-module(mlx_linalg).

%% Linear algebra functions for MLX
-export([
    %% Basic linear algebra
    dot/2, matmul/2, inner/2, outer/2,
    tensordot/2, tensordot/3,
    
    %% Matrix decompositions
    svd/1, svd/2,
    eig/1, eigh/1,
    qr/1, qr/2,
    cholesky/1,
    lu/1, lu/2,
    
    %% Matrix properties
    det/1, slogdet/1,
    trace/1, diagonal/1, diagonal/2,
    matrix_rank/1, matrix_rank/2,
    norm/1, norm/2, norm/3,
    
    %% Matrix operations
    inv/1, pinv/1, pinv/2,
    solve/2, lstsq/2,
    matrix_power/2,
    
    %% Vector operations
    cross/2, cross/3,
    
    %% Eigenvalues and eigenvectors
    eigvals/1, eigvalsh/1,
    
    %% Condition numbers
    condition_number/1, condition_number/2
]).

%% Type definitions
-type array() :: reference().
-type shape() :: [integer()].
-type dtype() :: atom().

%% Basic linear algebra
-spec dot(array(), array()) -> {ok, array()} | {error, term()}.
dot(A, B) ->
    mlx_linalg_nif:dot(A, B).

-spec matmul(array(), array()) -> {ok, array()} | {error, term()}.
matmul(A, B) ->
    mlx_linalg_nif:matmul(A, B).

-spec inner(array(), array()) -> {ok, array()} | {error, term()}.
inner(A, B) ->
    mlx_linalg_nif:inner(A, B).

-spec outer(array(), array()) -> {ok, array()} | {error, term()}.
outer(A, B) ->
    mlx_linalg_nif:outer(A, B).

-spec tensordot(array(), array()) -> {ok, array()} | {error, term()}.
tensordot(A, B) ->
    tensordot(A, B, 2).

-spec tensordot(array(), array(), integer()) -> {ok, array()} | {error, term()}.
tensordot(A, B, Axes) ->
    mlx_linalg_nif:tensordot(A, B, Axes).

%% Matrix decompositions
-spec svd(array()) -> {ok, {array(), array(), array()}} | {error, term()}.
svd(A) ->
    svd(A, true).

-spec svd(array(), boolean()) -> {ok, {array(), array(), array()}} | {error, term()}.
svd(A, FullMatrices) ->
    mlx_linalg_nif:svd(A, FullMatrices).

-spec eig(array()) -> {ok, {array(), array()}} | {error, term()}.
eig(A) ->
    mlx_linalg_nif:eig(A).

-spec eigh(array()) -> {ok, {array(), array()}} | {error, term()}.
eigh(A) ->
    mlx_linalg_nif:eigh(A).

-spec qr(array()) -> {ok, {array(), array()}} | {error, term()}.
qr(A) ->
    qr(A, reduced).

-spec qr(array(), atom()) -> {ok, {array(), array()}} | {error, term()}.
qr(A, Mode) ->
    mlx_linalg_nif:qr(A, Mode).

-spec cholesky(array()) -> {ok, array()} | {error, term()}.
cholesky(A) ->
    mlx_linalg_nif:cholesky(A).

-spec lu(array()) -> {ok, {array(), array(), array()}} | {error, term()}.
lu(A) ->
    lu(A, true).

-spec lu(array(), boolean()) -> {ok, {array(), array(), array()}} | {error, term()}.
lu(A, Permute) ->
    mlx_linalg_nif:lu(A, Permute).

%% Matrix properties
-spec det(array()) -> {ok, array()} | {error, term()}.
det(A) ->
    mlx_linalg_nif:det(A).

-spec slogdet(array()) -> {ok, {array(), array()}} | {error, term()}.
slogdet(A) ->
    mlx_linalg_nif:slogdet(A).

-spec trace(array()) -> {ok, array()} | {error, term()}.
trace(A) ->
    mlx_linalg_nif:trace(A).

-spec diagonal(array()) -> {ok, array()} | {error, term()}.
diagonal(A) ->
    diagonal(A, 0).

-spec diagonal(array(), integer()) -> {ok, array()} | {error, term()}.
diagonal(A, Offset) ->
    mlx_linalg_nif:diagonal(A, Offset).

-spec matrix_rank(array()) -> {ok, array()} | {error, term()}.
matrix_rank(A) ->
    matrix_rank(A, 1.0e-8).

-spec matrix_rank(array(), number()) -> {ok, array()} | {error, term()}.
matrix_rank(A, Tol) ->
    mlx_linalg_nif:matrix_rank(A, Tol).

-spec norm(array()) -> {ok, array()} | {error, term()}.
norm(A) ->
    norm(A, fro, []).

-spec norm(array(), atom() | number()) -> {ok, array()} | {error, term()}.
norm(A, Ord) ->
    norm(A, Ord, []).

-spec norm(array(), atom() | number(), [integer()]) -> {ok, array()} | {error, term()}.
norm(A, Ord, Axis) ->
    mlx_linalg_nif:norm(A, Ord, Axis).

%% Matrix operations
-spec inv(array()) -> {ok, array()} | {error, term()}.
inv(A) ->
    mlx_linalg_nif:inv(A).

-spec pinv(array()) -> {ok, array()} | {error, term()}.
pinv(A) ->
    pinv(A, 1.0e-15).

-spec pinv(array(), number()) -> {ok, array()} | {error, term()}.
pinv(A, Rcond) ->
    mlx_linalg_nif:pinv(A, Rcond).

-spec solve(array(), array()) -> {ok, array()} | {error, term()}.
solve(A, B) ->
    mlx_linalg_nif:solve(A, B).

-spec lstsq(array(), array()) -> {ok, {array(), array(), integer(), array()}} | {error, term()}.
lstsq(A, B) ->
    mlx_linalg_nif:lstsq(A, B).

-spec matrix_power(array(), integer()) -> {ok, array()} | {error, term()}.
matrix_power(A, N) ->
    mlx_linalg_nif:matrix_power(A, N).

%% Vector operations
-spec cross(array(), array()) -> {ok, array()} | {error, term()}.
cross(A, B) ->
    cross(A, B, -1).

-spec cross(array(), array(), integer()) -> {ok, array()} | {error, term()}.
cross(A, B, Axis) ->
    mlx_linalg_nif:cross(A, B, Axis).

%% Eigenvalues and eigenvectors
-spec eigvals(array()) -> {ok, array()} | {error, term()}.
eigvals(A) ->
    mlx_linalg_nif:eigvals(A).

-spec eigvalsh(array()) -> {ok, array()} | {error, term()}.
eigvalsh(A) ->
    mlx_linalg_nif:eigvalsh(A).

%% Condition numbers
-spec condition_number(array()) -> {ok, array()} | {error, term()}.
condition_number(A) ->
    condition_number(A, 2).

-spec condition_number(array(), atom() | number()) -> {ok, array()} | {error, term()}.
condition_number(A, P) ->
    mlx_linalg_nif:condition_number(A, P).