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SUBROUTINE DSTT22( N, M, KBAND, AD, AE, SD, SE, U, LDU, WORK,
$ LDWORK, RESULT )
*
* -- LAPACK test routine (version 3.1) --
* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
* November 2006
*
* .. Scalar Arguments ..
INTEGER KBAND, LDU, LDWORK, M, N
* ..
* .. Array Arguments ..
DOUBLE PRECISION AD( * ), AE( * ), RESULT( 2 ), SD( * ),
$ SE( * ), U( LDU, * ), WORK( LDWORK, * )
* ..
*
* Purpose
* =======
*
* 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 )
*
* Arguments
* =========
*
* N (input) INTEGER
* The size of the matrix. If it is zero, DSTT22 does nothing.
* It must be at least zero.
*
* M (input) INTEGER
* The number of eigenpairs to check. If it is zero, DSTT22
* does nothing. It must be at least zero.
*
* KBAND (input) 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.
*
* AD (input) DOUBLE PRECISION array, dimension (N)
* The diagonal of the original (unfactored) matrix A. A is
* assumed to be symmetric tridiagonal.
*
* AE (input) 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.
*
* SD (input) DOUBLE PRECISION array, dimension (N)
* The diagonal of the (symmetric tri-) diagonal matrix S.
*
* SE (input) 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.
*
* U (input) DOUBLE PRECISION array, dimension (LDU, N)
* The orthogonal matrix in the decomposition.
*
* LDU (input) INTEGER
* The leading dimension of U. LDU must be at least N.
*
* WORK (workspace) DOUBLE PRECISION array, dimension (LDWORK, M+1)
*
* LDWORK (input) INTEGER
* The leading dimension of WORK. LDWORK must be at least
* max(1,M).
*
* RESULT (output) 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.
*
* =====================================================================
*
* .. 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
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