LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
dspr.f
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00001 *> \brief \b DSPR
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 DSPR(UPLO,N,ALPHA,X,INCX,AP)
00012 * 
00013 *       .. Scalar Arguments ..
00014 *       DOUBLE PRECISION ALPHA
00015 *       INTEGER INCX,N
00016 *       CHARACTER UPLO
00017 *       ..
00018 *       .. Array Arguments ..
00019 *       DOUBLE PRECISION AP(*),X(*)
00020 *       ..
00021 *  
00022 *
00023 *> \par Purpose:
00024 *  =============
00025 *>
00026 *> \verbatim
00027 *>
00028 *> DSPR    performs the symmetric rank 1 operation
00029 *>
00030 *>    A := alpha*x*x**T + A,
00031 *>
00032 *> where alpha is a real scalar, x is an n element vector and A is an
00033 *> n by n symmetric matrix, supplied in packed form.
00034 *> \endverbatim
00035 *
00036 *  Arguments:
00037 *  ==========
00038 *
00039 *> \param[in] UPLO
00040 *> \verbatim
00041 *>          UPLO is CHARACTER*1
00042 *>           On entry, UPLO specifies whether the upper or lower
00043 *>           triangular part of the matrix A is supplied in the packed
00044 *>           array AP as follows:
00045 *>
00046 *>              UPLO = 'U' or 'u'   The upper triangular part of A is
00047 *>                                  supplied in AP.
00048 *>
00049 *>              UPLO = 'L' or 'l'   The lower triangular part of A is
00050 *>                                  supplied in AP.
00051 *> \endverbatim
00052 *>
00053 *> \param[in] N
00054 *> \verbatim
00055 *>          N is INTEGER
00056 *>           On entry, N specifies the order of the matrix A.
00057 *>           N must be at least zero.
00058 *> \endverbatim
00059 *>
00060 *> \param[in] ALPHA
00061 *> \verbatim
00062 *>          ALPHA is DOUBLE PRECISION.
00063 *>           On entry, ALPHA specifies the scalar alpha.
00064 *> \endverbatim
00065 *>
00066 *> \param[in] X
00067 *> \verbatim
00068 *>          X is DOUBLE PRECISION array of dimension at least
00069 *>           ( 1 + ( n - 1 )*abs( INCX ) ).
00070 *>           Before entry, the incremented array X must contain the n
00071 *>           element vector x.
00072 *> \endverbatim
00073 *>
00074 *> \param[in] INCX
00075 *> \verbatim
00076 *>          INCX is INTEGER
00077 *>           On entry, INCX specifies the increment for the elements of
00078 *>           X. INCX must not be zero.
00079 *> \endverbatim
00080 *>
00081 *> \param[in,out] AP
00082 *> \verbatim
00083 *>          AP is DOUBLE PRECISION 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 part of the symmetric matrix
00087 *>           packed sequentially, column by column, so that AP( 1 )
00088 *>           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
00089 *>           and a( 2, 2 ) respectively, and so on. On exit, the array
00090 *>           AP is overwritten by the upper triangular part of the
00091 *>           updated matrix.
00092 *>           Before entry with UPLO = 'L' or 'l', the array AP must
00093 *>           contain the lower triangular part of the symmetric matrix
00094 *>           packed sequentially, column by column, so that AP( 1 )
00095 *>           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )
00096 *>           and a( 3, 1 ) respectively, and so on. On exit, the array
00097 *>           AP is overwritten by the lower triangular part of the
00098 *>           updated matrix.
00099 *> \endverbatim
00100 *
00101 *  Authors:
00102 *  ========
00103 *
00104 *> \author Univ. of Tennessee 
00105 *> \author Univ. of California Berkeley 
00106 *> \author Univ. of Colorado Denver 
00107 *> \author NAG Ltd. 
00108 *
00109 *> \date November 2011
00110 *
00111 *> \ingroup double_blas_level2
00112 *
00113 *> \par Further Details:
00114 *  =====================
00115 *>
00116 *> \verbatim
00117 *>
00118 *>  Level 2 Blas routine.
00119 *>
00120 *>  -- Written on 22-October-1986.
00121 *>     Jack Dongarra, Argonne National Lab.
00122 *>     Jeremy Du Croz, Nag Central Office.
00123 *>     Sven Hammarling, Nag Central Office.
00124 *>     Richard Hanson, Sandia National Labs.
00125 *> \endverbatim
00126 *>
00127 *  =====================================================================
00128       SUBROUTINE DSPR(UPLO,N,ALPHA,X,INCX,AP)
00129 *
00130 *  -- Reference BLAS level2 routine (version 3.4.0) --
00131 *  -- Reference BLAS is a software package provided by Univ. of Tennessee,    --
00132 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00133 *     November 2011
00134 *
00135 *     .. Scalar Arguments ..
00136       DOUBLE PRECISION ALPHA
00137       INTEGER INCX,N
00138       CHARACTER UPLO
00139 *     ..
00140 *     .. Array Arguments ..
00141       DOUBLE PRECISION AP(*),X(*)
00142 *     ..
00143 *
00144 *  =====================================================================
00145 *
00146 *     .. Parameters ..
00147       DOUBLE PRECISION ZERO
00148       PARAMETER (ZERO=0.0D+0)
00149 *     ..
00150 *     .. Local Scalars ..
00151       DOUBLE PRECISION TEMP
00152       INTEGER I,INFO,IX,J,JX,K,KK,KX
00153 *     ..
00154 *     .. External Functions ..
00155       LOGICAL LSAME
00156       EXTERNAL LSAME
00157 *     ..
00158 *     .. External Subroutines ..
00159       EXTERNAL XERBLA
00160 *     ..
00161 *
00162 *     Test the input parameters.
00163 *
00164       INFO = 0
00165       IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
00166           INFO = 1
00167       ELSE IF (N.LT.0) THEN
00168           INFO = 2
00169       ELSE IF (INCX.EQ.0) THEN
00170           INFO = 5
00171       END IF
00172       IF (INFO.NE.0) THEN
00173           CALL XERBLA('DSPR  ',INFO)
00174           RETURN
00175       END IF
00176 *
00177 *     Quick return if possible.
00178 *
00179       IF ((N.EQ.0) .OR. (ALPHA.EQ.ZERO)) RETURN
00180 *
00181 *     Set the start point in X if the increment is not unity.
00182 *
00183       IF (INCX.LE.0) THEN
00184           KX = 1 - (N-1)*INCX
00185       ELSE IF (INCX.NE.1) THEN
00186           KX = 1
00187       END IF
00188 *
00189 *     Start the operations. In this version the elements of the array AP
00190 *     are accessed sequentially with one pass through AP.
00191 *
00192       KK = 1
00193       IF (LSAME(UPLO,'U')) THEN
00194 *
00195 *        Form  A  when upper triangle is stored in AP.
00196 *
00197           IF (INCX.EQ.1) THEN
00198               DO 20 J = 1,N
00199                   IF (X(J).NE.ZERO) THEN
00200                       TEMP = ALPHA*X(J)
00201                       K = KK
00202                       DO 10 I = 1,J
00203                           AP(K) = AP(K) + X(I)*TEMP
00204                           K = K + 1
00205    10                 CONTINUE
00206                   END IF
00207                   KK = KK + J
00208    20         CONTINUE
00209           ELSE
00210               JX = KX
00211               DO 40 J = 1,N
00212                   IF (X(JX).NE.ZERO) THEN
00213                       TEMP = ALPHA*X(JX)
00214                       IX = KX
00215                       DO 30 K = KK,KK + J - 1
00216                           AP(K) = AP(K) + X(IX)*TEMP
00217                           IX = IX + INCX
00218    30                 CONTINUE
00219                   END IF
00220                   JX = JX + INCX
00221                   KK = KK + J
00222    40         CONTINUE
00223           END IF
00224       ELSE
00225 *
00226 *        Form  A  when lower triangle is stored in AP.
00227 *
00228           IF (INCX.EQ.1) THEN
00229               DO 60 J = 1,N
00230                   IF (X(J).NE.ZERO) THEN
00231                       TEMP = ALPHA*X(J)
00232                       K = KK
00233                       DO 50 I = J,N
00234                           AP(K) = AP(K) + X(I)*TEMP
00235                           K = K + 1
00236    50                 CONTINUE
00237                   END IF
00238                   KK = KK + N - J + 1
00239    60         CONTINUE
00240           ELSE
00241               JX = KX
00242               DO 80 J = 1,N
00243                   IF (X(JX).NE.ZERO) THEN
00244                       TEMP = ALPHA*X(JX)
00245                       IX = JX
00246                       DO 70 K = KK,KK + N - J
00247                           AP(K) = AP(K) + X(IX)*TEMP
00248                           IX = IX + INCX
00249    70                 CONTINUE
00250                   END IF
00251                   JX = JX + INCX
00252                   KK = KK + N - J + 1
00253    80         CONTINUE
00254           END IF
00255       END IF
00256 *
00257       RETURN
00258 *
00259 *     End of DSPR  .
00260 *
00261       END
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