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SUBROUTINE DSPMV(UPLO,N,ALPHA,AP,X,INCX,BETA,Y,INCY)* .. Scalar Arguments .. DOUBLE PRECISION ALPHA,BETA INTEGER INCX,INCY,N CHARACTER UPLO* ..* .. Array Arguments .. DOUBLE PRECISION AP(*),X(*),Y(*)* ..** Purpose* =======** DSPMV 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 - 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 - 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.** AP - DOUBLE PRECISION array of 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 - 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.** Further Details* ===============** 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,K,KK,KX,KY* ..* .. External Functions .. LOGICAL LSAME EXTERNAL LSAME* ..* .. External Subroutines .. EXTERNAL XERBLA* ..** 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('DSPMV ',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 DSPMV .* END
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