Class NumericalMethods

Namespace

Utils.Mathematics

Assembly

Utils.Mathematics.dll

Numerical integration and interpolation utilities.

public static class NumericalMethods

Inheritance

object

NumericalMethods

Inherited Members

object.Equals(object)

object.Equals(object, object)

object.GetHashCode()

object.GetType()

object.MemberwiseClone()

object.ReferenceEquals(object, object)

object.ToString()

Methods

Integrate<T>(Func<T, T>, T, T, int)

Numerically integrates f over [a, b] using the composite Simpson's 1/3 rule.

public static T Integrate<T>(Func<T, T> f, T a, T b, int steps = 1000) where T : struct, IFloatingPoint<T>

Parameters

f Func<T, T>

Integrand function. Must be defined and finite on [a, b].

a T

Lower bound of integration.

b T

Upper bound of integration.

steps int

Number of sub-intervals. Must be positive and even; an odd value is rounded up by one. Higher values increase accuracy at the cost of more function evaluations.

Returns

T

The approximate value of ∫f(x)dx from a to b. If f returns a non-finite value anywhere in the interval, that non-finite value propagates into the result (visible to the caller as NaN or an infinity) rather than being silently discarded.

Type Parameters

T

Floating-point scalar type.

Exceptions

ArgumentNullException

Thrown when f is null.

ArgumentOutOfRangeException

Thrown when steps is not positive, when steps is the odd value MaxValue (which cannot be rounded up to an even count without overflowing), or when a/b is not finite.

Lagrange<T>(IEnumerable<(T x, T y)>, T)

Evaluates the Lagrange interpolating polynomial at at, given a set of data points.

public static T Lagrange<T>(IEnumerable<(T x, T y)> points, T at) where T : struct, IFloatingPoint<T>

Parameters

points IEnumerable<(T x, T y)>

Sequence of (x, y) data points. All x values must be distinct and every coordinate finite.

at T

The point at which to evaluate the interpolating polynomial. Must be finite.

Returns

T

The interpolated value at at.

Type Parameters

T

Floating-point scalar type.

Remarks

The result is exact at each data point and provides a polynomial approximation elsewhere. For large point sets, consider alternative methods as Lagrange interpolation can exhibit Runge's phenomenon near the boundaries.

Exceptions

ArgumentException

Thrown when no points are provided, a coordinate is not finite, or x values are not distinct.

ArgumentOutOfRangeException

Thrown when at is not finite.