radau2a Namespace Reference

Functions
static void	scale (const double *__restrict__ y0, const double *__restrict__ y, double *__restrict__ sc)
	Computes error weight scaling from initial and current state. More...
static void	scale_init (const double *__restrict__ y0, double *__restrict__ sc)
	Computes error weight scaling from initial state. More...
static void	RK_Decomp (const double H, double *__restrict__ E1, double complex *__restrict__ E2, const double *__restrict__ Jac, int *__restrict__ ipiv1, int *__restrict__ ipiv2, int *__restrict__ info)
	Compute E1 & E2 matricies and their LU Decomposition. More...
static void	RK_Make_Interpolate (const double *__restrict__ Z1, const double *__restrict__ Z2, const double *__restrict__ Z3, double *__restrict__ CONT)
	Compute Quadaratic interpolate. More...
static void	RK_Interpolate (const double H, const double Hold, double *__restrict__ Z1, double *__restrict__ Z2, double *__restrict__ Z3, const double *__restrict__ CONT)
	Apply quadaratic interpolate to get initial values. More...
static void	WADD (const double *__restrict__ X, const double *__restrict__ Y, double *__restrict__ Z)
	Performs \(Z:= X + Y\) with unrolled (or at least bounds known at compile time) loops. More...
static void	DAXPY3 (const double DA1, const double DA2, const double DA3, const double *__restrict__ DX, double *__restrict__ DY1, double *__restrict__ DY2, double *__restrict__ DY3)
	Sepcialization of DAXPY with unrolled (or at least bounds known at compile time) loops. More...
static void	RK_PrepareRHS (const double t, const double pr, const double H, const double *__restrict__ Y, const double *__restrict__ Z1, const double *__restrict__ Z2, const double *__restrict__ Z3, double *__restrict__ R1, double *__restrict__ R2, double *__restrict__ R3)
	Prepare the right-hand side for Newton iterations: \(R = Z - hA * F\). More...
static void	RK_Solve (const double H, double *__restrict__ E1, double complex *__restrict__ E2, double *__restrict__ R1, double *__restrict__ R2, double *__restrict__ R3, int *__restrict__ ipiv1, int *__restrict__ ipiv2)
	Solves for the RHS values in the Newton iteration. More...
static double	RK_ErrorNorm (const double *__restrict__ scale, double *__restrict__ DY)
	Computes the scaled error norm from the given scale and DY vectors. More...
static double	RK_ErrorEstimate (const double H, const double t, const double pr, const double *__restrict__ Y, const double *__restrict__ F0, const double *__restrict__ Z1, const double *__restrict__ Z2, const double *__restrict__ Z3, const double *__restrict__ scale, double *__restrict__ E1, int *__restrict__ ipiv1, const bool FirstStep, const bool Reject)
	Computes and returns the error estimate for this step. More...
int	integrate (const double t_start, const double t_end, const double pr, double *y)
	5th-order Radau2A CPU implementation More...
void	initialize_solver ()
const char *	solver_name ()
	Returns a descriptive solver name. More...
void	cleanup_solver ()
void	init_solver_log ()
void	solver_log ()

Variables
static const double	rkA [3][3]
static const double	rkB [3]
static const double	rkC [3]
static const double	rkE [4]
static const double	rkTheta [3]
static const double	rkGamma = 3.637834252744495732208418513577775
static const double	rkAlpha = 2.681082873627752133895790743211112
static const double	rkBeta = 3.050430199247410569426377624787569
static const double	rkT [3][3]
static const double	rkTinv [3][3]
static const double	rkTinvAinv [3][3]
static const double	rkAinvT [3][3]
static const double	rkELO = 4
static char	TRANS = 'N'
	Lapack - non-transpose. More...
static int	NRHS = 1
	Lapack - 1 RHS solve. More...
static int	ARRSIZE = NSP
	Lapack - Array size. More...

Function Documentation

cleanup_solver()

void radau2a::cleanup_solver

(

)

Definition at line 26 of file radau2a_init.c.

DAXPY3()

static void radau2a::DAXPY3 ( const double  DA1, const double  DA2, const double  DA3, const double *__restrict__  DX, double *__restrict__  DY1, double *__restrict__  DY2, double *__restrict__  DY3  )

inlinestatic

Sepcialization of DAXPY with unrolled (or at least bounds known at compile time) loops.

Performs:

• \(DY1:= DA1 * DX\)
• \(DY2:= DA2 * DX\)
• \(DY3:= DA3 * DX\)

Definition at line 338 of file radau2a.c.

init_solver_log()

void radau2a::init_solver_log

(

)

Definition at line 30 of file radau2a_init.c.

initialize_solver()

void radau2a::initialize_solver

(

)

Definition at line 14 of file radau2a_init.c.

integrate()

int radau2a::integrate	(	const double	t_start,
		const double	t_end,
		const double	pr,
		double *	y
	)

5th-order Radau2A CPU implementation

A header definition of the integrate method, that must be implemented by various solvers.

Parameters

[in]	t_start	The starting time
[in]	t_end	The end integration time
[in]	pr	The system constant variable (pressure/density)
[in,out]	y	The system state vector at time t_start. Overwritten with the system state at time t_end

Returns

Return code,

See also

Return codes of Radau-IIa integrator

Definition at line 520 of file radau2a.c.

RK_Decomp()

static void radau2a::RK_Decomp ( const double  H, double *__restrict__  E1, double complex *__restrict__  E2, const double *__restrict__  Jac, int *__restrict__  ipiv1, int *__restrict__  ipiv2, int *__restrict__  info  )

static

Compute E1 & E2 matricies and their LU Decomposition.

Parameters

[in]	H	The timestep size
[in,out]	E1	The non-complex matrix system
[in,out]	E2	The complex matrix system
[in]	Jac	The Jacobian matrix
[out]	ipiv1	The pivot indicies for E1
[out]	ipiv2	The pivot indicies for E2
[out]	info	An indicator variable determining if an error occured.

Definition at line 256 of file radau2a.c.

RK_ErrorEstimate()

static double radau2a::RK_ErrorEstimate ( const double  H, const double  t, const double  pr, const double *__restrict__  Y, const double *__restrict__  F0, const double *__restrict__  Z1, const double *__restrict__  Z2, const double *__restrict__  Z3, const double *__restrict__  scale, double *__restrict__  E1, int *__restrict__  ipiv1, const bool  FirstStep, const bool  Reject  )

static

Computes and returns the error estimate for this step.

Definition at line 458 of file radau2a.c.

RK_ErrorNorm()

static double radau2a::RK_ErrorNorm ( const double *__restrict__  scale, double *__restrict__  DY  )

inlinestatic

Computes the scaled error norm from the given scale and DY vectors.

Definition at line 446 of file radau2a.c.

RK_Interpolate()

static void radau2a::RK_Interpolate ( const double  H, const double  Hold, double *__restrict__  Z1, double *__restrict__  Z2, double *__restrict__  Z3, const double *__restrict__  CONT  )

static

Apply quadaratic interpolate to get initial values.

Definition at line 302 of file radau2a.c.

RK_Make_Interpolate()

static void radau2a::RK_Make_Interpolate ( const double *__restrict__  Z1, const double *__restrict__  Z2, const double *__restrict__  Z3, double *__restrict__  CONT  )

static

Compute Quadaratic interpolate.

Definition at line 283 of file radau2a.c.

RK_PrepareRHS()

static void radau2a::RK_PrepareRHS ( const double  t, const double  pr, const double  H, const double *__restrict__  Y, const double *__restrict__  Z1, const double *__restrict__  Z2, const double *__restrict__  Z3, double *__restrict__  R1, double *__restrict__  R2, double *__restrict__  R3  )

static

Prepare the right-hand side for Newton iterations: \(R = Z - hA * F\).

Definition at line 353 of file radau2a.c.

RK_Solve()

static void radau2a::RK_Solve ( const double  H, double *__restrict__  E1, double complex *__restrict__  E2, double *__restrict__  R1, double *__restrict__  R2, double *__restrict__  R3, int *__restrict__  ipiv1, int *__restrict__  ipiv2  )

static

Solves for the RHS values in the Newton iteration.

Definition at line 388 of file radau2a.c.

scale()

static void radau2a::scale ( const double *__restrict__  y0, const double *__restrict__  y, double *__restrict__  sc  )

inlinestatic

Computes error weight scaling from initial and current state.

Parameters

[in]	y0	the initial state vector to use
[in]	y	the current state vector
[out]	sc	the populated error weight scalings

Definition at line 74 of file radau2a.c.

scale_init()

static void radau2a::scale_init ( const double *__restrict__  y0, double *__restrict__  sc  )

inlinestatic

Computes error weight scaling from initial state.

Parameters

[in]	y0	the initial state vector to use
[out]	sc	the populated error weight scalings

Definition at line 88 of file radau2a.c.

solver_log()

void radau2a::solver_log

(

)

Definition at line 34 of file radau2a_init.c.

solver_name()

char * radau2a::solver_name

(

)

Returns a descriptive solver name.

Definition at line 21 of file radau2a_init.c.

WADD()

static void radau2a::WADD ( const double *__restrict__  X, const double *__restrict__  Y, double *__restrict__  Z  )

inlinestatic

Performs \(Z:= X + Y\) with unrolled (or at least bounds known at compile time) loops.

Definition at line 320 of file radau2a.c.

Variable Documentation

ARRSIZE

int radau2a::ARRSIZE = NSP

static

Lapack - Array size.

Definition at line 242 of file radau2a.c.

NRHS

int radau2a::NRHS = 1

static

Lapack - 1 RHS solve.

Definition at line 240 of file radau2a.c.

TRANS

char radau2a::TRANS = 'N'

static

Lapack - non-transpose.

Definition at line 238 of file radau2a.c.