LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
ztrsv.f
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00001 *> \brief \b ZTRSV
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 ZTRSV(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 *       COMPLEX*16 A(LDA,*),X(*)
00019 *       ..
00020 *  
00021 *
00022 *> \par Purpose:
00023 *  =============
00024 *>
00025 *> \verbatim
00026 *>
00027 *> ZTRSV  solves one of the systems of equations
00028 *>
00029 *>    A*x = b,   or   A**T*x = b,   or   A**H*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**H*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 COMPLEX*16 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 COMPLEX*16 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 *> \endverbatim
00122 *
00123 *  Authors:
00124 *  ========
00125 *
00126 *> \author Univ. of Tennessee 
00127 *> \author Univ. of California Berkeley 
00128 *> \author Univ. of Colorado Denver 
00129 *> \author NAG Ltd. 
00130 *
00131 *> \date November 2011
00132 *
00133 *> \ingroup complex16_blas_level2
00134 *
00135 *> \par Further Details:
00136 *  =====================
00137 *>
00138 *> \verbatim
00139 *>
00140 *>  Level 2 Blas routine.
00141 *>
00142 *>  -- Written on 22-October-1986.
00143 *>     Jack Dongarra, Argonne National Lab.
00144 *>     Jeremy Du Croz, Nag Central Office.
00145 *>     Sven Hammarling, Nag Central Office.
00146 *>     Richard Hanson, Sandia National Labs.
00147 *> \endverbatim
00148 *>
00149 *  =====================================================================
00150       SUBROUTINE ZTRSV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX)
00151 *
00152 *  -- Reference BLAS level2 routine (version 3.4.0) --
00153 *  -- Reference BLAS is a software package provided by Univ. of Tennessee,    --
00154 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00155 *     November 2011
00156 *
00157 *     .. Scalar Arguments ..
00158       INTEGER INCX,LDA,N
00159       CHARACTER DIAG,TRANS,UPLO
00160 *     ..
00161 *     .. Array Arguments ..
00162       COMPLEX*16 A(LDA,*),X(*)
00163 *     ..
00164 *
00165 *  =====================================================================
00166 *
00167 *     .. Parameters ..
00168       COMPLEX*16 ZERO
00169       PARAMETER (ZERO= (0.0D+0,0.0D+0))
00170 *     ..
00171 *     .. Local Scalars ..
00172       COMPLEX*16 TEMP
00173       INTEGER I,INFO,IX,J,JX,KX
00174       LOGICAL NOCONJ,NOUNIT
00175 *     ..
00176 *     .. External Functions ..
00177       LOGICAL LSAME
00178       EXTERNAL LSAME
00179 *     ..
00180 *     .. External Subroutines ..
00181       EXTERNAL XERBLA
00182 *     ..
00183 *     .. Intrinsic Functions ..
00184       INTRINSIC DCONJG,MAX
00185 *     ..
00186 *
00187 *     Test the input parameters.
00188 *
00189       INFO = 0
00190       IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
00191           INFO = 1
00192       ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND.
00193      +         .NOT.LSAME(TRANS,'C')) THEN
00194           INFO = 2
00195       ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN
00196           INFO = 3
00197       ELSE IF (N.LT.0) THEN
00198           INFO = 4
00199       ELSE IF (LDA.LT.MAX(1,N)) THEN
00200           INFO = 6
00201       ELSE IF (INCX.EQ.0) THEN
00202           INFO = 8
00203       END IF
00204       IF (INFO.NE.0) THEN
00205           CALL XERBLA('ZTRSV ',INFO)
00206           RETURN
00207       END IF
00208 *
00209 *     Quick return if possible.
00210 *
00211       IF (N.EQ.0) RETURN
00212 *
00213       NOCONJ = LSAME(TRANS,'T')
00214       NOUNIT = LSAME(DIAG,'N')
00215 *
00216 *     Set up the start point in X if the increment is not unity. This
00217 *     will be  ( N - 1 )*INCX  too small for descending loops.
00218 *
00219       IF (INCX.LE.0) THEN
00220           KX = 1 - (N-1)*INCX
00221       ELSE IF (INCX.NE.1) THEN
00222           KX = 1
00223       END IF
00224 *
00225 *     Start the operations. In this version the elements of A are
00226 *     accessed sequentially with one pass through A.
00227 *
00228       IF (LSAME(TRANS,'N')) THEN
00229 *
00230 *        Form  x := inv( A )*x.
00231 *
00232           IF (LSAME(UPLO,'U')) THEN
00233               IF (INCX.EQ.1) THEN
00234                   DO 20 J = N,1,-1
00235                       IF (X(J).NE.ZERO) THEN
00236                           IF (NOUNIT) X(J) = X(J)/A(J,J)
00237                           TEMP = X(J)
00238                           DO 10 I = J - 1,1,-1
00239                               X(I) = X(I) - TEMP*A(I,J)
00240    10                     CONTINUE
00241                       END IF
00242    20             CONTINUE
00243               ELSE
00244                   JX = KX + (N-1)*INCX
00245                   DO 40 J = N,1,-1
00246                       IF (X(JX).NE.ZERO) THEN
00247                           IF (NOUNIT) X(JX) = X(JX)/A(J,J)
00248                           TEMP = X(JX)
00249                           IX = JX
00250                           DO 30 I = J - 1,1,-1
00251                               IX = IX - INCX
00252                               X(IX) = X(IX) - TEMP*A(I,J)
00253    30                     CONTINUE
00254                       END IF
00255                       JX = JX - INCX
00256    40             CONTINUE
00257               END IF
00258           ELSE
00259               IF (INCX.EQ.1) THEN
00260                   DO 60 J = 1,N
00261                       IF (X(J).NE.ZERO) THEN
00262                           IF (NOUNIT) X(J) = X(J)/A(J,J)
00263                           TEMP = X(J)
00264                           DO 50 I = J + 1,N
00265                               X(I) = X(I) - TEMP*A(I,J)
00266    50                     CONTINUE
00267                       END IF
00268    60             CONTINUE
00269               ELSE
00270                   JX = KX
00271                   DO 80 J = 1,N
00272                       IF (X(JX).NE.ZERO) THEN
00273                           IF (NOUNIT) X(JX) = X(JX)/A(J,J)
00274                           TEMP = X(JX)
00275                           IX = JX
00276                           DO 70 I = J + 1,N
00277                               IX = IX + INCX
00278                               X(IX) = X(IX) - TEMP*A(I,J)
00279    70                     CONTINUE
00280                       END IF
00281                       JX = JX + INCX
00282    80             CONTINUE
00283               END IF
00284           END IF
00285       ELSE
00286 *
00287 *        Form  x := inv( A**T )*x  or  x := inv( A**H )*x.
00288 *
00289           IF (LSAME(UPLO,'U')) THEN
00290               IF (INCX.EQ.1) THEN
00291                   DO 110 J = 1,N
00292                       TEMP = X(J)
00293                       IF (NOCONJ) THEN
00294                           DO 90 I = 1,J - 1
00295                               TEMP = TEMP - A(I,J)*X(I)
00296    90                     CONTINUE
00297                           IF (NOUNIT) TEMP = TEMP/A(J,J)
00298                       ELSE
00299                           DO 100 I = 1,J - 1
00300                               TEMP = TEMP - DCONJG(A(I,J))*X(I)
00301   100                     CONTINUE
00302                           IF (NOUNIT) TEMP = TEMP/DCONJG(A(J,J))
00303                       END IF
00304                       X(J) = TEMP
00305   110             CONTINUE
00306               ELSE
00307                   JX = KX
00308                   DO 140 J = 1,N
00309                       IX = KX
00310                       TEMP = X(JX)
00311                       IF (NOCONJ) THEN
00312                           DO 120 I = 1,J - 1
00313                               TEMP = TEMP - A(I,J)*X(IX)
00314                               IX = IX + INCX
00315   120                     CONTINUE
00316                           IF (NOUNIT) TEMP = TEMP/A(J,J)
00317                       ELSE
00318                           DO 130 I = 1,J - 1
00319                               TEMP = TEMP - DCONJG(A(I,J))*X(IX)
00320                               IX = IX + INCX
00321   130                     CONTINUE
00322                           IF (NOUNIT) TEMP = TEMP/DCONJG(A(J,J))
00323                       END IF
00324                       X(JX) = TEMP
00325                       JX = JX + INCX
00326   140             CONTINUE
00327               END IF
00328           ELSE
00329               IF (INCX.EQ.1) THEN
00330                   DO 170 J = N,1,-1
00331                       TEMP = X(J)
00332                       IF (NOCONJ) THEN
00333                           DO 150 I = N,J + 1,-1
00334                               TEMP = TEMP - A(I,J)*X(I)
00335   150                     CONTINUE
00336                           IF (NOUNIT) TEMP = TEMP/A(J,J)
00337                       ELSE
00338                           DO 160 I = N,J + 1,-1
00339                               TEMP = TEMP - DCONJG(A(I,J))*X(I)
00340   160                     CONTINUE
00341                           IF (NOUNIT) TEMP = TEMP/DCONJG(A(J,J))
00342                       END IF
00343                       X(J) = TEMP
00344   170             CONTINUE
00345               ELSE
00346                   KX = KX + (N-1)*INCX
00347                   JX = KX
00348                   DO 200 J = N,1,-1
00349                       IX = KX
00350                       TEMP = X(JX)
00351                       IF (NOCONJ) THEN
00352                           DO 180 I = N,J + 1,-1
00353                               TEMP = TEMP - A(I,J)*X(IX)
00354                               IX = IX - INCX
00355   180                     CONTINUE
00356                           IF (NOUNIT) TEMP = TEMP/A(J,J)
00357                       ELSE
00358                           DO 190 I = N,J + 1,-1
00359                               TEMP = TEMP - DCONJG(A(I,J))*X(IX)
00360                               IX = IX - INCX
00361   190                     CONTINUE
00362                           IF (NOUNIT) TEMP = TEMP/DCONJG(A(J,J))
00363                       END IF
00364                       X(JX) = TEMP
00365                       JX = JX - INCX
00366   200             CONTINUE
00367               END IF
00368           END IF
00369       END IF
00370 *
00371       RETURN
00372 *
00373 *     End of ZTRSV .
00374 *
00375       END
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