SUBROUTINE DTPSV(UPLO,TRANS,DIAG,N,AP,X,INCX)
* .. Scalar Arguments ..
INTEGER INCX,N
CHARACTER DIAG,TRANS,UPLO
* ..
* .. Array Arguments ..
DOUBLE PRECISION AP(*),X(*)
* ..
*
* Purpose
* =======
*
* DTPSV solves one of the systems of equations
*
* A*x = b, or A**T*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, supplied in packed form.
*
* No test for singularity or near-singularity is included in this
* routine. Such tests must be performed before calling this routine.
*
* Arguments
* ==========
*
* 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**T*x = b.
*
* TRANS = 'C' or 'c' A**T*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.
*
* AP - DOUBLE PRECISION array of DIMENSION at least
* ( ( n*( n + 1 ) )/2 ).
* Before entry with UPLO = 'U' or 'u', the array AP must
* contain the upper triangular matrix packed sequentially,
* column by column, so that AP( 1 ) contains a( 1, 1 ),
* AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 )
* respectively, and so on.
* Before entry with UPLO = 'L' or 'l', the array AP must
* contain the lower triangular matrix packed sequentially,
* column by column, so that AP( 1 ) contains a( 1, 1 ),
* AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 )
* respectively, and so on.
* Note that when DIAG = 'U' or 'u', the diagonal elements of
* A are not referenced, but are assumed to be unity.
* 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.
*
* Further Details
* ===============
*
* 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,K,KK,KX
LOGICAL NOUNIT
* ..
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. External Subroutines ..
EXTERNAL XERBLA
* ..
*
* 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 (INCX.EQ.0) THEN
INFO = 7
END IF
IF (INFO.NE.0) THEN
CALL XERBLA('DTPSV ',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 AP are
* accessed sequentially with one pass through AP.
*
IF (LSAME(TRANS,'N')) THEN
*
* Form x := inv( A )*x.
*
IF (LSAME(UPLO,'U')) THEN
KK = (N* (N+1))/2
IF (INCX.EQ.1) THEN
DO 20 J = N,1,-1
IF (X(J).NE.ZERO) THEN
IF (NOUNIT) X(J) = X(J)/AP(KK)
TEMP = X(J)
K = KK - 1
DO 10 I = J - 1,1,-1
X(I) = X(I) - TEMP*AP(K)
K = K - 1
10 CONTINUE
END IF
KK = KK - J
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)/AP(KK)
TEMP = X(JX)
IX = JX
DO 30 K = KK - 1,KK - J + 1,-1
IX = IX - INCX
X(IX) = X(IX) - TEMP*AP(K)
30 CONTINUE
END IF
JX = JX - INCX
KK = KK - J
40 CONTINUE
END IF
ELSE
KK = 1
IF (INCX.EQ.1) THEN
DO 60 J = 1,N
IF (X(J).NE.ZERO) THEN
IF (NOUNIT) X(J) = X(J)/AP(KK)
TEMP = X(J)
K = KK + 1
DO 50 I = J + 1,N
X(I) = X(I) - TEMP*AP(K)
K = K + 1
50 CONTINUE
END IF
KK = KK + (N-J+1)
60 CONTINUE
ELSE
JX = KX
DO 80 J = 1,N
IF (X(JX).NE.ZERO) THEN
IF (NOUNIT) X(JX) = X(JX)/AP(KK)
TEMP = X(JX)
IX = JX
DO 70 K = KK + 1,KK + N - J
IX = IX + INCX
X(IX) = X(IX) - TEMP*AP(K)
70 CONTINUE
END IF
JX = JX + INCX
KK = KK + (N-J+1)
80 CONTINUE
END IF
END IF
ELSE
*
* Form x := inv( A**T )*x.
*
IF (LSAME(UPLO,'U')) THEN
KK = 1
IF (INCX.EQ.1) THEN
DO 100 J = 1,N
TEMP = X(J)
K = KK
DO 90 I = 1,J - 1
TEMP = TEMP - AP(K)*X(I)
K = K + 1
90 CONTINUE
IF (NOUNIT) TEMP = TEMP/AP(KK+J-1)
X(J) = TEMP
KK = KK + J
100 CONTINUE
ELSE
JX = KX
DO 120 J = 1,N
TEMP = X(JX)
IX = KX
DO 110 K = KK,KK + J - 2
TEMP = TEMP - AP(K)*X(IX)
IX = IX + INCX
110 CONTINUE
IF (NOUNIT) TEMP = TEMP/AP(KK+J-1)
X(JX) = TEMP
JX = JX + INCX
KK = KK + J
120 CONTINUE
END IF
ELSE
KK = (N* (N+1))/2
IF (INCX.EQ.1) THEN
DO 140 J = N,1,-1
TEMP = X(J)
K = KK
DO 130 I = N,J + 1,-1
TEMP = TEMP - AP(K)*X(I)
K = K - 1
130 CONTINUE
IF (NOUNIT) TEMP = TEMP/AP(KK-N+J)
X(J) = TEMP
KK = KK - (N-J+1)
140 CONTINUE
ELSE
KX = KX + (N-1)*INCX
JX = KX
DO 160 J = N,1,-1
TEMP = X(JX)
IX = KX
DO 150 K = KK,KK - (N- (J+1)),-1
TEMP = TEMP - AP(K)*X(IX)
IX = IX - INCX
150 CONTINUE
IF (NOUNIT) TEMP = TEMP/AP(KK-N+J)
X(JX) = TEMP
JX = JX - INCX
KK = KK - (N-J+1)
160 CONTINUE
END IF
END IF
END IF
*
RETURN
*
* End of DTPSV .
*
END