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sicmutils.numerical.quadrature.trapezoid

Trapezoid method.

Trapezoid method.
raw docstring

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 the Trapezoid method 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 trapezoid-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 closed interval $[a, b]$
using the Trapezoid method 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 `trapezoid-sequence` for information on the optional args in `opts` that
customize this function's behavior.
sourceraw docstring

single-trapezoidclj/s

(single-trapezoid f xl xr)
source

trapezoid-sequenceclj/s

(trapezoid-sequence f a b)
(trapezoid-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 Trapezoid method.

Optional arguments:

:n: If :n is a number, returns estimates with $n, 2n, 4n, ...$ slices, geometrically increasing by a factor of 2 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 Trapezoid method.

## Optional arguments:

`:n`: If `:n` is a number, returns estimates with $n, 2n, 4n, ...$ slices,
geometrically increasing by a factor of 2 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.
sourceraw docstring

trapezoid-sumclj/s

(trapezoid-sum f a b)

Returns a function of n, some number of slices of the total integration range, that returns an estimate for the definite integral of $f$ over the range $(a, b)$ using the trapezoid method.

Returns a function of `n`, some number of slices of the total integration
range, that returns an estimate for the definite integral of $f$ over the
range $(a, b)$ using the trapezoid method.
sourceraw docstring

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