csymv.f

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      SUBROUTINE csymv( UPLO, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY )
*
*  -- LAPACK auxiliary routine (version 3.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     November 2006
*
*     .. Scalar Arguments ..
      CHARACTER          uplo
      INTEGER            incx, incy, lda, n
      COMPLEX            alpha, beta
*     ..
*     .. Array Arguments ..
      COMPLEX            a( lda, * ), x( * ), y( * )
*     ..
*
*  Purpose
*  =======
*
*  CSYMV  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.
*
*  Arguments
*  ==========
*
*  UPLO     (input) 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        (input) INTEGER
*           On entry, N specifies the order of the matrix A.
*           N must be at least zero.
*           Unchanged on exit.
*
*  ALPHA    (input) COMPLEX
*           On entry, ALPHA specifies the scalar alpha.
*           Unchanged on exit.
*
*  A        (input) COMPLEX array, 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      (input) 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        (input) COMPLEX array, 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     (input) INTEGER
*           On entry, INCX specifies the increment for the elements of
*           X. INCX must not be zero.
*           Unchanged on exit.
*
*  BETA     (input) COMPLEX
*           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        (input/output) COMPLEX array, 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     (input) INTEGER
*           On entry, INCY specifies the increment for the elements of
*           Y. INCY must not be zero.
*           Unchanged on exit.
*
* =====================================================================
*
*     .. Parameters ..
      COMPLEX            one
      parameter( one = ( 1.0e+0, 0.0e+0 ) )
      COMPLEX            zero
      parameter( zero = ( 0.0e+0, 0.0e+0 ) )
*     ..
*     .. Local Scalars ..
      INTEGER            i, info, ix, iy, j, jx, jy, kx, ky
      COMPLEX            temp1, temp2
*     ..
*     .. 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( 'CSYMV ', 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 CSYMV
*
      END