Implementation of various linear algebra functions needed in the exponential integrators. More...

#include "exponential_linear_algebra.cuh"

Include dependency graph for exponential_linear_algebra.cu:

Functions
__device__ void	matvec_m_by_m (const int m, const double const __restrict__ A, const double const __restrict__ V, double *const __restrict__ Av)
	Matrix-vector multiplication of a matrix sized MxM and a vector Mx1. More...

__device__ void	matvec_m_by_m_plusequal (const int m, const double const __restrict__ A, const double const __restrict__ V, double *const __restrict__ Av)
	Matrix-vector plus equals for a matrix of size MxM and vector of size Mx1. That is, it returns (A + I) * v. More...

__device__ void	matvec_n_by_m_scale (const int m, const double scale, const double const __restrict__ A, const double const __restrict__ V, double *const __restrict__ Av)
	Matrix-vector multiplication of a matrix sized NSPxM and a vector of size Mx1 scaled by a specified factor That is, it returns A * v * scale. More...

__device__ void	matvec_n_by_m_scale_special (const int m, const double __restrict__ scale, const double __restrict__ A, double const __restrict__ V, double __restrict__ Av)
	Matrix-vector multiplication of a matrix sized NSPxM and a vector of size Mx1 scaled by a specified factor. More...

__device__ void	matvec_n_by_m_scale_special2 (const int m, const double __restrict__ scale, const double __restrict__ A, double const __restrict__ V, double __restrict__ Av)
	Matrix-vector multiplication of a matrix sized NSPxM and a vector of size Mx1 scaled by a specified factor. More...

__device__ void	matvec_n_by_m_scale_add (const int m, const double scale, const double __restrict__ A, const double __restrict__ V, double __restrict__ Av, const double __restrict__ add)
	Matrix-vector multiplication of a matrix sized NSPxM and a vector of size Mx1 scaled by a specified factor and added to another vector. More...

__device__ void	matvec_n_by_m_scale_add_subtract (const int m, const double scale, const double __restrict__ A, const double V, double __restrict__ Av, const double __restrict__ add, const double *__restrict__ sub)
	Matrix-vector multiplication of a matrix sized NSPxM and a vector of size Mx1 scaled by a specified factor and adds and subtracts the specified vectors note, the addition is twice the specified vector. More...

__device__ void	scale (const double __restrict__ y0, const double __restrict__ y1, double *__restrict__ sc)
	Get scaling for weighted norm. More...

__device__ void	scale_init (const double __restrict__ y0, double __restrict__ sc)
	Get scaling for weighted norm for the initial timestep (used in krylov process) More...

__device__ double	sc_norm (const double __restrict__ nums, const double __restrict__ sc)
	Perform weighted norm. More...

__device__ double	two_norm (const double *__restrict__ v)
	Computes and returns the two norm of a vector. More...

__device__ double	normalize (const double __restrict__ v, double __restrict__ v_out)
	Normalize the input vector using a 2-norm. More...

__device__ double	dotproduct (const double __restrict__ w, const double __restrict__ Vm)
	Performs the dot product of the w (NSP x 1) vector with the given subspace vector (NSP x 1) More...

__device__ void	scale_subtract (const double s, const double __restrict__ Vm, double __restrict__ w)
	Subtracts Vm scaled by s from w. More...

__device__ void	scale_mult (const double s, const double __restrict__ w, double __restrict__ Vm)
	Sets Vm to s * w. More...

Detailed Description

Implementation of various linear algebra functions needed in the exponential integrators.

Author: Nicholas Curtis

Date: 03/09/2015

Definition in file exponential_linear_algebra.cu.

Function Documentation

◆ dotproduct()

__device__ double dotproduct	(	const double *__restrict__	w,
		const double *__restrict__	Vm
	)

Performs the dot product of the w (NSP x 1) vector with the given subspace vector (NSP x 1)

returns \(Vm \dot w\)

Parameters

[in]	w	the vector with with to dot
[in]	Vm	the subspace vector

Returns: sum - the dot product of the specified vectors

Definition at line 217 of file exponential_linear_algebra.cu.

◆ matvec_m_by_m()

__device__ void matvec_m_by_m	(	const int	m,
		const double *const __restrict__	A,
		const double *const __restrict__	V,
		double *const __restrict__	Av
	)

Matrix-vector multiplication of a matrix sized MxM and a vector Mx1.

Parameters

[in]	m	size of the matrix
[in]	A	matrix of size MxM
[in]	V	vector of size Mx1
[out]	Av	vector that is A * v

Definition at line 15 of file exponential_linear_algebra.cu.

◆ matvec_m_by_m_plusequal()

__device__ void matvec_m_by_m_plusequal	(	const int	m,
		const double *const __restrict__	A,
		const double *const __restrict__	V,
		double *const __restrict__	Av
	)

Matrix-vector plus equals for a matrix of size MxM and vector of size Mx1. That is, it returns (A + I) * v.

Parameters

[in]	m	size of the matrix
[in]	A	matrix of size MxM
[in]	V	vector of size Mx1
[out]	Av	vector that is (A + I) * v

Definition at line 31 of file exponential_linear_algebra.cu.

◆ matvec_n_by_m_scale()

__device__ void matvec_n_by_m_scale	(	const int	m,
		const double	scale,
		const double *const __restrict__	A,
		const double *const __restrict__	V,
		double *const __restrict__	Av
	)

Matrix-vector multiplication of a matrix sized NSPxM and a vector of size Mx1 scaled by a specified factor That is, it returns A * v * scale.

Parameters

[in]	m	size of the matrix
[in]	scale	a number to scale the multplication by
[in]	A	matrix
[in]	V	the vector
[out]	Av	vector that is A * V * scale

Definition at line 48 of file exponential_linear_algebra.cu.

◆ matvec_n_by_m_scale_add()

__device__ void matvec_n_by_m_scale_add	(	const int	m,
		const double	scale,
		const double *__restrict__	add,
		const double *__restrict__	A,
		double *__restrict__	V,
		const double *__restrict__	Av
	)

Matrix-vector multiplication of a matrix sized NSPxM and a vector of size Mx1 scaled by a specified factor and added to another vector.

Computes \(A * V * scale + add\)

Parameters

[in]	m	size of the matrix
[in]	scale	a number to scale the multplication by
[in]	add	the vector to add to the result
[in]	A	matrix
[in]	V	the vector
[out]	Av	vector that is A * V * scale + add

Definition at line 114 of file exponential_linear_algebra.cu.

◆ matvec_n_by_m_scale_add_subtract()

__device__ void matvec_n_by_m_scale_add_subtract	(	const int	m,
		const double	scale,
		const double *__restrict__	A,
		const double *	V,
		double *__restrict__	Av,
		const double *__restrict__	add,
		const double *__restrict__	sub
	)

Matrix-vector multiplication of a matrix sized NSPxM and a vector of size Mx1 scaled by a specified factor and adds and subtracts the specified vectors note, the addition is twice the specified vector.

Computes \(scale * A * V + 2 * add - sub\)

Parameters

[in]	m	size of the matrix
[in]	scale	a number to scale the multplication by
[in]	A	matrix
[in]	V	the vector
[out]	Av	vector that is scale * A * V + 2 * add - sub
[in]	add	the vector to add to the result
[in]	sub	the vector to subtract from the result

Definition at line 134 of file exponential_linear_algebra.cu.

◆ matvec_n_by_m_scale_special()

__device__ void matvec_n_by_m_scale_special	(	const int	m,
		const double *__restrict__	scale,
		const double *__restrict__	A,
		double const __restrict__	V,
		double __restrict__	Av
	)

Matrix-vector multiplication of a matrix sized NSPxM and a vector of size Mx1 scaled by a specified factor.

Computes the following: \(Av1 = A * V1 * scale[0]\), \(Av2 = A * V2 * scale[1]\), and \(Av3 = A * V3 * scale[2] + V4 + V5\)

Parameters

[in]	m	size of the matrix
[in]	scale	a list of numbers to scale the multplication by
[in]	A	matrix
[in]	V	a list of 5 pointers corresponding to V1, V2, V3, V4, V5
[out]	Av	a list of 3 pointers corresponding to Av1, Av2, Av3

Definition at line 67 of file exponential_linear_algebra.cu.

◆ matvec_n_by_m_scale_special2()

__device__ void matvec_n_by_m_scale_special2	(	const int	m,
		const double *__restrict__	scale,
		const double *__restrict__	A,
		double const __restrict__	V,
		double __restrict__	Av
	)

Matrix-vector multiplication of a matrix sized NSPxM and a vector of size Mx1 scaled by a specified factor.

Computes the following: \(Av1 = A * V1 * scale[0]\) and: \(Av2 = A * V2 * scale[1]\)

Performs inline matrix-vector multiplication (with unrolled loops)

Parameters

[in]	m	size of the matrix
[in]	scale	a list of numbers to scale the multplication by
[in]	A	matrix
[in]	V	a list of 2 pointers corresponding to V1, V2
[out]	Av	a list of 2 pointers corresponding to Av1, Av2

Definition at line 92 of file exponential_linear_algebra.cu.

◆ normalize()

__device__ double normalize	(	const double *__restrict__	v,
		double *__restrict__	v_out
	)

Normalize the input vector using a 2-norm.

\(v_{out} = \frac{v}{\left| v \right|}_2\)

Parameters

[in]	v	vector to be normalized
[out]	v_out	where to stick the normalized part of v (in a column)

Definition at line 199 of file exponential_linear_algebra.cu.

◆ sc_norm()

__device__ double sc_norm	(	const double *__restrict__	nums,
		const double *__restrict__	sc
	)

Perform weighted norm.

Computes \(\left| nums * sc\right|_2\)

Parameters

[in]	nums	values to be normed
[in]	sc	scaling array for norm

Returns: norm weighted norm

Definition at line 176 of file exponential_linear_algebra.cu.

◆ scale()

__device__ void scale	(	const double *__restrict__	y0,
		const double *__restrict__	y1,
		double *__restrict__	sc
	)

Get scaling for weighted norm.

Computes \(\frac{1.0}{ATOL + \max\left(\left|y0\right|, \left|y1\right|) * RTOL\right)}\)

Parameters

[in]	y0	values at current timestep
[in]	y1	values at next timestep
[out]	sc	array of scaling values

Definition at line 156 of file exponential_linear_algebra.cu.

◆ scale_init()

__device__ void scale_init	(	const double *__restrict__	y0,
		double *__restrict__	sc
	)

Get scaling for weighted norm for the initial timestep (used in krylov process)

Parameters

[in]	y0	values at current timestep
[out]	sc	array of scaling values

Definition at line 166 of file exponential_linear_algebra.cu.

◆ scale_mult()

__device__ void scale_mult	(	const double	s,
		const double *__restrict__	w,
		double *__restrict__	Vm
	)

Sets Vm to s * w.

\(Vm = s * w\)

Parameters

[in]	s	the scale multiplier to use
[in]	w	the vector to use as a base
[out]	Vm	the subspace matrix to set

Definition at line 237 of file exponential_linear_algebra.cu.

◆ scale_subtract()

__device__ void scale_subtract	(	const double	s,
		const double *__restrict__	Vm,
		double *__restrict__	w
	)

Subtracts Vm scaled by s from w.

\( w -= Vm * s\)

Parameters

[in]	s	the scale multiplier to use
[in]	Vm	the subspace matrix
[out]	w	the vector to subtract from

Definition at line 228 of file exponential_linear_algebra.cu.

◆ two_norm()

__device__ double two_norm ( const double *__restrict__ v )

Computes and returns the two norm of a vector.

Computes \(\sqrt{\sum{v^2}}\)

Parameters

[in] v the vector

Definition at line 188 of file exponential_linear_algebra.cu.

Functions

Detailed Description

Function Documentation

◆ dotproduct()

◆ matvec_m_by_m()

◆ matvec_m_by_m_plusequal()

◆ matvec_n_by_m_scale()

◆ matvec_n_by_m_scale_add()

◆ matvec_n_by_m_scale_add_subtract()

◆ matvec_n_by_m_scale_special()

◆ matvec_n_by_m_scale_special2()

◆ normalize()

◆ sc_norm()

◆ scale()

◆ scale_init()

◆ scale_mult()

◆ scale_subtract()

◆ two_norm()