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1"""
2=============================================
3Integration and ODEs (:mod:`scipy.integrate`)
4=============================================
6.. currentmodule:: scipy.integrate
8Integrating functions, given function object
9============================================
11.. autosummary::
12 :toctree: generated/
14 quad -- General purpose integration
15 quad_vec -- General purpose integration of vector-valued functions
16 dblquad -- General purpose double integration
17 tplquad -- General purpose triple integration
18 nquad -- General purpose N-D integration
19 fixed_quad -- Integrate func(x) using Gaussian quadrature of order n
20 quadrature -- Integrate with given tolerance using Gaussian quadrature
21 romberg -- Integrate func using Romberg integration
22 quad_explain -- Print information for use of quad
23 newton_cotes -- Weights and error coefficient for Newton-Cotes integration
24 IntegrationWarning -- Warning on issues during integration
25 AccuracyWarning -- Warning on issues during quadrature integration
27Integrating functions, given fixed samples
28==========================================
30.. autosummary::
31 :toctree: generated/
33 trapz -- Use trapezoidal rule to compute integral.
34 cumtrapz -- Use trapezoidal rule to cumulatively compute integral.
35 simps -- Use Simpson's rule to compute integral from samples.
36 romb -- Use Romberg Integration to compute integral from
37 -- (2**k + 1) evenly-spaced samples.
39.. seealso::
41 :mod:`scipy.special` for orthogonal polynomials (special) for Gaussian
42 quadrature roots and weights for other weighting factors and regions.
44Solving initial value problems for ODE systems
45==============================================
47The solvers are implemented as individual classes, which can be used directly
48(low-level usage) or through a convenience function.
50.. autosummary::
51 :toctree: generated/
53 solve_ivp -- Convenient function for ODE integration.
54 RK23 -- Explicit Runge-Kutta solver of order 3(2).
55 RK45 -- Explicit Runge-Kutta solver of order 5(4).
56 DOP853 -- Explicit Runge-Kutta solver of order 8.
57 Radau -- Implicit Runge-Kutta solver of order 5.
58 BDF -- Implicit multi-step variable order (1 to 5) solver.
59 LSODA -- LSODA solver from ODEPACK Fortran package.
60 OdeSolver -- Base class for ODE solvers.
61 DenseOutput -- Local interpolant for computing a dense output.
62 OdeSolution -- Class which represents a continuous ODE solution.
65Old API
66-------
68These are the routines developed earlier for SciPy. They wrap older solvers
69implemented in Fortran (mostly ODEPACK). While the interface to them is not
70particularly convenient and certain features are missing compared to the new
71API, the solvers themselves are of good quality and work fast as compiled
72Fortran code. In some cases, it might be worth using this old API.
74.. autosummary::
75 :toctree: generated/
77 odeint -- General integration of ordinary differential equations.
78 ode -- Integrate ODE using VODE and ZVODE routines.
79 complex_ode -- Convert a complex-valued ODE to real-valued and integrate.
82Solving boundary value problems for ODE systems
83===============================================
85.. autosummary::
86 :toctree: generated/
88 solve_bvp -- Solve a boundary value problem for a system of ODEs.
89"""
90from ._quadrature import *
91from .odepack import *
92from .quadpack import *
93from ._ode import *
94from ._bvp import solve_bvp
95from ._ivp import (solve_ivp, OdeSolution, DenseOutput,
96 OdeSolver, RK23, RK45, DOP853, Radau, BDF, LSODA)
97from ._quad_vec import quad_vec
99__all__ = [s for s in dir() if not s.startswith('_')]
101from scipy._lib._testutils import PytestTester
102test = PytestTester(__name__)
103del PytestTester