[Docs] Add batched serial gbtrf/gbtrs

Signed-off-by: yasahi-hpc <y.asahi6412@gmail.com>

Author: yasahi-hpc

docs/source/API/batched/dense-index.rst

@@ -7,6 +7,8 @@ API: Batched Dense (DLA)
 
    dense/batched_getrf
    dense/batched_getrs
+   dense/batched_gbtrf
+   dense/batched_gbtrs
    dense/batched_pbtrf
    dense/batched_pbtrs
    dense/batched_pttrf
@@ -302,11 +304,11 @@ Below are tables summarizing the currently supported function calls in Kokkos Ke
      - `TeamGesv`
      - `TeamVectorGesv`
    * - gbtrf
-     - `SerialGbtrf`
+     - :doc:`SerialGbtrf <dense/batched_gbtrf>`
      - --
      - --
    * - gbtrs
-     - `SerialGbtrs`
+     - :doc:`SerialGbtrs <dense/batched_gbtrs>`
      - --
      - --
    * - pbtrf

docs/source/API/batched/dense/batched_gbtrf.rst

@@ -0,0 +1,52 @@
+KokkosBatched::Gbtrf
+####################
+
+Defined in header: :code:`KokkosBatched_Gbtrf.hpp`
+
+.. code:: c++
+
+    template <typename ArgAlgo>
+    struct SerialGbtrf {
+      template <typename ABViewType, typename PivViewType>
+      KOKKOS_INLINE_FUNCTION
+      static int
+      invoke(const ABViewType &Ab, const PivViewType &piv, const int kl, const int ku,
+             const int m = -1);
+    };
+
+Computes a LU factorization of a general m-by-n band matrix :math:`A` using partial pivoting with row interchanges. The factorization has the format
+:math:`A = P \cdot L \cdot U`. 
+
+where 
+
+- :math:`P` is a permutation matrix
+- :math:`L` is a lower triangular matrix with unit diagonal elements
+- :math:`U` is an upper triangular matrix
+
+Parameters
+==========
+
+:Ab: On input, :math:`Ab` is a m by n general band matrix :math:`A` in the band storage. On output, the factors :math:`L` and :math:`U` from the factorization :math:`A = P \cdot L \cdot U`. The unit diagonal elements of :math:`L` are not stored. See `LAPACK reference <https://www.netlib.org/lapack/lug/node124.html>`_ for the band storage format.
+:piv: On output, the pivot indices.
+:kl: The number of subdiagonals within the band of :math:`A`. kl >= 0
+:ku: The number of superdiagonals within the band of :math:`A`. ku >= 0
+:m: The number of rows of the matrix :math:`A`. (optional, default is -1, corresponding to m == n)
+
+Type Requirements
+-----------------
+
+- ``ArgAlgo`` must be ``KokkosBatched::Algo::Gbtrf::Unblocked`` for the unblocked algorithm
+- ``ABViewType`` must be a Kokkos `View <https://kokkos.org/kokkos-core-wiki/API/core/view/view.html>`_ of rank 2 containing the general band matrix :math:`A`
+- ``PivViewType`` must be a Kokkos `View <https://kokkos.org/kokkos-core-wiki/API/core/view/view.html>`_ of rank 1 containing the pivot indices
+
+Example
+=======
+
+.. literalinclude:: ../../../../../example/batched_solve/serial_gbtrs.cpp
+  :language: c++
+
+output:
+
+.. code::
+
+   gbtrf/gbtrs works correctly!

docs/source/API/batched/dense/batched_gbtrs.rst

@@ -0,0 +1,50 @@
+KokkosBatched::Gbtrs
+####################
+
+Defined in header: :code:`KokkosBatched_Gbtrs.hpp`
+
+.. code:: c++
+
+    template <typename ArgTrans, typename ArgAlgo>
+    struct SerialGbtrs {
+      template <typename AViewType, typename PivViewType, typename BViewType>
+      KOKKOS_INLINE_FUNCTION static int invoke(const AViewType &A, const PivViewType &piv, const BViewType &b, const int kl,
+                                               const int ku);
+    };
+
+Solves a system of the linear equations :math:`A \cdot X = B` or :math:`A^T \cdot X = B` or :math:`A^H \cdot X = B` with a general n-by-n band matrix :math:`A` using :math:`LU` factorization computed by ``Gbtrf``.
+This operation is equivalent to the LAPACK routine ``SGBTRS`` (``CGBTRS``) or ``DGBTRS`` (``ZGBTRS``) for single or double precision for real (complex) matrix. 
+
+Parameters
+==========
+
+:A: Input view containing the factors :math:`L` and :math:`U` from the factorization :math:`A = P \cdot L \cdot U` of the band matrix :math:`A` computed by ``Gbtrf``.  See `LAPACK reference <https://www.netlib.org/lapack/lug/node124.html>`_ for the band storage format.
+:piv: The pivot indices computed by ``Gbtrf``.
+:B: Input/output view containing the right-hand side on input and the solution on output.
+:kl: The number of subdiagonals within the band of :math:`A`. kl >= 0
+:ku: The number of superdiagonals within the band of :math:`A`. ku >= 0
+
+Type Requirements
+-----------------
+
+- ``ArgTrans`` must be one of the following:
+   - ``KokkosBatched::Trans::NoTranspose`` to solve a system :math:`A \cdot X = B`
+   - ``KokkosBatched::Trans::Transpose`` to solve a system :math:`A^T \cdot X = B`
+   - ``KokkosBatched::Trans::ConjTranspose`` to solve a system :math:`A^H \cdot X = B`
+- ``ArgAlgo`` must be ``KokkosBatched::Algo::Gbtrs::Unblocked`` for the unblocked algorithm
+- ``AViewType`` must be a Kokkos `View <https://kokkos.org/kokkos-core-wiki/API/core/view/view.html>`_ of rank 2 containing the general band matrix :math:`A`
+- ``PivViewType`` must be a Kokkos `View <https://kokkos.org/kokkos-core-wiki/API/core/view/view.html>`_ of rank 1 containing the pivot indices
+- ``BViewType`` must be a Kokkos `View <https://kokkos.org/kokkos-core-wiki/API/core/view/view.html>`_ of rank 1 containing the right-hand side that satisfies
+  - ``std::is_same_v<typename BViewType::value_type, typename BViewType::non_const_value_type> == true``
+
+Example
+=======
+
+.. literalinclude:: ../../../../../example/batched_solve/serial_gbtrs.cpp
+  :language: c++
+
+output:
+
+.. code::
+
+   gbtrf/gbtrs works correctly!