Brent

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../../_images/openturns-Brent-1.png
class Brent(*args)

Brent algorithm solver for 1D non linear equations.

Available constructor:

Brent()

Brent(absError, relError, resError, maximumFunctionEvaluation)

Parameters
absErrorpositive float

Absolute error: distance between two successive iterates at the end point. Default is 10^{-5}.

relErrorpositive float

Relative error: distance between the two last successive iterates with regards to the last iterate. Default is 10^{-5}.

resErrorpositive float

Residual error: difference between the last iterate value and the expected value. Default is 10^{-8}.

maximumFunctionEvaluationint

The maximum number of evaluations of the function. Default is 100.

See also

Solver, Bisection, Secant

Notes

The Brent solver is a mix of Bisection, Secant and inverse quadratic interpolation.

Examples

>>> import openturns as ot
>>> xMin = 0.0
>>> xMax= 3.0
>>> f = ot.MemoizeFunction(ot.SymbolicFunction('x', 'x^3-2*x^2-1'))
>>> solver = ot.Brent()
>>> root = solver.solve(f, 0.0, xMin, xMax)

Methods

getAbsoluteError()

Accessor to the absolute error.

getClassName()

Accessor to the object’s name.

getId()

Accessor to the object’s id.

getMaximumFunctionEvaluation()

Accessor to the maximum number of evaluations of the function.

getName()

Accessor to the object’s name.

getRelativeError()

Accessor to the relative error.

getResidualError()

Accessor to the residual error.

getShadowedId()

Accessor to the object’s shadowed id.

getUsedFunctionEvaluation()

Accessor to the number of evaluations of the function.

getVisibility()

Accessor to the object’s visibility state.

hasName()

Test if the object is named.

hasVisibleName()

Test if the object has a distinguishable name.

setAbsoluteError(absoluteError)

Accessor to the absolute error.

setMaximumFunctionEvaluation(…)

Accessor to the maximum number of evaluations of the function.

setName(name)

Accessor to the object’s name.

setRelativeError(relativeError)

Accessor to the relative error.

setResidualError(residualError)

Accessor to the residual error.

setShadowedId(id)

Accessor to the object’s shadowed id.

setVisibility(visible)

Accessor to the object’s visibility state.

solve(*args)

Solve an equation.
__init__(*args)

Initialize self. See help(type(self)) for accurate signature.

getAbsoluteError()

Accessor to the absolute error.

Returns
absErrorfloat

The absolute error: distance between two successive iterates at the end point.

getClassName()

Accessor to the object’s name.

Returns
class_namestr

The object class name (object.__class__.__name__).

getId()

Accessor to the object’s id.

Returns
idint

Internal unique identifier.

getMaximumFunctionEvaluation()

Accessor to the maximum number of evaluations of the function.

Returns
maxEvalint

The maximum number of evaluations of the function.

getName()

Accessor to the object’s name.

Returns
namestr

The name of the object.

getRelativeError()

Accessor to the relative error.

Returns
relErrorfloat

The relative error: distance between the two last successive iterates with regards to the last iterate.

getResidualError()

Accessor to the residual error.

Returns
resErrorfloat

The residual errors: difference between the last iterate value and the expected value.

getShadowedId()

Accessor to the object’s shadowed id.

Returns
idint

Internal unique identifier.

getUsedFunctionEvaluation()

Accessor to the number of evaluations of the function.

Returns
nEvalint

The number of evaluations of the function.

getVisibility()

Accessor to the object’s visibility state.

Returns
visiblebool

Visibility flag.

hasName()

Test if the object is named.

Returns
hasNamebool

True if the name is not empty.

hasVisibleName()

Test if the object has a distinguishable name.

Returns
hasVisibleNamebool

True if the name is not empty and not the default one.

setAbsoluteError(absoluteError)

Accessor to the absolute error.

Parameters
absErrorfloat

The absolute error: distance between two successive iterates at the end point.

setMaximumFunctionEvaluation(maximumFunctionEvaluation)

Accessor to the maximum number of evaluations of the function.

Parameters
maxEvalint

The maximum number of evaluations of the function.

setName(name)

Accessor to the object’s name.

Parameters
namestr

The name of the object.

setRelativeError(relativeError)

Accessor to the relative error.

Parameters
relErrorfloat

The relative error: distance between the two last successive iterates with regards to the last iterate.

setResidualError(residualError)

Accessor to the residual error.

Parameters
resErrorfloat

The residual errors: difference between the last iterate value and the expected value.

setShadowedId(id)

Accessor to the object’s shadowed id.

Parameters
idint

Internal unique identifier.

setVisibility(visible)

Accessor to the object’s visibility state.

Parameters
visiblebool

Visibility flag.

solve(*args)

Solve an equation.

Available usages:

solve(function, value, infPoint, supPoint)

solve(function, value, infPoint, supPoint, infValue, supValue)

Parameters
functionFunction

The function of the equation function(x) = value to be solved in the interval [infPoint, supPoint].

valuefloat

The value of which the function must be equal.

infPointfloat

Lower bound of the interval definition of the variable x.

supPointfloat

Upper bound of the interval definition of the variable x.

infValuefloat

The value such that infValue = function(infPoint). It must be of opposite sign of supValue.

supValuefloat

The value such that supValue = function(supPoint). It must be of opposite sign of infValue.

Returns
resultfloat

The result of the root research.

Notes

If the function f is continuous, the Brent solver will converge towards a root of the equation function(x) = value in [infPoint, supPoint]. If not, it will converge towards either a root or a discontinuity point of f on [infPoint, supPoint]. Bisection guarantees a convergence.