Multiplication of High Dimensional Matrices

Hello everyone!

I have a 4-D matrix and a 2-D matrix. I want to multiply the two and form a new 6-D matrix. Please see the following example.

corr_tauk=1:4;
corr_taun=1:4;
corr_tauc=1:4;
corr_g=1:4;
periods=2500;
vnodes_e=2000;
RtnDtr_e=randn(periods,vnodes_e);
r_itr=ones(length(corr_tauk),length(corr_taun),length(corr_tauc),length(corr_g));
Mtx_ridio=zeros(length(corr_tauk),length(corr_taun),length(corr_tauc),length(corr_g),periods,vnodes_e);

Now I confront a big problem to get Mtx_ridio. The idea is pointwise-multiplication to form an even higher dimensional matrix to reflect the cross-section at each period with each mix of parameters.

It seems like Mtx_ridio=r_itr.*RtnDtr_e, but definitely not.

Does anyone have an easy solution?

Answer 1

[Aneela]

Hi Meng Li,

The point-wise multiplication you mentioned:

Mt_ridio=r_itr.*RtnDtr_e 

This throws an error as “r_itr” and “RtnDtr_e” are having incompatible sizes.

I tried the below example in MATLAB, and it worked. I reduced the values of “periods” and “vnodes_e” to 10 each, to reduce the compilation time.

corr_tauk=1:4;
corr_taun=1:4;
corr_tauc=1:4;
corr_g=1:4;
periods=10;
vnodes_e=10;
RtnDtr_e=randn(periods,vnodes_e);
r_itr=ones(length(corr_tauk),length(corr_taun),length(corr_tauc),length(corr_g));
Mtx_ridio=zeros(length(corr_tauk),length(corr_taun),length(corr_tauc),length(corr_g),periods,vnodes_e);
for i = 1:length(corr_tauk)
    for j = 1:length(corr_taun)        
        for k = 1:length(corr_tauc)            
            for l = 1:length(corr_g)                
                Mtx_ridio(i,j,k,l,:,:) = r_itr(i,j,k,l) .* RtnDtr_e;
            end            
        end
    end    
end

For more information on point-wise multiplication, refer to the following MathWorks Documentation: https://www.mathworks.com/help/matlab/ref/times.html

Answer 2

[Steven Lord]

Either reshape or permute your matrix into a 6-dimensional array whose first four dimensions are singletons. Then use times. Here's a smaller example that creates a 4-dimensional array from two 2-dimensional matrices.

A = magic(3)

A = 3x3

8 1 6 3 5 7 4 9 2

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B = randi([10 20], 3, 3)

B = 3x3

15 10 12 18 17 16 18 17 20

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B4 = reshape(B, [1 1 3 3]) % or

B4 = 
B4(:,:,1,1) =

    15


B4(:,:,2,1) =

    18


B4(:,:,3,1) =

    18


B4(:,:,1,2) =

    10


B4(:,:,2,2) =

    17


B4(:,:,3,2) =

    17


B4(:,:,1,3) =

    12


B4(:,:,2,3) =

    16


B4(:,:,3,3) =

    20

B4 = permute(B, [3 4 1 2])

B4 = 
B4(:,:,1,1) =

    15


B4(:,:,2,1) =

    18


B4(:,:,3,1) =

    18


B4(:,:,1,2) =

    10


B4(:,:,2,2) =

    17


B4(:,:,3,2) =

    17


B4(:,:,1,3) =

    12


B4(:,:,2,3) =

    16


B4(:,:,3,3) =

    20

C = A.*B4

C = 
C(:,:,1,1) =

   120    15    90
    45    75   105
    60   135    30


C(:,:,2,1) =

   144    18   108
    54    90   126
    72   162    36


C(:,:,3,1) =

   144    18   108
    54    90   126
    72   162    36


C(:,:,1,2) =

    80    10    60
    30    50    70
    40    90    20


C(:,:,2,2) =

   136    17   102
    51    85   119
    68   153    34


C(:,:,3,2) =

   136    17   102
    51    85   119
    68   153    34


C(:,:,1,3) =

    96    12    72
    36    60    84
    48   108    24


C(:,:,2,3) =

   128    16    96
    48    80   112
    64   144    32


C(:,:,3,3) =

   160    20   120
    60   100   140
    80   180    40

To check let's multiply A by one of the elements in B then compare it against the appropriate section of C.

check1 = A.*B(2, 3)

check1 = 3x3

128 16 96 48 80 112 64 144 32

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check2 = C(:, :, 2, 3)

check2 = 3x3

128 16 96 48 80 112 64 144 32

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