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emmy.numerical.derivative

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 emmy.differential (for the backing implementation) and emmy.calculus.derivative (for the [[emmy.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 [[emmy.differential]] (for the backing implementation)
and [[emmy.calculus.derivative]] (for the [[emmy.operator/Operator]]
instances that make it pleasant to use this method.)
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emmy.numerical.minimize

Entrypoint for univariate and multivariate minimization routines.

Entrypoint for univariate and multivariate minimization routines.
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emmy.numerical.ode

ODE solvers for working with initial value problems.

ODE solvers for working with initial value problems.
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emmy.numerical.quadrature.common

Implements 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.
Implements 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.
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emmy.numerical.quadrature.substitute

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'.

### 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).
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emmy.numerical.roots.bisect

This namespace contains implementations of a number of methods for root-finding on real-valued functions of one argument.

NOTE: This namespace is not yet stable: Expect these functions to change as new root-finding methods are added.

This namespace contains implementations of a number of methods for root-finding
on real-valued functions of one argument.

NOTE: This namespace is not yet stable: Expect these functions to change as
new root-finding methods are added. 
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emmy.numerical.unimin.brent

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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