LSST Applications
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LSST Data Management Base Package
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A Basis2d formed from the product of a Basis1d for each of x and y, truncated at the sum of their orders. More...
#include <PackedBasis2d.h>
Public Types | |
using | Function = Function2d< PackedBasis2d > |
A Function2d object that uses this basis. More... | |
using | Scaled = ScaledBasis2d< PackedBasis2d > |
The type returned by scale(). More... | |
using | Workspace = PackedBasisWorkspace2d |
The type returned by makeWorkspace(). More... | |
using | IndexRange = PackedIndexRange< packing > |
The type returned by getIndices(). More... | |
Public Member Functions | |
PackedBasis2d (Basis1d const &basis1d) | |
Construct from a 1-d basis that will be used for both x and y. More... | |
template<typename ... Args> | |
PackedBasis2d (Args &&...args) | |
Construct by forwarding all arguments to the 1-d basis constructor. More... | |
PackedBasis2d (PackedBasis2d const &)=default | |
Default copy constructor. More... | |
PackedBasis2d (PackedBasis2d &&)=default | |
Default move constructor. More... | |
PackedBasis2d & | operator= (PackedBasis2d const &)=default |
Default copy assignment. More... | |
PackedBasis2d & | operator= (PackedBasis2d &&)=default |
Default move assignment. More... | |
std::size_t | getOrder () const noexcept |
Return the maximum order of the basis. More... | |
std::size_t | size () const noexcept |
Return the number of basis functions. More... | |
Scaled | scaled (Scaling2d const &first) const |
Return a scaled basis that delegates to a copy of this . More... | |
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. More... | |
IndexRange | getIndices () const noexcept |
Return a range of iterators that dereference to Index2d. More... | |
Workspace | makeWorkspace () const |
Allocate a workspace that can be passed to sumWith() and fill() to avoid repeated memory allocations. More... | |
template<typename Vector > | |
double | sumWith (geom::Point2D const &point, Vector const &coefficients, Workspace &workspace, SumMode mode=SumMode::FAST) const |
Evaluate a basis expansion with the given coefficients. More... | |
template<typename Vector > | |
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). More... | |
template<typename Vector > | |
void | fill (geom::Point2D const &point, Vector &&basis, Workspace &workspace) const |
Evaluate the basis at a given point. More... | |
template<typename Vector > | |
void | fill (geom::Point2D const &point, Vector &&basis) const |
Evaluate the basis at a given point (internal workspace version). More... | |
Static Public Member Functions | |
static constexpr std::size_t | computeSize (std::size_t order) |
Return the size of a PackedBasis with the given order. More... | |
A Basis2d formed from the product of a Basis1d for each of x and y, truncated at the sum of their orders.
If \(B_n(x)\) are the basis functions for the nested Basis1d, the basis functions of a PackedBasis2d with order \(N\) are \(B_m(x)B_n(y)\) for all combinations with \(m + n \le N\).
The ordering of the products of 1-d basis functions in this 2-d basis is defined by the PackedIndexRange class, which is accessible as the PackedBasis2d::IndexRange. Note that while PackedBasis2d uses this ordering, Basis2d objects in general are not required to.
Definition at line 75 of file PackedBasis2d.h.
using lsst::geom::polynomials::PackedBasis2d< Basis1d, packing >::Function = Function2d<PackedBasis2d> |
A Function2d object that uses this basis.
Definition at line 79 of file PackedBasis2d.h.
using lsst::geom::polynomials::PackedBasis2d< Basis1d, packing >::IndexRange = PackedIndexRange<packing> |
The type returned by getIndices().
Definition at line 88 of file PackedBasis2d.h.
using lsst::geom::polynomials::PackedBasis2d< Basis1d, packing >::Scaled = ScaledBasis2d<PackedBasis2d> |
The type returned by scale().
Definition at line 82 of file PackedBasis2d.h.
using lsst::geom::polynomials::PackedBasis2d< Basis1d, packing >::Workspace = PackedBasisWorkspace2d |
The type returned by makeWorkspace().
Definition at line 85 of file PackedBasis2d.h.
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inlineexplicit |
Construct from a 1-d basis that will be used for both x and y.
Definition at line 94 of file PackedBasis2d.h.
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inlineexplicit |
Construct by forwarding all arguments to the 1-d basis constructor.
Definition at line 98 of file PackedBasis2d.h.
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default |
Default copy constructor.
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default |
Default move constructor.
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inlinestaticconstexpr |
Return the size of a PackedBasis with the given order.
Definition at line 91 of file PackedBasis2d.h.
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inline |
Evaluate the basis at a given point (internal workspace version).
Definition at line 239 of file PackedBasis2d.h.
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inline |
Evaluate the basis at a given point.
[in] | point | Point at which to evaluate the basis functions. |
[out] | basis | Flattened output vector. See Basis1d::fill more information. |
[in] | workspace | Workspace object returned by makeWorkspace(). |
coefficients[n]
does, and provides basic exception safety if it does. Definition at line 228 of file PackedBasis2d.h.
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inlinenoexcept |
Return a range of iterators that dereference to Index2d.
This is the recommended way to interpret the packed coefficients and basis functions utilized by PackedBasis2d; for example,
See PackedIndexIterator for documentation of the actual order.
Definition at line 155 of file PackedBasis2d.h.
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inlinenoexcept |
Return the maximum order of the basis.
Definition at line 113 of file PackedBasis2d.h.
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inline |
Return the flattened index of the basis function with the given x and y orders.
Definition at line 129 of file PackedBasis2d.h.
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inline |
Allocate a workspace that can be passed to sumWith() and fill() to avoid repeated memory allocations.
Definition at line 160 of file PackedBasis2d.h.
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default |
Default move assignment.
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default |
Default copy assignment.
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inline |
Return a scaled basis that delegates to a copy of this
.
The scaled basis will transform all points by the given scaling before evaluating the basis functions in the same way as this
.
Definition at line 124 of file PackedBasis2d.h.
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inlinenoexcept |
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inline |
Evaluate a basis expansion with the given coefficients (internal workspace version).
Definition at line 210 of file PackedBasis2d.h.
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inline |
Evaluate a basis expansion with the given coefficients.
If the 1-d basis elements are \(B_n(x)\) and the given coefficients are a vector \(a_{p, q}\), this computes
\[ \sum_{p = 0, q = 0}^{p + q \le N} a_{p,q} B_{p}(x) B_{q}(y) \]
[in] | point | Point at which to evaluate the expansion. |
[in] | coefficients | Flattened coefficients vector. See Basis1d::sumWith for more information. |
[in] | workspace | Workspace object returned by makeWorkspace(). |
[in] | mode | Enum indicating the tradeoff to make between speed and numerical precision. |
coefficients[n]
does, and provides the same exception safety as it if it does. Definition at line 182 of file PackedBasis2d.h.