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.
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`.
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