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