stdlib_dtbsv Subroutine

     pure subroutine stdlib_dtbsv(uplo,trans,diag,n,k,a,lda,x,incx)
     !! DTBSV solves one of the systems of equations
     !! A*x = b,   or   A**T*x = b,
     !! where b and x are n element vectors and A is an n by n unit, or
     !! non-unit, upper or lower triangular band matrix, with ( k + 1 )
     !! diagonals.
     !! No test for singularity or near-singularity is included in this
     !! routine. Such tests must be performed before calling this routine.
        ! -- 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 
           integer(ilp), intent(in) :: incx, k, lda, n
           character, intent(in) :: diag, trans, uplo
           ! Array Arguments 
           real(dp), intent(in) :: a(lda,*)
           real(dp), intent(inout) :: x(*)
        ! =====================================================================
           
           ! Local Scalars 
           real(dp) :: temp
           integer(ilp) :: i, info, ix, j, jx, kplus1, kx, l
           logical(lk) :: nounit
           ! 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 (.not.stdlib_lsame(trans,'N') .and. .not.stdlib_lsame(trans,'T') &
                     .and..not.stdlib_lsame(trans,'C')) then
               info = 2
           else if (.not.stdlib_lsame(diag,'U') .and. .not.stdlib_lsame(diag,'N')) then
               info = 3
           else if (n<0) then
               info = 4
           else if (k<0) then
               info = 5
           else if (lda< (k+1)) then
               info = 7
           else if (incx==0) then
               info = 9
           end if
           if (info/=0) then
               call stdlib_xerbla('DTBSV ',info)
               return
           end if
           ! quick return if possible.
           if (n==0) return
           nounit = stdlib_lsame(diag,'N')
           ! set up the start point in x if the increment is not unity. this
           ! will be  ( n - 1 )*incx  too small for descending loops.
           if (incx<=0) then
               kx = 1 - (n-1)*incx
           else if (incx/=1) then
               kx = 1
           end if
           ! start the operations. in this version the elements of a are
           ! accessed by sequentially with one pass through a.
           if (stdlib_lsame(trans,'N')) then
              ! form  x := inv( a )*x.
               if (stdlib_lsame(uplo,'U')) then
                   kplus1 = k + 1
                   if (incx==1) then
                       do j = n,1,-1
                           if (x(j)/=zero) then
                               l = kplus1 - j
                               if (nounit) x(j) = x(j)/a(kplus1,j)
                               temp = x(j)
                               do i = j - 1,max(1,j-k),-1
                                   x(i) = x(i) - temp*a(l+i,j)
                               end do
                           end if
                       end do
                   else
                       kx = kx + (n-1)*incx
                       jx = kx
                       do j = n,1,-1
                           kx = kx - incx
                           if (x(jx)/=zero) then
                               ix = kx
                               l = kplus1 - j
                               if (nounit) x(jx) = x(jx)/a(kplus1,j)
                               temp = x(jx)
                               do i = j - 1,max(1,j-k),-1
                                   x(ix) = x(ix) - temp*a(l+i,j)
                                   ix = ix - incx
                               end do
                           end if
                           jx = jx - incx
                       end do
                   end if
               else
                   if (incx==1) then
                       do j = 1,n
                           if (x(j)/=zero) then
                               l = 1 - j
                               if (nounit) x(j) = x(j)/a(1,j)
                               temp = x(j)
                               do i = j + 1,min(n,j+k)
                                   x(i) = x(i) - temp*a(l+i,j)
                               end do
                           end if
                       end do
                   else
                       jx = kx
                       do j = 1,n
                           kx = kx + incx
                           if (x(jx)/=zero) then
                               ix = kx
                               l = 1 - j
                               if (nounit) x(jx) = x(jx)/a(1,j)
                               temp = x(jx)
                               do i = j + 1,min(n,j+k)
                                   x(ix) = x(ix) - temp*a(l+i,j)
                                   ix = ix + incx
                               end do
                           end if
                           jx = jx + incx
                       end do
                   end if
               end if
           else
              ! form  x := inv( a**t)*x.
               if (stdlib_lsame(uplo,'U')) then
                   kplus1 = k + 1
                   if (incx==1) then
                       do j = 1,n
                           temp = x(j)
                           l = kplus1 - j
                           do i = max(1,j-k),j - 1
                               temp = temp - a(l+i,j)*x(i)
                           end do
                           if (nounit) temp = temp/a(kplus1,j)
                           x(j) = temp
                       end do
                   else
                       jx = kx
                       do j = 1,n
                           temp = x(jx)
                           ix = kx
                           l = kplus1 - j
                           do i = max(1,j-k),j - 1
                               temp = temp - a(l+i,j)*x(ix)
                               ix = ix + incx
                           end do
                           if (nounit) temp = temp/a(kplus1,j)
                           x(jx) = temp
                           jx = jx + incx
                           if (j>k) kx = kx + incx
                       end do
                   end if
               else
                   if (incx==1) then
                       do j = n,1,-1
                           temp = x(j)
                           l = 1 - j
                           do i = min(n,j+k),j + 1,-1
                               temp = temp - a(l+i,j)*x(i)
                           end do
                           if (nounit) temp = temp/a(1,j)
                           x(j) = temp
                       end do
                   else
                       kx = kx + (n-1)*incx
                       jx = kx
                       do j = n,1,-1
                           temp = x(jx)
                           ix = kx
                           l = 1 - j
                           do i = min(n,j+k),j + 1,-1
                               temp = temp - a(l+i,j)*x(ix)
                               ix = ix - incx
                           end do
                           if (nounit) temp = temp/a(1,j)
                           x(jx) = temp
                           jx = jx - incx
                           if ((n-j)>=k) kx = kx - incx
                       end do
                   end if
               end if
           end if
           return
     end subroutine stdlib_dtbsv