divide the matrix (Rx2) into submatrices based on the values ​​of the second column

HI! I tried to split the 'matrix_out' matrix into submatrices with steps of 0.1 and for the most part I succeeded.

load matrix_out

% =======

matrix_out_0 = matrix_out(matrix_out(:,2) < 0.1, :);
tot_percent_matrix_out_0 = sum(matrix_out_0(:,2));
matrix_separation_0 = [{matrix_out_0}, tot_percent_matrix_out_0];

% =======

matrix_separation = {};

j = 0.1:0.1:1.2;

for K = 1:width(j)

    matrix_out_new = matrix_out((matrix_out(:,2) >= j(K) & matrix_out(:,2) < (0.1*K)+0.1), :);
    tot_percent_matrix_out_new = sum(matrix_out_new(:,2));

    matrix_separation = [matrix_separation; {matrix_out_new},tot_percent_matrix_out_new];

end

matrix_separation = [matrix_separation_0 ; matrix_separation]

matrix_separation = 13×2 cell array
    {31×2 double}    {[ 0.5500]}
    { 6×2 double}    {[ 0.9100]}
    {69×2 double}    {[17.9400]}
    {33×2 double}    {[11.3900]}
    {13×2 double}    {[ 5.7800]}
    {10×2 double}    {[ 5.5900]}
    {10×2 double}    {[ 6.4000]}
    { 8×2 double}    {[      6]}
    { 6×2 double}    {[ 5.1300]}
    {11×2 double}    {[10.4500]}
    {11×2 double}    {[11.4000]}
    {14×2 double}    {[15.9400]}
    { 3×2 double}    {[ 3.6900]}

In the code, however, I noticed that the value 423|1.2 is found both in the penultimate and in the last cell inside 'matrix_separation'.

The value 423|1.2 should only appear in the last cell given the range >=1.2 & <1.3! Thanks to whoever solves this doubt...

Answer 1

[Dyuman Joshi]

discretize and splitapply for the win!

load matrix_out

%Mention the bins to group data in
j = [0 0.1:0.1:1.2 Inf];
%Discretize the data
idx = discretize(matrix_out(:,2),j);

%Split the array according to the groups
out1 = splitapply(@(x) {x}, matrix_out, idx)

out1 = 13×1 cell array
    {31×2 double}
    { 6×2 double}
    {69×2 double}
    {33×2 double}
    {13×2 double}
    {10×2 double}
    {10×2 double}
    { 8×2 double}
    { 6×2 double}
    {11×2 double}
    {11×2 double}
    {13×2 double}
    { 3×2 double}

You can see above that the 2nd last group is 13x2 instead of 14x2. The sum obtained will be modified accordingly as well.

%Get the sum of the 2nd column according to the groups
out2 = splitapply(@(x) sum(x), matrix_out(:,2), idx)

out2 = 13×1

0.5500 0.9100 17.9400 11.3900 5.7800 5.5900 6.4000 6.0000 5.1300 10.4500

%Concatenate to get the final output
out = [out1 num2cell(out2)]

out = 13×2 cell array
    {31×2 double}    {[ 0.5500]}
    { 6×2 double}    {[ 0.9100]}
    {69×2 double}    {[17.9400]}
    {33×2 double}    {[11.3900]}
    {13×2 double}    {[ 5.7800]}
    {10×2 double}    {[ 5.5900]}
    {10×2 double}    {[ 6.4000]}
    { 8×2 double}    {[      6]}
    { 6×2 double}    {[ 5.1300]}
    {11×2 double}    {[10.4500]}
    {11×2 double}    {[11.4000]}
    {13×2 double}    {[14.7400]}
    { 3×2 double}    {[ 3.6900]}

[Alberto Acri]

Well done!

[Alberto Acri]

Hi @Dyuman Joshi!

I was checking your code.

I noticed that in out{3,1} there are values (in the second column) between 0.2 and 0.3 (0.2 and 0.3 inclusive).

p.s. It didn't happen on the other matrices because there weren't the most extreme values.

I need to have intervals in the following way:

<0.10
>=0.10 & <0.20
>=0.20 & <0.30
>=0.30 & <0.40
...

Can you modify the code you provided me?

[Dyuman Joshi]

What you are seeing is the limitation of floating point numbers.

load matrix_out

%Mention the bins to group data in
j = [0 0.1:0.1:1.2 Inf];


%% Let's see what the data is stored as
%First the matrix values
%Displayed value
disp(matrix_out(10:15,2))

    0.0100
    0.0100
    0.2200
    0.3000
    0.2600
    0.2400

%Stored value
fprintf('%0.42f\n',matrix_out(10:15,2))

0.010000000000000000208166817117216851329431
0.010000000000000000208166817117216851329431
0.220000000000000001110223024625156540423632
0.299999999999999988897769753748434595763683
0.260000000000000008881784197001252323389053
0.239999999999999991118215802998747676610947

%Now the values of the groups
%Displayed value
disp(j')

         0
    0.1000
    0.2000
    0.3000
    0.4000
    0.5000
    0.6000
    0.7000
    0.8000
    0.9000
    1.0000
    1.1000
    1.2000
       Inf

%Stored values
fprintf('%0.42f\n',j)

0.000000000000000000000000000000000000000000
0.100000000000000005551115123125782702118158
0.200000000000000011102230246251565404236317
0.300000000000000044408920985006261616945267
0.400000000000000022204460492503130808472633
0.500000000000000000000000000000000000000000
0.599999999999999977795539507496869191527367
0.699999999999999955591079014993738383054733
0.799999999999999933386618522490607574582100
0.899999999999999911182158029987476766109467
1.000000000000000000000000000000000000000000
1.099999999999999866773237044981215149164200
1.199999999999999955591079014993738383054733
Inf

You can see that the values are not exactly 0.1, 0.2, 0.3 etc. The only values that are stored exactly as their decimal representation are the powers of 2 (0.5 = 2^-1, 1 = 2^0).

This means there will be some errors while working with floating point numbers.

So, what to do now? There is a workaround - Scale up the data to integers and operate.

As the data in the 2nd column of the matrix_out have values upto the 2nd digit after the decimal, so scale up by a factor of 10^2.

%Scale up by a factor of 100
%Scaling the data
vec = floor(matrix_out(:,2)*100);

%Scaling the bins 
j = [0 10:10:120 Inf]; 

%Discretize the data according to the scaled values
idx = discretize(vec,j);

%Split the array according to the groups
out = splitapply(@(x) {x}, matrix_out, idx)

out = 13×1 cell array
    {31×2 double}
    { 6×2 double}
    {62×2 double}
    {40×2 double}
    {13×2 double}
    {10×2 double}
    {10×2 double}
    { 8×2 double}
    { 6×2 double}
    {11×2 double}
    {11×2 double}
    {13×2 double}
    { 3×2 double}

disp(out{3,1})

  262.0000    0.2200
  264.0000    0.2600
  265.0000    0.2400
  266.0000    0.2400
  267.0000    0.2000
  269.0000    0.2500
  270.0000    0.2600
  271.0000    0.2900
  274.0000    0.2700
  275.0000    0.2200
  276.0000    0.2500
  277.0000    0.2100
  278.0000    0.2700
  279.0000    0.2200
  280.0000    0.2300
  281.0000    0.2600
  282.0000    0.2900
  283.0000    0.2700
  284.0000    0.2200
  285.0000    0.2400
  286.0000    0.2300
  287.0000    0.2500
  288.0000    0.2600
  289.0000    0.2400
  290.0000    0.2500
  291.0000    0.2600
  292.0000    0.2400
  293.0000    0.2500
  295.0000    0.2900
  296.0000    0.2600
  297.0000    0.2500
  299.0000    0.2600
  300.0000    0.2800
  301.0000    0.2600
  302.0000    0.2400
  303.0000    0.2700
  304.0000    0.2500
  306.0000    0.2600
  308.0000    0.2500
  309.0000    0.2800
  310.0000    0.2500
  311.0000    0.2500
  313.0000    0.2500
  315.0000    0.2600
  316.0000    0.2700
  317.0000    0.2600
  319.0000    0.2600
  321.0000    0.2900
  322.0000    0.2100
  324.0000    0.2600
  325.0000    0.2700
  326.0000    0.2900
  327.0000    0.2900
  328.0000    0.2700
  330.0000    0.2600
  332.0000    0.2500
  337.0000    0.2900
  339.0000    0.2900
  345.0000    0.2800
  448.0000    0.2800
  449.0000    0.2600
  450.0000    0.2100