pycvodes package

Python binding for cvodes from the sundials library.

pycvodes.get_include()

pycvodes.integrate_adaptive(rhs, jac, y0, x0, xend, dx0, atol, rtol, dx_min=0.0, dx_max=0.0, nsteps=500, nderiv=0, roots=None, nroots=0, return_on_root=False, check_callable=False, check_indexing=False, **kwargs)

Integrates a system of ordinary differential equations.

Solves the initial value problem (IVP) defined by the user supplied arguments. The solver chooses at what values of the independent variable results should be reported.

Parameters:

rhs : callable

Function with signature f(t, y, fout) which modifies fout inplace.

jac : callable

Function with signature j(t, y, jmat_out, dfdx_out) which modifies jmat_out and dfdx_out inplace.

y0 : array_like

Initial values of the dependent variables.

x0 : float

Initial value of the independent variable.

xend : float

Stopping value for the independent variable.

dx0 : float

Initial step-size.

atol : float

Absolute tolerance.

rtol : float

Relative tolerance.

dx_min : float

Minimum step (default: 0.0).

dx_max : float

Maximum step (default: 0.0).

nsteps : int

Maximum number of steps (default: 500).

nderiv : int

Number of derivatives (default: 0).

roots : callback

With signature roots(x, yarr[:ny], out[:nroots]) -> None.

nroots : int

Number of root functions in roots.

return_on_root : bool

Exit early (on first found root).

check_callable : bool

perform signature sanity checks on rhs and jac

check_indexing : bool

Perform item setting sanity checks on rhs and jac.

**kwargs:

‘lband’: int

Number of lower bands. Indexing: banded[row_i - col_i + uband, col_i].

‘uband’: int

Number of upper bands. Indexing: banded[row_i - col_i + uband, col_i].

‘method’: str

One of: ‘adams’ or ‘bdf’ (default: ‘bdf’)

‘iter_type’: str (default: ‘default’)

One of: ‘default’, ‘functional’, ‘newton’

‘linear_solver’: str (default: ‘default’)

One of: ‘default’, ‘dense’, ‘banded’, ‘gmres’, ‘gmres_classic’, ‘bicgstab’, ‘tfqmr’

Returns:

(xout, yout, info):

xout: 1-dimensional array of values for the independent variable yout: 2-dimensional array of the dependent variables (axis 1) for

values corresponding to xout (axis 0).

info: Dictionary with information about the integration.

pycvodes.integrate_predefined(rhs, jac, y0, xout, dx0, atol, rtol, dx_min=0.0, dx_max=0.0, nsteps=500, nderiv=0, roots=None, nroots=0, check_callable=False, check_indexing=False, **kwargs)

Integrates a system of ordinary differential equations.

Solves the initial value problem (IVP) defined by the user supplied arguments. The user chooses at what values of the independent variable results should be reported.

Parameters:

rhs : callable

Function with signature f(t, y, fout) which modifies fout inplace.

jac : callable

Function with signature j(t, y, jmat_out, dfdx_out) which modifies jmat_out and dfdx_out inplace.

y0 : array_like

Initial values of the dependent variables.

xout : array_like

Values of the independent variable.

dx0 : float

Initial step-size.

atol : float

Absolute tolerance.

rtol : float

Relative tolerance.

dx_min : float

Minimum step (default: 0.0).

dx_max : float

Maximum step (default: 0.0).

nsteps : int

Maximum number of steps (default: 500).

nderiv : int

Number of derivatives (default: 0).

roots : callback (default: None)

With signature roots(x, yarr[:ny], out[:nroots]) -> None, see info[‘root_indices’], note that xout is unaffected.

nroots : int (default: 0)

Number of root functions in roots.

check_callable : bool (default: False)

Perform signature sanity checks on rhs and jac.

check_indexing : bool (default: False)

Perform item setting sanity checks on rhs and jac.

**kwargs:

‘lband’: int

Number of lower bands. Indexing: banded[row_i - col_i + uband, col_i].

‘uband’: int

Number of upper bands. Indexing: banded[row_i - col_i + uband, col_i].

‘method’: str

One of: ‘adams’ or ‘bdf’ (default: ‘bdf’).

‘iter_type’: str (default: ‘default’)

One of: ‘default’, ‘functional’, ‘newton’.

‘linear_solver’: str (default: ‘default’)

One of: ‘default’, ‘dense’, ‘banded’, ‘gmres’, ‘gmres_classic’, ‘bicgstab’, ‘tfqmr’.

Returns:

(yout, info):

yout: 2-dimensional array of the dependent variables (axis 1) for

values corresponding to xout (axis 0)

info: Dictionary with information about the integration.