Increase size of array within cellfun

I have a cell array with each cell containing a 4x4 double array. I want to add an additional value at position (5,5), and thus increase the size of each double array to 5x5. The double arrays will not always be 4x4, but whatever nxm is, I just need to append one additional element in the (n+1)x(m+1) position

I'd rather avoid looping over each cell, can this be done with cellfun? My code below uses '=' within cellfun which is not supported.

n = 4;
m = 4;
A = rand(n,m); B = rand(n,m); C = rand(n,m); D = rand(n,m);
ABCD = {A,B;C,D}; % 2x2 cell array

% ABCD = cellfun(@(x) x(end+1,end+1) = 0, ABCD) % code that doesn't work

Thanks!

Answer 1

[Voss]

cellfun performs a loop internally, so I think an explicit for loop in this case is fine.

However, if you want to use cellfun, here are a couple of ways:

n = 4;
m = 4;
A = rand(n,m); B = rand(n,m); C = rand(n,m); D = rand(n,m);
ABCD = {A,B;C,D}; % 2x2 cell array

Method 1: Use a helper function (here it's called extend_matrix_by_one and it's defined at the end):

ABCD_new = cellfun(@extend_matrix_by_one, ABCD, 'UniformOutput',false)

ABCD_new = 2×2 cell array
    {5×5 double}    {5×5 double}
    {5×5 double}    {5×5 double}

ABCD_new{1} % check the first cell

ans = 5×5

0.2104 0.2399 0.3693 0.1618 0 0.0287 0.2169 0.9291 0.0706 0 0.4770 0.9847 0.5352 0.5272 0 0.0211 0.3015 0.8597 0.8126 0 0 0 0 0 0

Method 2: Use subsasgn to do the assignment:

ABCD_new = cellfun(@(x) subsasgn(x,substruct('()',{size(x,1)+1,size(x,2)+1}),0), ABCD, 'UniformOutput',false)

ABCD_new = 2×2 cell array
    {5×5 double}    {5×5 double}
    {5×5 double}    {5×5 double}

ABCD_new{1} % check the first cell

ans = 5×5

0.2104 0.2399 0.3693 0.1618 0 0.0287 0.2169 0.9291 0.0706 0 0.4770 0.9847 0.5352 0.5272 0 0.0211 0.3015 0.8597 0.8126 0 0 0 0 0 0

% helper function definition
function x = extend_matrix_by_one(x)
x(end+1,end+1) = 0;
end

Answer 2

[Dyuman Joshi]

"I'd rather avoid looping over each cell, can this be done with cellfun?"

That's the thing - Cellfun is just a loop in disguise.

Looping is the way to go here.

%Bigger Cell array for testing
n = 800;
m = 1000;
A = rand(n,m); B = rand(n,m); C = rand(n,m); D = rand(n,m);
ABCD = {A,B;C,D;A,B;C,D;A,B;C,D;A,B;C,D;A,B;C,D;A,B;C,D;A,B;C,D;A,B;C,D}; 

%value to append
val = 2;

F1 = @() CELL(ABCD,n,m,val);
F2 = @() LOOP(ABCD,n,m,val);

isequal(F1(),F2())

ans = logical
   1

fprintf('Time taken by cellfun = %f seconds', timeit(F1))

Time taken by cellfun = 0.083916 seconds

fprintf('Time taken by loop = %f seconds', timeit(F2))

Time taken by loop = 0.062760 seconds

%% If you want to use cellfun, this is one way to do it
function z = CELL(z,n,m,val)
z = cellfun(@(x) [x zeros(n,1);zeros(1,m) val], z, 'uni', 0);
end

%% Loop method
function z = LOOP(z,n,m,val)
for k=1:numel(z)
    z{k}(n+1,m+1) = val; 
end
end

[Dyuman Joshi]

Let's compare the speed of all approaches in this thread -

%Bigger Cell array for testing
n = 800;
m = 1000;
A = rand(n,m); B = rand(n,m); C = rand(n,m); D = rand(n,m);
ABCD = {A,B,C,D;A,B,C,D;A,B,C,D;A,B,C,D;A,B,C,D;A,B,C,D}; 

%value to append
val = 2;

F1 = @() CELL(ABCD,n,m,val);
F2 = @() LOOP(ABCD,n,m,val);
F3 = @() SUBTITUTE(ABCD,n,m,val);
F4 = @() HELPER(ABCD,val);


%% Check if outputs are equal or not
isequal(F1(),F2(),F3(),F4())

ans = logical
   1

fprintf('Time taken by cellfun = %f seconds', timeit(F1))

Time taken by cellfun = 0.074146 seconds

fprintf('Time taken by loop = %f seconds', timeit(F2))

Time taken by loop = 0.060283 seconds

fprintf('Time taken by substitute = %f seconds', timeit(F3))

Time taken by substitute = 0.076276 seconds

fprintf('Time taken by helper = %f seconds', timeit(F4))

Time taken by helper = 0.076179 seconds

function z = CELL(z,n,m,val)
z = cellfun(@(x) [x zeros(n,1);zeros(1,m) val], z, 'uni', 0);
end


function z = LOOP(z,n,m,val)
for k=1:numel(z)
    z{k}(n+1,m+1) = val; 
end
end


function z = SUBTITUTE(z,n,m,val)
z = cellfun(@(x) subsasgn(x,substruct('()',{n+1,m+1}),val), z, 'UniformOutput',false);
end


function z = HELPER(z,val)
    z = cellfun(@(x) extend_matrix_by_one(x,val), z, 'UniformOutput',false);

    % helper function definition
    function x = extend_matrix_by_one(x,val)
        x(end+1,end+1) = val;
    end
end