--- /dev/null
+*> \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 ..
+* DOUBLE PRECISION 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 DOUBLE PRECISION array of 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 DOUBLE PRECISION array of 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
+*> tranformed 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 November 2011
+*
+*> \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 3.4.0) --
+* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
+* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+* November 2011
+*
+* .. Scalar Arguments ..
+ INTEGER INCX,LDA,N
+ CHARACTER DIAG,TRANS,UPLO
+* ..
+* .. Array Arguments ..
+ DOUBLE PRECISION A(LDA,*),X(*)
+* ..
+*
+* =====================================================================
+*
+* .. Parameters ..
+ DOUBLE PRECISION ZERO
+ PARAMETER (ZERO=0.0D+0)
+* ..
+* .. Local Scalars ..
+ DOUBLE PRECISION 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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