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bundles / scipy 1.17.1 / scipy / integrate / _ode / ode

class

scipy.integrate._ode:ode

source: /scipy/integrate/_ode.py :100

Signature

class   ode ( f ,  jac = None )

Members

Summary

A generic interface class to numeric integrators.

Extended Summary

Solve an equation system with (optional) jac = df/dy.

Note: The first two arguments of f(t, y, ...) are in the opposite order of the arguments in the system definition function used by scipy.integrate.odeint.

Parameters

f : callable ``f(t, y, *f_args)``

Right-hand side of the differential equation. t is a scalar, y.shape == (n,). f_args is set by calling set_f_params(*args). f should return a scalar, array or list (not a tuple).

jac : callable ``jac(t, y, *jac_args)``, optional

Jacobian of the right-hand side, jac[i,j] = d f[i] / d y[j]. jac_args is set by calling set_jac_params(*args).

Attributes

t : float

Current time.

y : ndarray

Current variable values.

Notes

Available integrators are listed below. They can be selected using the set_integrator method.

"vode"

Real-valued Variable-coefficient Ordinary Differential Equation solver, with fixed-leading-coefficient implementation. It provides implicit Adams method (for non-stiff problems) and a method based on backward differentiation formulas (BDF) (for stiff problems).

Source: http://www.netlib.org/ode/vode.f

This integrator accepts the following parameters in set_integrator method of the ode class:

  • atolfloat or sequence absolute tolerance for solution

  • rtolfloat or sequence relative tolerance for solution

  • lbandNone or int

  • ubandNone or int Jacobian band width, jac[i,j] != 0 for i-lband <= j <= i+uband. Setting these requires your jac routine to return the jacobian in packed format, jac_packed[i-j+uband, j] = jac[i,j]. The dimension of the matrix must be (lband+uband+1, len(y)).

  • method: 'adams' or 'bdf' Which solver to use, Adams (non-stiff) or BDF (stiff)

  • with_jacobianbool This option is only considered when the user has not supplied a Jacobian function and has not indicated (by setting either band) that the Jacobian is banded. In this case, with_jacobian specifies whether the iteration method of the ODE solver's correction step is chord iteration with an internally generated full Jacobian or functional iteration with no Jacobian.

  • nstepsint Maximum number of (internally defined) steps allowed during one call to the solver.

  • first_stepfloat

  • min_stepfloat

  • max_stepfloat Limits for the step sizes used by the integrator.

  • orderint Maximum order used by the integrator, order <= 12 for Adams, <= 5 for BDF.

"zvode"

Complex-valued Variable-coefficient Ordinary Differential Equation solver, with fixed-leading-coefficient implementation. It provides implicit Adams method (for non-stiff problems) and a method based on backward differentiation formulas (BDF) (for stiff problems).

Source: http://www.netlib.org/ode/zvode.f

This integrator accepts the same parameters in set_integrator as the "vode" solver.

"lsoda"

Real-valued Variable-coefficient Ordinary Differential Equation solver, with fixed-leading-coefficient implementation. It provides automatic method switching between implicit Adams method (for non-stiff problems) and a method based on backward differentiation formulas (BDF) (for stiff problems).

This integrator uses the C translation of the original Fortran 77 ODEPACK library, which can be found at http://www.netlib.org/odepack

This integrator accepts the following parameters in set_integrator method of the ode class:

  • atolfloat or sequence absolute tolerance for solution

  • rtolfloat or sequence relative tolerance for solution

  • lbandNone or int

  • ubandNone or int Jacobian band width, jac[i,j] != 0 for i-lband <= j <= i+uband. Setting these requires your jac routine to return the jacobian in packed format, jac_packed[i-j+uband, j] = jac[i,j].

  • with_jacobianbool Not used.

  • nstepsint Maximum number of (internally defined) steps allowed during one call to the solver.

  • first_stepfloat

  • min_stepfloat

  • max_stepfloat Limits for the step sizes used by the integrator.

  • max_order_nsint Maximum order used in the nonstiff case (default 12).

  • max_order_sint Maximum order used in the stiff case (default 5).

  • max_hnilint Maximum number of messages reporting too small step size (t + h = t) (default 0)

  • ixprint Whether to generate extra printing at method switches (default False).

"dopri5"

This is an explicit runge-kutta method of order (4)5 due to Dormand & Prince (with stepsize control and dense output).

Authors:

  • Hairer and G. Wanner

Universite de Geneve, Dept. de Mathematiques CH-1211 Geneve 24, Switzerland e-mail: ernst.hairer@math.unige.ch, gerhard.wanner@math.unige.ch

This code is described in [HNW93].

This integrator accepts the following parameters in set_integrator() method of the ode class:

  • atolfloat or sequence absolute tolerance for solution

  • rtolfloat or sequence relative tolerance for solution

  • nstepsint Maximum number of (internally defined) steps allowed during one call to the solver.

  • first_stepfloat

  • max_stepfloat

  • safetyfloat Safety factor on new step selection (default 0.9)

  • ifactorfloat

  • dfactorfloat Maximum factor to increase/decrease step size by in one step

  • betafloat Beta parameter for stabilised step size control.

  • verbosityint Switch for printing messages (< 0 for no messages).

"dop853"

This is an explicit runge-kutta method of order 8(5,3) due to Dormand & Prince (with stepsize control and dense output).

Options and references the same as "dopri5".

Examples

A problem to integrate and the corresponding jacobian: 
from scipy.integrate import ode
y0, t0 = [1.0j, 2.0], 0
def f(t, y, arg1):
    return [1j*arg1*y[0] + y[1], -arg1*y[1]**2]
def jac(t, y, arg1):
    return [[1j*arg1, 1], [0, -arg1*2*y[1]]]
✓
The integration: 
r = ode(f, jac).set_integrator('zvode', method='bdf')
✓
r.set_initial_value(y0, t0).set_f_params(2.0).set_jac_params(2.0)
✗
t1 = 10
dt = 1
✓
while r.successful() and r.t < t1:
    print(r.t+dt, r.integrate(r.t+dt))
✗

See also

odeint

an integrator with a simpler interface based on lsoda from ODEPACK

quad

for finding the area under a curve

Aliases

  • scipy.integrate.ode

Referenced by

This package