LAPACK 3.3.1
Linear Algebra PACKage

ztrmv.f

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00001       SUBROUTINE ZTRMV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX)
00002 *     .. Scalar Arguments ..
00003       INTEGER INCX,LDA,N
00004       CHARACTER DIAG,TRANS,UPLO
00005 *     ..
00006 *     .. Array Arguments ..
00007       DOUBLE COMPLEX A(LDA,*),X(*)
00008 *     ..
00009 *
00010 *  Purpose
00011 *  =======
00012 *
00013 *  ZTRMV  performs one of the matrix-vector operations
00014 *
00015 *     x := A*x,   or   x := A**T*x,   or   x := A**H*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.
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**H*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 *  A      - COMPLEX*16       array of DIMENSION ( LDA, n ).
00062 *           Before entry with  UPLO = 'U' or 'u', the leading n by n
00063 *           upper triangular part of the array A must contain the upper
00064 *           triangular matrix and the strictly lower triangular part of
00065 *           A is not referenced.
00066 *           Before entry with UPLO = 'L' or 'l', the leading n by n
00067 *           lower triangular part of the array A must contain the lower
00068 *           triangular matrix and the strictly upper triangular part of
00069 *           A is not referenced.
00070 *           Note that when  DIAG = 'U' or 'u', the diagonal elements of
00071 *           A are not referenced either, but are assumed to be unity.
00072 *           Unchanged on exit.
00073 *
00074 *  LDA    - INTEGER.
00075 *           On entry, LDA specifies the first dimension of A as declared
00076 *           in the calling (sub) program. LDA must be at least
00077 *           max( 1, n ).
00078 *           Unchanged on exit.
00079 *
00080 *  X      - COMPLEX*16       array of dimension at least
00081 *           ( 1 + ( n - 1 )*abs( INCX ) ).
00082 *           Before entry, the incremented array X must contain the n
00083 *           element vector x. On exit, X is overwritten with the
00084 *           tranformed vector x.
00085 *
00086 *  INCX   - INTEGER.
00087 *           On entry, INCX specifies the increment for the elements of
00088 *           X. INCX must not be zero.
00089 *           Unchanged on exit.
00090 *
00091 *  Further Details
00092 *  ===============
00093 *
00094 *  Level 2 Blas routine.
00095 *  The vector and matrix arguments are not referenced when N = 0, or M = 0
00096 *
00097 *  -- Written on 22-October-1986.
00098 *     Jack Dongarra, Argonne National Lab.
00099 *     Jeremy Du Croz, Nag Central Office.
00100 *     Sven Hammarling, Nag Central Office.
00101 *     Richard Hanson, Sandia National Labs.
00102 *
00103 *  =====================================================================
00104 *
00105 *     .. Parameters ..
00106       DOUBLE COMPLEX ZERO
00107       PARAMETER (ZERO= (0.0D+0,0.0D+0))
00108 *     ..
00109 *     .. Local Scalars ..
00110       DOUBLE COMPLEX TEMP
00111       INTEGER I,INFO,IX,J,JX,KX
00112       LOGICAL NOCONJ,NOUNIT
00113 *     ..
00114 *     .. External Functions ..
00115       LOGICAL LSAME
00116       EXTERNAL LSAME
00117 *     ..
00118 *     .. External Subroutines ..
00119       EXTERNAL XERBLA
00120 *     ..
00121 *     .. Intrinsic Functions ..
00122       INTRINSIC DCONJG,MAX
00123 *     ..
00124 *
00125 *     Test the input parameters.
00126 *
00127       INFO = 0
00128       IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
00129           INFO = 1
00130       ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND.
00131      +         .NOT.LSAME(TRANS,'C')) THEN
00132           INFO = 2
00133       ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN
00134           INFO = 3
00135       ELSE IF (N.LT.0) THEN
00136           INFO = 4
00137       ELSE IF (LDA.LT.MAX(1,N)) THEN
00138           INFO = 6
00139       ELSE IF (INCX.EQ.0) THEN
00140           INFO = 8
00141       END IF
00142       IF (INFO.NE.0) THEN
00143           CALL XERBLA('ZTRMV ',INFO)
00144           RETURN
00145       END IF
00146 *
00147 *     Quick return if possible.
00148 *
00149       IF (N.EQ.0) RETURN
00150 *
00151       NOCONJ = LSAME(TRANS,'T')
00152       NOUNIT = LSAME(DIAG,'N')
00153 *
00154 *     Set up the start point in X if the increment is not unity. This
00155 *     will be  ( N - 1 )*INCX  too small for descending loops.
00156 *
00157       IF (INCX.LE.0) THEN
00158           KX = 1 - (N-1)*INCX
00159       ELSE IF (INCX.NE.1) THEN
00160           KX = 1
00161       END IF
00162 *
00163 *     Start the operations. In this version the elements of A are
00164 *     accessed sequentially with one pass through A.
00165 *
00166       IF (LSAME(TRANS,'N')) THEN
00167 *
00168 *        Form  x := A*x.
00169 *
00170           IF (LSAME(UPLO,'U')) THEN
00171               IF (INCX.EQ.1) THEN
00172                   DO 20 J = 1,N
00173                       IF (X(J).NE.ZERO) THEN
00174                           TEMP = X(J)
00175                           DO 10 I = 1,J - 1
00176                               X(I) = X(I) + TEMP*A(I,J)
00177    10                     CONTINUE
00178                           IF (NOUNIT) X(J) = X(J)*A(J,J)
00179                       END IF
00180    20             CONTINUE
00181               ELSE
00182                   JX = KX
00183                   DO 40 J = 1,N
00184                       IF (X(JX).NE.ZERO) THEN
00185                           TEMP = X(JX)
00186                           IX = KX
00187                           DO 30 I = 1,J - 1
00188                               X(IX) = X(IX) + TEMP*A(I,J)
00189                               IX = IX + INCX
00190    30                     CONTINUE
00191                           IF (NOUNIT) X(JX) = X(JX)*A(J,J)
00192                       END IF
00193                       JX = JX + INCX
00194    40             CONTINUE
00195               END IF
00196           ELSE
00197               IF (INCX.EQ.1) THEN
00198                   DO 60 J = N,1,-1
00199                       IF (X(J).NE.ZERO) THEN
00200                           TEMP = X(J)
00201                           DO 50 I = N,J + 1,-1
00202                               X(I) = X(I) + TEMP*A(I,J)
00203    50                     CONTINUE
00204                           IF (NOUNIT) X(J) = X(J)*A(J,J)
00205                       END IF
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 I = N,J + 1,-1
00215                               X(IX) = X(IX) + TEMP*A(I,J)
00216                               IX = IX - INCX
00217    70                     CONTINUE
00218                           IF (NOUNIT) X(JX) = X(JX)*A(J,J)
00219                       END IF
00220                       JX = JX - INCX
00221    80             CONTINUE
00222               END IF
00223           END IF
00224       ELSE
00225 *
00226 *        Form  x := A**T*x  or  x := A**H*x.
00227 *
00228           IF (LSAME(UPLO,'U')) THEN
00229               IF (INCX.EQ.1) THEN
00230                   DO 110 J = N,1,-1
00231                       TEMP = X(J)
00232                       IF (NOCONJ) THEN
00233                           IF (NOUNIT) TEMP = TEMP*A(J,J)
00234                           DO 90 I = J - 1,1,-1
00235                               TEMP = TEMP + A(I,J)*X(I)
00236    90                     CONTINUE
00237                       ELSE
00238                           IF (NOUNIT) TEMP = TEMP*DCONJG(A(J,J))
00239                           DO 100 I = J - 1,1,-1
00240                               TEMP = TEMP + DCONJG(A(I,J))*X(I)
00241   100                     CONTINUE
00242                       END IF
00243                       X(J) = TEMP
00244   110             CONTINUE
00245               ELSE
00246                   JX = KX + (N-1)*INCX
00247                   DO 140 J = N,1,-1
00248                       TEMP = X(JX)
00249                       IX = JX
00250                       IF (NOCONJ) THEN
00251                           IF (NOUNIT) TEMP = TEMP*A(J,J)
00252                           DO 120 I = J - 1,1,-1
00253                               IX = IX - INCX
00254                               TEMP = TEMP + A(I,J)*X(IX)
00255   120                     CONTINUE
00256                       ELSE
00257                           IF (NOUNIT) TEMP = TEMP*DCONJG(A(J,J))
00258                           DO 130 I = J - 1,1,-1
00259                               IX = IX - INCX
00260                               TEMP = TEMP + DCONJG(A(I,J))*X(IX)
00261   130                     CONTINUE
00262                       END IF
00263                       X(JX) = TEMP
00264                       JX = JX - INCX
00265   140             CONTINUE
00266               END IF
00267           ELSE
00268               IF (INCX.EQ.1) THEN
00269                   DO 170 J = 1,N
00270                       TEMP = X(J)
00271                       IF (NOCONJ) THEN
00272                           IF (NOUNIT) TEMP = TEMP*A(J,J)
00273                           DO 150 I = J + 1,N
00274                               TEMP = TEMP + A(I,J)*X(I)
00275   150                     CONTINUE
00276                       ELSE
00277                           IF (NOUNIT) TEMP = TEMP*DCONJG(A(J,J))
00278                           DO 160 I = J + 1,N
00279                               TEMP = TEMP + DCONJG(A(I,J))*X(I)
00280   160                     CONTINUE
00281                       END IF
00282                       X(J) = TEMP
00283   170             CONTINUE
00284               ELSE
00285                   JX = KX
00286                   DO 200 J = 1,N
00287                       TEMP = X(JX)
00288                       IX = JX
00289                       IF (NOCONJ) THEN
00290                           IF (NOUNIT) TEMP = TEMP*A(J,J)
00291                           DO 180 I = J + 1,N
00292                               IX = IX + INCX
00293                               TEMP = TEMP + A(I,J)*X(IX)
00294   180                     CONTINUE
00295                       ELSE
00296                           IF (NOUNIT) TEMP = TEMP*DCONJG(A(J,J))
00297                           DO 190 I = J + 1,N
00298                               IX = IX + INCX
00299                               TEMP = TEMP + DCONJG(A(I,J))*X(IX)
00300   190                     CONTINUE
00301                       END IF
00302                       X(JX) = TEMP
00303                       JX = JX + INCX
00304   200             CONTINUE
00305               END IF
00306           END IF
00307       END IF
00308 *
00309       RETURN
00310 *
00311 *     End of ZTRMV .
00312 *
00313       END
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