How to speed up processing and reduce memory with nested for loops

This program calculates optical transmittance in seawater for different combinations of optical filters and then finds the best statistical match to a target curve. It appears to work well (experimentally unverified) with 16 filters and lower constraints but I needed to see the closest (theoretical) match that could be obtained with all the 48 filters that I have data for.

It basically does this calculation: by using 48 nested for loops to increment the a, b, n variables. This is workspace I start with I start with:

T_Calc = double.empty(0,1E6);
Index  = single.empty(0,1E6);

Total_FilterConstraint = 8; %This is the total number of filters used in the solution, not the number of filter's data sampled
Ind_FilterConstraint = 4;

for A= 0:1:Ind_FilterConstraint
    
    for B= 0:1:Ind_FilterConstraint
        Total = A+ B;
        if Total > Total_FilterConstraint 
            break;
        end
        for C= 0:1:Ind_FilterConstraint
            Total = A+ B+ C;
            if Total > Total_FilterConstraint 
                break;
            end
                .... Shortened for forum (there are 48 of these)

  for AV = 0:1:Ind_FilterConstraint              
      Total = A+ B+ C+ D+ E+ F+ G+ H+ I+ J+ K+ L+ M+ N+ O+ P+ Q+ R+ S+ T+ U+ V+ W+ X+ Y+ Z+ AA+ AB+	AC+	AD+	AE+	AF+	AG+ AH+ AI+ AJ+ AK+ AL+ AM+ AN+ AO+ AP+ AQ+ AR+...
            AS+ AT+ AU+ AV;  
      if Total >Total_FilterConstraint  
        break;
       end
                            
    Filter_Combos = {A; B;	C;	D;	E;	F;	G;	H; I; J; K; L;	M;	N;	O;	P;	Q;	R;	S;	T;	U;	V;	W;	X;	Y;	Z;	AA;	AB;	AC;	AD;	AE;	AF;	AG;	AH;	AI;	AJ;	AK;...
        AL;	AM;	AN;	AO;	AP;	AQ;	AR;	AS;	AT;	AU;	AV};
    
    Filter_Transmittance = (Filterdata.Glass.^A).*(Filterdata.BG40.^B).*(Filterdata.BG50.^C).*(Filterdata.B370.^D).*(Filterdata.EB390.^E).*(Filterdata.B410.^F).*...
        (Filterdata.B440.^G).*(Filterdata.B460.^H).*(Filterdata.G530.^I).*(Filterdata.G533.^J).*(Filterdata.G545.^K).*(Filterdata.G550.^L).*...
        (Filterdata.LA20.^M).*(Filterdata.LA40.^N).*(Filterdata.ELA80.^O).*(Filterdata.ELA100.^P).*(Filterdata.ELA120.^Q).*(Filterdata.ELA140.^R).*...
        (Filterdata.ELA200.^S).*(Filterdata.LB20.^T).*(Filterdata.LB40.^U).*(Filterdata.LB80.^V).*(Filterdata.LB100.^W).*(Filterdata.LB120.^X).*...
        (Filterdata.LB140.^Y).*(Filterdata.LB200.^Z).*(Filterdata.C500S.^AA).*(Filterdata.C5000.^AB).*(Filterdata.CD700.^AC).*(Filterdata.CM700.^AD).*...
        (Filterdata.L37.^AE).*(Filterdata.UV28N.^AF).*(Filterdata.UV30N.^AG).*(Filterdata.ND03.^AH).*(Filterdata.ND1.^AI).*(Filterdata.ND3.^AJ).*...
        (Filterdata.ND5.^AK).*(Filterdata.ND10.^AL).*(Filterdata.ND13.^AM).*(Filterdata.ND15.^AN).*(Filterdata.ND20.^AO).*(Filterdata.ND25.^AP).*...
        (Filterdata.ND30.^AQ).*(Filterdata.ND40.^AR).*(Filterdata.ND50.^AS).*(Filterdata.ND60.^AT).*(Filterdata.ND70.^AU).*(Filterdata.ND80.^AV).*(0.96^2);
    
    T_Calc = [T_Calc, Filter_Transmittance];
    Index = [Index, Filter_Combos];
 end % AV for loop

I ran into problems when I increased the total filters to 8 and duplicates of the same filters to 4. It ran for a whole week straight before I had to halt the process and the whole program crashed and said it ran out of memory when I tried to copy the data to excel.

Is there a way to make this faster and not so unstable?

It had completed ~750k calculations when i paused it and it crashed.

There are other sections that do least squares, sorting, and finally export to excel but I couldn't even get to those sections.

Answer 1

[Sulaymon Eshkabilov]

For most of calcs in your code can be done directly without [for .. end] loops, e.g.:

A= 0:Ind_FilterConstraint;
B=A;
C=B;
% for A= 0:1:Ind_FilterConstraint
%     
%     for B= 0:1:Ind_FilterConstraint
%         Total = A+ B;
%         if Total > Total_FilterConstraint 
%             break;
%         end
%         for C= 0:1:Ind_FilterConstraint
%             Total = A+ B+ C;
%             if Total > Total_FilterConstraint 
%                 break;
%             end
Total = A+B+C;
...
    

SImilarly, you can simplify the rest.

[phillip benoit]

I should have specified, the variables A, B, C... represent the number of individual filters used. There are two outputs needed from this section of code.

1. The transmittance which is a 41x1 array for a particular combination of filters
2. The combination of filters that it takes to make that curve

I was using the for loops to make it calculate Filter_Transmittance for all possible combinations of filters or the variables A,B,C, etc.

If I overwrite those variables to make the total combinations, won't I lose the ability to know what combinations made the transmittance curve?