Added sequential LU factorization from tnl-mhfem

src/TNL/Matrices/Factorization/LUsequential.h

+// Copyright (c) 2004-2022 Tomáš Oberhuber et al.
+//
+// This file is part of TNL - Template Numerical Library (https://tnl-project.org/)
+//
+// SPDX-License-Identifier: MIT
+
+// Implemented by: Jakub Klinkovský
+
+#pragma once
+
+#include <TNL/Assert.h>
+#include <TNL/Cuda/CudaCallable.h>
+
+namespace TNL {
+namespace Matrices {
+namespace Factorization {
+
+template< typename Matrix >
+__cuda_callable__
+void
+LU_sequential_factorize( Matrix& A )
+{
+   using IndexType = typename Matrix::IndexType;
+
+   static_assert( Matrix::getRows() == Matrix::getColumns(), "LU factorization is possible only for square matrices" );
+
+   constexpr IndexType n = Matrix::getRows();
+
+   for( IndexType k = 0; k < n; k++ ) {
+      const auto pivot = A( k, k );
+      // Update the (k+1 .. n-1)-th rows
+      for( IndexType j = k + 1; j < n; j++ ) {
+         const auto factor = A( j, k ) / pivot;
+         // Update elements of k-th column below pivot (i.e. elements of L)
+         A( j, k ) = factor;
+         // Subtract k-th row from j-th
+         for( IndexType i = k + 1; i < n; i++ ) {
+            A( j, i ) = A( j, i ) - factor * A( k, i );
+         }
+      }
+   }
+}
+
+template< typename Matrix, typename Vector >
+__cuda_callable__
+void
+LU_sequential_solve_inplace( const Matrix& A, Vector& x )
+{
+   using IndexType = typename Matrix::IndexType;
+   static_assert( std::is_signed< IndexType >::value, "LU got a matrix with an unsigned index type (2nd for loop won't work)" );
+
+   static_assert( Matrix::getRows() == Matrix::getColumns(), "LU factorization is possible only for square matrices" );
+
+   constexpr IndexType n = Matrix::getRows();
+
+   // Forward substitution
+   for( IndexType k = 1; k < n; k++ )
+      for( IndexType j = 0; j < k; j++ )
+         x[ k ] -= A( k, j ) * x[ j ];
+
+   // Back substitution
+   for( IndexType k = n - 1; k >= 0; k-- ) {
+      for( IndexType j = n - 1; j > k; j-- )
+         x[ k ] -= A( k, j ) * x[ j ];
+      x[ k ] /= A( k, k );
+   }
+}
+
+template< typename Matrix, typename Vector1, typename Vector2 >
+__cuda_callable__
+void
+LU_sequential_solve( const Matrix& A, const Vector1& b, Vector2& x )
+{
+   // Copy right hand side
+   x = b;
+
+   // Solve in-place
+   LU_sequential_solve_inplace( A, x );
+}
+
+}  // namespace Factorization
+}  // namespace Matrices
+}  // namespace TNL