[algorithms] initial algorithms implementation

include/CMakeLists.txt

@@ -75,11 +75,12 @@ target_sources(
             FILES
             "fcarouge/internal/detail.hpp"
             "fcarouge/internal/format.hpp"
-            "fcarouge/internal/kalman.hpp"
+            "fcarouge/internal/filter.hpp"
             "fcarouge/internal/utility.hpp"
             "fcarouge/algorithm.hpp"
             "fcarouge/filter.hpp"
-            "fcarouge/kalman.hpp")
+            "fcarouge/kalman.hpp"
+            "fcarouge/utility.hpp")
 target_compile_options(kalman INTERFACE ${OPTIONS})
 target_compile_features(kalman INTERFACE cxx_std_23)
 target_link_libraries(

include/fcarouge/algorithm.hpp

@@ -43,7 +43,21 @@ For more information, please refer to <https://unlicense.org> */
 //! @brief The collection of Kalman algorithms.
 //!
 //! @details Definitions and documentation.
-//!
-//! @todo Implement and test.
+
+namespace fcarouge {
+
+inline constexpr void update(const auto &h, auto &&p, const auto &r, auto &&x,
+                             const auto &z);
+//  {
+//   auto y{z - h * x};
+//   auto s{h * p * h + r};
+//   auto k{p * h / s};
+//   x += k * y;
+//   p *= 1 - k * h;
+// }
+
+inline constexpr void predict(const auto &f, auto &&p, const auto &q, auto &&x);
+
+} // namespace fcarouge
 
 #endif // FCAROUGE_ALGORITHM_HPP

include/fcarouge/filter.hpp

@@ -44,9 +44,8 @@ For more information, please refer to <https://unlicense.org> */
 //!
 //! @details Definitions and documentation.
 
-#include "internal/format.hpp"
-#include "internal/kalman.hpp"
-#include "internal/utility.hpp"
+#include "internal/filter.hpp"
+#include "utility.hpp"
 
 #include <concepts>
 #include <cstddef>
@@ -56,12 +55,6 @@ For more information, please refer to <https://unlicense.org> */
 
 namespace fcarouge {
 
-//! @brief Convenience tuple-like empty pack type.
-using empty_pack = internal::empty_pack;
-
-//! @brief Convenience tuple-like pack type.
-template <typename... Types> using pack = internal::pack<Types...>;
-
 //! @brief A generic Kalman filter for C++23.
 //!
 //! @details The Kalman filter is a Bayesian filter that uses multivariate

include/fcarouge/internal/detail.hpp

@@ -41,6 +41,8 @@ For more information, please refer to <https://unlicense.org> */
 
 #include "fcarouge/filter.hpp"
 
+#include "format.hpp"
+
 namespace fcarouge {
 
 template <typename State, typename Output, typename Input, typename Divide,

include/fcarouge/internal/format.hpp

@@ -39,16 +39,12 @@ For more information, please refer to <https://unlicense.org> */
 #ifndef FCAROUGE_INTERNAL_FORMAT_HPP
 #define FCAROUGE_INTERNAL_FORMAT_HPP
 
+#include "fcarouge/filter.hpp"
 #include "utility.hpp"
 
 #include <cstddef>
 #include <format>
 
-namespace fcarouge {
-template <typename, typename, typename, typename, typename, typename>
-class kalman;
-} // namespace fcarouge
-
 template <typename State, typename Output, typename Input, typename Divide,
           typename UpdateTypes, typename PredictionTypes, typename Char>
 // It is allowed to add template specializations for any standard library class