| Copyright | (c) Stéphane Laurent 2023-2024 |
|---|---|
| License | GPL-3 |
| Maintainer | laurent_step@outlook.fr |
| Safe Haskell | Safe-Inferred |
| Language | Haskell2010 |
Numeric.Integration.PolyhedralCubature
Description
Evaluation of integrals over a convex polytope. See README for examples.
Synopsis
- data Result = Result {
- value :: Double
- errorEstimate :: Double
- evaluations :: Int
- success :: Bool
- data Results = Results {
- values :: [Double]
- errorEstimates :: [Double]
- evaluations :: Int
- success :: Bool
- data Constraint a = Constraint (LinearCombination a) Sense (LinearCombination a)
- type VectorD = Vector Double
- integrateOnPolytopeN :: (VectorD -> VectorD) -> [[Double]] -> Int -> Int -> Double -> Double -> Int -> IO Results
- integrateOnPolytope :: (VectorD -> Double) -> [[Double]] -> Int -> Double -> Double -> Int -> IO Result
- integrateOnPolytopeN' :: Real a => (VectorD -> VectorD) -> [Constraint a] -> Int -> Int -> Double -> Double -> Int -> IO Results
- integrateOnPolytope' :: Real a => (VectorD -> Double) -> [Constraint a] -> Int -> Double -> Double -> Int -> IO Result
- integratePolynomialOnPolytope :: (RealFrac a, C a) => Spray a -> [[a]] -> IO a
- integratePolynomialOnPolytope' :: Spray Double -> [Constraint Double] -> IO Double
Documentation
Constructors
| Result | |
Fields
| |
Constructors
| Results | |
Fields
| |
data Constraint a #
Constructors
| Constraint (LinearCombination a) Sense (LinearCombination a) |
Instances
| Show a => Show (Constraint a) | |
Defined in Geometry.VertexEnum.Constraint Methods showsPrec :: Int -> Constraint a -> ShowS # show :: Constraint a -> String # showList :: [Constraint a] -> ShowS # | |
Arguments
| :: (VectorD -> VectorD) | integrand |
| -> [[Double]] | vertices of the polytope |
| -> Int | number of components of the integrand |
| -> Int | maximum number of evaluations |
| -> Double | desired absolute error |
| -> Double | desired relative error |
| -> Int | integration rule: 1, 2, 3 or 4 |
| -> IO Results | values, error estimate, evaluations, success |
Integral of a multivariate function over a convex polytope given by its vertices.
Arguments
| :: (VectorD -> Double) | integrand |
| -> [[Double]] | vertices of the polytope |
| -> Int | maximum number of evaluations |
| -> Double | desired absolute error |
| -> Double | desired relative error |
| -> Int | integration rule: 1, 2, 3 or 4 |
| -> IO Result | values, error estimate, evaluations, success |
Integral of a real-valued function over a convex polytope given by its vertices.
integrateOnPolytopeN' Source #
Arguments
| :: Real a | |
| => (VectorD -> VectorD) | integrand |
| -> [Constraint a] | linear inequalities defining the polytope |
| -> Int | number of components of the integrand |
| -> Int | maximum number of evaluations |
| -> Double | desired absolute error |
| -> Double | desired relative error |
| -> Int | integration rule: 1, 2, 3 or 4 |
| -> IO Results | values, error estimate, evaluations, success |
Integral of a multivariate function over a convex polytope given by linear inequalities.
Arguments
| :: Real a | |
| => (VectorD -> Double) | integrand |
| -> [Constraint a] | linear inequalities defining the polytope |
| -> Int | maximum number of evaluations |
| -> Double | desired absolute error |
| -> Double | desired relative error |
| -> Int | integration rule: 1, 2, 3 or 4 |
| -> IO Result | values, error estimate, evaluations, success |
Integral of a scalar-valued function over a convex polytope given by linear inequalities.
integratePolynomialOnPolytope Source #
Arguments
| :: (RealFrac a, C a) | |
| => Spray a | polynomial to be integrated |
| -> [[a]] | vertices of the polytope to integrate over |
| -> IO a |
Integral of a polynomial over a convex polytope given by its vertices.
integratePolynomialOnPolytope' Source #
Arguments
| :: Spray Double | polynomial to be integrated |
| -> [Constraint Double] | linear inequalities defining the polytope |
| -> IO Double |
Integral of a polynomial over a convex polytope given by linear inequalities.