diff options
author | Marc Glisse <marc.glisse@inria.fr> | 2020-05-13 23:19:35 +0200 |
---|---|---|
committer | Marc Glisse <marc.glisse@inria.fr> | 2020-05-13 23:19:35 +0200 |
commit | 4220ee79bf32aed1c8ee3bb9b04dea3888b74d2d (patch) | |
tree | c62ac12c03693d3a8f3abf6e8f7b00c7be0e55ea /src/python/include | |
parent | 8ba3ca48e03e379fca0a0b68a508d8357a367f52 (diff) | |
parent | 1efd71c502bacce375e1950e10a8112208acd0cf (diff) |
Merge remote-tracking branch 'origin/master' into tomato2
Diffstat (limited to 'src/python/include')
-rw-r--r-- | src/python/include/Alpha_complex_interface.h | 1 | ||||
-rw-r--r-- | src/python/include/Euclidean_strong_witness_complex_interface.h | 2 | ||||
-rw-r--r-- | src/python/include/Euclidean_witness_complex_interface.h | 2 | ||||
-rw-r--r-- | src/python/include/Nerve_gic_interface.h | 1 | ||||
-rw-r--r-- | src/python/include/Persistent_cohomology_interface.h | 152 | ||||
-rw-r--r-- | src/python/include/Rips_complex_interface.h | 1 | ||||
-rw-r--r-- | src/python/include/Simplex_tree_interface.h | 119 | ||||
-rw-r--r-- | src/python/include/Strong_witness_complex_interface.h | 2 | ||||
-rw-r--r-- | src/python/include/Tangential_complex_interface.h | 1 | ||||
-rw-r--r-- | src/python/include/Witness_complex_interface.h | 2 | ||||
-rw-r--r-- | src/python/include/pybind11_diagram_utils.h | 39 |
11 files changed, 241 insertions, 81 deletions
diff --git a/src/python/include/Alpha_complex_interface.h b/src/python/include/Alpha_complex_interface.h index 8614eee3..40de88f3 100644 --- a/src/python/include/Alpha_complex_interface.h +++ b/src/python/include/Alpha_complex_interface.h @@ -58,7 +58,6 @@ class Alpha_complex_interface { void create_simplex_tree(Simplex_tree_interface<>* simplex_tree, double max_alpha_square) { alpha_complex_->create_complex(*simplex_tree, max_alpha_square); - simplex_tree->initialize_filtration(); } private: diff --git a/src/python/include/Euclidean_strong_witness_complex_interface.h b/src/python/include/Euclidean_strong_witness_complex_interface.h index c1c72737..f94c51ef 100644 --- a/src/python/include/Euclidean_strong_witness_complex_interface.h +++ b/src/python/include/Euclidean_strong_witness_complex_interface.h @@ -50,12 +50,10 @@ class Euclidean_strong_witness_complex_interface { void create_simplex_tree(Gudhi::Simplex_tree<>* simplex_tree, double max_alpha_square, std::size_t limit_dimension) { witness_complex_->create_complex(*simplex_tree, max_alpha_square, limit_dimension); - simplex_tree->initialize_filtration(); } void create_simplex_tree(Gudhi::Simplex_tree<>* simplex_tree, double max_alpha_square) { witness_complex_->create_complex(*simplex_tree, max_alpha_square); - simplex_tree->initialize_filtration(); } std::vector<double> get_point(unsigned vh) { diff --git a/src/python/include/Euclidean_witness_complex_interface.h b/src/python/include/Euclidean_witness_complex_interface.h index 5d7dbdc2..4411ae79 100644 --- a/src/python/include/Euclidean_witness_complex_interface.h +++ b/src/python/include/Euclidean_witness_complex_interface.h @@ -49,12 +49,10 @@ class Euclidean_witness_complex_interface { void create_simplex_tree(Gudhi::Simplex_tree<>* simplex_tree, double max_alpha_square, std::size_t limit_dimension) { witness_complex_->create_complex(*simplex_tree, max_alpha_square, limit_dimension); - simplex_tree->initialize_filtration(); } void create_simplex_tree(Gudhi::Simplex_tree<>* simplex_tree, double max_alpha_square) { witness_complex_->create_complex(*simplex_tree, max_alpha_square); - simplex_tree->initialize_filtration(); } std::vector<double> get_point(unsigned vh) { diff --git a/src/python/include/Nerve_gic_interface.h b/src/python/include/Nerve_gic_interface.h index 5e7f8ae6..ab14c318 100644 --- a/src/python/include/Nerve_gic_interface.h +++ b/src/python/include/Nerve_gic_interface.h @@ -29,7 +29,6 @@ class Nerve_gic_interface : public Cover_complex<std::vector<double>> { public: void create_simplex_tree(Simplex_tree_interface<>* simplex_tree) { create_complex(*simplex_tree); - simplex_tree->initialize_filtration(); } void set_cover_from_Euclidean_Voronoi(int m) { set_cover_from_Voronoi(Gudhi::Euclidean_distance(), m); diff --git a/src/python/include/Persistent_cohomology_interface.h b/src/python/include/Persistent_cohomology_interface.h index 8c79e6f3..0de9bd5c 100644 --- a/src/python/include/Persistent_cohomology_interface.h +++ b/src/python/include/Persistent_cohomology_interface.h @@ -23,82 +23,162 @@ template<class FilteredComplex> class Persistent_cohomology_interface : public persistent_cohomology::Persistent_cohomology<FilteredComplex, persistent_cohomology::Field_Zp> { private: + typedef persistent_cohomology::Persistent_cohomology<FilteredComplex, persistent_cohomology::Field_Zp> Base; /* * Compare two intervals by dimension, then by length. */ struct cmp_intervals_by_dim_then_length { - explicit cmp_intervals_by_dim_then_length(FilteredComplex * sc) - : sc_(sc) { } - template<typename Persistent_interval> bool operator()(const Persistent_interval & p1, const Persistent_interval & p2) { - if (sc_->dimension(get < 0 > (p1)) == sc_->dimension(get < 0 > (p2))) - return (sc_->filtration(get < 1 > (p1)) - sc_->filtration(get < 0 > (p1)) - > sc_->filtration(get < 1 > (p2)) - sc_->filtration(get < 0 > (p2))); + if (std::get<0>(p1) == std::get<0>(p2)) { + auto& i1 = std::get<1>(p1); + auto& i2 = std::get<1>(p2); + return std::get<1>(i1) - std::get<0>(i1) > std::get<1>(i2) - std::get<0>(i2); + } else - return (sc_->dimension(get < 0 > (p1)) > sc_->dimension(get < 0 > (p2))); + return (std::get<0>(p1) > std::get<0>(p2)); + // Why does this sort by decreasing dimension? } - FilteredComplex* sc_; }; public: - Persistent_cohomology_interface(FilteredComplex* stptr) - : persistent_cohomology::Persistent_cohomology<FilteredComplex, persistent_cohomology::Field_Zp>(*stptr), - stptr_(stptr) { } - - Persistent_cohomology_interface(FilteredComplex* stptr, bool persistence_dim_max) - : persistent_cohomology::Persistent_cohomology<FilteredComplex, - persistent_cohomology::Field_Zp>(*stptr, persistence_dim_max), + Persistent_cohomology_interface(FilteredComplex* stptr, bool persistence_dim_max=false) + : Base(*stptr, persistence_dim_max), stptr_(stptr) { } - std::vector<std::pair<int, std::pair<double, double>>> get_persistence(int homology_coeff_field, - double min_persistence) { - persistent_cohomology::Persistent_cohomology<FilteredComplex, - persistent_cohomology::Field_Zp>::init_coefficients(homology_coeff_field); - persistent_cohomology::Persistent_cohomology<FilteredComplex, - persistent_cohomology::Field_Zp>::compute_persistent_cohomology(min_persistence); - - // Custom sort and output persistence - cmp_intervals_by_dim_then_length cmp(stptr_); - auto persistent_pairs = persistent_cohomology::Persistent_cohomology<FilteredComplex, - persistent_cohomology::Field_Zp>::get_persistent_pairs(); - std::sort(std::begin(persistent_pairs), std::end(persistent_pairs), cmp); + // TODO: move to the constructors? + void compute_persistence(int homology_coeff_field, double min_persistence) { + Base::init_coefficients(homology_coeff_field); + Base::compute_persistent_cohomology(min_persistence); + } + std::vector<std::pair<int, std::pair<double, double>>> get_persistence() { std::vector<std::pair<int, std::pair<double, double>>> persistence; + auto const& persistent_pairs = Base::get_persistent_pairs(); + persistence.reserve(persistent_pairs.size()); for (auto pair : persistent_pairs) { - persistence.push_back(std::make_pair(stptr_->dimension(get<0>(pair)), - std::make_pair(stptr_->filtration(get<0>(pair)), - stptr_->filtration(get<1>(pair))))); + persistence.emplace_back(stptr_->dimension(get<0>(pair)), + std::make_pair(stptr_->filtration(get<0>(pair)), + stptr_->filtration(get<1>(pair)))); } + // Custom sort and output persistence + cmp_intervals_by_dim_then_length cmp; + std::sort(std::begin(persistence), std::end(persistence), cmp); return persistence; } std::vector<std::pair<std::vector<int>, std::vector<int>>> persistence_pairs() { - auto pairs = persistent_cohomology::Persistent_cohomology<FilteredComplex, - persistent_cohomology::Field_Zp>::get_persistent_pairs(); - std::vector<std::pair<std::vector<int>, std::vector<int>>> persistence_pairs; + auto const& pairs = Base::get_persistent_pairs(); persistence_pairs.reserve(pairs.size()); + std::vector<int> birth; + std::vector<int> death; for (auto pair : pairs) { - std::vector<int> birth; + birth.clear(); if (get<0>(pair) != stptr_->null_simplex()) { for (auto vertex : stptr_->simplex_vertex_range(get<0>(pair))) { birth.push_back(vertex); } } - std::vector<int> death; + death.clear(); if (get<1>(pair) != stptr_->null_simplex()) { + death.reserve(birth.size()+1); for (auto vertex : stptr_->simplex_vertex_range(get<1>(pair))) { death.push_back(vertex); } } - persistence_pairs.push_back(std::make_pair(birth, death)); + persistence_pairs.emplace_back(birth, death); } return persistence_pairs; } + // TODO: (possibly at the python level) + // - an option to return only some of those vectors? + typedef std::pair<std::vector<std::vector<int>>, std::vector<std::vector<int>>> Generators; + + Generators lower_star_generators() { + Generators out; + // diags[i] should be interpreted as vector<array<int,2>> + auto& diags = out.first; + // diagsinf[i] should be interpreted as vector<int> + auto& diagsinf = out.second; + for (auto pair : Base::get_persistent_pairs()) { + auto s = std::get<0>(pair); + auto t = std::get<1>(pair); + int dim = stptr_->dimension(s); + auto v = stptr_->vertex_with_same_filtration(s); + if(t == stptr_->null_simplex()) { + while(diagsinf.size() < dim+1) diagsinf.emplace_back(); + diagsinf[dim].push_back(v); + } else { + while(diags.size() < dim+1) diags.emplace_back(); + auto w = stptr_->vertex_with_same_filtration(t); + auto& d = diags[dim]; + d.insert(d.end(), { v, w }); + } + } + return out; + } + + // An alternative, to avoid those different sizes, would be to "pad" vertex generator v as (v, v) or (v, -1). When using it as index, this corresponds to adding the vertex filtration values either on the diagonal of the distance matrix, or as an extra row or column. + // We could also merge the vectors for different dimensions into a single one, with an extra column for the dimension (converted to type double). + Generators flag_generators() { + Generators out; + // diags[0] should be interpreted as vector<array<int,3>> and other diags[i] as vector<array<int,4>> + auto& diags = out.first; + // diagsinf[0] should be interpreted as vector<int> and other diagsinf[i] as vector<array<int,2>> + auto& diagsinf = out.second; + for (auto pair : Base::get_persistent_pairs()) { + auto s = std::get<0>(pair); + auto t = std::get<1>(pair); + int dim = stptr_->dimension(s); + bool infinite = t == stptr_->null_simplex(); + if(infinite) { + if(dim == 0) { + auto v = *std::begin(stptr_->simplex_vertex_range(s)); + if(diagsinf.size()==0)diagsinf.emplace_back(); + diagsinf[0].push_back(v); + } else { + auto e = stptr_->edge_with_same_filtration(s); + auto&& e_vertices = stptr_->simplex_vertex_range(e); + auto i = std::begin(e_vertices); + auto v1 = *i; + auto v2 = *++i; + GUDHI_CHECK(++i==std::end(e_vertices), "must be an edge"); + while(diagsinf.size() < dim+1) diagsinf.emplace_back(); + auto& d = diagsinf[dim]; + d.insert(d.end(), { v1, v2 }); + } + } else { + auto et = stptr_->edge_with_same_filtration(t); + auto&& et_vertices = stptr_->simplex_vertex_range(et); + auto it = std::begin(et_vertices); + auto w1 = *it; + auto w2 = *++it; + GUDHI_CHECK(++it==std::end(et_vertices), "must be an edge"); + if(dim == 0) { + auto v = *std::begin(stptr_->simplex_vertex_range(s)); + if(diags.size()==0)diags.emplace_back(); + auto& d = diags[0]; + d.insert(d.end(), { v, w1, w2 }); + } else { + auto es = stptr_->edge_with_same_filtration(s); + auto&& es_vertices = stptr_->simplex_vertex_range(es); + auto is = std::begin(es_vertices); + auto v1 = *is; + auto v2 = *++is; + GUDHI_CHECK(++is==std::end(es_vertices), "must be an edge"); + while(diags.size() < dim+1) diags.emplace_back(); + auto& d = diags[dim]; + d.insert(d.end(), { v1, v2, w1, w2 }); + } + } + } + return out; + } + private: // A copy FilteredComplex* stptr_; diff --git a/src/python/include/Rips_complex_interface.h b/src/python/include/Rips_complex_interface.h index a66b0e5b..d98b0226 100644 --- a/src/python/include/Rips_complex_interface.h +++ b/src/python/include/Rips_complex_interface.h @@ -53,7 +53,6 @@ class Rips_complex_interface { rips_complex_->create_complex(*simplex_tree, dim_max); else sparse_rips_complex_->create_complex(*simplex_tree, dim_max); - simplex_tree->initialize_filtration(); } private: diff --git a/src/python/include/Simplex_tree_interface.h b/src/python/include/Simplex_tree_interface.h index 06f31341..56d7c41d 100644 --- a/src/python/include/Simplex_tree_interface.h +++ b/src/python/include/Simplex_tree_interface.h @@ -16,8 +16,6 @@ #include <gudhi/Simplex_tree.h> #include <gudhi/Points_off_io.h> -#include "Persistent_cohomology_interface.h" - #include <iostream> #include <vector> #include <utility> // std::pair @@ -33,19 +31,29 @@ class Simplex_tree_interface : public Simplex_tree<SimplexTreeOptions> { using Simplex_handle = typename Base::Simplex_handle; using Insertion_result = typename std::pair<Simplex_handle, bool>; using Simplex = std::vector<Vertex_handle>; - using Filtered_simplices = std::vector<std::pair<Simplex, Filtration_value>>; + using Simplex_and_filtration = std::pair<Simplex, Filtration_value>; + using Filtered_simplices = std::vector<Simplex_and_filtration>; + using Skeleton_simplex_iterator = typename Base::Skeleton_simplex_iterator; + using Complex_simplex_iterator = typename Base::Complex_simplex_iterator; + using Extended_filtration_data = typename Base::Extended_filtration_data; public: - bool find_simplex(const Simplex& vh) { - return (Base::find(vh) != Base::null_simplex()); + + Extended_filtration_data efd; + + bool find_simplex(const Simplex& simplex) { + return (Base::find(simplex) != Base::null_simplex()); } - void assign_simplex_filtration(const Simplex& vh, Filtration_value filtration) { - Base::assign_filtration(Base::find(vh), filtration); + void assign_simplex_filtration(const Simplex& simplex, Filtration_value filtration) { + Base::assign_filtration(Base::find(simplex), filtration); + Base::clear_filtration(); } bool insert(const Simplex& simplex, Filtration_value filtration = 0) { Insertion_result result = Base::insert_simplex_and_subfaces(simplex, filtration); + if (result.first != Base::null_simplex()) + Base::clear_filtration(); return (result.second); } @@ -79,32 +87,15 @@ class Simplex_tree_interface : public Simplex_tree<SimplexTreeOptions> { void remove_maximal_simplex(const Simplex& simplex) { Base::remove_maximal_simplex(Base::find(simplex)); - Base::initialize_filtration(); + Base::clear_filtration(); } - Filtered_simplices get_filtration() { - Base::initialize_filtration(); - Filtered_simplices filtrations; - for (auto f_simplex : Base::filtration_simplex_range()) { - Simplex simplex; - for (auto vertex : Base::simplex_vertex_range(f_simplex)) { - simplex.insert(simplex.begin(), vertex); - } - filtrations.push_back(std::make_pair(simplex, Base::filtration(f_simplex))); + Simplex_and_filtration get_simplex_and_filtration(Simplex_handle f_simplex) { + Simplex simplex; + for (auto vertex : Base::simplex_vertex_range(f_simplex)) { + simplex.insert(simplex.begin(), vertex); } - return filtrations; - } - - Filtered_simplices get_skeleton(int dimension) { - Filtered_simplices skeletons; - for (auto f_simplex : Base::skeleton_simplex_range(dimension)) { - Simplex simplex; - for (auto vertex : Base::simplex_vertex_range(f_simplex)) { - simplex.insert(simplex.begin(), vertex); - } - skeletons.push_back(std::make_pair(simplex, Base::filtration(f_simplex))); - } - return skeletons; + return std::make_pair(std::move(simplex), Base::filtration(f_simplex)); } Filtered_simplices get_star(const Simplex& simplex) { @@ -131,9 +122,71 @@ class Simplex_tree_interface : public Simplex_tree<SimplexTreeOptions> { return cofaces; } - void create_persistence(Gudhi::Persistent_cohomology_interface<Base>* pcoh) { - Base::initialize_filtration(); - pcoh = new Gudhi::Persistent_cohomology_interface<Base>(*this); + void compute_extended_filtration() { + this->efd = this->extend_filtration(); + return; + } + + std::vector<std::vector<std::pair<int, std::pair<Filtration_value, Filtration_value>>>> compute_extended_persistence_subdiagrams(const std::vector<std::pair<int, std::pair<Filtration_value, Filtration_value>>>& dgm, Filtration_value min_persistence){ + std::vector<std::vector<std::pair<int, std::pair<Filtration_value, Filtration_value>>>> new_dgm(4); + for (unsigned int i = 0; i < dgm.size(); i++){ + std::pair<Filtration_value, Extended_simplex_type> px = this->decode_extended_filtration(dgm[i].second.first, this->efd); + std::pair<Filtration_value, Extended_simplex_type> py = this->decode_extended_filtration(dgm[i].second.second, this->efd); + std::pair<int, std::pair<Filtration_value, Filtration_value>> pd_point = std::make_pair(dgm[i].first, std::make_pair(px.first, py.first)); + if(std::abs(px.first - py.first) > min_persistence){ + //Ordinary + if (px.second == Extended_simplex_type::UP && py.second == Extended_simplex_type::UP){ + new_dgm[0].push_back(pd_point); + } + // Relative + else if (px.second == Extended_simplex_type::DOWN && py.second == Extended_simplex_type::DOWN){ + new_dgm[1].push_back(pd_point); + } + else{ + // Extended+ + if (px.first < py.first){ + new_dgm[2].push_back(pd_point); + } + //Extended- + else{ + new_dgm[3].push_back(pd_point); + } + } + } + } + return new_dgm; + } + + // Iterator over the simplex tree + Complex_simplex_iterator get_simplices_iterator_begin() { + // this specific case works because the range is just a pair of iterators - won't work if range was a vector + return Base::complex_simplex_range().begin(); + } + + Complex_simplex_iterator get_simplices_iterator_end() { + // this specific case works because the range is just a pair of iterators - won't work if range was a vector + return Base::complex_simplex_range().end(); + } + + typename std::vector<Simplex_handle>::const_iterator get_filtration_iterator_begin() { + // Base::initialize_filtration(); already performed in filtration_simplex_range + // this specific case works because the range is just a pair of iterators - won't work if range was a vector + return Base::filtration_simplex_range().begin(); + } + + typename std::vector<Simplex_handle>::const_iterator get_filtration_iterator_end() { + // this specific case works because the range is just a pair of iterators - won't work if range was a vector + return Base::filtration_simplex_range().end(); + } + + Skeleton_simplex_iterator get_skeleton_iterator_begin(int dimension) { + // this specific case works because the range is just a pair of iterators - won't work if range was a vector + return Base::skeleton_simplex_range(dimension).begin(); + } + + Skeleton_simplex_iterator get_skeleton_iterator_end(int dimension) { + // this specific case works because the range is just a pair of iterators - won't work if range was a vector + return Base::skeleton_simplex_range(dimension).end(); } }; diff --git a/src/python/include/Strong_witness_complex_interface.h b/src/python/include/Strong_witness_complex_interface.h index cda5b514..e9ab0c7b 100644 --- a/src/python/include/Strong_witness_complex_interface.h +++ b/src/python/include/Strong_witness_complex_interface.h @@ -41,13 +41,11 @@ class Strong_witness_complex_interface { void create_simplex_tree(Simplex_tree_interface<>* simplex_tree, double max_alpha_square, std::size_t limit_dimension) { witness_complex_->create_complex(*simplex_tree, max_alpha_square, limit_dimension); - simplex_tree->initialize_filtration(); } void create_simplex_tree(Simplex_tree_interface<>* simplex_tree, double max_alpha_square) { witness_complex_->create_complex(*simplex_tree, max_alpha_square); - simplex_tree->initialize_filtration(); } private: diff --git a/src/python/include/Tangential_complex_interface.h b/src/python/include/Tangential_complex_interface.h index 698226cc..b1afce94 100644 --- a/src/python/include/Tangential_complex_interface.h +++ b/src/python/include/Tangential_complex_interface.h @@ -90,7 +90,6 @@ class Tangential_complex_interface { void create_simplex_tree(Simplex_tree<>* simplex_tree) { tangential_complex_->create_complex<Gudhi::Simplex_tree<Gudhi::Simplex_tree_options_full_featured>>(*simplex_tree); - simplex_tree->initialize_filtration(); } void set_max_squared_edge_length(double max_squared_edge_length) { diff --git a/src/python/include/Witness_complex_interface.h b/src/python/include/Witness_complex_interface.h index 45e14253..76947e53 100644 --- a/src/python/include/Witness_complex_interface.h +++ b/src/python/include/Witness_complex_interface.h @@ -41,13 +41,11 @@ class Witness_complex_interface { void create_simplex_tree(Simplex_tree_interface<>* simplex_tree, double max_alpha_square, std::size_t limit_dimension) { witness_complex_->create_complex(*simplex_tree, max_alpha_square, limit_dimension); - simplex_tree->initialize_filtration(); } void create_simplex_tree(Simplex_tree_interface<>* simplex_tree, double max_alpha_square) { witness_complex_->create_complex(*simplex_tree, max_alpha_square); - simplex_tree->initialize_filtration(); } private: diff --git a/src/python/include/pybind11_diagram_utils.h b/src/python/include/pybind11_diagram_utils.h new file mode 100644 index 00000000..d9627258 --- /dev/null +++ b/src/python/include/pybind11_diagram_utils.h @@ -0,0 +1,39 @@ +/* This file is part of the Gudhi Library - https://gudhi.inria.fr/ - which is released under MIT. + * See file LICENSE or go to https://gudhi.inria.fr/licensing/ for full license details. + * Author(s): Marc Glisse + * + * Copyright (C) 2020 Inria + * + * Modification(s): + * - YYYY/MM Author: Description of the modification + */ + +#include <pybind11/pybind11.h> +#include <pybind11/numpy.h> + +#include <boost/range/counting_range.hpp> +#include <boost/range/adaptor/transformed.hpp> + +namespace py = pybind11; +typedef py::array_t<double> Dgm; + +// Get m[i,0] and m[i,1] as a pair +static auto pairify(void* p, ssize_t h, ssize_t w) { + return [=](ssize_t i){ + char* birth = (char*)p + i * h; + char* death = birth + w; + return std::make_pair(*(double*)birth, *(double*)death); + }; +} + +inline auto numpy_to_range_of_pairs(py::array_t<double> dgm) { + py::buffer_info buf = dgm.request(); + // shape (n,2) or (0) for empty + if((buf.ndim!=2 || buf.shape[1]!=2) && (buf.ndim!=1 || buf.shape[0]!=0)) + throw std::runtime_error("Diagram must be an array of size n x 2"); + // In the case of shape (0), avoid reading non-existing strides[1] even if we won't use it. + ssize_t stride1 = buf.ndim == 2 ? buf.strides[1] : 0; + auto cnt = boost::counting_range<ssize_t>(0, buf.shape[0]); + return boost::adaptors::transform(cnt, pairify(buf.ptr, buf.strides[0], stride1)); + // Be careful that the returned range cannot contain references to dead temporaries. +} |