numeric library

Numeric algorithms and solutions.

Classes

CurveFit

Curve fitting is the process of constructing a curve, or mathematical function, that has the best fit to a series of data points, possibly subject to constraints.

CurveFitResult

Generic result of a curve fitting.

LevenbergMarquardt

The Levenberg–Marquardt algorithm, also known as the damped least-squares method, is used to solve non-linear least squares problems.

LevenbergMarquardtResult

ParametrizedUnaryFunction<T>

Abstract factory of parametrized unary functions of type UnaryFunction<T>.

PolynomialRegression

Polynomial least-squares regression, in which the relationship between the independent elements xs and the dependent elements ys is modelled as a polynomial of a given degree.

PolynomialRegressionResult

Enums

IntegrateWarning

Integration warnings that can be triggered for badly behaving functions or ill defined parameters.

Functions

derivative(UnaryFunction<double> function, double x, {int derivative = 1, int accuracy = 2, double epsilon = 1e-5}) → double

Returns the numerical derivative of the provided function function at x.

fft(List<Complex> values, {bool inverse = false}) → List<Complex>

Performs an in-place Discrete Fast Fourier transformation on the provided values. If necessary, extends the size the provided list to a power of two. Returns the modified collection of transformed values.

geometricSpaced(double start, double stop, {int count = 10, bool includeEndpoint = true, DataType<double>? dataType, VectorFormat? format}) → Vector<double>

Generates a Vector with a sequence of count evenly spaced values on a log scale (a geometric progression) on the interval between start and stop.

integrate(UnaryFunction<double> function, double a, double b, {int depth = 6, double epsilon = 1e-6, Iterable<double> poles = const [], void onWarning(IntegrateWarning type, double x)?}) → double

Returns the numerical integration of the provided function from a to b, that is the result of int(f(x), dx=a..b).

lagrangeInterpolation<T>(DataType<T> dataType, {required Vector<T> xs, required Vector<T> ys}) → UnaryFunction<T>

A function providing a Lagrange polynomial interpolation through the unique sample points xs and ys.

linearInterpolation<T>(DataType<T> dataType, {required Vector<T> xs, required Vector<T> ys, T? left, T? right}) → UnaryFunction<T>

A function providing linear interpolation of a discrete monotonically increasing set of sample points xs and ys. Returns left or right, if the point is outside the data range, by default extrapolate linearly.

linearSpaced(double start, double stop, {int count = 10, bool includeEndpoint = true, DataType<double>? dataType, VectorFormat? format}) → Vector<double>

Generates a Vector with a sequence of count evenly spaced values over an interval between start and stop.

logarithmicSpaced(double start, double stop, {int count = 10, double base = 10.0, bool includeEndpoint = true, DataType<double>? dataType, VectorFormat? format}) → Vector<double>

Generates a Vector with a sequence of count evenly spaced values on a log scale (a geometric progression) on the interval between base ^ start and base ^ stop.

nearestInterpolation({required Vector<double> xs, required Vector<double> ys, bool preferLower = true}) → UnaryFunction<double>

A function providing the nearest value of a discrete monotonically increasing set of sample points xs and ys.

nextInterpolation({required Vector<double> xs, required Vector<double> ys, double right = double.nan}) → UnaryFunction<double>

A function providing the next value of a discrete monotonically increasing set of sample points xs and ys. Returns right if there is no next sample point.

previousInterpolation({required Vector<double> xs, required Vector<double> ys, double left = double.nan}) → UnaryFunction<double>

A function providing the previous value of a discrete monotonically increasing set of sample points xs and ys. Returns left if there is no previous sample point.

solve(UnaryFunction<double> function, double a, double b, {double bracketEpsilon = 1e-10, double solutionEpsilon = 1e-50, int maxIterations = 50}) → double

Returns the root of the provided function bracketed between a and b, that is f(x) = 0 is solved for x in the range of [a, b].

Typedefs

UnaryFunction<T> = T Function(T x)

A function with a single argument and an identical return type. Typically used for numerical functions like f(x) where x ∈ T and f(x) ∈ T.

Exceptions / Errors

IntegrateError

Integration error that is thrown when warnings are not handled explicitly.