FunctionSolver
Searches a bounded interval for real roots of a univariate expression.
roots scans the configured interval from its center toward both endpoints. It refines sign-changing intervals with Brent's method or Newton-Raphson, verifies residuals, merges nearby results, and returns roots in ascending order. This is a heuristic search: an even-multiplicity root can be missed unless a scan point lands sufficiently close to it, and periodic functions are limited by both the interval and
`maxRoots`. Calculations use the ambient
`decimal.js`precision. An Expression supplied to the constructor is retained rather than copied, and the public settings may be adjusted before a search.
Examples
const solver = new FunctionSolver('cos(x)-x', 'x', {
lowerBound: 0,
upperBound: 1,
});
const roots = solver.roots();Members
Brent(a: Decimal, b: Decimal): RootMethodRefines a bracket using Brent's combination of bisection, secant, and inverse-quadratic interpolation.
Parameters
| Name | Type | Description |
|---|---|---|
a | Decimal | First bracket endpoint. |
b | Decimal | Second bracket endpoint. |
Returns
Root — Refinement metadata. Invalid brackets and exhausted iterations are represented in the returned Root; they are not thrown.
FunctionSolver(func: string | Expression, variable?: string, options: FunctionSolverOptions): FunctionSolverConstructorCreates a bounded real-root solver.
UnsupportedOperationError If
`variable`is omitted and the expression contains more than one variable.
Parameters
| Name | Type | Description |
|---|---|---|
func | string | Expression | Expression to evaluate, or a string parsed as an Expression. |
variable | string | Variable to substitute. When omitted, the expression must contain at most one variable. |
options | FunctionSolverOptions | Search interval, refinement method, and tolerances. |
Returns
derivativeStep: DecimalPropertyNo description is available yet.
df(x: Decimal, h: Decimal): DecimalMethodApproximates the derivative with a central difference.
Parameters
| Name | Type | Description |
|---|---|---|
x | Decimal | — |
h | Decimal | — |
Returns
Decimal
evaluate(at: string | number | Decimal): DecimalMethodEvaluates the configured expression at a real value.
UnexpectedInputError If evaluation does not produce a scalar Expression.
Parameters
| Name | Type | Description |
|---|---|---|
at | string | number | Decimal | — |
Returns
Decimal
func: ExpressionPropertyNo description is available yet.
lowerBound: DecimalPropertyNo description is available yet.
maxIters: numberPropertyNo description is available yet.
maxRoots: numberPropertyNo description is available yet.
method: RootFindingMethodPropertyNo description is available yet.
NewtonRaphson(guess: Decimal): { … } | { … }MethodRefines a root from an initial guess using Newton-Raphson and a numerical derivative.
Parameters
| Name | Type | Description |
|---|---|---|
guess | Decimal | — |
Returns
{ … } | { … } — Refinement metadata, including non-convergence or a zero derivative.
roots(): Expression[]MethodSearches the configured interval for real roots.
Returns
Expression[] — Verified, deduplicated roots in ascending order, limited by `maxRoots`. Failed evaluations and failed refinements are skipped.
stepSize: numberPropertyNo description is available yet.
tolerance: DecimalPropertyNo description is available yet.
upperBound: DecimalPropertyNo description is available yet.
variable: stringPropertyNo description is available yet.
verbose: booleanPropertyNo description is available yet.