package owl-base
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doc/owl-base/Owl_maths_root/index.html
Module Owl_maths_root
Root finding algorithms for nonlinear functions
Type definition
Core functions
val fzero :
?solver:solver ->
?max_iter:int ->
?xtol:float ->
(float -> float) ->
float ->
float ->
float``fzero ~solver f a b`` tries to find the root of univariate function ``f`` in the bracket ``a, b`` using method ``solver``. This is the hub function of the individual root finding algorithms in the following sections. You can certainly call each individual ones.
Parameters: * ``solver``: solver, default one is Brent method. * ``max_iter``: maximum number of iterations, default value is ``1000``. * ``xtol``: the tolerance of ``x`` on abscissa, default value is ``1e-6``. * ``f``: the univariate scalar function to find root. * ``a``: boundary of bracket. * ``b``: boundary of bracket.
Root of univariate functions
``bisec f a b`` tries to find the root of univariate function ``f`` in the bracket defined by ``a, b``.
Parameters: * ``max_iter``: maximum number of iterations. * ``xtol``: the tolerance of ``x`` on abscissa. * ``f``: the univariate scalar function to find root. * ``a``: boundary of bracket. * ``b``: boundary of bracket.
``false_pos f a b`` tries to find the root of univariate function ``f`` in the bracket defined by ``a, b``.
Parameters: * ``max_iter``: maximum number of iterations. * ``xtol``: the tolerance of ``x`` on abscissa. * ``f``: the univariate scalar function to find root. * ``a``: boundary of bracket. * ``b``: boundary of bracket.
``ridder f a b`` tries to find the root of univariate function ``f`` in the bracket defined by ``a, b``.
Parameters: * ``max_iter``: maximum number of iterations. * ``xtol``: the tolerance of ``x`` on abscissa. * ``f``: the univariate scalar function to find root. * ``a``: boundary of bracket. * ``b``: boundary of bracket.
``brent f a b`` tries to find the root of univariate function ``f`` in the bracket defined by ``a, b``.
Parameters: * ``max_iter``: maximum number of iterations. * ``xtol``: the tolerance of ``x`` on abscissa. * ``f``: the univariate scalar function to find root. * ``a``: boundary of bracket. * ``b``: boundary of bracket.
Refer to :cite:`brent2013algorithms`
Helper functions
val bracket_expand :
?rate:float ->
?max_iter:int ->
(float -> float) ->
float ->
float ->
(float * float) option``bracket_expand f a b`` expands the bracket ``a, b`` for a given function ``f`` until it finds ``f a`` and ``f b`` have different signs.
Parameters: * ``max_iter``: maximum number of iterations, the default is 100 * ``rate``: rate of growth, the default is 1.6 * ``f``: the univariate scalar function to find root. * ``a``: initial boundary of bracket. * ``b``: initial boundary of bracket.