Matlab if loop function, How to improve this function? - matlab

Question

I am new to matlab and I am trying to figure how to write the following function in a smart/efficient way.
First I create a matrix y with entries HL, and every line is a permutation of a predefined length n.
For example, for n=3 I get the first line of the matrix y : H H H. Then I want for each line, to create a matrix of size n x n where for example the entry (1,2) corresponds to a variable which links entry y(1,1) with y(1,2) , and entry y(3,2) corresponds to a variable which links entry y(1,3) with y(1,2). Is this possible?
function A1=mystupidfunction(s , n)
%n is the number of agents and s is the number of state, this function
%returns the matrix of influence. Stupid code must be improved to work for
%n agents
x = 'HL'; %// Set of possible types
K = n; %// Length of each permutation
%// Create all possible permutations (with repetition) of letters stored in x
C = cell(K, 1); %// Preallocate a cell array
[C{:}] = ndgrid(x);
y = cellfun(#(x){x(:)}, C);
y = [y{:}];
A1 = sym('A1',[n n], 'positive' );
syms H L A_HH A_HL A_LH A_LL
for k=s
for i=1:n
for j=1:n
if ( y(k,1)==H) && ( y(k,2)==H) && (y(k,3)==H)
A1(i,j)=A_HH
elseif ( y(k,1)==L) && ( y(k,2)==L) && (y(k,3)==L)
A1(i,j)=A_LL
elseif ( y(k,1)==H) && ( y(k,2)==L) && (y(k,3)==L)
A1(1,1)=A_HH
A1(1,2)=A_HL
A1(1,3)=A_HL
A1(2,1)=A_LH
A1(3,1)=A_LH
A1(2,2)=A_LL
A1(2,3)=A_LL
A1(3,3)=A_LL
A1(3,2)=A_LL
elseif ( y(k,1)==H) && ( y(k,2)==H) && (y(k,3)==L)
A1(1,1)=A_HH
A1(1,2)=A_HH
A1(1,3)=A_HL
A1(2,1)=A_HH
A1(3,1)=A_LH
A1(2,2)=A_HH
A1(2,3)=A_HL
A1(3,3)=A_LL
A1(3,2)=A_LH
elseif ( y(k,1)==L) && ( y(k,2)==L) && (y(k,3)==H)
A1(1,1)=A_LL
A1(1,2)=A_LL
A1(1,3)=A_LH
A1(2,1)=A_LL
A1(3,1)=A_LH
A1(2,2)=A_LL
A1(2,3)=A_LH
A1(3,3)=A_HH
A1(3,2)=A_HL
elseif ( y(k,1)==L) && ( y(k,2)==H) && (y(k,3)==H)
A1(1,1)=A_LL
A1(1,2)=A_LH
A1(1,3)=A_LH
A1(2,1)=A_HL
A1(3,1)=A_HL
A1(2,2)=A_HH
A1(2,3)=A_HH
A1(3,3)=A_HH
A1(3,2)=A_HH
elseif ( y(k,1)==L) && ( y(k,2)==H) && (y(k,3)==L)
A1(1,1)=A_LL
A1(1,2)=A_LH
A1(1,3)=A_LL
A1(2,1)=A_HL
A1(3,1)=A_LL
A1(2,2)=A_HH
A1(2,3)=A_HL
A1(3,3)=A_LL
A1(3,2)=A_LH
elseif ( y(k,1)==H) && ( y(k,2)==L) && (y(k,3)==H)
A1(1,1)=A_HH
A1(1,2)=A_HL
A1(1,3)=A_HH
A1(2,1)=A_LH
A1(3,1)=A_HH
A1(2,2)=A_LL
A1(2,3)=A_HL
A1(3,3)=A_HH
A1(3,2)=A_HL
else A(i,j)=0
end
end
end
end
For example when n=3 and s=1, then the function returns:
A =
[ A_HH, A_HH, A_HH]
[ A_HH, A_HH, A_HH]
[ A_HH, A_HH, A_HH]
notes:
C = cell(K, 1); %// Preallocate a cell array
[C{:}] = ndgrid(x); %// Create K grids of values
y = cellfun(#(x){x(:)}, C); %// Convert grids to column vectors
y = [y{:}];
the output is for n=3 :
y =
HHH
LHH
HLH
LLH
HHL
LHL
HLL
LLL
s is just a scalar that indicates the number of line in the matrix y (which corresponds to a "state")

Answer 1

if you only have 2 states H and L, as you said in comment you could just as well use 0 and 1, so a binary logic.
To get your y combinations, just count in binary until you have the right number of digit and convert each bit to the state you decide:
So for order n=3 you would have:
n = 3 ;
a = de2bi( (0:2^n-1).' )
which gives you all 3 digits binary combinations:
a =
0 0 0
1 0 0
0 1 0
1 1 0
0 0 1
1 0 1
0 1 1
1 1 1
If you want them in ascii format, you can then convert them:
b = char( ones(size(a))* 'L') ;
b(~a) = 'H' ;
To obtain:
b =
HHH
LHH
HLH
LLH
HHL
LHL
HLL
LLL
So if you want to keep a "ascii" character logic (and output), this could do the job:
function out = combiadjacent( k , n )
yb = de2bi( (0:2^n-1).' ) ; %'// get the combinations
y = char( ones(size(yb))* 'L') ;
y(~yb) = 'H' ;
A = char( zeros(n,2*n) ) ;
for col=1:n
Acol = [col col+1] + (col-1) ;
A(:,Acol) = [y(k,col)*ones(n,1) y(k,:).'] ;
end
out = reshape( cellstr( reshape(A.',2,[]).' ) , n , n ).' ;
Will give you a cell array as output like:
>> A = combiadjacent( 4 , 3 )
A =
'LL' 'LL' 'HL'
'LL' 'LL' 'HL'
'LH' 'LH' 'HH'
However, if you are not picky about the exact output format, the solution below will probably run significantly faster:
function out = combiadjacent( k , n )
y = de2bi( (0:2^n-1).' ) ; %'// get the combinations
b = ones(n,1)*y(k,:) ;
%// use that to get a cell array of characters
out = cellfun( #(a,b) char(cat(2,a+65,b+65)) , num2cell(b) ,num2cell(b.'),'uni',0) ;
%'// or use that to get a cell array of double in output (even faster)
%// out = cellfun( #(a,b) cat(2,a,b) , num2cell(b) ,num2cell(b.'),'uni',0)
%// or that to get a cell array of boolean
%// out = cellfun( #(a,b) logical(cat(2,a,b)) , num2cell(b) ,num2cell(b.'),'uni',0) ;
Which will give you
>> A = combiadjacent( 4 , 3 )
A =
'BB' 'BB' 'AB'
'BB' 'BB' 'AB'
'BA' 'BA' 'AA'
note: Whatever solution you choose, it would be prudent to add a checking condition for k to make sure the user will not request a line which doesn't exist.