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SUBROUTINE DSPMV(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 UPLO |
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* .. |
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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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* Arguments |
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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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* .. |
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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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* .. |
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* .. External Functions .. |
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LOGICAL LSAME |
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EXTERNAL LSAME |
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* .. |
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* .. External Subroutines .. |
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EXTERNAL XERBLA |
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* .. |
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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. .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))) 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) 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 |