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*> \brief \b ZSTT21
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE ZSTT21( N, KBAND, AD, AE, SD, SE, U, LDU, WORK, RWORK,
* RESULT )
*
* .. Scalar Arguments ..
* INTEGER KBAND, LDU, N
* ..
* .. Array Arguments ..
* DOUBLE PRECISION AD( * ), AE( * ), RESULT( 2 ), RWORK( * ),
* $ SD( * ), SE( * )
* COMPLEX*16 U( LDU, * ), WORK( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> ZSTT21 checks a decomposition of the form
*>
*> A = U S UC>
*> where * means conjugate transpose, A is real symmetric tridiagonal,
*> U is unitary, and S is real and diagonal (if KBAND=0) or symmetric
*> tridiagonal (if KBAND=1). Two tests are performed:
*>
*> RESULT(1) = | A - U S U* | / ( |A| n ulp )
*>
*> RESULT(2) = | I - UU* | / ( n ulp )
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The size of the matrix. If it is zero, ZSTT21 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 real symmetric tridiagonal.
*> \endverbatim
*>
*> \param[in] AE
*> \verbatim
*> AE is DOUBLE PRECISION array, dimension (N-1)
*> The off-diagonal of the original (unfactored) matrix A. A
*> is assumed to be symmetric tridiagonal. AE(1) is the (1,2)
*> and (2,1) element, AE(2) is the (2,3) and (3,2) element, etc.
*> \endverbatim
*>
*> \param[in] SD
*> \verbatim
*> SD is DOUBLE PRECISION array, dimension (N)
*> The diagonal of the real (symmetric tri-) diagonal matrix S.
*> \endverbatim
*>
*> \param[in] SE
*> \verbatim
*> SE is DOUBLE PRECISION array, dimension (N-1)
*> The off-diagonal of the (symmetric tri-) diagonal matrix S.
*> Not referenced if KBSND=0. If KBAND=1, then AE(1) is the
*> (1,2) and (2,1) element, SE(2) is the (2,3) and (3,2)
*> element, etc.
*> \endverbatim
*>
*> \param[in] U
*> \verbatim
*> U is COMPLEX*16 array, dimension (LDU, N)
*> The unitary 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 COMPLEX*16 array, dimension (N**2)
*> \endverbatim
*>
*> \param[out] RWORK
*> \verbatim
*> RWORK is DOUBLE PRECISION array, dimension (N)
*> \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.
*> RESULT(1) is always modified.
*> \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 ZSTT21( N, KBAND, AD, AE, SD, SE, U, LDU, 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 ..
INTEGER KBAND, LDU, N
* ..
* .. Array Arguments ..
DOUBLE PRECISION AD( * ), AE( * ), RESULT( 2 ), RWORK( * ),
$ SD( * ), SE( * )
COMPLEX*16 U( LDU, * ), 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 ..
INTEGER J
DOUBLE PRECISION ANORM, TEMP1, TEMP2, ULP, UNFL, WNORM
* ..
* .. External Functions ..
DOUBLE PRECISION DLAMCH, ZLANGE, ZLANHE
EXTERNAL DLAMCH, ZLANGE, ZLANHE
* ..
* .. External Subroutines ..
EXTERNAL ZGEMM, ZHER, ZHER2, ZLASET
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, DBLE, DCMPLX, MAX, MIN
* ..
* .. Executable Statements ..
*
* 1) Constants
*
RESULT( 1 ) = ZERO
RESULT( 2 ) = ZERO
IF( N.LE.0 )
$ RETURN
*
UNFL = DLAMCH( 'Safe minimum' )
ULP = DLAMCH( 'Precision' )
*
* Do Test 1
*
* Copy A & Compute its 1-Norm:
*
CALL ZLASET( 'Full', N, N, CZERO, CZERO, WORK, N )
*
ANORM = ZERO
TEMP1 = ZERO
*
DO 10 J = 1, N - 1
WORK( ( N+1 )*( J-1 )+1 ) = AD( J )
WORK( ( N+1 )*( J-1 )+2 ) = AE( J )
TEMP2 = ABS( AE( J ) )
ANORM = MAX( ANORM, ABS( AD( J ) )+TEMP1+TEMP2 )
TEMP1 = TEMP2
10 CONTINUE
*
WORK( N**2 ) = AD( N )
ANORM = MAX( ANORM, ABS( AD( N ) )+TEMP1, UNFL )
*
* Norm of A - USU*
*
DO 20 J = 1, N
CALL ZHER( 'L', N, -SD( J ), U( 1, J ), 1, WORK, N )
20 CONTINUE
*
IF( N.GT.1 .AND. KBAND.EQ.1 ) THEN
DO 30 J = 1, N - 1
CALL ZHER2( 'L', N, -DCMPLX( SE( J ) ), U( 1, J ), 1,
$ U( 1, J+1 ), 1, WORK, N )
30 CONTINUE
END IF
*
WNORM = ZLANHE( '1', 'L', N, WORK, N, RWORK )
*
IF( ANORM.GT.WNORM ) THEN
RESULT( 1 ) = ( WNORM / ANORM ) / ( N*ULP )
ELSE
IF( ANORM.LT.ONE ) THEN
RESULT( 1 ) = ( MIN( WNORM, N*ANORM ) / ANORM ) / ( N*ULP )
ELSE
RESULT( 1 ) = MIN( WNORM / ANORM, DBLE( N ) ) / ( N*ULP )
END IF
END IF
*
* Do Test 2
*
* Compute UU* - I
*
CALL ZGEMM( 'N', 'C', N, N, N, CONE, U, LDU, U, LDU, CZERO, WORK,
$ N )
*
DO 40 J = 1, N
WORK( ( N+1 )*( J-1 )+1 ) = WORK( ( N+1 )*( J-1 )+1 ) - CONE
40 CONTINUE
*
RESULT( 2 ) = MIN( DBLE( N ), ZLANGE( '1', N, N, WORK, N,
$ RWORK ) ) / ( N*ULP )
*
RETURN
*
* End of ZSTT21
*
END
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