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RecurrenceBasis1d.h
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22 #ifndef LSST_AFW_MATH_POLYNOMIALS_RecurrenceBasis1d_h_INCLUDED
23 #define LSST_AFW_MATH_POLYNOMIALS_RecurrenceBasis1d_h_INCLUDED
24 
27 
28 namespace lsst { namespace geom { namespace polynomials {
29 
30 template <typename Basis>
31 class Function1d;
32 
33 #ifdef DOXYGEN
34 
43 struct Recurrence {
44 
46  static double getB0(double x);
47 
49  static double getB1(double x);
50 
61  static double next(double x, std::size_t n, double current, double previous);
62 
63 };
64 
65 #endif // DOXYGEN
66 
67 
84 template <typename Recurrence>
86 public:
87 
90 
93 
95  explicit RecurrenceBasis1d(std::size_t order) noexcept :
96  _order(order)
97  {}
98 
101 
104 
107 
110 
112  std::size_t getOrder() const noexcept { return _order; }
113 
115  std::size_t size() const noexcept { return _order + 1; }
116 
123  Scaled scaled(Scaling1d const & scaling) const noexcept {
124  return Scaled(*this, scaling);
125  }
126 
145  template <typename Vector>
146  double sumWith(double x, Vector const & coefficients, SumMode mode=SumMode::FAST) const {
147  // This universal lambda lets us effectively template most of the
148  // implementation of this function on double vs. SafeSum<double>
149  // without having to define an external template.
150  auto accumulate = [x, coefficients, this](auto & sum) {
151  double previous = Recurrence::getB0(x);
152  if (_order > 0u) {
153  double current = Recurrence::getB1(x);
154  sum += coefficients[1]*current;
155  for (std::size_t n = 2; n <= _order; ++n) {
156  double next = Recurrence::next(x, n, current, previous);
157  sum += coefficients[n]*next;
158  previous = current;
159  current = next;
160  }
161  }
162  };
163  double result = 0.0;
164  if (mode == SumMode::FAST) {
165  double z = Recurrence::getB0(x)*coefficients[0];
166  accumulate(z);
167  result = z;
168  } else {
170  accumulate(z);
171  result = static_cast<double>(z);
172  }
173  return result;
174  }
175 
186  template <typename Vector>
187  void fill(double x, Vector && basis) const {
188  std::forward<Vector>(basis)[0] = Recurrence::getB0(x);
189  if (_order > 0u) {
190  std::forward<Vector>(basis)[1] = Recurrence::getB1(x);
191  for (std::size_t n = 2; n <= _order; ++n) {
192  std::forward<Vector>(basis)[n] = Recurrence::next(
193  x, n,
194  std::forward<Vector>(basis)[n - 1],
195  std::forward<Vector>(basis)[n - 2]
196  );
197  }
198  }
199  }
200 
201 private:
202  std::size_t _order;
203 };
204 
205 }}} // namespace lsst::geom::polynomials
206 
207 #endif // !LSST_AFW_MATH_POLYNOMIALS_RecurrenceBasis1d_h_INCLUDED
astshim.fitsChanContinued.next
def next(self)
Definition: fitsChanContinued.py:105
SafeSum.h
lsst::geom::polynomials::RecurrenceBasis1d::size
std::size_t size() const noexcept
Return the number of elements in the basis.
Definition: RecurrenceBasis1d.h:115
lsst::geom::polynomials::Recurrence::getB1
static double getB1(double x)
Return the first element of the basis, .
lsst::geom::polynomials::RecurrenceBasis1d::RecurrenceBasis1d
RecurrenceBasis1d(std::size_t order) noexcept
Construct a basis with the given order (inclusive).
Definition: RecurrenceBasis1d.h:95
coefficients
ndarray::Array< double const, 2, 2 > coefficients
Definition: ChebyshevBoundedField.cc:276
ScaledBasis1d.h
lsst::geom::polynomials::Recurrence::next
static double next(double x, std::size_t n, double current, double previous)
Return the next element in the recurrence.
lsst::geom::polynomials::Scaling1d
A 1-d affine transform that can be used to map one interval to another.
Definition: Scaling1d.h:46
lsst::geom::polynomials::RecurrenceBasis1d::operator=
RecurrenceBasis1d & operator=(RecurrenceBasis1d const &)=default
Default copy assignment.
lsst::geom::polynomials::RecurrenceBasis1d::operator=
RecurrenceBasis1d & operator=(RecurrenceBasis1d &&)=default
Default move assignment.
lsst::geom::polynomials::RecurrenceBasis1d::scaled
Scaled scaled(Scaling1d const &scaling) const noexcept
Return a scaled basis with the same order and recurrence.
Definition: RecurrenceBasis1d.h:123
lsst::geom::polynomials::ScaledBasis1d
A 1-d basis that transforms all input points before evaluating nested basis.
Definition: ScaledBasis1d.h:44
z
double z
Definition: Match.cc:44
x
double x
Definition: ChebyshevBoundedField.cc:277
lsst::geom::polynomials::Recurrence
A recurrence relation concept for RecurrenceBasis1d.
Definition: RecurrenceBasis1d.h:43
lsst::geom::polynomials::SumMode
SumMode
Enum used to control how to sum polynomial terms.
Definition: SafeSum.h:32
lsst::meas::modelfit::Vector
Eigen::Matrix< Scalar, Eigen::Dynamic, 1 > Vector
Definition: common.h:46
basis
table::Key< table::Array< double > > basis
Definition: PsfexPsf.cc:361
lsst::geom::polynomials::RecurrenceBasis1d::Scaled
ScaledBasis1d< RecurrenceBasis1d > Scaled
The type returned by scale().
Definition: RecurrenceBasis1d.h:92
lsst::geom::polynomials::Function1d
A 1-d function defined by a series expansion and its coefficients.
Definition: Function1d.h:42
result
py::object result
Definition: _schema.cc:429
lsst::geom::polynomials::RecurrenceBasis1d::RecurrenceBasis1d
RecurrenceBasis1d(RecurrenceBasis1d const &)=default
Default copy constructor.
lsst
A base class for image defects.
Definition: imageAlgorithm.dox:1
lsst::geom
Definition: geomOperators.dox:4
lsst::geom::polynomials::RecurrenceBasis1d::getOrder
std::size_t getOrder() const noexcept
Return the order of the basis.
Definition: RecurrenceBasis1d.h:112
lsst::geom::polynomials::RecurrenceBasis1d::RecurrenceBasis1d
RecurrenceBasis1d(RecurrenceBasis1d &&)=default
Default move constructor.
lsst::geom::polynomials::RecurrenceBasis1d::fill
void fill(double x, Vector &&basis) const
Evaluate the basis at a given point.
Definition: RecurrenceBasis1d.h:187
lsst::geom::polynomials::SafeSum
A numerically stable summation algorithm for floating-point numbers.
Definition: SafeSum.h:62
std::size_t
scaling
table::Key< double > scaling
Definition: PixelAreaBoundedField.cc:133
lsst::geom::polynomials::Recurrence::getB0
static double getB0(double x)
Return the zeroth element of the basis, .
lsst::geom::polynomials::SumMode::FAST
@ FAST
Summation using regular floating-point addition.
lsst::geom::polynomials::RecurrenceBasis1d
A basis for 1-d series expansions defined by a recurrence relation.
Definition: RecurrenceBasis1d.h:85
lsst::geom::polynomials::RecurrenceBasis1d::sumWith
double sumWith(double x, Vector const &coefficients, SumMode mode=SumMode::FAST) const
Evaluate a basis expansion with the given coefficients.
Definition: RecurrenceBasis1d.h:146