LAPACK 3.3.1
Linear Algebra PACKage

dtpmv.f

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00001       SUBROUTINE DTPMV(UPLO,TRANS,DIAG,N,AP,X,INCX)
00002 *     .. Scalar Arguments ..
00003       INTEGER INCX,N
00004       CHARACTER DIAG,TRANS,UPLO
00005 *     ..
00006 *     .. Array Arguments ..
00007       DOUBLE PRECISION AP(*),X(*)
00008 *     ..
00009 *
00010 *  Purpose
00011 *  =======
00012 *
00013 *  DTPMV  performs one of the matrix-vector operations
00014 *
00015 *     x := A*x,   or   x := A**T*x,
00016 *
00017 *  where x is an n element vector and  A is an n by n unit, or non-unit,
00018 *  upper or lower triangular matrix, supplied in packed form.
00019 *
00020 *  Arguments
00021 *  ==========
00022 *
00023 *  UPLO   - CHARACTER*1.
00024 *           On entry, UPLO specifies whether the matrix is an upper or
00025 *           lower triangular matrix as follows:
00026 *
00027 *              UPLO = 'U' or 'u'   A is an upper triangular matrix.
00028 *
00029 *              UPLO = 'L' or 'l'   A is a lower triangular matrix.
00030 *
00031 *           Unchanged on exit.
00032 *
00033 *  TRANS  - CHARACTER*1.
00034 *           On entry, TRANS specifies the operation to be performed as
00035 *           follows:
00036 *
00037 *              TRANS = 'N' or 'n'   x := A*x.
00038 *
00039 *              TRANS = 'T' or 't'   x := A**T*x.
00040 *
00041 *              TRANS = 'C' or 'c'   x := A**T*x.
00042 *
00043 *           Unchanged on exit.
00044 *
00045 *  DIAG   - CHARACTER*1.
00046 *           On entry, DIAG specifies whether or not A is unit
00047 *           triangular as follows:
00048 *
00049 *              DIAG = 'U' or 'u'   A is assumed to be unit triangular.
00050 *
00051 *              DIAG = 'N' or 'n'   A is not assumed to be unit
00052 *                                  triangular.
00053 *
00054 *           Unchanged on exit.
00055 *
00056 *  N      - INTEGER.
00057 *           On entry, N specifies the order of the matrix A.
00058 *           N must be at least zero.
00059 *           Unchanged on exit.
00060 *
00061 *  AP     - DOUBLE PRECISION array of DIMENSION at least
00062 *           ( ( n*( n + 1 ) )/2 ).
00063 *           Before entry with  UPLO = 'U' or 'u', the array AP must
00064 *           contain the upper triangular matrix packed sequentially,
00065 *           column by column, so that AP( 1 ) contains a( 1, 1 ),
00066 *           AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 )
00067 *           respectively, and so on.
00068 *           Before entry with UPLO = 'L' or 'l', the array AP must
00069 *           contain the lower triangular matrix packed sequentially,
00070 *           column by column, so that AP( 1 ) contains a( 1, 1 ),
00071 *           AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 )
00072 *           respectively, and so on.
00073 *           Note that when  DIAG = 'U' or 'u', the diagonal elements of
00074 *           A are not referenced, but are assumed to be unity.
00075 *           Unchanged on exit.
00076 *
00077 *  X      - DOUBLE PRECISION array of dimension at least
00078 *           ( 1 + ( n - 1 )*abs( INCX ) ).
00079 *           Before entry, the incremented array X must contain the n
00080 *           element vector x. On exit, X is overwritten with the
00081 *           tranformed vector x.
00082 *
00083 *  INCX   - INTEGER.
00084 *           On entry, INCX specifies the increment for the elements of
00085 *           X. INCX must not be zero.
00086 *           Unchanged on exit.
00087 *
00088 *  Further Details
00089 *  ===============
00090 *
00091 *  Level 2 Blas routine.
00092 *  The vector and matrix arguments are not referenced when N = 0, or M = 0
00093 *
00094 *  -- Written on 22-October-1986.
00095 *     Jack Dongarra, Argonne National Lab.
00096 *     Jeremy Du Croz, Nag Central Office.
00097 *     Sven Hammarling, Nag Central Office.
00098 *     Richard Hanson, Sandia National Labs.
00099 *
00100 *  =====================================================================
00101 *
00102 *     .. Parameters ..
00103       DOUBLE PRECISION ZERO
00104       PARAMETER (ZERO=0.0D+0)
00105 *     ..
00106 *     .. Local Scalars ..
00107       DOUBLE PRECISION TEMP
00108       INTEGER I,INFO,IX,J,JX,K,KK,KX
00109       LOGICAL NOUNIT
00110 *     ..
00111 *     .. External Functions ..
00112       LOGICAL LSAME
00113       EXTERNAL LSAME
00114 *     ..
00115 *     .. External Subroutines ..
00116       EXTERNAL XERBLA
00117 *     ..
00118 *
00119 *     Test the input parameters.
00120 *
00121       INFO = 0
00122       IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
00123           INFO = 1
00124       ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND.
00125      +         .NOT.LSAME(TRANS,'C')) THEN
00126           INFO = 2
00127       ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN
00128           INFO = 3
00129       ELSE IF (N.LT.0) THEN
00130           INFO = 4
00131       ELSE IF (INCX.EQ.0) THEN
00132           INFO = 7
00133       END IF
00134       IF (INFO.NE.0) THEN
00135           CALL XERBLA('DTPMV ',INFO)
00136           RETURN
00137       END IF
00138 *
00139 *     Quick return if possible.
00140 *
00141       IF (N.EQ.0) RETURN
00142 *
00143       NOUNIT = LSAME(DIAG,'N')
00144 *
00145 *     Set up the start point in X if the increment is not unity. This
00146 *     will be  ( N - 1 )*INCX  too small for descending loops.
00147 *
00148       IF (INCX.LE.0) THEN
00149           KX = 1 - (N-1)*INCX
00150       ELSE IF (INCX.NE.1) THEN
00151           KX = 1
00152       END IF
00153 *
00154 *     Start the operations. In this version the elements of AP are
00155 *     accessed sequentially with one pass through AP.
00156 *
00157       IF (LSAME(TRANS,'N')) THEN
00158 *
00159 *        Form  x:= A*x.
00160 *
00161           IF (LSAME(UPLO,'U')) THEN
00162               KK = 1
00163               IF (INCX.EQ.1) THEN
00164                   DO 20 J = 1,N
00165                       IF (X(J).NE.ZERO) THEN
00166                           TEMP = X(J)
00167                           K = KK
00168                           DO 10 I = 1,J - 1
00169                               X(I) = X(I) + TEMP*AP(K)
00170                               K = K + 1
00171    10                     CONTINUE
00172                           IF (NOUNIT) X(J) = X(J)*AP(KK+J-1)
00173                       END IF
00174                       KK = KK + J
00175    20             CONTINUE
00176               ELSE
00177                   JX = KX
00178                   DO 40 J = 1,N
00179                       IF (X(JX).NE.ZERO) THEN
00180                           TEMP = X(JX)
00181                           IX = KX
00182                           DO 30 K = KK,KK + J - 2
00183                               X(IX) = X(IX) + TEMP*AP(K)
00184                               IX = IX + INCX
00185    30                     CONTINUE
00186                           IF (NOUNIT) X(JX) = X(JX)*AP(KK+J-1)
00187                       END IF
00188                       JX = JX + INCX
00189                       KK = KK + J
00190    40             CONTINUE
00191               END IF
00192           ELSE
00193               KK = (N* (N+1))/2
00194               IF (INCX.EQ.1) THEN
00195                   DO 60 J = N,1,-1
00196                       IF (X(J).NE.ZERO) THEN
00197                           TEMP = X(J)
00198                           K = KK
00199                           DO 50 I = N,J + 1,-1
00200                               X(I) = X(I) + TEMP*AP(K)
00201                               K = K - 1
00202    50                     CONTINUE
00203                           IF (NOUNIT) X(J) = X(J)*AP(KK-N+J)
00204                       END IF
00205                       KK = KK - (N-J+1)
00206    60             CONTINUE
00207               ELSE
00208                   KX = KX + (N-1)*INCX
00209                   JX = KX
00210                   DO 80 J = N,1,-1
00211                       IF (X(JX).NE.ZERO) THEN
00212                           TEMP = X(JX)
00213                           IX = KX
00214                           DO 70 K = KK,KK - (N- (J+1)),-1
00215                               X(IX) = X(IX) + TEMP*AP(K)
00216                               IX = IX - INCX
00217    70                     CONTINUE
00218                           IF (NOUNIT) X(JX) = X(JX)*AP(KK-N+J)
00219                       END IF
00220                       JX = JX - INCX
00221                       KK = KK - (N-J+1)
00222    80             CONTINUE
00223               END IF
00224           END IF
00225       ELSE
00226 *
00227 *        Form  x := A**T*x.
00228 *
00229           IF (LSAME(UPLO,'U')) THEN
00230               KK = (N* (N+1))/2
00231               IF (INCX.EQ.1) THEN
00232                   DO 100 J = N,1,-1
00233                       TEMP = X(J)
00234                       IF (NOUNIT) TEMP = TEMP*AP(KK)
00235                       K = KK - 1
00236                       DO 90 I = J - 1,1,-1
00237                           TEMP = TEMP + AP(K)*X(I)
00238                           K = K - 1
00239    90                 CONTINUE
00240                       X(J) = TEMP
00241                       KK = KK - J
00242   100             CONTINUE
00243               ELSE
00244                   JX = KX + (N-1)*INCX
00245                   DO 120 J = N,1,-1
00246                       TEMP = X(JX)
00247                       IX = JX
00248                       IF (NOUNIT) TEMP = TEMP*AP(KK)
00249                       DO 110 K = KK - 1,KK - J + 1,-1
00250                           IX = IX - INCX
00251                           TEMP = TEMP + AP(K)*X(IX)
00252   110                 CONTINUE
00253                       X(JX) = TEMP
00254                       JX = JX - INCX
00255                       KK = KK - J
00256   120             CONTINUE
00257               END IF
00258           ELSE
00259               KK = 1
00260               IF (INCX.EQ.1) THEN
00261                   DO 140 J = 1,N
00262                       TEMP = X(J)
00263                       IF (NOUNIT) TEMP = TEMP*AP(KK)
00264                       K = KK + 1
00265                       DO 130 I = J + 1,N
00266                           TEMP = TEMP + AP(K)*X(I)
00267                           K = K + 1
00268   130                 CONTINUE
00269                       X(J) = TEMP
00270                       KK = KK + (N-J+1)
00271   140             CONTINUE
00272               ELSE
00273                   JX = KX
00274                   DO 160 J = 1,N
00275                       TEMP = X(JX)
00276                       IX = JX
00277                       IF (NOUNIT) TEMP = TEMP*AP(KK)
00278                       DO 150 K = KK + 1,KK + N - J
00279                           IX = IX + INCX
00280                           TEMP = TEMP + AP(K)*X(IX)
00281   150                 CONTINUE
00282                       X(JX) = TEMP
00283                       JX = JX + INCX
00284                       KK = KK + (N-J+1)
00285   160             CONTINUE
00286               END IF
00287           END IF
00288       END IF
00289 *
00290       RETURN
00291 *
00292 *     End of DTPMV .
00293 *
00294       END
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