SUBROUTINE DSTT21( N, KBAND, AD, AE, SD, SE, U, LDU, WORK,
$ RESULT )
*
* -- LAPACK test routine (version 3.0) --
* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
* Courant Institute, Argonne National Lab, and Rice University
* September 30, 1994
*
* .. Scalar Arguments ..
INTEGER KBAND, LDU, N
* ..
* .. Array Arguments ..
DOUBLE PRECISION AD( * ), AE( * ), RESULT( 2 ), SD( * ),
$ SE( * ), U( LDU, * ), WORK( * )
* ..
*
* Purpose
* =======
*
* 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 )
*
* Arguments
* =========
*
* N (input) INTEGER
* The size of the matrix. If it is zero, DSTT21 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-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.
*
* SD (input) DOUBLE PRECISION array, dimension (N)
* The diagonal of the (symmetric tri-) diagonal matrix S.
*
* SE (input) 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.
*
* 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 (N*(N+1))
*
* 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.
* RESULT(1) is always modified.
*
* =====================================================================
*
* .. 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