sicmutils.numerical.quadrature — net.littleredcomputer/sicmutils 0.13.0

available-methods clj/s

definite-integral clj/s

(definite-integral f a b)

(definite-integral f
                   a
                   b
                   {:keys [method compile? info?]
                    :or {method :open compile? false info? false}
                    :as opts})

Evaluates the definite integral of integrand f across the interval $a, b$. Optionally accepts a dictionary opts of customizing options; All opts will be passed through to the supplied integrate functions.

If you'd like more control, or to retrieve the integration function directly without looking it up via :method each time, see get-integrator.

All supplied options are passed through to the underlying integrator; see the specific integrator for information on what options are available.

Keyword arguments:

:method: Specifies the integration method used. Must be

• a keyword naming one of the available methods in available-methods
• a function with the proper integrator signature
• a dictionary of integrator options with a :method key

Defaults to :open, which specifies an adaptive bulirsch-stoer quadrature method.

:compile? If true, the generic function will be simplified and compiled before execution. (Clojure only for now.) Defaults to false.

:info? If true, definite-integral will return a map of integration information returned by the underlying integrator. Else, returns an estimate of the definite integral.

get-integrator clj/s

(get-integrator method a b)

(get-integrator method a b m)

Takes:

• An integration method, specified as either:

  • a keyword naming one of the available methods in available-methods
  • a function with the proper integrator signature
  • a dictionary of integrator options with a :method key

• a and b integration endpoints

• an optional dictionary of options m

And returns a pair of an integrator function and a possibly-enhanced options dictionary.

(Some integration functions require extra options, so the returned dictionary may have more entries than the m you pass in.)

If either endpoint is infinite, the returned integrator is wrapped in qi/improper and able to handle infinite endpoints (as well as non-infinite endpoints by passing through directly to the underlying integrator).