cheby.f90

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module cheby
  use krylov, only : ksp_t, ksp_monitor_t
  use precon, only : pc_t
  use ax_product, only : ax_t
  use num_types, only: rp
  use profiler, only : profiler_start_region, profiler_end_region
  use field, only : field_t
  use coefs, only : coef_t
  use mesh, only : mesh_t
  use space, only : space_t
  use gather_scatter, only : gs_t, gs_op_add
  use bc_list, only : bc_list_t
  use schwarz, only : schwarz_t
  use math, only : glsc3, rzero, rone, copy, sub2, cmult2, abscmp, glsc2, &
       add2s1, add2s2, sub3, cmult, add2
  implicit none
  private
 
  type, public, extends(ksp_t) :: cheby_t
     real(kind=rp), allocatable :: d(:)
     real(kind=rp), allocatable :: w(:)
     real(kind=rp), allocatable :: r(:)
     real(kind=rp) :: tha, dlt
     integer :: power_its = 150
     integer :: power_its_refresh = 20
     logical :: warm_start_eigs = .false.
     logical :: eigs_computed = .false.
     real(kind=rp), allocatable :: ev(:)
     logical :: recompute_eigs = .true.
     logical :: zero_initial_guess = .false.
     type(schwarz_t), pointer :: schwarz => null() 
   contains
     procedure, pass(this) :: init => cheby_init
     procedure, pass(this) :: free => cheby_free
     procedure, pass(this) :: solve => cheby_impl
     procedure, pass(this) :: solve_coupled => cheby_solve_coupled
  end type cheby_t
 
contains
 
  subroutine cheby_init(this, n, max_iter, M, rel_tol, abs_tol, monitor)
    class(cheby_t), intent(inout), target :: this
    integer, intent(in) :: max_iter
    class(pc_t), optional, intent(in), target :: M
    integer, intent(in) :: n
    real(kind=rp), optional, intent(in) :: rel_tol
    real(kind=rp), optional, intent(in) :: abs_tol
    logical, optional, intent(in) :: monitor
 
    call this%free()
    allocate(this%d(n))
    allocate(this%w(n))
    allocate(this%r(n))
 
    if (present(m)) then
       this%M => m
    end if
 
    if (present(rel_tol) .and. present(abs_tol) .and. present(monitor)) then
       call this%ksp_init(max_iter, rel_tol, abs_tol, monitor = monitor)
    else if (present(rel_tol) .and. present(abs_tol)) then
       call this%ksp_init(max_iter, rel_tol, abs_tol)
    else if (present(monitor) .and. present(abs_tol)) then
       call this%ksp_init(max_iter, abs_tol = abs_tol, monitor = monitor)
    else if (present(rel_tol) .and. present(monitor)) then
       call this%ksp_init(max_iter, rel_tol, monitor = monitor)
    else if (present(rel_tol)) then
       call this%ksp_init(max_iter, rel_tol = rel_tol)
    else if (present(abs_tol)) then
       call this%ksp_init(max_iter, abs_tol = abs_tol)
    else if (present(monitor)) then
       call this%ksp_init(max_iter, monitor = monitor)
    else
       call this%ksp_init(max_iter)
    end if
 
  end subroutine cheby_init
 
  subroutine cheby_free(this)
    class(cheby_t), intent(inout) :: this
    if (allocated(this%d)) then
       deallocate(this%d)
    end if
 
    if (allocated(this%w)) then
       deallocate(this%w)
    end if
 
    if (allocated(this%r)) then
       deallocate(this%r)
    end if
    if (allocated(this%ev)) then
       deallocate(this%ev)
    end if
  end subroutine cheby_free
 
  subroutine cheby_power(this, Ax, x, n, coef, blst, gs_h)
    class(cheby_t), intent(inout) :: this
    class(ax_t), intent(in) :: Ax
    type(field_t), intent(inout) :: x
    integer, intent(in) :: n
    type(coef_t), intent(inout) :: coef
    type(bc_list_t), intent(inout) :: blst
    type(gs_t), intent(inout) :: gs_h
    real(kind=rp) :: lam, b, a, rn
    real(kind=rp) :: boost = 1.1_rp
    real(kind=rp) :: lam_factor = 30.0_rp
    real(kind=rp) :: wtw, dtw, dtd
    integer, allocatable :: fixed_seed(:), saved_seed(:)
    integer :: i, rnd_n, its
    logical :: warm
 
    call profiler_start_region('cheby_power')
    warm = this%warm_start_eigs .and. this%eigs_computed .and. &
         allocated(this%ev)
    associate(w => this%w, d => this%d, r => this%r)
 
      if (warm) then
         its = this%power_its_refresh
         call copy(d, this%ev, n)
      else
         its = this%power_its
 
         ! Save current random seed and set a fixed seed
         call random_seed(size = rnd_n)
         allocate(saved_seed(rnd_n))
         allocate(fixed_seed(rnd_n))
         fixed_seed = 3901
         call random_seed(get = saved_seed)
         call random_seed(put = fixed_seed)
 
         do i = 1, n
            call random_number(rn)
            d(i) = rn + 10.0_rp
         end do
 
         ! Restore saved random seed
         call random_seed(put = saved_seed)
 
         call gs_h%op(d, n, gs_op_add)
         call blst%apply(d, n)
      end if
 
      !Power method to get lambda max
      do i = 1, its
         call ax%compute(w, d, coef, x%msh, x%Xh)
         call gs_h%op(w, n, gs_op_add)
         call blst%apply(w, n)
         if (associated(this%schwarz)) then
            call this%schwarz%compute(r, w)
            call copy(w, r, n)
         else
            call this%M%solve(r, w, n)
            call copy(w, r, n)
         end if
 
         wtw = glsc3(w, coef%mult, w, n)
         call cmult2(d, w, 1.0_rp/sqrt(wtw), n)
         call blst%apply(d, n)
      end do
 
      call ax%compute(w, d, coef, x%msh, x%Xh)
      call gs_h%op(w, n, gs_op_add)
      call blst%apply(w, n)
      if (associated(this%schwarz)) then
         call this%schwarz%compute(r, w)
         call copy(w, r, n)
      else
         call this%M%solve(r, w, n)
         call copy(w, r, n)
      end if
 
      dtw = glsc3(d, coef%mult, w, n)
      dtd = glsc3(d, coef%mult, d, n)
      lam = dtw / dtd
      b = lam * boost
      a = lam / lam_factor
      this%tha = (b+a)/2.0_rp
      this%dlt = (b-a)/2.0_rp
 
      if (this%warm_start_eigs) then
         if (.not. allocated(this%ev)) then
            allocate(this%ev(size(this%d)))
         end if
         call copy(this%ev, d, n)
      end if
      this%eigs_computed = .true.
 
      this%recompute_eigs = .false.
    end associate
    call profiler_end_region('cheby_power')
  end subroutine cheby_power
 
  function cheby_solve(this, Ax, x, f, n, coef, blst, gs_h, niter) &
       result(ksp_results)
    class(cheby_t), intent(inout) :: this
    class(ax_t), intent(in) :: ax
    type(field_t), intent(inout) :: x
    integer, intent(in) :: n
    real(kind=rp), dimension(n), intent(in) :: f
    type(coef_t), intent(inout) :: coef
    type(bc_list_t), intent(inout) :: blst
    type(gs_t), intent(inout) :: gs_h
    type(ksp_monitor_t) :: ksp_results
    integer, optional, intent(in) :: niter
    integer :: iter, max_iter
    real(kind=rp) :: a, b, rtr, rnorm, norm_fac
 
    if (this%recompute_eigs) then
       call cheby_power(this, ax, x, n, coef, blst, gs_h)
    end if
 
    if (present(niter)) then
       max_iter = niter
    else
       max_iter = this%max_iter
    end if
    norm_fac = 1.0_rp / sqrt(coef%volume)
 
    associate( w => this%w, r => this%r, d => this%d)
      ! calculate residual
      call copy(r, f, n)
      call ax%compute(w, x%x, coef, x%msh, x%Xh)
      call gs_h%op(w, n, gs_op_add)
      call blst%apply(w, n)
      call sub2(r, w, n)
 
      rtr = glsc3(r, coef%mult, r, n)
      rnorm = sqrt(rtr) * norm_fac
      ksp_results%res_start = rnorm
      ksp_results%res_final = rnorm
      ksp_results%iter = 0
 
      ! First iteration
      call this%M%solve(w, r, n)
      call copy(d, w, n)
      a = 2.0_rp / this%tha
      call add2s2(x%x, d, a, n)! x = x + a*d
 
      ! Rest of the iterations
      do iter = 2, max_iter
         ! calculate residual
         call copy(r, f, n)
         call ax%compute(w, x%x, coef, x%msh, x%Xh)
         call gs_h%op(w, n, gs_op_add)
         call blst%apply(w, n)
         call sub2(r, w, n)
 
         call this%M%solve(w, r, n)
 
         if (iter .eq. 2) then
            b = 0.5_rp * (this%dlt * a)**2
         else
            b = (this%dlt * a / 2.0_rp)**2
         end if
         a = 1.0_rp/(this%tha - b/a)
         call add2s1(d, w, b, n)! d = w + b*d
 
         call add2s2(x%x, d, a, n)! x = x + a*d
      end do
 
      ! calculate residual
      call copy(r, f, n)
      call ax%compute(w, x%x, coef, x%msh, x%Xh)
      call gs_h%op(w, n, gs_op_add)
      call blst%apply(w, n)
      call sub2(r, w, n)
      rtr = glsc3(r, coef%mult, r, n)
      rnorm = sqrt(rtr) * norm_fac
      ksp_results%res_final = rnorm
      ksp_results%iter = iter
      ksp_results%converged = this%is_converged(iter, rnorm)
    end associate
  end function cheby_solve
 
  function cheby_impl(this, Ax, x, f, n, coef, blst, gs_h, niter) &
       result(ksp_results)
    class(cheby_t), intent(inout) :: this
    class(ax_t), intent(in) :: ax
    type(field_t), intent(inout) :: x
    integer, intent(in) :: n
    real(kind=rp), dimension(n), intent(in) :: f
    type(coef_t), intent(inout) :: coef
    type(bc_list_t), intent(inout) :: blst
    type(gs_t), intent(inout) :: gs_h
    type(ksp_monitor_t) :: ksp_results
    integer, optional, intent(in) :: niter
    integer :: iter, max_iter, i
    real(kind=rp) :: a, b, rtr, rnorm, norm_fac
    real(kind=rp) :: rhok, rhokp1, sig1, tmp1, tmp2, inv_tha
 
    if (this%recompute_eigs) then
       call cheby_power(this, ax, x, n, coef, blst, gs_h)
    end if
 
    if (present(niter)) then
       max_iter = niter
    else
       max_iter = this%max_iter
    end if
    norm_fac = 1.0_rp / sqrt(coef%volume)
 
    associate( w => this%w, r => this%r, d => this%d)
      ! calculate residual
      if (.not.this%zero_initial_guess) then
         call ax%compute(w, x%x, coef, x%msh, x%Xh)
         call gs_h%op(w, n, gs_op_add)
         call blst%apply(w, n)
         call sub3(r, f, w, n)
      else
         call copy(r, f, n)
         this%zero_initial_guess = .false.
      end if
 
      ! First iteration
      if (associated(this%schwarz)) then
         call this%schwarz%compute(d, r)
      else
         call this%M%solve(d, r, n)
      end if
 
      inv_tha = 1.0_rp / this%tha
      !OCL NORECURRENCE, NOVREC, NOALIAS
      !DIR$ CONCURRENT
      !DIR$ IVDEP
      !GCC$ ivdep
      !$omp parallel do
      do i = 1, n
         d(i) = inv_tha * d(i)
         x%x(i,1,1,1) = x%x(i,1,1,1) + d(i)
      end do
      !$omp end parallel do
 
      sig1 = this%tha / this%dlt
      rhok = 1.0_rp / sig1
 
      ! Rest of the iterations
      do iter = 2, max_iter
         rhokp1 = 1.0_rp / (2.0_rp * sig1 - rhok)
         tmp1 = rhokp1 * rhok
         tmp2 = 2.0_rp * rhokp1 / this%dlt
         rhok = rhokp1
         ! calculate residual
         call ax%compute(w, x%x, coef, x%msh, x%Xh)
         call gs_h%op(w, n, gs_op_add)
         call blst%apply(w, n)
         call sub3(r, f, w, n)
 
         if (associated(this%schwarz)) then
            call this%schwarz%compute(w, r)
         else
            call this%M%solve(w, r, n)
         end if
         !OCL NORECURRENCE, NOVREC, NOALIAS
         !DIR$ CONCURRENT
         !DIR$ IVDEP
         !GCC$ ivdep
         !$omp parallel do
         do i = 1, n
            d(i) = tmp1 * d(i) + tmp2 * w(i)
            x%x(i,1,1,1) = x%x(i,1,1,1) + d(i)
         end do
         !$omp end parallel do
      end do
 
    end associate
  end function cheby_impl
 
  function cheby_solve_coupled(this, Ax, x, y, z, fx, fy, fz, &
       n, coef, blstx, blsty, blstz, gs_h, niter) result(ksp_results)
    class(cheby_t), intent(inout) :: this
    class(ax_t), intent(in) :: ax
    type(field_t), intent(inout) :: x
    type(field_t), intent(inout) :: y
    type(field_t), intent(inout) :: z
    integer, intent(in) :: n
    real(kind=rp), dimension(n), intent(in) :: fx
    real(kind=rp), dimension(n), intent(in) :: fy
    real(kind=rp), dimension(n), intent(in) :: fz
    type(coef_t), intent(inout) :: coef
    type(bc_list_t), intent(inout) :: blstx
    type(bc_list_t), intent(inout) :: blsty
    type(bc_list_t), intent(inout) :: blstz
    type(gs_t), intent(inout) :: gs_h
    type(ksp_monitor_t), dimension(3) :: ksp_results
    integer, optional, intent(in) :: niter
 
    ksp_results(1) = this%solve(ax, x, fx, n, coef, blstx, gs_h, niter)
    ksp_results(2) = this%solve(ax, y, fy, n, coef, blsty, gs_h, niter)
    ksp_results(3) = this%solve(ax, z, fz, n, coef, blstz, gs_h, niter)
 
  end function cheby_solve_coupled
 
end module cheby