Writing code for given general matrix in MATLAB

How do I write a code for the following matrix of order cM X cM?

Here, where are all known scalars and 's are function handles which I have defined using cell array as h_{i,j}.

Answer 1

[Walter Roberson]

c = 3

c = 3

M = 5

M = 5

syms h(T) [c, M]
syms t [c, M]
H = reshape(cellfun(@(C) reshape(C.', 1, []), h(t), 'uniform', 0).',[],1);
H = vertcat(H{:})

H = 

[Saurabh Madankar]

This does give me the required matrix but how do I replace 's from your code to my predefined function handles? This is how I have defined the function handles-

for c = 1:3
    for i=1:5
        h_{c,i} = @(t) H_{i}(t+1-c);
    end
end

[Walter Roberson]

for c = 1:3
    for i=1:5
        h_{c,i} = @(t) H_{i}(t+1-c);
    end
end

c = 3

c = 3

M = 5

M = 5

syms h(T) [c, M]
syms t [c, M]
H = reshape(cellfun(@(C) reshape(C.', 1, []), h(t), 'uniform', 0).',[],1);
H = vertcat(H{:})

H = 

subs(H, num2cell(h), h_)

Undefined variable H_.

Error in solution (line 3)
h_{c,i} = @(t) H_{i}(t+1-c);

Error in sym>funchandle2ref (line 1601)
S = x(S{:});

Error in sym>tomupad (line 1514)
x = funchandle2ref(x);

Error in sym (line 332)
S.s = tomupad(x);

Error in sym/subs>@(x)sym(x) (line 217)
Y = cellfun(@(x)sym(x),Y,'UniformOutput',false);

Error in sym/subs>normalize (line 217)
Y = cellfun(@(x)sym(x),Y,'UniformOutput',false);

Error in sym/subs>mupadsubs (line 165)
[X2,Y2,symX,symY] = normalize(X,Y); %#ok

Error in sym/subs (line 153)
G = mupadsubs(F,X,Y);

[Saurabh Madankar]

This is the error I am getting-

Error using sym/subs>normalize (line 239)
Entries in second argument must be scalar.

Error in sym/subs>mupadsubs (line 165)
[X2,Y2,symX,symY] = normalize(X,Y); %#ok

Error in sym/subs (line 153)
    G = mupadsubs(F,X,Y);

Error in Extended (line 34)
subs(H, num2cell(h), h_)
 

[Walter Roberson]

In the below, it is possible to write mappingfun as an anonymous function -- but it was a lot easier to debug as a real function.

The code is a bit clumsy. The challenge is in naming what to subs() . For example for h1_1(t1_1) call, if you try to subs h as a whole, something like subs(H, h, h_) then h is not an array: when gnerated by syms(T) [c,M] then the name h becomes a single symfun that returns an array... and you cannot break apart a symfun that returns an array into its component entries using any supported function.

If you invoke the function with a definite argument then you start getting mismatches for the purpose of substitution. The dummy functions like h2_3(T) exist but no references to those occur in the array: the array has entries such as h2_3(t1_4) and subs() will not pattern-match the (T) to the (t1_4) . So you start having to extract the symbol name and read the indices out of the name and use those...

The code would probably be easier (or cleaner) if it was permitted to generate the array with the function handle calls in place, instead of having to create the array as pure symbolic first, and then substitute in the function handles.

c = 3;
M = 5;

for i = 1:M
  H_{i} = @(x) besselj(i, x);
end

for c = 1:c
    for i=1:M
        h_{c,i} = @(t) H_{i}(t+1-c);
    end
end


syms h(T) [c, M]
syms t [c, M]
H = reshape(cellfun(@(C) reshape(C.', 1, []), h(t), 'uniform', 0).',[],1);
H = vertcat(H{:})

H = 

output = mapSymType(H, 'symfun', @(X) mappingfun(X,h_))

output = 

function mapped = mappingfun(F, h)
    symfunname = symFunType(F);
    idx = sscanf(symfunname, 'h%d_%d');
    mapped = h{idx(1), idx(2)}(children(F,1));
end

[Saurabh Madankar]

I haven't really understood the code totally, but I will give some time and see. Thanks for answering.