LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
ztrmv.f
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00001 *> \brief \b ZTRMV
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 ZTRMV(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 *       COMPLEX*16 A(LDA,*),X(*)
00019 *       ..
00020 *  
00021 *
00022 *> \par Purpose:
00023 *  =============
00024 *>
00025 *> \verbatim
00026 *>
00027 *> ZTRMV  performs one of the matrix-vector operations
00028 *>
00029 *>    x := A*x,   or   x := A**T*x,   or   x := A**H*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**H*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 COMPLEX*16 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] X
00105 *> \verbatim
00106 *>          X is (input/output) COMPLEX*16 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 complex16_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 ZTRMV(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       COMPLEX*16 A(LDA,*),X(*)
00161 *     ..
00162 *
00163 *  =====================================================================
00164 *
00165 *     .. Parameters ..
00166       COMPLEX*16 ZERO
00167       PARAMETER (ZERO= (0.0D+0,0.0D+0))
00168 *     ..
00169 *     .. Local Scalars ..
00170       COMPLEX*16 TEMP
00171       INTEGER I,INFO,IX,J,JX,KX
00172       LOGICAL NOCONJ,NOUNIT
00173 *     ..
00174 *     .. External Functions ..
00175       LOGICAL LSAME
00176       EXTERNAL LSAME
00177 *     ..
00178 *     .. External Subroutines ..
00179       EXTERNAL XERBLA
00180 *     ..
00181 *     .. Intrinsic Functions ..
00182       INTRINSIC DCONJG,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('ZTRMV ',INFO)
00204           RETURN
00205       END IF
00206 *
00207 *     Quick return if possible.
00208 *
00209       IF (N.EQ.0) RETURN
00210 *
00211       NOCONJ = LSAME(TRANS,'T')
00212       NOUNIT = LSAME(DIAG,'N')
00213 *
00214 *     Set up the start point in X if the increment is not unity. This
00215 *     will be  ( N - 1 )*INCX  too small for descending loops.
00216 *
00217       IF (INCX.LE.0) THEN
00218           KX = 1 - (N-1)*INCX
00219       ELSE IF (INCX.NE.1) THEN
00220           KX = 1
00221       END IF
00222 *
00223 *     Start the operations. In this version the elements of A are
00224 *     accessed sequentially with one pass through A.
00225 *
00226       IF (LSAME(TRANS,'N')) THEN
00227 *
00228 *        Form  x := A*x.
00229 *
00230           IF (LSAME(UPLO,'U')) THEN
00231               IF (INCX.EQ.1) THEN
00232                   DO 20 J = 1,N
00233                       IF (X(J).NE.ZERO) THEN
00234                           TEMP = X(J)
00235                           DO 10 I = 1,J - 1
00236                               X(I) = X(I) + TEMP*A(I,J)
00237    10                     CONTINUE
00238                           IF (NOUNIT) X(J) = X(J)*A(J,J)
00239                       END IF
00240    20             CONTINUE
00241               ELSE
00242                   JX = KX
00243                   DO 40 J = 1,N
00244                       IF (X(JX).NE.ZERO) THEN
00245                           TEMP = X(JX)
00246                           IX = KX
00247                           DO 30 I = 1,J - 1
00248                               X(IX) = X(IX) + TEMP*A(I,J)
00249                               IX = IX + INCX
00250    30                     CONTINUE
00251                           IF (NOUNIT) X(JX) = X(JX)*A(J,J)
00252                       END IF
00253                       JX = JX + INCX
00254    40             CONTINUE
00255               END IF
00256           ELSE
00257               IF (INCX.EQ.1) THEN
00258                   DO 60 J = N,1,-1
00259                       IF (X(J).NE.ZERO) THEN
00260                           TEMP = X(J)
00261                           DO 50 I = N,J + 1,-1
00262                               X(I) = X(I) + TEMP*A(I,J)
00263    50                     CONTINUE
00264                           IF (NOUNIT) X(J) = X(J)*A(J,J)
00265                       END IF
00266    60             CONTINUE
00267               ELSE
00268                   KX = KX + (N-1)*INCX
00269                   JX = KX
00270                   DO 80 J = N,1,-1
00271                       IF (X(JX).NE.ZERO) THEN
00272                           TEMP = X(JX)
00273                           IX = KX
00274                           DO 70 I = N,J + 1,-1
00275                               X(IX) = X(IX) + TEMP*A(I,J)
00276                               IX = IX - INCX
00277    70                     CONTINUE
00278                           IF (NOUNIT) X(JX) = X(JX)*A(J,J)
00279                       END IF
00280                       JX = JX - INCX
00281    80             CONTINUE
00282               END IF
00283           END IF
00284       ELSE
00285 *
00286 *        Form  x := A**T*x  or  x := A**H*x.
00287 *
00288           IF (LSAME(UPLO,'U')) THEN
00289               IF (INCX.EQ.1) THEN
00290                   DO 110 J = N,1,-1
00291                       TEMP = X(J)
00292                       IF (NOCONJ) THEN
00293                           IF (NOUNIT) TEMP = TEMP*A(J,J)
00294                           DO 90 I = J - 1,1,-1
00295                               TEMP = TEMP + A(I,J)*X(I)
00296    90                     CONTINUE
00297                       ELSE
00298                           IF (NOUNIT) TEMP = TEMP*DCONJG(A(J,J))
00299                           DO 100 I = J - 1,1,-1
00300                               TEMP = TEMP + DCONJG(A(I,J))*X(I)
00301   100                     CONTINUE
00302                       END IF
00303                       X(J) = TEMP
00304   110             CONTINUE
00305               ELSE
00306                   JX = KX + (N-1)*INCX
00307                   DO 140 J = N,1,-1
00308                       TEMP = X(JX)
00309                       IX = JX
00310                       IF (NOCONJ) THEN
00311                           IF (NOUNIT) TEMP = TEMP*A(J,J)
00312                           DO 120 I = J - 1,1,-1
00313                               IX = IX - INCX
00314                               TEMP = TEMP + A(I,J)*X(IX)
00315   120                     CONTINUE
00316                       ELSE
00317                           IF (NOUNIT) TEMP = TEMP*DCONJG(A(J,J))
00318                           DO 130 I = J - 1,1,-1
00319                               IX = IX - INCX
00320                               TEMP = TEMP + DCONJG(A(I,J))*X(IX)
00321   130                     CONTINUE
00322                       END IF
00323                       X(JX) = TEMP
00324                       JX = JX - INCX
00325   140             CONTINUE
00326               END IF
00327           ELSE
00328               IF (INCX.EQ.1) THEN
00329                   DO 170 J = 1,N
00330                       TEMP = X(J)
00331                       IF (NOCONJ) THEN
00332                           IF (NOUNIT) TEMP = TEMP*A(J,J)
00333                           DO 150 I = J + 1,N
00334                               TEMP = TEMP + A(I,J)*X(I)
00335   150                     CONTINUE
00336                       ELSE
00337                           IF (NOUNIT) TEMP = TEMP*DCONJG(A(J,J))
00338                           DO 160 I = J + 1,N
00339                               TEMP = TEMP + DCONJG(A(I,J))*X(I)
00340   160                     CONTINUE
00341                       END IF
00342                       X(J) = TEMP
00343   170             CONTINUE
00344               ELSE
00345                   JX = KX
00346                   DO 200 J = 1,N
00347                       TEMP = X(JX)
00348                       IX = JX
00349                       IF (NOCONJ) THEN
00350                           IF (NOUNIT) TEMP = TEMP*A(J,J)
00351                           DO 180 I = J + 1,N
00352                               IX = IX + INCX
00353                               TEMP = TEMP + A(I,J)*X(IX)
00354   180                     CONTINUE
00355                       ELSE
00356                           IF (NOUNIT) TEMP = TEMP*DCONJG(A(J,J))
00357                           DO 190 I = J + 1,N
00358                               IX = IX + INCX
00359                               TEMP = TEMP + DCONJG(A(I,J))*X(IX)
00360   190                     CONTINUE
00361                       END IF
00362                       X(JX) = TEMP
00363                       JX = JX + INCX
00364   200             CONTINUE
00365               END IF
00366           END IF
00367       END IF
00368 *
00369       RETURN
00370 *
00371 *     End of ZTRMV .
00372 *
00373       END
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