Secant

(Source code, png)

class Secant(*args)

Secant algorithm solver for 1D non linear equations.

Available constructor:

Secant()

Secant(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, Bisection, Brent

Notes

The Secant solver is based on the evaluation of a segment between the two last iterated points.

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)

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

The Secant solver is based on the evaluation of a segment between the two last iterated points. Secant might fail and not converge.