Solving an iterative procedure with respect to some criteria using MATLAB

I would like to solve the following iterative algorithm based on the given incomplete matrix A, where `-` refers to the missing entries of A (9 missing entries in total):

A = [...
    0.5 0.2  0.6 0.4;...
    -   0.5   -   - ;...
    -    -   0.5  - ;...
    -    -    -  0.5];

Now I want to fill in the incomplete matrix A by following an iterative algorithm using a function of two variables f(i,k) = i+k+3 and respecting the following criteria here

; ; and ;

**EMV_h** denotes the subset of missing values **MV** that can be estimated in step h; **UV_h** denotes Unknown Values in step h; **KV_h** denotes Known Values in step h; **KnownValue** denotes the nondiagonal nonzero entries of A. Hik_1, Hik_2, and Hik_3 are already written/defined in the Matlab code (it is fine!): i.e.,

; ; and .

For instance, in this matrix:

MV = {[2,1], [3,1], [4,1], [3,2], [4,2], [2,3], [4,3], [2,4],[3,4]}; KnownValue = {[1,2], [1,3], [1,4]};

when h=1, EMV_1 = {[3,2], [4,2], [2,3], [4,3], [2,4],[3,4]}; And when h=2, EMV_2 = {[2,1], [3,1], [4,1]};

The Algorithm is:

Step 0. EMV_0 = empty set;

Step 1. h=1;

Step 2. while EMV_h ~= empty set {

Step 3. for every (i,k) in EMV_h {

Step 4. f(i,k)

Step 5. }

Step 6. h=h++

Step 7. }

I wrote a MATLAB code as follows and it works correctly when h=1. i.e., when EMV_1 = MV. But I couldn't go further when `h=2,3,4,...` i.e. when `**EMV_h ~= MV**`. My question/challenge is to construct `EMV_h` and manage it in the Matlab code. How can I write the Matlab code for EMV_h, please? . Thanks in advance!

clear;clc
    global P1;
    global n;
  
    % % Incomplete Matrix
     % 0 indicates the missing entry position
    A = [...
    0.5 0.2 0.6 0.4 ;...
    0   0.5 0   0 ;...
    0  0   0.5  0 ;...
    0  0   0   0.5];
    
    n = size(A,1); 
    M = A; % to write Missing Values (MV)
    P1 = A; % to write the nondiagonal Known (Estimated) Values (EV)
    P1(1:n+1:end)=0; % To make the diagonal elements zero
                  %i.e, to make all P zero except the known entries in the nondiagonal position
    P1;
    % To write  Missing Values
    [r,s] = find(~M); % Find indices and values of zero elements of P
    MV = num2cell([r,s] ,2); %to write the missing values in array
    MV;
    
    % The algorithm
     EMV = {}; % Estimated missing value, EMV = empty set 
       h = 1;      
     while isempty(EMV)  
        EMV = MV; % Missing Values 
       
         index = 1;  % index
        % for every (i,k) in EMV 
        for m = 1:length(EMV) 
            i = EMV{m}(1); % row of EMV
            k = EMV{m}(2); % column of EMV
           EMV{index} = f(i,k); % puts value in the position of A(i,k)
           index = index+1;   
        end       
    EMV; % the value of A(i,k) for any given (i,k), cell array form
    EMV = cell2mat(EMV); % values in column form
        
    % To write a complete matrix
    for s = 1:length(EMV) % s is another index
        % put EMV(s) in the position (i,k);
        A(MV{s}(1),MV{s}(2)) = EMV(s); 
    end
    A
      
    % EMVh{h} = {EMV}
    %  h = h+1;
     end

pik = 0

pik = 0

pik = 0

pik = 8

pik = 9

pik = 8

pik = 10

pik = 9

pik = 10

A = 4×4

0.5000 0.2000 0.6000 0.4000 0 0.5000 8.0000 9.0000 0 8.0000 0.5000 10.0000 0 9.0000 10.0000 0.5000

       
    
    function pik = f(i,k) 
    global P1;
    global n;
     % to write the nondiagonal Known values (EV)
    [u,v]=find(P1); % Find indices and values of nonzero elements of P (nondiagonal)
    KnownValue = num2cell( [u,v] ,2); %to write the Known Values in array
    %
    % Hik_1 = {j~=i,k| (i,j),(j,k) in KnownValue}
    Hik_1=setdiff( intersect(v(u==i),u(v==k)) ,[i,k]);
    % Hik_2 = {j~=i,k| (j,k),(j,i) in KnownValue}
    Hik_2=setdiff( intersect(u(v==i),u(v==k)) ,[i,k]) ;
    % Hik_3 = {j~=i,k| (i,j),(k,j) in KnownValue}
    Hik_3=setdiff( intersect(v(u==i),v(u==k)) ,[i,k]) ;
     
    % To calculate pik
     if ~isempty(Hik_1)||~isempty(Hik_2)||~isempty(Hik_3)    
         pik = i+k+3;
     else
         pik =0;
     end  
     pik
    end

The answer I got: when h=1,

A = [...

0.5000 0.2000 0.6000 0.4000;...

0 0.5000 8.0000 9.0000;...

0 8.0000 0.5000 10.0000;...

0 9.0000 10.0000 0.5000];

When h=2, the answer should be the following, but I couldn't manage to run it inside the while loop at once. I obtained this result after I run it two times independently.

A = [...

0.5000 0.2000 0.6000 0.4000

6.0000 0.5000 8.0000 9.0000

7.0000 8.0000 0.5000 10.0000

8.0000 9.0000 10.0000 0.5000];

[Walter Roberson]

http://www.mathworks.com/help/matlab/math/parameterizing-functions.html

Answer 1

[Karthik P.V]

Please try this and confirm

clear;clc
global P1;
global n;

% % Incomplete Matrix
% 0 indicates the missing entry position
A = [...
    0.5 0.2 0.6 0.4 ;...
    0   0.5 0   0 ;...
    0  0   0.5  0 ;...
    0  0   0   0.5];
for j=1:4%Enter count of h    <New>
    n = size(A,1);
    M = A; % to write Missing Values (MV)
    P1 = A; % to write the nondiagonal Known (Estimated) Values (EV)
    P1(1:n+1:end)=0; % To make the diagonal elements zero
    %i.e, to make all P zero except the known entries in the nondiagonal position
    P1;
    % To write  Missing Values
    [r,s] = find(~M); % Find indices and values of zero elements of P
    MV = num2cell([r,s] ,2); %to write the missing values in array
    MV;
    
    % The algorithm
    EMV = {}; % Estimated missing value, EMV = empty set
    
    h = j; % <New>
    if isempty(EMV) && ~isempty(MV) % <Mod>
        EMV = MV; % Missing Values
        
        index = 1;  % index
        % for every (i,k) in EMV
        for m = 1:length(EMV)
            i = EMV{m}(1); % row of EMV
            k = EMV{m}(2); % column of EMV
            EMV{index} = f(i,k); % puts value in the position of A(i,k)
            index = index+1;
        end
        EMV; % the value of A(i,k) for any given (i,k), cell array form
        EMV = cell2mat(EMV); % values in column form
        
        % To write a complete matrix
        for s = 1:length(EMV) % s is another index
            % put EMV(s) in the position (i,k);
            A(MV{s}(1),MV{s}(2)) = EMV(s);
        end
        A
        
        % EMVh{h} = {EMV}
        %  h = h+1;
    end
    %     EMV = {};
end


function pik = f(i,k)
global P1;
global n;
% to write the nondiagonal Known values (EV)
[u,v]=find(P1); % Find indices and values of nonzero elements of P (nondiagonal)
KnownValue = num2cell( [u,v] ,2); %to write the Known Values in array
%
% Hik_1 = {j~=i,k| (i,j),(j,k) in KnownValue}
Hik_1=setdiff( intersect(v(u==i),u(v==k)) ,[i,k]);
% Hik_2 = {j~=i,k| (j,k),(j,i) in KnownValue}
Hik_2=setdiff( intersect(u(v==i),u(v==k)) ,[i,k]) ;
% Hik_3 = {j~=i,k| (i,j),(k,j) in KnownValue}
Hik_3=setdiff( intersect(v(u==i),v(u==k)) ,[i,k]) ;

% To calculate pik
if ~isempty(Hik_1)||~isempty(Hik_2)||~isempty(Hik_3)
    pik = i+k+3;
else
    pik =0;
end
pik
end

[HAT]

@Karthik Thanks. It works. However, I am still thinking on how to apply the "while loop" inside the matlab code, instead of the "for loop". Because in the case of "while loop" we don't have to restrict h value. In the case of "for loop", we must give a fixed h value in order to stop the execusion. By the way, I have edited the algorithm (Step 0) "MV_0" into "EMV_0". It was a type error (sorry!). Actually, it will not make a difference in the matlab code provided.

[Karthik P.V]

clear;clc
global P1;
global n;

% % Incomplete Matrix
% 0 indicates the missing entry position
A = [...
    0.5 0.2 0.6 0.4 ;...
    0   0.5 0   0 ;...
    0  0   0.5  0 ;...
    0  0   0   0.5];
h=0;
EMV=[];
MV=0;
while (isempty(EMV) && ~isempty(MV))%for j=1:2%Enter count of h    <New>
    n = size(A,1);
    M = A; % to write Missing Values (MV)
    P1 = A; % to write the nondiagonal Known (Estimated) Values (EV)
    P1(1:n+1:end)=0; % To make the diagonal elements zero
    %i.e, to make all P zero except the known entries in the nondiagonal position
    P1;
    % To write  Missing Values
    [r,s] = find(~M); % Find indices and values of zero elements of P
    MV = num2cell([r,s] ,2); %to write the missing values in array
    MV;
    
    % The algorithm
    EMV = {}; % Estimated missing value, EMV = empty set
    
%     h = j; % <New>
    while (isempty(EMV) && ~isempty(MV)) % <Mod>
        EMV = MV; % Missing Values
        
        index = 1;  % index
        % for every (i,k) in EMV
        for m = 1:length(EMV)
            i = EMV{m}(1); % row of EMV
            k = EMV{m}(2); % column of EMV
            EMV{index} = f(i,k); % puts value in the position of A(i,k)
            index = index+1;
        end
        EMV; % the value of A(i,k) for any given (i,k), cell array form
        EMV = cell2mat(EMV); % values in column form
        
        % To write a complete matrix
        for s = 1:length(EMV) % s is another index
            % put EMV(s) in the position (i,k);
            A(MV{s}(1),MV{s}(2)) = EMV(s);
        end
        A
        
        % EMVh{h} = {EMV}
         h = h+1;
    end
        EMV = {};
end


function pik = f(i,k)
global P1;
global n;
% to write the nondiagonal Known values (EV)
[u,v]=find(P1); % Find indices and values of nonzero elements of P (nondiagonal)
KnownValue = num2cell( [u,v] ,2); %to write the Known Values in array
%
% Hik_1 = {j~=i,k| (i,j),(j,k) in KnownValue}
Hik_1=setdiff( intersect(v(u==i),u(v==k)) ,[i,k]);
% Hik_2 = {j~=i,k| (j,k),(j,i) in KnownValue}
Hik_2=setdiff( intersect(u(v==i),u(v==k)) ,[i,k]) ;
% Hik_3 = {j~=i,k| (i,j),(k,j) in KnownValue}
Hik_3=setdiff( intersect(v(u==i),v(u==k)) ,[i,k]) ;

% To calculate pik
if ~isempty(Hik_1)||~isempty(Hik_2)||~isempty(Hik_3)
    pik = i+k+3;
else
    pik =0;
end
pik
end

Can you try this?

Note: I have not captured the algorithm changes here

[HAT]

Thank you so much Karthik.