MATLAB dct vs NAG c06rbf vs dfftpack dcost

Hi,

I've been trying to implement MATLAB's discrete cosine transform for a while now, converting some old code which uses the NAG routine c06rbf. My Google searching hasn't turned anything up so I thought I'd ask here.

• Documentation for the MATLAB routine: MATLAB dct
• Documentation for the NAG routine: NAG c06rbf
• Documentation for the dfftpack routine: dfftpack
• Minimal working example:

MATLAB:

N = 5; 
vin = (1:-0.25:0).';
vout = dct(vin,N,'Type',1);
vout = sqrt(N/2)*vout; %remove normalisation factor

Fortran:

integer N,j
parameter (N=5)
double precision vin(N),vout_nag(N),vout_dfft(N)

double precision work(3*N+15),ifail

! !!!!!!! NAG implementation !!!!!!! !
do j = 1,N
  vin(j) = 1-0.25*(j-1)
end do

ifail = 0
call c06rbf(1,N,vin,work,ifail)

do j = 1,N
  vout_nag(j) = sqrt(N/2)*vin(j)
end do

! !!!!!!! dfftpack implementation !!!!!!! !
do j = 1,N
  vin(j) = 1-0.25*(j-1)
end do

call dcosti(N,work)
call dcost(N,vin,work)

do j = 1,N
  vout_dfft(j) =  0.5*vin(j)
end do

MATLAB output:

vout = 

      1.7449
      1.1859
      0.23155
      0.39528
      0.16373

Fortran output:

vout_nag =

            2
        1.184
        0.125
     0.065983
        0.125

vout_dfft =

            2
        1.184
        0.125
     0.065983
        0.125

I just can't quite figure out what's going wrong. I thought it might be a scaling factor issue but I can't pin it down, and trying to dissect the individual methods hasn't got me anywhere.

Any help appreciated!