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Mise à jour de blas.

    1: *> \brief \b DSPR
    2: *
    3: *  =========== DOCUMENTATION ===========
    4: *
    5: * Online html documentation available at 
    6: *            http://www.netlib.org/lapack/explore-html/ 
    7: *
    8: *  Definition:
    9: *  ===========
   10: *
   11: *       SUBROUTINE DSPR(UPLO,N,ALPHA,X,INCX,AP)
   12: * 
   13: *       .. Scalar Arguments ..
   14: *       DOUBLE PRECISION ALPHA
   15: *       INTEGER INCX,N
   16: *       CHARACTER UPLO
   17: *       ..
   18: *       .. Array Arguments ..
   19: *       DOUBLE PRECISION AP(*),X(*)
   20: *       ..
   21: *  
   22: *
   23: *> \par Purpose:
   24: *  =============
   25: *>
   26: *> \verbatim
   27: *>
   28: *> DSPR    performs the symmetric rank 1 operation
   29: *>
   30: *>    A := alpha*x*x**T + A,
   31: *>
   32: *> where alpha is a real scalar, x is an n element vector and A is an
   33: *> n by n symmetric matrix, supplied in packed form.
   34: *> \endverbatim
   35: *
   36: *  Arguments:
   37: *  ==========
   38: *
   39: *> \param[in] UPLO
   40: *> \verbatim
   41: *>          UPLO is CHARACTER*1
   42: *>           On entry, UPLO specifies whether the upper or lower
   43: *>           triangular part of the matrix A is supplied in the packed
   44: *>           array AP as follows:
   45: *>
   46: *>              UPLO = 'U' or 'u'   The upper triangular part of A is
   47: *>                                  supplied in AP.
   48: *>
   49: *>              UPLO = 'L' or 'l'   The lower triangular part of A is
   50: *>                                  supplied in AP.
   51: *> \endverbatim
   52: *>
   53: *> \param[in] N
   54: *> \verbatim
   55: *>          N is INTEGER
   56: *>           On entry, N specifies the order of the matrix A.
   57: *>           N must be at least zero.
   58: *> \endverbatim
   59: *>
   60: *> \param[in] ALPHA
   61: *> \verbatim
   62: *>          ALPHA is DOUBLE PRECISION.
   63: *>           On entry, ALPHA specifies the scalar alpha.
   64: *> \endverbatim
   65: *>
   66: *> \param[in] X
   67: *> \verbatim
   68: *>          X is DOUBLE PRECISION array of dimension at least
   69: *>           ( 1 + ( n - 1 )*abs( INCX ) ).
   70: *>           Before entry, the incremented array X must contain the n
   71: *>           element vector x.
   72: *> \endverbatim
   73: *>
   74: *> \param[in] INCX
   75: *> \verbatim
   76: *>          INCX is INTEGER
   77: *>           On entry, INCX specifies the increment for the elements of
   78: *>           X. INCX must not be zero.
   79: *> \endverbatim
   80: *>
   81: *> \param[in,out] AP
   82: *> \verbatim
   83: *>          AP is DOUBLE PRECISION array of DIMENSION at least
   84: *>           ( ( n*( n + 1 ) )/2 ).
   85: *>           Before entry with  UPLO = 'U' or 'u', the array AP must
   86: *>           contain the upper triangular part of the symmetric matrix
   87: *>           packed sequentially, column by column, so that AP( 1 )
   88: *>           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
   89: *>           and a( 2, 2 ) respectively, and so on. On exit, the array
   90: *>           AP is overwritten by the upper triangular part of the
   91: *>           updated matrix.
   92: *>           Before entry with UPLO = 'L' or 'l', the array AP must
   93: *>           contain the lower triangular part of the symmetric matrix
   94: *>           packed sequentially, column by column, so that AP( 1 )
   95: *>           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )
   96: *>           and a( 3, 1 ) respectively, and so on. On exit, the array
   97: *>           AP is overwritten by the lower triangular part of the
   98: *>           updated matrix.
   99: *> \endverbatim
  100: *
  101: *  Authors:
  102: *  ========
  103: *
  104: *> \author Univ. of Tennessee 
  105: *> \author Univ. of California Berkeley 
  106: *> \author Univ. of Colorado Denver 
  107: *> \author NAG Ltd. 
  108: *
  109: *> \date November 2011
  110: *
  111: *> \ingroup double_blas_level2
  112: *
  113: *> \par Further Details:
  114: *  =====================
  115: *>
  116: *> \verbatim
  117: *>
  118: *>  Level 2 Blas routine.
  119: *>
  120: *>  -- Written on 22-October-1986.
  121: *>     Jack Dongarra, Argonne National Lab.
  122: *>     Jeremy Du Croz, Nag Central Office.
  123: *>     Sven Hammarling, Nag Central Office.
  124: *>     Richard Hanson, Sandia National Labs.
  125: *> \endverbatim
  126: *>
  127: *  =====================================================================
  128:       SUBROUTINE DSPR(UPLO,N,ALPHA,X,INCX,AP)
  129: *
  130: *  -- Reference BLAS level2 routine (version 3.4.0) --
  131: *  -- Reference BLAS is a software package provided by Univ. of Tennessee,    --
  132: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
  133: *     November 2011
  134: *
  135: *     .. Scalar Arguments ..
  136:       DOUBLE PRECISION ALPHA
  137:       INTEGER INCX,N
  138:       CHARACTER UPLO
  139: *     ..
  140: *     .. Array Arguments ..
  141:       DOUBLE PRECISION AP(*),X(*)
  142: *     ..
  143: *
  144: *  =====================================================================
  145: *
  146: *     .. Parameters ..
  147:       DOUBLE PRECISION ZERO
  148:       PARAMETER (ZERO=0.0D+0)
  149: *     ..
  150: *     .. Local Scalars ..
  151:       DOUBLE PRECISION TEMP
  152:       INTEGER I,INFO,IX,J,JX,K,KK,KX
  153: *     ..
  154: *     .. External Functions ..
  155:       LOGICAL LSAME
  156:       EXTERNAL LSAME
  157: *     ..
  158: *     .. External Subroutines ..
  159:       EXTERNAL XERBLA
  160: *     ..
  161: *
  162: *     Test the input parameters.
  163: *
  164:       INFO = 0
  165:       IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
  166:           INFO = 1
  167:       ELSE IF (N.LT.0) THEN
  168:           INFO = 2
  169:       ELSE IF (INCX.EQ.0) THEN
  170:           INFO = 5
  171:       END IF
  172:       IF (INFO.NE.0) THEN
  173:           CALL XERBLA('DSPR  ',INFO)
  174:           RETURN
  175:       END IF
  176: *
  177: *     Quick return if possible.
  178: *
  179:       IF ((N.EQ.0) .OR. (ALPHA.EQ.ZERO)) RETURN
  180: *
  181: *     Set the start point in X if the increment is not unity.
  182: *
  183:       IF (INCX.LE.0) THEN
  184:           KX = 1 - (N-1)*INCX
  185:       ELSE IF (INCX.NE.1) THEN
  186:           KX = 1
  187:       END IF
  188: *
  189: *     Start the operations. In this version the elements of the array AP
  190: *     are accessed sequentially with one pass through AP.
  191: *
  192:       KK = 1
  193:       IF (LSAME(UPLO,'U')) THEN
  194: *
  195: *        Form  A  when upper triangle is stored in AP.
  196: *
  197:           IF (INCX.EQ.1) THEN
  198:               DO 20 J = 1,N
  199:                   IF (X(J).NE.ZERO) THEN
  200:                       TEMP = ALPHA*X(J)
  201:                       K = KK
  202:                       DO 10 I = 1,J
  203:                           AP(K) = AP(K) + X(I)*TEMP
  204:                           K = K + 1
  205:    10                 CONTINUE
  206:                   END IF
  207:                   KK = KK + J
  208:    20         CONTINUE
  209:           ELSE
  210:               JX = KX
  211:               DO 40 J = 1,N
  212:                   IF (X(JX).NE.ZERO) THEN
  213:                       TEMP = ALPHA*X(JX)
  214:                       IX = KX
  215:                       DO 30 K = KK,KK + J - 1
  216:                           AP(K) = AP(K) + X(IX)*TEMP
  217:                           IX = IX + INCX
  218:    30                 CONTINUE
  219:                   END IF
  220:                   JX = JX + INCX
  221:                   KK = KK + J
  222:    40         CONTINUE
  223:           END IF
  224:       ELSE
  225: *
  226: *        Form  A  when lower triangle is stored in AP.
  227: *
  228:           IF (INCX.EQ.1) THEN
  229:               DO 60 J = 1,N
  230:                   IF (X(J).NE.ZERO) THEN
  231:                       TEMP = ALPHA*X(J)
  232:                       K = KK
  233:                       DO 50 I = J,N
  234:                           AP(K) = AP(K) + X(I)*TEMP
  235:                           K = K + 1
  236:    50                 CONTINUE
  237:                   END IF
  238:                   KK = KK + N - J + 1
  239:    60         CONTINUE
  240:           ELSE
  241:               JX = KX
  242:               DO 80 J = 1,N
  243:                   IF (X(JX).NE.ZERO) THEN
  244:                       TEMP = ALPHA*X(JX)
  245:                       IX = JX
  246:                       DO 70 K = KK,KK + N - J
  247:                           AP(K) = AP(K) + X(IX)*TEMP
  248:                           IX = IX + INCX
  249:    70                 CONTINUE
  250:                   END IF
  251:                   JX = JX + INCX
  252:                   KK = KK + N - J + 1
  253:    80         CONTINUE
  254:           END IF
  255:       END IF
  256: *
  257:       RETURN
  258: *
  259: *     End of DSPR  .
  260: *
  261:       END