Secant¶

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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 $10^{-5}$ .
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, Brent

Notes

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

Methods

`getAbsoluteError`(self)	Accessor to the absolute error.
`getClassName`(self)	Accessor to the object’s name.
`getId`(self)	Accessor to the object’s id.
`getMaximumFunctionEvaluation`(self)	Accessor to the maximum number of evaluations of the function.
`getName`(self)	Accessor to the object’s name.
`getRelativeError`(self)	Accessor to the relative error.
`getResidualError`(self)	Accessor to the residual error.
`getShadowedId`(self)	Accessor to the object’s shadowed id.
`getUsedFunctionEvaluation`(self)	Accessor to the number of evaluations of the function.
`getVisibility`(self)	Accessor to the object’s visibility state.
`hasName`(self)	Test if the object is named.
`hasVisibleName`(self)	Test if the object has a distinguishable name.
`setAbsoluteError`(self, absoluteError)	Accessor to the absolute error.
`setMaximumFunctionEvaluation`(self, …)	Accessor to the maximum number of evaluations of the function.
`setName`(self, name)	Accessor to the object’s name.
`setRelativeError`(self, relativeError)	Accessor to the relative error.
`setResidualError`(self, residualError)	Accessor to the residual error.
`setShadowedId`(self, id)	Accessor to the object’s shadowed id.
`setVisibility`(self, visible)	Accessor to the object’s visibility state.
`solve`(self, \*args)	Solve an equation.

__init__(self, \*args)¶: Initialize self. See help(type(self)) for accurate signature.

getAbsoluteError(self)¶

Accessor to the absolute error.

Returns

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

getClassName(self)¶

Accessor to the object’s name.

Returns

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

getId(self)¶

Accessor to the object’s id.

Returns

idint: Internal unique identifier.

getMaximumFunctionEvaluation(self)¶

Accessor to the maximum number of evaluations of the function.

Returns

maxEvalint: The maximum number of evaluations of the function.

getName(self)¶

Accessor to the object’s name.

Returns

namestr: The name of the object.

getRelativeError(self)¶

Accessor to the relative error.

Returns

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

getResidualError(self)¶

Accessor to the residual error.

Returns

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

getShadowedId(self)¶

Accessor to the object’s shadowed id.

Returns

idint: Internal unique identifier.

getUsedFunctionEvaluation(self)¶

Accessor to the number of evaluations of the function.

Returns

nEvalint: The number of evaluations of the function.

getVisibility(self)¶

Accessor to the object’s visibility state.

Returns

visiblebool: Visibility flag.

hasName(self)¶

Test if the object is named.

Returns

hasNamebool: True if the name is not empty.

hasVisibleName(self)¶

Test if the object has a distinguishable name.

Returns

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

setAbsoluteError(self, absoluteError)¶

Accessor to the absolute error.

Parameters

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

setMaximumFunctionEvaluation(self, maximumFunctionEvaluation)¶

Accessor to the maximum number of evaluations of the function.

Parameters

maxEvalint: The maximum number of evaluations of the function.

setName(self, name)¶

Accessor to the object’s name.

Parameters

namestr: The name of the object.

setRelativeError(self, 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(self, residualError)¶

Accessor to the residual error.

Parameters

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

setShadowedId(self, id)¶

Accessor to the object’s shadowed id.

Parameters

idint: Internal unique identifier.

setVisibility(self, visible)¶

Accessor to the object’s visibility state.

Parameters

visiblebool: Visibility flag.

solve(self, \*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