SUBROUTINE DTRMV ( UPLO, TRANS, DIAG, N, A, LDA, X, INCX ) 2,2
! .. Scalar Arguments ..
INTEGER INCX, LDA, N
CHARACTER*1 DIAG, TRANS, UPLO
! .. Array Arguments ..
DOUBLE PRECISION A( LDA, * ), X( * )
! ..
!
! Purpose
! =======
!
! DTRMV performs one of the matrix-vector operations
!
! x := A*x, or x := A'*x,
!
! where x is an n element vector and A is an n by n unit, or non-unit,
! upper or lower triangular matrix.
!
! Parameters
! ==========
!
! UPLO - 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.
!
! Unchanged on exit.
!
! TRANS - 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'*x.
!
! TRANS = 'C' or 'c' x := A'*x.
!
! Unchanged on exit.
!
! DIAG - 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.
!
! Unchanged on exit.
!
! N - INTEGER.
! On entry, N specifies the order of the matrix A.
! N must be at least zero.
! Unchanged on exit.
!
! A - 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.
! Unchanged on exit.
!
! LDA - 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 ).
! Unchanged on exit.
!
! X - 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.
!
! INCX - INTEGER.
! On entry, INCX specifies the increment for the elements of
! X. INCX must not be zero.
! Unchanged on exit.
!
!
! Level 2 Blas routine.
!
! -- 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.
!
!
! .. 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
! ..
! .. Executable Statements ..
!
! 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'*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 SUBROUTINE DTRMV