LSSTApplications
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LSSTDataManagementBasePackage
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A basis for 1-d series expansions defined by a recurrence relation. More...
#include <RecurrenceBasis1d.h>
Public Types | |
using | Function = Function1d< RecurrenceBasis1d > |
A Function1d object that uses this basis. More... | |
using | Scaled = ScaledBasis1d< RecurrenceBasis1d > |
The type returned by scale(). More... | |
Public Member Functions | |
RecurrenceBasis1d (std::size_t order) noexcept | |
Construct a basis with the given order (inclusive). More... | |
RecurrenceBasis1d (RecurrenceBasis1d const &)=default | |
Default copy constructor. More... | |
RecurrenceBasis1d (RecurrenceBasis1d &&)=default | |
Default move constructor. More... | |
RecurrenceBasis1d & | operator= (RecurrenceBasis1d const &)=default |
Default copy assignment. More... | |
RecurrenceBasis1d & | operator= (RecurrenceBasis1d &&)=default |
Default move assignment. More... | |
std::size_t | getOrder () const noexcept |
Return the order of the basis. More... | |
std::size_t | size () const noexcept |
Return the number of elements in the basis. More... | |
Scaled | scaled (Scaling1d const &scaling) const noexcept |
Return a scaled basis with the same order and recurrence. More... | |
template<typename Vector > | |
double | sumWith (double x, Vector const &coefficients, SumMode mode=SumMode::FAST) const |
Evaluate a basis expansion with the given coefficients. More... | |
template<typename Vector > | |
void | fill (double x, Vector &&basis) const |
Evaluate the basis at a given point. More... | |
A basis for 1-d series expansions defined by a recurrence relation.
The recurrence relations utilized by RecurrenceBasis1d must have the following form:
\[ B_{n+1}(x) = R(x, n, B_n(x), B_{n-1}(x)) \]
with explicit expressions for \(B_0(x)\) and \(B_1(x)\) also given. This includes all special polynomials (e.g. Chebyshev, Legendre, Hermite, Laguerre) and products of special polynomials with their natural weight functions (e.g. Gauss-Hermite functions). The template parameter must be a model of the Recurrence concept.
RecurrenceBasis1d is a model of the Basis1d concept.
Definition at line 85 of file RecurrenceBasis1d.h.
using lsst::geom::polynomials::RecurrenceBasis1d< Recurrence >::Function = Function1d<RecurrenceBasis1d> |
A Function1d object that uses this basis.
Definition at line 89 of file RecurrenceBasis1d.h.
using lsst::geom::polynomials::RecurrenceBasis1d< Recurrence >::Scaled = ScaledBasis1d<RecurrenceBasis1d> |
The type returned by scale().
Definition at line 92 of file RecurrenceBasis1d.h.
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inlineexplicitnoexcept |
Construct a basis with the given order (inclusive).
Definition at line 95 of file RecurrenceBasis1d.h.
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default |
Default copy constructor.
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default |
Default move constructor.
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inline |
Evaluate the basis at a given point.
[in] | x | Point at which to evaluate the basis functions. |
[out] | basis | Output vector. See Basis1d::fill more information. |
coefficients[n]
does, and provides basic exception safety if it does. Definition at line 187 of file RecurrenceBasis1d.h.
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inlinenoexcept |
Return the order of the basis.
Definition at line 112 of file RecurrenceBasis1d.h.
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default |
Default copy assignment.
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default |
Default move assignment.
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inlinenoexcept |
Return a scaled basis with the same order and recurrence.
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 123 of file RecurrenceBasis1d.h.
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inlinenoexcept |
Return the number of elements in the basis.
Definition at line 115 of file RecurrenceBasis1d.h.
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inline |
Evaluate a basis expansion with the given coefficients.
If the basis elements are \(B_n(x)\) and the given coefficients are a vector \(a_n\), this computes
\[ \sum_{n = 0}^{n \le N} a_n B_n(x) \]
[in] | x | Point at which to evaluate the expansion. |
[in] | coefficients | Coefficients vector. See Basis1d::sumWith for more information. |
[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 146 of file RecurrenceBasis1d.h.