Classes | |
struct | FacetData |
data for specifying a faceted weight. More... | |
Enumerations | |
enum | Kernel { B4, SQUARE, EPANECHNIKOV, POLYRAMP, INVSQRT, COULOMB, STEP } |
Kernel types. More... | |
enum | Geometry { ELLIPTIC, TENSOR, FACETED } |
Geometry types. More... | |
Functions | |
double | sign (double x) |
scalar sign function. More... | |
double | unit_step (double x) |
scalar step function More... | |
double | b4 (double x) |
scalar cubic b-spline. More... | |
double | db4 (double x) |
scalar cubic b-spline derivative. More... | |
double | ddb4 (double x) |
scalar cubic b-spline second derivative. More... | |
double | ib4 (double x) |
scalar cubic b-spline anti-derivative. More... | |
double | b4lh (double x) |
scalar left half cubic b-spline. More... | |
double | b4rh (double x) |
scalar right half cubic b-spline. More... | |
double | epanechnikov (double x) |
scalar epanechnikov kernel. More... | |
double | depanechnikov (double x) |
scalar epanechnikov kernel derivative. More... | |
double | ddepanechnikov (double x) |
scalar epanechnikov kernel second derivative. More... | |
double | square (double x) |
scalar square kernel. More... | |
double | dsquare (double x) |
scalar square kernel derivative. More... | |
double | ddsquare (double x) |
scalar square kernel second derivative. More... | |
double | polyramp (double x) |
scalar smooth ramp for faceted weight. More... | |
double | dpolyramp (double x) |
scalar smooth ramp for faceted weight derivative. More... | |
double | ddpolyramp (double x) |
scalar smooth ramp for faceted weight derivative. More... | |
double | invsqrt (double x) |
inverse square root kernel. More... | |
double | dinvsqrt (double x) |
derivative of inverse square root kernel. More... | |
double | ddinvsqrt (double x) |
second derivative of inverse square root kernel. More... | |
double | coulomb (double x) |
coulomb weight. More... | |
double | dcoulomb (double x) |
coulomb weight derivative. More... | |
double | ddcoulomb (double x) |
coulomb weight second derivative. More... | |
double | step (double x) |
step weight. More... | |
double | dstep (double x) |
step weight derivative. More... | |
double | ddstep (double x) |
step weight second derivative. More... | |
double | kernel (const Kernel kern, double x) |
General kernel function. More... | |
template<int dim> | |
double | elliptic (Wonton::Point< dim > const &x, Wonton::Point< dim > const &y, std::array< double, dim > const &h) |
generic elliptically symmetric weight function argument. More... | |
template<int dim> | |
std::array< double, dim > | tensor (Wonton::Point< dim > const &x, Wonton::Point< dim > const &y, std::array< double, dim > const &h) |
generic tensor weight function arguments. More... | |
template<int dim> | |
double | eval (Geometry const geometry, Kernel const kern, Wonton::Point< dim > const &x, Wonton::Point< dim > const &y, std::array< double, dim > const &h) |
evaluation function for elliptic or tensor product weights. More... | |
template<int dim> | |
double | faceted (Kernel const kern, Wonton::Point< dim > const &x, Wonton::Point< dim > const &y, std::vector< FacetData< dim >> const &facets, size_t nsides) |
faceted weight function More... | |
template<int dim> | |
double | eval (Geometry const geo, Kernel const kern, Wonton::Point< dim > const &x, Wonton::Point< dim > const &y, std::vector< std::vector< double >> const &vh) |
evaluation function for any weight. More... | |
Variables | |
double const | normconst [4] = { 2./3., 1./(.7 * M_PI), 1./M_PI, 1./M_PI } |
normalization constants for cubic B-spline (linear, cylindrical, and spherical). More... | |
double const | epsilon = std::numeric_limits<double>::epsilon() |
Numerical tolerance. More... | |
Enumeration Type Documentation
◆ Geometry
◆ Kernel
Function Documentation
◆ b4()
|
inline |
scalar cubic b-spline.
- Parameters
-
x given scalar
- Returns
- its value at x.
◆ b4lh()
|
inline |
scalar left half cubic b-spline.
- Parameters
-
x given scalar
- Returns
- its value at x.
◆ b4rh()
|
inline |
scalar right half cubic b-spline.
- Parameters
-
x given scalar
- Returns
- its value at x.
◆ coulomb()
|
inline |
coulomb weight.
- Parameters
-
x given scalar.
- Returns
- its value at x.
◆ db4()
|
inline |
scalar cubic b-spline derivative.
- Parameters
-
x given scalar
- Returns
- its value at x.
◆ dcoulomb()
|
inline |
coulomb weight derivative.
- Parameters
-
x given scalar.
- Returns
- its value at x.
◆ ddb4()
|
inline |
scalar cubic b-spline second derivative.
- Parameters
-
x given scalar
- Returns
- its value at x.
◆ ddcoulomb()
|
inline |
coulomb weight second derivative.
- Parameters
-
x given scalar.
- Returns
- its value at x.
◆ ddepanechnikov()
|
inline |
scalar epanechnikov kernel second derivative.
- Parameters
-
x given scalar.
- Returns
- its value at x.
◆ ddinvsqrt()
|
inline |
second derivative of inverse square root kernel.
- Parameters
-
x given scalar.
- Returns
- its value at x.
◆ ddpolyramp()
|
inline |
scalar smooth ramp for faceted weight derivative.
- Parameters
-
x given scalar.
- Returns
- its value at x.
◆ ddsquare()
|
inline |
scalar square kernel second derivative.
- Parameters
-
x given scalar.
- Returns
- its value at x.
◆ ddstep()
|
inline |
step weight second derivative.
- Parameters
-
x given scalar.
- Returns
- its value at x.
◆ depanechnikov()
|
inline |
scalar epanechnikov kernel derivative.
- Parameters
-
x given scalar.
- Returns
- its value at x.
◆ dinvsqrt()
|
inline |
derivative of inverse square root kernel.
- Parameters
-
x given scalar.
- Returns
- its value at x.
◆ dpolyramp()
|
inline |
scalar smooth ramp for faceted weight derivative.
- Parameters
-
x given scalar.
- Returns
- its value at x.
◆ dsquare()
|
inline |
scalar square kernel derivative.
- Parameters
-
x given scalar.
- Returns
- its value at x.
◆ dstep()
|
inline |
step weight derivative.
- Parameters
-
x given scalar.
- Returns
- its value at x.
◆ elliptic()
double Portage::Meshfree::Weight::elliptic | ( | Wonton::Point< dim > const & | x, |
Wonton::Point< dim > const & | y, | ||
std::array< double, dim > const & | h | ||
) |
generic elliptically symmetric weight function argument.
- Template Parameters
-
dim spatial dimension.
- Parameters
-
x first point y second point h size metric
- Returns
- sqrt(sum_i (xi - yi)^2 / hi^2)
◆ epanechnikov()
|
inline |
scalar epanechnikov kernel.
- Parameters
-
x given scalar
- Returns
- its value at x.
◆ eval() [1/2]
double Portage::Meshfree::Weight::eval | ( | Geometry const | geometry, |
Kernel const | kern, | ||
Wonton::Point< dim > const & | x, | ||
Wonton::Point< dim > const & | y, | ||
std::array< double, dim > const & | h | ||
) |
evaluation function for elliptic or tensor product weights.
- Template Parameters
-
dim spatial dimension.
- Parameters
-
geometry the geometry to consider. kern the kernel to consider. x first point y second point h size metric
- Returns
- evaluated kernel value.
◆ eval() [2/2]
double Portage::Meshfree::Weight::eval | ( | Geometry const | geo, |
Kernel const | kern, | ||
Wonton::Point< dim > const & | x, | ||
Wonton::Point< dim > const & | y, | ||
std::vector< std::vector< double >> const & | vh | ||
) |
evaluation function for any weight.
- Template Parameters
-
dim spatial dimension.
- Parameters
-
geo the geometry to consider. kern the kernel to consider. x first point. y second point. vh size matrix.
- Returns
- evaluated kernel value.
◆ faceted()
double Portage::Meshfree::Weight::faceted | ( | Kernel const | kern, |
Wonton::Point< dim > const & | x, | ||
Wonton::Point< dim > const & | y, | ||
std::vector< FacetData< dim >> const & | facets, | ||
size_t | nsides | ||
) |
faceted weight function
- Template Parameters
-
dim spatial dimension.
- Parameters
-
kern the kernel to use. x first point. y second point. facets list of facets. nsides number of sides.
- Returns
- evaluated kernel value.
◆ ib4()
|
inline |
scalar cubic b-spline anti-derivative.
- Parameters
-
x given scalar
- Returns
- its value at x.
◆ invsqrt()
|
inline |
inverse square root kernel.
- Parameters
-
x given scalar.
- Returns
- its value at x.
◆ kernel()
|
inline |
General kernel function.
- Parameters
-
kern kernel type. x given scalar.
- Returns
- related value.
◆ polyramp()
|
inline |
scalar smooth ramp for faceted weight.
- Parameters
-
x given scalar.
- Returns
- its value at x.
◆ sign()
|
inline |
scalar sign function.
- Parameters
-
x given scalar.
- Returns
- its sign.
◆ square()
|
inline |
scalar square kernel.
- Parameters
-
x given scalar.
- Returns
- its value at x.
◆ step()
|
inline |
step weight.
- Parameters
-
x given scalar.
- Returns
- its value at x.
◆ tensor()
std::array<double,dim> Portage::Meshfree::Weight::tensor | ( | Wonton::Point< dim > const & | x, |
Wonton::Point< dim > const & | y, | ||
std::array< double, dim > const & | h | ||
) |
generic tensor weight function arguments.
- Template Parameters
-
dim spatial dimension.
- Parameters
-
x first point y second point h size metric
- Returns
- [(xi - yi) / hi]_{i=0,dim-1}
◆ unit_step()
|
inline |
scalar step function
Variable Documentation
◆ epsilon
double const Portage::Meshfree::Weight::epsilon = std::numeric_limits<double>::epsilon() |
Numerical tolerance.
◆ normconst
double const Portage::Meshfree::Weight::normconst[4] = { 2./3., 1./(.7 * M_PI), 1./M_PI, 1./M_PI } |
normalization constants for cubic B-spline (linear, cylindrical, and spherical).