mirror of
https://github.com/triqs/dft_tools
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200 lines
6.6 KiB
C++
200 lines
6.6 KiB
C++
/*******************************************************************************
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*
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* TRIQS: a Toolbox for Research in Interacting Quantum Systems
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*
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* Copyright (C) 2011 by O. Parcollet
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*
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* TRIQS is free software: you can redistribute it and/or modify it under the
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* terms of the GNU General Public License as published by the Free Software
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* Foundation, either version 3 of the License, or (at your option) any later
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* version.
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*
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* TRIQS is distributed in the hope that it will be useful, but WITHOUT ANY
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* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
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* FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
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* details.
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*
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* You should have received a copy of the GNU General Public License along with
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* TRIQS. If not, see <http://www.gnu.org/licenses/>.
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*
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******************************************************************************/
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#ifndef TRIQS_ARRAYS_LINALG_DET_INV_H
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#define TRIQS_ARRAYS_LINALG_DET_INV_H
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#include "../impl/common.hpp"
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#include "../matrix.hpp"
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#include "../blas_lapack/getrf.hpp"
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#include "../blas_lapack/getri.hpp"
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namespace triqs {
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namespace arrays {
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/// Error which occurs during the matrix inversion
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class matrix_inverse_exception : public triqs::runtime_error {};
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/**
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* Lazy result of inverse(M) where M can be :
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* * a matrix, a matrix_view
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* * any matrix expression
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* The object is lazy, it does not do any computation.
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* It can be copied at no cost
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* It keeps view of the object A if it a matrix, a copy if it is a formal expression.
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*/
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template <typename A> struct inverse_lazy;
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template <class A> inverse_lazy<typename utility::remove_rvalue_ref<A>::type> inverse(A &&a) {
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return {std::forward<A>(a)};
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}
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// ----------------- implementation -----------------------------------------
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// worker takes a contiguous view and compute the det and inverse in two steps.
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// it is separated in case of multiple use (no reallocation of ipvi, etc...)
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// A can be a matrix, a matrix_view
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template <typename A> class det_and_inverse_worker {
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typedef typename A::value_type value_type;
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typedef matrix_view<value_type> V_type;
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A a;
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int dim;
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triqs::arrays::vector<int> ipiv;
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int step, info;
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value_type _det;
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public:
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det_and_inverse_worker(A a_) : a(std::move(a_)), dim(first_dim(a)), ipiv(dim), step(0) {
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if (first_dim(a) != second_dim(a))
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TRIQS_RUNTIME_ERROR << "Inverse/Det error:non-square matrix. Dimensions are :(" << first_dim(a) << "," << second_dim(a)
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<< ")\n ";
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if (!(has_contiguous_data(a))) TRIQS_RUNTIME_ERROR << "det_and_inverse_worker only takes a contiguous view";
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}
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value_type det() {
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V_type W = fortran_view(a);
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_step1(W);
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_compute_det(W);
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return _det;
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}
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A const &inverse() {
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if (step < 2) {
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V_type W = fortran_view(a);
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_step1(W);
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_step2(W);
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}
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return a;
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}
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private:
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// no need of special traversal
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template <typename MT> V_type fortran_view(MT const &x) {
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if (x.indexmap().memory_layout_is_c())
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return x.transpose();
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else
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return x;
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}
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void _step1(V_type &W) {
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if (step > 0) return;
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step = 1;
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info = lapack::getrf(W, ipiv);
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if (info < 0) throw matrix_inverse_exception() << "Inverse/Det error : failure of getrf lapack routine ";
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}
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void _compute_det(V_type const &W) {
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if (step > 1) return;
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_det = 1;
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for (size_t i = 0; i < dim; i++) _det *= W(i, i);
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bool flip = false; // compute the sign of the permutation
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for (size_t i = 0; i < dim; i++) {
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if (ipiv(i) != int(i) + 1) flip = !(flip);
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}
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_det = (flip ? -_det : _det);
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}
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void _step2(V_type &W) {
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assert(step == 1); // if (step==1) return;
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step = 2;
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_compute_det(W);
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info = lapack::getri(W, ipiv);
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if (info != 0) throw matrix_inverse_exception() << "Inverse/Det error : matrix is not invertible";
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}
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};
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//-----------------------------------------------------------
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template <typename A> struct inverse_lazy : TRIQS_CONCEPT_TAG_NAME(ImmutableMatrix) {
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typedef typename std::remove_reference<A>::type A_t;
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typedef typename std::remove_const<typename A_t::value_type>::type value_type;
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typedef typename A_t::domain_type domain_type;
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typedef matrix<value_type> M_type;
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typedef matrix_view<value_type> M_view_type;
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template <typename AA> inverse_lazy(AA &&a_) : a(std::forward<AA>(a_)), M{}, computed{false} {
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if (first_dim(a) != second_dim(a))
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TRIQS_RUNTIME_ERROR << "Inverse : matrix is not square but of size " << first_dim(a) << " x " << second_dim(a);
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}
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domain_type domain() const { return a.domain(); }
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A const & input() const { return a;}
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template <typename K0, typename K1> value_type const &operator()(K0 const &k0, K1 const &k1) const {
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activate();
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return M(k0, k1);
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}
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M_type const &operator()() const {
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activate();
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return M;
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}
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friend std::ostream &operator<<(std::ostream &out, inverse_lazy const &x) { return out << "inverse(" << x.a << ")"; }
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private:
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A a;
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mutable M_type M;
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mutable bool computed;
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void activate() const {
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if (computed) return;
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M = a;
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auto worker = det_and_inverse_worker<M_view_type> {M};
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worker.inverse();
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computed = true;
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}
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};
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// Optimized implementation of =
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// if M = inverse(M) with the SAME object, then we do not need to copy the data
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template <typename A, typename MT>
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ENABLE_IF(is_matrix_or_view<typename std::remove_reference<A>::type>)
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triqs_arrays_assign_delegation(MT &lhs, inverse_lazy<A> const &rhs) {
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static_assert(is_matrix_or_view<MT>::value, "Can only assign an inverse matrix to a matrix or a matrix_view");
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bool M_eq_inverse_M = ((lhs.indexmap().memory_indices_layout() == rhs.input().indexmap().memory_indices_layout()) &&
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(lhs.data_start() == rhs.input().data_start()) && (has_contiguous_data(lhs)));
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if (!M_eq_inverse_M) {
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lhs = rhs();
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} else {
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blas_lapack_tools::reflexive_qcache<MT> C(lhs);
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// a reflexive cache will use a temporary "regrouping" copy if and only if needed
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det_and_inverse_worker<typename MT::view_type> W(C()); // the worker to make the inversion of the lhs...
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W.inverse(); // worker is working ...
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}
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}
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//------------------- det ----------------------------------------
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template <typename A> typename std::remove_reference<A>::type::value_type determinant(A &&a) {
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// makes a temporary copy of A if A is a const &
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// If a is a matrix &&, it is moved into the worker.
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auto worker = det_and_inverse_worker<matrix<typename std::remove_reference<A>::type::value_type>>(std::forward<A>(a));
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return worker.det();
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}
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}
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namespace clef {
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TRIQS_CLEF_MAKE_FNT_LAZY(determinant);
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}
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} // namespace triqs::arrays
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#endif
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