LSST Applications
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LSST Data Management Base Package
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A 1-d basis that transforms all input points before evaluating nested basis. More...
#include <ScaledBasis1d.h>
Public Types | |
using | Function = Function1d< ScaledBasis1d > |
A Function1d object that uses this basis. More... | |
using | Scaled = ScaledBasis1d< Nested > |
The type returned by scale(). More... | |
Public Member Functions | |
ScaledBasis1d (Nested const &nested, Scaling1d const &scaling) | |
Construct a scaled basis from a nested basis and a scaling transform. More... | |
ScaledBasis1d (std::size_t order, double min, double max) | |
Construct a basis that remaps the given interval to [-1, 1] before evaluating the nested basis. More... | |
ScaledBasis1d (ScaledBasis1d const &)=default | |
Default copy constructor. More... | |
ScaledBasis1d (ScaledBasis1d &&)=default | |
Default move constructor. More... | |
ScaledBasis1d & | operator= (ScaledBasis1d const &)=default |
Default copy assignment. More... | |
ScaledBasis1d & | operator= (ScaledBasis1d &&)=default |
Default move assignment. More... | |
Nested const & | getNested () const noexcept |
Return the nested basis. More... | |
Scaling1d const & | getScaling () const noexcept |
Return the scaling transform. More... | |
std::size_t | getOrder () const |
Return the order of the basis. More... | |
std::size_t | size () const |
Return the number of elements in the basis. More... | |
Scaled | scaled (Scaling1d const &first) const |
Return a further-scaled basis with the same order. 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 1-d basis that transforms all input points before evaluating nested basis.
If the nested basis is defined by basis functions \(B_n(x)\), the scaled basis functions are \(B_n(S(x))\), where \(S(x)\) is the scaling transform.
Both the nested basis and ScaledBasis1d itself are models of the Basis1d concept.
Definition at line 44 of file ScaledBasis1d.h.
using lsst::geom::polynomials::ScaledBasis1d< Nested >::Function = Function1d<ScaledBasis1d> |
A Function1d object that uses this basis.
Definition at line 48 of file ScaledBasis1d.h.
using lsst::geom::polynomials::ScaledBasis1d< Nested >::Scaled = ScaledBasis1d<Nested> |
The type returned by scale().
Definition at line 51 of file ScaledBasis1d.h.
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Construct a scaled basis from a nested basis and a scaling transform.
Definition at line 54 of file ScaledBasis1d.h.
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Construct a basis that remaps the given interval to [-1, 1] before evaluating the nested basis.
[in] | order | Maximum order of the basis (inclusive). |
[in] | min | Minimum point of the interval, mapped to -1. |
[in] | max | Maximum point of the interval, mapped to 1. |
This constructor is particularly useful for Chebyshev polynomials, for which most of the special functions of the basis are only active when the domain is limited to [-1, 1].
This signature requires that Nested(order) be a valid constructor.
Definition at line 73 of file ScaledBasis1d.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 146 of file ScaledBasis1d.h.
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inlinenoexcept |
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inline |
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inlinenoexcept |
Return the scaling transform.
Definition at line 94 of file ScaledBasis1d.h.
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default |
Default move assignment.
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default |
Default copy assignment.
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inline |
Return a further-scaled basis with the same order.
The scaled basis will transform all points by the given scaling before evaluating the basis functions in the same way as this
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Definition at line 108 of file ScaledBasis1d.h.
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inline |
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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 131 of file ScaledBasis1d.h.