emmy.numerical.quadrature.boole
boole-sequenceclj/s
(boole-sequence f a b)(boole-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 Boole's rule.
Boole's rule is equivalent to the trapezoid method subject to two refinements of Richardson extrapolation. The trapezoid method fits a line to each integration slice. Boole's rule fits a quartic to each slice.
Returns estimates with $n, 2n, 4n, ...$ slices, geometrically increasing by a factor of 2 with each estimate.
Optional arguments:
If supplied, :n (default 1) specifies the initial number of slices to use.
Returns a (lazy) sequence of successively refined estimates of the integral of `f` over the closed interval $[a, b]$ using Boole's rule. Boole's rule is equivalent to the trapezoid method subject to two refinements of Richardson extrapolation. The trapezoid method fits a line to each integration slice. Boole's rule fits a quartic to each slice. Returns estimates with $n, 2n, 4n, ...$ slices, geometrically increasing by a factor of 2 with each estimate. ### Optional arguments: If supplied, `:n` (default 1) specifies the initial number of slices to use.
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 Boole's rule with $1, 2, 4 ... 2^n$ 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 boole-sequence for more information about Boole's 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 Boole's rule with $1, 2, 4 ... 2^n$ 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 `boole-sequence` for more information about Boole's rule, caveats that might apply when using this integration method and information on the optional args in `opts` that customize this function's behavior.
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