dspmvf.f

SUBROUTINEDSPMVF( UPLO, N, ALPHA, AP, X, INCX, BETA, Y, INCY )
* .. Scalar Arguments ..
DOUBLE PRECISION ALPHA, BETA
INTEGER INCX, INCY, N
CHARACTER*1 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.
*
* Parameters
* ==========
*
* 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.
*
*
* 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
* ..
* .. Executable Statements ..
*
* Test the input parameters.
*
 INFO =0
IF ( .NOT.LSAME( UPLO, 'U' ).AND.
 $ .NOT.LSAME( UPLO, 'L' ) )THEN
 INFO =1
ELSEIF( N.LT.0 )THEN
 INFO =2
ELSEIF( INCX.EQ.0 )THEN
 INFO =6
ELSEIF( 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
DO10, I =1, N
 Y( I ) = ZERO
10CONTINUE
ELSE
DO20, I =1, N
 Y( I ) = BETA*Y( I )
20CONTINUE
END IF
ELSE
 IY = KY
IF( BETA.EQ.ZERO )THEN
DO30, I =1, N
 Y( IY ) = ZERO
 IY = IY + INCY
30CONTINUE
ELSE
DO40, I =1, N
 Y( IY ) = BETA*Y( IY )
 IY = IY + INCY
40CONTINUE
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
DO60, J =1, N
 TEMP1 = ALPHA*X( J )
 TEMP2 = ZERO
 K = KK
DO50, I =1, J -1
 Y( I ) = Y( I ) + TEMP1*AP( K )
 TEMP2 = TEMP2 + AP( K )*X( I )
 K = K +1
50CONTINUE
 Y( J ) = Y( J ) + TEMP1*AP( KK + J -1 ) + ALPHA*TEMP2
 KK = KK + J
60CONTINUE
ELSE
 JX = KX
 JY = KY
DO80, J =1, N
 TEMP1 = ALPHA*X( JX )
 TEMP2 = ZERO
 IX = KX
 IY = KY
DO70, K = KK, KK + J -2
 Y( IY ) = Y( IY ) + TEMP1*AP( K )
 TEMP2 = TEMP2 + AP( K )*X( IX )
 IX = IX + INCX
 IY = IY + INCY
70CONTINUE
 Y( JY ) = Y( JY ) + TEMP1*AP( KK + J -1 ) + ALPHA*TEMP2
 JX = JX + INCX
 JY = JY + INCY
 KK = KK + J
80CONTINUE
END IF
ELSE
*
* Form y when AP contains the lower triangle.
*
IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN
DO100, J =1, N
 TEMP1 = ALPHA*X( J )
 TEMP2 = ZERO
 Y( J ) = Y( J ) + TEMP1*AP( KK )
 K = KK +1
DO90, I = J +1, N
 Y( I ) = Y( I ) + TEMP1*AP( K )
 TEMP2 = TEMP2 + AP( K )*X( I )
 K = K +1
90CONTINUE
 Y( J ) = Y( J ) + ALPHA*TEMP2
 KK = KK + ( N - J +1 )
100CONTINUE
ELSE
 JX = KX
 JY = KY
DO120, J =1, N
 TEMP1 = ALPHA*X( JX )
 TEMP2 = ZERO
 Y( JY ) = Y( JY ) + TEMP1*AP( KK )
 IX = JX
 IY = JY
DO110, 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 )
110CONTINUE
 Y( JY ) = Y( JY ) + ALPHA*TEMP2
 JX = JX + INCX
 JY = JY + INCY
 KK = KK + ( N - J +1 )
120CONTINUE
END IF
END IF
*
RETURN
*
* End of DSPMV .
*
END