rewrite MATLAB to Maple

I have a small MATLAB symbolic script as following

syms z;
psi(2)=exp(2*z-exp(z))/(1-exp(-exp(z)));
psi(3)=exp(2*z-exp(z))/(1-exp(-exp(z)))*z;
psi(4)=exp(2*z-exp(z))/(1-exp(-exp(z)))*z^2;
f(1,1)=exp(2*z-exp(z))/(1-exp(-exp(z)));
for i=2:4
    f(i,1)=diff(psi(i),z);
    for j=2:i
        f(i,j)=diff(f(i,j-1)/f(j-1,j-1),z);
    end
end

given a symbolic vector psi consist of functions of z, it create a lower triangle symbolic matrix f. it works well.

I'm trying to rewrite this part in Maple, which I'm new to. I tried

psi(2) := exp(2*z-exp(z))/(1-exp(-exp(z)));
psi(3) := exp(2*z-exp(z))*z/(1-exp(-exp(z)));
psi(4) := exp(2*z-exp(z))*z^2/(1-exp(-exp(z)));  
f(1, 1) := exp(2*z-exp(z))/(1-exp(-exp(z)));   
for i from 2 to 4 do f(i,1):=exp(2*z-exp(z))/(1-exp(-exp(z)));     
for j from 2 to i do f(i,j):=diff(f(i,j-1)/f(j-1,j-1),z);   
od;    
od;

something ambiguous in the "diff" line, I just select function definition. if I let it output f(4,4), it report

Error, (in f) too many levels of recursion

but it did print f(4,1).

could some one tell what's wrong? Thanks!

Solution

Your code is pretty close (and reminds me how similar these two languages are at times). The reason for the error message is that you need to declare f before you start filling it with values.

Here's one possible solution:

psi[2] := exp(2*z-exp(z))/(1-exp(-exp(z)));
psi[3] := exp(2*z-exp(z))*z/(1-exp(-exp(z)));
psi[4] := exp(2*z-exp(z))*z^2/(1-exp(-exp(z)));

f := Matrix(1..4,1..4):

f[1, 1] := exp(2*z-exp(z))/(1-exp(-exp(z))):   
for i from 2 to 4 do 
    f[i,1] := diff(psi[i],z):
    for j from 2 to i do 
        f[i,j] := diff(f[i,j-1]/f[j-1,j-1],z):   
    end do:  
end do:
f;

Note here that I declare f to be a 4x4 Matrix before I start filling it. Also, here the [] notation is used for specifying indices.

Another option which may scale better for larger problems is to grow your data structure for f as you add values to it. Here we start with a 1x1 Array and add values to it.

psi[2] := exp(2*z-exp(z))/(1-exp(-exp(z)));
psi[3] := exp(2*z-exp(z))*z/(1-exp(-exp(z)));
psi[4] := exp(2*z-exp(z))*z^2/(1-exp(-exp(z)));  

f:=Array(1..1,1..1):

f(1, 1) := exp(2*z-exp(z))/(1-exp(-exp(z))):   
for i from 2 to 4 do 
    f(i,1):=diff(psi[i],z):
    for j from 2 to i do 
        f(i,j):=diff(f[i,j-1]/f[j-1,j-1],z):   
    end do:  
end do:
f;

Here you'll notice that we are using the () notation for Array indices at time of creation. If you use an Array for storage, this is one technique that allows for you to grow the Array as you add values.

Now in both cases you can also note that I've used [] to index a term that already exists; square brackets are the default notation in Maple for specifying indices in a data structure.

Also note that I've suppressed output in each loop using the : operator; this way you can just echo back the resulting Matrix f at the end.