*> \brief \b SSTT21
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE SSTT21( N, KBAND, AD, AE, SD, SE, U, LDU, WORK,
* RESULT )
*
* .. Scalar Arguments ..
* INTEGER KBAND, LDU, N
* ..
* .. Array Arguments ..
* REAL AD( * ), AE( * ), RESULT( 2 ), SD( * ),
* $ SE( * ), U( LDU, * ), WORK( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> SSTT21 checks a decomposition of the form
*>
*> A = U S U'
*>
*> where ' means transpose, A is symmetric tridiagonal, U is orthogonal,
*> and S is 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, SSTT21 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 REAL 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 REAL 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 REAL array, dimension (N)
*> The diagonal of the (symmetric tri-) diagonal matrix S.
*> \endverbatim
*>
*> \param[in] SE
*> \verbatim
*> SE is REAL 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 REAL 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 REAL array, dimension (N*(N+1))
*> \endverbatim
*>
*> \param[out] RESULT
*> \verbatim
*> RESULT is REAL 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 December 2016
*
*> \ingroup single_eig
*
* =====================================================================
SUBROUTINE SSTT21( N, KBAND, AD, AE, SD, SE, U, LDU, WORK,
$ 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 ..
INTEGER KBAND, LDU, N
* ..
* .. Array Arguments ..
REAL AD( * ), AE( * ), RESULT( 2 ), SD( * ),
$ SE( * ), U( LDU, * ), WORK( * )
* ..
*
* =====================================================================
*
* .. Parameters ..
REAL ZERO, ONE
PARAMETER ( ZERO = 0.0E0, ONE = 1.0E0 )
* ..
* .. Local Scalars ..
INTEGER J
REAL ANORM, TEMP1, TEMP2, ULP, UNFL, WNORM
* ..
* .. External Functions ..
REAL SLAMCH, SLANGE, SLANSY
EXTERNAL SLAMCH, SLANGE, SLANSY
* ..
* .. External Subroutines ..
EXTERNAL SGEMM, SLASET, SSYR, SSYR2
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, MAX, MIN, REAL
* ..
* .. Executable Statements ..
*
* 1) Constants
*
RESULT( 1 ) = ZERO
RESULT( 2 ) = ZERO
IF( N.LE.0 )
$ RETURN
*
UNFL = SLAMCH( 'Safe minimum' )
ULP = SLAMCH( 'Precision' )
*
* Do Test 1
*
* Copy A & Compute its 1-Norm:
*
CALL SLASET( 'Full', N, N, ZERO, ZERO, 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 SSYR( '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 SSYR2( 'L', N, -SE( J ), U( 1, J ), 1, U( 1, J+1 ), 1,
$ WORK, N )
30 CONTINUE
END IF
*
WNORM = SLANSY( '1', 'L', N, WORK, N, WORK( N**2+1 ) )
*
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, REAL( N ) ) / ( N*ULP )
END IF
END IF
*
* Do Test 2
*
* Compute UU' - I
*
CALL SGEMM( 'N', 'C', N, N, N, ONE, U, LDU, U, LDU, ZERO, WORK,
$ N )
*
DO 40 J = 1, N
WORK( ( N+1 )*( J-1 )+1 ) = WORK( ( N+1 )*( J-1 )+1 ) - ONE
40 CONTINUE
*
RESULT( 2 ) = MIN( REAL( N ), SLANGE( '1', N, N, WORK, N,
$ WORK( N**2+1 ) ) ) / ( N*ULP )
*
RETURN
*
* End of SSTT21
*
END