function Multiply(m,n,p)
% Multiply, 9/9/2023.
% Matrix Multiplication.
%
% Multiply(m,n,p)
% [m-by-n] * [n-by-p]
%
% '|' Rows or columns
% '/' Slow or fast
% 'S' Subscript or Magic square
% 'm' Row dimension
% 'n' Inner dimension
% 'p' Column dimension
% '#' Animation
%
% See: https://blogs.mathworks.com/cleve/2023/09/10/exploring-matrices 

%   Copyright 2016-2023 Cleve Moler

    if nargin == 0
        mfigure
        m = 4;
        n = 4;
        p = 1;  
        minit(m,n,p)
    elseif nargin == 1
        fud = get(gcf,'userdata');
        m = fud{1}; 
        n = fud{2}; 
        p = fud{3};
        HA = fud{4};
        HB = fud{5};
        HC = fud{6};
    else
        mfigure
        minit(m,n,p)
        fud = get(gcf,'userdata');
        HA = fud{4};
        HB = fud{5};
        HC = fud{6};
    end
        
    if nargin ~= 1
        return
    end  

    speed = get(findobj('callback',@mspeedcb),'value') == 1;
    if speed
        paws = 0.1;
    else
        paws = 0.5;
    end

    for i = 1:m
        for k = 1:p
            set(HC(i,k),'userdata',0, ... 
                'string','0')
        end
    end
    pause(paws)

    mx = get(findobj('callback',@mxcb),'value') == 1;
    objs = findobj('callback',@mroccb);
    ijk = get(objs(end),'string');
    switch ijk
        case {'|―#','|'}    
            for k = 1:p
                for j = 1:n
                    for i = 1:m
                        core(i,j,k)
                        if mx, break, end
                    end
                    pause(paws)
                    if mx, break, end
                end
                if mx, break, end
           end
        case {'―|#','―'}
            for k = 1:p
                for i = 1:m
                    for j = 1:n
                        core(i,j,k)
                    end
                    pause(paws)
                    if mx, break, end
                end
            end

        case '#|―'
            for j = 1:n
                for i = 1:m
                    for k = 1:p
                        core(i,j,k)
                    end
                    pause(paws)
                    if mx, break, end
                end
            end
        case '#―|'
            for i = 1:m
                for j = 1:n
                    for k = 1:p
                        core(i,j,k)
                    end
                    pause(paws)
                    if mx, break, end
                end
            end

        case '|#―'
            for j = 1:n
                for k = 1:p
                    for i = 1:m
                        core(i,j,k)
                    end
                    pause(paws)
                    if mx, break, end
                end
            end
        case '―#|'
            for i = 1:m
                for k = 1:p
                    for j = 1:n
                        core(i,j,k)
                    end
                    pause(paws)
                    if mx, break, end
                end
            end
    end

    function core(i,j,k)
            set(HC(i,k),'backgroundcolor',gold)
            set(HA(i,j),'backgroundcolor',gold)
            set(HB(j,k),'backgroundcolor',gold)
            aij = get(HA(i,j),'userdata');
            bjk = get(HB(j,k),'userdata');
            cik = get(HC(i,k),'userdata');
            cik = cik + aij*bjk;  
            set(HC(i,k),'userdata',cik, ...
               'string',num2str(cik))
            pause(paws)
            set(HC(i,k),'backgroundcolor','w')
            set(HA(i,j),'backgroundcolor','w')
            set(HB(j,k),'backgroundcolor','w')
    end
end