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