104 lines
3.9 KiB
Python
104 lines
3.9 KiB
Python
![]() |
"""
|
||
|
=============================================
|
||
|
Integration and ODEs (:mod:`scipy.integrate`)
|
||
|
=============================================
|
||
|
|
||
|
.. currentmodule:: scipy.integrate
|
||
|
|
||
|
Integrating functions, given function object
|
||
|
============================================
|
||
|
|
||
|
.. autosummary::
|
||
|
:toctree: generated/
|
||
|
|
||
|
quad -- General purpose integration
|
||
|
quad_vec -- General purpose integration of vector-valued functions
|
||
|
dblquad -- General purpose double integration
|
||
|
tplquad -- General purpose triple integration
|
||
|
nquad -- General purpose N-D integration
|
||
|
fixed_quad -- Integrate func(x) using Gaussian quadrature of order n
|
||
|
quadrature -- Integrate with given tolerance using Gaussian quadrature
|
||
|
romberg -- Integrate func using Romberg integration
|
||
|
quad_explain -- Print information for use of quad
|
||
|
newton_cotes -- Weights and error coefficient for Newton-Cotes integration
|
||
|
IntegrationWarning -- Warning on issues during integration
|
||
|
AccuracyWarning -- Warning on issues during quadrature integration
|
||
|
|
||
|
Integrating functions, given fixed samples
|
||
|
==========================================
|
||
|
|
||
|
.. autosummary::
|
||
|
:toctree: generated/
|
||
|
|
||
|
trapezoid -- Use trapezoidal rule to compute integral.
|
||
|
cumulative_trapezoid -- Use trapezoidal rule to cumulatively compute integral.
|
||
|
simpson -- Use Simpson's rule to compute integral from samples.
|
||
|
romb -- Use Romberg Integration to compute integral from
|
||
|
-- (2**k + 1) evenly-spaced samples.
|
||
|
|
||
|
.. seealso::
|
||
|
|
||
|
:mod:`scipy.special` for orthogonal polynomials (special) for Gaussian
|
||
|
quadrature roots and weights for other weighting factors and regions.
|
||
|
|
||
|
Solving initial value problems for ODE systems
|
||
|
==============================================
|
||
|
|
||
|
The solvers are implemented as individual classes, which can be used directly
|
||
|
(low-level usage) or through a convenience function.
|
||
|
|
||
|
.. autosummary::
|
||
|
:toctree: generated/
|
||
|
|
||
|
solve_ivp -- Convenient function for ODE integration.
|
||
|
RK23 -- Explicit Runge-Kutta solver of order 3(2).
|
||
|
RK45 -- Explicit Runge-Kutta solver of order 5(4).
|
||
|
DOP853 -- Explicit Runge-Kutta solver of order 8.
|
||
|
Radau -- Implicit Runge-Kutta solver of order 5.
|
||
|
BDF -- Implicit multi-step variable order (1 to 5) solver.
|
||
|
LSODA -- LSODA solver from ODEPACK Fortran package.
|
||
|
OdeSolver -- Base class for ODE solvers.
|
||
|
DenseOutput -- Local interpolant for computing a dense output.
|
||
|
OdeSolution -- Class which represents a continuous ODE solution.
|
||
|
|
||
|
|
||
|
Old API
|
||
|
-------
|
||
|
|
||
|
These are the routines developed earlier for SciPy. They wrap older solvers
|
||
|
implemented in Fortran (mostly ODEPACK). While the interface to them is not
|
||
|
particularly convenient and certain features are missing compared to the new
|
||
|
API, the solvers themselves are of good quality and work fast as compiled
|
||
|
Fortran code. In some cases, it might be worth using this old API.
|
||
|
|
||
|
.. autosummary::
|
||
|
:toctree: generated/
|
||
|
|
||
|
odeint -- General integration of ordinary differential equations.
|
||
|
ode -- Integrate ODE using VODE and ZVODE routines.
|
||
|
complex_ode -- Convert a complex-valued ODE to real-valued and integrate.
|
||
|
|
||
|
|
||
|
Solving boundary value problems for ODE systems
|
||
|
===============================================
|
||
|
|
||
|
.. autosummary::
|
||
|
:toctree: generated/
|
||
|
|
||
|
solve_bvp -- Solve a boundary value problem for a system of ODEs.
|
||
|
""" # noqa: E501
|
||
|
from ._quadrature import *
|
||
|
from .odepack import *
|
||
|
from .quadpack import *
|
||
|
from ._ode import *
|
||
|
from ._bvp import solve_bvp
|
||
|
from ._ivp import (solve_ivp, OdeSolution, DenseOutput,
|
||
|
OdeSolver, RK23, RK45, DOP853, Radau, BDF, LSODA)
|
||
|
from ._quad_vec import quad_vec
|
||
|
|
||
|
__all__ = [s for s in dir() if not s.startswith('_')]
|
||
|
|
||
|
from scipy._lib._testutils import PytestTester
|
||
|
test = PytestTester(__name__)
|
||
|
del PytestTester
|