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integration\n fixed_quad -- Integrate func(x) using Gaussian quadrature of order n\n newton_cotes -- Weights and error coefficient for Newton-Cotes integration\n lebedev_rule\n qmc_quad -- N-D integration using Quasi-Monte Carlo quadrature\n IntegrationWarning -- Warning on issues during integration", "execution_status": null } ], "title": [ { "__type": "Text", "__tag": 4046, "value": "Integrating functions, given function object" } ], "level": 1, "target": null }, { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Code", "__tag": 4050, "value": ".. autosummary:: \n :toctree:generated/\n trapezoid -- Use trapezoidal rule to compute integral.\n cumulative_trapezoid -- Use trapezoidal rule to cumulatively compute integral.\n simpson -- Use Simpson's rule to compute integral from samples.\n cumulative_simpson -- Use Simpson's rule to cumulatively compute integral from samples.\n romb -- Use Romberg Integration to compute integral from\n -- (2**k + 1) evenly-spaced samples.", "execution_status": null }, { "__type": "Admonition", "__tag": 4056, "kind": "seealso", "base_type": "note", "children": [ { "__type": "AdmonitionTitle", "__tag": 4055, "children": [ { "__type": "Text", "__tag": 4046, "value": "seealso " } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "CrossRef", "__tag": 4002, "value": "scipy.special", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.special" }, "kind": "module" }, { "__type": "Text", "__tag": 4046, "value": " for orthogonal polynomials (special) for Gaussian quadrature roots and weights for other weighting factors and regions." } ] } ] } ], "title": [ { "__type": "Text", "__tag": 4046, "value": "Integrating functions, given fixed samples" } ], "level": 1, "target": null }, { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Code", "__tag": 4050, "value": ".. autosummary:: \n :toctree:generated/\n nsum", "execution_status": null } ], "title": [ { "__type": "Text", "__tag": 4046, "value": "Summation" } ], "level": 1, "target": null }, { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "The solvers are implemented as individual classes, which can be used directly (low-level usage) or through a convenience function." } ] }, { "__type": "Code", "__tag": 4050, "value": ".. autosummary:: \n :toctree:generated/\n solve_ivp -- Convenient function for ODE integration.\n RK23 -- Explicit Runge-Kutta solver of order 3(2).\n RK45 -- Explicit Runge-Kutta solver of order 5(4).\n DOP853 -- Explicit Runge-Kutta solver of order 8.\n Radau -- Implicit Runge-Kutta solver of order 5.\n BDF -- Implicit multi-step variable order (1 to 5) solver.\n LSODA -- LSODA solver from ODEPACK Fortran package.\n OdeSolver -- Base class for ODE solvers.\n DenseOutput -- Local interpolant for computing a dense output.\n OdeSolution -- Class which represents a continuous ODE solution.", "execution_status": null } ], "title": [ { "__type": "Text", "__tag": 4046, "value": "Solving initial value problems for ODE systems" } ], "level": 1, "target": null }, { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "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." } ] }, { "__type": "Code", "__tag": 4050, "value": ".. autosummary:: \n :toctree:generated/\n odeint -- General integration of ordinary differential equations.\n ode -- Integrate ODE using VODE and ZVODE routines.\n complex_ode -- Convert a complex-valued ODE to real-valued and integrate.\n ODEintWarning -- Warning raised during the execution of `odeint`.", "execution_status": null } ], "title": [ { "__type": "Text", "__tag": 4046, "value": "Old API" } ], "level": 2, "target": null }, { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Code", "__tag": 4050, "value": ".. autosummary:: \n :toctree:generated/\n solve_bvp -- Solve a boundary value problem for a system of ODEs.", "execution_status": null } ], "title": [ { "__type": "Text", "__tag": 4046, "value": "Solving boundary value problems for ODE systems" } ], "level": 1, "target": null } ], "local_refs": [] }