mmf.math.integrate.integrate_1d.imt¶
| IMT(*varargin, **kwargs) | Class for performing the integral |
Inheritance diagram for mmf.math.integrate.integrate_1d.imt:
IMT Integration method (mmf.math.integrate.integrate_1d.imt)
| IMT(*varargin, **kwargs) | Class for performing the integral |
- class mmf.math.integrate.integrate_1d.imt.IMT(*varargin, **kwargs)[source]¶
Bases: mmf.objects.StateVars
Class for performing the integral
IMT(n_max=11, n=9, n_0=5, abs_tol=2.22044604925e-16, rel_tol=2.22044604925e-16, verbosity=0)
using the IMT method for evaluating integrals over [0,1]:
![\int_{0}^{1} f(x) \d{x} = \int_{0}^{1} f[x(t)] x'(t) \d{t}
\approx \frac{1}{N}\sum_{k=1}^{N-1} f(x_k) x'_{k},\\
t_{k} = \frac{k}{N},\\
x_{k} = \int_{0}^{t_{k}} x'(t)\d{t},\\
x'(t) = \frac{1}{Q}\exp\left(-\frac{1}{t} - \frac{1}{1-t}\right),\\
Q = \int_{0}^{1}\exp\left(-\frac{1}{t} - \frac{1}{1-t}\right).](../../../_images/math/8c3e1dd8b24c985a7404d9f7b9b1aa443e91276b.png)
Examples
>>> integrate = IMT() >>> integrate(np.sqrt, 0, 1) 0.666666666...
Attributes