Package edu.wpi.first.math.system

Class NumericalIntegration

java.lang.Object

edu.wpi.first.math.system.NumericalIntegration

public final class NumericalIntegration
extends Object

Numerical integration utilities.

Method Summary

Modifier and Type	Method	Description
static <States extends Num, Inputs extends Num> Matrix<States,N1>	rk4(BiFunction<Matrix<States,N1>,Matrix<Inputs,N1>,Matrix<States,N1>> f, Matrix<States,N1> x, Matrix<Inputs,N1> u, double dt)	Performs 4th order Runge-Kutta integration of dx/dt = f(x, u) for dt.
static <Rows extends Num, Cols extends Num> Matrix<Rows,Cols>	rk4(BiFunction<Double,Matrix<Rows,Cols>,Matrix<Rows,Cols>> f, double t, Matrix<Rows,Cols> y, double dt)	Performs 4th order Runge-Kutta integration of dx/dt = f(t, y) for dt.
static double	rk4(DoubleBinaryOperator f, double x, double u, double dt)	Performs 4th order Runge-Kutta integration of dx/dt = f(x, u) for dt.
static double	rk4(DoubleUnaryOperator f, double x, double dt)	Performs 4th order Runge-Kutta integration of dx/dt = f(x) for dt.
static <States extends Num> Matrix<States,N1>	rk4(UnaryOperator<Matrix<States,N1>> f, Matrix<States,N1> x, double dt)	Performs 4th order Runge-Kutta integration of dx/dt = f(x) for dt.
static <States extends Num, Inputs extends Num> Matrix<States,N1>	rkdp(BiFunction<Matrix<States,N1>,Matrix<Inputs,N1>,Matrix<States,N1>> f, Matrix<States,N1> x, Matrix<Inputs,N1> u, double dt)	Performs adaptive Dormand-Prince integration of dx/dt = f(x, u) for dt.
static <States extends Num, Inputs extends Num> Matrix<States,N1>	rkdp(BiFunction<Matrix<States,N1>,Matrix<Inputs,N1>,Matrix<States,N1>> f, Matrix<States,N1> x, Matrix<Inputs,N1> u, double dt, double maxError)	Performs adaptive Dormand-Prince integration of dx/dt = f(x, u) for dt.
static <Rows extends Num, Cols extends Num> Matrix<Rows,Cols>	rkdp(BiFunction<Double,Matrix<Rows,Cols>,Matrix<Rows,Cols>> f, double t, Matrix<Rows,Cols> y, double dt, double maxError)	Performs adaptive Dormand-Prince integration of dx/dt = f(t, y) for dt.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Method Details

rk4

public static double rk4(DoubleUnaryOperator f,
 double x,
 double dt)

Performs 4th order Runge-Kutta integration of dx/dt = f(x) for dt.

Parameters:

f - The function to integrate. It must take one argument x.

x - The initial value of x.

dt - The time over which to integrate in seconds.

Returns:

the integration of dx/dt = f(x) for dt.

rk4

public static double rk4(DoubleBinaryOperator f,
 double x,
 double u,
 double dt)

Performs 4th order Runge-Kutta integration of dx/dt = f(x, u) for dt.

Parameters:

f - The function to integrate. It must take two arguments x and u.

x - The initial value of x.

u - The value u held constant over the integration period.

dt - The time over which to integrate in seconds.

Returns:

the integration of dx/dt = f(x, u) for dt.

rk4

public static <States extends Num,
Inputs extends Num>
Matrix<States,N1> rk4(BiFunction<Matrix<States,N1>,Matrix<Inputs,N1>,Matrix<States,N1>> f,
 Matrix<States,N1> x,
 Matrix<Inputs,N1> u,
 double dt)

Performs 4th order Runge-Kutta integration of dx/dt = f(x, u) for dt.

Type Parameters:

States - A Num representing the states of the system to integrate.

Inputs - A Num representing the inputs of the system to integrate.

Parameters:

f - The function to integrate. It must take two arguments x and u.

x - The initial value of x.

u - The value u held constant over the integration period.

dt - The time over which to integrate in seconds.

Returns:

the integration of dx/dt = f(x, u) for dt.

rk4

public static <States extends Num>
Matrix<States,N1> rk4(UnaryOperator<Matrix<States,N1>> f,
 Matrix<States,N1> x,
 double dt)

Performs 4th order Runge-Kutta integration of dx/dt = f(x) for dt.

Type Parameters:

States - A Num representing the states of the system.

Parameters:

f - The function to integrate. It must take one argument x.

x - The initial value of x.

dt - The time over which to integrate in seconds.

Returns:

the integration of dx/dt = f(x) for dt.

rk4

public static <Rows extends Num,
Cols extends Num>
Matrix<Rows,Cols> rk4(BiFunction<Double,Matrix<Rows,Cols>,Matrix<Rows,Cols>> f,
 double t,
 Matrix<Rows,Cols> y,
 double dt)

Performs 4th order Runge-Kutta integration of dx/dt = f(t, y) for dt.

Type Parameters:

Rows - Rows in y.

Cols - Columns in y.

Parameters:

f - The function to integrate. It must take two arguments t and y.

t - The initial value of t.

y - The initial value of y.

dt - The time over which to integrate in seconds.

Returns:

the integration of dx/dt = f(x) for dt.

rkdp

public static <States extends Num,
Inputs extends Num>
Matrix<States,N1> rkdp(BiFunction<Matrix<States,N1>,Matrix<Inputs,N1>,Matrix<States,N1>> f,
 Matrix<States,N1> x,
 Matrix<Inputs,N1> u,
 double dt)

Performs adaptive Dormand-Prince integration of dx/dt = f(x, u) for dt. By default, the max error is 1e-6.

Type Parameters:

States - A Num representing the states of the system to integrate.

Inputs - A Num representing the inputs of the system to integrate.

Parameters:

f - The function to integrate. It must take two arguments x and u.

x - The initial value of x.

u - The value u held constant over the integration period.

dt - The time over which to integrate in seconds.

Returns:

the integration of dx/dt = f(x, u) for dt.

rkdp

public static <States extends Num,
Inputs extends Num>
Matrix<States,N1> rkdp(BiFunction<Matrix<States,N1>,Matrix<Inputs,N1>,Matrix<States,N1>> f,
 Matrix<States,N1> x,
 Matrix<Inputs,N1> u,
 double dt,
 double maxError)

Performs adaptive Dormand-Prince integration of dx/dt = f(x, u) for dt.

Type Parameters:

States - A Num representing the states of the system to integrate.

Inputs - A Num representing the inputs of the system to integrate.

Parameters:

f - The function to integrate. It must take two arguments x and u.

x - The initial value of x.

u - The value u held constant over the integration period.

dt - The time over which to integrate in seconds.

maxError - The maximum acceptable truncation error. Usually a small number like 1e-6.

Returns:

the integration of dx/dt = f(x, u) for dt.

rkdp

public static <Rows extends Num,
Cols extends Num>
Matrix<Rows,Cols> rkdp(BiFunction<Double,Matrix<Rows,Cols>,Matrix<Rows,Cols>> f,
 double t,
 Matrix<Rows,Cols> y,
 double dt,
 double maxError)

Performs adaptive Dormand-Prince integration of dx/dt = f(t, y) for dt.

Type Parameters:

Rows - Rows in y.

Cols - Columns in y.

Parameters:

f - The function to integrate. It must take two arguments t and y.

t - The initial value of t.

y - The initial value of y.

dt - The time over which to integrate in seconds.

maxError - The maximum acceptable truncation error. Usually a small number like 1e-6.

Returns:

the integration of dx/dt = f(x, u) for dt.