Grouping values in a matrix according to a value in a row & its index position

Hello, say I have the following matrix:

51 71 0

48.87 63.38 -2.30769230769231

42.15 55.97 -2.30769230769231

40.22 47.47 -2.30769230769231

39.84 38.75 -1.92307692307692

40.577 34.19 -1.15384615384615

50 30 0

And I wanted to group different rows together according to equal values of the 3rd column, but index position matters, so if I have two equal values in a 3rd column but they are not next to each other in their index position, do not group together.

Which would give me:

51 71 0

48.87 63.38 -2.30769230769231

42.15 55.97 -2.30769230769231

40.22 47.47 -2.30769230769231

39.84 38.75 -1.92307692307692

40.577 34.19 -1.15384615384615

50 30 0

Would I be using the unique function? Thanks

[Dyuman Joshi]

How have you grouped the 5th and 6th rows together? The corresponding values in 3rd column are not same.

[JIAN-HONG YE ZHU]

Fixed

Answer 1

[Dyuman Joshi]

Vectorized approach

mat=[51     71	    0
    48.87   63.38   -2.30769230769231
    42.15   55.97	-2.30769230769231
    40.22   47.47   -2.30769230769231
    39.84   38.75   -1.92307692307692
    40.577  34.19	-1.15384615384615
    50	    30      0];

vec=(1:size(mat,1))';

%Indices of rows in 3rd column which are not equal to the next row
%Using tolerance instead of comparing to zero
idx=vec([abs(diff(mat(:,3)))>1e-4;true])

idx = 5×1

1 4 5 6 7

%Corresponding number of rows in each group
elem=diff([0;idx])

elem = 5×1

1 3 1 1 1

%Output
out=mat2cell(mat,elem)

out = 5×1 cell array
    {[                51 71 0]}
    {3×3 double               }
    {[39.8400 38.7500 -1.9231]}
    {[40.5770 34.1900 -1.1538]}
    {[                50 30 0]}

"what if I wanted each group to be stored in a different matrix and each value is in its corresponding column"

Any particular reason why you want to do that?

You can do that, but it is not recommended, as it inefficient and difficult to work with. Read - Why Variables should not be named Dynamically

[JIAN-HONG YE ZHU]

I wanted to put it in different matrices cause I need to do some operations between matrices, cause all of these points are different points in a A* path planning function. So between group 1 and group 2 I would like to find for example the distance between these two points. And x and y are column 1 and column 2 respectively. So I find the hypotenuse between these points.

The reason for grouping is because if column 3 does not change (which is the angle), I know the points are from a same group. So to find the distance between group 2 and group 3. I would calculate the hypotenuse between 48.8700 63.3800 & 39.8400 38.7500.

[Dyuman Joshi]

You can do that from via the cell array as well.

mat=[51     71	    0
    48.87   63.38   -2.30769230769231
    42.15   55.97	-2.30769230769231
    40.22   47.47   -2.30769230769231
    39.84   38.75   -1.92307692307692
    40.577  34.19	-1.15384615384615
    50	    30      0];

vec=(1:size(mat,1))';
idx=vec([abs(diff(mat(:,3)))>1e-4;true]);
elem=diff([0;idx]);
%storing only 1st 2 columns
out=mat2cell(mat(:,1:2),elem);
out{2}(1,:)

ans = 1×2

48.8700 63.3800

out{3}

ans = 1×2

39.8400 38.7500

norm(out{2}(1,:)-out{3})

ans = 26.2331

Answer 2

[Amit Dhakite]

Hi Jian-Hong,

As per my understanding, you want to group different rows based on the equal values of the 3rd column, only if these rows are next to each other.

The unique() function can indeed be used to group rows based on equal values in a specific column. However, it does not take into account the index position of the rows, and therefore it would not meet your requirement of only grouping together rows with equal values in the 3rd column if they are next to each other in their index position.

To achieve this, you can manually loop through the matrix and group the rows. The approach is to initialize an empty cell array to store the groups of rows. Then, you loop through the sorted matrix and group the rows with equal 3rd column values together. Finally, you display the groups of rows. It can be done as follows:

% Example matrix
A = [51 71 0;    48.87 63.38   -2.30769230769231;    42.15 55.97   -2.30769230769231;    40.22 47.47   -2.30769230769231;    39.84 38.75 	-1.92307692307692;    40.577 34.19 -1.15384615384615;    50 30 0];

% Initialize cell array for storing groups of rows
groups = {};

% Loop through sorted matrix and group rows with equal 3rd column values together
currentGroup = [];
currentValue = A(1,3);
for i = 1:size(A,1)
    if A(i,3) == currentValue
        currentGroup = [currentGroup; A(i,:)];
    else
        groups = [groups; {currentGroup}];
        currentGroup = A(i,:);
        currentValue = A(i,3);
    end
    
    % if its the last row, then just add this currentGroup to the groups
    % array
    if i == size(A,1)
        groups = [groups; {currentGroup}];
    end
end

% Display the groups of rows
for i = 1:numel(groups)
    disp(['Group ', num2str(i), ':']);
    disp(groups{i});
end

Group 1:

    51    71     0

Group 2:

   48.8700   63.3800   -2.3077
   42.1500   55.9700   -2.3077
   40.2200   47.4700   -2.3077

Group 3:

   39.8400   38.7500   -1.9231

Group 4:

   40.5770   34.1900   -1.1538

Group 5:

    50    30     0

To know more about the functions used above, kindly refer to the following links:

1. size(): https://www.mathworks.com/help/matlab/ref/size.html
2. numel(): https://www.mathworks.com/help/matlab/ref/double.numel.html
3. num2str(): https://www.mathworks.com/help/matlab/ref/num2str.html

[JIAN-HONG YE ZHU]

Hello, thanks a lot for your explanation. I see the the groups are stored in a 5x1 cell, what if I wanted each group to be stored in a different matrix and each value is in its corresponding column?