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<- [[:programming]]

====== transform spectral coeff to physical data points ======

//emmanuel germaine, 2010-08-28 10:14 //



~~DISCUSSION~~
Dear Prof. Gibson,

We can determine the physical values from the spectral coefficients by evaluating the expansion sum (eqn 20 in the user's manual.) 
I wanted to compared the physical values computed by this sum with the values returned by the method u.makephysical(). This method use FFTW.
So I was just wondering if there is any difference. The fact is that, I do not obtained the same results.
 
I have attached part of the code I am using. Do you think that something is incorrect ?

As the width of the channel is [a,b] = [-1.0,1.0], I haven't normalized the Chebyshev polynomials.

Example of results displayed :
  0.00258953      // u computing Fourier series
  0.00604268      // return of u.makePhysical (FFTW)


Regards,
Emmanuel

  {
   double pi =3.1415926 ;
   Complex I(0.0,1.0);
   Complex sum_u(0.0,0.0);
   int pause; 
   nx = 5;
   ny = 5; 
   nz = 5;   
  //display gridpoint coordinates x,y,z
  std::cout << u.x(nx) << ' ' << u.y(ny) << ' ' << u.z(nz) << endl ;
  
  //compute physical value using expansion sum and display
   u.makeSpectral();
   for(int mz=0;mz<u.Mz();++mz)
     for(int my=0;my<u.My();++my)
       for(int mx=0;mx<u.Mx();++mx)
	          sum_u += u.cmplx(mx,my,mz,0) *  chebyshev(my,u.y(ny)) * exp(2.0 * pi * I*((u.kx(mx) * u.x(nx) /u.Lx()) + (u.kz(mz) * u.z(nz) / u.Lz()))) ;
          std::cout << 2.0 * sum_u.real()<< endl ;
   
    //display physical value  from makePhysical()   
    u.makePhysical();
    std::cout << u(nx,ny,nz,0)  <<  endl ;
  
    std::cin >> pause;	
    }
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