*> \brief \b DTPSV * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE DTPSV(UPLO,TRANS,DIAG,N,AP,X,INCX) * * .. Scalar Arguments .. * INTEGER INCX,N * CHARACTER DIAG,TRANS,UPLO * .. * .. Array Arguments .. * DOUBLE PRECISION AP(*),X(*) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> 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. *> \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 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. *> \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] AP *> \verbatim *> AP is DOUBLE PRECISION array, 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. *> \endverbatim *> *> \param[in,out] X *> \verbatim *> X is DOUBLE PRECISION array, 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. *> \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. * *> \ingroup double_blas_level2 * *> \par Further Details: * ===================== *> *> \verbatim *> *> 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. *> \endverbatim *> * ===================================================================== SUBROUTINE DTPSV(UPLO,TRANS,DIAG,N,AP,X,INCX) * * -- Reference BLAS level2 routine -- * -- Reference BLAS is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * * .. Scalar Arguments .. INTEGER INCX,N CHARACTER DIAG,TRANS,UPLO * .. * .. Array Arguments .. DOUBLE PRECISION AP(*),X(*) * .. * * ===================================================================== * * .. 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