mod_interpolation.t

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module mod_interpolation
  use mod_global_parameters
  implicit none
 
contains
 
  subroutine interp_linear(x_table,y_table,n_table,x_itp,y_itp,n_itp)
    ! linear interpolation
    ! 1D method
 
    integer :: n_table,n_itp
    double precision :: x_table(n_table),y_table(n_table)
    double precision :: x_itp(n_itp),y_itp(n_itp)
 
    integer :: i,j
 
    !if (x_table(1)>x_itp(1) .or. x_table(n_table)<x_itp(n_itp)) then
    !  call mpistop("out of interpolation table")
    !endif
 
    do i=1,n_itp
      if(x_itp(i)<x_table(1)) then
        y_itp(i)=y_table(1)
        exit
      end if
      if(x_itp(i)>=x_table(n_table)) then
        y_itp(i)=y_table(n_table)
        exit
      end if
      loopt: do j=1,n_table-1
        if (x_itp(i)>=x_table(j) .and. x_itp(i)<x_table(j+1)) then
          y_itp(i)=y_table(j) + (x_itp(i)-x_table(j))*&
                   (y_table(j+1)-y_table(j))/(x_table(j+1)-x_table(j))
          exit loopt
        endif
      enddo loopt
    enddo
 
  end subroutine interp_linear
 
  subroutine interp_cubic_spline(x_table,y_table,n_table,x_itp,y_itp,n_itp)
    ! interpolation function fi=ai+bi*(x-xi)+ci*(x-xi)^2+di*(x-xi)^3
    ! first order derivative and second order derivative is continous 
    ! 1D method
 
    integer :: n_table,n_itp
    double precision :: x_table(n_table),y_table(n_table)
    double precision :: x_itp(n_itp),y_itp(n_itp)
 
    double precision :: at(n_table),bt(n_table),ct(n_table),dt(n_table)
    double precision :: dxi
    integer :: i,j
 
    if (x_table(1)>x_itp(1) .or. x_table(n_table)<x_itp(n_itp)) then
      call mpistop("out of interpolation table")
    endif
 
    call get_cubic_para(x_table,y_table,at,bt,ct,dt,n_table)
 
    do i=1,n_itp
      loopt: do j=1,n_table-1
        if (x_itp(i)>=x_table(j) .and. x_itp(i)<x_table(j+1)) then
          dxi=x_itp(i)-x_table(j)
          y_itp(i)=at(j)+bt(j)*dxi+ct(j)*dxi**2+dt(j)*dxi**3
          exit loopt
        endif
      enddo loopt
    enddo
 
    if (x_itp(n_itp)==x_table(n_table)) y_itp(n_itp)=y_table(n_table)
 
  end subroutine interp_cubic_spline
 
  subroutine get_cubic_para(xi,yi,ai,bi,ci,di,ni)
  ! get parameters for interpolation
 
    integer :: ni,i
    double precision :: xi(ni),yi(ni)
    double precision :: ai(ni),bi(ni),ci(ni),di(ni)
 
    double precision :: matrix1(ni,ni),ri1(ni)
    double precision :: matrix2(ni,ni),ri2(ni)
    double precision :: mi(ni),hi(ni)
 
    ! build equations
    matrix1=0.d0
    matrix2=0.d0
 
    do i=1,ni-1
      hi(i)=xi(i+1)-xi(i)
    enddo
 
    matrix1(1,1)=1.0
    matrix1(ni,ni)=1.0
    ri1(1)=0.d0
    ri1(ni)=0.d0
    do i=2,ni-1
      matrix1(i-1,i)=hi(i-1)
      matrix1(i,i)=2*(hi(i-1)+hi(i))
      matrix1(i+1,i)=hi(i)
      ri1(i)=(yi(i+1)-yi(i))/hi(i)-(yi(i)-yi(i-1))/hi(i-1)
    enddo
    ri1=ri1*6
 
    ! solve equations
    do i=1,ni
      matrix2(i,i)=1.d0
    enddo
 
    matrix2(2,1)=matrix1(2,1)/matrix1(1,1)
    ri2(1)=ri1(1)/matrix1(1,1)
 
    do i=2,ni-1
      matrix2(i+1,i)=matrix1(i+1,i)/(matrix1(i,i)-matrix1(i-1,i)*matrix2(i,i-1))
    enddo
 
    do i=2,ni
      ri2(i)=ri1(i)-matrix1(i-1,i)*ri2(i-1)
      ri2(i)=ri2(i)/(matrix1(i,i)-matrix1(i-1,i)*matrix2(i,i-1))
    enddo
 
    mi(ni)=ri2(ni)
    do i=ni-1,1,-1
      mi(i)=ri2(i)-matrix2(i+1,i)*mi(i+1)
    enddo
 
    ! get parameters for interpolation
    ai=yi
    ci=mi(1:ni)
    do i=1,ni-1
      bi(i)=(yi(i+1)-yi(i))/hi(i)-hi(i)*mi(i)/2.0-hi(i)*(mi(i+1)-mi(i))/6.0
      di(i)=(mi(i+1)-mi(i))/(6.0*hi(i))
    enddo
 
  end subroutine get_cubic_para
 
  subroutine get_interp_factor_linear(xc,xp,factor)
    ! get factor for linear interpolation
    ! multi-D method
   
    double precision :: xc(0:1^D&,1:ndim),xp(1:ndim),factor(0:1^D&)
    integer :: ix^D
    double precision :: dxc^D,xd^D
 
    ^d&dxc^d=xc(1^dd&,^d)-xc(0^dd&,^d)\
    ^d&xd^d=(xp(^d)-xc(0^dd&,^d))/dxc^d\
    ! interpolation factor
    {do ix^d=0,1\}
      factor(ix^d)={abs(1-ix^d-xd^d)*}
    {enddo\}
 
  end subroutine get_interp_factor_linear
 
  subroutine interp_linear_multid(xc,xp,wc,wp,nwc)
    ! get point values from nearby cells via linear interpolation
    ! multi-D method
 
    integer :: nwc
    double precision :: xc(0:1^D&,1:ndim),xp(1:ndim)
    double precision :: wc(0:1^D&,1:nwc),wp(1:nwc)
 
    integer :: ix^D,iw
    double precision :: factor(0:1^D&)
 
    call get_interp_factor_linear(xc,xp,factor)    
 
    wp=0.d0
    do iw=1,nwc
      {do ix^db=0,1\}
        wp(iw)=wp(iw)+wc(ix^d,iw)*factor(ix^d)
      {enddo\}
    enddo
 
  end subroutine interp_linear_multid
 
  subroutine interp_from_grid_linear(igrid,xp,wp)
    ! get point values from given grid via linear interpolation
    ! multi-D method
    
    integer :: igrid
    double precision :: xp(1:ndim),wp(1:nw)
 
    double precision :: dxb^D,xb^L
    integer :: inblock,ixO^L,j
    integer :: ixb^D,ixi^D
    double precision :: xc(0:1^D&,1:ndim),wc(0:1^D&,nw)
 
    ! block/grid boundaries
    ^d&xbmin^d=rnode(rpxmin^d_,igrid)\
    ^d&xbmax^d=rnode(rpxmax^d_,igrid)\
 
    ! whether or not next point is in this block/grid
    inblock=0
    {if (xp(^d)>=xbmin^d .and. xp(^d)<xbmax^d) inblock=inblock+1\}
    if (inblock/=ndim) then
      call mpistop('Interpolation error: given point is not in given grid')
    endif
 
    ! cell indexes for the point
    ^d&dxb^d=rnode(rpdx^d_,igrid)\
    ^d&ixomin^d=ixmlo^d\
    ^d&ixb^d=floor((xp(^d)-ps(igrid)%x(ixomin^dd,^d))/dxb^d)+ixomin^d\
 
    ! nearby cells for interpolation
    {do ixi^d=0,1\}
      xc(ixi^d,:)=ps(igrid)%x(ixb^d+ixi^d,:)
      wc(ixi^d,:)=ps(igrid)%w(ixb^d+ixi^d,:)
    {enddo\}
 
    call interp_linear_multid(xc,xp,wc,wp,nw)
 
  end subroutine interp_from_grid_linear
 
end module mod_interpolation