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|
*> \brief \b ZTRMV
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE ZTRMV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX)
*
* .. Scalar Arguments ..
* INTEGER INCX,LDA,N
* CHARACTER DIAG,TRANS,UPLO
* ..
* .. Array Arguments ..
* COMPLEX*16 A(LDA,*),X(*)
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> ZTRMV performs one of the matrix-vector operations
*>
*> x := A*x, or x := A**T*x, or x := A**H*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**H*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 COMPLEX*16 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] X
*> \verbatim
*> X is (input/output) COMPLEX*16 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
*> 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 complex16_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 ZTRMV(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
*
* .. Scalar Arguments ..
INTEGER INCX,LDA,N
CHARACTER DIAG,TRANS,UPLO
* ..
* .. Array Arguments ..
COMPLEX*16 A(LDA,*),X(*)
* ..
*
* =====================================================================
*
* .. Parameters ..
COMPLEX*16 ZERO
PARAMETER (ZERO= (0.0D+0,0.0D+0))
* ..
* .. Local Scalars ..
COMPLEX*16 TEMP
INTEGER I,INFO,IX,J,JX,KX
LOGICAL NOCONJ,NOUNIT
* ..
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. External Subroutines ..
EXTERNAL XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC DCONJG,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('ZTRMV ',INFO)
RETURN
END IF
*
* Quick return if possible.
*
IF (N.EQ.0) RETURN
*
NOCONJ = LSAME(TRANS,'T')
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 or x := A**H*x.
*
IF (LSAME(UPLO,'U')) THEN
IF (INCX.EQ.1) THEN
DO 110 J = N,1,-1
TEMP = X(J)
IF (NOCONJ) THEN
IF (NOUNIT) TEMP = TEMP*A(J,J)
DO 90 I = J - 1,1,-1
TEMP = TEMP + A(I,J)*X(I)
90 CONTINUE
ELSE
IF (NOUNIT) TEMP = TEMP*DCONJG(A(J,J))
DO 100 I = J - 1,1,-1
TEMP = TEMP + DCONJG(A(I,J))*X(I)
100 CONTINUE
END IF
X(J) = TEMP
110 CONTINUE
ELSE
JX = KX + (N-1)*INCX
DO 140 J = N,1,-1
TEMP = X(JX)
IX = JX
IF (NOCONJ) THEN
IF (NOUNIT) TEMP = TEMP*A(J,J)
DO 120 I = J - 1,1,-1
IX = IX - INCX
TEMP = TEMP + A(I,J)*X(IX)
120 CONTINUE
ELSE
IF (NOUNIT) TEMP = TEMP*DCONJG(A(J,J))
DO 130 I = J - 1,1,-1
IX = IX - INCX
TEMP = TEMP + DCONJG(A(I,J))*X(IX)
130 CONTINUE
END IF
X(JX) = TEMP
JX = JX - INCX
140 CONTINUE
END IF
ELSE
IF (INCX.EQ.1) THEN
DO 170 J = 1,N
TEMP = X(J)
IF (NOCONJ) THEN
IF (NOUNIT) TEMP = TEMP*A(J,J)
DO 150 I = J + 1,N
TEMP = TEMP + A(I,J)*X(I)
150 CONTINUE
ELSE
IF (NOUNIT) TEMP = TEMP*DCONJG(A(J,J))
DO 160 I = J + 1,N
TEMP = TEMP + DCONJG(A(I,J))*X(I)
160 CONTINUE
END IF
X(J) = TEMP
170 CONTINUE
ELSE
JX = KX
DO 200 J = 1,N
TEMP = X(JX)
IX = JX
IF (NOCONJ) THEN
IF (NOUNIT) TEMP = TEMP*A(J,J)
DO 180 I = J + 1,N
IX = IX + INCX
TEMP = TEMP + A(I,J)*X(IX)
180 CONTINUE
ELSE
IF (NOUNIT) TEMP = TEMP*DCONJG(A(J,J))
DO 190 I = J + 1,N
IX = IX + INCX
TEMP = TEMP + DCONJG(A(I,J))*X(IX)
190 CONTINUE
END IF
X(JX) = TEMP
JX = JX + INCX
200 CONTINUE
END IF
END IF
END IF
*
RETURN
*
* End of ZTRMV .
*
END
|
