cspmv.f

          SUBROUTINE CSPMV( UPLO, N, ALPHA, AP, X, INCX, BETA, Y, INCY )
    *
    *  -- LAPACK auxiliary routine (version 3.1) --
    *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
    *     November 2006
    *
    *     .. Scalar Arguments ..
          CHARACTER          UPLO
          INTEGER            INCX, INCY, N
          COMPLEX            ALPHA, BETA
    *     ..
    *     .. Array Arguments ..
          COMPLEX            AP( * ), X( * ), Y( * )
    *     ..
    *
    *  Purpose
    *  =======
    *
    *  CSPMV  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, supplied in packed form.
    *
    *  Arguments
    *  ==========
    *
    *  UPLO     (input) CHARACTER*1
    *           On entry, UPLO specifies whether the upper or lower
    *           triangular part of the matrix A is supplied in the packed
    *           array AP as follows:
    *
    *              UPLO = 'U' or 'u'   The upper triangular part of A is
    *                                  supplied in AP.
    *
    *              UPLO = 'L' or 'l'   The lower triangular part of A is
    *                                  supplied in AP.
    *
    *           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.
    *
    *  AP       (input) COMPLEX array, dimension at least
    *           ( ( N*( N + 1 ) )/2 ).
    *           Before entry, with UPLO = 'U' or 'u', the array AP must
    *           contain the upper triangular part of the symmetric matrix
    *           packed sequentially, column by column, so that AP( 1 )
    *           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
    *           and a( 2, 2 ) respectively, and so on.
    *           Before entry, with UPLO = 'L' or 'l', the array AP must
    *           contain the lower triangular part of the symmetric matrix
    *           packed sequentially, column by column, so that AP( 1 )
    *           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )
    *           and a( 3, 1 ) respectively, and so on.
    *           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, K, KK, KX, KY
          COMPLEX            TEMP1, TEMP2
    *     ..
    *     .. External Functions ..
          LOGICAL            LSAME
          EXTERNAL           LSAME
    *     ..
    *     .. External Subroutines ..
          EXTERNAL           XERBLA
    *     ..
    *     .. 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( INCX.EQ.0 ) THEN
             INFO = 6
          ELSE IF( INCY.EQ.0 ) THEN
             INFO = 9
          END IF
          IF( INFO.NE.0 ) THEN
             CALL XERBLA( 'CSPMV ', 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 the array AP
    *     are accessed sequentially with one pass through AP.
    *
    *     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
          KK = 1
          IF( LSAME( UPLO, 'U' ) ) THEN
    *
    *        Form  y  when AP contains the upper triangle.
    *
             IF( ( INCX.EQ.1 ) .AND. ( INCY.EQ.1 ) ) THEN
                DO 60 J = 1, N
                   TEMP1 = ALPHA*X( J )
                   TEMP2 = ZERO
                   K = KK
                   DO 50 I = 1, J - 1
                      Y( I ) = Y( I ) + TEMP1*AP( K )
                      TEMP2 = TEMP2 + AP( K )*X( I )
                      K = K + 1
       50          CONTINUE
                   Y( J ) = Y( J ) + TEMP1*AP( KK+J-1 ) + ALPHA*TEMP2
                   KK = KK + J
       60       CONTINUE
             ELSE
                JX = KX
                JY = KY
                DO 80 J = 1, N
                   TEMP1 = ALPHA*X( JX )
                   TEMP2 = ZERO
                   IX = KX
                   IY = KY
                   DO 70 K = KK, KK + J - 2
                      Y( IY ) = Y( IY ) + TEMP1*AP( K )
                      TEMP2 = TEMP2 + AP( K )*X( IX )
                      IX = IX + INCX
                      IY = IY + INCY
       70          CONTINUE
                   Y( JY ) = Y( JY ) + TEMP1*AP( KK+J-1 ) + ALPHA*TEMP2
                   JX = JX + INCX
                   JY = JY + INCY
                   KK = KK + J
       80       CONTINUE
             END IF
          ELSE
    *
    *        Form  y  when AP contains the 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*AP( KK )
                   K = KK + 1
                   DO 90 I = J + 1, N
                      Y( I ) = Y( I ) + TEMP1*AP( K )
                      TEMP2 = TEMP2 + AP( K )*X( I )
                      K = K + 1
       90          CONTINUE
                   Y( J ) = Y( J ) + ALPHA*TEMP2
                   KK = KK + ( N-J+1 )
      100       CONTINUE
             ELSE
                JX = KX
                JY = KY
                DO 120 J = 1, N
                   TEMP1 = ALPHA*X( JX )
                   TEMP2 = ZERO
                   Y( JY ) = Y( JY ) + TEMP1*AP( KK )
                   IX = JX
                   IY = JY
                   DO 110 K = KK + 1, KK + N - J
                      IX = IX + INCX
                      IY = IY + INCY
                      Y( IY ) = Y( IY ) + TEMP1*AP( K )
                      TEMP2 = TEMP2 + AP( K )*X( IX )
      110          CONTINUE
                   Y( JY ) = Y( JY ) + ALPHA*TEMP2
                   JX = JX + INCX
                   JY = JY + INCY
                   KK = KK + ( N-J+1 )
      120       CONTINUE
             END IF
          END IF
    *
          RETURN
    *
    *     End of CSPMV
    *
          END