comparison DEPENDENCIES/generic/include/boost/numeric/ublas/lu.hpp @ 16:2665513ce2d3

Add boost headers

+//
+//  Copyright (c) 2000-2002
+//  Joerg Walter, Mathias Koch
+//
+//  Distributed under the Boost Software License, Version 1.0. (See
+//  accompanying file LICENSE_1_0.txt or copy at
+//  http://www.boost.org/LICENSE_1_0.txt)
+//
+//  The authors gratefully acknowledge the support of
+//  GeNeSys mbH & Co. KG in producing this work.
+//
+
+#ifndef _BOOST_UBLAS_LU_
+#define _BOOST_UBLAS_LU_
+
+#include <boost/numeric/ublas/operation.hpp>
+#include <boost/numeric/ublas/vector_proxy.hpp>
+#include <boost/numeric/ublas/matrix_proxy.hpp>
+#include <boost/numeric/ublas/vector.hpp>
+#include <boost/numeric/ublas/triangular.hpp>
+
+// LU factorizations in the spirit of LAPACK and Golub & van Loan
+
+namespace boost { namespace numeric { namespace ublas {
+
+    /** \brief
+     *
+     * \tparam T
+     * \tparam A
+     */
+    template<class T = std::size_t, class A = unbounded_array<T> >
+    class permutation_matrix:
+        public vector<T, A> {
+    public:
+        typedef vector<T, A> vector_type;
+        typedef typename vector_type::size_type size_type;
+
+        // Construction and destruction
+        BOOST_UBLAS_INLINE
+        explicit
+        permutation_matrix (size_type size):
+            vector<T, A> (size) {
+            for (size_type i = 0; i < size; ++ i)
+                (*this) (i) = i;
+        }
+        BOOST_UBLAS_INLINE
+        explicit
+        permutation_matrix (const vector_type & init) 
+            : vector_type(init)
+        { }
+        BOOST_UBLAS_INLINE
+        ~permutation_matrix () {}
+
+        // Assignment
+        BOOST_UBLAS_INLINE
+        permutation_matrix &operator = (const permutation_matrix &m) {
+            vector_type::operator = (m);
+            return *this;
+        }
+    };
+
+    template<class PM, class MV>
+    BOOST_UBLAS_INLINE
+    void swap_rows (const PM &pm, MV &mv, vector_tag) {
+        typedef typename PM::size_type size_type;
+        typedef typename MV::value_type value_type;
+
+        size_type size = pm.size ();
+        for (size_type i = 0; i < size; ++ i) {
+            if (i != pm (i))
+                std::swap (mv (i), mv (pm (i)));
+        }
+    }
+    template<class PM, class MV>
+    BOOST_UBLAS_INLINE
+    void swap_rows (const PM &pm, MV &mv, matrix_tag) {
+        typedef typename PM::size_type size_type;
+        typedef typename MV::value_type value_type;
+
+        size_type size = pm.size ();
+        for (size_type i = 0; i < size; ++ i) {
+            if (i != pm (i))
+                row (mv, i).swap (row (mv, pm (i)));
+        }
+    }
+    // Dispatcher
+    template<class PM, class MV>
+    BOOST_UBLAS_INLINE
+    void swap_rows (const PM &pm, MV &mv) {
+        swap_rows (pm, mv, typename MV::type_category ());
+    }
+
+    // LU factorization without pivoting
+    template<class M>
+    typename M::size_type lu_factorize (M &m) {
+        typedef M matrix_type;
+        typedef typename M::size_type size_type;
+        typedef typename M::value_type value_type;
+
+#if BOOST_UBLAS_TYPE_CHECK
+        matrix_type cm (m);
+#endif
+        size_type singular = 0;
+        size_type size1 = m.size1 ();
+        size_type size2 = m.size2 ();
+        size_type size = (std::min) (size1, size2);
+        for (size_type i = 0; i < size; ++ i) {
+            matrix_column<M> mci (column (m, i));
+            matrix_row<M> mri (row (m, i));
+            if (m (i, i) != value_type/*zero*/()) {
+                value_type m_inv = value_type (1) / m (i, i);
+                project (mci, range (i + 1, size1)) *= m_inv;
+            } else if (singular == 0) {
+                singular = i + 1;
+            }
+            project (m, range (i + 1, size1), range (i + 1, size2)).minus_assign (
+                outer_prod (project (mci, range (i + 1, size1)),
+                            project (mri, range (i + 1, size2))));
+        }
+#if BOOST_UBLAS_TYPE_CHECK
+        BOOST_UBLAS_CHECK (singular != 0 ||
+                           detail::expression_type_check (prod (triangular_adaptor<matrix_type, unit_lower> (m),
+                                                                triangular_adaptor<matrix_type, upper> (m)), 
+                                                          cm), internal_logic ());
+#endif
+        return singular;
+    }
+
+    // LU factorization with partial pivoting
+    template<class M, class PM>
+    typename M::size_type lu_factorize (M &m, PM &pm) {
+        typedef M matrix_type;
+        typedef typename M::size_type size_type;
+        typedef typename M::value_type value_type;
+
+#if BOOST_UBLAS_TYPE_CHECK
+        matrix_type cm (m);
+#endif
+        size_type singular = 0;
+        size_type size1 = m.size1 ();
+        size_type size2 = m.size2 ();
+        size_type size = (std::min) (size1, size2);
+        for (size_type i = 0; i < size; ++ i) {
+            matrix_column<M> mci (column (m, i));
+            matrix_row<M> mri (row (m, i));
+            size_type i_norm_inf = i + index_norm_inf (project (mci, range (i, size1)));
+            BOOST_UBLAS_CHECK (i_norm_inf < size1, external_logic ());
+            if (m (i_norm_inf, i) != value_type/*zero*/()) {
+                if (i_norm_inf != i) {
+                    pm (i) = i_norm_inf;
+                    row (m, i_norm_inf).swap (mri);
+                } else {
+                    BOOST_UBLAS_CHECK (pm (i) == i_norm_inf, external_logic ());
+                }
+                value_type m_inv = value_type (1) / m (i, i);
+                project (mci, range (i + 1, size1)) *= m_inv;
+            } else if (singular == 0) {
+                singular = i + 1;
+            }
+            project (m, range (i + 1, size1), range (i + 1, size2)).minus_assign (
+                outer_prod (project (mci, range (i + 1, size1)),
+                            project (mri, range (i + 1, size2))));
+        }
+#if BOOST_UBLAS_TYPE_CHECK
+        swap_rows (pm, cm);
+        BOOST_UBLAS_CHECK (singular != 0 ||
+                           detail::expression_type_check (prod (triangular_adaptor<matrix_type, unit_lower> (m),
+                                                                triangular_adaptor<matrix_type, upper> (m)), cm), internal_logic ());
+#endif
+        return singular;
+    }
+
+    template<class M, class PM>
+    typename M::size_type axpy_lu_factorize (M &m, PM &pm) {
+        typedef M matrix_type;
+        typedef typename M::size_type size_type;
+        typedef typename M::value_type value_type;
+        typedef vector<value_type> vector_type;
+
+#if BOOST_UBLAS_TYPE_CHECK
+        matrix_type cm (m);
+#endif
+        size_type singular = 0;
+        size_type size1 = m.size1 ();
+        size_type size2 = m.size2 ();
+        size_type size = (std::min) (size1, size2);
+#ifndef BOOST_UBLAS_LU_WITH_INPLACE_SOLVE
+        matrix_type mr (m);
+        mr.assign (zero_matrix<value_type> (size1, size2));
+        vector_type v (size1);
+        for (size_type i = 0; i < size; ++ i) {
+            matrix_range<matrix_type> lrr (project (mr, range (0, i), range (0, i)));
+            vector_range<matrix_column<matrix_type> > urr (project (column (mr, i), range (0, i)));
+            urr.assign (solve (lrr, project (column (m, i), range (0, i)), unit_lower_tag ()));
+            project (v, range (i, size1)).assign (
+                project (column (m, i), range (i, size1)) -
+                axpy_prod<vector_type> (project (mr, range (i, size1), range (0, i)), urr));
+            size_type i_norm_inf = i + index_norm_inf (project (v, range (i, size1)));
+            BOOST_UBLAS_CHECK (i_norm_inf < size1, external_logic ());
+            if (v (i_norm_inf) != value_type/*zero*/()) {
+                if (i_norm_inf != i) {
+                    pm (i) = i_norm_inf;
+                    std::swap (v (i_norm_inf), v (i));
+                    project (row (m, i_norm_inf), range (i + 1, size2)).swap (project (row (m, i), range (i + 1, size2)));
+                } else {
+                    BOOST_UBLAS_CHECK (pm (i) == i_norm_inf, external_logic ());
+                }
+                project (column (mr, i), range (i + 1, size1)).assign (
+                    project (v, range (i + 1, size1)) / v (i));
+                if (i_norm_inf != i) {
+                    project (row (mr, i_norm_inf), range (0, i)).swap (project (row (mr, i), range (0, i)));
+                }
+            } else if (singular == 0) {
+                singular = i + 1;
+            }
+            mr (i, i) = v (i);
+        }
+        m.assign (mr);
+#else
+        matrix_type lr (m);
+        matrix_type ur (m);
+        lr.assign (identity_matrix<value_type> (size1, size2));
+        ur.assign (zero_matrix<value_type> (size1, size2));
+        vector_type v (size1);
+        for (size_type i = 0; i < size; ++ i) {
+            matrix_range<matrix_type> lrr (project (lr, range (0, i), range (0, i)));
+            vector_range<matrix_column<matrix_type> > urr (project (column (ur, i), range (0, i)));
+            urr.assign (project (column (m, i), range (0, i)));
+            inplace_solve (lrr, urr, unit_lower_tag ());
+            project (v, range (i, size1)).assign (
+                project (column (m, i), range (i, size1)) -
+                axpy_prod<vector_type> (project (lr, range (i, size1), range (0, i)), urr));
+            size_type i_norm_inf = i + index_norm_inf (project (v, range (i, size1)));
+            BOOST_UBLAS_CHECK (i_norm_inf < size1, external_logic ());
+            if (v (i_norm_inf) != value_type/*zero*/()) {
+                if (i_norm_inf != i) {
+                    pm (i) = i_norm_inf;
+                    std::swap (v (i_norm_inf), v (i));
+                    project (row (m, i_norm_inf), range (i + 1, size2)).swap (project (row (m, i), range (i + 1, size2)));
+                } else {
+                    BOOST_UBLAS_CHECK (pm (i) == i_norm_inf, external_logic ());
+                }
+                project (column (lr, i), range (i + 1, size1)).assign (
+                    project (v, range (i + 1, size1)) / v (i));
+                if (i_norm_inf != i) {
+                    project (row (lr, i_norm_inf), range (0, i)).swap (project (row (lr, i), range (0, i)));
+                }
+            } else if (singular == 0) {
+                singular = i + 1;
+            }
+            ur (i, i) = v (i);
+        }
+        m.assign (triangular_adaptor<matrix_type, strict_lower> (lr) +
+                  triangular_adaptor<matrix_type, upper> (ur));
+#endif
+#if BOOST_UBLAS_TYPE_CHECK
+        swap_rows (pm, cm);
+        BOOST_UBLAS_CHECK (singular != 0 ||
+                           detail::expression_type_check (prod (triangular_adaptor<matrix_type, unit_lower> (m),
+                                                                triangular_adaptor<matrix_type, upper> (m)), cm), internal_logic ());
+#endif
+        return singular;
+    }
+
+    // LU substitution
+    template<class M, class E>
+    void lu_substitute (const M &m, vector_expression<E> &e) {
+        typedef const M const_matrix_type;
+        typedef vector<typename E::value_type> vector_type;
+
+#if BOOST_UBLAS_TYPE_CHECK
+        vector_type cv1 (e);
+#endif
+        inplace_solve (m, e, unit_lower_tag ());
+#if BOOST_UBLAS_TYPE_CHECK
+        BOOST_UBLAS_CHECK (detail::expression_type_check (prod (triangular_adaptor<const_matrix_type, unit_lower> (m), e), cv1), internal_logic ());
+        vector_type cv2 (e);
+#endif
+        inplace_solve (m, e, upper_tag ());
+#if BOOST_UBLAS_TYPE_CHECK
+        BOOST_UBLAS_CHECK (detail::expression_type_check (prod (triangular_adaptor<const_matrix_type, upper> (m), e), cv2), internal_logic ());
+#endif
+    }
+    template<class M, class E>
+    void lu_substitute (const M &m, matrix_expression<E> &e) {
+        typedef const M const_matrix_type;
+        typedef matrix<typename E::value_type> matrix_type;
+
+#if BOOST_UBLAS_TYPE_CHECK
+        matrix_type cm1 (e);
+#endif
+        inplace_solve (m, e, unit_lower_tag ());
+#if BOOST_UBLAS_TYPE_CHECK
+        BOOST_UBLAS_CHECK (detail::expression_type_check (prod (triangular_adaptor<const_matrix_type, unit_lower> (m), e), cm1), internal_logic ());
+        matrix_type cm2 (e);
+#endif
+        inplace_solve (m, e, upper_tag ());
+#if BOOST_UBLAS_TYPE_CHECK
+        BOOST_UBLAS_CHECK (detail::expression_type_check (prod (triangular_adaptor<const_matrix_type, upper> (m), e), cm2), internal_logic ());
+#endif
+    }
+    template<class M, class PMT, class PMA, class MV>
+    void lu_substitute (const M &m, const permutation_matrix<PMT, PMA> &pm, MV &mv) {
+        swap_rows (pm, mv);
+        lu_substitute (m, mv);
+    }
+    template<class E, class M>
+    void lu_substitute (vector_expression<E> &e, const M &m) {
+        typedef const M const_matrix_type;
+        typedef vector<typename E::value_type> vector_type;
+
+#if BOOST_UBLAS_TYPE_CHECK
+        vector_type cv1 (e);
+#endif
+        inplace_solve (e, m, upper_tag ());
+#if BOOST_UBLAS_TYPE_CHECK
+        BOOST_UBLAS_CHECK (detail::expression_type_check (prod (e, triangular_adaptor<const_matrix_type, upper> (m)), cv1), internal_logic ());
+        vector_type cv2 (e);
+#endif
+        inplace_solve (e, m, unit_lower_tag ());
+#if BOOST_UBLAS_TYPE_CHECK
+        BOOST_UBLAS_CHECK (detail::expression_type_check (prod (e, triangular_adaptor<const_matrix_type, unit_lower> (m)), cv2), internal_logic ());
+#endif
+    }
+    template<class E, class M>
+    void lu_substitute (matrix_expression<E> &e, const M &m) {
+        typedef const M const_matrix_type;
+        typedef matrix<typename E::value_type> matrix_type;
+
+#if BOOST_UBLAS_TYPE_CHECK
+        matrix_type cm1 (e);
+#endif
+        inplace_solve (e, m, upper_tag ());
+#if BOOST_UBLAS_TYPE_CHECK
+        BOOST_UBLAS_CHECK (detail::expression_type_check (prod (e, triangular_adaptor<const_matrix_type, upper> (m)), cm1), internal_logic ());
+        matrix_type cm2 (e);
+#endif
+        inplace_solve (e, m, unit_lower_tag ());
+#if BOOST_UBLAS_TYPE_CHECK
+        BOOST_UBLAS_CHECK (detail::expression_type_check (prod (e, triangular_adaptor<const_matrix_type, unit_lower> (m)), cm2), internal_logic ());
+#endif
+    }
+    template<class MV, class M, class PMT, class PMA>
+    void lu_substitute (MV &mv, const M &m, const permutation_matrix<PMT, PMA> &pm) {
+        swap_rows (pm, mv);
+        lu_substitute (mv, m);
+    }
+
+}}}
+
+#endif