started an implementation of BandMatrix: at least the read/write access

to the main/sub/super diagonals seems to work well.

Eigen/Core

@@ -185,6 +185,7 @@ namespace Eigen {
 #include "src/Core/SolveTriangular.h"
 #include "src/Core/products/SelfadjointRank2Update.h"
 #include "src/Core/products/TriangularMatrixVector.h"
+#include "src/Core/BandMatrix.h"
 
 } // namespace Eigen
 

Eigen/src/Core/BandMatrix.h

@@ -0,0 +1,154 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Gael Guennebaud <g.gael@free.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_BANDMATRIX_H
+#define EIGEN_BANDMATRIX_H
+
+/** \nonstableyet
+  * \class BandMatrix
+  *
+  * \brief 
+  *
+  * \param
+  *
+  * \sa 
+  */
+template<typename _Scalar, int Size, int Supers, int Subs, int Options>
+struct ei_traits<BandMatrix<_Scalar,Size,Supers,Subs,Options> >
+{
+  typedef _Scalar Scalar;
+  enum {
+    CoeffReadCost = NumTraits<Scalar>::ReadCost,
+    RowsAtCompileTime = Size,
+    ColsAtCompileTime = Size,
+    MaxRowsAtCompileTime = Size,
+    MaxColsAtCompileTime = Size,
+    Flags = 0
+  };
+};
+
+template<typename _Scalar, int Size, int Supers, int Subs, int Options>
+class BandMatrix : public MultiplierBase<BandMatrix<_Scalar,Supers,Subs,Options> >
+{
+  public:
+
+    enum {
+      Flags = ei_traits<BandMatrix>::Flags,
+      CoeffReadCost = ei_traits<BandMatrix>::CoeffReadCost,
+      RowsAtCompileTime = ei_traits<BandMatrix>::RowsAtCompileTime,
+      ColsAtCompileTime = ei_traits<BandMatrix>::ColsAtCompileTime,
+      MaxRowsAtCompileTime = ei_traits<BandMatrix>::MaxRowsAtCompileTime,
+      MaxColsAtCompileTime = ei_traits<BandMatrix>::MaxColsAtCompileTime
+    };
+    typedef typename ei_traits<BandMatrix>::Scalar Scalar;
+    typedef Matrix<Scalar,RowsAtCompileTime,ColsAtCompileTime> PlainMatrixType;
+    
+  protected:
+    enum {
+      DataSizeAtCompileTime = ((Size!=Dynamic) && (Supers!=Dynamic) && (Subs!=Dynamic))
+                            ? Size*(Supers+Subs+1) - (Supers*Supers+Subs*Subs)/2
+                            : Dynamic
+    };
+    typedef Matrix<Scalar,DataSizeAtCompileTime,1> DataType;
+    
+  public:
+
+//     inline BandMatrix() { }
+
+    inline BandMatrix(int size=Size, int supers=Supers, int subs=Subs)
+      : m_data(size*(supers+subs+1) - (supers*supers+subs*subs)/2),
+        m_size(size), m_supers(supers), m_subs(subs)
+    { }
+
+    inline int rows() const { return m_size.value(); }
+    inline int cols() const { return m_size.value(); }
+
+    inline int supers() const { return m_supers.value(); }
+    inline int subs() const { return m_subs.value(); }
+
+    inline VectorBlock<DataType,Size> diagonal()
+    { return VectorBlock<DataType,Size>(m_data,0,m_size.value()); }
+
+    inline const VectorBlock<DataType,Size> diagonal() const
+    { return VectorBlock<DataType,Size>(m_data,0,m_size.value()); }
+
+    template<int Index>
+    VectorBlock<DataType,Size==Dynamic?Dynamic:Size-(Index<0?-Index:Index)>
+    diagonal()
+    {
+      return VectorBlock<DataType,Size==Dynamic?Dynamic:Size-(Index<0?-Index:Index)>
+        (m_data,Index<0 ? subDiagIndex(-Index) : superDiagIndex(Index), m_size.value()-ei_abs(Index));
+    }
+
+    template<int Index>
+    const VectorBlock<DataType,Size==Dynamic?Dynamic:Size-(Index<0?-Index:Index)>
+    diagonal() const
+    {
+      return VectorBlock<DataType,Size==Dynamic?Dynamic:Size-(Index<0?-Index:Index)>
+        (m_data,Index<0 ? subDiagIndex(-Index) : superDiagIndex(Index), m_size.value()-ei_abs(Index));
+    }
+
+    inline VectorBlock<DataType,Dynamic> diagonal(int index)
+    {
+      ei_assert((index<0 && -index<=subs()) || (index>=0 && index<=supers()));
+      return VectorBlock<DataType,Dynamic>(m_data,
+              index<0 ? subDiagIndex(-index) : superDiagIndex(index), m_size.value()-ei_abs(index));
+    }
+    const VectorBlock<DataType,Dynamic> diagonal(int index) const
+    {
+      ei_assert((index<0 && -index<=subs()) || (index>=0 && index<=supers()));
+      return VectorBlock<DataType,Dynamic>(m_data,
+              index<0 ? subDiagIndex(-index) : superDiagIndex(index), m_size.value()-ei_abs(index));
+    }
+
+//     inline VectorBlock<DataType,Size> subDiagonal()
+//     { return VectorBlock<DataType,Size>(m_data,0,m_size.value()); }
+
+    PlainMatrixType toDense() const
+    {
+      PlainMatrixType res(rows(),cols());
+      res.setZero();
+      res.diagonal() = diagonal();
+      for (int i=1; i<=supers();++i)
+        res.diagonal(i) = diagonal(i);
+      for (int i=1; i<=subs();++i)
+        res.diagonal(-i) = diagonal(-i);
+      return res;
+    }
+
+  protected:
+
+    inline int subDiagIndex(int i) const
+    { return m_size.value()*(m_supers.value()+i)-(ei_abs2(i-1) + ei_abs2(m_supers.value()))/2; }
+
+    inline int superDiagIndex(int i) const
+    { return m_size.value()*i-ei_abs2(i-1)/2; }
+
+    DataType m_data;
+    ei_int_if_dynamic<Size>   m_size;
+    ei_int_if_dynamic<Supers> m_supers;
+    ei_int_if_dynamic<Subs>   m_subs;
+};
+
+#endif // EIGEN_BANDMATRIX_H

Eigen/src/Core/util/ForwardDeclarations.h

@@ -66,6 +66,8 @@ template<typename ExpressionType> class WithFormat;
 template<typename MatrixType> struct CommaInitializer;
 template<typename Functor, typename EvalType> class ReturnByValue;
 
+template<typename _Scalar, int Size=Dynamic, int Supers=Dynamic, int Subs=Dynamic, int Options=0> class BandMatrix;
+
 
 template<typename Lhs, typename Rhs> struct ei_product_mode;
 template<typename Lhs, typename Rhs, int ProductMode = ei_product_mode<Lhs,Rhs>::value> struct ProductReturnType;

test/CMakeLists.txt

@@ -111,6 +111,7 @@ ei_add_test(array_replicate)
 ei_add_test(array_reverse)
 ei_add_test(triangular)
 ei_add_test(product_triangular)
+ei_add_test(bandmatrix)
 ei_add_test(cholesky " " "${GSL_LIBRARIES}")
 ei_add_test(lu ${EI_OFLAG})
 ei_add_test(determinant)

test/bandmatrix.cpp

@@ -0,0 +1,61 @@
+// This file is triangularView of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@gmail.com>
+//
+// 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/>.
+
+#include "main.h"
+
+template<typename MatrixType> void bandmatrix(MatrixType& m)
+{
+  typedef typename MatrixType::Scalar Scalar;
+  typedef typename NumTraits<Scalar>::Real RealScalar;
+  typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrixType;
+
+  int size = m.rows();
+
+  DenseMatrixType dm1(size,size);
+  dm1.setZero();
+
+  m.diagonal().setConstant(123);
+  dm1.diagonal().setConstant(123);
+  for (int i=1; i<=m.supers();++i)
+  {
+    m.diagonal(i).setConstant(i);
+    dm1.diagonal(i).setConstant(i);
+  }
+  for (int i=1; i<=m.subs();++i)
+  {
+    m.diagonal(-i).setConstant(-i);
+    dm1.diagonal(-i).setConstant(-i);
+  }
+  std::cerr << m.toDense() << "\n\n" << dm1 << "\n\n";
+  VERIFY_IS_APPROX(dm1,m.toDense());
+
+}
+
+void test_bandmatrix()
+{
+  for(int i = 0; i < g_repeat ; i++) {
+    BandMatrix<float,Dynamic,Dynamic,Dynamic> m(6,3,2);
+    CALL_SUBTEST( bandmatrix(m) );
+  }
+}