LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
dtpt03.f
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00001 *> \brief \b DTPT03
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 DTPT03( UPLO, TRANS, DIAG, N, NRHS, AP, SCALE, CNORM,
00012 *                          TSCAL, X, LDX, B, LDB, WORK, RESID )
00013 * 
00014 *       .. Scalar Arguments ..
00015 *       CHARACTER          DIAG, TRANS, UPLO
00016 *       INTEGER            LDB, LDX, N, NRHS
00017 *       DOUBLE PRECISION   RESID, SCALE, TSCAL
00018 *       ..
00019 *       .. Array Arguments ..
00020 *       DOUBLE PRECISION   AP( * ), B( LDB, * ), CNORM( * ), WORK( * ),
00021 *      $                   X( LDX, * )
00022 *       ..
00023 *  
00024 *
00025 *> \par Purpose:
00026 *  =============
00027 *>
00028 *> \verbatim
00029 *>
00030 *> DTPT03 computes the residual for the solution to a scaled triangular
00031 *> system of equations A*x = s*b  or  A'*x = s*b  when the triangular
00032 *> matrix A is stored in packed format.  Here A' is the transpose of A,
00033 *> s is a scalar, and x and b are N by NRHS matrices.  The test ratio is
00034 *> the maximum over the number of right hand sides of
00035 *>    norm(s*b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ),
00036 *> where op(A) denotes A or A' and EPS is the machine epsilon.
00037 *> \endverbatim
00038 *
00039 *  Arguments:
00040 *  ==========
00041 *
00042 *> \param[in] UPLO
00043 *> \verbatim
00044 *>          UPLO is CHARACTER*1
00045 *>          Specifies whether the matrix A is upper or lower triangular.
00046 *>          = 'U':  Upper triangular
00047 *>          = 'L':  Lower triangular
00048 *> \endverbatim
00049 *>
00050 *> \param[in] TRANS
00051 *> \verbatim
00052 *>          TRANS is CHARACTER*1
00053 *>          Specifies the operation applied to A.
00054 *>          = 'N':  A *x = s*b  (No transpose)
00055 *>          = 'T':  A'*x = s*b  (Transpose)
00056 *>          = 'C':  A'*x = s*b  (Conjugate transpose = Transpose)
00057 *> \endverbatim
00058 *>
00059 *> \param[in] DIAG
00060 *> \verbatim
00061 *>          DIAG is CHARACTER*1
00062 *>          Specifies whether or not the matrix A is unit triangular.
00063 *>          = 'N':  Non-unit triangular
00064 *>          = 'U':  Unit triangular
00065 *> \endverbatim
00066 *>
00067 *> \param[in] N
00068 *> \verbatim
00069 *>          N is INTEGER
00070 *>          The order of the matrix A.  N >= 0.
00071 *> \endverbatim
00072 *>
00073 *> \param[in] NRHS
00074 *> \verbatim
00075 *>          NRHS is INTEGER
00076 *>          The number of right hand sides, i.e., the number of columns
00077 *>          of the matrices X and B.  NRHS >= 0.
00078 *> \endverbatim
00079 *>
00080 *> \param[in] AP
00081 *> \verbatim
00082 *>          AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
00083 *>          The upper or lower triangular matrix A, packed columnwise in
00084 *>          a linear array.  The j-th column of A is stored in the array
00085 *>          AP as follows:
00086 *>          if UPLO = 'U', AP((j-1)*j/2 + i) = A(i,j) for 1<=i<=j;
00087 *>          if UPLO = 'L',
00088 *>             AP((j-1)*(n-j) + j*(j+1)/2 + i-j) = A(i,j) for j<=i<=n.
00089 *> \endverbatim
00090 *>
00091 *> \param[in] SCALE
00092 *> \verbatim
00093 *>          SCALE is DOUBLE PRECISION
00094 *>          The scaling factor s used in solving the triangular system.
00095 *> \endverbatim
00096 *>
00097 *> \param[in] CNORM
00098 *> \verbatim
00099 *>          CNORM is DOUBLE PRECISION array, dimension (N)
00100 *>          The 1-norms of the columns of A, not counting the diagonal.
00101 *> \endverbatim
00102 *>
00103 *> \param[in] TSCAL
00104 *> \verbatim
00105 *>          TSCAL is DOUBLE PRECISION
00106 *>          The scaling factor used in computing the 1-norms in CNORM.
00107 *>          CNORM actually contains the column norms of TSCAL*A.
00108 *> \endverbatim
00109 *>
00110 *> \param[in] X
00111 *> \verbatim
00112 *>          X is DOUBLE PRECISION array, dimension (LDX,NRHS)
00113 *>          The computed solution vectors for the system of linear
00114 *>          equations.
00115 *> \endverbatim
00116 *>
00117 *> \param[in] LDX
00118 *> \verbatim
00119 *>          LDX is INTEGER
00120 *>          The leading dimension of the array X.  LDX >= max(1,N).
00121 *> \endverbatim
00122 *>
00123 *> \param[in] B
00124 *> \verbatim
00125 *>          B is DOUBLE PRECISION array, dimension (LDB,NRHS)
00126 *>          The right hand side vectors for the system of linear
00127 *>          equations.
00128 *> \endverbatim
00129 *>
00130 *> \param[in] LDB
00131 *> \verbatim
00132 *>          LDB is INTEGER
00133 *>          The leading dimension of the array B.  LDB >= max(1,N).
00134 *> \endverbatim
00135 *>
00136 *> \param[out] WORK
00137 *> \verbatim
00138 *>          WORK is DOUBLE PRECISION array, dimension (N)
00139 *> \endverbatim
00140 *>
00141 *> \param[out] RESID
00142 *> \verbatim
00143 *>          RESID is DOUBLE PRECISION
00144 *>          The maximum over the number of right hand sides of
00145 *>          norm(op(A)*x - s*b) / ( norm(op(A)) * norm(x) * EPS ).
00146 *> \endverbatim
00147 *
00148 *  Authors:
00149 *  ========
00150 *
00151 *> \author Univ. of Tennessee 
00152 *> \author Univ. of California Berkeley 
00153 *> \author Univ. of Colorado Denver 
00154 *> \author NAG Ltd. 
00155 *
00156 *> \date November 2011
00157 *
00158 *> \ingroup double_lin
00159 *
00160 *  =====================================================================
00161       SUBROUTINE DTPT03( UPLO, TRANS, DIAG, N, NRHS, AP, SCALE, CNORM,
00162      $                   TSCAL, X, LDX, B, LDB, WORK, RESID )
00163 *
00164 *  -- LAPACK test routine (version 3.4.0) --
00165 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00166 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00167 *     November 2011
00168 *
00169 *     .. Scalar Arguments ..
00170       CHARACTER          DIAG, TRANS, UPLO
00171       INTEGER            LDB, LDX, N, NRHS
00172       DOUBLE PRECISION   RESID, SCALE, TSCAL
00173 *     ..
00174 *     .. Array Arguments ..
00175       DOUBLE PRECISION   AP( * ), B( LDB, * ), CNORM( * ), WORK( * ),
00176      $                   X( LDX, * )
00177 *     ..
00178 *
00179 *  =====================================================================
00180 *
00181 *     .. Parameters ..
00182       DOUBLE PRECISION   ONE, ZERO
00183       PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
00184 *     ..
00185 *     .. Local Scalars ..
00186       INTEGER            IX, J, JJ
00187       DOUBLE PRECISION   BIGNUM, EPS, ERR, SMLNUM, TNORM, XNORM, XSCAL
00188 *     ..
00189 *     .. External Functions ..
00190       LOGICAL            LSAME
00191       INTEGER            IDAMAX
00192       DOUBLE PRECISION   DLAMCH
00193       EXTERNAL           LSAME, IDAMAX, DLAMCH
00194 *     ..
00195 *     .. External Subroutines ..
00196       EXTERNAL           DAXPY, DCOPY, DLABAD, DSCAL, DTPMV
00197 *     ..
00198 *     .. Intrinsic Functions ..
00199       INTRINSIC          ABS, DBLE, MAX
00200 *     ..
00201 *     .. Executable Statements ..
00202 *
00203 *     Quick exit if N = 0.
00204 *
00205       IF( N.LE.0 .OR. NRHS.LE.0 ) THEN
00206          RESID = ZERO
00207          RETURN
00208       END IF
00209       EPS = DLAMCH( 'Epsilon' )
00210       SMLNUM = DLAMCH( 'Safe minimum' )
00211       BIGNUM = ONE / SMLNUM
00212       CALL DLABAD( SMLNUM, BIGNUM )
00213 *
00214 *     Compute the norm of the triangular matrix A using the column
00215 *     norms already computed by DLATPS.
00216 *
00217       TNORM = ZERO
00218       IF( LSAME( DIAG, 'N' ) ) THEN
00219          IF( LSAME( UPLO, 'U' ) ) THEN
00220             JJ = 1
00221             DO 10 J = 1, N
00222                TNORM = MAX( TNORM, TSCAL*ABS( AP( JJ ) )+CNORM( J ) )
00223                JJ = JJ + J + 1
00224    10       CONTINUE
00225          ELSE
00226             JJ = 1
00227             DO 20 J = 1, N
00228                TNORM = MAX( TNORM, TSCAL*ABS( AP( JJ ) )+CNORM( J ) )
00229                JJ = JJ + N - J + 1
00230    20       CONTINUE
00231          END IF
00232       ELSE
00233          DO 30 J = 1, N
00234             TNORM = MAX( TNORM, TSCAL+CNORM( J ) )
00235    30    CONTINUE
00236       END IF
00237 *
00238 *     Compute the maximum over the number of right hand sides of
00239 *        norm(op(A)*x - s*b) / ( norm(op(A)) * norm(x) * EPS ).
00240 *
00241       RESID = ZERO
00242       DO 40 J = 1, NRHS
00243          CALL DCOPY( N, X( 1, J ), 1, WORK, 1 )
00244          IX = IDAMAX( N, WORK, 1 )
00245          XNORM = MAX( ONE, ABS( X( IX, J ) ) )
00246          XSCAL = ( ONE / XNORM ) / DBLE( N )
00247          CALL DSCAL( N, XSCAL, WORK, 1 )
00248          CALL DTPMV( UPLO, TRANS, DIAG, N, AP, WORK, 1 )
00249          CALL DAXPY( N, -SCALE*XSCAL, B( 1, J ), 1, WORK, 1 )
00250          IX = IDAMAX( N, WORK, 1 )
00251          ERR = TSCAL*ABS( WORK( IX ) )
00252          IX = IDAMAX( N, X( 1, J ), 1 )
00253          XNORM = ABS( X( IX, J ) )
00254          IF( ERR*SMLNUM.LE.XNORM ) THEN
00255             IF( XNORM.GT.ZERO )
00256      $         ERR = ERR / XNORM
00257          ELSE
00258             IF( ERR.GT.ZERO )
00259      $         ERR = ONE / EPS
00260          END IF
00261          IF( ERR*SMLNUM.LE.TNORM ) THEN
00262             IF( TNORM.GT.ZERO )
00263      $         ERR = ERR / TNORM
00264          ELSE
00265             IF( ERR.GT.ZERO )
00266      $         ERR = ONE / EPS
00267          END IF
00268          RESID = MAX( RESID, ERR )
00269    40 CONTINUE
00270 *
00271       RETURN
00272 *
00273 *     End of DTPT03
00274 *
00275       END
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