LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
stpsv.f
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00001 *> \brief \b STPSV
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 STPSV(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 *       REAL AP(*),X(*)
00019 *       ..
00020 *  
00021 *
00022 *> \par Purpose:
00023 *  =============
00024 *>
00025 *> \verbatim
00026 *>
00027 *> STPSV  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, 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**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] AP
00085 *> \verbatim
00086 *>          AP is REAL 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 REAL 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 single_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 STPSV(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       REAL AP(*),X(*)
00158 *     ..
00159 *
00160 *  =====================================================================
00161 *
00162 *     .. Parameters ..
00163       REAL ZERO
00164       PARAMETER (ZERO=0.0E+0)
00165 *     ..
00166 *     .. Local Scalars ..
00167       REAL TEMP
00168       INTEGER I,INFO,IX,J,JX,K,KK,KX
00169       LOGICAL NOUNIT
00170 *     ..
00171 *     .. External Functions ..
00172       LOGICAL LSAME
00173       EXTERNAL LSAME
00174 *     ..
00175 *     .. External Subroutines ..
00176       EXTERNAL XERBLA
00177 *     ..
00178 *
00179 *     Test the input parameters.
00180 *
00181       INFO = 0
00182       IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
00183           INFO = 1
00184       ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND.
00185      +         .NOT.LSAME(TRANS,'C')) THEN
00186           INFO = 2
00187       ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN
00188           INFO = 3
00189       ELSE IF (N.LT.0) THEN
00190           INFO = 4
00191       ELSE IF (INCX.EQ.0) THEN
00192           INFO = 7
00193       END IF
00194       IF (INFO.NE.0) THEN
00195           CALL XERBLA('STPSV ',INFO)
00196           RETURN
00197       END IF
00198 *
00199 *     Quick return if possible.
00200 *
00201       IF (N.EQ.0) RETURN
00202 *
00203       NOUNIT = LSAME(DIAG,'N')
00204 *
00205 *     Set up the start point in X if the increment is not unity. This
00206 *     will be  ( N - 1 )*INCX  too small for descending loops.
00207 *
00208       IF (INCX.LE.0) THEN
00209           KX = 1 - (N-1)*INCX
00210       ELSE IF (INCX.NE.1) THEN
00211           KX = 1
00212       END IF
00213 *
00214 *     Start the operations. In this version the elements of AP are
00215 *     accessed sequentially with one pass through AP.
00216 *
00217       IF (LSAME(TRANS,'N')) THEN
00218 *
00219 *        Form  x := inv( A )*x.
00220 *
00221           IF (LSAME(UPLO,'U')) THEN
00222               KK = (N* (N+1))/2
00223               IF (INCX.EQ.1) THEN
00224                   DO 20 J = N,1,-1
00225                       IF (X(J).NE.ZERO) THEN
00226                           IF (NOUNIT) X(J) = X(J)/AP(KK)
00227                           TEMP = X(J)
00228                           K = KK - 1
00229                           DO 10 I = J - 1,1,-1
00230                               X(I) = X(I) - TEMP*AP(K)
00231                               K = K - 1
00232    10                     CONTINUE
00233                       END IF
00234                       KK = KK - J
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)/AP(KK)
00241                           TEMP = X(JX)
00242                           IX = JX
00243                           DO 30 K = KK - 1,KK - J + 1,-1
00244                               IX = IX - INCX
00245                               X(IX) = X(IX) - TEMP*AP(K)
00246    30                     CONTINUE
00247                       END IF
00248                       JX = JX - INCX
00249                       KK = KK - J
00250    40             CONTINUE
00251               END IF
00252           ELSE
00253               KK = 1
00254               IF (INCX.EQ.1) THEN
00255                   DO 60 J = 1,N
00256                       IF (X(J).NE.ZERO) THEN
00257                           IF (NOUNIT) X(J) = X(J)/AP(KK)
00258                           TEMP = X(J)
00259                           K = KK + 1
00260                           DO 50 I = J + 1,N
00261                               X(I) = X(I) - TEMP*AP(K)
00262                               K = K + 1
00263    50                     CONTINUE
00264                       END IF
00265                       KK = KK + (N-J+1)
00266    60             CONTINUE
00267               ELSE
00268                   JX = KX
00269                   DO 80 J = 1,N
00270                       IF (X(JX).NE.ZERO) THEN
00271                           IF (NOUNIT) X(JX) = X(JX)/AP(KK)
00272                           TEMP = X(JX)
00273                           IX = JX
00274                           DO 70 K = KK + 1,KK + N - J
00275                               IX = IX + INCX
00276                               X(IX) = X(IX) - TEMP*AP(K)
00277    70                     CONTINUE
00278                       END IF
00279                       JX = JX + INCX
00280                       KK = KK + (N-J+1)
00281    80             CONTINUE
00282               END IF
00283           END IF
00284       ELSE
00285 *
00286 *        Form  x := inv( A**T )*x.
00287 *
00288           IF (LSAME(UPLO,'U')) THEN
00289               KK = 1
00290               IF (INCX.EQ.1) THEN
00291                   DO 100 J = 1,N
00292                       TEMP = X(J)
00293                       K = KK
00294                       DO 90 I = 1,J - 1
00295                           TEMP = TEMP - AP(K)*X(I)
00296                           K = K + 1
00297    90                 CONTINUE
00298                       IF (NOUNIT) TEMP = TEMP/AP(KK+J-1)
00299                       X(J) = TEMP
00300                       KK = KK + J
00301   100             CONTINUE
00302               ELSE
00303                   JX = KX
00304                   DO 120 J = 1,N
00305                       TEMP = X(JX)
00306                       IX = KX
00307                       DO 110 K = KK,KK + J - 2
00308                           TEMP = TEMP - AP(K)*X(IX)
00309                           IX = IX + INCX
00310   110                 CONTINUE
00311                       IF (NOUNIT) TEMP = TEMP/AP(KK+J-1)
00312                       X(JX) = TEMP
00313                       JX = JX + INCX
00314                       KK = KK + J
00315   120             CONTINUE
00316               END IF
00317           ELSE
00318               KK = (N* (N+1))/2
00319               IF (INCX.EQ.1) THEN
00320                   DO 140 J = N,1,-1
00321                       TEMP = X(J)
00322                       K = KK
00323                       DO 130 I = N,J + 1,-1
00324                           TEMP = TEMP - AP(K)*X(I)
00325                           K = K - 1
00326   130                 CONTINUE
00327                       IF (NOUNIT) TEMP = TEMP/AP(KK-N+J)
00328                       X(J) = TEMP
00329                       KK = KK - (N-J+1)
00330   140             CONTINUE
00331               ELSE
00332                   KX = KX + (N-1)*INCX
00333                   JX = KX
00334                   DO 160 J = N,1,-1
00335                       TEMP = X(JX)
00336                       IX = KX
00337                       DO 150 K = KK,KK - (N- (J+1)),-1
00338                           TEMP = TEMP - AP(K)*X(IX)
00339                           IX = IX - INCX
00340   150                 CONTINUE
00341                       IF (NOUNIT) TEMP = TEMP/AP(KK-N+J)
00342                       X(JX) = TEMP
00343                       JX = JX - INCX
00344                       KK = KK - (N-J+1)
00345   160             CONTINUE
00346               END IF
00347           END IF
00348       END IF
00349 *
00350       RETURN
00351 *
00352 *     End of STPSV .
00353 *
00354       END
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