LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
dppt02.f
Go to the documentation of this file.
00001 *> \brief \b DPPT02
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 DPPT02( UPLO, N, NRHS, A, X, LDX, B, LDB, RWORK,
00012 *                          RESID )
00013 * 
00014 *       .. Scalar Arguments ..
00015 *       CHARACTER          UPLO
00016 *       INTEGER            LDB, LDX, N, NRHS
00017 *       DOUBLE PRECISION   RESID
00018 *       ..
00019 *       .. Array Arguments ..
00020 *       DOUBLE PRECISION   A( * ), B( LDB, * ), RWORK( * ), X( LDX, * )
00021 *       ..
00022 *  
00023 *
00024 *> \par Purpose:
00025 *  =============
00026 *>
00027 *> \verbatim
00028 *>
00029 *> DPPT02 computes the residual in the solution of a symmetric system
00030 *> of linear equations  A*x = b  when packed storage is used for the
00031 *> coefficient matrix.  The ratio computed is
00032 *>
00033 *>    RESID = norm(B - A*X) / ( norm(A) * norm(X) * EPS),
00034 *>
00035 *> where EPS is the machine precision.
00036 *> \endverbatim
00037 *
00038 *  Arguments:
00039 *  ==========
00040 *
00041 *> \param[in] UPLO
00042 *> \verbatim
00043 *>          UPLO is CHARACTER*1
00044 *>          Specifies whether the upper or lower triangular part of the
00045 *>          symmetric matrix A is stored:
00046 *>          = 'U':  Upper triangular
00047 *>          = 'L':  Lower triangular
00048 *> \endverbatim
00049 *>
00050 *> \param[in] N
00051 *> \verbatim
00052 *>          N is INTEGER
00053 *>          The number of rows and columns of the matrix A.  N >= 0.
00054 *> \endverbatim
00055 *>
00056 *> \param[in] NRHS
00057 *> \verbatim
00058 *>          NRHS is INTEGER
00059 *>          The number of columns of B, the matrix of right hand sides.
00060 *>          NRHS >= 0.
00061 *> \endverbatim
00062 *>
00063 *> \param[in] A
00064 *> \verbatim
00065 *>          A is DOUBLE PRECISION array, dimension (N*(N+1)/2)
00066 *>          The original symmetric matrix A, stored as a packed
00067 *>          triangular matrix.
00068 *> \endverbatim
00069 *>
00070 *> \param[in] X
00071 *> \verbatim
00072 *>          X is DOUBLE PRECISION array, dimension (LDX,NRHS)
00073 *>          The computed solution vectors for the system of linear
00074 *>          equations.
00075 *> \endverbatim
00076 *>
00077 *> \param[in] LDX
00078 *> \verbatim
00079 *>          LDX is INTEGER
00080 *>          The leading dimension of the array X.   LDX >= max(1,N).
00081 *> \endverbatim
00082 *>
00083 *> \param[in,out] B
00084 *> \verbatim
00085 *>          B is DOUBLE PRECISION array, dimension (LDB,NRHS)
00086 *>          On entry, the right hand side vectors for the system of
00087 *>          linear equations.
00088 *>          On exit, B is overwritten with the difference B - A*X.
00089 *> \endverbatim
00090 *>
00091 *> \param[in] LDB
00092 *> \verbatim
00093 *>          LDB is INTEGER
00094 *>          The leading dimension of the array B.  LDB >= max(1,N).
00095 *> \endverbatim
00096 *>
00097 *> \param[out] RWORK
00098 *> \verbatim
00099 *>          RWORK is DOUBLE PRECISION array, dimension (N)
00100 *> \endverbatim
00101 *>
00102 *> \param[out] RESID
00103 *> \verbatim
00104 *>          RESID is DOUBLE PRECISION
00105 *>          The maximum over the number of right hand sides of
00106 *>          norm(B - A*X) / ( norm(A) * norm(X) * EPS ).
00107 *> \endverbatim
00108 *
00109 *  Authors:
00110 *  ========
00111 *
00112 *> \author Univ. of Tennessee 
00113 *> \author Univ. of California Berkeley 
00114 *> \author Univ. of Colorado Denver 
00115 *> \author NAG Ltd. 
00116 *
00117 *> \date November 2011
00118 *
00119 *> \ingroup double_lin
00120 *
00121 *  =====================================================================
00122       SUBROUTINE DPPT02( UPLO, N, NRHS, A, X, LDX, B, LDB, RWORK,
00123      $                   RESID )
00124 *
00125 *  -- LAPACK test routine (version 3.4.0) --
00126 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00127 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00128 *     November 2011
00129 *
00130 *     .. Scalar Arguments ..
00131       CHARACTER          UPLO
00132       INTEGER            LDB, LDX, N, NRHS
00133       DOUBLE PRECISION   RESID
00134 *     ..
00135 *     .. Array Arguments ..
00136       DOUBLE PRECISION   A( * ), B( LDB, * ), RWORK( * ), X( LDX, * )
00137 *     ..
00138 *
00139 *  =====================================================================
00140 *
00141 *     .. Parameters ..
00142       DOUBLE PRECISION   ZERO, ONE
00143       PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0 )
00144 *     ..
00145 *     .. Local Scalars ..
00146       INTEGER            J
00147       DOUBLE PRECISION   ANORM, BNORM, EPS, XNORM
00148 *     ..
00149 *     .. External Functions ..
00150       DOUBLE PRECISION   DASUM, DLAMCH, DLANSP
00151       EXTERNAL           DASUM, DLAMCH, DLANSP
00152 *     ..
00153 *     .. External Subroutines ..
00154       EXTERNAL           DSPMV
00155 *     ..
00156 *     .. Intrinsic Functions ..
00157       INTRINSIC          MAX
00158 *     ..
00159 *     .. Executable Statements ..
00160 *
00161 *     Quick exit if N = 0 or NRHS = 0.
00162 *
00163       IF( N.LE.0 .OR. NRHS.LE.0 ) THEN
00164          RESID = ZERO
00165          RETURN
00166       END IF
00167 *
00168 *     Exit with RESID = 1/EPS if ANORM = 0.
00169 *
00170       EPS = DLAMCH( 'Epsilon' )
00171       ANORM = DLANSP( '1', UPLO, N, A, RWORK )
00172       IF( ANORM.LE.ZERO ) THEN
00173          RESID = ONE / EPS
00174          RETURN
00175       END IF
00176 *
00177 *     Compute  B - A*X  for the matrix of right hand sides B.
00178 *
00179       DO 10 J = 1, NRHS
00180          CALL DSPMV( UPLO, N, -ONE, A, X( 1, J ), 1, ONE, B( 1, J ), 1 )
00181    10 CONTINUE
00182 *
00183 *     Compute the maximum over the number of right hand sides of
00184 *        norm( B - A*X ) / ( norm(A) * norm(X) * EPS ) .
00185 *
00186       RESID = ZERO
00187       DO 20 J = 1, NRHS
00188          BNORM = DASUM( N, B( 1, J ), 1 )
00189          XNORM = DASUM( N, X( 1, J ), 1 )
00190          IF( XNORM.LE.ZERO ) THEN
00191             RESID = ONE / EPS
00192          ELSE
00193             RESID = MAX( RESID, ( ( BNORM / ANORM ) / XNORM ) / EPS )
00194          END IF
00195    20 CONTINUE
00196 *
00197       RETURN
00198 *
00199 *     End of DPPT02
00200 *
00201       END
 All Files Functions