Bisection

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class Bisection(*args)

Bisection algorithm solver for 1D non linear equations.

Available constructor:

Bisection()

Bisection(absError, relError, resError, maximumFunctionEvaluation)

Parameters

absErrorpositive float

Absolute error: distance between two successive iterates at the end point. Default is .

relErrorpositive float

Relative error: distance between the two last successive iterates with regards to the last iterate. Default is .

resErrorpositive float

Residual error: difference between the last iterate value and the expected value. Default is .

maximumFunctionEvaluationint

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

See also

Solver, Brent, Secant

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 to be solved in the interval .

valuefloat

The value of which the function must be equal.

infPointfloat

Lower bound of the interval definition of the variable .

supPointfloat

Upper bound of the interval definition of the variable .

infValuefloat

The value such that . It must be of opposite sign of .

supValuefloat

The value such that . It must be of opposite sign of .

Returns

resultfloat

The result of the root research.

Notes

If the function is continuous, the Bisection solver will converge towards a root of the equation in . If not, it will converge towards either a root or a discontinuity point of on . Bisection guarantees a convergence.