mlx

-module(mlx_advanced).

%% Advanced mathematical operations for SOTA MLX implementation
-export([
    %% Einstein summation and tensor operations
    einsum/2, einsum/3,
    
    %% Statistical functions
    median/1, median/2,
    percentile/2, percentile/3,
    histogram/2, histogram/3,
    covariance/2, correlation/2,
    
    %% Advanced linear algebra
    svd/1, eig/1, qr/1, cholesky/1,
    pinv/1, matrix_rank/1,
    trace/1, det/1,
    
    %% Signal processing
    fft/1, ifft/1, fft2/1, ifft2/1,
    convolve/2, correlate/2,
    
    %% Complex number operations
    real/1, imag/1, conj/1, angle/1,
    complex/2,
    
    %% Advanced activation functions
    gelu/1, swish/1, mish/1, selu/1,
    leaky_relu/1, leaky_relu/2,
    elu/1, elu/2,
    
    %% Normalization operations
    layer_norm/1, layer_norm/2, layer_norm/3,
    batch_norm/1, batch_norm/2, batch_norm/3,
    group_norm/2, group_norm/3,
    rms_norm/1, rms_norm/2,
    
    %% Loss functions
    cross_entropy/2, cross_entropy/3,
    focal_loss/2, focal_loss/3, focal_loss/4,
    kl_divergence/2, js_divergence/2,
    huber_loss/2, huber_loss/3,
    
    %% Optimization functions
    gradient_norm/1, gradient_clip/2, gradient_clip/3,
    spectral_norm/1, weight_norm/1
]).

%% Einstein summation - fundamental for tensor operations
einsum(Equation, Arrays) ->
    einsum(Equation, Arrays, []).

einsum(Equation, Arrays, Options) ->
    mlx_nif:einsum(Equation, Arrays, Options).

%% Statistical functions
median(Array) ->
    median(Array, -1).

median(Array, Axis) ->
    mlx_nif:median(Array, Axis).

percentile(Array, Q) ->
    percentile(Array, Q, -1).

percentile(Array, Q, Axis) ->
    mlx_nif:percentile(Array, Q, Axis).

histogram(Array, Bins) ->
    histogram(Array, Bins, []).

histogram(Array, Bins, Options) ->
    mlx_nif:histogram(Array, Bins, Options).

covariance(X, Y) ->
    % Compute covariance matrix
    XMean = mlx:mean(X, 0),
    YMean = mlx:mean(Y, 0),
    XCentered = mlx:subtract(X, XMean),
    YCentered = mlx:subtract(Y, YMean),
    N = element(1, mlx:shape(X)),
    Cov = mlx:matmul(mlx:transpose(XCentered), YCentered),
    mlx:divide(Cov, mlx:array(N - 1)).

correlation(X, Y) ->
    % Pearson correlation coefficient
    case covariance(X, Y) of
        {ok, Cov} ->
            {ok, StdX} = mlx:std(X, 0),
            {ok, StdY} = mlx:std(Y, 0),
            {ok, StdProd} = mlx:outer(StdX, StdY),
            mlx:divide(Cov, StdProd);
        Error -> Error
    end.

%% Advanced linear algebra
svd(Array) ->
    mlx_nif:svd(Array).

eig(Array) ->
    mlx_nif:eig(Array).

qr(Array) ->
    mlx_nif:qr(Array).

cholesky(Array) ->
    mlx_nif:cholesky(Array).

pinv(Array) ->
    % Pseudo-inverse using SVD
    case svd(Array) of
        {ok, {U, S, Vt}} ->
            % Create S_inv with threshold for numerical stability
            {ok, Threshold} = mlx:multiply(mlx:array(1.0e-15), mlx:max(S)),
            {ok, SMask} = mlx:greater(S, Threshold),
            {ok, SInv} = mlx:where(SMask, mlx:reciprocal(S), mlx:array(0.0)),
            {ok, SInvDiag} = mlx:diag(SInv),
            {ok, Temp} = mlx:matmul(Vt, SInvDiag),
            mlx:matmul(mlx:transpose(Temp), mlx:transpose(U));
        Error -> Error
    end.

matrix_rank(Array) ->
    case svd(Array) of
        {ok, {_U, S, _Vt}} ->
            {ok, Threshold} = mlx:multiply(mlx:array(1.0e-12), mlx:max(S)),
            {ok, Mask} = mlx:greater(S, Threshold),
            mlx:sum(mlx:cast(Mask, int32));
        Error -> Error
    end.

trace(Array) ->
    mlx_nif:trace(Array).

det(Array) ->
    mlx_nif:det(Array).

%% Signal processing
fft(Array) ->
    mlx_nif:fft(Array).

ifft(Array) ->
    mlx_nif:ifft(Array).

fft2(Array) ->
    mlx_nif:fft2(Array).

ifft2(Array) ->
    mlx_nif:ifft2(Array).

convolve(A, B) ->
    mlx_nif:convolve(A, B).

correlate(A, B) ->
    mlx_nif:correlate(A, B).

%% Complex number operations
real(Array) ->
    mlx_nif:real(Array).

imag(Array) ->
    mlx_nif:imag(Array).

conj(Array) ->
    mlx_nif:conj(Array).

angle(Array) ->
    mlx_nif:angle(Array).

complex(Real, Imag) ->
    mlx_nif:complex(Real, Imag).

%% Advanced activation functions
gelu(X) ->
    % Gaussian Error Linear Unit
    {ok, Half} = mlx:array(0.5),
    {ok, One} = mlx:array(1.0),
    {ok, Sqrt2} = mlx:array(1.4142135623730951),
    {ok, XDivSqrt2} = mlx:divide(X, Sqrt2),
    {ok, Erf} = mlx:erf(XDivSqrt2),
    {ok, OnePlusErf} = mlx:add(One, Erf),
    {ok, HalfX} = mlx:multiply(Half, X),
    mlx:multiply(HalfX, OnePlusErf).

swish(X) ->
    % Swish activation: x * sigmoid(x)
    case mlx:sigmoid(X) of
        {ok, Sig} -> mlx:multiply(X, Sig);
        Error -> Error
    end.

mish(X) ->
    % Mish activation: x * tanh(softplus(x))
    {ok, Softplus} = mlx:log(mlx:add(mlx:array(1.0), mlx:exp(X))),
    {ok, TanhSoftplus} = mlx:tanh(Softplus),
    mlx:multiply(X, TanhSoftplus).

selu(X) ->
    % Scaled Exponential Linear Unit
    Alpha = 1.6732632423543772848170429916717,
    Scale = 1.0507009873554804934193349852946,
    {ok, Zero} = mlx:array(0.0),
    {ok, AlphaArray} = mlx:array(Alpha),
    {ok, ScaleArray} = mlx:array(Scale),
    {ok, Mask} = mlx:greater(X, Zero),
    {ok, ExpPart} = mlx:subtract(mlx:exp(X), mlx:array(1.0)),
    {ok, NegPart} = mlx:multiply(AlphaArray, ExpPart),
    {ok, Result} = mlx:where(Mask, X, NegPart),
    mlx:multiply(ScaleArray, Result).

leaky_relu(X) ->
    leaky_relu(X, 0.01).

leaky_relu(X, Alpha) ->
    {ok, Zero} = mlx:array(0.0),
    {ok, AlphaArray} = mlx:array(Alpha),
    {ok, Mask} = mlx:greater(X, Zero),
    {ok, LeakyPart} = mlx:multiply(AlphaArray, X),
    mlx:where(Mask, X, LeakyPart).

elu(X) ->
    elu(X, 1.0).

elu(X, Alpha) ->
    {ok, Zero} = mlx:array(0.0),
    {ok, AlphaArray} = mlx:array(Alpha),
    {ok, One} = mlx:array(1.0),
    {ok, Mask} = mlx:greater(X, Zero),
    {ok, ExpPart} = mlx:subtract(mlx:exp(X), One),
    {ok, EluPart} = mlx:multiply(AlphaArray, ExpPart),
    mlx:where(Mask, X, EluPart).

%% Normalization operations
layer_norm(X) ->
    layer_norm(X, [], 1.0e-5).

layer_norm(X, Axes) ->
    layer_norm(X, Axes, 1.0e-5).

layer_norm(X, Axes, Eps) ->
    % Layer normalization
    {ok, Mean} = mlx:mean(X, Axes, true),
    {ok, Var} = mlx:var(X, Axes, true),
    {ok, EpsArray} = mlx:array(Eps),
    {ok, VarEps} = mlx:add(Var, EpsArray),
    {ok, Std} = mlx:sqrt(VarEps),
    {ok, Centered} = mlx:subtract(X, Mean),
    mlx:divide(Centered, Std).

batch_norm(X) ->
    batch_norm(X, 0, 1.0e-5).

batch_norm(X, Axis) ->
    batch_norm(X, Axis, 1.0e-5).

batch_norm(X, Axis, Eps) ->
    % Batch normalization
    {ok, Mean} = mlx:mean(X, Axis, true),
    {ok, Var} = mlx:var(X, Axis, true),
    {ok, EpsArray} = mlx:array(Eps),
    {ok, VarEps} = mlx:add(Var, EpsArray),
    {ok, Std} = mlx:sqrt(VarEps),
    {ok, Centered} = mlx:subtract(X, Mean),
    mlx:divide(Centered, Std).

group_norm(X, NumGroups) ->
    group_norm(X, NumGroups, 1.0e-5).

group_norm(X, NumGroups, Eps) ->
    % Group normalization - simplified implementation
    {ok, Shape} = mlx:shape(X),
    [N, C | Rest] = Shape,
    GroupSize = C div NumGroups,
    NewShape = [N, NumGroups, GroupSize | Rest],
    {ok, Reshaped} = mlx:reshape(X, NewShape),
    {ok, Normalized} = layer_norm(Reshaped, [2], Eps),
    mlx:reshape(Normalized, Shape).

rms_norm(X) ->
    rms_norm(X, 1.0e-8).

rms_norm(X, Eps) ->
    % Root Mean Square normalization
    {ok, Square} = mlx:square(X),
    {ok, MeanSquare} = mlx:mean(Square, -1, true),
    {ok, EpsArray} = mlx:array(Eps),
    {ok, MeanSquareEps} = mlx:add(MeanSquare, EpsArray),
    {ok, Rms} = mlx:sqrt(MeanSquareEps),
    mlx:divide(X, Rms).

%% Loss functions
cross_entropy(Predictions, Targets) ->
    cross_entropy(Predictions, Targets, -1).

cross_entropy(Predictions, Targets, Axis) ->
    {ok, LogSoftmax} = log_softmax(Predictions, Axis),
    {ok, NegLogProb} = mlx:negative(LogSoftmax),
    {ok, Loss} = mlx:multiply(Targets, NegLogProb),
    mlx:sum(Loss, Axis).

focal_loss(Predictions, Targets) ->
    focal_loss(Predictions, Targets, 2.0, 0.25).

focal_loss(Predictions, Targets, Gamma) ->
    focal_loss(Predictions, Targets, Gamma, 0.25).

focal_loss(Predictions, Targets, Gamma, Alpha) ->
    % Focal loss for addressing class imbalance
    {ok, CE} = cross_entropy(Predictions, Targets),
    {ok, P} = mlx:exp(mlx:negative(CE)),
    {ok, One} = mlx:array(1.0),
    {ok, OneMiusP} = mlx:subtract(One, P),
    {ok, GammaArray} = mlx:array(Gamma),
    {ok, AlphaArray} = mlx:array(Alpha),
    {ok, FocalWeight} = mlx:power(OneMiusP, GammaArray),
    {ok, WeightedCE} = mlx:multiply(AlphaArray, CE),
    mlx:multiply(FocalWeight, WeightedCE).

kl_divergence(P, Q) ->
    % Kullback-Leibler divergence
    {ok, LogP} = mlx:log(P),
    {ok, LogQ} = mlx:log(Q),
    {ok, LogRatio} = mlx:subtract(LogP, LogQ),
    {ok, KL} = mlx:multiply(P, LogRatio),
    mlx:sum(KL).

js_divergence(P, Q) ->
    % Jensen-Shannon divergence
    {ok, Half} = mlx:array(0.5),
    {ok, M} = mlx:multiply(Half, mlx:add(P, Q)),
    {ok, KL1} = kl_divergence(P, M),
    {ok, KL2} = kl_divergence(Q, M),
    {ok, Sum} = mlx:add(KL1, KL2),
    mlx:multiply(Half, Sum).

huber_loss(Predictions, Targets) ->
    huber_loss(Predictions, Targets, 1.0).

huber_loss(Predictions, Targets, Delta) ->
    % Huber loss (smooth L1 loss)
    {ok, Diff} = mlx:subtract(Predictions, Targets),
    {ok, AbsDiff} = mlx:abs(Diff),
    {ok, DeltaArray} = mlx:array(Delta),
    {ok, Mask} = mlx:less_equal(AbsDiff, DeltaArray),
    {ok, Half} = mlx:array(0.5),
    {ok, QuadraticPart} = mlx:multiply(Half, mlx:square(Diff)),
    {ok, LinearPart} = mlx:subtract(mlx:multiply(DeltaArray, AbsDiff), 
                                    mlx:multiply(Half, mlx:square(DeltaArray))),
    mlx:where(Mask, QuadraticPart, LinearPart).

%% Optimization functions
gradient_norm(Gradients) ->
    % Compute L2 norm of gradients
    {ok, Squares} = lists:foldl(fun(Grad, {ok, Acc}) ->
        {ok, Square} = mlx:square(Grad),
        case Acc of
            undefined -> {ok, Square};
            _ -> {ok, Sum} = mlx:add(Acc, Square), {ok, Sum}
        end
    end, {ok, undefined}, Gradients),
    mlx:sqrt(mlx:sum(Squares)).

gradient_clip(Gradients, MaxNorm) ->
    gradient_clip(Gradients, MaxNorm, l2).

gradient_clip(Gradients, MaxNorm, NormType) ->
    case NormType of
        l2 ->
            {ok, TotalNorm} = gradient_norm(Gradients),
            {ok, MaxNormArray} = mlx:array(MaxNorm),
            {ok, ClipCoeff} = mlx:minimum(mlx:divide(MaxNormArray, TotalNorm), mlx:array(1.0)),
            lists:map(fun(Grad) ->
                {ok, Clipped} = mlx:multiply(Grad, ClipCoeff),
                Clipped
            end, Gradients);
        value ->
            MaxNormArray = mlx:array(MaxNorm),
            MinNormArray = mlx:array(-MaxNorm),
            lists:map(fun(Grad) ->
                {ok, Clipped} = mlx:clip(Grad, MinNormArray, MaxNormArray),
                Clipped
            end, Gradients)
    end.

spectral_norm(Weight) ->
    % Spectral normalization using power iteration
    case svd(Weight) of
        {ok, {_U, S, _Vt}} ->
            {ok, MaxS} = mlx:max(S),
            mlx:divide(Weight, MaxS);
        Error -> Error
    end.

weight_norm(Weight) ->
    % Weight normalization
    {ok, Norm} = mlx:sqrt(mlx:sum(mlx:square(Weight))),
    mlx:divide(Weight, Norm).

%% Helper functions
log_softmax(X, Axis) ->
    {ok, MaxX} = mlx:max(X, Axis, true),
    {ok, Shifted} = mlx:subtract(X, MaxX),
    {ok, LogSumExp} = mlx:log(mlx:sum(mlx:exp(Shifted), Axis, true)),
    mlx:subtract(Shifted, LogSumExp).