263 lines
8.0 KiB
Fortran
263 lines
8.0 KiB
Fortran
SUBROUTINE DSPMVF( UPLO, N, ALPHA, AP, X, INCX, BETA, Y, INCY )
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* .. Scalar Arguments ..
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DOUBLE PRECISION ALPHA, BETA
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INTEGER INCX, INCY, N
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CHARACTER*1 UPLO
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* .. Array Arguments ..
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DOUBLE PRECISION AP( * ), X( * ), Y( * )
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* ..
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*
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* Purpose
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* =======
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*
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* DSPMV performs the matrix-vector operation
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*
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* y := alpha*A*x + beta*y,
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*
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* where alpha and beta are scalars, x and y are n element vectors and
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* A is an n by n symmetric matrix, supplied in packed form.
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*
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* Parameters
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* ==========
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*
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* UPLO - CHARACTER*1.
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* On entry, UPLO specifies whether the upper or lower
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* triangular part of the matrix A is supplied in the packed
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* array AP as follows:
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*
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* UPLO = 'U' or 'u' The upper triangular part of A is
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* supplied in AP.
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*
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* UPLO = 'L' or 'l' The lower triangular part of A is
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* supplied in AP.
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*
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* Unchanged on exit.
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*
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* N - INTEGER.
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* On entry, N specifies the order of the matrix A.
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* N must be at least zero.
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* Unchanged on exit.
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*
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* ALPHA - DOUBLE PRECISION.
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* On entry, ALPHA specifies the scalar alpha.
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* Unchanged on exit.
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*
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* AP - DOUBLE PRECISION array of DIMENSION at least
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* ( ( n*( n + 1 ) )/2 ).
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* Before entry with UPLO = 'U' or 'u', the array AP must
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* contain the upper triangular part of the symmetric matrix
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* packed sequentially, column by column, so that AP( 1 )
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* contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
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* and a( 2, 2 ) respectively, and so on.
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* Before entry with UPLO = 'L' or 'l', the array AP must
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* contain the lower triangular part of the symmetric matrix
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* packed sequentially, column by column, so that AP( 1 )
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* contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )
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* and a( 3, 1 ) respectively, and so on.
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* Unchanged on exit.
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*
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* X - DOUBLE PRECISION array of dimension at least
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* ( 1 + ( n - 1 )*abs( INCX ) ).
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* Before entry, the incremented array X must contain the n
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* element vector x.
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* Unchanged on exit.
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*
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* INCX - INTEGER.
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* On entry, INCX specifies the increment for the elements of
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* X. INCX must not be zero.
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* Unchanged on exit.
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*
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* BETA - DOUBLE PRECISION.
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* On entry, BETA specifies the scalar beta. When BETA is
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* supplied as zero then Y need not be set on input.
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* Unchanged on exit.
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*
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* Y - DOUBLE PRECISION array of dimension at least
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* ( 1 + ( n - 1 )*abs( INCY ) ).
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* Before entry, the incremented array Y must contain the n
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* element vector y. On exit, Y is overwritten by the updated
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* vector y.
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*
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* INCY - INTEGER.
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* On entry, INCY specifies the increment for the elements of
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* Y. INCY must not be zero.
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* Unchanged on exit.
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*
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*
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* Level 2 Blas routine.
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*
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* -- Written on 22-October-1986.
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* Jack Dongarra, Argonne National Lab.
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* Jeremy Du Croz, Nag Central Office.
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* Sven Hammarling, Nag Central Office.
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* Richard Hanson, Sandia National Labs.
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*
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*
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* .. Parameters ..
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DOUBLE PRECISION ONE , ZERO
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PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
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* .. Local Scalars ..
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DOUBLE PRECISION TEMP1, TEMP2
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INTEGER I, INFO, IX, IY, J, JX, JY, K, KK, KX, KY
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* .. External Functions ..
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LOGICAL LSAME
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EXTERNAL LSAME
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* .. External Subroutines ..
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EXTERNAL XERBLA
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* ..
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* .. Executable Statements ..
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*
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* Test the input parameters.
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*
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INFO = 0
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IF ( .NOT.LSAME( UPLO, 'U' ).AND.
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$ .NOT.LSAME( UPLO, 'L' ) )THEN
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INFO = 1
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ELSE IF( N.LT.0 )THEN
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INFO = 2
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ELSE IF( INCX.EQ.0 )THEN
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INFO = 6
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ELSE IF( INCY.EQ.0 )THEN
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INFO = 9
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END IF
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IF( INFO.NE.0 )THEN
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CALL XERBLA( 'DSPMV ', INFO )
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RETURN
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END IF
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*
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* Quick return if possible.
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*
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IF( ( N.EQ.0 ).OR.( ( ALPHA.EQ.ZERO ).AND.( BETA.EQ.ONE ) ) )
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$ RETURN
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*
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* Set up the start points in X and Y.
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*
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IF( INCX.GT.0 )THEN
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KX = 1
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ELSE
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KX = 1 - ( N - 1 )*INCX
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END IF
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IF( INCY.GT.0 )THEN
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KY = 1
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ELSE
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KY = 1 - ( N - 1 )*INCY
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END IF
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*
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* Start the operations. In this version the elements of the array AP
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* are accessed sequentially with one pass through AP.
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*
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* First form y := beta*y.
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*
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IF( BETA.NE.ONE )THEN
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IF( INCY.EQ.1 )THEN
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IF( BETA.EQ.ZERO )THEN
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DO 10, I = 1, N
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Y( I ) = ZERO
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10 CONTINUE
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ELSE
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DO 20, I = 1, N
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Y( I ) = BETA*Y( I )
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20 CONTINUE
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END IF
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ELSE
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IY = KY
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IF( BETA.EQ.ZERO )THEN
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DO 30, I = 1, N
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Y( IY ) = ZERO
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IY = IY + INCY
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30 CONTINUE
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ELSE
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DO 40, I = 1, N
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Y( IY ) = BETA*Y( IY )
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IY = IY + INCY
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40 CONTINUE
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END IF
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END IF
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END IF
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IF( ALPHA.EQ.ZERO )
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$ RETURN
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KK = 1
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IF( LSAME( UPLO, 'U' ) )THEN
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*
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* Form y when AP contains the upper triangle.
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*
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IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN
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DO 60, J = 1, N
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TEMP1 = ALPHA*X( J )
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TEMP2 = ZERO
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K = KK
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DO 50, I = 1, J - 1
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Y( I ) = Y( I ) + TEMP1*AP( K )
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TEMP2 = TEMP2 + AP( K )*X( I )
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K = K + 1
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50 CONTINUE
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Y( J ) = Y( J ) + TEMP1*AP( KK + J - 1 ) + ALPHA*TEMP2
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KK = KK + J
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60 CONTINUE
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ELSE
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JX = KX
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JY = KY
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DO 80, J = 1, N
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TEMP1 = ALPHA*X( JX )
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TEMP2 = ZERO
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IX = KX
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IY = KY
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DO 70, K = KK, KK + J - 2
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Y( IY ) = Y( IY ) + TEMP1*AP( K )
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TEMP2 = TEMP2 + AP( K )*X( IX )
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IX = IX + INCX
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IY = IY + INCY
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70 CONTINUE
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Y( JY ) = Y( JY ) + TEMP1*AP( KK + J - 1 ) + ALPHA*TEMP2
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JX = JX + INCX
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JY = JY + INCY
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KK = KK + J
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80 CONTINUE
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END IF
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ELSE
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*
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* Form y when AP contains the lower triangle.
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*
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IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN
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DO 100, J = 1, N
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TEMP1 = ALPHA*X( J )
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TEMP2 = ZERO
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Y( J ) = Y( J ) + TEMP1*AP( KK )
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K = KK + 1
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DO 90, I = J + 1, N
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Y( I ) = Y( I ) + TEMP1*AP( K )
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TEMP2 = TEMP2 + AP( K )*X( I )
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K = K + 1
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90 CONTINUE
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Y( J ) = Y( J ) + ALPHA*TEMP2
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KK = KK + ( N - J + 1 )
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100 CONTINUE
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ELSE
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JX = KX
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JY = KY
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DO 120, J = 1, N
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TEMP1 = ALPHA*X( JX )
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TEMP2 = ZERO
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Y( JY ) = Y( JY ) + TEMP1*AP( KK )
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IX = JX
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IY = JY
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DO 110, K = KK + 1, KK + N - J
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IX = IX + INCX
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IY = IY + INCY
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Y( IY ) = Y( IY ) + TEMP1*AP( K )
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TEMP2 = TEMP2 + AP( K )*X( IX )
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110 CONTINUE
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Y( JY ) = Y( JY ) + ALPHA*TEMP2
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JX = JX + INCX
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JY = JY + INCY
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KK = KK + ( N - J + 1 )
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120 CONTINUE
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END IF
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END IF
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*
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RETURN
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*
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* End of DSPMV .
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*
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END
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