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      1       SUBROUTINE DSPR(UPLO,N,ALPHA,X,INCX,AP)
      2 *     .. Scalar Arguments ..
      3       DOUBLE PRECISION ALPHA
      4       INTEGER INCX,N
      5       CHARACTER UPLO
      6 *     ..
      7 *     .. Array Arguments ..
      8       DOUBLE PRECISION AP(*),X(*)
      9 *     ..
     10 *
     11 *  Purpose
     12 *  =======
     13 *
     14 *  DSPR    performs the symmetric rank 1 operation
     15 *
     16 *     A := alpha*x*x' + A,
     17 *
     18 *  where alpha is a real scalar, x is an n element vector and A is an
     19 *  n by n symmetric matrix, supplied in packed form.
     20 *
     21 *  Arguments
     22 *  ==========
     23 *
     24 *  UPLO   - CHARACTER*1.
     25 *           On entry, UPLO specifies whether the upper or lower
     26 *           triangular part of the matrix A is supplied in the packed
     27 *           array AP as follows:
     28 *
     29 *              UPLO = 'U' or 'u'   The upper triangular part of A is
     30 *                                  supplied in AP.
     31 *
     32 *              UPLO = 'L' or 'l'   The lower triangular part of A is
     33 *                                  supplied in AP.
     34 *
     35 *           Unchanged on exit.
     36 *
     37 *  N      - INTEGER.
     38 *           On entry, N specifies the order of the matrix A.
     39 *           N must be at least zero.
     40 *           Unchanged on exit.
     41 *
     42 *  ALPHA  - DOUBLE PRECISION.
     43 *           On entry, ALPHA specifies the scalar alpha.
     44 *           Unchanged on exit.
     45 *
     46 *  X      - DOUBLE PRECISION array of dimension at least
     47 *           ( 1 + ( n - 1 )*abs( INCX ) ).
     48 *           Before entry, the incremented array X must contain the n
     49 *           element vector x.
     50 *           Unchanged on exit.
     51 *
     52 *  INCX   - INTEGER.
     53 *           On entry, INCX specifies the increment for the elements of
     54 *           X. INCX must not be zero.
     55 *           Unchanged on exit.
     56 *
     57 *  AP     - DOUBLE PRECISION array of DIMENSION at least
     58 *           ( ( n*( n + 1 ) )/2 ).
     59 *           Before entry with  UPLO = 'U' or 'u', the array AP must
     60 *           contain the upper triangular part of the symmetric matrix
     61 *           packed sequentially, column by column, so that AP( 1 )
     62 *           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
     63 *           and a( 2, 2 ) respectively, and so on. On exit, the array
     64 *           AP is overwritten by the upper triangular part of the
     65 *           updated matrix.
     66 *           Before entry with UPLO = 'L' or 'l', the array AP must
     67 *           contain the lower triangular part of the symmetric matrix
     68 *           packed sequentially, column by column, so that AP( 1 )
     69 *           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )
     70 *           and a( 3, 1 ) respectively, and so on. On exit, the array
     71 *           AP is overwritten by the lower triangular part of the
     72 *           updated matrix.
     73 *
     74 *  Further Details
     75 *  ===============
     76 *
     77 *  Level 2 Blas routine.
     78 *
     79 *  -- Written on 22-October-1986.
     80 *     Jack Dongarra, Argonne National Lab.
     81 *     Jeremy Du Croz, Nag Central Office.
     82 *     Sven Hammarling, Nag Central Office.
     83 *     Richard Hanson, Sandia National Labs.
     84 *
     85 *  =====================================================================
     86 *
     87 *     .. Parameters ..
     88       DOUBLE PRECISION ZERO
     89       PARAMETER (ZERO=0.0D+0)
     90 *     ..
     91 *     .. Local Scalars ..
     92       DOUBLE PRECISION TEMP
     93       INTEGER I,INFO,IX,J,JX,K,KK,KX
     94 *     ..
     95 *     .. External Functions ..
     96       LOGICAL LSAME
     97       EXTERNAL LSAME
     98 *     ..
     99 *     .. External Subroutines ..
    100       EXTERNAL XERBLA
    101 *     ..
    102 *
    103 *     Test the input parameters.
    104 *
    105       INFO = 0
    106       IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
    107           INFO = 1
    108       ELSE IF (N.LT.0) THEN
    109           INFO = 2
    110       ELSE IF (INCX.EQ.0) THEN
    111           INFO = 5
    112       END IF
    113       IF (INFO.NE.0) THEN
    114           CALL XERBLA('DSPR  ',INFO)
    115           RETURN
    116       END IF
    117 *
    118 *     Quick return if possible.
    119 *
    120       IF ((N.EQ.0) .OR. (ALPHA.EQ.ZERO)) RETURN
    121 *
    122 *     Set the start point in X if the increment is not unity.
    123 *
    124       IF (INCX.LE.0) THEN
    125           KX = 1 - (N-1)*INCX
    126       ELSE IF (INCX.NE.1) THEN
    127           KX = 1
    128       END IF
    129 *
    130 *     Start the operations. In this version the elements of the array AP
    131 *     are accessed sequentially with one pass through AP.
    132 *
    133       KK = 1
    134       IF (LSAME(UPLO,'U')) THEN
    135 *
    136 *        Form  A  when upper triangle is stored in AP.
    137 *
    138           IF (INCX.EQ.1) THEN
    139               DO 20 J = 1,N
    140                   IF (X(J).NE.ZERO) THEN
    141                       TEMP = ALPHA*X(J)
    142                       K = KK
    143                       DO 10 I = 1,J
    144                           AP(K) = AP(K) + X(I)*TEMP
    145                           K = K + 1
    146    10                 CONTINUE
    147                   END IF
    148                   KK = KK + J
    149    20         CONTINUE
    150           ELSE
    151               JX = KX
    152               DO 40 J = 1,N
    153                   IF (X(JX).NE.ZERO) THEN
    154                       TEMP = ALPHA*X(JX)
    155                       IX = KX
    156                       DO 30 K = KK,KK + J - 1
    157                           AP(K) = AP(K) + X(IX)*TEMP
    158                           IX = IX + INCX
    159    30                 CONTINUE
    160                   END IF
    161                   JX = JX + INCX
    162                   KK = KK + J
    163    40         CONTINUE
    164           END IF
    165       ELSE
    166 *
    167 *        Form  A  when lower triangle is stored in AP.
    168 *
    169           IF (INCX.EQ.1) THEN
    170               DO 60 J = 1,N
    171                   IF (X(J).NE.ZERO) THEN
    172                       TEMP = ALPHA*X(J)
    173                       K = KK
    174                       DO 50 I = J,N
    175                           AP(K) = AP(K) + X(I)*TEMP
    176                           K = K + 1
    177    50                 CONTINUE
    178                   END IF
    179                   KK = KK + N - J + 1
    180    60         CONTINUE
    181           ELSE
    182               JX = KX
    183               DO 80 J = 1,N
    184                   IF (X(JX).NE.ZERO) THEN
    185                       TEMP = ALPHA*X(JX)
    186                       IX = JX
    187                       DO 70 K = KK,KK + N - J
    188                           AP(K) = AP(K) + X(IX)*TEMP
    189                           IX = IX + INCX
    190    70                 CONTINUE
    191                   END IF
    192                   JX = JX + INCX
    193                   KK = KK + N - J + 1
    194    80         CONTINUE
    195           END IF
    196       END IF
    197 *
    198       RETURN
    199 *
    200 *     End of DSPR  .
    201 *
    202       END
    203