sicmutils.numerical.quadrature.romberg
closed-integralclj/s
(closed-integral f a b)(closed-integral f a b opts)Returns an estimate of the integral of f over the closed interval $[a, b]$
generated by applying Richardson extrapolation to successive integral
estimates from the Trapezoid rule.
Considers $1, 2, 4 ... 2^n$ windows into $[a, b]$ for each successive estimate.
Optionally accepts opts, a dict of optional arguments. All of these get
passed on to us/seq-limit to configure convergence checking.
See closed-sequence for more information about Romberg integration, 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 $[a, b]$ generated by applying Richardson extrapolation to successive integral estimates from the Trapezoid rule. Considers $1, 2, 4 ... 2^n$ windows into $[a, b]$ for each successive estimate. Optionally accepts `opts`, a dict of optional arguments. All of these get passed on to `us/seq-limit` to configure convergence checking. See `closed-sequence` for more information about Romberg integration, caveats that might apply when using this integration method and information on the optional args in `opts` that customize this function's behavior.
closed-sequenceclj/s
(closed-sequence f a b)(closed-sequence f a b {:keys [n] :or {n 1} :as opts})Returns a (lazy) sequence of successively refined estimates of the integral of
f over the closed interval $[a, b]$ by applying Richardson extrapolation to
successive integral estimates from the Trapezoid rule.
Returns estimates formed by combining $n, 2n, 4n, ...$ slices, geometrically increasing by a factor of 2 with each estimate.
Romberg integration converges quite fast by cancelling one error term in the taylor series expansion of $f$ with each examined term. If your function is /not/ smooth this may cause you trouble, and you may want to investigate a lower-order method.
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 $[a, b]$ by applying Richardson extrapolation to successive integral estimates from the Trapezoid rule. Returns estimates formed by combining $n, 2n, 4n, ...$ slices, geometrically increasing by a factor of 2 with each estimate. Romberg integration converges quite fast by cancelling one error term in the taylor series expansion of $f$ with each examined term. If your function is /not/ smooth this may cause you trouble, and you may want to investigate a lower-order method. ## Optional arguments: If supplied, `:n` (default 1) specifies the initial number of slices to use.
open-integralclj/s
(open-integral f a b)(open-integral f a b opts)Returns an estimate of the integral of f over the open interval $(a, b)$
generated by applying Richardson extrapolation to successive integral
estimates from the Midpoint rule.
Considers $1, 3, 9 ... 3^n$ windows into $(a, b)$ for each successive estimate.
Optionally accepts opts, a dict of optional arguments. All of these get
passed on to us/seq-limit to configure convergence checking.
See open-sequence for more information about Romberg integration, 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 open interval $(a, b)$ generated by applying Richardson extrapolation to successive integral estimates from the Midpoint rule. Considers $1, 3, 9 ... 3^n$ windows into $(a, b)$ for each successive estimate. Optionally accepts `opts`, a dict of optional arguments. All of these get passed on to `us/seq-limit` to configure convergence checking. See `open-sequence` for more information about Romberg integration, caveats that might apply when using this integration method and information on the optional args in `opts` that customize this function's behavior.
open-sequenceclj/s
(open-sequence f a b)(open-sequence f a b {:keys [n] :or {n 1} :as opts})Returns a (lazy) sequence of successively refined estimates of the integral of
f over the open interval $(a, b)$ by applying Richardson extrapolation to
successive integral estimates from the Midpoint rule.
Returns estimates formed by combining $n, 3n, 9n, ...$ slices, geometrically increasing by a factor of 3 with each estimate. This factor of 3 is because, internally, the Midpoint method is able to recycle old function evaluations through this factor of 3.
Romberg integration converges quite fast by cancelling one error term in the taylor series expansion of $f$ with each examined term. If your function is /not/ smooth this may cause you trouble, and you may want to investigate a lower-order method.
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 open interval $(a, b)$ by applying Richardson extrapolation to successive integral estimates from the Midpoint rule. Returns estimates formed by combining $n, 3n, 9n, ...$ slices, geometrically increasing by a factor of 3 with each estimate. This factor of 3 is because, internally, the Midpoint method is able to recycle old function evaluations through this factor of 3. Romberg integration converges quite fast by cancelling one error term in the taylor series expansion of $f$ with each examined term. If your function is /not/ smooth this may cause you trouble, and you may want to investigate a lower-order method. ## Optional arguments: If supplied, `:n` (default 1) specifies the initial number of slices to use.
romberg-sequenceclj/s
(romberg-sequence f a b)(romberg-sequence f a b opts)Higher-level abstraction over closed-sequence and open-sequence. Identical
to those functions (see their docstrings), but internally chooses either
implementation based on the interval specified inside of opts.
Defaults to the same behavior as open-sequence.
Higher-level abstraction over `closed-sequence` and `open-sequence`. Identical to those functions (see their docstrings), but internally chooses either implementation based on the interval specified inside of `opts`. Defaults to the same behavior as `open-sequence`.
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