Utility functions. More...

#include "utils.h"

Include dependency graph for utils.cpp:

Macros
#define	ERRCON 6.0E-4

#define	FCOR 0.06666666

#define	MAXSTP 10000

#define	PGROW -0.20

#define	PSHRNK -0.25

#define	SAFETY 0.9

#define	TINY 1.0e-30

Functions
ReturnMatrix	Integ_Trap (const ColumnVector &present, ColumnVector &past, const Real dt)
	Trapezoidal integration. More...

void	odeint (ReturnMatrix(*xdot)(Real time, const Matrix &xin), Matrix &xo, Real to, Real tf, Real eps, Real h1, Real hmin, int &nok, int &nbad, RowVector &tout, Matrix &xout, Real dtsav)
	Integrate the ordinary differential equation xdot from time to to time tf using an adaptive step size strategy. More...

ReturnMatrix	pinv (const Matrix &M)
	Matrix pseudo inverse using SVD. More...

ReturnMatrix	rk4 (const Matrix &x, const Matrix &dxdt, Real t, Real h, ReturnMatrix(*xdot)(Real time, const Matrix &xin))
	Compute one Runge-Kutta fourth order step. More...

void	rkqc (Matrix &x, Matrix &dxdt, Real &t, Real htry, Real eps, Matrix &xscal, Real &hdid, Real &hnext, ReturnMatrix(*xdot)(Real time, const Matrix &xin))
	Compute one adaptive step based on two rk4. More...

void	Runge_Kutta4 (ReturnMatrix(*xdot)(Real time, const Matrix &xin), const Matrix &xo, Real to, Real tf, int nsteps, RowVector &tout, Matrix &xout)
	Fixed step size fourth-order Runge-Kutta integrator. More...

void	Runge_Kutta4_Real_time (ReturnMatrix(*xdot)(Real time, const Matrix &xin, bool &exit, bool &init), const Matrix &xo, Real to, Real tf, int nsteps)
	Fixed step size fourth-order Runge-Kutta integrator. More...

void	Runge_Kutta4_Real_time (ReturnMatrix(*xdot)(const Real time, const Matrix &xin), const Matrix &xo, const Real to, const Real tf, const int nsteps)

ReturnMatrix	sign (const Matrix &x)
	Sign of a matrix. More...

short	sign (const Real x)
	Sign of real. More...

ReturnMatrix	x_prod_matrix (const ColumnVector &x)
	Cross product matrix. More...

Variables
static const char	rcsid [] = "$Id: utils.cpp,v 1.26 2006/05/16 16:11:15 gourdeau Exp $"
	RCS/CVS version. More...

Detailed Description

Utility functions.

Definition in file utils.cpp.

Macro Definition Documentation

#define ERRCON 6.0E-4

Definition at line 293 of file utils.cpp.

#define FCOR 0.06666666

Definition at line 291 of file utils.cpp.

#define MAXSTP 10000

Definition at line 344 of file utils.cpp.

#define PGROW -0.20

Definition at line 289 of file utils.cpp.

#define PSHRNK -0.25

Definition at line 290 of file utils.cpp.

#define SAFETY 0.9

Definition at line 292 of file utils.cpp.

#define TINY 1.0e-30

Definition at line 345 of file utils.cpp.

Function Documentation

ReturnMatrix Integ_Trap	(	const ColumnVector &	present,
		ColumnVector &	past,
		const Real	dt
	)

Trapezoidal integration.

Definition at line 165 of file utils.cpp.

void odeint	(	ReturnMatrix(*)(Real time, const Matrix &xin)	xdot,
		Matrix &	xo,
		Real	to,
		Real	tf,
		Real	eps,
		Real	h1,
		Real	hmin,
		int &	nok,
		int &	nbad,
		RowVector &	tout,
		Matrix &	xout,
		Real	dtsav
	)

Integrate the ordinary differential equation xdot from time to to time tf using an adaptive step size strategy.

adapted from: Numerical Recipes in C, The Art of Scientific Computing, Press, William H. and Flannery, Brian P. and Teukolsky, Saul A. and Vetterling, William T., Cambridge University Press, 1988.

Definition at line 347 of file utils.cpp.

ReturnMatrix pinv ( const Matrix & M )

Matrix pseudo inverse using SVD.

If $A = U^{*}QV$ is a singular value decomposition of A, then $A^{\dagger} = V^{*}Q^{\dagger}U$ where $X^{*}$ is the conjugate transpose of $ X $ and $Q^{\dagger} = \left [ \begin{array}{cccc} 1/\sigma_1 & & & \\ & 1/\sigma_2& & \\ & & \ddots & \\ & & & 0 \end{array} \right ]$ where the $1/\sigma_i$ are replaced by 0 when $1/\sigma_i < tol$

Definition at line 99 of file utils.cpp.

ReturnMatrix rk4	(	const Matrix &	x,
		const Matrix &	dxdt,
		Real	t,
		Real	h,
		ReturnMatrix(*)(Real time, const Matrix &xin)	xdot
	)

Compute one Runge-Kutta fourth order step.

adapted from: Numerical Recipes in C, The Art of Scientific Computing, Press, William H. and Flannery, Brian P. and Teukolsky, Saul A. and Vetterling, William T., Cambridge University Press, 1988.

Definition at line 260 of file utils.cpp.

void rkqc	(	Matrix &	x,
		Matrix &	dxdt,
		Real &	t,
		Real	htry,
		Real	eps,
		Matrix &	xscal,
		Real &	hdid,
		Real &	hnext,
		ReturnMatrix(*)(Real time, const Matrix &xin)	xdot
	)

Compute one adaptive step based on two rk4.

adapted from: Numerical Recipes in C, The Art of Scientific Computing, Press, William H. and Flannery, Brian P. and Teukolsky, Saul A. and Vetterling, William T., Cambridge University Press, 1988.

Definition at line 295 of file utils.cpp.

void Runge_Kutta4	(	ReturnMatrix(*)(Real time, const Matrix &xin)	xdot,
		const Matrix &	xo,
		Real	to,
		Real	tf,
		int	nsteps,
		RowVector &	tout,
		Matrix &	xout
	)

Fixed step size fourth-order Runge-Kutta integrator.

Definition at line 232 of file utils.cpp.

void Runge_Kutta4_Real_time	(	ReturnMatrix(*)(Real time, const Matrix &xin, bool &exit, bool &init)	xdot,
		const Matrix &	xo,
		Real	to,
		Real	tf,
		int	nsteps
	)

Fixed step size fourth-order Runge-Kutta integrator.

Definition at line 178 of file utils.cpp.

void Runge_Kutta4_Real_time	(	ReturnMatrix(*)(const Real time, const Matrix &xin)	xdot,
		const Matrix &	xo,
		const Real	to,
		const Real	tf,
		const int	nsteps
	)

Definition at line 207 of file utils.cpp.

ReturnMatrix sign ( const Matrix & x )

Sign of a matrix.

Definition at line 406 of file utils.cpp.

short sign ( const Real x )

Sign of real.

Definition at line 425 of file utils.cpp.

ReturnMatrix x_prod_matrix ( const ColumnVector & x )

Cross product matrix.

Definition at line 88 of file utils.cpp.

Variable Documentation

const char rcsid[] = "$Id: utils.cpp,v 1.26 2006/05/16 16:11:15 gourdeau Exp $"

static

RCS/CVS version.

Definition at line 60 of file utils.cpp.

Macros

Functions

Variables

Detailed Description

Macro Definition Documentation

Function Documentation

Variable Documentation