LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
dtrmv.f
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00001 *> \brief \b DTRMV
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 DTRMV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX)
00012 * 
00013 *       .. Scalar Arguments ..
00014 *       INTEGER INCX,LDA,N
00015 *       CHARACTER DIAG,TRANS,UPLO
00016 *       ..
00017 *       .. Array Arguments ..
00018 *       DOUBLE PRECISION A(LDA,*),X(*)
00019 *       ..
00020 *  
00021 *
00022 *> \par Purpose:
00023 *  =============
00024 *>
00025 *> \verbatim
00026 *>
00027 *> DTRMV  performs one of the matrix-vector operations
00028 *>
00029 *>    x := A*x,   or   x := A**T*x,
00030 *>
00031 *> where x is an n element vector and  A is an n by n unit, or non-unit,
00032 *> upper or lower triangular matrix.
00033 *> \endverbatim
00034 *
00035 *  Arguments:
00036 *  ==========
00037 *
00038 *> \param[in] UPLO
00039 *> \verbatim
00040 *>          UPLO is CHARACTER*1
00041 *>           On entry, UPLO specifies whether the matrix is an upper or
00042 *>           lower triangular matrix as follows:
00043 *>
00044 *>              UPLO = 'U' or 'u'   A is an upper triangular matrix.
00045 *>
00046 *>              UPLO = 'L' or 'l'   A is a lower triangular matrix.
00047 *> \endverbatim
00048 *>
00049 *> \param[in] TRANS
00050 *> \verbatim
00051 *>          TRANS is CHARACTER*1
00052 *>           On entry, TRANS specifies the operation to be performed as
00053 *>           follows:
00054 *>
00055 *>              TRANS = 'N' or 'n'   x := A*x.
00056 *>
00057 *>              TRANS = 'T' or 't'   x := A**T*x.
00058 *>
00059 *>              TRANS = 'C' or 'c'   x := A**T*x.
00060 *> \endverbatim
00061 *>
00062 *> \param[in] DIAG
00063 *> \verbatim
00064 *>          DIAG is CHARACTER*1
00065 *>           On entry, DIAG specifies whether or not A is unit
00066 *>           triangular as follows:
00067 *>
00068 *>              DIAG = 'U' or 'u'   A is assumed to be unit triangular.
00069 *>
00070 *>              DIAG = 'N' or 'n'   A is not assumed to be unit
00071 *>                                  triangular.
00072 *> \endverbatim
00073 *>
00074 *> \param[in] N
00075 *> \verbatim
00076 *>          N is INTEGER
00077 *>           On entry, N specifies the order of the matrix A.
00078 *>           N must be at least zero.
00079 *> \endverbatim
00080 *>
00081 *> \param[in] A
00082 *> \verbatim
00083 *>          A is DOUBLE PRECISION array of DIMENSION ( LDA, n ).
00084 *>           Before entry with  UPLO = 'U' or 'u', the leading n by n
00085 *>           upper triangular part of the array A must contain the upper
00086 *>           triangular matrix and the strictly lower triangular part of
00087 *>           A is not referenced.
00088 *>           Before entry with UPLO = 'L' or 'l', the leading n by n
00089 *>           lower triangular part of the array A must contain the lower
00090 *>           triangular matrix and the strictly upper triangular part of
00091 *>           A is not referenced.
00092 *>           Note that when  DIAG = 'U' or 'u', the diagonal elements of
00093 *>           A are not referenced either, but are assumed to be unity.
00094 *> \endverbatim
00095 *>
00096 *> \param[in] LDA
00097 *> \verbatim
00098 *>          LDA is INTEGER
00099 *>           On entry, LDA specifies the first dimension of A as declared
00100 *>           in the calling (sub) program. LDA must be at least
00101 *>           max( 1, n ).
00102 *> \endverbatim
00103 *>
00104 *> \param[in,out] X
00105 *> \verbatim
00106 *>          X is DOUBLE PRECISION array of dimension at least
00107 *>           ( 1 + ( n - 1 )*abs( INCX ) ).
00108 *>           Before entry, the incremented array X must contain the n
00109 *>           element vector x. On exit, X is overwritten with the
00110 *>           tranformed vector x.
00111 *> \endverbatim
00112 *>
00113 *> \param[in] INCX
00114 *> \verbatim
00115 *>          INCX is INTEGER
00116 *>           On entry, INCX specifies the increment for the elements of
00117 *>           X. INCX must not be zero.
00118 *> \endverbatim
00119 *
00120 *  Authors:
00121 *  ========
00122 *
00123 *> \author Univ. of Tennessee 
00124 *> \author Univ. of California Berkeley 
00125 *> \author Univ. of Colorado Denver 
00126 *> \author NAG Ltd. 
00127 *
00128 *> \date November 2011
00129 *
00130 *> \ingroup double_blas_level2
00131 *
00132 *> \par Further Details:
00133 *  =====================
00134 *>
00135 *> \verbatim
00136 *>
00137 *>  Level 2 Blas routine.
00138 *>  The vector and matrix arguments are not referenced when N = 0, or M = 0
00139 *>
00140 *>  -- Written on 22-October-1986.
00141 *>     Jack Dongarra, Argonne National Lab.
00142 *>     Jeremy Du Croz, Nag Central Office.
00143 *>     Sven Hammarling, Nag Central Office.
00144 *>     Richard Hanson, Sandia National Labs.
00145 *> \endverbatim
00146 *>
00147 *  =====================================================================
00148       SUBROUTINE DTRMV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX)
00149 *
00150 *  -- Reference BLAS level2 routine (version 3.4.0) --
00151 *  -- Reference BLAS is a software package provided by Univ. of Tennessee,    --
00152 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00153 *     November 2011
00154 *
00155 *     .. Scalar Arguments ..
00156       INTEGER INCX,LDA,N
00157       CHARACTER DIAG,TRANS,UPLO
00158 *     ..
00159 *     .. Array Arguments ..
00160       DOUBLE PRECISION A(LDA,*),X(*)
00161 *     ..
00162 *
00163 *  =====================================================================
00164 *
00165 *     .. Parameters ..
00166       DOUBLE PRECISION ZERO
00167       PARAMETER (ZERO=0.0D+0)
00168 *     ..
00169 *     .. Local Scalars ..
00170       DOUBLE PRECISION TEMP
00171       INTEGER I,INFO,IX,J,JX,KX
00172       LOGICAL NOUNIT
00173 *     ..
00174 *     .. External Functions ..
00175       LOGICAL LSAME
00176       EXTERNAL LSAME
00177 *     ..
00178 *     .. External Subroutines ..
00179       EXTERNAL XERBLA
00180 *     ..
00181 *     .. Intrinsic Functions ..
00182       INTRINSIC MAX
00183 *     ..
00184 *
00185 *     Test the input parameters.
00186 *
00187       INFO = 0
00188       IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
00189           INFO = 1
00190       ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND.
00191      +         .NOT.LSAME(TRANS,'C')) THEN
00192           INFO = 2
00193       ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN
00194           INFO = 3
00195       ELSE IF (N.LT.0) THEN
00196           INFO = 4
00197       ELSE IF (LDA.LT.MAX(1,N)) THEN
00198           INFO = 6
00199       ELSE IF (INCX.EQ.0) THEN
00200           INFO = 8
00201       END IF
00202       IF (INFO.NE.0) THEN
00203           CALL XERBLA('DTRMV ',INFO)
00204           RETURN
00205       END IF
00206 *
00207 *     Quick return if possible.
00208 *
00209       IF (N.EQ.0) RETURN
00210 *
00211       NOUNIT = LSAME(DIAG,'N')
00212 *
00213 *     Set up the start point in X if the increment is not unity. This
00214 *     will be  ( N - 1 )*INCX  too small for descending loops.
00215 *
00216       IF (INCX.LE.0) THEN
00217           KX = 1 - (N-1)*INCX
00218       ELSE IF (INCX.NE.1) THEN
00219           KX = 1
00220       END IF
00221 *
00222 *     Start the operations. In this version the elements of A are
00223 *     accessed sequentially with one pass through A.
00224 *
00225       IF (LSAME(TRANS,'N')) THEN
00226 *
00227 *        Form  x := A*x.
00228 *
00229           IF (LSAME(UPLO,'U')) THEN
00230               IF (INCX.EQ.1) THEN
00231                   DO 20 J = 1,N
00232                       IF (X(J).NE.ZERO) THEN
00233                           TEMP = X(J)
00234                           DO 10 I = 1,J - 1
00235                               X(I) = X(I) + TEMP*A(I,J)
00236    10                     CONTINUE
00237                           IF (NOUNIT) X(J) = X(J)*A(J,J)
00238                       END IF
00239    20             CONTINUE
00240               ELSE
00241                   JX = KX
00242                   DO 40 J = 1,N
00243                       IF (X(JX).NE.ZERO) THEN
00244                           TEMP = X(JX)
00245                           IX = KX
00246                           DO 30 I = 1,J - 1
00247                               X(IX) = X(IX) + TEMP*A(I,J)
00248                               IX = IX + INCX
00249    30                     CONTINUE
00250                           IF (NOUNIT) X(JX) = X(JX)*A(J,J)
00251                       END IF
00252                       JX = JX + INCX
00253    40             CONTINUE
00254               END IF
00255           ELSE
00256               IF (INCX.EQ.1) THEN
00257                   DO 60 J = N,1,-1
00258                       IF (X(J).NE.ZERO) THEN
00259                           TEMP = X(J)
00260                           DO 50 I = N,J + 1,-1
00261                               X(I) = X(I) + TEMP*A(I,J)
00262    50                     CONTINUE
00263                           IF (NOUNIT) X(J) = X(J)*A(J,J)
00264                       END IF
00265    60             CONTINUE
00266               ELSE
00267                   KX = KX + (N-1)*INCX
00268                   JX = KX
00269                   DO 80 J = N,1,-1
00270                       IF (X(JX).NE.ZERO) THEN
00271                           TEMP = X(JX)
00272                           IX = KX
00273                           DO 70 I = N,J + 1,-1
00274                               X(IX) = X(IX) + TEMP*A(I,J)
00275                               IX = IX - INCX
00276    70                     CONTINUE
00277                           IF (NOUNIT) X(JX) = X(JX)*A(J,J)
00278                       END IF
00279                       JX = JX - INCX
00280    80             CONTINUE
00281               END IF
00282           END IF
00283       ELSE
00284 *
00285 *        Form  x := A**T*x.
00286 *
00287           IF (LSAME(UPLO,'U')) THEN
00288               IF (INCX.EQ.1) THEN
00289                   DO 100 J = N,1,-1
00290                       TEMP = X(J)
00291                       IF (NOUNIT) TEMP = TEMP*A(J,J)
00292                       DO 90 I = J - 1,1,-1
00293                           TEMP = TEMP + A(I,J)*X(I)
00294    90                 CONTINUE
00295                       X(J) = TEMP
00296   100             CONTINUE
00297               ELSE
00298                   JX = KX + (N-1)*INCX
00299                   DO 120 J = N,1,-1
00300                       TEMP = X(JX)
00301                       IX = JX
00302                       IF (NOUNIT) TEMP = TEMP*A(J,J)
00303                       DO 110 I = J - 1,1,-1
00304                           IX = IX - INCX
00305                           TEMP = TEMP + A(I,J)*X(IX)
00306   110                 CONTINUE
00307                       X(JX) = TEMP
00308                       JX = JX - INCX
00309   120             CONTINUE
00310               END IF
00311           ELSE
00312               IF (INCX.EQ.1) THEN
00313                   DO 140 J = 1,N
00314                       TEMP = X(J)
00315                       IF (NOUNIT) TEMP = TEMP*A(J,J)
00316                       DO 130 I = J + 1,N
00317                           TEMP = TEMP + A(I,J)*X(I)
00318   130                 CONTINUE
00319                       X(J) = TEMP
00320   140             CONTINUE
00321               ELSE
00322                   JX = KX
00323                   DO 160 J = 1,N
00324                       TEMP = X(JX)
00325                       IX = JX
00326                       IF (NOUNIT) TEMP = TEMP*A(J,J)
00327                       DO 150 I = J + 1,N
00328                           IX = IX + INCX
00329                           TEMP = TEMP + A(I,J)*X(IX)
00330   150                 CONTINUE
00331                       X(JX) = TEMP
00332                       JX = JX + INCX
00333   160             CONTINUE
00334               END IF
00335           END IF
00336       END IF
00337 *
00338       RETURN
00339 *
00340 *     End of DTRMV .
00341 *
00342       END
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