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      1       SUBROUTINE SSPMV(UPLO,N,ALPHA,AP,X,INCX,BETA,Y,INCY)
      2 *     .. Scalar Arguments ..
      3       REAL ALPHA,BETA
      4       INTEGER INCX,INCY,N
      5       CHARACTER UPLO
      6 *     ..
      7 *     .. Array Arguments ..
      8       REAL AP(*),X(*),Y(*)
      9 *     ..
     10 *
     11 *  Purpose
     12 *  =======
     13 *
     14 *  SSPMV  performs the matrix-vector operation
     15 *
     16 *     y := alpha*A*x + beta*y,
     17 *
     18 *  where alpha and beta are scalars, x and y are n element vectors and
     19 *  A is an 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  - REAL            .
     43 *           On entry, ALPHA specifies the scalar alpha.
     44 *           Unchanged on exit.
     45 *
     46 *  AP     - REAL             array of DIMENSION at least
     47 *           ( ( n*( n + 1 ) )/2 ).
     48 *           Before entry with UPLO = 'U' or 'u', the array AP must
     49 *           contain the upper triangular part of the symmetric matrix
     50 *           packed sequentially, column by column, so that AP( 1 )
     51 *           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
     52 *           and a( 2, 2 ) respectively, and so on.
     53 *           Before entry with UPLO = 'L' or 'l', the array AP must
     54 *           contain the lower triangular part of the symmetric matrix
     55 *           packed sequentially, column by column, so that AP( 1 )
     56 *           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )
     57 *           and a( 3, 1 ) respectively, and so on.
     58 *           Unchanged on exit.
     59 *
     60 *  X      - REAL             array of dimension at least
     61 *           ( 1 + ( n - 1 )*abs( INCX ) ).
     62 *           Before entry, the incremented array X must contain the n
     63 *           element vector x.
     64 *           Unchanged on exit.
     65 *
     66 *  INCX   - INTEGER.
     67 *           On entry, INCX specifies the increment for the elements of
     68 *           X. INCX must not be zero.
     69 *           Unchanged on exit.
     70 *
     71 *  BETA   - REAL            .
     72 *           On entry, BETA specifies the scalar beta. When BETA is
     73 *           supplied as zero then Y need not be set on input.
     74 *           Unchanged on exit.
     75 *
     76 *  Y      - REAL             array of dimension at least
     77 *           ( 1 + ( n - 1 )*abs( INCY ) ).
     78 *           Before entry, the incremented array Y must contain the n
     79 *           element vector y. On exit, Y is overwritten by the updated
     80 *           vector y.
     81 *
     82 *  INCY   - INTEGER.
     83 *           On entry, INCY specifies the increment for the elements of
     84 *           Y. INCY must not be zero.
     85 *           Unchanged on exit.
     86 *
     87 *  Further Details
     88 *  ===============
     89 *
     90 *  Level 2 Blas routine.
     91 *
     92 *  -- Written on 22-October-1986.
     93 *     Jack Dongarra, Argonne National Lab.
     94 *     Jeremy Du Croz, Nag Central Office.
     95 *     Sven Hammarling, Nag Central Office.
     96 *     Richard Hanson, Sandia National Labs.
     97 *
     98 *  =====================================================================
     99 *
    100 *     .. Parameters ..
    101       REAL ONE,ZERO
    102       PARAMETER (ONE=1.0E+0,ZERO=0.0E+0)
    103 *     ..
    104 *     .. Local Scalars ..
    105       REAL TEMP1,TEMP2
    106       INTEGER I,INFO,IX,IY,J,JX,JY,K,KK,KX,KY
    107 *     ..
    108 *     .. External Functions ..
    109       LOGICAL LSAME
    110       EXTERNAL LSAME
    111 *     ..
    112 *     .. External Subroutines ..
    113       EXTERNAL XERBLA
    114 *     ..
    115 *
    116 *     Test the input parameters.
    117 *
    118       INFO = 0
    119       IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
    120           INFO = 1
    121       ELSE IF (N.LT.0) THEN
    122           INFO = 2
    123       ELSE IF (INCX.EQ.0) THEN
    124           INFO = 6
    125       ELSE IF (INCY.EQ.0) THEN
    126           INFO = 9
    127       END IF
    128       IF (INFO.NE.0) THEN
    129           CALL XERBLA('SSPMV ',INFO)
    130           RETURN
    131       END IF
    132 *
    133 *     Quick return if possible.
    134 *
    135       IF ((N.EQ.0) .OR. ((ALPHA.EQ.ZERO).AND. (BETA.EQ.ONE))) RETURN
    136 *
    137 *     Set up the start points in  X  and  Y.
    138 *
    139       IF (INCX.GT.0) THEN
    140           KX = 1
    141       ELSE
    142           KX = 1 - (N-1)*INCX
    143       END IF
    144       IF (INCY.GT.0) THEN
    145           KY = 1
    146       ELSE
    147           KY = 1 - (N-1)*INCY
    148       END IF
    149 *
    150 *     Start the operations. In this version the elements of the array AP
    151 *     are accessed sequentially with one pass through AP.
    152 *
    153 *     First form  y := beta*y.
    154 *
    155       IF (BETA.NE.ONE) THEN
    156           IF (INCY.EQ.1) THEN
    157               IF (BETA.EQ.ZERO) THEN
    158                   DO 10 I = 1,N
    159                       Y(I) = ZERO
    160    10             CONTINUE
    161               ELSE
    162                   DO 20 I = 1,N
    163                       Y(I) = BETA*Y(I)
    164    20             CONTINUE
    165               END IF
    166           ELSE
    167               IY = KY
    168               IF (BETA.EQ.ZERO) THEN
    169                   DO 30 I = 1,N
    170                       Y(IY) = ZERO
    171                       IY = IY + INCY
    172    30             CONTINUE
    173               ELSE
    174                   DO 40 I = 1,N
    175                       Y(IY) = BETA*Y(IY)
    176                       IY = IY + INCY
    177    40             CONTINUE
    178               END IF
    179           END IF
    180       END IF
    181       IF (ALPHA.EQ.ZERO) RETURN
    182       KK = 1
    183       IF (LSAME(UPLO,'U')) THEN
    184 *
    185 *        Form  y  when AP contains the upper triangle.
    186 *
    187           IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN
    188               DO 60 J = 1,N
    189                   TEMP1 = ALPHA*X(J)
    190                   TEMP2 = ZERO
    191                   K = KK
    192                   DO 50 I = 1,J - 1
    193                       Y(I) = Y(I) + TEMP1*AP(K)
    194                       TEMP2 = TEMP2 + AP(K)*X(I)
    195                       K = K + 1
    196    50             CONTINUE
    197                   Y(J) = Y(J) + TEMP1*AP(KK+J-1) + ALPHA*TEMP2
    198                   KK = KK + J
    199    60         CONTINUE
    200           ELSE
    201               JX = KX
    202               JY = KY
    203               DO 80 J = 1,N
    204                   TEMP1 = ALPHA*X(JX)
    205                   TEMP2 = ZERO
    206                   IX = KX
    207                   IY = KY
    208                   DO 70 K = KK,KK + J - 2
    209                       Y(IY) = Y(IY) + TEMP1*AP(K)
    210                       TEMP2 = TEMP2 + AP(K)*X(IX)
    211                       IX = IX + INCX
    212                       IY = IY + INCY
    213    70             CONTINUE
    214                   Y(JY) = Y(JY) + TEMP1*AP(KK+J-1) + ALPHA*TEMP2
    215                   JX = JX + INCX
    216                   JY = JY + INCY
    217                   KK = KK + J
    218    80         CONTINUE
    219           END IF
    220       ELSE
    221 *
    222 *        Form  y  when AP contains the lower triangle.
    223 *
    224           IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN
    225               DO 100 J = 1,N
    226                   TEMP1 = ALPHA*X(J)
    227                   TEMP2 = ZERO
    228                   Y(J) = Y(J) + TEMP1*AP(KK)
    229                   K = KK + 1
    230                   DO 90 I = J + 1,N
    231                       Y(I) = Y(I) + TEMP1*AP(K)
    232                       TEMP2 = TEMP2 + AP(K)*X(I)
    233                       K = K + 1
    234    90             CONTINUE
    235                   Y(J) = Y(J) + ALPHA*TEMP2
    236                   KK = KK + (N-J+1)
    237   100         CONTINUE
    238           ELSE
    239               JX = KX
    240               JY = KY
    241               DO 120 J = 1,N
    242                   TEMP1 = ALPHA*X(JX)
    243                   TEMP2 = ZERO
    244                   Y(JY) = Y(JY) + TEMP1*AP(KK)
    245                   IX = JX
    246                   IY = JY
    247                   DO 110 K = KK + 1,KK + N - J
    248                       IX = IX + INCX
    249                       IY = IY + INCY
    250                       Y(IY) = Y(IY) + TEMP1*AP(K)
    251                       TEMP2 = TEMP2 + AP(K)*X(IX)
    252   110             CONTINUE
    253                   Y(JY) = Y(JY) + ALPHA*TEMP2
    254                   JX = JX + INCX
    255                   JY = JY + INCY
    256                   KK = KK + (N-J+1)
    257   120         CONTINUE
    258           END IF
    259       END IF
    260 *
    261       RETURN
    262 *
    263 *     End of SSPMV .
    264 *
    265       END
    266