MATLAB: Product of three 1d vectors and a 3d array

arrayMATLAB

Say I am given three n-dimesional vectors

and an

array T. Is there a way to compute the quantity

without using a for loop?

Best Answer

aPermuted = a(:);
bPermuted = permute (b(:),[2,1,3]);
cPermuted = permute (c(:),[3,2,1]);
Z = T .* aPermuted .* bPermuted .* cPermuted;
Result = sum (Z,'all');

Related Solutions

MATLAB: 1D Advection-Diffusion

Perhaps this will help

% Concentration Distribution of contaminant (C)
T = 4000*24;        % [hrs] total time 
D = (1E-6)*3600;   % [m^2/hr] diffusion constant 
V = (1E-7)*3600;   % [m/hr] velocity 
L = 100;           % [m] Total length
N = 20;      % apatial grid sections
M = 40;      % temporal grid sections
dx = L/N;     % spatial spacing
dt = T/M;     % time spacing
C=zeros(N+1,M+1); % allocate space for concentrations
% (C(x,t+dt) - C(x,t))/dt = -V*(C(x,t)-C(x-dx,t))/dx 
%                           +D*(C(x+dx,t)-2*C(x,t)+C(x-dx,t))/dx^2
%
% C(x,t+dt) = C(x,t) + (D*dt/dx^2)*(C(x+dx,t)-2C(x,t)+C(x-dx,t))
%                    - (V*dt/dx)*(C(x,t)-C(x-dx,t))
F = D*dt/dx^2;
G = V*dt/dx;
C(1,:) = 100;   % inlet concentration set to 100 for all time
for c = 1:M   % timesteps
   
    for r = 2:N  % spatial steps
        C(r,c+1) = C(r,c)+F*(C(r+1,c)-2*C(r,c)+C(r-1,c)) ...
                         -G*(C(r,c)-C(r-1,c));            
    end
     
end
t = 0:dt:T;
x = 0:dx:L;
plot(x,C(:,M/2),x,C(:,M)),grid
xlabel('x'),ylabel('C')
legend(['C at time ' num2str(M*dt/(2*24)) ' days'],['C at time ' num2str(M*dt/24) ' days']) 
figure
[t,x] = meshgrid(t,x);
surf(t,x,C)
xlabel('time [hrs]'),ylabel('distance [m]'),zlabel('Concentration')

MATLAB: 1D array combinations

This will generate a cell array of all combinations of all possible lengths:

C = cell(size(A));
for k = 1:numel(C)
    C{k} = nchoosek(A,k);
end

contained inside this cell array:

>> C{:}
ans =
   1
   2
   3
   4
   5
ans =
   1   2
   1   3
   1   4
   1   5
   2   3
   2   4
   2   5
   3   4
   3   5
   4   5
ans =
   1   2   3
   1   2   4
   1   2   5
   1   3   4
   1   3   5
   1   4   5
   2   3   4
   2   3   5
   2   4   5
   3   4   5
ans =
   1   2   3   4
   1   2   3   5
   1   2   4   5
   1   3   4   5
   2   3   4   5
ans =
   1   2   3   4   5

Without padding they will not fit into one numeric array, as they have different number of columns. To pad them try this:

C = cell(size(A));
for k = 1:numel(C)
    tmp = nchoosek(A,k);
    C{k} = [tmp,NaN(size(tmp,1),numel(A)-k)];
end
N = cell2mat(C);

which creates this numeric array:

>> N
N =
     1   NaN   NaN   NaN   NaN
     2   NaN   NaN   NaN   NaN
     3   NaN   NaN   NaN   NaN
     4   NaN   NaN   NaN   NaN
     5   NaN   NaN   NaN   NaN
     1     2   NaN   NaN   NaN
     1     3   NaN   NaN   NaN
     1     4   NaN   NaN   NaN
     1     5   NaN   NaN   NaN
     2     3   NaN   NaN   NaN
     2     4   NaN   NaN   NaN
     2     5   NaN   NaN   NaN
     3     4   NaN   NaN   NaN
     3     5   NaN   NaN   NaN
     4     5   NaN   NaN   NaN
     1     2     3   NaN   NaN
     1     2     4   NaN   NaN
     1     2     5   NaN   NaN
     1     3     4   NaN   NaN
     1     3     5   NaN   NaN
     1     4     5   NaN   NaN
     2     3     4   NaN   NaN
     2     3     5   NaN   NaN
     2     4     5   NaN   NaN
     3     4     5   NaN   NaN
     1     2     3     4   NaN
     1     2     3     5   NaN
     1     2     4     5   NaN
     1     3     4     5   NaN
     2     3     4     5   NaN
     1     2     3     4     5

Best Answer

Related Solutions

MATLAB: 1D Advection-Diffusion

MATLAB: 1D array combinations

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