emmy.numerical.quadrature.midpoint
integralclj/s
(integral f a b)(integral f a b opts)Returns an estimate of the integral of f over the open interval $(a, b)$
using the Midpoint method 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 midpoint-sequence for information on the optional args in opts that
customize this function's behavior.
Returns an estimate of the integral of `f` over the open interval $(a, b)$ using the Midpoint method 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 [[midpoint-sequence]] for information on the optional args in `opts` that customize this function's behavior.
midpoint-sequenceclj/s
(midpoint-sequence f a b)(midpoint-sequence f a b {:keys [n accelerate?] :or {n 1}})Returns a (lazy) sequence of successively refined estimates of the integral of
f over the open interval $(a, b)$ using the Midpoint method.
Optional arguments:
:n: If :n is a number, returns estimates with $n, 3n, 9n, ...$ slices,
geometrically increasing by a factor of 3 with each estimate.
If :n is a sequence, the resulting sequence will hold an estimate for each
integer number of slices in that sequence.
:accelerate?: if supplied (and n is a number), attempts to accelerate
convergence using Richardson extrapolation. If n is a sequence this option
is ignored.
Returns a (lazy) sequence of successively refined estimates of the integral of `f` over the open interval $(a, b)$ using the Midpoint method. ### Optional arguments: `:n`: If `:n` is a number, returns estimates with $n, 3n, 9n, ...$ slices, geometrically increasing by a factor of 3 with each estimate. If `:n` is a sequence, the resulting sequence will hold an estimate for each integer number of slices in that sequence. `:accelerate?`: if supplied (and `n` is a number), attempts to accelerate convergence using Richardson extrapolation. If `n` is a sequence this option is ignored.
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