This namespace contains implementations of various approaches to numerical differentiation.
Each of these methods uses Richardson extrapolation to accelerate convergence, and roundoff error estimation to bail out of the computation when roundoff error threatens to overwhelm the calculation.
For an implementation of forward-mode automatic
differentiation,
see sicmutils.differential
(for the backing implementation)
and sicmutils.calculus.derivative
(for the sicmutils.operator/Operator
instances that make it pleasant to use this method.)
This namespace contains implementations of various approaches to [numerical differentiation](https://en.wikipedia.org/wiki/Numerical_differentiation). Each of these methods uses [Richardson extrapolation](https://en.wikipedia.org/wiki/Richardson_extrapolation) to accelerate convergence, and roundoff error estimation to bail out of the computation when roundoff error threatens to overwhelm the calculation. For an implementation of [forward-mode automatic differentiation](https://en.wikipedia.org/wiki/Automatic_differentiation), see [[sicmutils.differential]] (for the backing implementation) and [[sicmutils.calculus.derivative]] (for the [[sicmutils.operator/Operator]] instances that make it pleasant to use this method.)
This namespace contains function to compute various elliptic integrals in Carlson symmetric form, as well as the Jacobi elliptic functions.
This namespace contains function to compute various [elliptic integrals](https://en.wikipedia.org/wiki/Elliptic_integral) in [Carlson symmetric form](https://en.wikipedia.org/wiki/Carlson_symmetric_form), as well as the [Jacobi elliptic functions](https://en.wikipedia.org/wiki/Jacobi_elliptic_functions).
This namespace contains a discussion of polynomial interpolation, and different
methods for fitting a polynomial of degree N-1
to N
points and evaluating
that polynomial at some different x
.
This namespace contains a discussion of polynomial interpolation, and different methods for fitting a polynomial of degree `N-1` to `N` points and evaluating that polynomial at some different `x`.
This namespace contains a discussion of rational function interpolation, and
different methods for fitting rational functions to N
points and evaluating
them at some value x
.
This namespace contains a discussion of rational function interpolation, and different methods for fitting rational functions to `N` points and evaluating them at some value `x`.
Richardson interpolation is a special case of polynomial interpolation; knowing
the ratios of successive x
coordinates in the point sequence allows a more
efficient calculation.
Richardson interpolation is a special case of polynomial interpolation; knowing the ratios of successive `x` coordinates in the point sequence allows a more efficient calculation.
Entrypoint for univariate and multivariate minimization routines.
Entrypoint for univariate and multivariate minimization routines.
ODE solvers for working with initial value problems.
ODE solvers for working with initial value problems.
Implements utilities shared by all integrators, for example:
integrator
interfaceImplements utilities shared by all integrators, for example: - code to wrap a sequence of progressively better estimates in a common `integrator` interface - data structures implementing various integration intervals.
This namespace provides implementations of functions that accept an
integrator
and perform a variable change to address some singularity, like
an infinite endpoint, in the definite integral.
The strategies currently implemented were each described by Press, et al. in section 4.4 of 'Numerical Recipes'.
### U Substitution and Variable Changes This namespace provides implementations of functions that accept an `integrator` and perform a variable change to address some singularity, like an infinite endpoint, in the definite integral. The strategies currently implemented were each described by Press, et al. in section 4.4 of ['Numerical Recipes'](http://phys.uri.edu/nigh/NumRec/bookfpdf/f4-4.pdf).
Trapezoid method.
Trapezoid method.
This namespace contains an implementation of Brent's method for finding the minimum of a real-valued function.
This namespace contains an implementation of Brent's method for finding the minimum of a real-valued function.
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