viva_tensor

-module(viva_tensor@core@linalg).
-compile([no_auto_import, nowarn_unused_vars, nowarn_unused_function, nowarn_nomatch, inline]).
-define(FILEPATH, "src/viva_tensor/core/linalg.gleam").
-export([solve/2, eye/1, inv/1, det/1, lu/1, cholesky/1, qr/1, svd/1, eig/1]).
-export_type([lu_failure/0, lu_decomp/0]).

-if(?OTP_RELEASE >= 27).
-define(MODULEDOC(Str), -moduledoc(Str)).
-define(DOC(Str), -doc(Str)).
-else.
-define(MODULEDOC(Str), -compile([])).
-define(DOC(Str), -compile([])).
-endif.

?MODULEDOC(false).

-type lu_failure() :: lu_singular |
    {lu_error, viva_tensor@core@error:tensor_error()}.

-type lu_decomp() :: {lu_decomp,
        list(list(float())),
        list(list(float())),
        list(integer()),
        integer()}.

-file("src/viva_tensor/core/linalg.gleam", 901).
?DOC(false).
-spec set_at(list(QZR), integer(), QZR) -> list(QZR).
set_at(Lst, Idx, Value) ->
    _pipe = Lst,
    gleam@list:index_map(_pipe, fun(Item, I) -> case I =:= Idx of
                true ->
                    Value;

                false ->
                    Item
            end end).

-file("src/viva_tensor/core/linalg.gleam", 814).
?DOC(false).
-spec list_at(list(QYX), integer()) -> {ok, QYX} | {error, nil}.
list_at(Lst, Idx) ->
    case {Lst, Idx} of
        {[], _} ->
            {error, nil};

        {[Head | _], 0} ->
            {ok, Head};

        {[_ | Rest], _} ->
            list_at(Rest, Idx - 1)
    end.

-file("src/viva_tensor/core/linalg.gleam", 809).
?DOC(false).
-spec unsafe_at(list(QYV), integer()) -> QYV.
unsafe_at(Lst, Idx) ->
    Value@1 = case list_at(Lst, Idx) of
        {ok, Value} -> Value;
        _assert_fail ->
            erlang:error(#{gleam_error => let_assert,
                        message => <<"Pattern match failed, no pattern matched the value."/utf8>>,
                        file => <<?FILEPATH/utf8>>,
                        module => <<"viva_tensor/core/linalg"/utf8>>,
                        function => <<"unsafe_at"/utf8>>,
                        line => 810,
                        value => _assert_fail,
                        start => 22689,
                        'end' => 22729,
                        pattern_start => 22700,
                        pattern_end => 22709})
    end,
    Value@1.

-file("src/viva_tensor/core/linalg.gleam", 795).
?DOC(false).
-spec int_range(integer(), integer()) -> list(integer()).
int_range(Start, Stop) ->
    case Stop < Start of
        true ->
            [];

        false ->
            gleam@list:range(Start, Stop)
    end.

-file("src/viva_tensor/core/linalg.gleam", 489).
?DOC(false).
-spec back_substitute_loop(
    list(list(float())),
    list(list(float())),
    integer(),
    integer(),
    integer()
) -> list(list(float())).
back_substitute_loop(Rows, Solution, I, N, Nrhs) ->
    case I < 0 of
        true ->
            Solution;

        false ->
            Row = unsafe_at(Rows, I),
            A_ii = unsafe_at(Row, I),
            B_part = begin
                _pipe = Row,
                _pipe@1 = gleam@list:drop(_pipe, N),
                gleam@list:take(_pipe@1, Nrhs)
            end,
            Summed = begin
                _pipe@2 = int_range(I + 1, N - 1),
                gleam@list:fold(
                    _pipe@2,
                    B_part,
                    fun(Acc, J) ->
                        A_ij = unsafe_at(Row, J),
                        X_j = unsafe_at(Solution, J),
                        _pipe@3 = gleam@list:zip(Acc, X_j),
                        gleam@list:map(
                            _pipe@3,
                            fun(Pair) ->
                                {A_val, X_val} = Pair,
                                A_val - (A_ij * X_val)
                            end
                        )
                    end
                )
            end,
            X_i = gleam@list:map(Summed, fun(V) -> case A_ii of
                        +0.0 -> +0.0;
                        -0.0 -> -0.0;
                        Gleam@denominator -> V / Gleam@denominator
                    end end),
            New_solution = set_at(Solution, I, X_i),
            back_substitute_loop(Rows, New_solution, I - 1, N, Nrhs)
    end.

-file("src/viva_tensor/core/linalg.gleam", 478).
?DOC(false).
-spec back_substitute(list(list(float())), integer(), integer()) -> list(list(float())).
back_substitute(Rows, N, Nrhs) ->
    Row_array = Rows,
    Solution_init = gleam@list:repeat(gleam@list:repeat(+0.0, Nrhs), N),
    back_substitute_loop(Row_array, Solution_init, N - 1, N, Nrhs).

-file("src/viva_tensor/core/linalg.gleam", 466).
?DOC(false).
-spec eliminate_row(list(float()), list(float()), float()) -> list(float()).
eliminate_row(Row, Pivot_row, Factor) ->
    _pipe = gleam@list:zip(Row, Pivot_row),
    gleam@list:map(
        _pipe,
        fun(Pair) ->
            {R, P} = Pair,
            R - (Factor * P)
        end
    ).

-file("src/viva_tensor/core/linalg.gleam", 826).
?DOC(false).
-spec swap_rows(list(list(float())), integer(), integer()) -> list(list(float())).
swap_rows(Rows, I, J) ->
    case I =:= J of
        true ->
            Rows;

        false ->
            Row_i = unsafe_at(Rows, I),
            Row_j = unsafe_at(Rows, J),
            _pipe = Rows,
            gleam@list:index_map(
                _pipe,
                fun(Row, Idx) -> case {Idx =:= I, Idx =:= J} of
                        {true, _} ->
                            Row_j;

                        {_, true} ->
                            Row_i;

                        {_, _} ->
                            Row
                    end end
            )
    end.

-file("src/viva_tensor/core/linalg.gleam", 822).
?DOC(false).
-spec value_at(list(list(float())), integer(), integer()) -> float().
value_at(Rows, I, J) ->
    unsafe_at(unsafe_at(Rows, I), J).

-file("src/viva_tensor/core/linalg.gleam", 442).
?DOC(false).
-spec find_pivot(list(list(float())), integer(), integer()) -> {ok, integer()} |
    {error, nil}.
find_pivot(Rows, K, N) ->
    Candidates = begin
        _pipe = gleam@list:range(K, N - 1),
        gleam@list:map(
            _pipe,
            fun(I) -> {I, gleam@float:absolute_value(value_at(Rows, I, K))} end
        )
    end,
    case Candidates of
        [] ->
            {error, nil};

        [First | Rest] ->
            {Best_idx, Best_val} = gleam@list:fold(
                Rest,
                First,
                fun(Acc, Candidate) ->
                    {_, Acc_val} = Acc,
                    {_, Cand_val} = Candidate,
                    case Cand_val > Acc_val of
                        true ->
                            Candidate;

                        false ->
                            Acc
                    end
                end
            ),
            case Best_val < 1.0e-12 of
                true ->
                    {error, nil};

                false ->
                    {ok, Best_idx}
            end
    end.

-file("src/viva_tensor/core/linalg.gleam", 404).
?DOC(false).
-spec eliminate_loop(list(list(float())), integer(), integer()) -> {ok,
        list(list(float()))} |
    {error, viva_tensor@core@error:tensor_error()}.
eliminate_loop(Rows, K, N) ->
    case K =:= N of
        true ->
            {ok, Rows};

        false ->
            Pivot_idx = find_pivot(Rows, K, N),
            case Pivot_idx of
                {error, _} ->
                    {error, {invalid_shape, <<"matrix is singular"/utf8>>}};

                {ok, Idx} ->
                    Swapped = swap_rows(Rows, K, Idx),
                    Pivot_row = unsafe_at(Swapped, K),
                    Pivot_value = unsafe_at(Pivot_row, K),
                    case gleam@float:absolute_value(Pivot_value) < 1.0e-12 of
                        true ->
                            {error,
                                {invalid_shape, <<"matrix is singular"/utf8>>}};

                        false ->
                            Updated = begin
                                _pipe = Swapped,
                                gleam@list:index_map(
                                    _pipe,
                                    fun(Row, I) -> case I =:= K of
                                            true ->
                                                Row;

                                            false ->
                                                Factor = case Pivot_value of
                                                    +0.0 -> +0.0;
                                                    -0.0 -> -0.0;
                                                    Gleam@denominator -> unsafe_at(
                                                        Row,
                                                        K
                                                    )
                                                    / Gleam@denominator
                                                end,
                                                eliminate_row(
                                                    Row,
                                                    Pivot_row,
                                                    Factor
                                                )
                                        end end
                                )
                            end,
                            eliminate_loop(Updated, K + 1, N)
                    end
            end
    end.

-file("src/viva_tensor/core/linalg.gleam", 393).
?DOC(false).
-spec gauss_eliminate(list(list(float())), integer(), integer()) -> {ok,
        list(list(float()))} |
    {error, viva_tensor@core@error:tensor_error()}.
gauss_eliminate(Rows, N, Nrhs) ->
    case eliminate_loop(Rows, 0, N) of
        {error, E} ->
            {error, E};

        {ok, Triangular} ->
            {ok, back_substitute(Triangular, N, Nrhs)}
    end.

-file("src/viva_tensor/core/linalg.gleam", 802).
?DOC(false).
-spec chunk(list(float()), integer()) -> list(list(float())).
chunk(Data, N) ->
    case Data of
        [] ->
            [];

        _ ->
            [gleam@list:take(Data, N) | chunk(gleam@list:drop(Data, N), N)]
    end.

-file("src/viva_tensor/core/linalg.gleam", 359).
?DOC(false).
-spec rows_with_rhs(
    list(list(float())),
    viva_tensor@tensor:tensor(),
    integer(),
    integer()
) -> {ok, list(list(float()))} | {error, viva_tensor@core@error:tensor_error()}.
rows_with_rhs(A_rows, B, N, Nrhs) ->
    gleam@result:'try'(
        viva_tensor@tensor:try_to_list(B),
        fun(B_data) -> case erlang:length(B_data) =:= (N * Nrhs) of
                false ->
                    {error,
                        {invalid_shape,
                            <<<<<<"right-hand side data length "/utf8,
                                        (erlang:integer_to_binary(
                                            erlang:length(B_data)
                                        ))/binary>>/binary,
                                    " does not match expected "/utf8>>/binary,
                                (erlang:integer_to_binary(N * Nrhs))/binary>>}};

                true ->
                    B_rows = chunk(B_data, Nrhs),
                    {ok,
                        begin
                            _pipe = gleam@list:zip(A_rows, B_rows),
                            gleam@list:map(
                                _pipe,
                                fun(Pair) ->
                                    {Arow, Brow} = Pair,
                                    lists:append(Arow, Brow)
                                end
                            )
                        end}
            end end
    ).

-file("src/viva_tensor/core/linalg.gleam", 328).
?DOC(false).
-spec rhs_rows(viva_tensor@tensor:tensor(), integer()) -> {ok,
        {integer(), integer(), boolean()}} |
    {error, viva_tensor@core@error:tensor_error()}.
rhs_rows(B, N) ->
    case erlang:element(3, B) of
        [Rows] ->
            {ok, {Rows, 1, true}};

        [Rows@1, Cols] ->
            {ok, {Rows@1, Cols, false}};

        _ ->
            _ = N,
            {error,
                {dimension_error, <<"right-hand side must be 1D or 2D"/utf8>>}}
    end.

-file("src/viva_tensor/core/linalg.gleam", 339).
?DOC(false).
-spec to_rows(viva_tensor@tensor:tensor(), integer(), integer()) -> {ok,
        list(list(float()))} |
    {error, viva_tensor@core@error:tensor_error()}.
to_rows(A, M, N) ->
    gleam@result:'try'(
        viva_tensor@tensor:try_to_list(A),
        fun(Data) -> case erlang:length(Data) =:= (M * N) of
                true ->
                    {ok, chunk(Data, N)};

                false ->
                    {error,
                        {invalid_shape,
                            <<<<<<<<<<"tensor data length "/utf8,
                                                (erlang:integer_to_binary(
                                                    erlang:length(Data)
                                                ))/binary>>/binary,
                                            " does not match shape "/utf8>>/binary,
                                        (erlang:integer_to_binary(M))/binary>>/binary,
                                    "x"/utf8>>/binary,
                                (erlang:integer_to_binary(N))/binary>>}}
            end end
    ).

-file("src/viva_tensor/core/linalg.gleam", 315).
?DOC(false).
-spec square_matrix_rows(viva_tensor@tensor:tensor()) -> {ok,
        {integer(), list(list(float()))}} |
    {error, viva_tensor@core@error:tensor_error()}.
square_matrix_rows(A) ->
    case erlang:element(3, A) of
        [N, M] when N =:= M ->
            gleam@result:'try'(
                to_rows(A, N, N),
                fun(Rows) -> {ok, {N, Rows}} end
            );

        [N@1, M@1] ->
            {error, {shape_mismatch, [N@1, N@1], [N@1, M@1]}};

        _ ->
            {error, {dimension_error, <<"expected a 2D square matrix"/utf8>>}}
    end.

-file("src/viva_tensor/core/linalg.gleam", 53).
?DOC(false).
-spec solve(viva_tensor@tensor:tensor(), viva_tensor@tensor:tensor()) -> {ok,
        viva_tensor@tensor:tensor()} |
    {error, viva_tensor@core@error:tensor_error()}.
solve(A, B) ->
    gleam@result:'try'(
        square_matrix_rows(A),
        fun(_use0) ->
            {N, A_rows} = _use0,
            gleam@result:'try'(
                rhs_rows(B, N),
                fun(_use0@1) ->
                    {B_rows, Nrhs, B_is_vector} = _use0@1,
                    case B_rows =:= N of
                        false ->
                            {error, {shape_mismatch, [N, Nrhs], [B_rows, Nrhs]}};

                        true ->
                            gleam@result:'try'(
                                rows_with_rhs(A_rows, B, N, Nrhs),
                                fun(Rows) ->
                                    gleam@result:'try'(
                                        gauss_eliminate(Rows, N, Nrhs),
                                        fun(Solved) ->
                                            Flat = lists:append(Solved),
                                            case B_is_vector of
                                                true ->
                                                    {ok, {tensor, Flat, [N]}};

                                                false ->
                                                    {ok,
                                                        {tensor,
                                                            Flat,
                                                            [N, Nrhs]}}
                                            end
                                        end
                                    )
                                end
                            )
                    end
                end
            )
        end
    ).

-file("src/viva_tensor/core/linalg.gleam", 243).
?DOC(false).
-spec eye(integer()) -> viva_tensor@tensor:tensor().
eye(N) ->
    Data = begin
        _pipe = gleam@list:range(0, N - 1),
        gleam@list:flat_map(
            _pipe,
            fun(I) -> _pipe@1 = gleam@list:range(0, N - 1),
                gleam@list:map(_pipe@1, fun(J) -> case I =:= J of
                            true ->
                                1.0;

                            false ->
                                +0.0
                        end end) end
        )
    end,
    {tensor, Data, [N, N]}.

-file("src/viva_tensor/core/linalg.gleam", 85).
?DOC(false).
-spec inv(viva_tensor@tensor:tensor()) -> {ok, viva_tensor@tensor:tensor()} |
    {error, viva_tensor@core@error:tensor_error()}.
inv(A) ->
    gleam@result:'try'(
        square_matrix_rows(A),
        fun(_use0) ->
            {N, _} = _use0,
            Identity = eye(N),
            case solve(A, Identity) of
                {ok, X} ->
                    {ok, X};

                {error, {invalid_shape, <<"matrix is singular"/utf8>>}} ->
                    {error, {invalid_shape, <<"matrix is singular"/utf8>>}};

                {error, Other} ->
                    {error, Other}
            end
        end
    ).

-file("src/viva_tensor/core/linalg.gleam", 911).
?DOC(false).
-spec set_in_row(list(float()), integer(), float()) -> list(float()).
set_in_row(Row, Idx, Value) ->
    set_at(Row, Idx, Value).

-file("src/viva_tensor/core/linalg.gleam", 606).
?DOC(false).
-spec lu_eliminate_below(
    list(list(float())),
    list(list(float())),
    list(float()),
    integer(),
    integer()
) -> {list(list(float())), list(list(float()))}.
lu_eliminate_below(Working, L, Pivot_row, K, N) ->
    Pivot_val = unsafe_at(Pivot_row, K),
    Updated = begin
        _pipe = Working,
        gleam@list:index_map(_pipe, fun(Row, I) -> case I =< K of
                    true ->
                        {Row, +0.0};

                    false ->
                        Factor = case Pivot_val of
                            +0.0 -> +0.0;
                            -0.0 -> -0.0;
                            Gleam@denominator -> unsafe_at(Row, K) / Gleam@denominator
                        end,
                        New_row = eliminate_row(Row, Pivot_row, Factor),
                        {New_row, Factor}
                end end)
    end,
    Working_next = begin
        _pipe@1 = Updated,
        gleam@list:map(_pipe@1, fun(Pair) -> erlang:element(1, Pair) end)
    end,
    _ = N,
    L_next = begin
        _pipe@2 = L,
        gleam@list:index_map(_pipe@2, fun(Row@1, I@1) -> case I@1 =< K of
                    true ->
                        Row@1;

                    false ->
                        Factor@1 = case gleam@list:drop(Updated, I@1) of
                            [{_, F} | _] ->
                                F;

                            _ ->
                                +0.0
                        end,
                        set_in_row(Row@1, K, Factor@1)
                end end)
    end,
    {Working_next, L_next}.

-file("src/viva_tensor/core/linalg.gleam", 885).
?DOC(false).
-spec take_below_k_from(list(float()), list(float()), integer()) -> list(float()).
take_below_k_from(Source, Target, K) ->
    _pipe = gleam@list:zip(Source, Target),
    gleam@list:index_map(
        _pipe,
        fun(Pair, Idx) ->
            {S, T} = Pair,
            case Idx < K of
                true ->
                    S;

                false ->
                    T
            end
        end
    ).

-file("src/viva_tensor/core/linalg.gleam", 867).
?DOC(false).
-spec swap_l_below_k(list(list(float())), integer(), integer()) -> list(list(float())).
swap_l_below_k(L, I, J) ->
    Row_i = unsafe_at(L, I),
    Row_j = unsafe_at(L, J),
    New_i = take_below_k_from(Row_j, Row_i, I),
    New_j = take_below_k_from(Row_i, Row_j, J),
    _pipe = L,
    gleam@list:index_map(_pipe, fun(Row, Idx) -> case {Idx =:= I, Idx =:= J} of
                {true, _} ->
                    New_i;

                {_, true} ->
                    New_j;

                {_, _} ->
                    Row
            end end).

-file("src/viva_tensor/core/linalg.gleam", 862).
?DOC(false).
-spec unsafe_at_int(list(integer()), integer()) -> integer().
unsafe_at_int(Lst, Idx) ->
    V@1 = case list_at(Lst, Idx) of
        {ok, V} -> V;
        _assert_fail ->
            erlang:error(#{gleam_error => let_assert,
                        message => <<"Pattern match failed, no pattern matched the value."/utf8>>,
                        file => <<?FILEPATH/utf8>>,
                        module => <<"viva_tensor/core/linalg"/utf8>>,
                        function => <<"unsafe_at_int"/utf8>>,
                        line => 863,
                        value => _assert_fail,
                        start => 23837,
                        'end' => 23873,
                        pattern_start => 23848,
                        pattern_end => 23853})
    end,
    V@1.

-file("src/viva_tensor/core/linalg.gleam", 844).
?DOC(false).
-spec swap_int_list(list(integer()), integer(), integer()) -> list(integer()).
swap_int_list(Lst, I, J) ->
    case I =:= J of
        true ->
            Lst;

        false ->
            V_i = unsafe_at_int(Lst, I),
            V_j = unsafe_at_int(Lst, J),
            _pipe = Lst,
            gleam@list:index_map(
                _pipe,
                fun(V, Idx) -> case {Idx =:= I, Idx =:= J} of
                        {true, _} ->
                            V_j;

                        {_, true} ->
                            V_i;

                        {_, _} ->
                            V
                    end end
            )
    end.

-file("src/viva_tensor/core/linalg.gleam", 602).
?DOC(false).
-spec find_pivot_lu(list(list(float())), integer(), integer()) -> {ok,
        integer()} |
    {error, nil}.
find_pivot_lu(Rows, K, N) ->
    find_pivot(Rows, K, N).

-file("src/viva_tensor/core/linalg.gleam", 549).
?DOC(false).
-spec lu_loop(
    list(list(float())),
    list(list(float())),
    list(list(float())),
    list(integer()),
    integer(),
    integer(),
    integer()
) -> {ok, lu_decomp()} | {error, lu_failure()}.
lu_loop(Working, L, U, Perm, K, Swaps, N) ->
    case K =:= N of
        true ->
            {ok, {lu_decomp, L, U, Perm, Swaps}};

        false ->
            Pivot_idx = find_pivot_lu(Working, K, N),
            case Pivot_idx of
                {error, _} ->
                    {error, lu_singular};

                {ok, Idx} ->
                    {Swapped, Swap_inc} = case Idx =:= K of
                        true ->
                            {Working, 0};

                        false ->
                            {swap_rows(Working, K, Idx), 1}
                    end,
                    Perm_swapped = case Idx =:= K of
                        true ->
                            Perm;

                        false ->
                            swap_int_list(Perm, K, Idx)
                    end,
                    L_swapped = case Idx =:= K of
                        true ->
                            L;

                        false ->
                            swap_l_below_k(L, K, Idx)
                    end,
                    Pivot_row = unsafe_at(Swapped, K),
                    Pivot_val = unsafe_at(Pivot_row, K),
                    case gleam@float:absolute_value(Pivot_val) < 1.0e-12 of
                        true ->
                            {error, lu_singular};

                        false ->
                            U_updated = set_at(U, K, Pivot_row),
                            {Working_next, L_next} = lu_eliminate_below(
                                Swapped,
                                L_swapped,
                                Pivot_row,
                                K,
                                N
                            ),
                            lu_loop(
                                Working_next,
                                L_next,
                                U_updated,
                                Perm_swapped,
                                K + 1,
                                Swaps + Swap_inc,
                                N
                            )
                    end
            end
    end.

-file("src/viva_tensor/core/linalg.gleam", 529).
?DOC(false).
-spec lu_decompose(list(list(float())), integer()) -> {ok, lu_decomp()} |
    {error, lu_failure()}.
lu_decompose(Rows, N) ->
    Perm = gleam@list:range(0, N - 1),
    L_init = begin
        _pipe = gleam@list:range(0, N - 1),
        gleam@list:map(_pipe, fun(I) -> _pipe@1 = gleam@list:range(0, N - 1),
                gleam@list:map(_pipe@1, fun(J) -> case I =:= J of
                            true ->
                                1.0;

                            false ->
                                +0.0
                        end end) end)
    end,
    U_init = gleam@list:repeat(gleam@list:repeat(+0.0, N), N),
    lu_loop(Rows, L_init, U_init, Perm, 0, 0, N).

-file("src/viva_tensor/core/linalg.gleam", 112).
?DOC(false).
-spec det(viva_tensor@tensor:tensor()) -> {ok, float()} |
    {error, viva_tensor@core@error:tensor_error()}.
det(A) ->
    gleam@result:'try'(
        square_matrix_rows(A),
        fun(_use0) ->
            {N, Rows} = _use0,
            case lu_decompose(Rows, N) of
                {error, lu_singular} ->
                    {ok, +0.0};

                {error, {lu_error, E}} ->
                    {error, E};

                {ok, Decomp} ->
                    Diag_product = begin
                        _pipe = gleam@list:range(0, N - 1),
                        gleam@list:fold(
                            _pipe,
                            1.0,
                            fun(Acc, I) ->
                                Row = unsafe_at(erlang:element(3, Decomp), I),
                                Acc * unsafe_at(Row, I)
                            end
                        )
                    end,
                    Sign = case gleam@int:is_even(erlang:element(5, Decomp)) of
                        true ->
                            1.0;

                        false ->
                            -1.0
                    end,
                    {ok, Sign * Diag_product}
            end
        end
    ).

-file("src/viva_tensor/core/linalg.gleam", 152).
?DOC(false).
-spec lu(viva_tensor@tensor:tensor()) -> {ok,
        {viva_tensor@tensor:tensor(),
            viva_tensor@tensor:tensor(),
            list(integer())}} |
    {error, viva_tensor@core@error:tensor_error()}.
lu(A) ->
    gleam@result:'try'(
        square_matrix_rows(A),
        fun(_use0) ->
            {N, Rows} = _use0,
            case lu_decompose(Rows, N) of
                {error, lu_singular} ->
                    {error, {invalid_shape, <<"matrix is singular"/utf8>>}};

                {error, {lu_error, E}} ->
                    {error, E};

                {ok, Decomp} ->
                    L_flat = lists:append(erlang:element(2, Decomp)),
                    U_flat = lists:append(erlang:element(3, Decomp)),
                    {ok,
                        {{tensor, L_flat, [N, N]},
                            {tensor, U_flat, [N, N]},
                            erlang:element(4, Decomp)}}
            end
        end
    ).

-file("src/viva_tensor/core/linalg.gleam", 686).
?DOC(false).
-spec cholesky_row_loop(
    list(float()),
    list(list(float())),
    integer(),
    integer()
) -> {ok, list(list(float()))} | {error, viva_tensor@core@error:tensor_error()}.
cholesky_row_loop(A_i, L, I, J) ->
    case J > I of
        true ->
            {ok, L};

        false ->
            A_ij = unsafe_at(A_i, J),
            L_i = unsafe_at(L, I),
            L_j = unsafe_at(L, J),
            Dot_sum = begin
                _pipe = int_range(0, J - 1),
                gleam@list:fold(
                    _pipe,
                    +0.0,
                    fun(Acc, K) ->
                        Acc + (unsafe_at(L_i, K) * unsafe_at(L_j, K))
                    end
                )
            end,
            Raw = A_ij - Dot_sum,
            case I =:= J of
                true ->
                    case Raw =< +0.0 of
                        true ->
                            {error,
                                {invalid_shape,
                                    <<"matrix is not positive definite"/utf8>>}};

                        false ->
                            Value = math:sqrt(Raw),
                            New_l_i = set_in_row(L_i, J, Value),
                            {ok, set_at(L, I, New_l_i)}
                    end;

                false ->
                    L_jj = unsafe_at(L_j, J),
                    case gleam@float:absolute_value(L_jj) < 1.0e-15 of
                        true ->
                            {error,
                                {invalid_shape,
                                    <<"matrix is not positive definite"/utf8>>}};

                        false ->
                            Value@1 = case L_jj of
                                +0.0 -> +0.0;
                                -0.0 -> -0.0;
                                Gleam@denominator -> Raw / Gleam@denominator
                            end,
                            New_l_i@1 = set_in_row(L_i, J, Value@1),
                            New_l = set_at(L, I, New_l_i@1),
                            cholesky_row_loop(A_i, New_l, I, J + 1)
                    end
            end
    end.

-file("src/viva_tensor/core/linalg.gleam", 676).
?DOC(false).
-spec cholesky_row(
    list(list(float())),
    list(list(float())),
    integer(),
    integer()
) -> {ok, list(list(float()))} | {error, viva_tensor@core@error:tensor_error()}.
cholesky_row(A, L, I, _) ->
    A_i = unsafe_at(A, I),
    cholesky_row_loop(A_i, L, I, 0).

-file("src/viva_tensor/core/linalg.gleam", 659).
?DOC(false).
-spec cholesky_loop(
    list(list(float())),
    list(list(float())),
    integer(),
    integer()
) -> {ok, list(list(float()))} | {error, viva_tensor@core@error:tensor_error()}.
cholesky_loop(A, L, I, N) ->
    case I =:= N of
        true ->
            {ok, L};

        false ->
            case cholesky_row(A, L, I, N) of
                {error, E} ->
                    {error, E};

                {ok, New_l} ->
                    cholesky_loop(A, New_l, I + 1, N)
            end
    end.

-file("src/viva_tensor/core/linalg.gleam", 651).
?DOC(false).
-spec cholesky_rows(list(list(float())), integer()) -> {ok, list(list(float()))} |
    {error, viva_tensor@core@error:tensor_error()}.
cholesky_rows(Rows, N) ->
    L_init = gleam@list:repeat(gleam@list:repeat(+0.0, N), N),
    cholesky_loop(Rows, L_init, 0, N).

-file("src/viva_tensor/core/linalg.gleam", 188).
?DOC(false).
-spec cholesky(viva_tensor@tensor:tensor()) -> {ok, viva_tensor@tensor:tensor()} |
    {error, viva_tensor@core@error:tensor_error()}.
cholesky(A) ->
    gleam@result:'try'(
        square_matrix_rows(A),
        fun(_use0) ->
            {N, Rows} = _use0,
            gleam@result:'try'(
                cholesky_rows(Rows, N),
                fun(L_rows) -> {ok, {tensor, lists:append(L_rows), [N, N]}} end
            )
        end
    ).

-file("src/viva_tensor/core/linalg.gleam", 923).
?DOC(false).
-spec transpose_rows(list(list(float())), integer(), integer()) -> list(list(float())).
transpose_rows(Rows, _, N) ->
    _pipe = gleam@list:range(0, N - 1),
    gleam@list:map(_pipe, fun(J) -> _pipe@1 = Rows,
            gleam@list:map(_pipe@1, fun(Row) -> unsafe_at(Row, J) end) end).

-file("src/viva_tensor/core/linalg.gleam", 915).
?DOC(false).
-spec dot(list(float()), list(float())) -> float().
dot(A, B) ->
    _pipe = gleam@list:zip(A, B),
    gleam@list:fold(
        _pipe,
        +0.0,
        fun(Acc, Pair) ->
            {X, Y} = Pair,
            Acc + (X * Y)
        end
    ).

-file("src/viva_tensor/core/linalg.gleam", 745).
?DOC(false).
-spec gram_schmidt_loop(
    list(list(float())),
    list(list(float())),
    list(list(float())),
    integer(),
    integer()
) -> {ok, {list(list(float())), list(list(float()))}} |
    {error, viva_tensor@core@error:tensor_error()}.
gram_schmidt_loop(Cols, Q, R, K, N) ->
    case K =:= N of
        true ->
            {ok, {Q, R}};

        false ->
            A_k = unsafe_at(Cols, K),
            {V, R_updated} = begin
                _pipe = int_range(0, K - 1),
                gleam@list:fold(
                    _pipe,
                    {A_k, R},
                    fun(Acc, J) ->
                        {Current_v, Current_r} = Acc,
                        Q_j = unsafe_at(Q, J),
                        R_jk = dot(Q_j, A_k),
                        New_v = begin
                            _pipe@1 = gleam@list:zip(Current_v, Q_j),
                            gleam@list:map(
                                _pipe@1,
                                fun(Pair) ->
                                    {Vv, Qq} = Pair,
                                    Vv - (R_jk * Qq)
                                end
                            )
                        end,
                        R_row_j = unsafe_at(Current_r, J),
                        New_r_row_j = set_in_row(R_row_j, K, R_jk),
                        New_r = set_at(Current_r, J, New_r_row_j),
                        {New_v, New_r}
                    end
                )
            end,
            Norm_v = math:sqrt(dot(V, V)),
            case Norm_v < 1.0e-15 of
                true ->
                    {error,
                        {invalid_shape,
                            <<"qr: columns are linearly dependent"/utf8>>}};

                false ->
                    Q_k = gleam@list:map(V, fun(X) -> case Norm_v of
                                +0.0 -> +0.0;
                                -0.0 -> -0.0;
                                Gleam@denominator -> X / Gleam@denominator
                            end end),
                    Q_next = set_at(Q, K, Q_k),
                    R_row_k = unsafe_at(R_updated, K),
                    New_r_row_k = set_in_row(R_row_k, K, Norm_v),
                    R_next = set_at(R_updated, K, New_r_row_k),
                    gram_schmidt_loop(Cols, Q_next, R_next, K + 1, N)
            end
    end.

-file("src/viva_tensor/core/linalg.gleam", 735).
?DOC(false).
-spec gram_schmidt(list(list(float())), integer(), integer()) -> {ok,
        {list(list(float())), list(list(float()))}} |
    {error, viva_tensor@core@error:tensor_error()}.
gram_schmidt(Cols, M, N) ->
    R_init = gleam@list:repeat(gleam@list:repeat(+0.0, N), N),
    Q_init = gleam@list:repeat(gleam@list:repeat(+0.0, M), N),
    gram_schmidt_loop(Cols, Q_init, R_init, 0, N).

-file("src/viva_tensor/core/linalg.gleam", 214).
?DOC(false).
-spec qr(viva_tensor@tensor:tensor()) -> {ok,
        {viva_tensor@tensor:tensor(), viva_tensor@tensor:tensor()}} |
    {error, viva_tensor@core@error:tensor_error()}.
qr(A) ->
    case erlang:element(3, A) of
        [M, N] ->
            gleam@result:'try'(
                to_rows(A, M, N),
                fun(Rows) ->
                    Cols = transpose_rows(Rows, M, N),
                    gleam@result:'try'(
                        gram_schmidt(Cols, M, N),
                        fun(_use0) ->
                            {Q_cols, R_rows} = _use0,
                            Q_rows = transpose_rows(Q_cols, N, M),
                            {ok,
                                {{tensor, lists:append(Q_rows), [M, N]},
                                    {tensor, lists:append(R_rows), [N, N]}}}
                        end
                    )
                end
            );

        _ ->
            {error, {dimension_error, <<"qr requires a 2D matrix"/utf8>>}}
    end.

-file("src/viva_tensor/core/linalg.gleam", 271).
?DOC(false).
-spec svd(viva_tensor@tensor:tensor()) -> {ok,
        {viva_tensor@tensor:tensor(),
            viva_tensor@tensor:tensor(),
            viva_tensor@tensor:tensor()}} |
    {error, viva_tensor@core@error:tensor_error()}.
svd(_) ->
    {error,
        {dimension_error,
            <<"svd: not implemented in v1; use a NIF in v2"/utf8>>}}.

-file("src/viva_tensor/core/linalg.gleam", 289).
?DOC(false).
-spec eig(viva_tensor@tensor:tensor()) -> {ok,
        {viva_tensor@tensor:tensor(), viva_tensor@tensor:tensor()}} |
    {error, viva_tensor@core@error:tensor_error()}.
eig(_) ->
    {error,
        {dimension_error,
            <<"eig: not implemented in v1; use a NIF in v2"/utf8>>}}.