MATLAB: Error in size of matrix and vectorization and loop not working and non-singleton rhs dimension

errorMATLABmatrix arrayvectorization

Hi,
I have been trying to create a code, where I end up with temperature values for different surfaces over a time period and should end up with 5×5 array. However, I only seem to end up getting a 1×5 array and also the calculation is not correct as it does not use the element I want it to. The script is below.
Thank you
clc,clear
V = [1;2;3;4;5]
ho = 0.6 + 6.64.*sqrt(V)
k = [1 2 3 4 5]
lamda = [6 7 8 9 10]
hi = 2
x = (1./ho)
y = (1/hi)
z = (lamda./k)
S = [11 12 13 14 15;]
U = x + y + z 
ma=1
ca=2
DTM=1
deltat=1
Tout=5
ms=1
cs=1
index=1:5;
SQAmb = zeros(numel(index), numel(S));    %Preallocation of Ambient Load (Surface) matrix
SQAmb_Tot = zeros(size(index));           %Preallocation of Total Ambient Load (Surface) matrix
QAmb = zeros(numel(index), numel(S));     %Preallocation of Ambient Load (Air) matrix
QAmb_Tot = zeros(size(index));            %Preallocation of Total Ambient Load (Air) matrix
SQTot = zeros(size(index));               %Preallocation of Total Surface Heat Load matrix
deltaTs = zeros(size(index));             %Preallocation of deltaTs matrix
Ts = zeros(size(index));                  %Preallocation of Surface temperature matrix
QTot = zeros(size(index));                %Preallocation of Total Heat Load matrix
deltaTin = zeros(size(index));            %Preallocation of deltaTin matrix
Tin = zeros(size(index));                 %Preallocation of car cabin temperature matrix
for i=index
if (i)==1
%Ambient Load (Surface), where 20 is the intial temperature at t=0   
    
    SQAmb(i,:) = S*U*(Tout-20)
(the first value of this array should be: the first element of S which is (11) * first element of U* temp diff (-15), this should come out to -1095.2865 but does not)
(if vectorization is used i.e. S.*U.*(Tout-20) then an error to do with "Assignment has more non-singleton rhs dimensions than non-singleton subscripts is produced")
(and if element is selected one at a time by SQAmb(i,:) = S*U(i)*(Tout-20) , the array that is formed for the Temperature at the end is not a 5×5 array)
%Total Ambient Load (Surface) in Array Form

   
    SQAmb_Tot(i) = sum(SQAmb(i,:))
    
%Ambient Load (Air), where 20 is the intial air and surface temperatures at t=0
    QAmb(i,:) = S*U*(20-20);
%Total Ambient Load (Air) in Array Form

   
    QAmb_Tot(i) = sum(QAmb(i,:))
%Total Surface Heat Transfer Load

    SQTot(i) = SQAmb_Tot(i)
    
%change in surface temperature where deltat is timestep    

    
    deltaTs(i) = (SQTot(i)/((ms*cs)+DTM))*(deltat)
%New surface temperature         

    
    Ts(i) = 20 + deltaTs(i)    
    
%Total Heat Transfer Load

    
    QTot(i) = QAmb_Tot(i) 
%change in air cabin temperature where deltat is timestep

    
    deltaTin(i) = (QTot(i)/((ma*ca)+DTM))*(deltat)
%New car cabin temperature          

   
    Tin(i) = 20 + deltaTin(i)
else 
%Ambient Load (Surface)   
   
    SQAmb(i,:) = S*U*(Tout-(2*Ts(i-1))+Tin(i-1)) 
%Total Ambient Load (Surface) in Array Form
    
    SQAmb_Tot(i) = sum(SQAmb(i,:)) 
%Ambient Load (Air)
    
    QAmb(i,:) = S*U*((Ts(i-1))-Tin(i-1))
%Total Ambient Load (Air) in Array Form
    
    QAmb_Tot(i) = sum(QAmb(i,:))
%Total Surface Heat Transfer Load
    SQTot(i) = SQAmb_Tot(i)
    
%change in surface temperature where deltat is timestep    
    
    deltaTs(i) = (SQTot(i)/((ms*cs)+DTM))*(deltat)
%New surface temperature         
    
    Ts(i) = Ts(i-1) + deltaTs(i)   
    
    
%Total Heat Transfer Load
QTot(i) =  QAmb_Tot(i) 
%change in air cabin temperature where deltat is timestep
deltaTin(i) = (QTot(i)/((ma*ca)+DTM))*(deltat)
%New car cabin temperature          
Tin(i) = Tin(i-1)+deltaTin(i)
end
end

Best Answer

Your S is 1 x 5. Your U is 5 x 5. Your Tout is scalar.
S*U is valid in MATLAB because the "inner dimensions" agree for the matrix multiplication: (1x5) * (5x5) gives a 1 x 5 resulting inner product. The first element of that output would be dot(S,U(:,1)) * (Tout-20)
When you vectorize S.*U.*(Tout-20) you are asking to do element-by-element multiplication between a 1 x 5 and a 5 x 5. In R2016a and earlier, that was an error. In R2016b and later, the effect is as-if you had done
bsxfun(@times, S, U) .* (Tout-20)
which would be like
repmat(S, size(U,1), 1) .* U .* (Tout-20)
and the size of that output is going to be 5 x 5, same size as U.
If you are wondering why U is 5 x 5: U = x + y + z. x is 5 x 1, y is scalar, z is 1 x 5. The operation is like 
bsxfun(@plus, bsxfun(@plus, x, y), z)
which is like
repmat(x, 1, size(z,2)) + y + repmat(z, size(x,1), 1)
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