Numeric.GSL.Interpolation

Interpolation routines.

https://www.gnu.org/software/gsl/manual/html_node/Interpolation.html#Interpolation

The GSL routines gsl_spline_eval and friends are used, but in spite of the names, they are not restricted to spline interpolation. The functions in this module will work for any InterpolationMethod.

Interpolation methods

data InterpolationMethod

Constructors

Linear

Polynomial

CSpline

CSplinePeriodic

Akima

AkimaPeriodic

Instances

Eq InterpolationMethod

Read InterpolationMethod

Show InterpolationMethod

Evaluation of interpolated functions

evaluate

Arguments

:: InterpolationMethod

What method to use to interpolate

-> [(Double, Double)]

(domain, range) values sampling the function

-> Double

Point at which to evaluate the function

-> Double

Interpolated result

Evaluate a function by interpolating within the given dataset. For example:

>>> let xs = [1..10]
>>> let ys map (**2) [1..10]
>>> evaluate Akima (zip xs ys) 2.2
4.840000000000001

To successfully evaluate points x, the domain (x) values in points must be monotonically increasing. The evaluation point x must lie between the smallest and largest values in the sampled domain.

evaluateV

Arguments

:: InterpolationMethod

What method to use to interpolate

-> Vector Double

Data points sampling the domain of the function

-> Vector Double

Data points sampling the range of the function

-> Double

Point at which to evaluate the function

-> Double

Interpolated result

Evaluate a function by interpolating within the given dataset. For example:

>>> let xs = vector [1..10]
>>> let ys = vector $ map (**2) [1..10]
>>> evaluateV CSpline xs ys 2.2
4.818867924528303

To successfully evaluateV xs ys x, the vectors of corresponding domain-range values xs and ys must have identical lengths, and xs must be monotonically increasing. The evaluation point x must lie between the smallest and largest values in xs.

Evaluation of derivatives of interpolated functions

evaluateDerivative

Arguments

:: InterpolationMethod

What method to use to interpolate

-> [(Double, Double)]

(domain, range) points sampling the function

-> Double

Point x at which to evaluate the derivative

-> Double

Interpolated result

Evaluate the derivative of a function by interpolating within the given dataset. For example:

>>> let xs = [1..10]
>>> let ys map (**2) [1..10]
>>> evaluateDerivative Akima (zip xs ys) 2.2
4.4

To successfully evaluateDerivative points x, the domain (x) values in points must be monotonically increasing. The evaluation point x must lie between the smallest and largest values in the sampled domain.

evaluateDerivative2

Arguments

:: InterpolationMethod

What method to use to interpolate

-> [(Double, Double)]

(domain, range) points sampling the function

-> Double

Point x at which to evaluate the second derivative

-> Double

Interpolated result

Evaluate the second derivative of a function by interpolating within the given dataset. For example:

>>> let xs = [1..10]
>>> let ys map (**2) [1..10]
>>> evaluateDerivative2 Akima (zip xs ys) 2.2
2.0

To successfully evaluateDerivative2 points x, the domain (x) values in points must be monotonically increasing. The evaluation point x must lie between the smallest and largest values in the sampled domain.

evaluateDerivativeV

Arguments

:: InterpolationMethod

What method to use to interpolate

-> Vector Double

Data points xs sampling the domain of the function

-> Vector Double

Data points ys sampling the range of the function

-> Double

Point x at which to evaluate the derivative

-> Double

Interpolated result

Evaluate the derivative of a function by interpolating within the given dataset. For example:

>>> let xs = vector [1..10]
>>> let ys = vector $ map (**2) [1..10]
>>> evaluateDerivativeV CSpline xs ys 2.2
4.338867924528302

To successfully evaluateDerivativeV xs ys x, the vectors of corresponding domain-range values xs and ys must have identical lengths, and xs must be monotonically increasing. The interpolation point x must lie between the smallest and largest values in xs.

evaluateDerivative2V

Arguments

:: InterpolationMethod

What method to use to interpolate

-> Vector Double

Data points xs sampling the domain of the function

-> Vector Double

Data points ys sampling the range of the function

-> Double

Point x at which to evaluate the second derivative

-> Double

Interpolated result

Evaluate the second derivative of a function by interpolating within the given dataset. For example:

>>> let xs = vector [1..10]
>>> let ys = vector $ map (**2) [1..10]
>>> evaluateDerivative2V CSpline xs ys 2.2
2.4

To successfully evaluateDerivative2V xs ys x, the vectors xs and ys must have identical lengths, and xs must be monotonically increasing. The evaluation point x must lie between the smallest and largest values in xs.

Evaluation of integrals of interpolated functions

evaluateIntegral

Arguments

:: InterpolationMethod

What method to use to interpolate

-> [(Double, Double)]

(domain, range) points sampling the function

-> (Double, Double)

Integration bounds (a, b)

-> Double

Resulting area

Evaluate the definite integral of a function by interpolating within the given dataset. For example:

>>> let xs = [1..10]
>>> let ys = map (**2) [1..10]
>>> evaluateIntegralV CSpline (zip xs ys) (2.2, 5.5)
51.909

To successfully evaluateIntegral points (a, b), the domain (x) values of points must be monotonically increasing. The integration bounds a and b must lie between the smallest and largest values in the sampled domain..

evaluateIntegralV

Arguments

:: InterpolationMethod

What method to use to interpolate

-> Vector Double

Data points xs sampling the domain of the function

-> Vector Double

Data points ys sampling the range of the function

-> Double

Lower integration bound a

-> Double

Upper integration bound b

-> Double

Resulting area

Evaluate the definite integral of a function by interpolating within the given dataset. For example:

>>> let xs = vector [1..10]
>>> let ys = vector $ map (**2) [1..10]
>>> evaluateIntegralV CSpline xs ys 2.2 5.5
51.89853207547169

To successfully evaluateIntegralV xs ys a b, the vectors xs and ys must have identical lengths, and xs must be monotonically increasing. The integration bounds a and b must lie between the smallest and largest values in xs.