stdlib_ssbmv Subroutine

     pure subroutine stdlib_ssbmv(uplo,n,k,alpha,a,lda,x,incx,beta,y,incy)
     !! SSBMV 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 band matrix, with k super-diagonals.
        ! -- reference blas level2 routine --
        ! -- reference blas is a software package provided by univ. of tennessee,    --
        ! -- univ. of california berkeley, univ. of colorado denver and nag ltd..--
           ! Scalar Arguments 
           real(sp), intent(in) :: alpha, beta
           integer(ilp), intent(in) :: incx, incy, k, lda, n
           character, intent(in) :: uplo
           ! Array Arguments 
           real(sp), intent(in) :: a(lda,*), x(*)
           real(sp), intent(inout) :: y(*)
        ! =====================================================================
           
           ! Local Scalars 
           real(sp) :: temp1, temp2
           integer(ilp) :: i, info, ix, iy, j, jx, jy, kplus1, kx, ky, l
           ! Intrinsic Functions 
           intrinsic :: max,min
           ! test the input parameters.
           info = 0
           if (.not.stdlib_lsame(uplo,'U') .and. .not.stdlib_lsame(uplo,'L')) then
               info = 1
           else if (n<0) then
               info = 2
           else if (k<0) then
               info = 3
           else if (lda< (k+1)) then
               info = 6
           else if (incx==0) then
               info = 8
           else if (incy==0) then
               info = 11
           end if
           if (info/=0) then
               call stdlib_xerbla('SSBMV ',info)
               return
           end if
           ! quick return if possible.
           if ((n==0) .or. ((alpha==zero).and. (beta==one))) return
           ! set up the start points in  x  and  y.
           if (incx>0) then
               kx = 1
           else
               kx = 1 - (n-1)*incx
           end if
           if (incy>0) then
               ky = 1
           else
               ky = 1 - (n-1)*incy
           end if
           ! start the operations. in this version the elements of the array a
           ! are accessed sequentially with one pass through a.
           ! first form  y := beta*y.
           if (beta/=one) then
               if (incy==1) then
                   if (beta==zero) then
                       do i = 1,n
                           y(i) = zero
                       end do
                   else
                       do i = 1,n
                           y(i) = beta*y(i)
                       end do
                   end if
               else
                   iy = ky
                   if (beta==zero) then
                       do i = 1,n
                           y(iy) = zero
                           iy = iy + incy
                       end do
                   else
                       do i = 1,n
                           y(iy) = beta*y(iy)
                           iy = iy + incy
                       end do
                   end if
               end if
           end if
           if (alpha==zero) return
           if (stdlib_lsame(uplo,'U')) then
              ! form  y  when upper triangle of a is stored.
               kplus1 = k + 1
               if ((incx==1) .and. (incy==1)) then
                   do j = 1,n
                       temp1 = alpha*x(j)
                       temp2 = zero
                       l = kplus1 - j
                       do i = max(1,j-k),j - 1
                           y(i) = y(i) + temp1*a(l+i,j)
                           temp2 = temp2 + a(l+i,j)*x(i)
                       end do
                       y(j) = y(j) + temp1*a(kplus1,j) + alpha*temp2
                   end do
               else
                   jx = kx
                   jy = ky
                   do j = 1,n
                       temp1 = alpha*x(jx)
                       temp2 = zero
                       ix = kx
                       iy = ky
                       l = kplus1 - j
                       do i = max(1,j-k),j - 1
                           y(iy) = y(iy) + temp1*a(l+i,j)
                           temp2 = temp2 + a(l+i,j)*x(ix)
                           ix = ix + incx
                           iy = iy + incy
                       end do
                       y(jy) = y(jy) + temp1*a(kplus1,j) + alpha*temp2
                       jx = jx + incx
                       jy = jy + incy
                       if (j>k) then
                           kx = kx + incx
                           ky = ky + incy
                       end if
                   end do
               end if
           else
              ! form  y  when lower triangle of a is stored.
               if ((incx==1) .and. (incy==1)) then
                   do j = 1,n
                       temp1 = alpha*x(j)
                       temp2 = zero
                       y(j) = y(j) + temp1*a(1,j)
                       l = 1 - j
                       do i = j + 1,min(n,j+k)
                           y(i) = y(i) + temp1*a(l+i,j)
                           temp2 = temp2 + a(l+i,j)*x(i)
                       end do
                       y(j) = y(j) + alpha*temp2
                   end do
               else
                   jx = kx
                   jy = ky
                   do j = 1,n
                       temp1 = alpha*x(jx)
                       temp2 = zero
                       y(jy) = y(jy) + temp1*a(1,j)
                       l = 1 - j
                       ix = jx
                       iy = jy
                       do i = j + 1,min(n,j+k)
                           ix = ix + incx
                           iy = iy + incy
                           y(iy) = y(iy) + temp1*a(l+i,j)
                           temp2 = temp2 + a(l+i,j)*x(ix)
                       end do
                       y(jy) = y(jy) + alpha*temp2
                       jx = jx + incx
                       jy = jy + incy
                   end do
               end if
           end if
           return
     end subroutine stdlib_ssbmv