LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
cget07.f
Go to the documentation of this file.
00001 *> \brief \b CGET07
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 CGET07( TRANS, N, NRHS, A, LDA, B, LDB, X, LDX, XACT,
00012 *                          LDXACT, FERR, CHKFERR, BERR, RESLTS )
00013 * 
00014 *       .. Scalar Arguments ..
00015 *       CHARACTER          TRANS
00016 *       LOGICAL            CHKFERR
00017 *       INTEGER            LDA, LDB, LDX, LDXACT, N, NRHS
00018 *       ..
00019 *       .. Array Arguments ..
00020 *       REAL               BERR( * ), FERR( * ), RESLTS( * )
00021 *       COMPLEX            A( LDA, * ), B( LDB, * ), X( LDX, * ),
00022 *      $                   XACT( LDXACT, * )
00023 *       ..
00024 *  
00025 *
00026 *> \par Purpose:
00027 *  =============
00028 *>
00029 *> \verbatim
00030 *>
00031 *> CGET07 tests the error bounds from iterative refinement for the
00032 *> computed solution to a system of equations op(A)*X = B, where A is a
00033 *> general n by n matrix and op(A) = A or A**T, depending on TRANS.
00034 *>
00035 *> RESLTS(1) = test of the error bound
00036 *>           = norm(X - XACT) / ( norm(X) * FERR )
00037 *>
00038 *> A large value is returned if this ratio is not less than one.
00039 *>
00040 *> RESLTS(2) = residual from the iterative refinement routine
00041 *>           = the maximum of BERR / ( (n+1)*EPS + (*) ), where
00042 *>             (*) = (n+1)*UNFL / (min_i (abs(op(A))*abs(X) +abs(b))_i )
00043 *> \endverbatim
00044 *
00045 *  Arguments:
00046 *  ==========
00047 *
00048 *> \param[in] TRANS
00049 *> \verbatim
00050 *>          TRANS is CHARACTER*1
00051 *>          Specifies the form of the system of equations.
00052 *>          = 'N':  A * X = B     (No transpose)
00053 *>          = 'T':  A**T * X = B  (Transpose)
00054 *>          = 'C':  A**H * X = B  (Conjugate transpose = Transpose)
00055 *> \endverbatim
00056 *>
00057 *> \param[in] N
00058 *> \verbatim
00059 *>          N is INTEGER
00060 *>          The number of rows of the matrices X and XACT.  N >= 0.
00061 *> \endverbatim
00062 *>
00063 *> \param[in] NRHS
00064 *> \verbatim
00065 *>          NRHS is INTEGER
00066 *>          The number of columns of the matrices X and XACT.  NRHS >= 0.
00067 *> \endverbatim
00068 *>
00069 *> \param[in] A
00070 *> \verbatim
00071 *>          A is COMPLEX array, dimension (LDA,N)
00072 *>          The original n by n matrix A.
00073 *> \endverbatim
00074 *>
00075 *> \param[in] LDA
00076 *> \verbatim
00077 *>          LDA is INTEGER
00078 *>          The leading dimension of the array A.  LDA >= max(1,N).
00079 *> \endverbatim
00080 *>
00081 *> \param[in] B
00082 *> \verbatim
00083 *>          B is COMPLEX array, dimension (LDB,NRHS)
00084 *>          The right hand side vectors for the system of linear
00085 *>          equations.
00086 *> \endverbatim
00087 *>
00088 *> \param[in] LDB
00089 *> \verbatim
00090 *>          LDB is INTEGER
00091 *>          The leading dimension of the array B.  LDB >= max(1,N).
00092 *> \endverbatim
00093 *>
00094 *> \param[in] X
00095 *> \verbatim
00096 *>          X is COMPLEX array, dimension (LDX,NRHS)
00097 *>          The computed solution vectors.  Each vector is stored as a
00098 *>          column of the matrix X.
00099 *> \endverbatim
00100 *>
00101 *> \param[in] LDX
00102 *> \verbatim
00103 *>          LDX is INTEGER
00104 *>          The leading dimension of the array X.  LDX >= max(1,N).
00105 *> \endverbatim
00106 *>
00107 *> \param[in] XACT
00108 *> \verbatim
00109 *>          XACT is COMPLEX array, dimension (LDX,NRHS)
00110 *>          The exact solution vectors.  Each vector is stored as a
00111 *>          column of the matrix XACT.
00112 *> \endverbatim
00113 *>
00114 *> \param[in] LDXACT
00115 *> \verbatim
00116 *>          LDXACT is INTEGER
00117 *>          The leading dimension of the array XACT.  LDXACT >= max(1,N).
00118 *> \endverbatim
00119 *>
00120 *> \param[in] FERR
00121 *> \verbatim
00122 *>          FERR is REAL array, dimension (NRHS)
00123 *>          The estimated forward error bounds for each solution vector
00124 *>          X.  If XTRUE is the true solution, FERR bounds the magnitude
00125 *>          of the largest entry in (X - XTRUE) divided by the magnitude
00126 *>          of the largest entry in X.
00127 *> \endverbatim
00128 *>
00129 *> \param[in] CHKFERR
00130 *> \verbatim
00131 *>          CHKFERR is LOGICAL
00132 *>          Set to .TRUE. to check FERR, .FALSE. not to check FERR.
00133 *>          When the test system is ill-conditioned, the "true"
00134 *>          solution in XACT may be incorrect.
00135 *> \endverbatim
00136 *>
00137 *> \param[in] BERR
00138 *> \verbatim
00139 *>          BERR is REAL array, dimension (NRHS)
00140 *>          The componentwise relative backward error of each solution
00141 *>          vector (i.e., the smallest relative change in any entry of A
00142 *>          or B that makes X an exact solution).
00143 *> \endverbatim
00144 *>
00145 *> \param[out] RESLTS
00146 *> \verbatim
00147 *>          RESLTS is REAL array, dimension (2)
00148 *>          The maximum over the NRHS solution vectors of the ratios:
00149 *>          RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR )
00150 *>          RESLTS(2) = BERR / ( (n+1)*EPS + (*) )
00151 *> \endverbatim
00152 *
00153 *  Authors:
00154 *  ========
00155 *
00156 *> \author Univ. of Tennessee 
00157 *> \author Univ. of California Berkeley 
00158 *> \author Univ. of Colorado Denver 
00159 *> \author NAG Ltd. 
00160 *
00161 *> \date November 2011
00162 *
00163 *> \ingroup complex_lin
00164 *
00165 *  =====================================================================
00166       SUBROUTINE CGET07( TRANS, N, NRHS, A, LDA, B, LDB, X, LDX, XACT,
00167      $                   LDXACT, FERR, CHKFERR, BERR, RESLTS )
00168 *
00169 *  -- LAPACK test routine (version 3.4.0) --
00170 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00171 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00172 *     November 2011
00173 *
00174 *     .. Scalar Arguments ..
00175       CHARACTER          TRANS
00176       LOGICAL            CHKFERR
00177       INTEGER            LDA, LDB, LDX, LDXACT, N, NRHS
00178 *     ..
00179 *     .. Array Arguments ..
00180       REAL               BERR( * ), FERR( * ), RESLTS( * )
00181       COMPLEX            A( LDA, * ), B( LDB, * ), X( LDX, * ),
00182      $                   XACT( LDXACT, * )
00183 *     ..
00184 *
00185 *  =====================================================================
00186 *
00187 *     .. Parameters ..
00188       REAL               ZERO, ONE
00189       PARAMETER          ( ZERO = 0.0E+0, ONE = 1.0E+0 )
00190 *     ..
00191 *     .. Local Scalars ..
00192       LOGICAL            NOTRAN
00193       INTEGER            I, IMAX, J, K
00194       REAL               AXBI, DIFF, EPS, ERRBND, OVFL, TMP, UNFL, XNORM
00195       COMPLEX            ZDUM
00196 *     ..
00197 *     .. External Functions ..
00198       LOGICAL            LSAME
00199       INTEGER            ICAMAX
00200       REAL               SLAMCH
00201       EXTERNAL           LSAME, ICAMAX, SLAMCH
00202 *     ..
00203 *     .. Intrinsic Functions ..
00204       INTRINSIC          ABS, AIMAG, MAX, MIN, REAL
00205 *     ..
00206 *     .. Statement Functions ..
00207       REAL               CABS1
00208 *     ..
00209 *     .. Statement Function definitions ..
00210       CABS1( ZDUM ) = ABS( REAL( ZDUM ) ) + ABS( AIMAG( ZDUM ) )
00211 *     ..
00212 *     .. Executable Statements ..
00213 *
00214 *     Quick exit if N = 0 or NRHS = 0.
00215 *
00216       IF( N.LE.0 .OR. NRHS.LE.0 ) THEN
00217          RESLTS( 1 ) = ZERO
00218          RESLTS( 2 ) = ZERO
00219          RETURN
00220       END IF
00221 *
00222       EPS = SLAMCH( 'Epsilon' )
00223       UNFL = SLAMCH( 'Safe minimum' )
00224       OVFL = ONE / UNFL
00225       NOTRAN = LSAME( TRANS, 'N' )
00226 *
00227 *     Test 1:  Compute the maximum of
00228 *        norm(X - XACT) / ( norm(X) * FERR )
00229 *     over all the vectors X and XACT using the infinity-norm.
00230 *
00231       ERRBND = ZERO
00232       IF( CHKFERR ) THEN
00233          DO 30 J = 1, NRHS
00234             IMAX = ICAMAX( N, X( 1, J ), 1 )
00235             XNORM = MAX( CABS1( X( IMAX, J ) ), UNFL )
00236             DIFF = ZERO
00237             DO 10 I = 1, N
00238                DIFF = MAX( DIFF, CABS1( X( I, J )-XACT( I, J ) ) )
00239  10         CONTINUE
00240 *
00241             IF( XNORM.GT.ONE ) THEN
00242                GO TO 20
00243             ELSE IF( DIFF.LE.OVFL*XNORM ) THEN
00244                GO TO 20
00245             ELSE
00246                ERRBND = ONE / EPS
00247                GO TO 30
00248             END IF
00249 *
00250  20         CONTINUE
00251             IF( DIFF / XNORM.LE.FERR( J ) ) THEN
00252                ERRBND = MAX( ERRBND, ( DIFF / XNORM ) / FERR( J ) )
00253             ELSE
00254                ERRBND = ONE / EPS
00255             END IF
00256  30      CONTINUE
00257       END IF
00258       RESLTS( 1 ) = ERRBND
00259 *
00260 *     Test 2:  Compute the maximum of BERR / ( (n+1)*EPS + (*) ), where
00261 *     (*) = (n+1)*UNFL / (min_i (abs(op(A))*abs(X) +abs(b))_i )
00262 *
00263       DO 70 K = 1, NRHS
00264          DO 60 I = 1, N
00265             TMP = CABS1( B( I, K ) )
00266             IF( NOTRAN ) THEN
00267                DO 40 J = 1, N
00268                   TMP = TMP + CABS1( A( I, J ) )*CABS1( X( J, K ) )
00269    40          CONTINUE
00270             ELSE
00271                DO 50 J = 1, N
00272                   TMP = TMP + CABS1( A( J, I ) )*CABS1( X( J, K ) )
00273    50          CONTINUE
00274             END IF
00275             IF( I.EQ.1 ) THEN
00276                AXBI = TMP
00277             ELSE
00278                AXBI = MIN( AXBI, TMP )
00279             END IF
00280    60    CONTINUE
00281          TMP = BERR( K ) / ( ( N+1 )*EPS+( N+1 )*UNFL /
00282      $         MAX( AXBI, ( N+1 )*UNFL ) )
00283          IF( K.EQ.1 ) THEN
00284             RESLTS( 2 ) = TMP
00285          ELSE
00286             RESLTS( 2 ) = MAX( RESLTS( 2 ), TMP )
00287          END IF
00288    70 CONTINUE
00289 *
00290       RETURN
00291 *
00292 *     End of CGET07
00293 *
00294       END
 All Files Functions