matrex

defmodule Matrex do
  @moduledoc """
  Performs fast operations on matrices using native C code and CBLAS library.
  """

  alias Matrex.NIFs

  @enforce_keys [:data]
  defstruct [:data]
  @type element :: float
  @type index :: pos_integer
  @type matrex :: %Matrex{data: binary}

  @compile {:inline,
            add: 2,
            argmax: 1,
            at: 3,
            column_to_list: 2,
            divide: 2,
            dot: 2,
            dot_and_add: 3,
            dot_nt: 2,
            dot_tn: 2,
            eye: 1,
            fill: 3,
            fill: 2,
            first: 1,
            max: 1,
            multiply: 2,
            multiply_with_scalar: 2,
            ones: 2,
            ones: 1,
            random: 2,
            random: 1,
            row_to_list: 2,
            row: 2,
            size: 1,
            substract: 2,
            substract_inverse: 2,
            sum: 1,
            to_list: 1,
            to_list_of_lists: 1,
            transpose: 1,
            zeros: 2,
            zeros: 1}

  @behaviour Access

  # Horizontal vector
  @impl Access
  def fetch(
        %Matrex{
          data: <<
            rows::unsigned-integer-little-32,
            _columns::unsigned-integer-little-32,
            _rest::binary
          >>
        } = matrex,
        key
      )
      when is_integer(key) and key > 0 and rows == 1,
      do: {:ok, at(matrex, 1, key)}

  # Vertical vector
  @impl Access
  def fetch(
        %Matrex{
          data: <<
            _rows::unsigned-integer-little-32,
            columns::unsigned-integer-little-32,
            _rest::binary
          >>
        } = matrex,
        key
      )
      when is_integer(key) and key > 0 and columns == 1,
      do: {:ok, at(matrex, key, 1)}

  # Return a row
  @impl Access
  def fetch(
        %Matrex{} = matrex,
        key
      )
      when is_integer(key) and key > 0,
      do: {:ok, row(matrex, key)}

  @impl Access
  def fetch(
        %Matrex{
          data: <<
            rows::unsigned-integer-little-32,
            _columns::unsigned-integer-little-32,
            _rest::binary
          >>
        },
        :rows
      ),
      do: {:ok, rows}

  @impl Access
  def fetch(
        %Matrex{
          data: <<
            _rows::unsigned-integer-little-32,
            columns::unsigned-integer-little-32,
            _rest::binary
          >>
        },
        :cols
      ),
      do: {:ok, columns}

  @impl Access
  def get(%Matrex{} = matrex, key, default) do
    case fetch(matrex, key) do
      {:ok, value} -> value
      :error -> default
    end
  end

  defimpl Inspect do
    def inspect(%Matrex{} = matrex, %{width: screen_width}),
      do: Matrex.Inspect.do_inspect(matrex, screen_width)
  end

  @doc """
  Adds two matrices. NIF.

  ## Example

      iex> Matrex.add(Matrex.new([[1,2,3],[4,5,6]]), Matrex.new([[7,8,9],[10,11,12]]))
      #Matrex[2×3]
      ┌                         ┐
      │     8.0    10.0    12.0 │
      │    14.0    16.0    18.0 │
      └                         ┘

  """
  @spec add(matrex, matrex) :: matrex
  def add(%Matrex{data: first}, %Matrex{data: second}), do: %Matrex{data: NIFs.add(first, second)}

  @doc """
  Apply math function to matrix elementwise. NIF, multithreaded.
  Uses eight native threads, if matrix size is greater, than 100 000 elements.

  ## Example

      iex> Matrex.magic(5) |> Matrex.apply(:sigmoid)
      #Matrex[5×5]
      ┌                                         ┐
      │-0.95766-0.53283 0.28366  0.7539 0.13674 │
      │-0.99996-0.65364 0.96017 0.90745 0.40808 │
      │-0.98999-0.83907 0.84385  0.9887-0.54773 │
      │-0.91113 0.00443 0.66032  0.9912-0.41615 │
      │-0.75969-0.27516 0.42418  0.5403 -0.1455 │
      └                                         ┘

  """
  @spec apply(matrex, atom) :: matrex
  def apply(%Matrex{data: data} = matrix, function)
      when function in [
             :exp,
             :exp2,
             :sigmoid,
             :expm1,
             :log,
             :log2,
             :sqrt,
             :cbrt,
             :ceil,
             :floor,
             :trunc,
             :round,
             :sin,
             :cos,
             :tan,
             :asin,
             :acos,
             :atan,
             :sinh,
             :cosh,
             :tanh,
             :asinh,
             :acosh,
             :atanh,
             :erf,
             :erfc,
             :tgamma,
             :lgamma
           ] do
    {rows, cols} = size(matrix)

    %Matrex{
      data:
        if(
          rows * cols < 100_000,
          do: NIFs.apply_math(data, function),
          else: NIFs.apply_parallel_math(data, function)
        )
    }
  end

  @doc """
  Applies the given function on each element of the matrix. Implemented in Elixir, so it's not fast.

  ## Example

      iex> Matrex.magic(5) |> Matrex.apply(&:math.cos/1)
      #Matrex[5×5]
      ┌                                         ┐
      │-0.95766-0.53283 0.28366  0.7539 0.13674 │
      │-0.99996-0.65364 0.96017 0.90745 0.40808 │
      │-0.98999-0.83907 0.84385  0.9887-0.54773 │
      │-0.91113 0.00443 0.66032  0.9912-0.41615 │
      │-0.75969-0.27516 0.42418  0.5403 -0.1455 │
      └                                         ┘

  """
  @spec apply(matrex, (element -> element)) :: matrex
  def apply(
        %Matrex{
          data:
            <<rows::unsigned-integer-little-32, columns::unsigned-integer-little-32,
              data::binary>>
        },
        function
      )
      when is_function(function, 1) do
    initial = <<rows::unsigned-integer-little-32, columns::unsigned-integer-little-32>>

    %Matrex{data: apply_on_matrix(data, function, initial)}
  end

  @doc """

  Applies function to each element of the matrix.

  Zero-based index of element in the matix is
  passed to the function along with the element value.


  ## Examples

      iex> Matrex.ones(5) |> Matrex.apply(fn val, index -> val + index end)
      #Matrex[5×5]
      ┌                                         ┐
      │     2.0     3.0     4.0     5.0     6.0 │
      │     7.0     8.0     9.0    10.0    11.0 │
      │    12.0    13.0    14.0    15.0    16.0 │
      │    17.0    18.0    19.0    20.0    21.0 │
      │    22.0    23.0    24.0    25.0    26.0 │
      └                                         ┘

  """
  @spec apply(matrex, (element, index -> element)) :: matrex
  def apply(
        %Matrex{
          data: <<
            rows::unsigned-integer-little-32,
            columns::unsigned-integer-little-32,
            data::binary
          >>
        },
        function
      )
      when is_function(function, 2) do
    initial = <<rows::unsigned-integer-little-32, columns::unsigned-integer-little-32>>
    size = rows * columns

    %Matrex{data: apply_on_matrix(data, function, 1, size, initial)}
  end

  @spec apply(matrex, (element, index, index -> element)) :: matrex
  def apply(
        %Matrex{
          data: <<
            rows::unsigned-integer-little-32,
            columns::unsigned-integer-little-32,
            data::binary
          >>
        },
        function
      )
      when is_function(function, 3) do
    initial = <<rows::unsigned-integer-little-32, columns::unsigned-integer-little-32>>

    %Matrex{data: apply_on_matrix(data, function, 1, 1, columns, initial)}
  end

  defp apply_on_matrix(<<>>, _, accumulator), do: accumulator

  defp apply_on_matrix(<<value::float-little-32, rest::binary>>, function, accumulator) do
    new_value = function.(value)

    apply_on_matrix(rest, function, <<accumulator::binary, new_value::float-little-32>>)
  end

  defp apply_on_matrix(<<>>, _, _, _, accumulator), do: accumulator

  defp apply_on_matrix(
         <<value::float-little-32, rest::binary>>,
         function,
         index,
         size,
         accumulator
       ) do
    new_value = function.(value, index)

    apply_on_matrix(
      rest,
      function,
      index + 1,
      size,
      <<accumulator::binary, new_value::float-little-32>>
    )
  end

  defp apply_on_matrix(<<>>, _, _, _, _, accumulator), do: accumulator

  defp apply_on_matrix(
         <<value::float-little-32, rest::binary>>,
         function,
         row_index,
         column_index,
         columns,
         accumulator
       ) do
    new_value = function.(value, row_index, column_index)
    new_accumulator = <<accumulator::binary, new_value::float-little-32>>

    case column_index < columns do
      true ->
        apply_on_matrix(rest, function, row_index, column_index + 1, columns, new_accumulator)

      false ->
        apply_on_matrix(rest, function, row_index + 1, 1, columns, new_accumulator)
    end
  end

  @doc """
  Applies function to elements of two matrices and returns matrix of function results.
  """
  @spec apply(matrex, matrex, (element, element -> element)) :: matrex
  def apply(
        %Matrex{
          data: <<
            rows::unsigned-integer-little-32,
            columns::unsigned-integer-little-32,
            first_data::binary
          >>
        },
        %Matrex{
          data: <<
            _::unsigned-integer-little-32,
            _::unsigned-integer-little-32,
            second_data::binary
          >>
        },
        function
      )
      when is_function(function, 2) do
    initial = <<rows::unsigned-integer-little-32, columns::unsigned-integer-little-32>>

    %Matrex{data: apply_on_matrices(first_data, second_data, function, initial)}
  end

  defp apply_on_matrices(<<>>, <<>>, _, accumulator), do: accumulator

  defp apply_on_matrices(
         <<first_value::float-little-32, first_rest::binary>>,
         <<second_value::float-little-32, second_rest::binary>>,
         function,
         accumulator
       )
       when is_function(function, 2) do
    new_value = function.(first_value, second_value)
    new_accumulator = <<accumulator::binary, new_value::float-little-32>>

    apply_on_matrices(first_rest, second_rest, function, new_accumulator)
  end

  @doc """
  Returns zero-based index of the biggest element. NIF.

  ## Example

      iex> m = Matrex.magic(3)
      #Matrex[3×3]
      ┌                         ┐
      │     8.0     1.0     6.0 │
      │     3.0     5.0     7.0 │
      │     4.0     9.0     2.0 │
      └                         ┘
      iex> Matrex.argmax(m)
      7

  """
  @spec argmax(matrex) :: index
  def argmax(%Matrex{data: data}), do: NIFs.argmax(data)

  @doc """
  Get element of a matrix at given one-based (row, column) position.

  ## Example

      iex> m = Matrex.magic(3)
      #Matrex[3×3]
      ┌                         ┐
      │     8.0     1.0     6.0 │
      │     3.0     5.0     7.0 │
      │     4.0     9.0     2.0 │
      └                         ┘
      iex> Matrex.at(m, 3, 2)
      9.0

  You can use `Access` behaviour square brackets for the same purpose,
  but it will be slower:

      iex> m[3][2]
      9.0

  """
  @spec at(matrex, index, index) :: element
  def at(
        %Matrex{
          data: <<
            rows::unsigned-integer-little-32,
            columns::unsigned-integer-little-32,
            data::binary
          >>
        },
        row,
        col
      )
      when is_integer(row) and is_integer(col) do
    if row < 1 or row > rows,
      do: raise(ArgumentError, message: "Row position out of range: #{row}")

    if col < 1 or col > columns,
      do: raise(ArgumentError, message: "Column position out of range: #{col}")

    <<elem::float-little-32>> = binary_part(data, ((row - 1) * columns + (col - 1)) * 4, 4)
    elem
  end

  @doc """
  Get column of matrix as matrix (vector) in matrex form. One-based.

  ## Example

      iex> m = Matrex.magic(3)
      #Matrex[3×3]
      ┌                         ┐
      │     8.0     1.0     6.0 │
      │     3.0     5.0     7.0 │
      │     4.0     9.0     2.0 │
      └                         ┘
      iex> Matrex.column(m, 2)
      #Matrex[3×1]
      ┌         ┐
      │     1.0 │
      │     5.0 │
      │     9.0 │
      └         ┘

  """
  @spec column(matrex, index) :: matrex
  def column(
        %Matrex{
          data: <<
            rows::unsigned-integer-little-32,
            columns::unsigned-integer-little-32,
            data::binary
          >>
        },
        col
      )
      when is_integer(col) and col > 0 and col <= columns do
    column = <<rows::unsigned-integer-little-32, 1::unsigned-integer-little-32>>

    %Matrex{
      data:
        0..(rows - 1)
        |> Enum.reduce(column, fn row, acc ->
          <<acc::binary, binary_part(data, (row * columns + (col - 1)) * 4, 4)::binary>>
        end)
    }
  end

  @doc """
  Get column of matrix as list of floats. One-based, NIF.


  ## Example

      iex> m = Matrex.magic(3)
      #Matrex[3×3]
      ┌                         ┐
      │     8.0     1.0     6.0 │
      │     3.0     5.0     7.0 │
      │     4.0     9.0     2.0 │
      └                         ┘
      iex> Matrex.column_to_list(m, 3)
      [6.0, 7.0, 2.0]

  """
  @spec column_to_list(matrex, index) :: [element]
  def column_to_list(%Matrex{data: matrix}, column) when is_integer(column) and column > 0,
    do: NIFs.column_to_list(matrix, column - 1)

  @doc """
  Divides two matrices element-wise. NIF.

  Raises `ErlangError` if matrices' sizes do not match.

  ## Example

      iex> Matrex.new([[10, 20, 25], [8, 9, 4]])
      ...> |> Matrex.divide(Matrex.new([[5, 10, 5], [4, 3, 4]]))
      #Matrex[2×3]
      ┌                         ┐
      │     2.0     2.0     5.0 │
      │     2.0     3.0     1.0 │
      └                         ┘
  """
  @spec divide(matrex, matrex) :: matrex
  def divide(%Matrex{data: dividend}, %Matrex{data: divisor}),
    do: %Matrex{data: NIFs.divide(dividend, divisor)}

  @doc """
  Matrix multiplication. NIF, via `cblas_sgemm()`.

  Number of columns of the first matrix must be equal to the number of rows of the second matrix.

  Raises `ErlangError` if matrices' sizes do not match.

  ## Example

      iex> Matrex.new([[1, 2, 3], [4, 5, 6]]) |>
      ...> Matrex.dot(Matrex.new([[1, 2], [3, 4], [5, 6]]))
      #Matrex[2×2]
      ┌                 ┐
      │    22.0    28.0 │
      │    49.0    64.0 │
      └                 ┘

  """
  @spec dot(matrex, matrex) :: matrex
  def dot(%Matrex{data: first}, %Matrex{data: second}), do: %Matrex{data: NIFs.dot(first, second)}

  @doc """
  Matrix multiplication with addition of thitd matrix.  NIF, via `cblas_sgemm()`.

  Raises `ErlangError` if matrices' sizes do not match.

  ## Example

      iex> Matrex.new([[1, 2, 3], [4, 5, 6]]) |>
      ...> Matrex.dot_and_add(Matrex.new([[1, 2], [3, 4], [5, 6]]), Matrex.new([[1, 2], [3, 4]]))
      #Matrex[2×2]
      ┌                 ┐
      │    23.0    30.0 │
      │    52.0    68.0 │
      └                 ┘

  """
  @spec dot_and_add(matrex, matrex, matrex) :: matrex
  def dot_and_add(%Matrex{data: first}, %Matrex{data: second}, %Matrex{data: third}),
    do: %Matrex{data: NIFs.dot_and_add(first, second, third)}

  @doc """
  Matrix multiplication where the second matrix needs to be transposed.  NIF, via `cblas_sgemm()`.

  Raises `ErlangError` if matrices' sizes do not match.

  ## Example

      iex> Matrex.new([[1, 2, 3], [4, 5, 6]]) |>
      ...> Matrex.dot_nt(Matrex.new([[1, 3, 5], [2, 4, 6]]))
      #Matrex[2×2]
      ┌                 ┐
      │    22.0    28.0 │
      │    49.0    64.0 │
      └                 ┘

  """
  @spec dot_nt(matrex, matrex) :: matrex
  def dot_nt(%Matrex{data: first}, %Matrex{data: second}),
    do: %Matrex{data: NIFs.dot_nt(first, second)}

  @doc """
  Matrix multiplication where the first matrix needs to be transposed.  NIF, via `cblas_sgemm()`.

  Raises `ErlangError` if matrices' sizes do not match.

  ## Example

      iex> Matrex.new([[1, 4], [2, 5], [3, 6]]) |>
      ...> Matrex.dot_tn(Matrex.new([[1, 2], [3, 4], [5, 6]]))
      #Matrex[2×2]
      ┌                 ┐
      │    22.0    28.0 │
      │    49.0    64.0 │
      └                 ┘

  """
  @spec dot_tn(matrex, matrex) :: matrex
  def dot_tn(%Matrex{data: first}, %Matrex{data: second}),
    do: %Matrex{data: NIFs.dot_tn(first, second)}

  @doc """
  Create eye square matrix of given size

  ## Example

      iex> Matrex.eye(3)
      #Matrex[3×3]
      ┌                         ┐
      │     1.0     0.0     0.0 │
      │     0.0     1.0     0.0 │
      │     0.0     0.0     1.0 │
      └                         ┘
  """
  @spec eye(index) :: matrex
  def eye(size) when is_integer(size), do: %Matrex{data: NIFs.eye(size)}

  @doc """
  Create matrix filled with given value. NIF.

  ## Example

      iex> Matrex.fill(4,3, 55)
      #Matrex[4×3]
      ┌                         ┐
      │    55.0    55.0    55.0 │
      │    55.0    55.0    55.0 │
      │    55.0    55.0    55.0 │
      │    55.0    55.0    55.0 │
      └                         ┘
  """
  @spec fill(index, index, number) :: matrex
  def fill(rows, cols, value)
      when is_integer(rows) and is_integer(cols) and is_number(value),
      do: %Matrex{data: NIFs.fill(rows, cols, value)}

  @doc """
  Create square matrix filled with given value. Inlined.

  ## Example

      iex> Matrex.fill(3, 55)
      #Matrex[3×3]
      ┌                         ┐
      │    33.0    33.0    33.0 │
      │    33.0    33.0    33.0 │
      │    33.0    33.0    33.0 │
      └                         ┘
  """
  @spec fill(index, number) :: matrex
  def fill(size, value), do: fill(size, size, value)

  @doc """
  Return first element of a matrix.

  ## Example

      iex> Matrex.new([[6,5,4],[3,2,1]]) |> Matrex.first()
      6.0

  """
  @spec first(matrex) :: element
  def first(%Matrex{
        data: <<
          _rows::unsigned-integer-little-32,
          _columns::unsigned-integer-little-32,
          element::float-little-32,
          _rest::binary
        >>
      }),
      do: element

  @doc """
  Displays a visualization of the matrix.

  Set the second parameter to true to show full numbers.
  Otherwise, they are truncated.

  """
  @spec inspect(matrex, boolean) :: matrex
  def inspect(
        %Matrex{
          data: <<
            rows::unsigned-integer-little-32,
            columns::unsigned-integer-little-32,
            rest::binary
          >>
        } = matrex,
        full \\ false
      ) do
    IO.puts("Rows: #{rows} Columns: #{columns}")

    inspect_element(1, columns, rest, full)

    matrex
  end

  defp inspect_element(_, _, <<>>, _), do: :ok

  defp inspect_element(column, columns, <<element::float-little-32, rest::binary>>, full) do
    next_column =
      case column == columns do
        true ->
          IO.puts(undot(element, full))

          1.0

        false ->
          IO.write("#{undot(element, full)} ")

          column + 1.0
      end

    inspect_element(next_column, columns, rest, full)
  end

  defp undot(f, false) when is_float(f) and f - trunc(f) == 0.0, do: trunc(f)
  defp undot(f, false) when is_float(f), do: :io_lib.format("~7.3f", [f])
  defp undot(f, true) when is_float(f), do: f

  @doc """
  Creates "magic" n*n matrix, where sums of all dimensions are equal


  ## Example

      iex> Matrex.magic(5)
      #Matrex[5×5]
      ┌                                         ┐
      │    16.0    23.0     5.0     7.0    14.0 │
      │    22.0     4.0     6.0    13.0    20.0 │
      │     3.0    10.0    12.0    19.0    21.0 │
      │     9.0    11.0    18.0    25.0     2.0 │
      │    15.0    17.0    24.0     1.0     8.0 │
      └                                         ┘
  """
  @spec magic(index) :: matrex
  def magic(n) when is_integer(n), do: Matrex.MagicSquare.new(n) |> new()

  @doc """
  Maximum element in a matrix. NIF.

  ## Example

      iex> m = Matrex.magic(5)
      #Matrex[5×5]
      ┌                                         ┐
      │    16.0    23.0     5.0     7.0    14.0 │
      │    22.0     4.0     6.0    13.0    20.0 │
      │     3.0    10.0    12.0    19.0    21.0 │
      │     9.0    11.0    18.0    25.0     2.0 │
      │    15.0    17.0    24.0     1.0     8.0 │
      └                                         ┘
      iex> Matrex.max(m)
      25.0

  """
  @spec max(matrex) :: element
  def max(%Matrex{data: matrix}), do: NIFs.max(matrix)

  @doc """
  Elementwise multiplication of two matrices. NIF.

  Raises `ErlangError` if matrices' sizes do not match.

  ## Example

      iex> Matrex.new([[1, 2, 3], [4, 5, 6]]) |>
      ...> Matrex.multiply(Matrex.new([[5, 2, 1], [3, 4, 6]]))
      #Matrex[2×3]
      ┌                         ┐
      │     5.0     4.0     3.0 │
      │    12.0    20.0    36.0 │
      └                         ┘
  """
  @spec multiply(matrex, matrex) :: matrex
  def multiply(%Matrex{data: first}, %Matrex{data: second}),
    do: %Matrex{data: NIFs.multiply(first, second)}

  @doc """
  Elementwise multiplication of a scalar. NIF.

  ## Example

      iex> Matrex.new([[1, 2, 3], [4, 5, 6]]) |> Matrex.multiply_with_scalar(2)
      #Matrex[2×3]
      ┌                         ┐
      │     2.0     4.0     6.0 │
      │     8.0    10.0    12.0 │
      └                         ┘
  """
  @spec multiply_with_scalar(matrex, number) :: matrex
  def multiply_with_scalar(%Matrex{data: matrix}, scalar) when is_number(scalar),
    do: %Matrex{data: NIFs.multiply_with_scalar(matrix, scalar)}

  @doc """
  Creates new matrix with values provided by the given function.

  ## Example

      iex> Matrex.new(3, 3, fn -> :rand.uniform() end)
      #Matrex[3×3]
      ┌                         ┐
      │ 0.45643 0.91533 0.25332 │
      │ 0.29095 0.21241  0.9776 │
      │ 0.42451 0.05422 0.92863 │
      └                         ┘
  """
  @spec new(index, index, (() -> element)) :: matrex
  def new(rows, columns, function) when is_function(function, 0) do
    initial = <<rows::unsigned-integer-little-32, columns::unsigned-integer-little-32>>

    new_matrix_from_function(rows * columns, function, initial)
  end

  @doc """
  Creates new matrix with values provided by function.

  One-based row and column of each element are passed to the function.

  ## Example

      iex> Matrex.new(3, 3, fn row, col -> row*col end)
      #Matrex[3×3]
      ┌                         ┐
      │     1.0     2.0     3.0 │
      │     2.0     4.0     6.0 │
      │     3.0     6.0     9.0 │
      └                         ┘
  """
  @spec new(index, index, (index, index -> element)) :: matrex
  def new(rows, columns, function) when is_function(function, 2) do
    initial = <<rows::unsigned-integer-little-32, columns::unsigned-integer-little-32>>
    size = rows * columns

    new_matrix_from_function(size, rows, columns, function, initial)
  end

  @doc """
  Creates new matrix from list of lists, with number of rows and columns given.

  Works faster, than new() without matrix size, but it will be noticeable only with big matrices.

  ## Example

      iex> Matrex.new(2, 3, [[1, 2, 3], [4, 5, 6]])
      #Matrex[2×3]
      ┌                         ┐
      │     1.0     2.0     3.0 │
      │     4.0     5.0     6.0 │
      └                         ┘
  """
  @spec new(index, index, [[element]]) :: matrex
  def new(rows, columns, list_of_lists) when is_list(list_of_lists) do
    initial = <<rows::unsigned-integer-little-32, columns::unsigned-integer-little-32>>

    %Matrex{
      data:
        Enum.reduce(list_of_lists, initial, fn list, accumulator ->
          accumulator <>
            Enum.reduce(list, <<>>, fn element, partial ->
              <<partial::binary, element::float-little-32>>
            end)
        end)
    }
  end

  @doc """
  Creates new matrix from list of lists.

  ## Example

      iex> Matrex.new([[1, 2, 3], [4, 5, 6]])
      #Matrex[2×3]
      ┌                         ┐
      │     1.0     2.0     3.0 │
      │     4.0     5.0     6.0 │
      └                         ┘
  """
  @spec new([[element]]) :: matrex
  def new([first_list | _] = list_of_lists) when is_list(first_list) do
    rows = length(list_of_lists)
    cols = length(first_list)
    new(rows, cols, list_of_lists)
  end

  defp new_matrix_from_function(0, _, accumulator), do: %Matrex{data: accumulator}

  defp new_matrix_from_function(size, function, accumulator),
    do:
      new_matrix_from_function(
        size - 1,
        function,
        <<accumulator::binary, function.()::float-little-32>>
      )

  defp new_matrix_from_function(0, _, _, _, accumulator), do: %Matrex{data: accumulator}

  defp new_matrix_from_function(size, rows, columns, function, accumulator) do
    {row, col} =
      if rem(size, columns) == 0 do
        {rows - div(size, columns), 0}
      else
        {rows - 1 - div(size, columns), columns - rem(size, columns)}
      end

    new_accumulator = <<accumulator::binary, function.(row + 1, col + 1)::float-little-32>>

    new_matrix_from_function(size - 1, rows, columns, function, new_accumulator)
  end

  @doc """
  Create matrix filled with ones.
  """
  @spec ones(index, index) :: matrex
  def ones(rows, cols) when is_integer(rows) and is_integer(cols), do: fill(rows, cols, 1)

  @doc """
  Create square matrix filled with ones.

  ## Example

      iex> Matrex.ones(3)
      #Matrex[3×3]
      ┌                         ┐
      │     1.0     1.0     1.0 │
      │     1.0     1.0     1.0 │
      │     1.0     1.0     1.0 │
      └                         ┘
  """
  @spec ones(index) :: matrex
  def ones(size) when is_integer(size), do: fill(size, 1)

  @doc """
  Create matrix of random floats in [0, 1] range. NIF.

  ## Example

      iex> Matrex.random(4,3)
      #Matrex[4×3]
      ┌                         ┐
      │ 0.32994 0.28736 0.88012 │
      │ 0.51782 0.68608 0.29976 │
      │ 0.52953  0.9071 0.26743 │
      │ 0.82189 0.59311  0.8451 │
      └                         ┘

  """
  @spec random(index, index) :: matrex
  def random(rows, columns) when is_integer(rows) and is_integer(columns),
    do: %Matrex{data: NIFs.random(rows, columns)}

  @doc """
  Create square matrix of random floats.

  ## Example

      iex> Matrex.random(3)
      #Matrex[3×3]
      ┌                         ┐
      │ 0.66438 0.31026 0.98602 │
      │ 0.82127 0.04701 0.13278 │
      │ 0.96935 0.70772 0.98738 │
      └                         ┘
  """
  @spec random(index) :: matrex
  def random(size) when is_integer(size), do: random(size, size)

  @doc """
  Return matrix row as list by one-based index.

  ## Example

      iex> m = Matrex.magic(5)
      #Matrex[5×5]
      ┌                                         ┐
      │    16.0    23.0     5.0     7.0    14.0 │
      │    22.0     4.0     6.0    13.0    20.0 │
      │     3.0    10.0    12.0    19.0    21.0 │
      │     9.0    11.0    18.0    25.0     2.0 │
      │    15.0    17.0    24.0     1.0     8.0 │
      └                                         ┘
      iex> Matrex.row_to_list(m, 3)
      [3.0, 10.0, 12.0, 19.0, 21.0]
  """
  @spec row_to_list(matrex, index) :: [element]
  def row_to_list(%Matrex{data: matrix}, row) when is_integer(row) and row > 0,
    do: NIFs.row_to_list(matrix, row - 1)

  @doc """
  Get row of matrix as matrix (vector) in matrex form. One-based.

  ## Example

      iex> m = Matrex.magic(5)
      #Matrex[5×5]
      ┌                                         ┐
      │    16.0    23.0     5.0     7.0    14.0 │
      │    22.0     4.0     6.0    13.0    20.0 │
      │     3.0    10.0    12.0    19.0    21.0 │
      │     9.0    11.0    18.0    25.0     2.0 │
      │    15.0    17.0    24.0     1.0     8.0 │
      └                                         ┘
      iex> Matrex.row(m, 4)
      #Matrex[1×5]
      ┌                                         ┐
      │     9.0    11.0    18.0    25.0     2.0 │
      └                                         ┘
  """
  @spec row(matrex, index) :: matrex
  def row(
        %Matrex{
          data: <<
            rows::unsigned-integer-little-32,
            columns::unsigned-integer-little-32,
            data::binary
          >>
        },
        row
      )
      when is_integer(row) and row > 0 and row <= rows,
      do: %Matrex{
        data:
          <<1::unsigned-integer-little-32, columns::unsigned-integer-little-32,
            binary_part(data, (row - 1) * columns * 4, columns * 4)::binary>>
      }

  @doc """
  Return size of matrix as {rows, cols}

  ## Example

      iex> m = Matrex.random(2,3)
      #Matrex[2×3]
      ┌                         ┐
      │ 0.69745 0.23668 0.36376 │
      │ 0.63423 0.29651 0.22844 │
      └                         ┘
      iex> Matrex.size(m)
      {2, 3}
  """
  @spec size(matrex) :: {index, index}
  def size(%Matrex{
        data: <<
          rows::unsigned-integer-little-32,
          cols::unsigned-integer-little-32,
          _rest::binary
        >>
      }),
      do: {rows, cols}

  @doc """
  Substracts two matrices element-wise. NIF.

  Raises `ErlangError` if matrices' sizes do not match.

  ## Example

      iex> Matrex.new([[1, 2, 3], [4, 5, 6]]) |>
      ...> Matrex.substract(Matrex.new([[5, 2, 1], [3, 4, 6]]))
      #Matrex[2×3]
      ┌                         ┐
      │    -4.0     0.0     2.0 │
      │     1.0     1.0     0.0 │
      └                         ┘
  """
  @spec substract(matrex, matrex) :: matrex
  def substract(%Matrex{data: first}, %Matrex{data: second}),
    do: %Matrex{data: NIFs.substract(first, second)}

  @doc """
  Substracts the second matrix from the first. Inlined.

  Raises `ErlangError` if matrices' sizes do not match.

  ## Example

      iex> Matrex.new([[1, 2, 3], [4, 5, 6]]) |>
      ...> Matrex.substract_inverse(Matrex.new([[5, 2, 1], [3, 4, 6]]))
      #Matrex[2×3]
      ┌                         ┐
      │     4.0     0.0    -2.0 │
      │    -1.0    -1.0     0.0 │
      └                         ┘
  """
  @spec substract_inverse(matrex, matrex) :: matrex
  def substract_inverse(%Matrex{} = first, %Matrex{} = second), do: substract(second, first)

  @doc """
  Sums all elements. NIF.

  ## Example

      iex> m = Matrex.magic(3)
      #Matrex[3×3]
      ┌                         ┐
      │     8.0     1.0     6.0 │
      │     3.0     5.0     7.0 │
      │     4.0     9.0     2.0 │
      └                         ┘
      iex> Matrex.sum(m)
      45.0
  """
  @spec sum(matrex) :: element
  def sum(%Matrex{data: matrix}), do: NIFs.sum(matrix)

  @doc """
  Converts to flat list. NIF.

  ## Example

      iex> m = Matrex.magic(3)
      #Matrex[3×3]
      ┌                         ┐
      │     8.0     1.0     6.0 │
      │     3.0     5.0     7.0 │
      │     4.0     9.0     2.0 │
      └                         ┘
      iex> Matrex.to_list(m)
      [8.0, 1.0, 6.0, 3.0, 5.0, 7.0, 4.0, 9.0, 2.0]
  """
  @spec to_list(matrex) :: list(element)
  def to_list(%Matrex{data: matrix}), do: NIFs.to_list(matrix)

  @doc """
  Converts to list of lists

  ## Example

      iex> m = Matrex.magic(3)
      #Matrex[3×3]
      ┌                         ┐
      │     8.0     1.0     6.0 │
      │     3.0     5.0     7.0 │
      │     4.0     9.0     2.0 │
      └                         ┘
      iex> Matrex.to_list_of_lists(m)
      [[8.0, 1.0, 6.0], [3.0, 5.0, 7.0], [4.0, 9.0, 2.0]]
  """
  @spec to_list_of_lists(matrex) :: list(list(element))
  def to_list_of_lists(%Matrex{data: matrix}), do: NIFs.to_list_of_lists(matrix)

  @doc """
  Transposes a matrix. NIF.

  ## Example

      iex> m = Matrex.new([[1,2,3],[4,5,6]])
      #Matrex[2×3]
      ┌                         ┐
      │     1.0     2.0     3.0 │
      │     4.0     5.0     6.0 │
      └                         ┘
      iex> Matrex.transpose(m)
      #Matrex[3×2]
      ┌                 ┐
      │     1.0     4.0 │
      │     2.0     5.0 │
      │     3.0     6.0 │
      └                 ┘
  """
  @spec transpose(matrex) :: matrex
  def transpose(%Matrex{data: matrix}), do: %Matrex{data: NIFs.transpose(matrix)}

  @doc """
  Create matrix of zeros of the specified size. NIF, using `memset()`.

  Faster, than `fill(rows, cols, 0)`.

  ## Example

      iex> Matrex.zeros(4,3)
      #Matrex[4×3]
      ┌                         ┐
      │     0.0     0.0     0.0 │
      │     0.0     0.0     0.0 │
      │     0.0     0.0     0.0 │
      │     0.0     0.0     0.0 │
      └                         ┘
  """
  @spec zeros(index, index) :: matrex
  def zeros(rows, cols) when is_integer(rows) and is_integer(cols),
    do: %Matrex{data: NIFs.zeros(rows, cols)}

  @doc """
  Create square matrix of zeros. Inlined.

  ## Example

      iex> Matrex.zeros(3)
      #Matrex[3×3]
      ┌                         ┐
      │     0.0     0.0     0.0 │
      │     0.0     0.0     0.0 │
      │     0.0     0.0     0.0 │
      └                         ┘
  """
  @spec zeros(index) :: matrex
  def zeros(size), do: zeros(size, size)
end