Utility functions. More...

#include "utils.h"

Macros
#define	PGROW -0.20

#define	PSHRNK -0.25

#define	FCOR 0.06666666

#define	SAFETY 0.9

#define	ERRCON 6.0E-4

#define	MAXSTP 10000

#define	TINY 1.0e-30

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

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

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

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.

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)

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.

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

short	sign (const Real x)
	Sign of real.

Detailed Description

Utility functions.

Definition in file utils.cpp.

Function Documentation

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 346 of file utils.cpp.

References rkqc().

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 98 of file utils.cpp.

References pinv().

Referenced by pinv().

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 259 of file utils.cpp.

Referenced by rkqc().

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 294 of file utils.cpp.

References rk4().

Referenced by odeint().

Macros

Functions

Detailed Description

Function Documentation