add code for band triangular problems:

- currently available from the BLAS interface only - and for vectors only
2026-04-10 11:34:33 +08:00 · 2011-12-01 18:06:28 +01:00
parent 9fdb6a2ead
commit 3a4c78b588
4 changed files with 236 additions and 12 deletions
--- a/blas/BandTriangularSolver.h
+++ b/blas/BandTriangularSolver.h
@@ -0,0 +1,112 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2011 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_BAND_TRIANGULARSOLVER_H
+#define EIGEN_BAND_TRIANGULARSOLVER_H
+
+namespace internal {
+
+ /* \internal
+  * Solve Ax=b with A a band triangular matrix
+  * TODO: extend it to matrices for x abd b */
+template<typename Index, int Mode, typename LhsScalar, bool ConjLhs, typename RhsScalar, int StorageOrder>
+struct band_solve_triangular_selector;
+
+
+template<typename Index, int Mode, typename LhsScalar, bool ConjLhs, typename RhsScalar>
+struct band_solve_triangular_selector<Index,Mode,LhsScalar,ConjLhs,RhsScalar,RowMajor>
+{
+  typedef Map<const Matrix<LhsScalar,Dynamic,Dynamic,RowMajor>, 0, OuterStride<> > LhsMap;
+  typedef Map<Matrix<RhsScalar,Dynamic,1> > RhsMap;
+  enum { IsLower = (Mode&Lower) ? 1 : 0 };
+  static void run(Index size, Index k, const LhsScalar* _lhs, Index lhsStride, RhsScalar* _other)
+  {
+    const LhsMap lhs(_lhs,size,k+1,OuterStride<>(lhsStride));
+    RhsMap other(_other,size,1);
+    typename internal::conditional<
+                          ConjLhs,
+                          const CwiseUnaryOp<typename internal::scalar_conjugate_op<LhsScalar>,LhsMap>,
+                          const LhsMap&>
+                        ::type cjLhs(lhs);
+                        
+    for(int col=0 ; col<other.cols() ; ++col)
+    {
+      for(int ii=0; ii<size; ++ii)
+      {
+        int i = IsLower ? ii : size-ii-1;
+        int actual_k = (std::min)(k,ii);
+        int actual_start = IsLower ? k-actual_k : 1;
+        
+        if(actual_k>0)
+          other.coeffRef(i,col) -= cjLhs.row(i).segment(actual_start,actual_k).transpose()
+                                  .cwiseProduct(other.col(col).segment(IsLower ? i-actual_k : i+1,actual_k)).sum();
+
+        if((Mode&UnitDiag)==0)
+          other.coeffRef(i,col) /= cjLhs(i,IsLower ? k : 0);
+      }
+    }
+  }
+  
+};
+
+template<typename Index, int Mode, typename LhsScalar, bool ConjLhs, typename RhsScalar>
+struct band_solve_triangular_selector<Index,Mode,LhsScalar,ConjLhs,RhsScalar,ColMajor>
+{
+  typedef Map<const Matrix<LhsScalar,Dynamic,Dynamic,ColMajor>, 0, OuterStride<> > LhsMap;
+  typedef Map<Matrix<RhsScalar,Dynamic,1> > RhsMap;
+  enum { IsLower = (Mode&Lower) ? 1 : 0 };
+  static void run(Index size, Index k, const LhsScalar* _lhs, Index lhsStride, RhsScalar* _other)
+  {
+    const LhsMap lhs(_lhs,k+1,size,OuterStride<>(lhsStride));
+    RhsMap other(_other,size,1);
+    typename internal::conditional<
+                          ConjLhs,
+                          const CwiseUnaryOp<typename internal::scalar_conjugate_op<LhsScalar>,LhsMap>,
+                          const LhsMap&>
+                        ::type cjLhs(lhs);
+                        
+    for(int col=0 ; col<other.cols() ; ++col)
+    {
+      for(int ii=0; ii<size; ++ii)
+      {
+        int i = IsLower ? ii : size-ii-1;
+        int actual_k = (std::min)(k,size-ii-1);
+        int actual_start = IsLower ? 1 : k-actual_k;
+        
+        if((Mode&UnitDiag)==0)
+          other.coeffRef(i,col) /= cjLhs(IsLower ? 0 : k, i);
+
+        if(actual_k>0)
+          other.col(col).segment(IsLower ? i+1 : i-actual_k, actual_k)
+              -= other.coeff(i,col) * cjLhs.col(i).segment(actual_start,actual_k);
+        
+      }
+    }
+  }
+};
+
+
+} // end namespace internal
+
+#endif // EIGEN_BAND_TRIANGULARSOLVER_H