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SUBROUTINE SSTT22( 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 .. REAL AD( * ), AE( * ), RESULT( 2 ), SD( * ), $ SE( * ), U( LDU, * ), WORK( LDWORK, * ) * .. * * Purpose * ======= * * SSTT22 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, SSTT22 does nothing. * It must be at least zero. * * M (input) INTEGER * The number of eigenpairs to check. If it is zero, SSTT22 * 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) REAL array, dimension (N) * The diagonal of the original (unfactored) matrix A. A is * assumed to be symmetric tridiagonal. * * AE (input) REAL 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) REAL array, dimension (N) * The diagonal of the (symmetric tri-) diagonal matrix S. * * SE (input) REAL 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) REAL 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) REAL array, dimension (LDWORK, M+1) * * LDWORK (input) INTEGER * The leading dimension of WORK. LDWORK must be at least * max(1,M). * * RESULT (output) REAL array, dimension (2) * The values computed by the two tests described above. The * values are currently limited to 1/ulp, to avoid overflow. * * ===================================================================== * * .. Parameters .. REAL ZERO, ONE PARAMETER ( ZERO = 0.0E0, ONE = 1.0E0 ) * .. * .. Local Scalars .. INTEGER I, J, K REAL ANORM, AUKJ, ULP, UNFL, WNORM * .. * .. External Functions .. REAL SLAMCH, SLANGE, SLANSY EXTERNAL SLAMCH, SLANGE, SLANSY * .. * .. External Subroutines .. EXTERNAL SGEMM * .. * .. Intrinsic Functions .. INTRINSIC ABS, MAX, MIN, REAL * .. * .. Executable Statements .. * RESULT( 1 ) = ZERO RESULT( 2 ) = ZERO IF( N.LE.0 .OR. M.LE.0 ) $ RETURN * UNFL = SLAMCH( 'Safe minimum' ) ULP = SLAMCH( '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 = SLANSY( '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, REAL( M ) ) / ( M*ULP ) END IF END IF * * Do Test 2 * * Compute U'U - I * CALL SGEMM( '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( REAL( M ), SLANGE( '1', M, M, WORK, M, WORK( 1, $ M+1 ) ) ) / ( M*ULP ) * RETURN * * End of SSTT22 * END |