mlx

-module(mlx_autograd).

%% Comprehensive automatic differentiation system for MLX
-export([
    %% Core autograd functions
    enable_grad/0, disable_grad/0, no_grad/1,
    set_grad/2, get_grad/1, zero_grad/1,
    backward/1, backward/2,
    
    %% Gradient computation
    grad/2, grad/3, grad/4,
    value_and_grad/2, value_and_grad/3,
    jacobian/2, jacobian/3,
    hessian/2, hessian/3,
    
    %% Function transformation
    vjp/2, vjp/3,
    jvp/3, jvp/4,
    
    %% Checkpointing for memory efficiency
    checkpoint/1, checkpoint/2,
    
    %% Advanced gradient operations
    stop_gradient/1,
    detach/1,
    custom_vjp/3,
    
    %% Optimization helpers
    clip_grad_norm/2, clip_grad_value/2,
    accumulate_gradients/2,
    
    %% Higher-order derivatives
    grad_grad/3, laplacian/2
]).

%% Internal state for gradient tracking
-record(autograd_state, {
    enabled = true,
    graph = #{},
    grad_cache = #{}
}).

%% Core autograd functions
enable_grad() ->
    put(autograd_enabled, true),
    ok.

disable_grad() ->
    put(autograd_enabled, false),
    ok.

no_grad(Fun) ->
    OldState = get(autograd_enabled),
    disable_grad(),
    try
        Fun()
    after
        case OldState of
            true -> enable_grad();
            _ -> disable_grad()
        end
    end.

set_grad(Array, Gradient) ->
    case is_grad_enabled() of
        true ->
            GradDict = get_grad_dict(),
            ArrayId = get_array_id(Array),
            put(grad_dict, maps:put(ArrayId, Gradient, GradDict)),
            ok;
        false ->
            {error, gradients_disabled}
    end.

get_grad(Array) ->
    GradDict = get_grad_dict(),
    ArrayId = get_array_id(Array),
    maps:get(ArrayId, GradDict, undefined).

zero_grad(Arrays) when is_list(Arrays) ->
    lists:foreach(fun(Array) ->
        ArrayId = get_array_id(Array),
        GradDict = get_grad_dict(),
        put(grad_dict, maps:remove(ArrayId, GradDict))
    end, Arrays),
    ok;
zero_grad(Array) ->
    zero_grad([Array]).

backward(Loss) ->
    backward(Loss, []).

backward(Loss, Options) ->
    RetainGraph = proplists:get_value(retain_graph, Options, false),
    CreateGraph = proplists:get_value(create_graph, Options, false),
    
    case is_grad_enabled() of
        true ->
            % Start backward pass from loss
            {ok, OnesLike} = mlx:ones(mlx:shape(Loss)),
            backward_internal(Loss, OnesLike, RetainGraph, CreateGraph);
        false ->
            {error, gradients_disabled}
    end.

%% Gradient computation functions
grad(Fun, Args) ->
    grad(Fun, Args, []).

grad(Fun, Args, Argnums) ->
    grad(Fun, Args, Argnums, []).

grad(Fun, Args, Argnums, Options) ->
    % Compute gradient of Fun with respect to Args[Argnums]
    HasAux = proplists:get_value(has_aux, Options, false),
    
    % Enable gradient tracking
    enable_grad(),
    
    % Mark input arrays as requiring gradients
    ArgsWithGrad = mark_arrays_for_grad(Args, Argnums),
    
    % Forward pass
    case HasAux of
        true ->
            {Output, Aux} = Fun(ArgsWithGrad),
            % Backward pass
            {ok, Grads} = compute_gradients(Output, ArgsWithGrad, Argnums),
            {Grads, Aux};
        false ->
            Output = Fun(ArgsWithGrad),
            % Backward pass
            compute_gradients(Output, ArgsWithGrad, Argnums)
    end.

value_and_grad(Fun, Args) ->
    value_and_grad(Fun, Args, []).

value_and_grad(Fun, Args, Argnums) ->
    % Compute both value and gradient
    enable_grad(),
    ArgsWithGrad = mark_arrays_for_grad(Args, Argnums),
    Output = Fun(ArgsWithGrad),
    {ok, Grads} = compute_gradients(Output, ArgsWithGrad, Argnums),
    {Output, Grads}.

jacobian(Fun, Args) ->
    jacobian(Fun, Args, []).

jacobian(Fun, Args, Argnums) ->
    % Compute Jacobian matrix
    enable_grad(),
    ArgsWithGrad = mark_arrays_for_grad(Args, Argnums),
    
    % Get output to determine dimensions
    Output = Fun(ArgsWithGrad),
    {ok, OutputShape} = mlx:shape(Output),
    OutputSize = lists:foldl(fun(Dim, Acc) -> Dim * Acc end, 1, OutputShape),
    
    % Compute Jacobian row by row
    JacobianRows = lists:map(fun(I) ->
        % Create unit vector for this output component
        {ok, UnitVec} = create_unit_vector(OutputSize, I),
        {ok, UnitVecReshaped} = mlx:reshape(UnitVec, OutputShape),
        
        % Compute gradient for this output component
        {ok, Grads} = compute_gradients_with_output_grad(Output, ArgsWithGrad, 
                                                        Argnums, UnitVecReshaped),
        Grads
    end, lists:seq(0, OutputSize - 1)),
    
    {ok, mlx:stack(JacobianRows, 0)}.

hessian(Fun, Args) ->
    hessian(Fun, Args, []).

hessian(Fun, Args, Argnums) ->
    % Compute Hessian matrix using grad(grad(...))
    GradFun = fun(X) ->
        {_Value, Grad} = value_and_grad(Fun, X, Argnums),
        Grad
    end,
    jacobian(GradFun, Args, Argnums).

%% Vector-Jacobian and Jacobian-vector products
vjp(Fun, Args) ->
    vjp(Fun, Args, []).

vjp(Fun, Args, Argnums) ->
    % Vector-Jacobian product
    enable_grad(),
    ArgsWithGrad = mark_arrays_for_grad(Args, Argnums),
    Output = Fun(ArgsWithGrad),
    
    VjpFun = fun(Cotangent) ->
        compute_gradients_with_output_grad(Output, ArgsWithGrad, Argnums, Cotangent)
    end,
    
    {Output, VjpFun}.

jvp(Fun, Args, Tangents) ->
    jvp(Fun, Args, Tangents, []).

jvp(Fun, Args, Tangents, Argnums) ->
    % Jacobian-vector product using forward-mode AD
    enable_grad(),
    
    % Create dual numbers for forward-mode AD
    DualArgs = create_dual_numbers(Args, Tangents, Argnums),
    DualOutput = Fun(DualArgs),
    
    % Extract primal and tangent parts
    {Primal, TangentOut} = extract_dual_parts(DualOutput),
    {Primal, TangentOut}.

%% Checkpointing for memory efficiency
checkpoint(Fun) ->
    checkpoint(Fun, []).

checkpoint(Fun, Args) ->
    % Gradient checkpointing to save memory
    % Store only inputs, recompute during backward pass
    CheckpointId = make_ref(),
    put({checkpoint, CheckpointId}, {Fun, Args}),
    
    % Forward pass without storing intermediate values
    Output = no_grad(fun() -> Fun(Args) end),
    
    % Create custom backward function
    set_backward_hook(Output, fun(Grad) ->
        % Retrieve function and args
        {StoredFun, StoredArgs} = get({checkpoint, CheckpointId}),
        % Recompute forward pass with gradients
        enable_grad(),
        RecomputedOutput = StoredFun(StoredArgs),
        % Continue backward pass
        backward(RecomputedOutput, [{output_grad, Grad}])
    end),
    
    Output.

%% Advanced gradient operations
stop_gradient(Array) ->
    % Stop gradient flow through this array
    mlx_nif:stop_gradient(Array).

detach(Array) ->
    % Detach array from computation graph
    mlx_nif:detach(Array).

custom_vjp(Fun, FwdFun, BwdFun) ->
    % Custom vector-Jacobian product
    fun(Args) ->
        % Forward pass using custom forward function
        {Output, Aux} = FwdFun(Args),
        
        % Set custom backward function
        set_backward_hook(Output, fun(Grad) ->
            BwdFun(Aux, Grad)
        end),
        
        Output
    end.

%% Optimization helpers
clip_grad_norm(Gradients, MaxNorm) ->
    % Clip gradients by global norm
    TotalNorm = compute_total_norm(Gradients),
    ClipCoeff = erlang:min(1.0, MaxNorm / TotalNorm),
    lists:map(fun(Grad) ->
        {ok, Clipped} = mlx:multiply(Grad, mlx:array(ClipCoeff)),
        Clipped
    end, Gradients).

clip_grad_value(Gradients, ClipValue) ->
    % Clip gradients by value
    lists:map(fun(Grad) ->
        {ok, Clipped} = mlx:clip(Grad, mlx:array(-ClipValue), mlx:array(ClipValue)),
        Clipped
    end, Gradients).

accumulate_gradients(GradList1, GradList2) ->
    % Accumulate gradients from multiple sources
    lists:zipwith(fun(G1, G2) ->
        case {G1, G2} of
            {undefined, G} -> G;
            {G, undefined} -> G;
            {G1, G2} -> 
                {ok, Sum} = mlx:add(G1, G2),
                Sum
        end
    end, GradList1, GradList2).

%% Higher-order derivatives
grad_grad(Fun, Args, Argnums) ->
    % Second-order gradients
    GradFun = fun(X) ->
        {_Value, Grad} = value_and_grad(Fun, X, Argnums),
        % Return sum of gradient for scalar output
        mlx:sum(Grad)
    end,
    grad(GradFun, Args, Argnums).

laplacian(Fun, Args) ->
    % Compute Laplacian (trace of Hessian)
    {ok, H} = hessian(Fun, Args),
    mlx_nif:trace(H).

%% Internal helper functions
is_grad_enabled() ->
    get(autograd_enabled) =:= true.

get_grad_dict() ->
    case get(grad_dict) of
        undefined -> #{};
        Dict -> Dict
    end.

get_array_id(Array) ->
    % Generate unique ID for array (simplified)
    erlang:phash2(Array).

mark_arrays_for_grad(Args, []) ->
    % Mark all arrays
    lists:map(fun mark_for_grad/1, Args);
mark_arrays_for_grad(Args, Argnums) ->
    % Mark specific indices
    lists:map(fun({I, Arg}) ->
        case lists:member(I, Argnums) of
            true -> mark_for_grad(Arg);
            false -> Arg
        end
    end, lists:zip(lists:seq(0, length(Args) - 1), Args)).

mark_for_grad(Array) ->
    % Mark array as requiring gradients
    mlx_nif:set_requires_grad(Array, true).

compute_gradients(Output, Args, Argnums) ->
    % Compute gradients with respect to specified arguments
    backward(Output),
    Grads = lists:map(fun(I) ->
        Arg = lists:nth(I + 1, Args),
        get_grad(Arg)
    end, Argnums),
    {ok, Grads}.

compute_gradients_with_output_grad(Output, Args, Argnums, OutputGrad) ->
    % Compute gradients with custom output gradient
    backward(Output, [{output_grad, OutputGrad}]),
    Grads = lists:map(fun(I) ->
        Arg = lists:nth(I + 1, Args),
        get_grad(Arg)
    end, Argnums),
    {ok, Grads}.

backward_internal(Array, Grad, RetainGraph, CreateGraph) ->
    % Internal backward pass implementation
    % This would interface with the MLX C++ autograd system
    mlx_nif:backward(Array, Grad, #{
        retain_graph => RetainGraph,
        create_graph => CreateGraph
    }).

create_unit_vector(Size, Index) ->
    % Create unit vector with 1 at Index, 0 elsewhere
    {ok, Zeros} = mlx:zeros([Size]),
    {ok, One} = mlx:array(1.0),
    mlx_nif:set_item(Zeros, Index, One).

set_backward_hook(Array, HookFun) ->
    % Set custom backward hook for array
    mlx_nif:register_hook(Array, HookFun).

create_dual_numbers(Args, Tangents, Argnums) ->
    % Create dual numbers for forward-mode AD
    lists:zipwith3(fun(I, Arg, Tangent) ->
        case lists:member(I, Argnums) of
            true -> {dual, Arg, Tangent};
            false -> Arg
        end
    end, lists:seq(0, length(Args) - 1), Args, Tangents).

extract_dual_parts(DualOutput) ->
    % Extract primal and tangent from dual number
    case DualOutput of
        {dual, Primal, Tangent} -> {Primal, Tangent};
        Primal -> {Primal, undefined}
    end.

compute_total_norm(Gradients) ->
    % Compute total L2 norm of gradients
    TotalSquared = lists:foldl(fun(Grad, Acc) ->
        {ok, Square} = mlx:square(Grad),
        {ok, Sum} = mlx:sum(Square),
        case Acc of
            0.0 -> Sum;
            _ -> 
                {ok, NewAcc} = mlx:add(mlx:array(Acc), Sum),
                mlx:to_list(NewAcc)
        end
    end, 0.0, Gradients),
    math:sqrt(TotalSquared).