[求助] 有偿求助点云曲面拟合函数接口

　　program Test_SurfaceFitting
      INCLUDE 'link_fnl_shared.h'
      use numerical_libraries
  
      USE surface_fitting_int
      USE rand_int
      USE norm_int

      implicit none

! This is Example 1 for SURFACE_FITTING, tensor product
! B-splines approximation.  Use the function
! exp(-x**2-y**2) on the square (0, 2) x (0, 2) for samples.
! The spline order is "nord" and the number of cells is
! "(ngrid-1)**2".  There are "ndata" data values in the square.

      integer :: i
      integer, parameter :: ngrid=9, nord=4, ndegree=nord-1, &
      nbkpt=ngrid+2*ndegree, ndata = 2000, nvalues=100
      real(kind(1d0)), parameter :: zero=0d0, one=1d0, two=2d0
      real(kind(1d0)), parameter :: TOLERANCE=1d-3
      real(kind(1d0)), target :: spline_data (4, ndata), bkpt(nbkpt), &
             & coeff(ngrid+ndegree-1,ngrid+ndegree-1), delta, sizev, &
             & x(nvalues), y(nvalues), values(nvalues, nvalues)
      real(kind(1d0)), pointer :: pointer_bkpt(:)
      type (d_spline_knots) knotsx, knotsy

! Set Random Number generator seed
                                             
      real(kind(1d0)),parameter::zero_par=0.d0
      real(kind(1d0))::dummy_par(0)
      integer iseed_par,lev_par
      type(d_options)::iopti_par(2)

      iseed_par = 53976279
      iopti_par(1)=d_options(d_rand_gen_generator_seed,zero_par)
      iopti_par(2)=d_options(iseed_par,zero_par)

      call rand_gen(dummy_par,iopt=iopti_par)

! Generate random (x,y) pairs and evaluate the
! example exponential function at these values.   
      spline_data(1:2,:)=two*rand(spline_data(1:2,:))
      spline_data(3,:)=exp(-sum(spline_data(1:2,:)**2,dim=1))
      spline_data(4,:)=one

! Define the knots for the tensor product data fitting problem.
      delta = two/(ngrid-1)
      bkpt(1:ndegree) = zero
      bkpt(nbkpt-ndegree+1:nbkpt) =  two
      bkpt(nord:nbkpt-ndegree)=(/(i*delta,i=0,ngrid-1)/)

! Assign the degree of the polynomial and the knots.
      knotsx%spline_degree=ndegree
      knotsx%d_knots=>bkpt
      knotsy%spline_degree=knotsx%spline_degree
      knotsy%d_knots=>knotsx%d_knots

! Fit the data and obtain the coefficients.
      coeff = surface_fitting(spline_data, knotsx, knotsy)

! Evaluate the residual = spline - function
! at a grid of points inside the square.
      delta=two/(nvalues+1)
      x=(/(i*delta,i=1,nvalues)/); y=x

      values=exp(-spread(x**2,1,nvalues)-spread(y**2,2,nvalues))
      values=surface_values((/0,0/), x, y, knotsx, knotsy, coeff)-values
            
! Compute the R.M.S. error:
      sizev=norm(pack(values, (values == values)))/nvalues

      if (sizev <= TOLERANCE) then
         write (*,*) 'SURFACE_FITTING_EX1 Passed on pcdsms.'
      else
         write(*,*) 'SURFACE_FITTING_EX1 ********** Failed on pcdsms **********'
      end if
end program

Module surface_fitting_int
  USE norm_int
  implicit none
  interface surface_fitting
    function D_SURFACE_FITTING(DATA,KNOTSX,KNOTSY,CONSTRAINTS,COVARIANCE,IOPT,epack)
      import
      implicit none
      type (d_spline_knots) :: knotsx, knotsy
      real(kind(1d0)) :: DATA(:,:)
      type (d_SURFACE_CONSTRAINTS) , optional :: CONSTRAINTS(:)
      real(kind(1d0)) , optional :: COVARIANCE(:,:)
      type (d_options) , optional :: iopt(:)
      type (d_error) , optional :: epack
      real(kind(1d0)) :: D_SURFACE_FITTING(size(KNOTSX%D_KNOTS)-KNOTSX%SPLINE_DEGREE-1,size(KNOTSY%D_KNOTS)-KNOTSY%SPLINE_DEGREE-1)
    end function D_SURFACE_FITTING    
  end interface surface_fitting

  interface SURFACE_VALUES    
    function DV_SURFACE_VALUES(DERIVATIVE, VARIABLESX, VARIABLESY, KNOTSX, KNOTSY, COEFFS)
      import
      implicit none
      integer :: DERIVATIVE(2)
      real(kind(1d0)) :: VARIABLESX(:), VARIABLESY(:)
      type (d_spline_knots) :: knotsx, knotsy
      real(kind(1d0)) :: COEFFS(:,:)
      real(kind(1d0)) :: DV_SURFACE_VALUES(size(VARIABLESX),size(VARIABLESY))
    end function DV_SURFACE_VALUES
  end interface SURFACE_VALUES

End Module surface_fitting_int