239 lines
6.4 KiB
Fortran
239 lines
6.4 KiB
Fortran
*> \brief \b DSTT21
|
|
*
|
|
* =========== DOCUMENTATION ===========
|
|
*
|
|
* Online html documentation available at
|
|
* http://www.netlib.org/lapack/explore-html/
|
|
*
|
|
* Definition:
|
|
* ===========
|
|
*
|
|
* SUBROUTINE DSTT21( N, KBAND, AD, AE, SD, SE, U, LDU, WORK,
|
|
* RESULT )
|
|
*
|
|
* .. Scalar Arguments ..
|
|
* INTEGER KBAND, LDU, N
|
|
* ..
|
|
* .. Array Arguments ..
|
|
* DOUBLE PRECISION AD( * ), AE( * ), RESULT( 2 ), SD( * ),
|
|
* $ SE( * ), U( LDU, * ), WORK( * )
|
|
* ..
|
|
*
|
|
*
|
|
*> \par Purpose:
|
|
* =============
|
|
*>
|
|
*> \verbatim
|
|
*>
|
|
*> DSTT21 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, DSTT21 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-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 (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 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 (N*(N+1))
|
|
*> \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 double_eig
|
|
*
|
|
* =====================================================================
|
|
SUBROUTINE DSTT21( N, KBAND, AD, AE, SD, SE, U, LDU, WORK,
|
|
$ 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 ), SD( * ),
|
|
$ SE( * ), U( LDU, * ), WORK( * )
|
|
* ..
|
|
*
|
|
* =====================================================================
|
|
*
|
|
* .. Parameters ..
|
|
DOUBLE PRECISION ZERO, ONE
|
|
PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 )
|
|
* ..
|
|
* .. Local Scalars ..
|
|
INTEGER J
|
|
DOUBLE PRECISION ANORM, TEMP1, TEMP2, ULP, UNFL, WNORM
|
|
* ..
|
|
* .. External Functions ..
|
|
DOUBLE PRECISION DLAMCH, DLANGE, DLANSY
|
|
EXTERNAL DLAMCH, DLANGE, DLANSY
|
|
* ..
|
|
* .. External Subroutines ..
|
|
EXTERNAL DGEMM, DLASET, DSYR, DSYR2
|
|
* ..
|
|
* .. Intrinsic Functions ..
|
|
INTRINSIC ABS, DBLE, 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 DLASET( '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 DSYR( '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 DSYR2( 'L', N, -SE( J ), U( 1, J ), 1, U( 1, J+1 ), 1,
|
|
$ WORK, N )
|
|
30 CONTINUE
|
|
END IF
|
|
*
|
|
WNORM = DLANSY( '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, DBLE( N ) ) / ( N*ULP )
|
|
END IF
|
|
END IF
|
|
*
|
|
* Do Test 2
|
|
*
|
|
* Compute UU' - I
|
|
*
|
|
CALL DGEMM( '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( DBLE( N ), DLANGE( '1', N, N, WORK, N,
|
|
$ WORK( N**2+1 ) ) ) / ( N*ULP )
|
|
*
|
|
RETURN
|
|
*
|
|
* End of DSTT21
|
|
*
|
|
END
|