LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
stpmv.f
Go to the documentation of this file.
00001 *> \brief \b STPMV
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 STPMV(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 *> STPMV  performs one of the matrix-vector operations
00028 *>
00029 *>    x := A*x,   or   x := A**T*x,
00030 *>
00031 *> where x is an n element vector and  A is an n by n unit, or non-unit,
00032 *> upper or lower triangular matrix, supplied in packed form.
00033 *> \endverbatim
00034 *
00035 *  Arguments:
00036 *  ==========
00037 *
00038 *> \param[in] UPLO
00039 *> \verbatim
00040 *>          UPLO is CHARACTER*1
00041 *>           On entry, UPLO specifies whether the matrix is an upper or
00042 *>           lower triangular matrix as follows:
00043 *>
00044 *>              UPLO = 'U' or 'u'   A is an upper triangular matrix.
00045 *>
00046 *>              UPLO = 'L' or 'l'   A is a lower triangular matrix.
00047 *> \endverbatim
00048 *>
00049 *> \param[in] TRANS
00050 *> \verbatim
00051 *>          TRANS is CHARACTER*1
00052 *>           On entry, TRANS specifies the operation to be performed as
00053 *>           follows:
00054 *>
00055 *>              TRANS = 'N' or 'n'   x := A*x.
00056 *>
00057 *>              TRANS = 'T' or 't'   x := A**T*x.
00058 *>
00059 *>              TRANS = 'C' or 'c'   x := A**T*x.
00060 *> \endverbatim
00061 *>
00062 *> \param[in] DIAG
00063 *> \verbatim
00064 *>          DIAG is CHARACTER*1
00065 *>           On entry, DIAG specifies whether or not A is unit
00066 *>           triangular as follows:
00067 *>
00068 *>              DIAG = 'U' or 'u'   A is assumed to be unit triangular.
00069 *>
00070 *>              DIAG = 'N' or 'n'   A is not assumed to be unit
00071 *>                                  triangular.
00072 *> \endverbatim
00073 *>
00074 *> \param[in] N
00075 *> \verbatim
00076 *>          N is INTEGER
00077 *>           On entry, N specifies the order of the matrix A.
00078 *>           N must be at least zero.
00079 *> \endverbatim
00080 *>
00081 *> \param[in] AP
00082 *> \verbatim
00083 *>          AP is REAL array of DIMENSION at least
00084 *>           ( ( n*( n + 1 ) )/2 ).
00085 *>           Before entry with  UPLO = 'U' or 'u', the array AP must
00086 *>           contain the upper triangular matrix packed sequentially,
00087 *>           column by column, so that AP( 1 ) contains a( 1, 1 ),
00088 *>           AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 )
00089 *>           respectively, and so on.
00090 *>           Before entry with UPLO = 'L' or 'l', the array AP must
00091 *>           contain the lower triangular matrix packed sequentially,
00092 *>           column by column, so that AP( 1 ) contains a( 1, 1 ),
00093 *>           AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 )
00094 *>           respectively, and so on.
00095 *>           Note that when  DIAG = 'U' or 'u', the diagonal elements of
00096 *>           A are not referenced, but are assumed to be unity.
00097 *> \endverbatim
00098 *>
00099 *> \param[in,out] X
00100 *> \verbatim
00101 *>          X is REAL array of dimension at least
00102 *>           ( 1 + ( n - 1 )*abs( INCX ) ).
00103 *>           Before entry, the incremented array X must contain the n
00104 *>           element vector x. On exit, X is overwritten with the
00105 *>           tranformed vector x.
00106 *> \endverbatim
00107 *>
00108 *> \param[in] INCX
00109 *> \verbatim
00110 *>          INCX is INTEGER
00111 *>           On entry, INCX specifies the increment for the elements of
00112 *>           X. INCX must not be zero.
00113 *> \endverbatim
00114 *
00115 *  Authors:
00116 *  ========
00117 *
00118 *> \author Univ. of Tennessee 
00119 *> \author Univ. of California Berkeley 
00120 *> \author Univ. of Colorado Denver 
00121 *> \author NAG Ltd. 
00122 *
00123 *> \date November 2011
00124 *
00125 *> \ingroup single_blas_level2
00126 *
00127 *> \par Further Details:
00128 *  =====================
00129 *>
00130 *> \verbatim
00131 *>
00132 *>  Level 2 Blas routine.
00133 *>  The vector and matrix arguments are not referenced when N = 0, or M = 0
00134 *>
00135 *>  -- Written on 22-October-1986.
00136 *>     Jack Dongarra, Argonne National Lab.
00137 *>     Jeremy Du Croz, Nag Central Office.
00138 *>     Sven Hammarling, Nag Central Office.
00139 *>     Richard Hanson, Sandia National Labs.
00140 *> \endverbatim
00141 *>
00142 *  =====================================================================
00143       SUBROUTINE STPMV(UPLO,TRANS,DIAG,N,AP,X,INCX)
00144 *
00145 *  -- Reference BLAS level2 routine (version 3.4.0) --
00146 *  -- Reference BLAS is a software package provided by Univ. of Tennessee,    --
00147 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00148 *     November 2011
00149 *
00150 *     .. Scalar Arguments ..
00151       INTEGER INCX,N
00152       CHARACTER DIAG,TRANS,UPLO
00153 *     ..
00154 *     .. Array Arguments ..
00155       REAL AP(*),X(*)
00156 *     ..
00157 *
00158 *  =====================================================================
00159 *
00160 *     .. Parameters ..
00161       REAL ZERO
00162       PARAMETER (ZERO=0.0E+0)
00163 *     ..
00164 *     .. Local Scalars ..
00165       REAL TEMP
00166       INTEGER I,INFO,IX,J,JX,K,KK,KX
00167       LOGICAL NOUNIT
00168 *     ..
00169 *     .. External Functions ..
00170       LOGICAL LSAME
00171       EXTERNAL LSAME
00172 *     ..
00173 *     .. External Subroutines ..
00174       EXTERNAL XERBLA
00175 *     ..
00176 *
00177 *     Test the input parameters.
00178 *
00179       INFO = 0
00180       IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
00181           INFO = 1
00182       ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND.
00183      +         .NOT.LSAME(TRANS,'C')) THEN
00184           INFO = 2
00185       ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN
00186           INFO = 3
00187       ELSE IF (N.LT.0) THEN
00188           INFO = 4
00189       ELSE IF (INCX.EQ.0) THEN
00190           INFO = 7
00191       END IF
00192       IF (INFO.NE.0) THEN
00193           CALL XERBLA('STPMV ',INFO)
00194           RETURN
00195       END IF
00196 *
00197 *     Quick return if possible.
00198 *
00199       IF (N.EQ.0) RETURN
00200 *
00201       NOUNIT = LSAME(DIAG,'N')
00202 *
00203 *     Set up the start point in X if the increment is not unity. This
00204 *     will be  ( N - 1 )*INCX  too small for descending loops.
00205 *
00206       IF (INCX.LE.0) THEN
00207           KX = 1 - (N-1)*INCX
00208       ELSE IF (INCX.NE.1) THEN
00209           KX = 1
00210       END IF
00211 *
00212 *     Start the operations. In this version the elements of AP are
00213 *     accessed sequentially with one pass through AP.
00214 *
00215       IF (LSAME(TRANS,'N')) THEN
00216 *
00217 *        Form  x:= A*x.
00218 *
00219           IF (LSAME(UPLO,'U')) THEN
00220               KK = 1
00221               IF (INCX.EQ.1) THEN
00222                   DO 20 J = 1,N
00223                       IF (X(J).NE.ZERO) THEN
00224                           TEMP = X(J)
00225                           K = KK
00226                           DO 10 I = 1,J - 1
00227                               X(I) = X(I) + TEMP*AP(K)
00228                               K = K + 1
00229    10                     CONTINUE
00230                           IF (NOUNIT) X(J) = X(J)*AP(KK+J-1)
00231                       END IF
00232                       KK = KK + J
00233    20             CONTINUE
00234               ELSE
00235                   JX = KX
00236                   DO 40 J = 1,N
00237                       IF (X(JX).NE.ZERO) THEN
00238                           TEMP = X(JX)
00239                           IX = KX
00240                           DO 30 K = KK,KK + J - 2
00241                               X(IX) = X(IX) + TEMP*AP(K)
00242                               IX = IX + INCX
00243    30                     CONTINUE
00244                           IF (NOUNIT) X(JX) = X(JX)*AP(KK+J-1)
00245                       END IF
00246                       JX = JX + INCX
00247                       KK = KK + J
00248    40             CONTINUE
00249               END IF
00250           ELSE
00251               KK = (N* (N+1))/2
00252               IF (INCX.EQ.1) THEN
00253                   DO 60 J = N,1,-1
00254                       IF (X(J).NE.ZERO) THEN
00255                           TEMP = X(J)
00256                           K = KK
00257                           DO 50 I = N,J + 1,-1
00258                               X(I) = X(I) + TEMP*AP(K)
00259                               K = K - 1
00260    50                     CONTINUE
00261                           IF (NOUNIT) X(J) = X(J)*AP(KK-N+J)
00262                       END IF
00263                       KK = KK - (N-J+1)
00264    60             CONTINUE
00265               ELSE
00266                   KX = KX + (N-1)*INCX
00267                   JX = KX
00268                   DO 80 J = N,1,-1
00269                       IF (X(JX).NE.ZERO) THEN
00270                           TEMP = X(JX)
00271                           IX = KX
00272                           DO 70 K = KK,KK - (N- (J+1)),-1
00273                               X(IX) = X(IX) + TEMP*AP(K)
00274                               IX = IX - INCX
00275    70                     CONTINUE
00276                           IF (NOUNIT) X(JX) = X(JX)*AP(KK-N+J)
00277                       END IF
00278                       JX = JX - INCX
00279                       KK = KK - (N-J+1)
00280    80             CONTINUE
00281               END IF
00282           END IF
00283       ELSE
00284 *
00285 *        Form  x := A**T*x.
00286 *
00287           IF (LSAME(UPLO,'U')) THEN
00288               KK = (N* (N+1))/2
00289               IF (INCX.EQ.1) THEN
00290                   DO 100 J = N,1,-1
00291                       TEMP = X(J)
00292                       IF (NOUNIT) TEMP = TEMP*AP(KK)
00293                       K = KK - 1
00294                       DO 90 I = J - 1,1,-1
00295                           TEMP = TEMP + AP(K)*X(I)
00296                           K = K - 1
00297    90                 CONTINUE
00298                       X(J) = TEMP
00299                       KK = KK - J
00300   100             CONTINUE
00301               ELSE
00302                   JX = KX + (N-1)*INCX
00303                   DO 120 J = N,1,-1
00304                       TEMP = X(JX)
00305                       IX = JX
00306                       IF (NOUNIT) TEMP = TEMP*AP(KK)
00307                       DO 110 K = KK - 1,KK - J + 1,-1
00308                           IX = IX - INCX
00309                           TEMP = TEMP + AP(K)*X(IX)
00310   110                 CONTINUE
00311                       X(JX) = TEMP
00312                       JX = JX - INCX
00313                       KK = KK - J
00314   120             CONTINUE
00315               END IF
00316           ELSE
00317               KK = 1
00318               IF (INCX.EQ.1) THEN
00319                   DO 140 J = 1,N
00320                       TEMP = X(J)
00321                       IF (NOUNIT) TEMP = TEMP*AP(KK)
00322                       K = KK + 1
00323                       DO 130 I = J + 1,N
00324                           TEMP = TEMP + AP(K)*X(I)
00325                           K = K + 1
00326   130                 CONTINUE
00327                       X(J) = TEMP
00328                       KK = KK + (N-J+1)
00329   140             CONTINUE
00330               ELSE
00331                   JX = KX
00332                   DO 160 J = 1,N
00333                       TEMP = X(JX)
00334                       IX = JX
00335                       IF (NOUNIT) TEMP = TEMP*AP(KK)
00336                       DO 150 K = KK + 1,KK + N - J
00337                           IX = IX + INCX
00338                           TEMP = TEMP + AP(K)*X(IX)
00339   150                 CONTINUE
00340                       X(JX) = TEMP
00341                       JX = JX + INCX
00342                       KK = KK + (N-J+1)
00343   160             CONTINUE
00344               END IF
00345           END IF
00346       END IF
00347 *
00348       RETURN
00349 *
00350 *     End of STPMV .
00351 *
00352       END
 All Files Functions