Provides solver quadrature, indexing, RNG, and radial-boundary transforms. More...

#include "math_util.hpp"

Collaboration diagram for orb5x::MathUtil:

Public Types
using	HostRealView = Kokkos::View< Real *, Kokkos::LayoutStride, Kokkos::HostSpace >
	Strided host vector accepted by quadrature helpers.

Static Public Member Functions
static int	computeMapping2to1 (int i, int j, int nj)
	Flatten a one-based two-dimensional index.

static int	computeMapping2to1_0 (int i, int j, int nj)
	Flatten a zero-based two-dimensional index.

template<typename PointsView , typename WeightsView >
static void	computeQuadraturePoints (Real x1, Real x2, PointsView points, WeightsView weights, int nbq, int method)
	Fill quadrature abscissae and weights on interval \([x_1,x_2]\).

static void	computeVelocitySpaceDiscretization (Real dx, int nqw, int nqa, Real lw, int &nw, int &na)
	Choose velocity-magnitude and pitch grid counts consistent with spatial spacing.

static Real	gaussian_number ()
	Draw a standard-normal variate via Box–Muller.

static Real	plusminus ()
	Draw a random sign.

static void	seed (unsigned int s)
	Reset the utility random stream.

static Real	uniform ()
	Draw a unit-uniform variate.

Static Public Attributes
static constexpr Real	coeffsc [3] = {5.0, -4.0, -1.0}
	Cubic endpoint constraint coefficients.

static constexpr Real	coeffsq [2] = {1.0, -1.0}
	Quadratic endpoint constraint coefficients.

static constexpr Complex	CPONE = Complex(1.0, 0.0)
	Complex multiplicative identity.

static constexpr Complex	CPZERO = Complex(0.0, 0.0)
	Complex additive identity.

static constexpr int	QUAD_EQUID = 2
	Equidistant Newton–Cotes-like selector.

static constexpr int	QUAD_GAUSS = 1
	Gauss–Legendre quadrature selector.

static constexpr Real	Tlc [3][3]
	Left cubic boundary transform.

static constexpr Real	Tlc_deboor [3][3]
	Left cubic de Boor endpoint conversion.

static constexpr Real	Tlc_inv [3][3]
	Inverse left cubic transform.

static constexpr Real	Tlc_tr [3][3]
	Transpose of left cubic transform.

static constexpr Real	Tlq [2][2]
	Left quadratic boundary transform.

static constexpr Real	Tlq_inv [2][2]
	Inverse left quadratic transform.

static constexpr Real	Tlq_tr [2][2]
	Transpose of left quadratic transform.

static constexpr Real	Trc [3][3]
	Right cubic boundary transform.

static constexpr Real	Trc_deboor [3][3]
	Right cubic de Boor endpoint conversion.

static constexpr Real	Trc_inv [3][3]
	Inverse right cubic transform.

static constexpr Real	Trc_tr [3][3]
	Transpose of right cubic transform.

static constexpr Real	Trq [2][2]
	Right quadratic boundary transform.

static constexpr Real	Trq_inv [2][2]
	Inverse right quadratic transform.

static constexpr Real	Trq_tr [2][2]
	Transpose of right quadratic transform.

Detailed Description

Provides solver quadrature, indexing, RNG, and radial-boundary transforms.

Boundary matrices are transcribed so M_cpp[i][j] equals Fortran M(i+1,j+1) despite the languages' different initializer/reshape ordering.

Fortran reference solver/MathUtil.F90, module MathUtil.

Member Typedef Documentation

◆ HostRealView

using orb5x::MathUtil::HostRealView = Kokkos::View<Real*, Kokkos::LayoutStride, Kokkos::HostSpace>

Strided host vector accepted by quadrature helpers.

Member Function Documentation

◆ computeMapping2to1()

static int orb5x::MathUtil::computeMapping2to1	(	int	i,
		int	j,
		int	nj
	)

static

Flatten a one-based two-dimensional index.

Parameters

[in]	i	One-based first index.
[in]	j	One-based second index.
[in]	nj	Extent of the second dimension.

Returns: One-based flattened index j + nj*(i-1).

◆ computeMapping2to1_0()

static int orb5x::MathUtil::computeMapping2to1_0	(	int	i,
		int	j,
		int	nj
	)

static

Flatten a zero-based two-dimensional index.

Parameters

[in]	i	Zero-based first index.
[in]	j	Zero-based second index.
[in]	nj	Extent of the second dimension.

Returns: Zero-based flattened index j + nj*i.

◆ computeQuadraturePoints()

template<typename PointsView , typename WeightsView >

static void orb5x::MathUtil::computeQuadraturePoints	(	Real	x1,
		Real	x2,
		PointsView	points,
		WeightsView	weights,
		int	nbq,
		int	method
	)

inlinestatic

Fill quadrature abscissae and weights on interval \([x_1,x_2]\).

Parameters

[in]	x1	Lower integration bound.
[in]	x2	Upper integration bound.
[out]	points	View with at least `nbq` entries.
[out]	weights	Corresponding integration weights.
[in]	nbq	Number of quadrature points.
[in]	method	`QUAD_GAUSS` or `QUAD_EQUID`.

◆ computeVelocitySpaceDiscretization()

static void orb5x::MathUtil::computeVelocitySpaceDiscretization	(	Real	dx,
		int	nqw,
		int	nqa,
		Real	lw,
		int &	nw,
		int &	na
	)

static

Choose velocity-magnitude and pitch grid counts consistent with spatial spacing.

Parameters

[in]	dx	Spatial grid scale entering resolution estimates.
[in]	nqw	Quadrature order in speed.
[in]	nqa	Quadrature order in pitch angle.
[in]	lw	Maximum normalized speed coordinate.
[out]	nw	Number of speed intervals/points selected.
[out]	na	Number of pitch intervals/points selected.

◆ gaussian_number()

static Real orb5x::MathUtil::gaussian_number ( )

static

Draw a standard-normal variate via Box–Muller.

Returns: Dimensionless pseudorandom value with zero mean and unit variance.

◆ plusminus()

static Real orb5x::MathUtil::plusminus ( )

static

Draw a random sign.

Returns: -1 or +1 with equal probability.

◆ seed()

static void orb5x::MathUtil::seed ( unsigned int s )

static

Reset the utility random stream.

Parameters

[in] s Unsigned engine seed.

◆ uniform()

static Real orb5x::MathUtil::uniform ( )

static

Draw a unit-uniform variate.

Returns: Dimensionless pseudorandom value in [0,1).

Member Data Documentation

◆ coeffsc

constexpr Real orb5x::MathUtil::coeffsc[3] = {5.0, -4.0, -1.0}

staticconstexpr

Cubic endpoint constraint coefficients.

◆ coeffsq

constexpr Real orb5x::MathUtil::coeffsq[2] = {1.0, -1.0}

staticconstexpr

Quadratic endpoint constraint coefficients.

◆ CPONE

constexpr Complex orb5x::MathUtil::CPONE = Complex(1.0, 0.0)

staticconstexpr

Complex multiplicative identity.

◆ CPZERO

constexpr Complex orb5x::MathUtil::CPZERO = Complex(0.0, 0.0)

staticconstexpr

Complex additive identity.

◆ QUAD_EQUID

constexpr int orb5x::MathUtil::QUAD_EQUID = 2

staticconstexpr

Equidistant Newton–Cotes-like selector.

◆ QUAD_GAUSS

constexpr int orb5x::MathUtil::QUAD_GAUSS = 1

staticconstexpr

Gauss–Legendre quadrature selector.

◆ Tlc

constexpr Real orb5x::MathUtil::Tlc[3][3]

staticconstexpr

Initial value:

= {
    { 6.0,  0.0,  0.0},
    {-4.0,  1.0,  0.0},
    {-1.0,  0.0,  1.0}
  }

Left cubic boundary transform.

◆ Tlc_deboor

constexpr Real orb5x::MathUtil::Tlc_deboor[3][3]

staticconstexpr

Initial value:

= {
    {1.0/6.0, 0.0,     0.0},
    {2.0/3.0, 2.0/3.0, 0.0},
    {1.0/6.0, 1.0/3.0, 1.0}
  }

Left cubic de Boor endpoint conversion.

◆ Tlc_inv

constexpr Real orb5x::MathUtil::Tlc_inv[3][3]

staticconstexpr

Initial value:

= {
    {1.0/6.0, 0.0, 0.0},
    {2.0/3.0, 1.0, 0.0},
    {1.0/6.0, 0.0, 1.0}
  }

Inverse left cubic transform.

◆ Tlc_tr

constexpr Real orb5x::MathUtil::Tlc_tr[3][3]

staticconstexpr

Initial value:

= {
    { 6.0, -4.0, -1.0},
    { 0.0,  1.0,  0.0},
    { 0.0,  0.0,  1.0}
  }

Transpose of left cubic transform.

◆ Tlq

constexpr Real orb5x::MathUtil::Tlq[2][2]

staticconstexpr

Initial value:

= {
    { 2.0,  0.0},
    {-1.0,  1.0}
  }

Left quadratic boundary transform.

◆ Tlq_inv

constexpr Real orb5x::MathUtil::Tlq_inv[2][2]

staticconstexpr

Initial value:

= {
    {0.5, 0.0},
    {0.5, 1.0}
  }

Inverse left quadratic transform.

◆ Tlq_tr

constexpr Real orb5x::MathUtil::Tlq_tr[2][2]

staticconstexpr

Initial value:

= {
    { 2.0, -1.0},
    { 0.0,  1.0}
  }

Transpose of left quadratic transform.

◆ Trc

constexpr Real orb5x::MathUtil::Trc[3][3]

staticconstexpr

Initial value:

= {
    {1.0,  0.0, -1.0},
    {0.0,  1.0, -4.0},
    {0.0,  0.0,  6.0}
  }

Right cubic boundary transform.

◆ Trc_deboor

constexpr Real orb5x::MathUtil::Trc_deboor[3][3]

staticconstexpr

Initial value:

= {
    {1.0,     1.0/3.0, 1.0/6.0},
    {0.0,     2.0/3.0, 2.0/3.0},
    {0.0,     0.0,     1.0/6.0}
  }

Right cubic de Boor endpoint conversion.

◆ Trc_inv

constexpr Real orb5x::MathUtil::Trc_inv[3][3]

staticconstexpr

Initial value:

= {
    {1.0, 0.0, 1.0/6.0},
    {0.0, 1.0, 2.0/3.0},
    {0.0, 0.0, 1.0/6.0}
  }

Inverse right cubic transform.

◆ Trc_tr

constexpr Real orb5x::MathUtil::Trc_tr[3][3]

staticconstexpr

Initial value:

= {
    { 1.0,  0.0,  0.0},
    { 0.0,  1.0,  0.0},
    {-1.0, -4.0,  6.0}
  }

Transpose of right cubic transform.

◆ Trq

constexpr Real orb5x::MathUtil::Trq[2][2]

staticconstexpr

Initial value:

= {
    {1.0, -1.0},
    {0.0,  2.0}
  }

Right quadratic boundary transform.

◆ Trq_inv

constexpr Real orb5x::MathUtil::Trq_inv[2][2]

staticconstexpr

Initial value:

= {
    {1.0, 0.5},
    {0.0, 0.5}
  }

Inverse right quadratic transform.

◆ Trq_tr

constexpr Real orb5x::MathUtil::Trq_tr[2][2]

staticconstexpr

Initial value:

= {
    { 1.0,  0.0},
    {-1.0,  2.0}
  }

Transpose of right quadratic transform.

The documentation for this class was generated from the following file:

math_util.hpp

Public Types

Static Public Member Functions

Static Public Attributes

Detailed Description

Member Typedef Documentation

◆ HostRealView

Member Function Documentation

◆ computeMapping2to1()

◆ computeMapping2to1_0()

◆ computeQuadraturePoints()

◆ computeVelocitySpaceDiscretization()

◆ gaussian_number()

◆ plusminus()

◆ seed()

◆ uniform()

Member Data Documentation

◆ coeffsc

◆ coeffsq

◆ CPONE

◆ CPZERO

◆ QUAD_EQUID

◆ QUAD_GAUSS

◆ Tlc

◆ Tlc_deboor

◆ Tlc_inv

◆ Tlc_tr

◆ Tlq

◆ Tlq_inv

◆ Tlq_tr

◆ Trc

◆ Trc_deboor

◆ Trc_inv

◆ Trc_tr

◆ Trq

◆ Trq_inv

◆ Trq_tr