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C DTRMV     SOURCE    BP208322  20/09/18    21:16:14     10718          *> \brief \b DTRMV**  =========== DOCUMENTATION ===========** Online html documentation available at*            http://www.netlib.org/lapack/explore-html/**  Definition:*  ===========**       SUBROUTINE DTRMV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX)**       .. Scalar Arguments ..*       INTEGER INCX,LDA,N*       CHARACTER DIAG,TRANS,UPLO*       ..*       .. Array Arguments ..*       REAL*8 A(LDA,*),X(*)*       ..***> \par Purpose:*  =============*>*> \verbatim*>*> DTRMV  performs one of the matrix-vector operations*>*>    x := A*x,   or   x := A**T*x,*>*> where x is an n element vector and  A is an n by n unit, or non-unit,*> upper or lower triangular matrix.*> \endverbatim**  Arguments:*  ==========**> \param[in] UPLO*> \verbatim*>          UPLO is CHARACTER*1*>           On entry, UPLO specifies whether the matrix is an upper or*>           lower triangular matrix as follows:*>*>              UPLO = 'U' or 'u'   A is an upper triangular matrix.*>*>              UPLO = 'L' or 'l'   A is a lower triangular matrix.*> \endverbatim*>*> \param[in] TRANS*> \verbatim*>          TRANS is CHARACTER*1*>           On entry, TRANS specifies the operation to be performed as*>           follows:*>*>              TRANS = 'N' or 'n'   x := A*x.*>*>              TRANS = 'T' or 't'   x := A**T*x.*>*>              TRANS = 'C' or 'c'   x := A**T*x.*> \endverbatim*>*> \param[in] DIAG*> \verbatim*>          DIAG is CHARACTER*1*>           On entry, DIAG specifies whether or not A is unit*>           triangular as follows:*>*>              DIAG = 'U' or 'u'   A is assumed to be unit triangular.*>*>              DIAG = 'N' or 'n'   A is not assumed to be unit*>                                  triangular.*> \endverbatim*>*> \param[in] N*> \verbatim*>          N is INTEGER*>           On entry, N specifies the order of the matrix A.*>           N must be at least zero.*> \endverbatim*>*> \param[in] A*> \verbatim*>          A is REAL*8 array, dimension ( LDA, N )*>           Before entry with  UPLO = 'U' or 'u', the leading n by n*>           upper triangular part of the array A must contain the upper*>           triangular matrix and the strictly lower triangular part of*>           A is not referenced.*>           Before entry with UPLO = 'L' or 'l', the leading n by n*>           lower triangular part of the array A must contain the lower*>           triangular matrix and the strictly upper triangular part of*>           A is not referenced.*>           Note that when  DIAG = 'U' or 'u', the diagonal elements of*>           A are not referenced either, but are assumed to be unity.*> \endverbatim*>*> \param[in] LDA*> \verbatim*>          LDA is INTEGER*>           On entry, LDA specifies the first dimension of A as declared*>           in the calling (sub) program. LDA must be at least*>           max( 1, n ).*> \endverbatim*>*> \param[in,out] X*> \verbatim*>          X is REAL*8 array, dimension at least*>           ( 1 + ( n - 1 )*abs( INCX ) ).*>           Before entry, the incremented array X must contain the n*>           element vector x. On exit, X is overwritten with the*>           transformed vector x.*> \endverbatim*>*> \param[in] INCX*> \verbatim*>          INCX is INTEGER*>           On entry, INCX specifies the increment for the elements of*>           X. INCX must not be zero.*> \endverbatim**  Authors:*  ========**> \author Univ. of Tennessee*> \author Univ. of California Berkeley*> \author Univ. of Colorado Denver*> \author NAG Ltd.**> \date December 2016**> \ingroup double_blas_level2**> \par Further Details:*  =====================*>*> \verbatim*>*>  Level 2 Blas routine.*>  The vector and matrix arguments are not referenced when N = 0, or M = 0*>*>  -- Written on 22-October-1986.*>     Jack Dongarra, Argonne National Lab.*>     Jeremy Du Croz, Nag Central Office.*>     Sven Hammarling, Nag Central Office.*>     Richard Hanson, Sandia National Labs.*> \endverbatim*>*  =====================================================================      SUBROUTINE DTRMV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX)**  -- Reference BLAS level2 routine (version 3.7.0) --*  -- Reference BLAS is a software package provided by Univ. of Tennessee,    --*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--*     December 2016       IMPLICIT INTEGER(I-N)      IMPLICIT REAL*8(A-H,O-Z)**     .. Scalar Arguments ..      INTEGER INCX,LDA,N      CHARACTER DIAG,TRANS,UPLO*     ..*     .. Array Arguments ..      REAL*8 A(LDA,*),X(*)*     ..**  =====================================================================**     .. Parameters ..      REAL*8 ZERO      PARAMETER (ZERO=0.0D+0)*     ..*     .. Local Scalars ..      REAL*8 TEMP      INTEGER I,INFO,IX,J,JX,KX      LOGICAL NOUNIT*     ..*     .. External Functions ..      LOGICAL LSAME*      EXTERNAL LSAME*     ..*     .. External Subroutines ..*      EXTERNAL XERBLA*     ..*     .. Intrinsic Functions ..*      INTRINSIC MAX*     ..**     Test the input parameters.*      INFO = 0      IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN          INFO = 1      ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND.     +         .NOT.LSAME(TRANS,'C')) THEN          INFO = 2      ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN          INFO = 3      ELSE IF (N.LT.0) THEN          INFO = 4      ELSE IF (LDA.LT.MAX(1,N)) THEN          INFO = 6      ELSE IF (INCX.EQ.0) THEN          INFO = 8      END IF      IF (INFO.NE.0) THEN          CALL XERBLA('DTRMV ',INFO)          RETURN      END IF**     Quick return if possible.*      IF (N.EQ.0) RETURN*      NOUNIT = LSAME(DIAG,'N')**     Set up the start point in X if the increment is not unity. This*     will be  ( N - 1 )*INCX  too small for descending loops.*      IF (INCX.LE.0) THEN          KX = 1 - (N-1)*INCX      ELSE IF (INCX.NE.1) THEN          KX = 1      END IF**     Start the operations. In this version the elements of A are*     accessed sequentially with one pass through A.*      IF (LSAME(TRANS,'N')) THEN**        Form  x := A*x.*          IF (LSAME(UPLO,'U')) THEN              IF (INCX.EQ.1) THEN                  DO 20 J = 1,N                      IF (X(J).NE.ZERO) THEN                          TEMP = X(J)                          DO 10 I = 1,J - 1                              X(I) = X(I) + TEMP*A(I,J)   10                     CONTINUE                          IF (NOUNIT) X(J) = X(J)*A(J,J)                      END IF   20             CONTINUE              ELSE                  JX = KX                  DO 40 J = 1,N                      IF (X(JX).NE.ZERO) THEN                          TEMP = X(JX)                          IX = KX                          DO 30 I = 1,J - 1                              X(IX) = X(IX) + TEMP*A(I,J)                              IX = IX + INCX   30                     CONTINUE                          IF (NOUNIT) X(JX) = X(JX)*A(J,J)                      END IF                      JX = JX + INCX   40             CONTINUE              END IF          ELSE              IF (INCX.EQ.1) THEN                  DO 60 J = N,1,-1                      IF (X(J).NE.ZERO) THEN                          TEMP = X(J)                          DO 50 I = N,J + 1,-1                              X(I) = X(I) + TEMP*A(I,J)   50                     CONTINUE                          IF (NOUNIT) X(J) = X(J)*A(J,J)                      END IF   60             CONTINUE              ELSE                  KX = KX + (N-1)*INCX                  JX = KX                  DO 80 J = N,1,-1                      IF (X(JX).NE.ZERO) THEN                          TEMP = X(JX)                          IX = KX                          DO 70 I = N,J + 1,-1                              X(IX) = X(IX) + TEMP*A(I,J)                              IX = IX - INCX   70                     CONTINUE                          IF (NOUNIT) X(JX) = X(JX)*A(J,J)                      END IF                      JX = JX - INCX   80             CONTINUE              END IF          END IF      ELSE**        Form  x := A**T*x.*          IF (LSAME(UPLO,'U')) THEN              IF (INCX.EQ.1) THEN                  DO 100 J = N,1,-1                      TEMP = X(J)                      IF (NOUNIT) TEMP = TEMP*A(J,J)                      DO 90 I = J - 1,1,-1                          TEMP = TEMP + A(I,J)*X(I)   90                 CONTINUE                      X(J) = TEMP  100             CONTINUE              ELSE                  JX = KX + (N-1)*INCX                  DO 120 J = N,1,-1                      TEMP = X(JX)                      IX = JX                      IF (NOUNIT) TEMP = TEMP*A(J,J)                      DO 110 I = J - 1,1,-1                          IX = IX - INCX                          TEMP = TEMP + A(I,J)*X(IX)  110                 CONTINUE                      X(JX) = TEMP                      JX = JX - INCX  120             CONTINUE              END IF          ELSE              IF (INCX.EQ.1) THEN                  DO 140 J = 1,N                      TEMP = X(J)                      IF (NOUNIT) TEMP = TEMP*A(J,J)                      DO 130 I = J + 1,N                          TEMP = TEMP + A(I,J)*X(I)  130                 CONTINUE                      X(J) = TEMP  140             CONTINUE              ELSE                  JX = KX                  DO 160 J = 1,N                      TEMP = X(JX)                      IX = JX                      IF (NOUNIT) TEMP = TEMP*A(J,J)                      DO 150 I = J + 1,N                          IX = IX + INCX                          TEMP = TEMP + A(I,J)*X(IX)  150                 CONTINUE                      X(JX) = TEMP                      JX = JX + INCX  160             CONTINUE              END IF          END IF      END IF*      RETURN**     End of DTRMV .*      END

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