common_math.h File Reference

Common math functions. More...

#include <array>
#include <vector>
#include <limits>
#include <Kokkos_Core.hpp>
#include "common_typedef.h"

Go to the source code of this file.

Functions
template<uint32_t N>
KOKKOS_INLINE_FUNCTION rtype	dot (const rtype *a, const rtype *b)
	Compute the dot product of two arrays.
template<>
KOKKOS_INLINE_FUNCTION rtype	dot< 2 > (const rtype *a, const rtype *b)
template<>
KOKKOS_INLINE_FUNCTION rtype	dot< 3 > (const rtype *a, const rtype *b)
template<uint32_t N>
KOKKOS_INLINE_FUNCTION rtype	norm_2 (const rtype *v)
	Compute the 2-norm of a vector.
template<>
KOKKOS_INLINE_FUNCTION rtype	norm_2< 2 > (const rtype *v)
template<>
KOKKOS_INLINE_FUNCTION rtype	norm_2< 3 > (const rtype *v)
template<uint32_t N>
KOKKOS_INLINE_FUNCTION void	unit (const rtype *v, rtype *u)
	Compute the unit vector of a vector.
template<>
KOKKOS_INLINE_FUNCTION void	unit< 2 > (const rtype *v, rtype *u)
template<>
KOKKOS_INLINE_FUNCTION void	unit< 3 > (const rtype *v, rtype *u)
KOKKOS_INLINE_FUNCTION void	tangent_basis (const rtype *n, rtype *t1, rtype *t2)
	Unit tangents completing the unit normal n to an orthonormal, right-handed basis: (n, t1) in 2D, (n, t1, t2) in 3D. In 2D, t1 = (-n_y, n_x) and t2 is not written.
KOKKOS_INLINE_FUNCTION void	transpose (const rtype *A, rtype *AT, const uint16_t m, const uint16_t n)
	Transpose a matrix. Only intended for use with small matrices within kernels.
template<uint32_t N>
KOKKOS_INLINE_FUNCTION void	invert_matrix (const rtype *A, rtype *A_inv)
	Invert a matrix. Will be instantiated for 2x2 and 3x3 matrices.
template<>
KOKKOS_INLINE_FUNCTION void	invert_matrix< 2 > (const rtype *A, rtype *A_inv)
template<>
KOKKOS_INLINE_FUNCTION void	invert_matrix< 3 > (const rtype *A, rtype *A_inv)
template<uint32_t N>
KOKKOS_INLINE_FUNCTION void	gemv (const rtype *A, const rtype *x, rtype *y)
	General matrix-vector multiplication. Will be instantiated for 2x2 and 3x3 matrices.
template<>
KOKKOS_INLINE_FUNCTION void	gemv< 2 > (const rtype *A, const rtype *x, rtype *y)
template<>
KOKKOS_INLINE_FUNCTION void	gemv< 3 > (const rtype *A, const rtype *x, rtype *y)
KOKKOS_INLINE_FUNCTION void	gemm (const rtype *A, const rtype *B, rtype *C, const uint16_t m, const uint16_t n, const uint16_t p, const uint16_t q, const bool tA, const bool tB, const bool print_debug=false)
	General matrix-matrix multiplication. Only intended for use with small matrices within kernels.
KOKKOS_INLINE_FUNCTION void	QR_householder_noQ (const rtype *A, rtype *R, const uint16_t m, const uint16_t n)
	Compute the R part of the QR decomposition of a matrix.
KOKKOS_INLINE_FUNCTION void	forward_substitution (const rtype *L, const rtype *B, rtype *X, const uint16_t m, const uint16_t n, const uint16_t p, const bool tL, const bool tB)
	Perform forward substitution to solve a lower triangular system.
KOKKOS_INLINE_FUNCTION void	back_substitution (const rtype *U, const rtype *B, rtype *X, const uint16_t m, const uint16_t n, const uint16_t p, const bool tU, const bool tB)
	Perform back substitution to solve an upper triangular system.
template<uint32_t N>
KOKKOS_INLINE_FUNCTION rtype	triangle_area (const rtype *v0, const rtype *v1, const rtype *v2)
	Compute the area of a triangle from its vertices.
template<>
KOKKOS_INLINE_FUNCTION rtype	triangle_area< 2 > (const rtype *v0, const rtype *v1, const rtype *v2)
KOKKOS_INLINE_FUNCTION void	triangle_J (const rtype *v0, const rtype *v1, const rtype *v2, rtype *J)
	Get the transformation matrix into a triangle's local coordinates.
KOKKOS_INLINE_FUNCTION void	tetrahedron_J (const rtype *v0, const rtype *v1, const rtype *v2, const rtype *v3, rtype *J)
	Get the transformation matrix into a tetrahedron's local coordinates.
template<uint32_t N>
std::array< rtype, N >	max_array (Kokkos::View< rtype ** > a)
	Compute the maximum of each element along the first dimension of a.
template<uint32_t N>
std::array< rtype, N >	min_array (Kokkos::View< rtype ** > a)
	Compute the minimum of each element along the first dimension of a.

Detailed Description

Common math functions.

Author

Matthew Bonanni (mbona.nosp@m.nni0.nosp@m.01@gm.nosp@m.ail..nosp@m.com)

Version

0.1

Date

2023-12-18

Copyright

Copyright (c) 2023 Matthew Bonanni

Function Documentation

back_substitution()

KOKKOS_INLINE_FUNCTION void back_substitution	(	const rtype *	U,
		const rtype *	B,
		rtype *	X,
		const uint16_t	m,
		const uint16_t	n,
		const uint16_t	p,
		const bool	tU,
		const bool	tB
	)

Perform back substitution to solve an upper triangular system.

Parameters

U	Upper triangular matrix [m x n].
B	Right-hand side matrix [n x p].
X	Solution matrix [m x p].
m	Number of rows in U.
n	Number of columns in U.
p	Number of columns in B.
tU	Transpose U.
tB	Transpose B.

dot()

template<uint32_t N>

KOKKOS_INLINE_FUNCTION rtype dot	(	const rtype *	a,
		const rtype *	b
	)

Compute the dot product of two arrays.

Parameters

a	First array.
b	Second array.

Template Parameters

N	Length of the arrays.

Returns

Dot product.

dot< 2 >()

template<>

KOKKOS_INLINE_FUNCTION rtype dot< 2 >	(	const rtype *	a,
		const rtype *	b
	)

dot< 3 >()

template<>

KOKKOS_INLINE_FUNCTION rtype dot< 3 >	(	const rtype *	a,
		const rtype *	b
	)

forward_substitution()

KOKKOS_INLINE_FUNCTION void forward_substitution	(	const rtype *	L,
		const rtype *	B,
		rtype *	X,
		const uint16_t	m,
		const uint16_t	n,
		const uint16_t	p,
		const bool	tL,
		const bool	tB
	)

Perform forward substitution to solve a lower triangular system.

Parameters

L	Lower triangular matrix [m x n].
B	Right-hand side matrix [n x p].
X	Solution matrix [m x p].
m	Number of rows in L.
n	Number of columns in L.
p	Number of columns in B.
tL	Transpose L.
tB	Transpose B.

gemm()

KOKKOS_INLINE_FUNCTION void gemm	(	const rtype *	A,
		const rtype *	B,
		rtype *	C,
		const uint16_t	m,
		const uint16_t	n,
		const uint16_t	p,
		const uint16_t	q,
		const bool	tA,
		const bool	tB,
		const bool	print_debug = false
	)

General matrix-matrix multiplication. Only intended for use with small matrices within kernels.

Parameters

A	Matrix.
B	Matrix.
C	Resulting matrix.
m	Number of rows in A.
n	Number of columns in A.
p	Number of rows in B.
q	Number of columns in B.
tA	Transpose A.
tB	Transpose B.
print_debug	Print the operands and result.

gemv()

template<uint32_t N>

KOKKOS_INLINE_FUNCTION void gemv	(	const rtype *	A,
		const rtype *	x,
		rtype *	y
	)

General matrix-vector multiplication. Will be instantiated for 2x2 and 3x3 matrices.

Parameters

A	Matrix.
x	Vector.
y	Resulting vector.

gemv< 2 >()

template<>

KOKKOS_INLINE_FUNCTION void gemv< 2 >	(	const rtype *	A,
		const rtype *	x,
		rtype *	y
	)

gemv< 3 >()

template<>

KOKKOS_INLINE_FUNCTION void gemv< 3 >	(	const rtype *	A,
		const rtype *	x,
		rtype *	y
	)

invert_matrix()

template<uint32_t N>

KOKKOS_INLINE_FUNCTION void invert_matrix	(	const rtype *	A,
		rtype *	A_inv
	)

Invert a matrix. Will be instantiated for 2x2 and 3x3 matrices.

Parameters

A	Matrix to invert.
A_inv	Inverted matrix.

invert_matrix< 2 >()

template<>

KOKKOS_INLINE_FUNCTION void invert_matrix< 2 >	(	const rtype *	A,
		rtype *	A_inv
	)

invert_matrix< 3 >()

template<>

KOKKOS_INLINE_FUNCTION void invert_matrix< 3 >	(	const rtype *	A,
		rtype *	A_inv
	)

max_array()

template<uint32_t N>

std::array< rtype, N > max_array

(

Kokkos::View< rtype ** >

a

)

Compute the maximum of each element along the first dimension of a.

Parameters

a

Array.

Returns

Maximum of each element.

min_array()

template<uint32_t N>

std::array< rtype, N > min_array

(

Kokkos::View< rtype ** >

a

)

Compute the minimum of each element along the first dimension of a.

Parameters

a

Array.

Returns

Minimum of each element.

norm_2()

template<uint32_t N>

KOKKOS_INLINE_FUNCTION rtype norm_2

(

const rtype *

v

)

Compute the 2-norm of a vector.

Parameters

v

Vector.

Template Parameters

N	Length of the vector.

Returns

Norm.

norm_2< 2 >()

template<>

KOKKOS_INLINE_FUNCTION rtype norm_2< 2 >

(

const rtype *

v

)

norm_2< 3 >()

template<>

KOKKOS_INLINE_FUNCTION rtype norm_2< 3 >

(

const rtype *

v

)

QR_householder_noQ()

KOKKOS_INLINE_FUNCTION void QR_householder_noQ	(	const rtype *	A,
		rtype *	R,
		const uint16_t	m,
		const uint16_t	n
	)

Compute the R part of the QR decomposition of a matrix.

Parameters

A	Matrix.
R	Upper triangular matrix.
m	Number of rows.
n	Number of columns.

tangent_basis()

KOKKOS_INLINE_FUNCTION void tangent_basis	(	const rtype *	n,
		rtype *	t1,
		rtype *	t2
	)

Unit tangents completing the unit normal n to an orthonormal, right-handed basis: (n, t1) in 2D, (n, t1, t2) in 3D. In 2D, t1 = (-n_y, n_x) and t2 is not written.

Parameters

n	Unit normal.
t1	First tangent.
t2	Second tangent (3D only).

tetrahedron_J()

KOKKOS_INLINE_FUNCTION void tetrahedron_J	(	const rtype *	v0,
		const rtype *	v1,
		const rtype *	v2,
		const rtype *	v3,
		rtype *	J
	)

Get the transformation matrix into a tetrahedron's local coordinates.

Parameters

v0	Coordinates of the first vertex.
v1	Coordinates of the second vertex.
v2	Coordinates of the third vertex.
v3	Coordinates of the fourth vertex.
J	Transformation matrix.

transpose()

KOKKOS_INLINE_FUNCTION void transpose	(	const rtype *	A,
		rtype *	AT,
		const uint16_t	m,
		const uint16_t	n
	)

Transpose a matrix. Only intended for use with small matrices within kernels.

Parameters

A	Matrix
AT	Transposed matrix
m	Number of rows in A
n	Number of columns in A

triangle_area()

template<uint32_t N>

KOKKOS_INLINE_FUNCTION rtype triangle_area	(	const rtype *	v0,
		const rtype *	v1,
		const rtype *	v2
	)

Compute the area of a triangle from its vertices.

Parameters

v0	Coordinates of the first vertex.
v1	Coordinates of the second vertex.
v2	Coordinates of the third vertex.

Returns

Area of the triangle.

triangle_area< 2 >()

template<>

KOKKOS_INLINE_FUNCTION rtype triangle_area< 2 >	(	const rtype *	v0,
		const rtype *	v1,
		const rtype *	v2
	)

triangle_J()

KOKKOS_INLINE_FUNCTION void triangle_J	(	const rtype *	v0,
		const rtype *	v1,
		const rtype *	v2,
		rtype *	J
	)

Get the transformation matrix into a triangle's local coordinates.

Parameters

v0	Coordinates of the first vertex.
v1	Coordinates of the second vertex.
v2	Coordinates of the third vertex.
J	Transformation matrix.

unit()

template<uint32_t N>

KOKKOS_INLINE_FUNCTION void unit	(	const rtype *	v,
		rtype *	u
	)

Compute the unit vector of a vector.

Parameters

v	Vector.
u	Unit vector.

Template Parameters

N	Length of the vector.

unit< 2 >()

template<>

KOKKOS_INLINE_FUNCTION void unit< 2 >	(	const rtype *	v,
		rtype *	u
	)

unit< 3 >()

template<>

KOKKOS_INLINE_FUNCTION void unit< 3 >	(	const rtype *	v,
		rtype *	u
	)