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LSST Data Management Base Package
PackedBasis2d.h
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22 #ifndef LSST_AFW_MATH_POLYNOMIALS_PackedBasis2d_h_INCLUDED
23 #define LSST_AFW_MATH_POLYNOMIALS_PackedBasis2d_h_INCLUDED
24 
25 #include "lsst/geom/Point.h"
29 
30 namespace lsst { namespace geom { namespace polynomials {
31 
32 template <typename Basis1d, PackingOrder packing>
33 class PackedBasis2d;
34 
35 
41 public:
42 
44  explicit PackedBasisWorkspace2d(std::size_t order) : _x(order + 1), _y(order + 1) {}
45 
47  std::size_t getOrder() const { return _x.size() - 1; }
48 
49 private:
50 
51  template <typename Recurrence, PackingOrder packing>
52  friend class PackedBasis2d;
53 
54  Eigen::VectorXd _x;
55  Eigen::VectorXd _y;
56 };
57 
58 template <typename Basis>
59 class Function2d;
60 
74 template <typename Basis1d, PackingOrder packing>
76 public:
77 
80 
83 
86 
89 
91  static constexpr std::size_t computeSize(std::size_t order) { return IndexRange::computeSize(order); }
92 
94  explicit PackedBasis2d(Basis1d const & basis1d) : _basis1d(basis1d) {}
95 
97  template <typename ...Args>
98  explicit PackedBasis2d(Args&& ...args) : _basis1d(std::forward<Args>(args)...) {}
99 
101  PackedBasis2d(PackedBasis2d const &) = default;
102 
105 
107  PackedBasis2d & operator=(PackedBasis2d const &) = default;
108 
111 
113  std::size_t getOrder() const noexcept { return _basis1d.getOrder(); }
114 
116  std::size_t size() const noexcept{ return IndexRange::computeSize(getOrder()); }
117 
124  Scaled scaled(Scaling2d const & first) const {
125  return Scaled(*this, first);
126  }
127 
130  return IndexRange::computeIndex(x, y);
131  }
132 
155  IndexRange getIndices() const noexcept {
157  }
158 
161 
181  template <typename Vector>
182  double sumWith(geom::Point2D const & point, Vector const & coefficients,
183  Workspace & workspace, SumMode mode=SumMode::FAST) const {
184  assert(workspace.getOrder() >= getOrder());
185  _basis1d.fill(point.getX(), workspace._x);
186  _basis1d.fill(point.getY(), workspace._y);
187  // This universal lambda lets us effectively template most of the
188  // implementation of this function on double vs. SafeSum<double>
189  // without having to define an external template.
190  auto accumulate = [coefficients, &workspace, this](auto & sum) {
191  for (auto const & index : getIndices()) {
192  sum += coefficients[index.flat]*workspace._x[index.nx]*workspace._y[index.ny];
193  }
194  };
195  double result = 0.0;
196  if (mode == SumMode::FAST) {
197  double z = 0.0;
198  accumulate(z);
199  result = z;
200  } else {
202  accumulate(z);
203  result = static_cast<double>(z);
204  }
205  return result;
206  }
207 
209  template <typename Vector>
210  double sumWith(geom::Point2D const & point, Vector const & coefficients,
211  SumMode mode=SumMode::FAST) const {
212  auto workspace = makeWorkspace();
213  return sumWith(point, coefficients, workspace, mode);
214  }
215 
227  template <typename Vector>
228  void fill(geom::Point2D const & point, Vector && basis, Workspace & workspace) const {
229  assert(workspace.getOrder() >= getOrder());
230  _basis1d.fill(point.getX(), workspace._x);
231  _basis1d.fill(point.getY(), workspace._y);
232  for (auto const & index : getIndices()) {
233  std::forward<Vector>(basis)[index.flat] = workspace._x[index.nx]*workspace._y[index.ny];
234  }
235  }
236 
238  template <typename Vector>
239  void fill(geom::Point2D const & point, Vector && basis) const {
240  auto workspace = makeWorkspace();
241  fill(point, std::forward<Vector>(basis), workspace);
242  }
243 
244 private:
245  Basis1d _basis1d;
246 };
247 
248 }}} // namespace lsst::geom::polynomials
249 
250 #endif // !LSST_AFW_MATH_POLYNOMIALS_PackedBasis2d_h_INCLUDED
py::object result
Definition: _schema.cc:430
ndarray::Array< double const, 2, 2 > coefficients
double x
double z
Definition: Match.cc:44
int y
Definition: SpanSet.cc:49
A basis interface for 1-d series expansions.
Definition: Basis1d.h:36
std::size_t getOrder() const
Return the order of the basis.
void fill(double x, Vector &&basis) const
Evaluate the basis at a given point.
A 2-d function defined by a series expansion and its coefficients.
Definition: Function2d.h:42
A Basis2d formed from the product of a Basis1d for each of x and y, truncated at the sum of their ord...
Definition: PackedBasis2d.h:75
void fill(geom::Point2D const &point, Vector &&basis, Workspace &workspace) const
Evaluate the basis at a given point.
double sumWith(geom::Point2D const &point, Vector const &coefficients, SumMode mode=SumMode::FAST) const
Evaluate a basis expansion with the given coefficients (internal workspace version).
void fill(geom::Point2D const &point, Vector &&basis) const
Evaluate the basis at a given point (internal workspace version).
PackedBasis2d(PackedBasis2d &&)=default
Default move constructor.
PackedBasis2d & operator=(PackedBasis2d &&)=default
Default move assignment.
static constexpr std::size_t computeSize(std::size_t order)
Return the size of a PackedBasis with the given order.
Definition: PackedBasis2d.h:91
PackedBasis2d(PackedBasis2d const &)=default
Default copy constructor.
PackedBasis2d(Basis1d const &basis1d)
Construct from a 1-d basis that will be used for both x and y.
Definition: PackedBasis2d.h:94
std::size_t index(std::size_t x, std::size_t y) const
Return the flattened index of the basis function with the given x and y orders.
IndexRange getIndices() const noexcept
Return a range of iterators that dereference to Index2d.
double sumWith(geom::Point2D const &point, Vector const &coefficients, Workspace &workspace, SumMode mode=SumMode::FAST) const
Evaluate a basis expansion with the given coefficients.
PackedBasis2d & operator=(PackedBasis2d const &)=default
Default copy assignment.
std::size_t getOrder() const noexcept
Return the maximum order of the basis.
ScaledBasis2d< PackedBasis2d > Scaled
The type returned by scale().
Definition: PackedBasis2d.h:82
Workspace makeWorkspace() const
Allocate a workspace that can be passed to sumWith() and fill() to avoid repeated memory allocations.
Scaled scaled(Scaling2d const &first) const
Return a scaled basis that delegates to a copy of this.
PackedBasisWorkspace2d Workspace
The type returned by makeWorkspace().
Definition: PackedBasis2d.h:85
PackedBasis2d(Args &&...args)
Construct by forwarding all arguments to the 1-d basis constructor.
Definition: PackedBasis2d.h:98
PackedIndexRange< packing > IndexRange
The type returned by getIndices().
Definition: PackedBasis2d.h:88
std::size_t size() const noexcept
Return the number of basis functions.
A workspace object that can be used to avoid extra memory allocations in repeated calls to PackedBasi...
Definition: PackedBasis2d.h:40
std::size_t getOrder() const
Return the maximum order this workspace supports.
Definition: PackedBasis2d.h:47
PackedBasisWorkspace2d(std::size_t order)
Construct workspace for a basis with the given order.
Definition: PackedBasis2d.h:44
An iterator for traversing "packed" triangular 2-d series expansions, in which two 1-d expansions are...
Definition: PackedIndex.h:164
static constexpr PackedIndexIterator makeEnd(std::size_t order) noexcept
Construct an iterator one past the end of an expansion with the given order.
Definition: PackedIndex.h:190
A specialized iterator range class for PackedIndexIterator, providing size calculation,...
Definition: PackedIndex.h:248
static constexpr std::size_t computeSize(std::size_t order) noexcept
Return the flattened size of an expansion with the given maximum order (inclusive).
Definition: PackedIndex.h:265
static constexpr std::size_t computeIndex(std::size_t nx, std::size_t ny) noexcept
Return the flattened index for the element with the given x and y orders.
Definition: PackedIndex.h:270
A numerically stable summation algorithm for floating-point numbers.
Definition: SafeSum.h:62
A 2-d basis that transforms all input points before evaluating nested basis.
Definition: ScaledBasis2d.h:43
A 2-d separable affine transform that can be used to map one interval to another.
Definition: Scaling2d.h:48
SumMode
Enum used to control how to sum polynomial terms.
Definition: SafeSum.h:32
@ FAST
Summation using regular floating-point addition.
Eigen::Matrix< Scalar, Eigen::Dynamic, 1 > Vector
Definition: common.h:46
A base class for image defects.
STL namespace.
table::Key< table::Array< double > > basis
Definition: PsfexPsf.cc:361