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104 lines
3.9 KiB
Python
104 lines
3.9 KiB
Python
"""
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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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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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fixed_quad -- Integrate func(x) using Gaussian quadrature of order n
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quadrature -- Integrate with given tolerance using Gaussian quadrature
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romberg -- Integrate func using Romberg integration
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quad_explain -- Print information for use of quad
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newton_cotes -- Weights and error coefficient for Newton-Cotes integration
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IntegrationWarning -- Warning on issues during integration
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AccuracyWarning -- Warning on issues during quadrature 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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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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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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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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""" # noqa: E501
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from ._quadrature import *
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from .odepack import *
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from .quadpack 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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__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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