dsymv.f

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      SUBROUTINE dsymv ( UPLO, N, ALPHA, A, LDA, X, INCX,
     $                   BETA, Y, INCY )
*     .. Scalar Arguments ..
      DOUBLE PRECISION   ALPHA, BETA
      INTEGER            INCX, INCY, LDA, N
      CHARACTER*1        UPLO
*     .. Array Arguments ..
      DOUBLE PRECISION   A( LDA, * ), X( * ), Y( * )
*     ..
*
*  Purpose
*  =======
*
*  DSYMV  performs the matrix-vector  operation
*
*     y := alpha*A*x + beta*y,
*
*  where alpha and beta are scalars, x and y are n element vectors and
*  A is an n by n symmetric matrix.
*
*  Parameters
*  ==========
*
*  UPLO   - CHARACTER*1.
*           On entry, UPLO specifies whether the upper or lower
*           triangular part of the array A is to be referenced as
*           follows:
*
*              UPLO = 'U' or 'u'   Only the upper triangular part of A
*                                  is to be referenced.
*
*              UPLO = 'L' or 'l'   Only the lower triangular part of A
*                                  is to be referenced.
*
*           Unchanged on exit.
*
*  N      - INTEGER.
*           On entry, N specifies the order of the matrix A.
*           N must be at least zero.
*           Unchanged on exit.
*
*  ALPHA  - DOUBLE PRECISION.
*           On entry, ALPHA specifies the scalar alpha.
*           Unchanged on exit.
*
*  A      - DOUBLE PRECISION array of DIMENSION ( LDA, n ).
*           Before entry with  UPLO = 'U' or 'u', the leading n by n
*           upper triangular part of the array A must contain the upper
*           triangular part of the symmetric matrix and the strictly
*           lower triangular part of A is not referenced.
*           Before entry with UPLO = 'L' or 'l', the leading n by n
*           lower triangular part of the array A must contain the lower
*           triangular part of the symmetric matrix and the strictly
*           upper triangular part of A is not referenced.
*           Unchanged on exit.
*
*  LDA    - INTEGER.
*           On entry, LDA specifies the first dimension of A as declared
*           in the calling (sub) program. LDA must be at least
*           max( 1, n ).
*           Unchanged on exit.
*
*  X      - DOUBLE PRECISION array of dimension at least
*           ( 1 + ( n - 1 )*abs( INCX ) ).
*           Before entry, the incremented array X must contain the n
*           element vector x.
*           Unchanged on exit.
*
*  INCX   - INTEGER.
*           On entry, INCX specifies the increment for the elements of
*           X. INCX must not be zero.
*           Unchanged on exit.
*
*  BETA   - DOUBLE PRECISION.
*           On entry, BETA specifies the scalar beta. When BETA is
*           supplied as zero then Y need not be set on input.
*           Unchanged on exit.
*
*  Y      - DOUBLE PRECISION array of dimension at least
*           ( 1 + ( n - 1 )*abs( INCY ) ).
*           Before entry, the incremented array Y must contain the n
*           element vector y. On exit, Y is overwritten by the updated
*           vector y.
*
*  INCY   - INTEGER.
*           On entry, INCY specifies the increment for the elements of
*           Y. INCY must not be zero.
*           Unchanged on exit.
*
*
*  Level 2 Blas routine.
*
*  -- Written on 22-October-1986.
*     Jack Dongarra, Argonne National Lab.
*     Jeremy Du Croz, Nag Central Office.
*     Sven Hammarling, Nag Central Office.
*     Richard Hanson, Sandia National Labs.
*
*
*     .. Parameters ..
      DOUBLE PRECISION   ONE         , ZERO
      parameter( one = 1.0d+0, zero = 0.0d+0 )
*     .. Local Scalars ..
      DOUBLE PRECISION   TEMP1, TEMP2
      INTEGER            I, INFO, IX, IY, J, JX, JY, KX, KY
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           lsame
*     .. External Subroutines ..
      EXTERNAL           xerbla
*     .. Intrinsic Functions ..
      INTRINSIC          max
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
      info = 0
      IF     ( .NOT.lsame( uplo, 'U' ).AND.
     $         .NOT.lsame( uplo, 'L' )      )THEN
         info = 1
      ELSE IF( n.LT.0 )THEN
         info = 2
      ELSE IF( lda.LT.max( 1, n ) )THEN
         info = 5
      ELSE IF( incx.EQ.0 )THEN
         info = 7
      ELSE IF( incy.EQ.0 )THEN
         info = 10
      END IF
      IF( info.NE.0 )THEN
         CALL xerbla( 'DSYMV ', info )
         RETURN
      END IF
*
*     Quick return if possible.
*
      IF( ( n.EQ.0 ).OR.( ( alpha.EQ.zero ).AND.( beta.EQ.one ) ) )
     $   RETURN
*
*     Set up the start points in  X  and  Y.
*
      IF( incx.GT.0 )THEN
         kx = 1
      ELSE
         kx = 1 - ( n - 1 )*incx
      END IF
      IF( incy.GT.0 )THEN
         ky = 1
      ELSE
         ky = 1 - ( n - 1 )*incy
      END IF
*
*     Start the operations. In this version the elements of A are
*     accessed sequentially with one pass through the triangular part
*     of A.
*
*     First form  y := beta*y.
*
      IF( beta.NE.one )THEN
         IF( incy.EQ.1 )THEN
            IF( beta.EQ.zero )THEN
               DO 10, i = 1, n
                  y( i ) = zero
   10          CONTINUE
            ELSE
               DO 20, i = 1, n
                  y( i ) = beta*y( i )
   20          CONTINUE
            END IF
         ELSE
            iy = ky
            IF( beta.EQ.zero )THEN
               DO 30, i = 1, n
                  y( iy ) = zero
                  iy      = iy   + incy
   30          CONTINUE
            ELSE
               DO 40, i = 1, n
                  y( iy ) = beta*y( iy )
                  iy      = iy           + incy
   40          CONTINUE
            END IF
         END IF
      END IF
      IF( alpha.EQ.zero )
     $   RETURN
      IF( lsame( uplo, 'U' ) )THEN
*
*        Form  y  when A is stored in upper triangle.
*
         IF( ( incx.EQ.1 ).AND.( incy.EQ.1 ) )THEN
            DO 60, j = 1, n
               temp1 = alpha*x( j )
               temp2 = zero
               DO 50, i = 1, j - 1
                  y( i ) = y( i ) + temp1*a( i, j )
                  temp2  = temp2  + a( i, j )*x( i )
   50          CONTINUE
               y( j ) = y( j ) + temp1*a( j, j ) + alpha*temp2
   60       CONTINUE
         ELSE
            jx = kx
            jy = ky
            DO 80, j = 1, n
               temp1 = alpha*x( jx )
               temp2 = zero
               ix    = kx
               iy    = ky
               DO 70, i = 1, j - 1
                  y( iy ) = y( iy ) + temp1*a( i, j )
                  temp2   = temp2   + a( i, j )*x( ix )
                  ix      = ix      + incx
                  iy      = iy      + incy
   70          CONTINUE
               y( jy ) = y( jy ) + temp1*a( j, j ) + alpha*temp2
               jx      = jx      + incx
               jy      = jy      + incy
   80       CONTINUE
         END IF
      ELSE
*
*        Form  y  when A is stored in lower triangle.
*
         IF( ( incx.EQ.1 ).AND.( incy.EQ.1 ) )THEN
            DO 100, j = 1, n
               temp1  = alpha*x( j )
               temp2  = zero
               y( j ) = y( j )       + temp1*a( j, j )
               DO 90, i = j + 1, n
                  y( i ) = y( i ) + temp1*a( i, j )
                  temp2  = temp2  + a( i, j )*x( i )
   90          CONTINUE
               y( j ) = y( j ) + alpha*temp2
  100       CONTINUE
         ELSE
            jx = kx
            jy = ky
            DO 120, j = 1, n
               temp1   = alpha*x( jx )
               temp2   = zero
               y( jy ) = y( jy )       + temp1*a( j, j )
               ix      = jx
               iy      = jy
               DO 110, i = j + 1, n
                  ix      = ix      + incx
                  iy      = iy      + incy
                  y( iy ) = y( iy ) + temp1*a( i, j )
                  temp2   = temp2   + a( i, j )*x( ix )
  110          CONTINUE
               y( jy ) = y( jy ) + alpha*temp2
               jx      = jx      + incx
               jy      = jy      + incy
  120       CONTINUE
         END IF
      END IF
*
      RETURN
*
*     End of DSYMV .
*
      END