Learning Matlab through Algebra examples.

algebra2.m

%% Multiplying a Matrix by Another Matrix
% https://www.mathsisfun.com/algebra/matrix-multiplying.html

% But to multiply a matrix by another matrix we need to
% do the "dot product" of rows and columns ...
% what does that mean? Let us see with an example:

% Method 1: Using MATLAB.
A = [1 2 3
    4 5 6]

B = [7   8
    9  10
    11 12]

C = A * B


[A_rows, A_columns] = size(A)
[B_rows, B_columns] = size(B)

% Method 2:
% Matrix result has this shape.
% help zeros
C2 = zeros(A_rows, B_columns)
% Loop through each row, using the dot product.
for A_row_index = 1:A_rows
    fprintf('Calculating A Row %d\n', A_row_index)
    % And through each column.
    for B_column_index = 1:B_columns
        fprintf('Calculating B Column %d\n', B_column_index)
        % To calculate the result.
        row = A(A_row_index,:)
        column = B(:, B_column_index)
        % The
        C2(A_row_index, B_column_index) = dot(row, column)
    end
end

% Method 3:
% Loops on loops.
C3 = zeros(A_rows, B_columns)
% Loop through each row, using the dot product.
for A_row_index = 1:A_rows
    fprintf('Calculating A Row %d\n', A_row_index)
    % And through each column.
    for B_column_index = 1:B_columns
        fprintf('Calculating B Column %d\n', B_column_index)
        % To calculate the result.
        row = A(A_row_index,:)
        column = B(:, B_column_index)
        assert(length(row)==length(column))
        accumulator = 0
        for index = 1:length(row)
            Number1 = row(index)
            Number2 = column(index)
            % Other languages have += operators:
            % accumulator += Number1*Number2
            accumulator = accumulator + Number1*Number2
            C3(A_row_index, B_column_index) = dot(row, column)
        end
    end
end

assert(all(all(C==C2)))
assert(all(all(C==C3)))
assert(all(all(C2==C3)))