SUBROUTINEDTRSVF(UPLO,TRANS,DIAG,N,A,LDA,X,INCX)
*..ScalarArguments..
INTEGERINCX,LDA,N
CHARACTER*1DIAG,TRANS,UPLO
*..ArrayArguments..
DOUBLE PRECISIONA(LDA,*),X(*)
*..
*
*Purpose
*=======
*
*DTRSVsolvesoneofthesystemsofequations
*
*A*x=b,orA'*x = b,
*
* where b and x are n element vectors and A is an n by n unit, or
* non-unit, upper or lower triangular matrix.
*
* No test for singularity or near-singularity is included in this
* routine. Such tests must be performed before calling this routine.
*
* 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 equations to be solved as
* follows:
*
* TRANS = 'N' or 'n' A*x = b.
*
* TRANS = 'T' or 't' A'*x=b.
*
*TRANS='C'or'c'A'*x = b.
*
* 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 right-hand side vector b. On exit, X is overwritten
* with the solution 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( 'DTRSV', 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 := inv( A )*x.
*
 IF( LSAME( UPLO, 'U' ) )THEN
 IF( INCX.EQ.1 )THEN
 DO 20, J = N, 1, -1
 IF( X( J ).NE.ZERO )THEN
 IF( NOUNIT )
 $ X( J ) = X( J )/A( J, J )
 TEMP = X( J )
 DO 10, I = J - 1, 1, -1
 X( I ) = X( I ) - TEMP*A( I, J )
 10 CONTINUE
 END IF
 20 CONTINUE
 ELSE
 JX = KX + ( N - 1 )*INCX
 DO 40, J = N, 1, -1
 IF( X( JX ).NE.ZERO )THEN
 IF( NOUNIT )
 $ X( JX ) = X( JX )/A( J, J )
 TEMP = X( JX )
 IX = JX
 DO 30, I = J - 1, 1, -1
 IX = IX - INCX
 X( IX ) = X( IX ) - TEMP*A( I, J )
 30 CONTINUE
 END IF
 JX = JX - INCX
 40 CONTINUE
 END IF
 ELSE
 IF( INCX.EQ.1 )THEN
 DO 60, J = 1, N
 IF( X( J ).NE.ZERO )THEN
 IF( NOUNIT )
 $ X( J ) = X( J )/A( J, J )
 TEMP = X( J )
 DO 50, I = J + 1, N
 X( I ) = X( I ) - TEMP*A( I, J )
 50 CONTINUE
 END IF
 60 CONTINUE
 ELSE
 JX = KX
 DO 80, J = 1, N
 IF( X( JX ).NE.ZERO )THEN
 IF( NOUNIT )
 $ X( JX ) = X( JX )/A( J, J )
 TEMP = X( JX )
 IX = JX
 DO 70, I = J + 1, N
 IX = IX + INCX
 X( IX ) = X( IX ) - TEMP*A( I, J )
 70 CONTINUE
 END IF
 JX = JX + INCX
 80 CONTINUE
 END IF
 END IF
 ELSE
*
* Form x := inv( A')*x.
*
IF(LSAME(UPLO,'U'))THEN
IF(INCX.EQ.1)THEN
DO100,J=1,N
TEMP=X(J)
DO90,I=1,J-1
TEMP=TEMP-A(I,J)*X(I)
90CONTINUE
IF(NOUNIT)
$TEMP=TEMP/A(J,J)
X(J)=TEMP
100CONTINUE
ELSE
JX=KX
DO120,J=1,N
TEMP=X(JX)
IX=KX
DO110,I=1,J-1
TEMP=TEMP-A(I,J)*X(IX)
IX=IX+INCX
110CONTINUE
IF(NOUNIT)
$TEMP=TEMP/A(J,J)
X(JX)=TEMP
JX=JX+INCX
120CONTINUE
ENDIF
ELSE
IF(INCX.EQ.1)THEN
DO140,J=N,1,-1
TEMP=X(J)
DO130,I=N,J+1,-1
TEMP=TEMP-A(I,J)*X(I)
130CONTINUE
IF(NOUNIT)
$TEMP=TEMP/A(J,J)
X(J)=TEMP
140CONTINUE
ELSE
KX=KX+(N-1)*INCX
JX=KX
DO160,J=N,1,-1
TEMP=X(JX)
IX=KX
DO150,I=N,J+1,-1
TEMP=TEMP-A(I,J)*X(IX)
IX=IX-INCX
150CONTINUE
IF(NOUNIT)
$TEMP=TEMP/A(J,J)
X(JX)=TEMP
JX=JX-INCX
160CONTINUE
ENDIF
ENDIF
ENDIF
*
RETURN
*
*EndofDTRSV.
*
END