sspmv(3f) - [BLAS:SINGLE_BLAS_LEVEL2] SY:=alpha*A*SX+beta*SY, A a packed symmetric matrix.
subroutine sspmv(uplo,n,alpha,ap,x,incx,beta,y,incy)
.. Scalar Arguments ..
real,intent(in) :: alpha,beta
integer,intent(in) :: incx,incy,n
character,intent(in) :: uplo
..
.. Array Arguments ..
real,intent(in) :: ap(*),x(*)
real,intent(inout) :: y(*)
..
SSPMV 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.
UPLO
UPLO is 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.
N
N is INTEGER
On entry, N specifies the order of the matrix A.
N must be at least zero.
ALPHA
ALPHA is REAL
On entry, ALPHA specifies the scalar alpha.
AP
AP is REAL array, 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.
X
X is REAL array, dimension at least
( 1 + ( n - 1 )*abs( INCX ) ).
Before entry, the incremented array X must contain the n
element vector x.
INCX
INCX is INTEGER
On entry, INCX specifies the increment for the elements of
X. INCX must not be zero.
BETA
BETA is REAL
On entry, BETA specifies the scalar beta. When BETA is
supplied as zero then Y need not be set on input.
Y
Y is REAL array, 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
INCY is INTEGER
On entry, INCY specifies the increment for the elements of
Y. INCY must not be zero.
date:December 2016
FURTHER DETAILS
Level 2 Blas routine. The vector and matrix arguments are not referenced when N = 0, or M = 0
– 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.
Online html documentation available at
http://www.netlib.org/lapack/explore-html/
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| character(len=1), | intent(in) | :: | uplo | |||
| integer, | intent(in) | :: | n | |||
| real, | intent(in) | :: | alpha | |||
| real, | intent(in) | :: | ap(*) | |||
| real, | intent(in) | :: | x(*) | |||
| integer, | intent(in) | :: | incx | |||
| real, | intent(in) | :: | beta | |||
| real, | intent(inout) | :: | y(*) | |||
| integer, | intent(in) | :: | incy |
| Type | Visibility | Attributes | Name | Initial | |||
|---|---|---|---|---|---|---|---|
| integer, | public | :: | i | ||||
| integer, | public | :: | info | ||||
| integer, | public | :: | ix | ||||
| integer, | public | :: | iy | ||||
| integer, | public | :: | j | ||||
| integer, | public | :: | jx | ||||
| integer, | public | :: | jy | ||||
| integer, | public | :: | k | ||||
| integer, | public | :: | kk | ||||
| integer, | public | :: | kx | ||||
| integer, | public | :: | ky | ||||
| real, | public, | parameter | :: | one | = | 1.0e+0 | |
| real, | public | :: | temp1 | ||||
| real, | public | :: | temp2 | ||||
| real, | public, | parameter | :: | zero | = | 0.0e+0 |
subroutine sspmv(uplo,n,alpha,ap,x,incx,beta,y,incy)
implicit none
!
! -- Reference BLAS level2 routine (version 3.7.0) --
! -- Reference BLAS is a software package provided by Univ. of Tennessee, --
! -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! December 2016
!
! .. Scalar Arguments ..
real,intent(in) :: alpha,beta
integer,intent(in) :: incx,incy,n
character,intent(in) :: uplo
! ..
! .. Array Arguments ..
real,intent(in) :: ap(*),x(*)
real,intent(inout) :: y(*)
! ..
!
! =====================================================================
!
! .. Parameters ..
real one,zero
parameter (one=1.0e+0,zero=0.0e+0)
! ..
! .. Local Scalars ..
real temp1,temp2
integer i,info,ix,iy,j,jx,jy,k,kk,kx,ky
! ..
! .. External Functions .. LOGICAL LSAME
! ..
! .. External Subroutines .. EXTERNAL XERBLA
! ..
!
! 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
endif
if (info.ne.0) then
call xerbla('SSPMV ',info)
return
endif
!
! 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
endif
if (incy.gt.0) then
ky = 1
else
ky = 1 - (n-1)*incy
endif
!
! 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
y(1:n) = zero
else
y(1:n) = beta*y(1:n)
endif
else
iy = ky
if (beta.eq.zero) then
do i = 1,n
y(iy) = zero
iy = iy + incy
enddo
else
do i = 1,n
y(iy) = beta*y(iy)
iy = iy + incy
enddo
endif
endif
endif
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 j = 1,n
temp1 = alpha*x(j)
temp2 = zero
k = kk
do i = 1,j - 1
y(i) = y(i) + temp1*ap(k)
temp2 = temp2 + ap(k)*x(i)
k = k + 1
enddo
y(j) = y(j) + temp1*ap(kk+j-1) + alpha*temp2
kk = kk + j
enddo
else
jx = kx
jy = ky
do j = 1,n
temp1 = alpha*x(jx)
temp2 = zero
ix = kx
iy = ky
do k = kk,kk + j - 2
y(iy) = y(iy) + temp1*ap(k)
temp2 = temp2 + ap(k)*x(ix)
ix = ix + incx
iy = iy + incy
enddo
y(jy) = y(jy) + temp1*ap(kk+j-1) + alpha*temp2
jx = jx + incx
jy = jy + incy
kk = kk + j
enddo
endif
else
!
! Form y when AP contains the lower triangle.
!
if ((incx.eq.1) .and. (incy.eq.1)) then
do j = 1,n
temp1 = alpha*x(j)
temp2 = zero
y(j) = y(j) + temp1*ap(kk)
k = kk + 1
do i = j + 1,n
y(i) = y(i) + temp1*ap(k)
temp2 = temp2 + ap(k)*x(i)
k = k + 1
enddo
y(j) = y(j) + alpha*temp2
kk = kk + (n-j+1)
enddo
else
jx = kx
jy = ky
do j = 1,n
temp1 = alpha*x(jx)
temp2 = zero
y(jy) = y(jy) + temp1*ap(kk)
ix = jx
iy = jy
do 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)
enddo
y(jy) = y(jy) + alpha*temp2
jx = jx + incx
jy = jy + incy
kk = kk + (n-j+1)
enddo
endif
endif
end subroutine sspmv