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emmy.numerical.quadrature.simpson38


integralclj/s

(integral f a b)
(integral f a b opts)

Returns an estimate of the integral of f over the closed interval $[a, b]$ using Simpson's 3/8 rule with $1, 3, 9 ... 3^n$ windows for each estimate.

Optionally accepts opts, a dict of optional arguments. All of these get passed on to us/seq-limit to configure convergence checking.

See simpson38-sequence for more information about Simpson's 3/8 rule, caveats that might apply when using this integration method and information on the optional args in opts that customize this function's behavior.

Returns an estimate of the integral of `f` over the closed interval $[a, b]$
using Simpson's 3/8 rule with $1, 3, 9 ... 3^n$ windows for each estimate.

Optionally accepts `opts`, a dict of optional arguments. All of these get
passed on to `us/seq-limit` to configure convergence checking.

See [[simpson38-sequence]] for more information about Simpson's 3/8 rule, caveats
that might apply when using this integration method and information on the
optional args in `opts` that customize this function's behavior.
sourceraw docstring

simpson38-sequenceclj/s

(simpson38-sequence f a b)
(simpson38-sequence f a b {:keys [n] :or {n 1}})

Returns a (lazy) sequence of successively refined estimates of the integral of f over the closed interval $[a, b]$ using Simpson's 3/8 rule.

Simpson's 3/8 rule is equivalent to the trapezoid method subject to:

  • one refinement of Richardson extrapolation, and

  • a geometric increase of integration slices by a factor of 3 for each sequence element. (the Trapezoid method increases by a factor of 2 by default.)

The trapezoid method fits a line to each integration slice. Simpson's 3/8 rule fits a cubic to each slice.

Returns estimates with $n, 3n, 9n, ...n3^i$ slices, geometrically increasing by a factor of 3 with each estimate.

Optional arguments:

If supplied, :n (default 1) specifies the initial number of slices to use.

NOTE: the Trapezoid method is able to reuse function evaluations as its windows narrow /only/ when increasing the number of integration slices by 2. Simpson's 3/8 rule increases the number of slices geometrically by a factor of 3 each time, so it will never hit the incremental path. You may want to memoize your function before calling simpson38-sequence.

Returns a (lazy) sequence of successively refined estimates of the integral of
`f` over the closed interval $[a, b]$ using Simpson's 3/8 rule.

Simpson's 3/8 rule is equivalent to the trapezoid method subject to:

- one refinement of Richardson extrapolation, and

- a geometric increase of integration slices by a factor of 3 for each
sequence element. (the Trapezoid method increases by a factor of 2 by
default.)

The trapezoid method fits a line to each integration slice. Simpson's 3/8 rule
fits a cubic to each slice.

Returns estimates with $n, 3n, 9n, ...n3^i$ slices, geometrically increasing by a
factor of 3 with each estimate.

### Optional arguments:

If supplied, `:n` (default 1) specifies the initial number of slices to use.

NOTE: the Trapezoid method is able to reuse function evaluations as its
windows narrow /only/ when increasing the number of integration slices by 2.
Simpson's 3/8 rule increases the number of slices geometrically by a factor of
3 each time, so it will never hit the incremental path. You may want to
memoize your function before calling `simpson38-sequence`.
sourceraw docstring

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