| """ |
| ============================================= |
| 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 |
| newton_cotes -- Weights and error coefficient for Newton-Cotes integration |
| qmc_quad -- N-D integration using Quasi-Monte Carlo quadrature |
| 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. |
| cumulative_simpson -- Use Simpson's rule to cumulatively 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. |
| ODEintWarning -- Warning raised during the execution of `odeint`. |
| |
| |
| Solving boundary value problems for ODE systems |
| =============================================== |
| |
| .. autosummary:: |
| :toctree: generated/ |
| |
| solve_bvp -- Solve a boundary value problem for a system of ODEs. |
| """ |
|
|
|
|
| from ._quadrature import * |
| from ._odepack_py import * |
| from ._quadpack_py 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 |
|
|
| |
| from . import dop, lsoda, vode, odepack, quadpack |
|
|
| __all__ = [s for s in dir() if not s.startswith('_')] |
|
|
| from scipy._lib._testutils import PytestTester |
| test = PytestTester(__name__) |
| del PytestTester |
|
|
