emmy.numerical.quadrature.bulirsch-stoer
bulirsch-stoer-stepsclj/s
Default step sizes used by the Bulirsch-Stoer quadrature algorithm:
2, 3, 4, 6, 8, 12, 16, 24, 32, ...
Default step sizes used by the Bulirsch-Stoer quadrature algorithm: ``` 2, 3, 4, 6, 8, 12, 16, 24, 32, ... ```
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 rational polynomial extrapolation to successive integral
estimates from the Trapezoid rule.
Considers successive numbers of windows into $[a, b]$ specified by
bulirsch-stoer-steps.
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 Bulirsch-Stoer quadrature,
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 rational polynomial extrapolation to successive integral estimates from the Trapezoid rule. Considers successive numbers of windows into $[a, b]$ specified by `bulirsch-stoer-steps`. 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 Bulirsch-Stoer quadrature, 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
Returns a (lazy) sequence of successively refined estimates of the
integral of f over the closed interval $[a, b]$ by applying rational
polynomial extrapolation to successive integral estimates from the Trapezoid
rule.
Returns estimates formed from the same estimates used by the Bulirsch-Stoer
ODE solver, stored in bulirsch-stoer-steps.
Optional arguments:
:n: If supplied, :n (sequence) overrides the sequence of steps to use.
:bs-extrapolator: Pass :polynomial to override the default rational
function extrapolation and enable polynomial extrapolation using the modified
Neville's algorithm implemented in poly/modified-neville.
Returns a (lazy) sequence of successively refined estimates of the integral of `f` over the closed interval $[a, b]$ by applying rational polynomial extrapolation to successive integral estimates from the Trapezoid rule. Returns estimates formed from the same estimates used by the Bulirsch-Stoer ODE solver, stored in `bulirsch-stoer-steps`. ### Optional arguments: `:n`: If supplied, `:n` (sequence) overrides the sequence of steps to use. `:bs-extrapolator`: Pass `:polynomial` to override the default rational function extrapolation and enable polynomial extrapolation using the modified Neville's algorithm implemented in `poly/modified-neville`.
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 rational polynomial extrapolation to successive integral
estimates from the Midpoint rule.
Considers successive numbers of windows into $(a, b)$ specified by
bulirsch-stoer-steps.
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 Bulirsch-Stoer quadrature,
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 rational polynomial extrapolation to successive integral estimates from the Midpoint rule. Considers successive numbers of windows into $(a, b)$ specified by `bulirsch-stoer-steps`. 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 Bulirsch-Stoer quadrature, 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
Returns a (lazy) sequence of successively refined estimates of the
integral of f over the closed interval $[a, b]$ by applying rational
polynomial extrapolation to successive integral estimates from the Midpoint
rule.
Returns estimates formed from the same estimates used by the Bulirsch-Stoer
ODE solver, stored in bulirsch-stoer-steps.
Optional arguments:
:n: If supplied, n (sequence) overrides the sequence of steps to use.
:bs-extrapolator: Pass :polynomial to override the default rational
function extrapolation and enable polynomial extrapolation using the modified
Neville's algorithm implemented in poly/modified-neville.
Returns a (lazy) sequence of successively refined estimates of the integral of `f` over the closed interval $[a, b]$ by applying rational polynomial extrapolation to successive integral estimates from the Midpoint rule. Returns estimates formed from the same estimates used by the Bulirsch-Stoer ODE solver, stored in `bulirsch-stoer-steps`. ### Optional arguments: `:n`: If supplied, `n` (sequence) overrides the sequence of steps to use. `:bs-extrapolator`: Pass `:polynomial` to override the default rational function extrapolation and enable polynomial extrapolation using the modified Neville's algorithm implemented in `poly/modified-neville`.
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