LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
zgtt02.f
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00001 *> \brief \b ZGTT02
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 ZGTT02( TRANS, N, NRHS, DL, D, DU, X, LDX, B, LDB,
00012 *                          RESID )
00013 * 
00014 *       .. Scalar Arguments ..
00015 *       CHARACTER          TRANS
00016 *       INTEGER            LDB, LDX, N, NRHS
00017 *       DOUBLE PRECISION   RESID
00018 *       ..
00019 *       .. Array Arguments ..
00020 *       COMPLEX*16         B( LDB, * ), D( * ), DL( * ), DU( * ),
00021 *      $                   X( LDX, * )
00022 *       ..
00023 *  
00024 *
00025 *> \par Purpose:
00026 *  =============
00027 *>
00028 *> \verbatim
00029 *>
00030 *> ZGTT02 computes the residual for the solution to a tridiagonal
00031 *> system of equations:
00032 *>    RESID = norm(B - op(A)*X) / (norm(A) * norm(X) * EPS),
00033 *> where EPS is the machine epsilon.
00034 *> \endverbatim
00035 *
00036 *  Arguments:
00037 *  ==========
00038 *
00039 *> \param[in] TRANS
00040 *> \verbatim
00041 *>          TRANS is CHARACTER
00042 *>          Specifies the form of the residual.
00043 *>          = 'N':  B - A * X     (No transpose)
00044 *>          = 'T':  B - A**T * X  (Transpose)
00045 *>          = 'C':  B - A**H * X  (Conjugate transpose)
00046 *> \endverbatim
00047 *>
00048 *> \param[in] N
00049 *> \verbatim
00050 *>          N is INTEGTER
00051 *>          The order of the matrix A.  N >= 0.
00052 *> \endverbatim
00053 *>
00054 *> \param[in] NRHS
00055 *> \verbatim
00056 *>          NRHS is INTEGER
00057 *>          The number of right hand sides, i.e., the number of columns
00058 *>          of the matrices B and X.  NRHS >= 0.
00059 *> \endverbatim
00060 *>
00061 *> \param[in] DL
00062 *> \verbatim
00063 *>          DL is COMPLEX*16 array, dimension (N-1)
00064 *>          The (n-1) sub-diagonal elements of A.
00065 *> \endverbatim
00066 *>
00067 *> \param[in] D
00068 *> \verbatim
00069 *>          D is COMPLEX*16 array, dimension (N)
00070 *>          The diagonal elements of A.
00071 *> \endverbatim
00072 *>
00073 *> \param[in] DU
00074 *> \verbatim
00075 *>          DU is COMPLEX*16 array, dimension (N-1)
00076 *>          The (n-1) super-diagonal elements of A.
00077 *> \endverbatim
00078 *>
00079 *> \param[in] X
00080 *> \verbatim
00081 *>          X is COMPLEX*16 array, dimension (LDX,NRHS)
00082 *>          The computed solution vectors X.
00083 *> \endverbatim
00084 *>
00085 *> \param[in] LDX
00086 *> \verbatim
00087 *>          LDX is INTEGER
00088 *>          The leading dimension of the array X.  LDX >= max(1,N).
00089 *> \endverbatim
00090 *>
00091 *> \param[in,out] B
00092 *> \verbatim
00093 *>          B is COMPLEX*16 array, dimension (LDB,NRHS)
00094 *>          On entry, the right hand side vectors for the system of
00095 *>          linear equations.
00096 *>          On exit, B is overwritten with the difference B - op(A)*X.
00097 *> \endverbatim
00098 *>
00099 *> \param[in] LDB
00100 *> \verbatim
00101 *>          LDB is INTEGER
00102 *>          The leading dimension of the array B.  LDB >= max(1,N).
00103 *> \endverbatim
00104 *>
00105 *> \param[out] RESID
00106 *> \verbatim
00107 *>          RESID is DOUBLE PRECISION
00108 *>          norm(B - op(A)*X) / (norm(A) * norm(X) * EPS)
00109 *> \endverbatim
00110 *
00111 *  Authors:
00112 *  ========
00113 *
00114 *> \author Univ. of Tennessee 
00115 *> \author Univ. of California Berkeley 
00116 *> \author Univ. of Colorado Denver 
00117 *> \author NAG Ltd. 
00118 *
00119 *> \date November 2011
00120 *
00121 *> \ingroup complex16_lin
00122 *
00123 *  =====================================================================
00124       SUBROUTINE ZGTT02( TRANS, N, NRHS, DL, D, DU, X, LDX, B, LDB,
00125      $                   RESID )
00126 *
00127 *  -- LAPACK test routine (version 3.4.0) --
00128 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00129 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00130 *     November 2011
00131 *
00132 *     .. Scalar Arguments ..
00133       CHARACTER          TRANS
00134       INTEGER            LDB, LDX, N, NRHS
00135       DOUBLE PRECISION   RESID
00136 *     ..
00137 *     .. Array Arguments ..
00138       COMPLEX*16         B( LDB, * ), D( * ), DL( * ), DU( * ),
00139      $                   X( LDX, * )
00140 *     ..
00141 *
00142 *  =====================================================================
00143 *
00144 *     .. Parameters ..
00145       DOUBLE PRECISION   ONE, ZERO
00146       PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
00147 *     ..
00148 *     .. Local Scalars ..
00149       INTEGER            J
00150       DOUBLE PRECISION   ANORM, BNORM, EPS, XNORM
00151 *     ..
00152 *     .. External Functions ..
00153       LOGICAL            LSAME
00154       DOUBLE PRECISION   DLAMCH, DZASUM, ZLANGT
00155       EXTERNAL           LSAME, DLAMCH, DZASUM, ZLANGT
00156 *     ..
00157 *     .. External Subroutines ..
00158       EXTERNAL           ZLAGTM
00159 *     ..
00160 *     .. Intrinsic Functions ..
00161       INTRINSIC          MAX
00162 *     ..
00163 *     .. Executable Statements ..
00164 *
00165 *     Quick exit if N = 0 or NRHS = 0
00166 *
00167       RESID = ZERO
00168       IF( N.LE.0 .OR. NRHS.EQ.0 )
00169      $   RETURN
00170 *
00171 *     Compute the maximum over the number of right hand sides of
00172 *        norm(B - op(A)*X) / ( norm(A) * norm(X) * EPS ).
00173 *
00174       IF( LSAME( TRANS, 'N' ) ) THEN
00175          ANORM = ZLANGT( '1', N, DL, D, DU )
00176       ELSE
00177          ANORM = ZLANGT( 'I', N, DL, D, DU )
00178       END IF
00179 *
00180 *     Exit with RESID = 1/EPS if ANORM = 0.
00181 *
00182       EPS = DLAMCH( 'Epsilon' )
00183       IF( ANORM.LE.ZERO ) THEN
00184          RESID = ONE / EPS
00185          RETURN
00186       END IF
00187 *
00188 *     Compute B - op(A)*X.
00189 *
00190       CALL ZLAGTM( TRANS, N, NRHS, -ONE, DL, D, DU, X, LDX, ONE, B,
00191      $             LDB )
00192 *
00193       DO 10 J = 1, NRHS
00194          BNORM = DZASUM( N, B( 1, J ), 1 )
00195          XNORM = DZASUM( N, X( 1, J ), 1 )
00196          IF( XNORM.LE.ZERO ) THEN
00197             RESID = ONE / EPS
00198          ELSE
00199             RESID = MAX( RESID, ( ( BNORM / ANORM ) / XNORM ) / EPS )
00200          END IF
00201    10 CONTINUE
00202 *
00203       RETURN
00204 *
00205 *     End of ZGTT02
00206 *
00207       END
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