Can this be written in a easier way?

Hi all,

I have two 21 x1 cells containg 100x18 tables (attached).

My aim is to calculate mean correlation coeffiient for each variable (18 variables) across all tables (21 tables) between to data sets. The below is my attempt to do is using an example of just one variable. Can this be written in a easier way?

load ('Data1');             %Load data
load('Data2');

n_tables_1 = numel(data1);      % Data 1 - put all tables' data into a 3D array: 100x18x21
all_data_1 = zeros([size(data1{1}),n_tables_1]);       
for ii = 1:n_tables_1
    all_data_1(:,:,ii) = table2array(data1{ii});
end

n_tables_2 = numel(data2);      % Data 2 - put all tables' data into a 3D array: 100x18x21
all_data_2 = zeros([size(data2{1}),n_tables_2]);       
for ii = 1:n_tables_2
    all_data_2(:,:,ii) = table2array(data2{ii});
end

%% Calculate r for variable 1
data1_var1 = all_data_1(:,1,:);                 % Data 1 - access variable 1
data2_var1 = all_data_2(:,1,:);                 % Data 2 - access variable 1

data1_var1 = reshape(data1_var1,[100,21]);      % reshape to two-dimenasional matrix
data2_var1 = reshape(data2_var1,[100,21]);

r1=corrcoef(data1_var1(:,1),data2_var1(:,1));   % get r for each column until 21
r2=corrcoef(data1_var1(:,2),data2_var1(:,2));
r3=corrcoef(data1_var1(:,3),data2_var1(:,3));
r4=corrcoef(data1_var1(:,4),data2_var1(:,4));
r5=corrcoef(data1_var1(:,5),data2_var1(:,5));
etc.....
r21=corrcoef(data1_var1(:,21),data2_var1(:,21));

r_mean = (r1+r2+r3+....+r21)/21                 %get mean r
    
%% Repeat the above for variables 2 to 21. 

[Tomaszzz]

@_ Many thanks for your help. Happy to accept if you post this as an answer.

I have also asked a simialr question that builds upon this where I have a rmaining part of the code and not sure how to apply cellfun there:

https://uk.mathworks.com/matlabcentral/answers/1677509-how-to-use-cellfun

[Voss]

@Tomaszzz I have moved the comment to an answer. Thanks! I will look at the other question too.

Answer 1

[Voss]

See my answer below, which was for your similar previous question, which has since been deleted.

I realize this new question is not exactly the same, but this approach (using cellfun) may be of use:

load('Data1'); % t_sq_mtw
load('Data2'); % t_sq_dot_1
whos

  Name             Size             Bytes  Class    Attributes

  ans              1x34                68  char               
  t_sq_dot_1      21x1             411789  cell               
  t_sq_mtw        21x1             411789  cell               

% do polyfit() of P_acc_z_meancycle for each pair of tables
% (each pair is a table from t_sq_mtw and the corresponding table from t_sq_dot_1):
p = cellfun(@(x,y)polyfit(x.P_acc_z_meancycle,y.P_acc_z_meancycle,1), ...
    t_sq_mtw,t_sq_dot_1,'UniformOutput',false);

% p is a 21-by-2 matrix of coefficients from polyfit(), p = [a1 a0]
p = cell2mat(p)

p = 21×2

0.9867 0.1336 1.0177 0.1576 0.9638 0.1300 -0.4362 0.0891 0.7685 0.1178 0.5379 0.1677 1.0999 0.1258 0.9652 0.1466 0.9787 0.2405 1.2832 0.4761

% do corrcoef() of P_acc_z_meancycle for each pair of tables:
% (each pair is a table from t_sq_mtw and the corresponding table from t_sq_dot_1):
r = cellfun(@(x,y)corrcoef(x.P_acc_z_meancycle,y.P_acc_z_meancycle), ...
    t_sq_mtw,t_sq_dot_1,'UniformOutput',false);

% rSq is a 21-by-1 column vector of r-squared values from corrcoef():
rSq = cellfun(@(x)x(1,2)^2,r)

rSq = 21×1

0.9849 0.9866 0.8919 0.3034 0.8005 0.2836 0.9708 0.8687 0.9272 0.6527

% calculate the mean and std of [p rSq] (= [a1 a0 rSq]) over all tables:
mean([p rSq],1) % mean of a1, a0, rSq, over all tables

ans = 1×3

0.8564 0.1619 0.7536

std([p rSq],0,1) % standard deviation of a1, a0, rSq, over all tables

ans = 1×3

0.4049 0.0889 0.2948