SUBROUTINE CSTT21( N, KBAND, AD, AE, SD, SE, U, LDU, WORK, RWORK, \$ 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 .. REAL AD( * ), AE( * ), RESULT( 2 ), RWORK( * ), \$ SD( * ), SE( * ) COMPLEX U( LDU, * ), WORK( * ) * .. * * Purpose * ======= * * CSTT21 checks a decomposition of the form * * A = U S U* * * where * means conjugate transpose, A is real symmetric tridiagonal, * U is unitary, and S is real and 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, CSTT21 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 real symmetric tridiagonal. * * AE (input) REAL 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) REAL array, dimension (N) * The diagonal of the real (symmetric tri-) diagonal matrix S. * * SE (input) REAL 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) COMPLEX array, dimension (LDU, N) * The unitary matrix in the decomposition. * * LDU (input) INTEGER * The leading dimension of U. LDU must be at least N. * * WORK (workspace) COMPLEX array, dimension (N**2) * * RWORK (workspace) REAL array, dimension (N) * * 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. * RESULT(1) is always modified. * * ===================================================================== * * .. Parameters .. REAL ZERO, ONE PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 ) COMPLEX CZERO, CONE PARAMETER ( CZERO = ( 0.0E+0, 0.0E+0 ), \$ CONE = ( 1.0E+0, 0.0E+0 ) ) * .. * .. Local Scalars .. INTEGER J REAL ANORM, TEMP1, TEMP2, ULP, UNFL, WNORM * .. * .. External Functions .. REAL CLANGE, CLANHE, SLAMCH EXTERNAL CLANGE, CLANHE, SLAMCH * .. * .. External Subroutines .. EXTERNAL CGEMM, CHER, CHER2, CLASET * .. * .. Intrinsic Functions .. INTRINSIC ABS, CMPLX, MAX, MIN, REAL * .. * .. Executable Statements .. * * 1) Constants * RESULT( 1 ) = ZERO RESULT( 2 ) = ZERO IF( N.LE.0 ) \$ RETURN * UNFL = SLAMCH( 'Safe minimum' ) ULP = SLAMCH( 'Precision' ) * * Do Test 1 * * Copy A & Compute its 1-Norm: * CALL CLASET( 'Full', N, N, CZERO, CZERO, 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 CHER( '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 CHER2( 'L', N, -CMPLX( SE( J ) ), U( 1, J ), 1, \$ U( 1, J+1 ), 1, WORK, N ) 30 CONTINUE END IF * WNORM = CLANHE( '1', 'L', N, WORK, N, RWORK ) * 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, REAL( N ) ) / ( N*ULP ) END IF END IF * * Do Test 2 * * Compute UU* - I * CALL CGEMM( 'N', 'C', N, N, N, CONE, U, LDU, U, LDU, CZERO, WORK, \$ N ) * DO 40 J = 1, N WORK( ( N+1 )*( J-1 )+1 ) = WORK( ( N+1 )*( J-1 )+1 ) - CONE 40 CONTINUE * RESULT( 2 ) = MIN( REAL( N ), CLANGE( '1', N, N, WORK, N, \$ RWORK ) ) / ( N*ULP ) * RETURN * * End of CSTT21 * END