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+// Ceres Solver - A fast non-linear least squares minimizer
+// Copyright 2022 Google Inc. All rights reserved.
+// http://ceres-solver.org/
+//
+// Redistribution and use in source and binary forms, with or without
+// modification, are permitted provided that the following conditions are met:
+//
+// * Redistributions of source code must retain the above copyright notice,
+// this list of conditions and the following disclaimer.
+// * Redistributions in binary form must reproduce the above copyright notice,
+// this list of conditions and the following disclaimer in the documentation
+// and/or other materials provided with the distribution.
+// * Neither the name of Google Inc. nor the names of its contributors may be
+// used to endorse or promote products derived from this software without
+// specific prior written permission.
+//
+// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
+// AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+// ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
+// LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
+// CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
+// SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
+// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
+// CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
+// ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+// POSSIBILITY OF SUCH DAMAGE.
+//
+// Author: sameeragarwal@google.com (Sameer Agarwal)
+// sergiu.deitsch@gmail.com (Sergiu Deitsch)
+//
+
+#ifndef CERES_PUBLIC_PRODUCT_MANIFOLD_H_
+#define CERES_PUBLIC_PRODUCT_MANIFOLD_H_
+
+#include <algorithm>
+#include <array>
+#include <cassert>
+#include <cstddef>
+#include <numeric>
+#include <tuple>
+#include <type_traits>
+#include <utility>
+
+#include "ceres/internal/eigen.h"
+#include "ceres/internal/fixed_array.h"
+#include "ceres/internal/port.h"
+#include "ceres/manifold.h"
+
+namespace ceres {
+
+// Construct a manifold by taking the Cartesian product of a number of other
+// manifolds. This is useful, when a parameter block is the Cartesian product
+// of two or more manifolds. For example the parameters of a camera consist of
+// a rotation and a translation, i.e., SO(3) x R^3.
+//
+// Example usage:
+//
+// ProductManifold<QuaternionManifold, EuclideanManifold<3>> se3;
+//
+// is the manifold for a rigid transformation, where the rotation is
+// represented using a quaternion.
+//
+// Manifolds can be copied and moved to ProductManifold:
+//
+// SubsetManifold manifold1(5, {2});
+// SubsetManifold manifold2(3, {0, 1});
+// ProductManifold<SubsetManifold, SubsetManifold> manifold(manifold1,
+// manifold2);
+//
+// In advanced use cases, manifolds can be dynamically allocated and passed as
+// (smart) pointers:
+//
+// ProductManifold<std::unique_ptr<QuaternionManifold>, EuclideanManifold<3>>
+// se3{std::make_unique<QuaternionManifold>(), EuclideanManifold<3>{}};
+//
+// In C++17, the template parameters can be left out as they are automatically
+// deduced making the initialization much simpler:
+//
+// ProductManifold se3{QuaternionManifold{}, EuclideanManifold<3>{}};
+//
+// The manifold implementations must be either default constructible, copyable
+// or moveable to be usable in a ProductManifold.
+template <typename Manifold0, typename Manifold1, typename... ManifoldN>
+class ProductManifold final : public Manifold {
+ public:
+ // ProductManifold constructor perfect forwards arguments to store manifolds.
+ //
+ // Either use default construction or if you need to copy or move-construct a
+ // manifold instance, you need to pass an instance as an argument for all
+ // types given as class template parameters.
+ template <typename... Args,
+ std::enable_if_t<std::is_constructible<
+ std::tuple<Manifold0, Manifold1, ManifoldN...>,
+ Args...>::value>* = nullptr>
+ explicit ProductManifold(Args&&... manifolds)
+ : ProductManifold{std::make_index_sequence<kNumManifolds>{},
+ std::forward<Args>(manifolds)...} {}
+
+ int AmbientSize() const override { return ambient_size_; }
+ int TangentSize() const override { return tangent_size_; }
+
+ bool Plus(const double* x,
+ const double* delta,
+ double* x_plus_delta) const override {
+ return PlusImpl(
+ x, delta, x_plus_delta, std::make_index_sequence<kNumManifolds>{});
+ }
+
+ bool Minus(const double* y,
+ const double* x,
+ double* y_minus_x) const override {
+ return MinusImpl(
+ y, x, y_minus_x, std::make_index_sequence<kNumManifolds>{});
+ }
+
+ bool PlusJacobian(const double* x, double* jacobian_ptr) const override {
+ MatrixRef jacobian(jacobian_ptr, AmbientSize(), TangentSize());
+ jacobian.setZero();
+ internal::FixedArray<double> buffer(buffer_size_);
+
+ return PlusJacobianImpl(
+ x, jacobian, buffer, std::make_index_sequence<kNumManifolds>{});
+ }
+
+ bool MinusJacobian(const double* x, double* jacobian_ptr) const override {
+ MatrixRef jacobian(jacobian_ptr, TangentSize(), AmbientSize());
+ jacobian.setZero();
+ internal::FixedArray<double> buffer(buffer_size_);
+
+ return MinusJacobianImpl(
+ x, jacobian, buffer, std::make_index_sequence<kNumManifolds>{});
+ }
+
+ private:
+ static constexpr std::size_t kNumManifolds = 2 + sizeof...(ManifoldN);
+
+ template <std::size_t... Indices, typename... Args>
+ explicit ProductManifold(std::index_sequence<Indices...>, Args&&... manifolds)
+ : manifolds_{std::forward<Args>(manifolds)...},
+ buffer_size_{(std::max)(
+ {(Dereference(std::get<Indices>(manifolds_)).TangentSize() *
+ Dereference(std::get<Indices>(manifolds_)).AmbientSize())...})},
+ ambient_sizes_{
+ Dereference(std::get<Indices>(manifolds_)).AmbientSize()...},
+ tangent_sizes_{
+ Dereference(std::get<Indices>(manifolds_)).TangentSize()...},
+ ambient_offsets_{ExclusiveScan(ambient_sizes_)},
+ tangent_offsets_{ExclusiveScan(tangent_sizes_)},
+ ambient_size_{
+ std::accumulate(ambient_sizes_.begin(), ambient_sizes_.end(), 0)},
+ tangent_size_{
+ std::accumulate(tangent_sizes_.begin(), tangent_sizes_.end(), 0)} {}
+
+ template <std::size_t Index0, std::size_t... Indices>
+ bool PlusImpl(const double* x,
+ const double* delta,
+ double* x_plus_delta,
+ std::index_sequence<Index0, Indices...>) const {
+ if (!Dereference(std::get<Index0>(manifolds_))
+ .Plus(x + ambient_offsets_[Index0],
+ delta + tangent_offsets_[Index0],
+ x_plus_delta + ambient_offsets_[Index0])) {
+ return false;
+ }
+
+ return PlusImpl(x, delta, x_plus_delta, std::index_sequence<Indices...>{});
+ }
+
+ static constexpr bool PlusImpl(const double* /*x*/,
+ const double* /*delta*/,
+ double* /*x_plus_delta*/,
+ std::index_sequence<>) noexcept {
+ return true;
+ }
+
+ template <std::size_t Index0, std::size_t... Indices>
+ bool MinusImpl(const double* y,
+ const double* x,
+ double* y_minus_x,
+ std::index_sequence<Index0, Indices...>) const {
+ if (!Dereference(std::get<Index0>(manifolds_))
+ .Minus(y + ambient_offsets_[Index0],
+ x + ambient_offsets_[Index0],
+ y_minus_x + tangent_offsets_[Index0])) {
+ return false;
+ }
+
+ return MinusImpl(y, x, y_minus_x, std::index_sequence<Indices...>{});
+ }
+
+ static constexpr bool MinusImpl(const double* /*y*/,
+ const double* /*x*/,
+ double* /*y_minus_x*/,
+ std::index_sequence<>) noexcept {
+ return true;
+ }
+
+ template <std::size_t Index0, std::size_t... Indices>
+ bool PlusJacobianImpl(const double* x,
+ MatrixRef& jacobian,
+ internal::FixedArray<double>& buffer,
+ std::index_sequence<Index0, Indices...>) const {
+ if (!Dereference(std::get<Index0>(manifolds_))
+ .PlusJacobian(x + ambient_offsets_[Index0], buffer.data())) {
+ return false;
+ }
+
+ jacobian.block(ambient_offsets_[Index0],
+ tangent_offsets_[Index0],
+ ambient_sizes_[Index0],
+ tangent_sizes_[Index0]) =
+ MatrixRef(
+ buffer.data(), ambient_sizes_[Index0], tangent_sizes_[Index0]);
+
+ return PlusJacobianImpl(
+ x, jacobian, buffer, std::index_sequence<Indices...>{});
+ }
+
+ static constexpr bool PlusJacobianImpl(
+ const double* /*x*/,
+ MatrixRef& /*jacobian*/,
+ internal::FixedArray<double>& /*buffer*/,
+ std::index_sequence<>) noexcept {
+ return true;
+ }
+
+ template <std::size_t Index0, std::size_t... Indices>
+ bool MinusJacobianImpl(const double* x,
+ MatrixRef& jacobian,
+ internal::FixedArray<double>& buffer,
+ std::index_sequence<Index0, Indices...>) const {
+ if (!Dereference(std::get<Index0>(manifolds_))
+ .MinusJacobian(x + ambient_offsets_[Index0], buffer.data())) {
+ return false;
+ }
+
+ jacobian.block(tangent_offsets_[Index0],
+ ambient_offsets_[Index0],
+ tangent_sizes_[Index0],
+ ambient_sizes_[Index0]) =
+ MatrixRef(
+ buffer.data(), tangent_sizes_[Index0], ambient_sizes_[Index0]);
+
+ return MinusJacobianImpl(
+ x, jacobian, buffer, std::index_sequence<Indices...>{});
+ }
+
+ static constexpr bool MinusJacobianImpl(
+ const double* /*x*/,
+ MatrixRef& /*jacobian*/,
+ internal::FixedArray<double>& /*buffer*/,
+ std::index_sequence<>) noexcept {
+ return true;
+ }
+
+ template <typename T, std::size_t N>
+ static std::array<T, N> ExclusiveScan(const std::array<T, N>& values) {
+ std::array<T, N> result;
+ T init = 0;
+
+ // TODO Replace by std::exclusive_scan once C++17 is available
+ for (std::size_t i = 0; i != N; ++i) {
+ result[i] = init;
+ init += values[i];
+ }
+
+ return result;
+ }
+
+ // TODO Replace by std::void_t once C++17 is available
+ template <typename... Types>
+ struct Void {
+ using type = void;
+ };
+
+ template <typename T, typename E = void>
+ struct IsDereferenceable : std::false_type {};
+
+ template <typename T>
+ struct IsDereferenceable<T, typename Void<decltype(*std::declval<T>())>::type>
+ : std::true_type {};
+
+ template <typename T,
+ std::enable_if_t<!IsDereferenceable<T>::value>* = nullptr>
+ static constexpr decltype(auto) Dereference(T& value) {
+ return value;
+ }
+
+ // Support dereferenceable types such as std::unique_ptr, std::shared_ptr, raw
+ // pointers etc.
+ template <typename T,
+ std::enable_if_t<IsDereferenceable<T>::value>* = nullptr>
+ static constexpr decltype(auto) Dereference(T& value) {
+ return *value;
+ }
+
+ template <typename T>
+ static constexpr decltype(auto) Dereference(T* p) {
+ assert(p != nullptr);
+ return *p;
+ }
+
+ std::tuple<Manifold0, Manifold1, ManifoldN...> manifolds_;
+ int buffer_size_;
+ std::array<int, kNumManifolds> ambient_sizes_;
+ std::array<int, kNumManifolds> tangent_sizes_;
+ std::array<int, kNumManifolds> ambient_offsets_;
+ std::array<int, kNumManifolds> tangent_offsets_;
+ int ambient_size_;
+ int tangent_size_;
+};
+
+#ifdef CERES_HAS_CPP17
+// C++17 deduction guide that allows the user to avoid explicitly specifying
+// the template parameters of ProductManifold. The class can instead be
+// instantiated as follows:
+//
+// ProductManifold manifold{QuaternionManifold{}, EuclideanManifold<3>{}};
+//
+template <typename Manifold0, typename Manifold1, typename... Manifolds>
+ProductManifold(Manifold0&&, Manifold1&&, Manifolds&&...)
+ -> ProductManifold<Manifold0, Manifold1, Manifolds...>;
+#endif
+
+} // namespace ceres
+
+#endif // CERES_PUBLIC_PRODUCT_MANIFOLD_H_