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SciPy Reference Guide, Release 0.8.dev See Also: ode Array containing the value of y for each desired time in t, with the initial value y0 in the first row. infodict : dict, only returned if full_output == True Dictionary containing additional output information key meaning ‘hu’ vector of step sizes successfully used for each time step. ‘tcur’ vector with the value of t reached for each time step. (will always be at least as large as the input time ‘tolsf’ vector of tolerance scale factors, greater than 1.0, computed when a request for too much accuracy wa detected. ‘tsw’ value of t at the time of the last method switch (given for each time step) ‘nst’ cumulative number of time steps ‘nfe’ cumulative number of function evaluations for each time step ‘nje’ cumulative number of jacobian evaluations for each time step ‘nqu’ a vector of method orders for each successful step. ‘imxer’ index of the component of largest magnitude in the weighted local error vector (e / ewt) on an error return, -1 otherwise. ‘lenrw’ the length of the double work array required. ‘leniw’ the length of integer work array required. ‘mused’ a vector of method indicators for each successful time step: 1: adams (nonstiff), 2: bdf (stiff) a more object-oriented integrator based on VODE quad for finding the area under a curve class ode(f, jac=None) A generic interface class to numeric integrators. See Also: odeint an integrator with a simpler interface based on lsoda from ODEPACK quad for finding the area under a curve Examples A problem to integrate and the corresponding jacobian: >>> from scipy import eye >>> from scipy.integrate import ode >>> >>> y0, t0 = [1.0j, 2.0], 0 >>> >>> def f(t, y, arg1): >>> return [1j*arg1*y[0] + y[1], -arg1*y[1]**2] >>> def jac(t, y, arg1): >>> return [[1j*arg1, 1], [0, -arg1*2*y[1]]] The integration: 186 Chapter 3. Reference
SciPy Reference Guide, Release 0.8.dev >>> r = ode(f, jac).set_integrator(’zvode’, method=’bdf’, with_jacobian=True) >>> r.set_initial_value(y0, t0).set_f_params(2.0).set_jac_params(2.0) >>> t1 = 10 >>> dt = 1 >>> while r.successful() and r.t < t1: >>> r.integrate(r.t+dt) >>> print r.t, r.y Methods ode.integrate ode.set_f_params ode.set_initial_value ode.set_integrator ode.set_jac_params ode.successful 3.5 Interpolation (scipy.interpolate) 3.5.1 Univariate interpolation interp1d(x, y[, kind, axis, copy, ...]) Interpolate a 1D function. BarycentricInterpolator(xi[, yi]) The interpolating polynomial for a set of points KroghInterpolator(xi, yi) The interpolating polynomial for a set of points PiecewisePolynomial(xi, yi[, orders, Piecewise polynomial curve specified by points and direction]) derivatives barycentric_interpolate(xi, yi, x) Convenience function for polynomial interpolation krogh_interpolate(xi, yi, x[, der]) Convenience function for polynomial interpolation. piecewise_polynomial_interpolate(xi, Convenience function for piecewise polynomial yi, x) interpolation class interp1d(x, y, kind=’linear’, axis=-1, copy=True, bounds_error=True, fill_value=nan) Interpolate a 1D function. See Also: splrep, splev, UnivariateSpline class BarycentricInterpolator(xi, yi=None) The interpolating polynomial for a set of points Constructs a polynomial that passes through a given set of points. Allows evaluation of the polynomial, efficient changing of the y values to be interpolated, and updating by adding more x values. For reasons of numerical stability, this function does not compute the coefficients of the polynomial. This class uses a “barycentric interpolation” method that treats the problem as a special case of rational function interpolation. This algorithm is quite stable, numerically, but even in a world of exact computation, unless the x coordinates are chosen very carefully - Chebyshev zeros (e.g. cos(i*pi/n)) are a good choice - polynomial interpolation itself is a very ill-conditioned process due to the Runge phenomenon. Based on Berrut and Trefethen 2004, “Barycentric Lagrange Interpolation”. Methods add_xi(xi[, yi]) Add more x values to the set to be interpolated set_yi(yi) Update the y values to be interpolated 3.5. Interpolation (scipy.interpolate) 187
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