LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
dtrsv.f
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00001 *> \brief \b DTRSV
00002 *
00003 *  =========== DOCUMENTATION ===========
00004 *
00005 * Online html documentation available at 
00006 *            http://www.netlib.org/lapack/explore-html/ 
00007 *
00008 *  Definition:
00009 *  ===========
00010 *
00011 *       SUBROUTINE DTRSV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX)
00012 * 
00013 *       .. Scalar Arguments ..
00014 *       INTEGER INCX,LDA,N
00015 *       CHARACTER DIAG,TRANS,UPLO
00016 *       ..
00017 *       .. Array Arguments ..
00018 *       DOUBLE PRECISION A(LDA,*),X(*)
00019 *       ..
00020 *  
00021 *
00022 *> \par Purpose:
00023 *  =============
00024 *>
00025 *> \verbatim
00026 *>
00027 *> DTRSV  solves one of the systems of equations
00028 *>
00029 *>    A*x = b,   or   A**T*x = b,
00030 *>
00031 *> where b and x are n element vectors and A is an n by n unit, or
00032 *> non-unit, upper or lower triangular matrix.
00033 *>
00034 *> No test for singularity or near-singularity is included in this
00035 *> routine. Such tests must be performed before calling this routine.
00036 *> \endverbatim
00037 *
00038 *  Arguments:
00039 *  ==========
00040 *
00041 *> \param[in] UPLO
00042 *> \verbatim
00043 *>          UPLO is CHARACTER*1
00044 *>           On entry, UPLO specifies whether the matrix is an upper or
00045 *>           lower triangular matrix as follows:
00046 *>
00047 *>              UPLO = 'U' or 'u'   A is an upper triangular matrix.
00048 *>
00049 *>              UPLO = 'L' or 'l'   A is a lower triangular matrix.
00050 *> \endverbatim
00051 *>
00052 *> \param[in] TRANS
00053 *> \verbatim
00054 *>          TRANS is CHARACTER*1
00055 *>           On entry, TRANS specifies the equations to be solved as
00056 *>           follows:
00057 *>
00058 *>              TRANS = 'N' or 'n'   A*x = b.
00059 *>
00060 *>              TRANS = 'T' or 't'   A**T*x = b.
00061 *>
00062 *>              TRANS = 'C' or 'c'   A**T*x = b.
00063 *> \endverbatim
00064 *>
00065 *> \param[in] DIAG
00066 *> \verbatim
00067 *>          DIAG is CHARACTER*1
00068 *>           On entry, DIAG specifies whether or not A is unit
00069 *>           triangular as follows:
00070 *>
00071 *>              DIAG = 'U' or 'u'   A is assumed to be unit triangular.
00072 *>
00073 *>              DIAG = 'N' or 'n'   A is not assumed to be unit
00074 *>                                  triangular.
00075 *> \endverbatim
00076 *>
00077 *> \param[in] N
00078 *> \verbatim
00079 *>          N is INTEGER
00080 *>           On entry, N specifies the order of the matrix A.
00081 *>           N must be at least zero.
00082 *> \endverbatim
00083 *>
00084 *> \param[in] A
00085 *> \verbatim
00086 *>          A is DOUBLE PRECISION array of DIMENSION ( LDA, n ).
00087 *>           Before entry with  UPLO = 'U' or 'u', the leading n by n
00088 *>           upper triangular part of the array A must contain the upper
00089 *>           triangular matrix and the strictly lower triangular part of
00090 *>           A is not referenced.
00091 *>           Before entry with UPLO = 'L' or 'l', the leading n by n
00092 *>           lower triangular part of the array A must contain the lower
00093 *>           triangular matrix and the strictly upper triangular part of
00094 *>           A is not referenced.
00095 *>           Note that when  DIAG = 'U' or 'u', the diagonal elements of
00096 *>           A are not referenced either, but are assumed to be unity.
00097 *> \endverbatim
00098 *>
00099 *> \param[in] LDA
00100 *> \verbatim
00101 *>          LDA is INTEGER
00102 *>           On entry, LDA specifies the first dimension of A as declared
00103 *>           in the calling (sub) program. LDA must be at least
00104 *>           max( 1, n ).
00105 *> \endverbatim
00106 *>
00107 *> \param[in,out] X
00108 *> \verbatim
00109 *>          X is DOUBLE PRECISION array of dimension at least
00110 *>           ( 1 + ( n - 1 )*abs( INCX ) ).
00111 *>           Before entry, the incremented array X must contain the n
00112 *>           element right-hand side vector b. On exit, X is overwritten
00113 *>           with the solution vector x.
00114 *> \endverbatim
00115 *>
00116 *> \param[in] INCX
00117 *> \verbatim
00118 *>          INCX is INTEGER
00119 *>           On entry, INCX specifies the increment for the elements of
00120 *>           X. INCX must not be zero.
00121 *>
00122 *>  Level 2 Blas routine.
00123 *>
00124 *>  -- Written on 22-October-1986.
00125 *>     Jack Dongarra, Argonne National Lab.
00126 *>     Jeremy Du Croz, Nag Central Office.
00127 *>     Sven Hammarling, Nag Central Office.
00128 *>     Richard Hanson, Sandia National Labs.
00129 *> \endverbatim
00130 *
00131 *  Authors:
00132 *  ========
00133 *
00134 *> \author Univ. of Tennessee 
00135 *> \author Univ. of California Berkeley 
00136 *> \author Univ. of Colorado Denver 
00137 *> \author NAG Ltd. 
00138 *
00139 *> \date November 2011
00140 *
00141 *> \ingroup double_blas_level1
00142 *
00143 *  =====================================================================
00144       SUBROUTINE DTRSV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX)
00145 *
00146 *  -- Reference BLAS level1 routine (version 3.4.0) --
00147 *  -- Reference BLAS is a software package provided by Univ. of Tennessee,    --
00148 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00149 *     November 2011
00150 *
00151 *     .. Scalar Arguments ..
00152       INTEGER INCX,LDA,N
00153       CHARACTER DIAG,TRANS,UPLO
00154 *     ..
00155 *     .. Array Arguments ..
00156       DOUBLE PRECISION A(LDA,*),X(*)
00157 *     ..
00158 *
00159 *  =====================================================================
00160 *
00161 *     .. Parameters ..
00162       DOUBLE PRECISION ZERO
00163       PARAMETER (ZERO=0.0D+0)
00164 *     ..
00165 *     .. Local Scalars ..
00166       DOUBLE PRECISION TEMP
00167       INTEGER I,INFO,IX,J,JX,KX
00168       LOGICAL NOUNIT
00169 *     ..
00170 *     .. External Functions ..
00171       LOGICAL LSAME
00172       EXTERNAL LSAME
00173 *     ..
00174 *     .. External Subroutines ..
00175       EXTERNAL XERBLA
00176 *     ..
00177 *     .. Intrinsic Functions ..
00178       INTRINSIC MAX
00179 *     ..
00180 *
00181 *     Test the input parameters.
00182 *
00183       INFO = 0
00184       IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
00185           INFO = 1
00186       ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND.
00187      +         .NOT.LSAME(TRANS,'C')) THEN
00188           INFO = 2
00189       ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN
00190           INFO = 3
00191       ELSE IF (N.LT.0) THEN
00192           INFO = 4
00193       ELSE IF (LDA.LT.MAX(1,N)) THEN
00194           INFO = 6
00195       ELSE IF (INCX.EQ.0) THEN
00196           INFO = 8
00197       END IF
00198       IF (INFO.NE.0) THEN
00199           CALL XERBLA('DTRSV ',INFO)
00200           RETURN
00201       END IF
00202 *
00203 *     Quick return if possible.
00204 *
00205       IF (N.EQ.0) RETURN
00206 *
00207       NOUNIT = LSAME(DIAG,'N')
00208 *
00209 *     Set up the start point in X if the increment is not unity. This
00210 *     will be  ( N - 1 )*INCX  too small for descending loops.
00211 *
00212       IF (INCX.LE.0) THEN
00213           KX = 1 - (N-1)*INCX
00214       ELSE IF (INCX.NE.1) THEN
00215           KX = 1
00216       END IF
00217 *
00218 *     Start the operations. In this version the elements of A are
00219 *     accessed sequentially with one pass through A.
00220 *
00221       IF (LSAME(TRANS,'N')) THEN
00222 *
00223 *        Form  x := inv( A )*x.
00224 *
00225           IF (LSAME(UPLO,'U')) THEN
00226               IF (INCX.EQ.1) THEN
00227                   DO 20 J = N,1,-1
00228                       IF (X(J).NE.ZERO) THEN
00229                           IF (NOUNIT) X(J) = X(J)/A(J,J)
00230                           TEMP = X(J)
00231                           DO 10 I = J - 1,1,-1
00232                               X(I) = X(I) - TEMP*A(I,J)
00233    10                     CONTINUE
00234                       END IF
00235    20             CONTINUE
00236               ELSE
00237                   JX = KX + (N-1)*INCX
00238                   DO 40 J = N,1,-1
00239                       IF (X(JX).NE.ZERO) THEN
00240                           IF (NOUNIT) X(JX) = X(JX)/A(J,J)
00241                           TEMP = X(JX)
00242                           IX = JX
00243                           DO 30 I = J - 1,1,-1
00244                               IX = IX - INCX
00245                               X(IX) = X(IX) - TEMP*A(I,J)
00246    30                     CONTINUE
00247                       END IF
00248                       JX = JX - INCX
00249    40             CONTINUE
00250               END IF
00251           ELSE
00252               IF (INCX.EQ.1) THEN
00253                   DO 60 J = 1,N
00254                       IF (X(J).NE.ZERO) THEN
00255                           IF (NOUNIT) X(J) = X(J)/A(J,J)
00256                           TEMP = X(J)
00257                           DO 50 I = J + 1,N
00258                               X(I) = X(I) - TEMP*A(I,J)
00259    50                     CONTINUE
00260                       END IF
00261    60             CONTINUE
00262               ELSE
00263                   JX = KX
00264                   DO 80 J = 1,N
00265                       IF (X(JX).NE.ZERO) THEN
00266                           IF (NOUNIT) X(JX) = X(JX)/A(J,J)
00267                           TEMP = X(JX)
00268                           IX = JX
00269                           DO 70 I = J + 1,N
00270                               IX = IX + INCX
00271                               X(IX) = X(IX) - TEMP*A(I,J)
00272    70                     CONTINUE
00273                       END IF
00274                       JX = JX + INCX
00275    80             CONTINUE
00276               END IF
00277           END IF
00278       ELSE
00279 *
00280 *        Form  x := inv( A**T )*x.
00281 *
00282           IF (LSAME(UPLO,'U')) THEN
00283               IF (INCX.EQ.1) THEN
00284                   DO 100 J = 1,N
00285                       TEMP = X(J)
00286                       DO 90 I = 1,J - 1
00287                           TEMP = TEMP - A(I,J)*X(I)
00288    90                 CONTINUE
00289                       IF (NOUNIT) TEMP = TEMP/A(J,J)
00290                       X(J) = TEMP
00291   100             CONTINUE
00292               ELSE
00293                   JX = KX
00294                   DO 120 J = 1,N
00295                       TEMP = X(JX)
00296                       IX = KX
00297                       DO 110 I = 1,J - 1
00298                           TEMP = TEMP - A(I,J)*X(IX)
00299                           IX = IX + INCX
00300   110                 CONTINUE
00301                       IF (NOUNIT) TEMP = TEMP/A(J,J)
00302                       X(JX) = TEMP
00303                       JX = JX + INCX
00304   120             CONTINUE
00305               END IF
00306           ELSE
00307               IF (INCX.EQ.1) THEN
00308                   DO 140 J = N,1,-1
00309                       TEMP = X(J)
00310                       DO 130 I = N,J + 1,-1
00311                           TEMP = TEMP - A(I,J)*X(I)
00312   130                 CONTINUE
00313                       IF (NOUNIT) TEMP = TEMP/A(J,J)
00314                       X(J) = TEMP
00315   140             CONTINUE
00316               ELSE
00317                   KX = KX + (N-1)*INCX
00318                   JX = KX
00319                   DO 160 J = N,1,-1
00320                       TEMP = X(JX)
00321                       IX = KX
00322                       DO 150 I = N,J + 1,-1
00323                           TEMP = TEMP - A(I,J)*X(IX)
00324                           IX = IX - INCX
00325   150                 CONTINUE
00326                       IF (NOUNIT) TEMP = TEMP/A(J,J)
00327                       X(JX) = TEMP
00328                       JX = JX - INCX
00329   160             CONTINUE
00330               END IF
00331           END IF
00332       END IF
00333 *
00334       RETURN
00335 *
00336 *     End of DTRSV .
00337 *
00338       END
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