LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
ztpsv.f
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00001 *> \brief \b ZTPSV
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 ZTPSV(UPLO,TRANS,DIAG,N,AP,X,INCX)
00012 * 
00013 *       .. Scalar Arguments ..
00014 *       INTEGER INCX,N
00015 *       CHARACTER DIAG,TRANS,UPLO
00016 *       ..
00017 *       .. Array Arguments ..
00018 *       COMPLEX*16 AP(*),X(*)
00019 *       ..
00020 *  
00021 *
00022 *> \par Purpose:
00023 *  =============
00024 *>
00025 *> \verbatim
00026 *>
00027 *> ZTPSV  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, supplied in packed form.
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] AP
00085 *> \verbatim
00086 *>          AP is COMPLEX*16 array of DIMENSION at least
00087 *>           ( ( n*( n + 1 ) )/2 ).
00088 *>           Before entry with  UPLO = 'U' or 'u', the array AP must
00089 *>           contain the upper triangular matrix packed sequentially,
00090 *>           column by column, so that AP( 1 ) contains a( 1, 1 ),
00091 *>           AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 )
00092 *>           respectively, and so on.
00093 *>           Before entry with UPLO = 'L' or 'l', the array AP must
00094 *>           contain the lower triangular matrix packed sequentially,
00095 *>           column by column, so that AP( 1 ) contains a( 1, 1 ),
00096 *>           AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 )
00097 *>           respectively, and so on.
00098 *>           Note that when  DIAG = 'U' or 'u', the diagonal elements of
00099 *>           A are not referenced, but are assumed to be unity.
00100 *> \endverbatim
00101 *>
00102 *> \param[in,out] X
00103 *> \verbatim
00104 *>          X is COMPLEX*16 array of dimension at least
00105 *>           ( 1 + ( n - 1 )*abs( INCX ) ).
00106 *>           Before entry, the incremented array X must contain the n
00107 *>           element right-hand side vector b. On exit, X is overwritten
00108 *>           with the solution vector x.
00109 *> \endverbatim
00110 *>
00111 *> \param[in] INCX
00112 *> \verbatim
00113 *>          INCX is INTEGER
00114 *>           On entry, INCX specifies the increment for the elements of
00115 *>           X. INCX must not be zero.
00116 *> \endverbatim
00117 *
00118 *  Authors:
00119 *  ========
00120 *
00121 *> \author Univ. of Tennessee 
00122 *> \author Univ. of California Berkeley 
00123 *> \author Univ. of Colorado Denver 
00124 *> \author NAG Ltd. 
00125 *
00126 *> \date November 2011
00127 *
00128 *> \ingroup complex16_blas_level2
00129 *
00130 *> \par Further Details:
00131 *  =====================
00132 *>
00133 *> \verbatim
00134 *>
00135 *>  Level 2 Blas routine.
00136 *>
00137 *>  -- Written on 22-October-1986.
00138 *>     Jack Dongarra, Argonne National Lab.
00139 *>     Jeremy Du Croz, Nag Central Office.
00140 *>     Sven Hammarling, Nag Central Office.
00141 *>     Richard Hanson, Sandia National Labs.
00142 *> \endverbatim
00143 *>
00144 *  =====================================================================
00145       SUBROUTINE ZTPSV(UPLO,TRANS,DIAG,N,AP,X,INCX)
00146 *
00147 *  -- Reference BLAS level2 routine (version 3.4.0) --
00148 *  -- Reference BLAS is a software package provided by Univ. of Tennessee,    --
00149 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00150 *     November 2011
00151 *
00152 *     .. Scalar Arguments ..
00153       INTEGER INCX,N
00154       CHARACTER DIAG,TRANS,UPLO
00155 *     ..
00156 *     .. Array Arguments ..
00157       COMPLEX*16 AP(*),X(*)
00158 *     ..
00159 *
00160 *  =====================================================================
00161 *
00162 *     .. Parameters ..
00163       COMPLEX*16 ZERO
00164       PARAMETER (ZERO= (0.0D+0,0.0D+0))
00165 *     ..
00166 *     .. Local Scalars ..
00167       COMPLEX*16 TEMP
00168       INTEGER I,INFO,IX,J,JX,K,KK,KX
00169       LOGICAL NOCONJ,NOUNIT
00170 *     ..
00171 *     .. External Functions ..
00172       LOGICAL LSAME
00173       EXTERNAL LSAME
00174 *     ..
00175 *     .. External Subroutines ..
00176       EXTERNAL XERBLA
00177 *     ..
00178 *     .. Intrinsic Functions ..
00179       INTRINSIC DCONJG
00180 *     ..
00181 *
00182 *     Test the input parameters.
00183 *
00184       INFO = 0
00185       IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
00186           INFO = 1
00187       ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND.
00188      +         .NOT.LSAME(TRANS,'C')) THEN
00189           INFO = 2
00190       ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN
00191           INFO = 3
00192       ELSE IF (N.LT.0) THEN
00193           INFO = 4
00194       ELSE IF (INCX.EQ.0) THEN
00195           INFO = 7
00196       END IF
00197       IF (INFO.NE.0) THEN
00198           CALL XERBLA('ZTPSV ',INFO)
00199           RETURN
00200       END IF
00201 *
00202 *     Quick return if possible.
00203 *
00204       IF (N.EQ.0) RETURN
00205 *
00206       NOCONJ = LSAME(TRANS,'T')
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 AP are
00219 *     accessed sequentially with one pass through AP.
00220 *
00221       IF (LSAME(TRANS,'N')) THEN
00222 *
00223 *        Form  x := inv( A )*x.
00224 *
00225           IF (LSAME(UPLO,'U')) THEN
00226               KK = (N* (N+1))/2
00227               IF (INCX.EQ.1) THEN
00228                   DO 20 J = N,1,-1
00229                       IF (X(J).NE.ZERO) THEN
00230                           IF (NOUNIT) X(J) = X(J)/AP(KK)
00231                           TEMP = X(J)
00232                           K = KK - 1
00233                           DO 10 I = J - 1,1,-1
00234                               X(I) = X(I) - TEMP*AP(K)
00235                               K = K - 1
00236    10                     CONTINUE
00237                       END IF
00238                       KK = KK - J
00239    20             CONTINUE
00240               ELSE
00241                   JX = KX + (N-1)*INCX
00242                   DO 40 J = N,1,-1
00243                       IF (X(JX).NE.ZERO) THEN
00244                           IF (NOUNIT) X(JX) = X(JX)/AP(KK)
00245                           TEMP = X(JX)
00246                           IX = JX
00247                           DO 30 K = KK - 1,KK - J + 1,-1
00248                               IX = IX - INCX
00249                               X(IX) = X(IX) - TEMP*AP(K)
00250    30                     CONTINUE
00251                       END IF
00252                       JX = JX - INCX
00253                       KK = KK - J
00254    40             CONTINUE
00255               END IF
00256           ELSE
00257               KK = 1
00258               IF (INCX.EQ.1) THEN
00259                   DO 60 J = 1,N
00260                       IF (X(J).NE.ZERO) THEN
00261                           IF (NOUNIT) X(J) = X(J)/AP(KK)
00262                           TEMP = X(J)
00263                           K = KK + 1
00264                           DO 50 I = J + 1,N
00265                               X(I) = X(I) - TEMP*AP(K)
00266                               K = K + 1
00267    50                     CONTINUE
00268                       END IF
00269                       KK = KK + (N-J+1)
00270    60             CONTINUE
00271               ELSE
00272                   JX = KX
00273                   DO 80 J = 1,N
00274                       IF (X(JX).NE.ZERO) THEN
00275                           IF (NOUNIT) X(JX) = X(JX)/AP(KK)
00276                           TEMP = X(JX)
00277                           IX = JX
00278                           DO 70 K = KK + 1,KK + N - J
00279                               IX = IX + INCX
00280                               X(IX) = X(IX) - TEMP*AP(K)
00281    70                     CONTINUE
00282                       END IF
00283                       JX = JX + INCX
00284                       KK = KK + (N-J+1)
00285    80             CONTINUE
00286               END IF
00287           END IF
00288       ELSE
00289 *
00290 *        Form  x := inv( A**T )*x  or  x := inv( A**H )*x.
00291 *
00292           IF (LSAME(UPLO,'U')) THEN
00293               KK = 1
00294               IF (INCX.EQ.1) THEN
00295                   DO 110 J = 1,N
00296                       TEMP = X(J)
00297                       K = KK
00298                       IF (NOCONJ) THEN
00299                           DO 90 I = 1,J - 1
00300                               TEMP = TEMP - AP(K)*X(I)
00301                               K = K + 1
00302    90                     CONTINUE
00303                           IF (NOUNIT) TEMP = TEMP/AP(KK+J-1)
00304                       ELSE
00305                           DO 100 I = 1,J - 1
00306                               TEMP = TEMP - DCONJG(AP(K))*X(I)
00307                               K = K + 1
00308   100                     CONTINUE
00309                           IF (NOUNIT) TEMP = TEMP/DCONJG(AP(KK+J-1))
00310                       END IF
00311                       X(J) = TEMP
00312                       KK = KK + J
00313   110             CONTINUE
00314               ELSE
00315                   JX = KX
00316                   DO 140 J = 1,N
00317                       TEMP = X(JX)
00318                       IX = KX
00319                       IF (NOCONJ) THEN
00320                           DO 120 K = KK,KK + J - 2
00321                               TEMP = TEMP - AP(K)*X(IX)
00322                               IX = IX + INCX
00323   120                     CONTINUE
00324                           IF (NOUNIT) TEMP = TEMP/AP(KK+J-1)
00325                       ELSE
00326                           DO 130 K = KK,KK + J - 2
00327                               TEMP = TEMP - DCONJG(AP(K))*X(IX)
00328                               IX = IX + INCX
00329   130                     CONTINUE
00330                           IF (NOUNIT) TEMP = TEMP/DCONJG(AP(KK+J-1))
00331                       END IF
00332                       X(JX) = TEMP
00333                       JX = JX + INCX
00334                       KK = KK + J
00335   140             CONTINUE
00336               END IF
00337           ELSE
00338               KK = (N* (N+1))/2
00339               IF (INCX.EQ.1) THEN
00340                   DO 170 J = N,1,-1
00341                       TEMP = X(J)
00342                       K = KK
00343                       IF (NOCONJ) THEN
00344                           DO 150 I = N,J + 1,-1
00345                               TEMP = TEMP - AP(K)*X(I)
00346                               K = K - 1
00347   150                     CONTINUE
00348                           IF (NOUNIT) TEMP = TEMP/AP(KK-N+J)
00349                       ELSE
00350                           DO 160 I = N,J + 1,-1
00351                               TEMP = TEMP - DCONJG(AP(K))*X(I)
00352                               K = K - 1
00353   160                     CONTINUE
00354                           IF (NOUNIT) TEMP = TEMP/DCONJG(AP(KK-N+J))
00355                       END IF
00356                       X(J) = TEMP
00357                       KK = KK - (N-J+1)
00358   170             CONTINUE
00359               ELSE
00360                   KX = KX + (N-1)*INCX
00361                   JX = KX
00362                   DO 200 J = N,1,-1
00363                       TEMP = X(JX)
00364                       IX = KX
00365                       IF (NOCONJ) THEN
00366                           DO 180 K = KK,KK - (N- (J+1)),-1
00367                               TEMP = TEMP - AP(K)*X(IX)
00368                               IX = IX - INCX
00369   180                     CONTINUE
00370                           IF (NOUNIT) TEMP = TEMP/AP(KK-N+J)
00371                       ELSE
00372                           DO 190 K = KK,KK - (N- (J+1)),-1
00373                               TEMP = TEMP - DCONJG(AP(K))*X(IX)
00374                               IX = IX - INCX
00375   190                     CONTINUE
00376                           IF (NOUNIT) TEMP = TEMP/DCONJG(AP(KK-N+J))
00377                       END IF
00378                       X(JX) = TEMP
00379                       JX = JX - INCX
00380                       KK = KK - (N-J+1)
00381   200             CONTINUE
00382               END IF
00383           END IF
00384       END IF
00385 *
00386       RETURN
00387 *
00388 *     End of ZTPSV .
00389 *
00390       END
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