layer_dimensions    =   [11 22 33 22 11]';

ld_size             =   size(layer_dimensions   ,   1);

% what is deal

[x rx dx rdx y ry dy rdy dphi] = deal( cell( ld_size    ,   1 ) );

[W rW dW rdW]                  = deal( cell( ld_size-1  , 1 ) );

numsamples  =   100;

%initialize weight and x,y, always allocate memory first

for i   =   1:ld_size

    x{i}    =   zeros(  layer_dimensions(   i  )   ,  numsamples );

    y{i}    =   x{i};

    if i<ld_size

        W{i}    =   rand(   layer_dimensions(   i  ) ,layer_dimensions(   i+1 )   );

    end

end

%initialize

inputs  =   0*ones(layer_dimensions(1),numsamples);

y{1}    =   inputs;

dphi{1} =   zeros(size(y{1}));

ry{1}   =   dphi{1};

numepoches  =   100;

numbatches  =   10;

for iii =   1:numepoches

    for ii  =   1:numbatches

        % f0 pass

        for i   =   2:ld_size

            x{i}    =   W{i-1}'*y{i-1};

            y{i}    =   sigmoid(x{i});

            dphi{i} =   y{i}.*(1-y{i});  %for backpropagate

        end

        % r1 pass

        dy{ld_size}     =   y{ld_size}  -   y{1};

        error=sum(sum(abs(dy{ld_size})))

        dx{ld_size}     =   dphi{ld_size}   .*  dy{ld_size};

        dW{ld_size-1}   =   y{ld_size-1}    *   dx{ld_size}';

        for i   =   ld_size-1:-1:2

            dy{i}   =   W{i}    *   dx{i+1};

            W{i}    =   W{i}    -   0.3 *   dW{i};

            dx{i}   =   dphi{i} .*   dy{i};

            dW{i-1}   =   y{i-1}  *   dx{i}';

        end

        % f1 pass

    end

end

%test

numtestsamples=3;

for i   =   1:ld_size

    x{i}    =   zeros(  layer_dimensions(   i  )   ,  numtestsamples );

    y{i}    =   x{i};

end

inputs  =   zeros(layer_dimensions(1),numtestsamples);

y{1}    =   inputs;

dphi{1} =   zeros(size(y{1}));

ry{1}   =   dphi{1};

for i   =   2:ld_size

            x{i}    =   W{i-1}'*y{i-1};

            y{i}    =   sigmoid(x{i});

            dphi{i} =   y{i}.*(1-y{i});  %for backpropagate

end

y{ld_size}