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*> \brief \b DSTT22
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE DSTT22( N, M, KBAND, AD, AE, SD, SE, U, LDU, WORK,
* LDWORK, RESULT )
*
* .. Scalar Arguments ..
* INTEGER KBAND, LDU, LDWORK, M, N
* ..
* .. Array Arguments ..
* DOUBLE PRECISION AD( * ), AE( * ), RESULT( 2 ), SD( * ),
* $ SE( * ), U( LDU, * ), WORK( LDWORK, * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> DSTT22 checks a set of M eigenvalues and eigenvectors,
*>
*> A U = U S
*>
*> where A is symmetric tridiagonal, the columns of U are orthogonal,
*> and S is diagonal (if KBAND=0) or symmetric tridiagonal (if KBAND=1).
*> Two tests are performed:
*>
*> RESULT(1) = | U' A U - S | / ( |A| m ulp )
*>
*> RESULT(2) = | I - U'U | / ( m ulp )
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The size of the matrix. If it is zero, DSTT22 does nothing.
*> It must be at least zero.
*> \endverbatim
*>
*> \param[in] M
*> \verbatim
*> M is INTEGER
*> The number of eigenpairs to check. If it is zero, DSTT22
*> does nothing. It must be at least zero.
*> \endverbatim
*>
*> \param[in] KBAND
*> \verbatim
*> KBAND is INTEGER
*> The bandwidth of the matrix S. It may only be zero or one.
*> If zero, then S is diagonal, and SE is not referenced. If
*> one, then S is symmetric tri-diagonal.
*> \endverbatim
*>
*> \param[in] AD
*> \verbatim
*> AD is DOUBLE PRECISION array, dimension (N)
*> The diagonal of the original (unfactored) matrix A. A is
*> assumed to be symmetric tridiagonal.
*> \endverbatim
*>
*> \param[in] AE
*> \verbatim
*> AE is DOUBLE PRECISION array, dimension (N)
*> The off-diagonal of the original (unfactored) matrix A. A
*> is assumed to be symmetric tridiagonal. AE(1) is ignored,
*> AE(2) is the (1,2) and (2,1) element, etc.
*> \endverbatim
*>
*> \param[in] SD
*> \verbatim
*> SD is DOUBLE PRECISION array, dimension (N)
*> The diagonal of the (symmetric tri-) diagonal matrix S.
*> \endverbatim
*>
*> \param[in] SE
*> \verbatim
*> SE is DOUBLE PRECISION array, dimension (N)
*> The off-diagonal of the (symmetric tri-) diagonal matrix S.
*> Not referenced if KBSND=0. If KBAND=1, then AE(1) is
*> ignored, SE(2) is the (1,2) and (2,1) element, etc.
*> \endverbatim
*>
*> \param[in] U
*> \verbatim
*> U is DOUBLE PRECISION array, dimension (LDU, N)
*> The orthogonal matrix in the decomposition.
*> \endverbatim
*>
*> \param[in] LDU
*> \verbatim
*> LDU is INTEGER
*> The leading dimension of U. LDU must be at least N.
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*> WORK is DOUBLE PRECISION array, dimension (LDWORK, M+1)
*> \endverbatim
*>
*> \param[in] LDWORK
*> \verbatim
*> LDWORK is INTEGER
*> The leading dimension of WORK. LDWORK must be at least
*> max(1,M).
*> \endverbatim
*>
*> \param[out] RESULT
*> \verbatim
*> RESULT is DOUBLE PRECISION array, dimension (2)
*> The values computed by the two tests described above. The
*> values are currently limited to 1/ulp, to avoid overflow.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date November 2011
*
*> \ingroup double_eig
*
* =====================================================================
SUBROUTINE DSTT22( N, M, KBAND, AD, AE, SD, SE, U, LDU, WORK,
$ LDWORK, 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 ..
INTEGER KBAND, LDU, LDWORK, M, N
* ..
* .. Array Arguments ..
DOUBLE PRECISION AD( * ), AE( * ), RESULT( 2 ), SD( * ),
$ SE( * ), U( LDU, * ), WORK( LDWORK, * )
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ZERO, ONE
PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 )
* ..
* .. Local Scalars ..
INTEGER I, J, K
DOUBLE PRECISION ANORM, AUKJ, ULP, UNFL, WNORM
* ..
* .. External Functions ..
DOUBLE PRECISION DLAMCH, DLANGE, DLANSY
EXTERNAL DLAMCH, DLANGE, DLANSY
* ..
* .. External Subroutines ..
EXTERNAL DGEMM
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, DBLE, MAX, MIN
* ..
* .. Executable Statements ..
*
RESULT( 1 ) = ZERO
RESULT( 2 ) = ZERO
IF( N.LE.0 .OR. M.LE.0 )
$ RETURN
*
UNFL = DLAMCH( 'Safe minimum' )
ULP = DLAMCH( 'Epsilon' )
*
* Do Test 1
*
* Compute the 1-norm of A.
*
IF( N.GT.1 ) THEN
ANORM = ABS( AD( 1 ) ) + ABS( AE( 1 ) )
DO 10 J = 2, N - 1
ANORM = MAX( ANORM, ABS( AD( J ) )+ABS( AE( J ) )+
$ ABS( AE( J-1 ) ) )
10 CONTINUE
ANORM = MAX( ANORM, ABS( AD( N ) )+ABS( AE( N-1 ) ) )
ELSE
ANORM = ABS( AD( 1 ) )
END IF
ANORM = MAX( ANORM, UNFL )
*
* Norm of U'AU - S
*
DO 40 I = 1, M
DO 30 J = 1, M
WORK( I, J ) = ZERO
DO 20 K = 1, N
AUKJ = AD( K )*U( K, J )
IF( K.NE.N )
$ AUKJ = AUKJ + AE( K )*U( K+1, J )
IF( K.NE.1 )
$ AUKJ = AUKJ + AE( K-1 )*U( K-1, J )
WORK( I, J ) = WORK( I, J ) + U( K, I )*AUKJ
20 CONTINUE
30 CONTINUE
WORK( I, I ) = WORK( I, I ) - SD( I )
IF( KBAND.EQ.1 ) THEN
IF( I.NE.1 )
$ WORK( I, I-1 ) = WORK( I, I-1 ) - SE( I-1 )
IF( I.NE.N )
$ WORK( I, I+1 ) = WORK( I, I+1 ) - SE( I )
END IF
40 CONTINUE
*
WNORM = DLANSY( '1', 'L', M, WORK, M, WORK( 1, M+1 ) )
*
IF( ANORM.GT.WNORM ) THEN
RESULT( 1 ) = ( WNORM / ANORM ) / ( M*ULP )
ELSE
IF( ANORM.LT.ONE ) THEN
RESULT( 1 ) = ( MIN( WNORM, M*ANORM ) / ANORM ) / ( M*ULP )
ELSE
RESULT( 1 ) = MIN( WNORM / ANORM, DBLE( M ) ) / ( M*ULP )
END IF
END IF
*
* Do Test 2
*
* Compute U'U - I
*
CALL DGEMM( 'T', 'N', M, M, N, ONE, U, LDU, U, LDU, ZERO, WORK,
$ M )
*
DO 50 J = 1, M
WORK( J, J ) = WORK( J, J ) - ONE
50 CONTINUE
*
RESULT( 2 ) = MIN( DBLE( M ), DLANGE( '1', M, M, WORK, M, WORK( 1,
$ M+1 ) ) ) / ( M*ULP )
*
RETURN
*
* End of DSTT22
*
END
|
