LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
zhbt21.f
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00001 *> \brief \b ZHBT21
00002 *
00003 *  =========== DOCUMENTATION ===========
00004 *
00005 * Online html documentation available at 
00006 *            http://www.netlib.org/lapack/explore-html/ 
00007 *
00008 *  Definition:
00009 *  ===========
00010 *
00011 *       SUBROUTINE ZHBT21( UPLO, N, KA, KS, A, LDA, D, E, U, LDU, WORK,
00012 *                          RWORK, RESULT )
00013 * 
00014 *       .. Scalar Arguments ..
00015 *       CHARACTER          UPLO
00016 *       INTEGER            KA, KS, LDA, LDU, N
00017 *       ..
00018 *       .. Array Arguments ..
00019 *       DOUBLE PRECISION   D( * ), E( * ), RESULT( 2 ), RWORK( * )
00020 *       COMPLEX*16         A( LDA, * ), U( LDU, * ), WORK( * )
00021 *       ..
00022 *  
00023 *
00024 *> \par Purpose:
00025 *  =============
00026 *>
00027 *> \verbatim
00028 *>
00029 *> ZHBT21  generally checks a decomposition of the form
00030 *>
00031 *>         A = U S UC>
00032 *> where * means conjugate transpose, A is hermitian banded, U is
00033 *> unitary, and S is diagonal (if KS=0) or symmetric
00034 *> tridiagonal (if KS=1).
00035 *>
00036 *> Specifically:
00037 *>
00038 *>         RESULT(1) = | A - U S U* | / ( |A| n ulp ) *andC>         RESULT(2) = | I - UU* | / ( n ulp )
00039 *> \endverbatim
00040 *
00041 *  Arguments:
00042 *  ==========
00043 *
00044 *> \param[in] UPLO
00045 *> \verbatim
00046 *>          UPLO is CHARACTER
00047 *>          If UPLO='U', the upper triangle of A and V will be used and
00048 *>          the (strictly) lower triangle will not be referenced.
00049 *>          If UPLO='L', the lower triangle of A and V will be used and
00050 *>          the (strictly) upper triangle will not be referenced.
00051 *> \endverbatim
00052 *>
00053 *> \param[in] N
00054 *> \verbatim
00055 *>          N is INTEGER
00056 *>          The size of the matrix.  If it is zero, ZHBT21 does nothing.
00057 *>          It must be at least zero.
00058 *> \endverbatim
00059 *>
00060 *> \param[in] KA
00061 *> \verbatim
00062 *>          KA is INTEGER
00063 *>          The bandwidth of the matrix A.  It must be at least zero.  If
00064 *>          it is larger than N-1, then max( 0, N-1 ) will be used.
00065 *> \endverbatim
00066 *>
00067 *> \param[in] KS
00068 *> \verbatim
00069 *>          KS is INTEGER
00070 *>          The bandwidth of the matrix S.  It may only be zero or one.
00071 *>          If zero, then S is diagonal, and E is not referenced.  If
00072 *>          one, then S is symmetric tri-diagonal.
00073 *> \endverbatim
00074 *>
00075 *> \param[in] A
00076 *> \verbatim
00077 *>          A is COMPLEX*16 array, dimension (LDA, N)
00078 *>          The original (unfactored) matrix.  It is assumed to be
00079 *>          hermitian, and only the upper (UPLO='U') or only the lower
00080 *>          (UPLO='L') will be referenced.
00081 *> \endverbatim
00082 *>
00083 *> \param[in] LDA
00084 *> \verbatim
00085 *>          LDA is INTEGER
00086 *>          The leading dimension of A.  It must be at least 1
00087 *>          and at least min( KA, N-1 ).
00088 *> \endverbatim
00089 *>
00090 *> \param[in] D
00091 *> \verbatim
00092 *>          D is DOUBLE PRECISION array, dimension (N)
00093 *>          The diagonal of the (symmetric tri-) diagonal matrix S.
00094 *> \endverbatim
00095 *>
00096 *> \param[in] E
00097 *> \verbatim
00098 *>          E is DOUBLE PRECISION array, dimension (N-1)
00099 *>          The off-diagonal of the (symmetric tri-) diagonal matrix S.
00100 *>          E(1) is the (1,2) and (2,1) element, E(2) is the (2,3) and
00101 *>          (3,2) element, etc.
00102 *>          Not referenced if KS=0.
00103 *> \endverbatim
00104 *>
00105 *> \param[in] U
00106 *> \verbatim
00107 *>          U is COMPLEX*16 array, dimension (LDU, N)
00108 *>          The unitary matrix in the decomposition, expressed as a
00109 *>          dense matrix (i.e., not as a product of Householder
00110 *>          transformations, Givens transformations, etc.)
00111 *> \endverbatim
00112 *>
00113 *> \param[in] LDU
00114 *> \verbatim
00115 *>          LDU is INTEGER
00116 *>          The leading dimension of U.  LDU must be at least N and
00117 *>          at least 1.
00118 *> \endverbatim
00119 *>
00120 *> \param[out] WORK
00121 *> \verbatim
00122 *>          WORK is COMPLEX*16 array, dimension (N**2)
00123 *> \endverbatim
00124 *>
00125 *> \param[out] RWORK
00126 *> \verbatim
00127 *>          RWORK is DOUBLE PRECISION array, dimension (N)
00128 *> \endverbatim
00129 *>
00130 *> \param[out] RESULT
00131 *> \verbatim
00132 *>          RESULT is DOUBLE PRECISION array, dimension (2)
00133 *>          The values computed by the two tests described above.  The
00134 *>          values are currently limited to 1/ulp, to avoid overflow.
00135 *> \endverbatim
00136 *
00137 *  Authors:
00138 *  ========
00139 *
00140 *> \author Univ. of Tennessee 
00141 *> \author Univ. of California Berkeley 
00142 *> \author Univ. of Colorado Denver 
00143 *> \author NAG Ltd. 
00144 *
00145 *> \date November 2011
00146 *
00147 *> \ingroup complex16_eig
00148 *
00149 *  =====================================================================
00150       SUBROUTINE ZHBT21( UPLO, N, KA, KS, A, LDA, D, E, U, LDU, WORK,
00151      $                   RWORK, RESULT )
00152 *
00153 *  -- LAPACK test routine (version 3.4.0) --
00154 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00155 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00156 *     November 2011
00157 *
00158 *     .. Scalar Arguments ..
00159       CHARACTER          UPLO
00160       INTEGER            KA, KS, LDA, LDU, N
00161 *     ..
00162 *     .. Array Arguments ..
00163       DOUBLE PRECISION   D( * ), E( * ), RESULT( 2 ), RWORK( * )
00164       COMPLEX*16         A( LDA, * ), U( LDU, * ), WORK( * )
00165 *     ..
00166 *
00167 *  =====================================================================
00168 *
00169 *     .. Parameters ..
00170       COMPLEX*16         CZERO, CONE
00171       PARAMETER          ( CZERO = ( 0.0D+0, 0.0D+0 ),
00172      $                   CONE = ( 1.0D+0, 0.0D+0 ) )
00173       DOUBLE PRECISION   ZERO, ONE
00174       PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0 )
00175 *     ..
00176 *     .. Local Scalars ..
00177       LOGICAL            LOWER
00178       CHARACTER          CUPLO
00179       INTEGER            IKA, J, JC, JR
00180       DOUBLE PRECISION   ANORM, ULP, UNFL, WNORM
00181 *     ..
00182 *     .. External Functions ..
00183       LOGICAL            LSAME
00184       DOUBLE PRECISION   DLAMCH, ZLANGE, ZLANHB, ZLANHP
00185       EXTERNAL           LSAME, DLAMCH, ZLANGE, ZLANHB, ZLANHP
00186 *     ..
00187 *     .. External Subroutines ..
00188       EXTERNAL           ZGEMM, ZHPR, ZHPR2
00189 *     ..
00190 *     .. Intrinsic Functions ..
00191       INTRINSIC          DBLE, DCMPLX, MAX, MIN
00192 *     ..
00193 *     .. Executable Statements ..
00194 *
00195 *     Constants
00196 *
00197       RESULT( 1 ) = ZERO
00198       RESULT( 2 ) = ZERO
00199       IF( N.LE.0 )
00200      $   RETURN
00201 *
00202       IKA = MAX( 0, MIN( N-1, KA ) )
00203 *
00204       IF( LSAME( UPLO, 'U' ) ) THEN
00205          LOWER = .FALSE.
00206          CUPLO = 'U'
00207       ELSE
00208          LOWER = .TRUE.
00209          CUPLO = 'L'
00210       END IF
00211 *
00212       UNFL = DLAMCH( 'Safe minimum' )
00213       ULP = DLAMCH( 'Epsilon' )*DLAMCH( 'Base' )
00214 *
00215 *     Some Error Checks
00216 *
00217 *     Do Test 1
00218 *
00219 *     Norm of A:
00220 *
00221       ANORM = MAX( ZLANHB( '1', CUPLO, N, IKA, A, LDA, RWORK ), UNFL )
00222 *
00223 *     Compute error matrix:    Error = A - U S U*
00224 *
00225 *     Copy A from SB to SP storage format.
00226 *
00227       J = 0
00228       DO 50 JC = 1, N
00229          IF( LOWER ) THEN
00230             DO 10 JR = 1, MIN( IKA+1, N+1-JC )
00231                J = J + 1
00232                WORK( J ) = A( JR, JC )
00233    10       CONTINUE
00234             DO 20 JR = IKA + 2, N + 1 - JC
00235                J = J + 1
00236                WORK( J ) = ZERO
00237    20       CONTINUE
00238          ELSE
00239             DO 30 JR = IKA + 2, JC
00240                J = J + 1
00241                WORK( J ) = ZERO
00242    30       CONTINUE
00243             DO 40 JR = MIN( IKA, JC-1 ), 0, -1
00244                J = J + 1
00245                WORK( J ) = A( IKA+1-JR, JC )
00246    40       CONTINUE
00247          END IF
00248    50 CONTINUE
00249 *
00250       DO 60 J = 1, N
00251          CALL ZHPR( CUPLO, N, -D( J ), U( 1, J ), 1, WORK )
00252    60 CONTINUE
00253 *
00254       IF( N.GT.1 .AND. KS.EQ.1 ) THEN
00255          DO 70 J = 1, N - 1
00256             CALL ZHPR2( CUPLO, N, -DCMPLX( E( J ) ), U( 1, J ), 1,
00257      $                  U( 1, J+1 ), 1, WORK )
00258    70    CONTINUE
00259       END IF
00260       WNORM = ZLANHP( '1', CUPLO, N, WORK, RWORK )
00261 *
00262       IF( ANORM.GT.WNORM ) THEN
00263          RESULT( 1 ) = ( WNORM / ANORM ) / ( N*ULP )
00264       ELSE
00265          IF( ANORM.LT.ONE ) THEN
00266             RESULT( 1 ) = ( MIN( WNORM, N*ANORM ) / ANORM ) / ( N*ULP )
00267          ELSE
00268             RESULT( 1 ) = MIN( WNORM / ANORM, DBLE( N ) ) / ( N*ULP )
00269          END IF
00270       END IF
00271 *
00272 *     Do Test 2
00273 *
00274 *     Compute  UU* - I
00275 *
00276       CALL ZGEMM( 'N', 'C', N, N, N, CONE, U, LDU, U, LDU, CZERO, WORK,
00277      $            N )
00278 *
00279       DO 80 J = 1, N
00280          WORK( ( N+1 )*( J-1 )+1 ) = WORK( ( N+1 )*( J-1 )+1 ) - CONE
00281    80 CONTINUE
00282 *
00283       RESULT( 2 ) = MIN( ZLANGE( '1', N, N, WORK, N, RWORK ),
00284      $              DBLE( N ) ) / ( N*ULP )
00285 *
00286       RETURN
00287 *
00288 *     End of ZHBT21
00289 *
00290       END
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