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SUBROUTINE DSTT21( N, KBAND, AD, AE, SD, SE, U, LDU, WORK,
$ RESULT ) * * -- LAPACK test routine (version 3.1) -- * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. * November 2006 * * .. 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 |