES + ONE / RES
   80    CONTINUE
         LOC = LOC + 2
      ELSE
*
*        1 by 1 block
*
         DO 90 I = LOC + 1, N
            IF( T2( I, LOC ).NE.ZERO )
     $         RES = RES + ONE / RES
   90    CONTINUE
         LOC = LOC + 1
      END IF
      IF( LOC.LT.N )
     $   GO TO 70
      IF( RES.GT.RMAX ) THEN
         RMAX = RES
         LMAX = KNT
      END IF
      GO TO 10
*
*     End of DGET36
*
      END