find the position of all non-zero minimum values in each column of a matrix

Hello,

I need your help with the below problem:

I have a matrix something like that:

a = [2 0 3;1 2 5;0 0 0;1 3 3;0 0 6;0 2 7;1 0 0]

and i need to find the position of all minimum (non-zero) values of each column. For example in the first column the position of the three ones, in the second column the position of the two two etc...

I think that it is very easy but I'm stuck

Thanks in advance

Answer 1

[Bruno Luong]

a = [2 0 3;1 2 5;0 0 0;1 3 3;0 0 6;0 2 7;1 0 0]
b=a;
b(b==0)=NaN;
[r,c]=find(b==min(b,[],1));
rmin=accumarray(c(:),r(:),[size(a,2),1],@(r){r});
if ~iscell(rmin) % exceptional case where a contains all 0
    rmin = cell(size(rmin));
end

celldisp(rmin)

Answer 2

[Walter Roberson]

a = [2 0 3;1 2 5;0 0 0;1 3 3;0 0 6;0 2 7;1 0 0] 

a = 7×3

2 0 3 1 2 5 0 0 0 1 3 3 0 0 6 0 2 7 1 0 0

positions = cellfun(@(A) find(A==min(A)), num2cell(a,1), 'uniform', 0)

positions = 1×3 cell array
    {3×1 double}    {4×1 double}    {2×1 double}

The result has to be a cell array because there are a different number of matches in each column.

[Giannis Nikolopoulos]

Hello!! thank you for your answer

I am trying your suggested code to my matlab (R2019a) and the result is only zero in all cells... something must be wrong

[Walter Roberson]

a = [2 0 3;1 2 5;0 0 0;1 3 3;0 0 6;0 2 7;1 0 0] 

a = 7×3

2 0 3 1 2 5 0 0 0 1 3 3 0 0 6 0 2 7 1 0 0

positions = cellfun(@(A) find(A==min(A(A~=0))), num2cell(a,1), 'uniform', 0)

positions = 1×3 cell array
    {3×1 double}    {2×1 double}    {2×1 double}

celldisp(positions)

 
positions{1} =
 
     2
     4
     7

 
 
positions{2} =
 
     2
     6

 
 
positions{3} =
 
     1
     4

 

[Giannis Nikolopoulos]

Thank you for your answer. Indeed there is what I need but I dont know what happened in my matlab. See my results.... there are different and wrong. I only copy paste your suggested code!!

[Walter Roberson]

I wonder if you are using a third-party find() ?

which -all find

[Giannis Nikolopoulos]

Hello,

This is the result of "which -all find", I dont know if it is a third-party or not!!

%%%%%%%%%%%%%%%%%%%%%%

which -all find

find is a variable.

built-in (C:\Program Files\Polyspace\R2019a\toolbox\matlab\elmat\@char\find) % Shadowed char method

built-in (C:\Program Files\Polyspace\R2019a\toolbox\matlab\elmat\@double\find) % Shadowed double method

built-in (C:\Program Files\Polyspace\R2019a\toolbox\matlab\elmat\@int16\find) % Shadowed int16 method

built-in (C:\Program Files\Polyspace\R2019a\toolbox\matlab\elmat\@int32\find) % Shadowed int32 method

built-in (C:\Program Files\Polyspace\R2019a\toolbox\matlab\elmat\@int64\find) % Shadowed int64 method

built-in (C:\Program Files\Polyspace\R2019a\toolbox\matlab\elmat\@int8\find) % Shadowed int8 method

built-in (C:\Program Files\Polyspace\R2019a\toolbox\matlab\elmat\@logical\find) % Shadowed logical method

built-in (C:\Program Files\Polyspace\R2019a\toolbox\matlab\elmat\@single\find) % Shadowed single method

built-in (C:\Program Files\Polyspace\R2019a\toolbox\matlab\elmat\@uint16\find) % Shadowed uint16 method

built-in (C:\Program Files\Polyspace\R2019a\toolbox\matlab\elmat\@uint32\find) % Shadowed uint32 method

built-in (C:\Program Files\Polyspace\R2019a\toolbox\matlab\elmat\@uint64\find) % Shadowed uint64 method

built-in (C:\Program Files\Polyspace\R2019a\toolbox\matlab\elmat\@uint8\find) % Shadowed uint8 method

find is a built-in method % Shadowed javahandle.com.mathworks.hg.peer.Echo method

find is a built-in method % Shadowed schema.class method

find is a built-in method % Shadowed COM.Excel_Application method

find is a built-in method % Shadowed handle.handle method

find is a built-in method % Shadowed handle.subreference__ method

find is a built-in method % Shadowed schema.prop method

find is a built-in method % Shadowed schema.method method

find is a built-in method % Shadowed schema.event method

find is a built-in method % Shadowed handle.listener method

find is a built-in method % Shadowed Interface.000208DB_0000_0000_C000_000000000046 method

find is a built-in method % Shadowed Excel_Application0.WorkbookActivateData method

find is a built-in method % Shadowed handle.EventData method

find is a built-in method % Shadowed Interface.000208DA_0000_0000_C000_000000000046 method

find is a built-in method % Shadowed Interface.000208D7_0000_0000_C000_000000000046 method

find is a built-in method % Shadowed Interface.000208D8_0000_0000_C000_000000000046 method

find is a built-in method % Shadowed Interface.000208D5_0000_0000_C000_000000000046 method

find is a built-in method % Shadowed Interface.00020846_0000_0000_C000_000000000046 method

find is a built-in method % Shadowed javahandle.com.mathworks.hg.peer.HG2FigurePeer method

find is a built-in method % Shadowed javahandle.com.mathworks.hg.peer.ToolbarPeer method

find is a built-in method % Shadowed javahandle.com.mathworks.hg.peer.ToolPushButtonPeer method

find is a built-in method % Shadowed javahandle.com.mathworks.hg.peer.ToolToggleButtonPeer method

find is a built-in method % Shadowed javahandle.com.mathworks.hg.peer.MenuPeer method

find is a built-in method % Shadowed matlab.lang.OnOffSwitchState method

find is a built-in method % Shadowed javahandle.com.mathworks.timer.TimerTask method

find is a Java method % Shadowed com.mathworks.mlwidgets.help.functionregistry.UnlicensedFunctionRegistry method

C:\Program Files\Polyspace\R2019a\toolbox\matlab\bigdata\@tall\find.m % Shadowed tall method

C:\Program Files\Polyspace\R2019a\toolbox\matlab\codetools\@mtree\find.m % Shadowed mtree method

C:\Program Files\Polyspace\R2019a\toolbox\distcomp\parallel\@codistributed\find.m % Shadowed codistributed method

C:\Program Files\Polyspace\R2019a\toolbox\distcomp\gpu\@gpuArray\find.m % Shadowed gpuArray method

built-in (C:\Program Files\Polyspace\R2019a\toolbox\matlab\elmat\find) % Shadowed

>>

[Bruno Luong]

This method fails if a contains all-zero column

a=zeros(3);
positions = cellfun(@(A) find(A==min(A)), num2cell(a,1), 'uniform', 0);
celldisp(positions);

 
positions{1} =
 
     1
     2
     3

 
 
positions{2} =
 
     1
     2
     3

 
 
positions{3} =
 
     1
     2
     3

 

[Walter Roberson]

find is a variable.

Do not assign to a variable named find

[Walter Roberson]

a = zeros(3);
positions = cellfun(@(A) find(A==reshape(min(A(A~=0)),1,[])), num2cell(a,1), 'uniform', 0)

positions = 1×3 cell array
    {0×1 double}    {0×1 double}    {0×1 double}

celldisp(positions)

 
positions{1} =
 
     []
 
 
positions{2} =
 
     []
 
 
positions{3} =
 
     []
 

Answer 3

[Image Analyst]

If you want a lengthier, but less cryptic brute force way of finding the min in each column and the row(s) it occurs at, see this:

a = [2 0 3;1 2 5;0 0 0;1 3 3;0 0 6;0 2 7;1 0 0]
[rows, columns] = size(a)
minOfEachColumn = zeros(columns, 1);
indexesOfEachColumn = cell(columns, 1);
for col = 1 : columns
	thisColumn = a(:, col);
	% Ignore zeros by setting them to inf.
	thisColumn(thisColumn == 0) = inf;
	% Get the min value of what's left.
	minOfEachColumn(col) = min(thisColumn);
	fprintf('For column #%d, the min non-zero value is %f.\n', col, minOfEachColumn(col));
	% Get what index(es) that that min occurs at.
	indexesOfEachColumn{col} = find(thisColumn == minOfEachColumn(col));
end
minOfEachColumn % Display in command window.
celldisp(indexesOfEachColumn)

Answer 4

[Giannis Nikolopoulos]

Hello,

Thank you all (@Image Analyst, @Bruno Luong, @Walter Roberson) for your help. All suggestions are good for me with the prefered results.

@Walter Roberson I restarted my matlab and the result were fine then!!

Best,

Giannis

[Image Analyst]

That should not have been needed. Worst case, you would have just had to do a "clear all". I think your "a" was not what you thought it was.