dynamics

package dynamics

The dynamics package contains classes, traits and objects for system dynamics simulations using Ordinary Differential Equations (ODEs).

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class DynamicEq extends Error
The DynamicEq class may be used for determining trajectories 'x_t' from a system of dynamic equations.
The DynamicEq class may be used for determining trajectories 'x_t' from a system of dynamic equations.
x_t = f(t)
'f(t)' is the vector function of time.
trait Integrator extends Error
The Integrator trait provides a template for writing numerical integrators (e.g., Runge-Kutta 'RK4' or Dormand-Prince 'DOPRI') to produce trajectories for first-order Ordinary Differential Equations 'ODE's.
The Integrator trait provides a template for writing numerical integrators (e.g., Runge-Kutta 'RK4' or Dormand-Prince 'DOPRI') to produce trajectories for first-order Ordinary Differential Equations 'ODE's. The ODE is of the form:
d/dt y(t) = f(t, y) with initial condition y0 = y(t0)
If 'f' is a linear function of the form 'a(t) * y(t) + b(t)', then the ODE is linear, if 'a(t) = a' (i.e., a constant) the ODE has constant coefficients and if 'b(t) = 0' the ODE is homogeneous. Note this package provides a solver (not an integrator) as an option for linear, constant coefficient, homogeneous, first-order ODE.

See also
scalation.dynamics.LinearDiffEq.scala
class LinearDiffEq extends Error
The LinearDiffEq class may be used for solving a system of linear differential equations that are ordinary and first-order with constant coefficients of the form
The LinearDiffEq class may be used for solving a system of linear differential equations that are ordinary and first-order with constant coefficients of the form
d/dt y(t) = a * y(t)
'y(t)' is the vector function of time and 'a' is the coefficient matrix. The initial value vector 'y0 = y(0)' must also be given. Note, higher-order differential equations may be converted to first-order by introducing additional variables. The above equation is the homogeneous case. Caveats: the following cases are not currently handled: (1) The non-homogeneous equation: 'd/dt y(t) = a * y(t) + f(t)'. (2) Complex or repeated eigenvalues.
class NLS_ODE extends Predictor with Error
Given an Ordinary Differential Equation 'ODE' parameterized using the vector 'b' with Initial Value 'IV' 'y0', estimate the parameter values 'b' for the ODE using weighted Non-linear Least Squares 'NLS'.
Given an Ordinary Differential Equation 'ODE' parameterized using the vector 'b' with Initial Value 'IV' 'y0', estimate the parameter values 'b' for the ODE using weighted Non-linear Least Squares 'NLS'.
ODE: dy/dt = f(t, y) IV: y(t0) = y0
Times series data: z(t0), z(t1), ... z(tn)
class SSA extends Error
The SSA class implements the Gillespie Stochastic Simulation Algorithm 'SSA'.

Value Members

object Derivatives
The Derivatives object is used to define types of time derivative functions.
object DormandPrince extends Integrator
The DormandPrince object provides a state-of-the-art numerical ODE solver.
The DormandPrince object provides a state-of-the-art numerical ODE solver. Given an unknown, time-dependent function 'y(t)' governed by an Ordinary Differential Equation (ODE) of the form
d/dt y(t) = f(t, y)
compute 'y(t)' using a (4,5)-order Dormand-Prince Integrator 'DOPRI'. Note: the 'integrateV' method for a system of separable ODEs is mixed in from the Integrator trait.

See also
http://adorio-research.org/wordpress/?p=6565
object DormandPrinceTest extends App
The DormandPrinceTest object is used to test the DormandPrince object.
object DynamicEqTest extends App
The DynamicEqTest object to test the DynamicEq class using example at in Introduction to Computational Data Science using ScalaTion, section 13.1.
The DynamicEqTest object to test the DynamicEq class using example at in Introduction to Computational Data Science using ScalaTion, section 13.1. > runMain scalation.dynamics.DynamicEqTest
object LinearDiffEqTest extends App
The LinearDiffEqTest object to test the LinearDiffEq class using example at
The LinearDiffEqTest object to test the LinearDiffEq class using example at

See also
biomed.tamu.edu/faculty/wu/BMEN_452/Eigenvalue%20Problems.doc The eigenvalues should be (-3, -1) The constant matrix should be [ (.375, .625), (-.75, 1.25) ]
object NLS_ODETest extends App
The VectorDTest object tests the operations provided by VectorD.
The VectorDTest object tests the operations provided by VectorD. > runMain scalation.dynamics.NLS_ODETest
object Radau extends Integrator
The Radau object implements Radau IIA, which is a simple Ordinary Differential Equation 'ODE' solver for moderately stiff systems.
The Radau object implements Radau IIA, which is a simple Ordinary Differential Equation 'ODE' solver for moderately stiff systems. Solve for 'y' given
d/dt y = f(t, y).
object RadauTest extends App
This object is used to test the Radau5 object.
object RungeKutta extends Integrator
The RungeKutta object provides an implementation of a classical numerical ODE solver.
The RungeKutta object provides an implementation of a classical numerical ODE solver. Given an unknown, time-dependent function 'y(t)' governed by an Ordinary Differential Equation (ODE) of the form:
d/dt y(t) = f(t, y)
Compute 'y(t)' using a 4th-order Runge-Kutta Integrator 'RK4'. Note: the 'integrateV' method for a system of separable ODEs is mixed in from the Integrator trait.
object RungeKuttaTest extends App
The RungeKuttaTest object is used to test the RungeKutta object.
object SSATest extends App
The SSATest object tests the SSA class.

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dynamics

package dynamics

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package dynamics

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dynamics