Need help with this code- Chevyshev rational function on matlab

I am trying to approximate some data. Matlab couldn't approximate polynomial so I approximated using another software which can generate matlab file. This is the actual function.

%F(x,y)=(a+dT1(x )+eT1(y )+hT2(x)+iT2(y)+lT3(x )+mT3(y )+pT4(x)+qT4(y )+tT5(x )+uT5(y )... +abT6(x)+acT6(y)+afT7(x)+agT7(y )+ajT8(x )+akT8(y )+anT9(x)+aoT9(y)+arT10(x)+... asT10(y))/((1+bT1(x)+cT1(y)+fT2(x)+gT2(y )+jT3(x)+kT3(y )+nT4(x)+oT4(y )+... rT5(x )+sT5(y)+vT6(x)+aaT6(y)+adT7(x)+aeT7(y)+ahT8(x)+aiT8(y)+alT9(x)+amT9(y 1)+... apT10(x)+aqT10(y ) )+atT11(x )+auT11(y ))

% where Tn(x) = 2xTn-1(x) - Tn-2(x), n≥2 is chebysheb rational function

I do understand in this code is I need to provide input x and y and matrix c is the coefficient of above function. I get lost in function z = evalcratl(order, logx, logy, x, y, p,... s0, s1, s2, s3, s4, s5, s6, s7, s8, s9). How is this function working. Meaning of Evalcratl and tcnt .

 Any help on this would be appreciated.

--------------------------------------------------------------------------------

 [rowx colx]=size(xa);

if(rowx~=1 & colx~=1)
  error('x must be scalar or 1D array');
  return;
end
[rowy coly]=size(ya);
if(rowy~=1 & coly~=1)
  error('y must be scalar or 1D array');
  return;
end
c=[
  0.7823326556648382,
  -0.003073888389053987,
  6.311956873270135E-16,
  -0.0003235701036352635,
  0,
  0.1184529306672700,
  0.7000618410087535,
  -0.06699883001305451,
  0.6882427553087074,
  -0.001289845952369463,
  7.834476942891433E-16,
  0.0003263428678678636,
  0,
  -0.01433571833230648,
  -0.2173515431820155,
  0.01552171410016730,
  -0.2211421352264687,
  -0.0001289154504598550,
  6.559509737139252E-16,
  0.0004529420876541368,
  0,
  -0.01218726621626016,
  -0.09562258140958195,
  0.003063157214620869,
  -0.08732570079084124,
  0.0002432826238712180,
  4.144106621110242E-16,
  0.0003501722099832917,
  0,
  -0.008018886525623193,
  -0.04998847489715176,
  0.003499439465963643,
  -0.04330683933474295,
  6.716713718394032E-05,
  1.191551227290313E-16,
  8.914863235537785E-05,
 0,
  0.001270750287501435,
  -0.0001942757598005615,
  ];
lenx=length(xa);
leny=length(ya);
for(j=1:leny)
  for(i=1:lenx)
    x=xa(i);
    y=ya(j);
    z=evalcratl(38,0,0,x,y,c,...
      0.000000000000000,5.000000000000000,...
      0.000000000000000,0.000000000000000,...
      0.000000000000000,5.000000000000000,...
      0.000000000000000,0.000000000000000,...
      0.1962500000000000,0.8042500000000000);
     za(i,j)=z;
     end
   end
%--------------------------------------------------------------
function z = evalcratl(order, logx, logy, x, y, p,...
s0, s1, s2, s3, s4, s5, s6, s7, s8, s9)
%--------------------------------------------------------------
tx=[];
ty=[];
if(logx==0)
  x=(x-s0)/s1;
else
  x=(log(x)-s2)/s3;
end
if(logy==0)
  y=(y-s4)/s5;
else
  y=(log(y)-s6)/s7;
end
if (order==6)
  tcnt=3;
elseif (order==10)
  tcnt=4;
elseif (order==14)
  tcnt=5;
elseif (order==18)
  tcnt=6;
elseif (order==22)
  tcnt=7;
elseif (order==26)
  tcnt=8;
elseif (order==30)
  tcnt=9;
elseif (order==34)
  tcnt=10;
elseif (order==38)
  tcnt=11;
elseif (order==42)
  tcnt=12;
else
  return;
end
if(tcnt>7)
  if(x<-1.0)
    x=-1.0;
  end
  if(x>1.0)
    x= 1.0;
  end
  if(y<-1.0)
    y=-1.0;
  end
  if(y>1.0)
    y= 1.0;
  end
end
tx(1)=1.0;
ty(1)=1.0;
tx(2)=x;
ty(2)=y;
for j=2:1:tcnt-1
  tx(j+1)=2*x*tx(j)-tx(j-1);
  ty(j+1)=2*y*ty(j)-ty(j-1);
end
m=2;
num=p(1);
den=1.0+p(2)*tx(m)+p(3)*ty(m);
for(j=3:4:order-1)
  num=num+p(j+1)*tx(m);
  num=num+p(j+2)*ty(m);
  m=m+1;
  den=den+p(j+3)*tx(m);
  den=den+p(j+4)*ty(m);
end
if (den==0)
  z=0;
else
  z=(num/den)*s8+s9;
end
return;

Thank You in advance

[John D'Errico]

I'm pretty sure that matlab COULD have solved for that approximating polynomial, just that you did not know how to do it. There is a big difference.

[sagar pokhrel]

I tried to approximate using matlab but it could approximate polynomial only in X^5 and Y^5. I was looking for a approximation that can go to x^10 and Y^10. Is there other way I can approximate to this limit.

Matlab could run code after the inputs are given. Since I know the equation and coefficient I want to use the first equation but I dont know how this code is working.

[John D'Errico]

Again, those limits were more about your understanding of the numerical analysis involved than about the true capabilities of a numerical tool.

As far as an explanation of the code you have been given, I don't see much purpose to it. Sorry, but reading undocumented code that does something you don't understand is a losing proposition. Either trust the provider or don't use it.