scijit.integrate.OdeSolution¶

class scijit.integrate.OdeSolution(*args, **kwargs)¶

Bases: OdeSolution

Continuous solution over the integrated span, res.sol.

solve_ivp(..., dense_output=True) returns one as res.sol, which is how most callers meet it. Building one by hand is for a step history obtained some other way.

sol(t) evaluates it, from Python and from inside @njit. A float gives (n_states,); a float64 array of k times gives (n_states, k). A Python list raises; wrap it in np.array.

Parameters:

t, hfloat64 array, shape (s,): Start time and signed step size of each accepted step.
ysfloat64 array, shape (s, n): State at the start of each accepted step.
Cfloat64 array, shape (s, 7, n): Interpolation coefficients per step.
methodint: METHOD_RK45, METHOD_RK23 or METHOD_DOP853, the method the history was produced with. A mismatch reads the coefficients under the wrong polynomial and returns wrong values silently.

Attributes:

tfloat64 array, shape (s,): Start time of each accepted step.
hfloat64 array, shape (s,): Signed step size of each accepted step.
ysfloat64 array, shape (s, n): State at the start of each accepted step.
Cfloat64 array, shape (s, 7, n): Interpolation coefficients per step.
methodint: The method the history was produced with.

Raises:

ValueError: If t is not strictly increasing or strictly decreasing, or if h, ys and C do not all carry one entry per time stamp. A two-entry t whose ends are equal is a zero-length span and is accepted.

See also

scipy.integrate._ivp.common.OdeSolution: The scipy routine this mirrors.

Notes

The constructor takes different arguments from scipy’s. scipy builds one as OdeSolution(ts, interpolants, alt_segment=False) from a list of DenseOutput objects; this one takes a step history as five arrays, and no parameter name is shared.

A constructor default is Python-only. Inside @njit every argument is passed explicitly, so a scipy-shaped OdeSolution(ts, interpolants), which leaves alt_segment to its default, has no compiled spelling.

The attribute sets are disjoint. A scipy instance carries ts, interpolants, n_segments, t_min, t_max, ascending, side and ts_sorted. This one carries t, h, ys, C and method.

sol(t) takes a float or a 1-D float64 array. scipy runs np.asarray(t) and accepts any array_like, a list included. On an empty array sol(np.array([])) returns shape (n, 0) and scipy raises ValueError('need at least one array to concatenate').

One scipy class covers every method. Here solve_ivp(method='LSODA', dense_output=True) returns a different type, _LsodaSolution built from a Nordsieck history, and a complex y0 returns a third, _OdeSolutionC.

Examples

>>> import numpy as np
>>> from numba import njit
>>> import scijit.integrate as si
>>> from scijit.integrate import OdeSolution
>>> @njit
... def rhs(t, y):
...     out = np.empty(2)
...     out[0] = y[1]
...     out[1] = -4.0 * y[0]
...     return out
>>> res = si.solve_ivp(rhs, (0.0, 1.0), np.array([1.0, 0.0]),
...                    'RK45', None, True)
>>> isinstance(res.sol, OdeSolution)
True
>>> res.sol(0.5)
array([ 0.54038693, -1.68337531])

__init__(t, h, ys, C, method)¶: Validate the step history and store it. Every argument is required; see the class docstring.

Methods

`__init__`(t, h, ys, C, method)	Validate the step history and store it.
`ev`(tt)	Evaluate at an array of times.
`ev_one`(tt)	Evaluate at a single time.

Attributes

class_type

class_type = jitclass.OdeSolution#7fad13b53250<t:array(float64, 1d, A),h:array(float64, 1d, A),ys:array(float64, 2d, A),C:array(float64, 3d, A),method:int64>¶