*> \brief \b ZSTT21 * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE ZSTT21( N, KBAND, AD, AE, SD, SE, U, LDU, WORK, RWORK, * RESULT ) * * .. Scalar Arguments .. * INTEGER KBAND, LDU, N * .. * .. Array Arguments .. * DOUBLE PRECISION AD( * ), AE( * ), RESULT( 2 ), RWORK( * ), * $ SD( * ), SE( * ) * COMPLEX*16 U( LDU, * ), WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZSTT21 checks a decomposition of the form *> *> A = U S U**H *> *> where **H 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**H | / ( |A| n ulp ) *> *> RESULT(2) = | I - U U**H | / ( n ulp ) *> \endverbatim * * Arguments: * ========== * *> \param[in] N *> \verbatim *> N is INTEGER *> The size of the matrix. If it is zero, ZSTT21 does nothing. *> It must be at least zero. *> \endverbatim *> *> \param[in] KBAND *> \verbatim *> KBAND is 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. *> \endverbatim *> *> \param[in] AD *> \verbatim *> AD is DOUBLE PRECISION array, dimension (N) *> The diagonal of the original (unfactored) matrix A. A is *> assumed to be real symmetric tridiagonal. *> \endverbatim *> *> \param[in] AE *> \verbatim *> AE is 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. *> \endverbatim *> *> \param[in] SD *> \verbatim *> SD is DOUBLE PRECISION array, dimension (N) *> The diagonal of the real (symmetric tri-) diagonal matrix S. *> \endverbatim *> *> \param[in] SE *> \verbatim *> SE is 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. *> \endverbatim *> *> \param[in] U *> \verbatim *> U is COMPLEX*16 array, dimension (LDU, N) *> The unitary matrix in the decomposition. *> \endverbatim *> *> \param[in] LDU *> \verbatim *> LDU is INTEGER *> The leading dimension of U. LDU must be at least N. *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is COMPLEX*16 array, dimension (N**2) *> \endverbatim *> *> \param[out] RWORK *> \verbatim *> RWORK is DOUBLE PRECISION array, dimension (N) *> \endverbatim *> *> \param[out] RESULT *> \verbatim *> RESULT is 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. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup complex16_eig * * ===================================================================== SUBROUTINE ZSTT21( N, KBAND, AD, AE, SD, SE, U, LDU, WORK, RWORK, $ RESULT ) * * -- LAPACK test routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. INTEGER KBAND, LDU, N * .. * .. Array Arguments .. DOUBLE PRECISION AD( * ), AE( * ), RESULT( 2 ), RWORK( * ), $ SD( * ), SE( * ) COMPLEX*16 U( LDU, * ), WORK( * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, ONE PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) COMPLEX*16 CZERO, CONE PARAMETER ( CZERO = ( 0.0D+0, 0.0D+0 ), $ CONE = ( 1.0D+0, 0.0D+0 ) ) * .. * .. Local Scalars .. INTEGER J DOUBLE PRECISION ANORM, TEMP1, TEMP2, ULP, UNFL, WNORM * .. * .. External Functions .. DOUBLE PRECISION DLAMCH, ZLANGE, ZLANHE EXTERNAL DLAMCH, ZLANGE, ZLANHE * .. * .. External Subroutines .. EXTERNAL ZGEMM, ZHER, ZHER2, ZLASET * .. * .. Intrinsic Functions .. INTRINSIC ABS, DBLE, DCMPLX, 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 ZLASET( '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 ZHER( '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 ZHER2( 'L', N, -DCMPLX( SE( J ) ), U( 1, J ), 1, $ U( 1, J+1 ), 1, WORK, N ) 30 CONTINUE END IF * WNORM = ZLANHE( '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, DBLE( N ) ) / ( N*ULP ) END IF END IF * * Do Test 2 * * Compute U U**H - I * CALL ZGEMM( '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( DBLE( N ), ZLANGE( '1', N, N, WORK, N, $ RWORK ) ) / ( N*ULP ) * RETURN * * End of ZSTT21 * END