Numeric.GSL.Root

Multidimensional root finding.

http://www.gnu.org/software/gsl/manual/html_node/Multidimensional-Root_002dFinding.html

The example in the GSL manual:

>>> let rosenbrock a b [x,y] = [ a*(1-x), b*(y-x^2) ]
>>> let (sol,path) = root Hybrids 1E-7 30 (rosenbrock 1 10) [-10,-5]
>>> sol
[1.0,1.0]
>>> disp 3 path
11x5
 1.000  -10.000  -5.000  11.000  -1050.000
 2.000   -3.976  24.827   4.976     90.203
 3.000   -3.976  24.827   4.976     90.203
 4.000   -3.976  24.827   4.976     90.203
 5.000   -1.274  -5.680   2.274    -73.018
 6.000   -1.274  -5.680   2.274    -73.018
 7.000    0.249   0.298   0.751      2.359
 8.000    0.249   0.298   0.751      2.359
 9.000    1.000   0.878  -0.000     -1.218
10.000    1.000   0.989  -0.000     -0.108
11.000    1.000   1.000   0.000      0.000

Documentation

uniRoot :: UniRootMethod -> Double -> Int -> (Double -> Double) -> Double -> Double -> (Double, Matrix Double)

data UniRootMethod

Constructors

Bisection

FalsePos

Brent

Instances

Bounded UniRootMethod

Methods

minBound :: UniRootMethod

maxBound :: UniRootMethod

Enum UniRootMethod

Methods

succ :: UniRootMethod -> UniRootMethod

pred :: UniRootMethod -> UniRootMethod

toEnum :: Int -> UniRootMethod

fromEnum :: UniRootMethod -> Int

enumFrom :: UniRootMethod -> [UniRootMethod]

enumFromThen :: UniRootMethod -> UniRootMethod -> [UniRootMethod]

enumFromTo :: UniRootMethod -> UniRootMethod -> [UniRootMethod]

enumFromThenTo :: UniRootMethod -> UniRootMethod -> UniRootMethod -> [UniRootMethod]

Eq UniRootMethod

Methods

(==) :: UniRootMethod -> UniRootMethod -> Bool

(/=) :: UniRootMethod -> UniRootMethod -> Bool

Show UniRootMethod

Methods

showsPrec :: Int -> UniRootMethod -> ShowS

show :: UniRootMethod -> String

showList :: [UniRootMethod] -> ShowS

uniRootJ :: UniRootMethodJ -> Double -> Int -> (Double -> Double) -> (Double -> Double) -> Double -> (Double, Matrix Double)

data UniRootMethodJ

Constructors

UNewton

Secant

Steffenson

Instances

Bounded UniRootMethodJ

Methods

minBound :: UniRootMethodJ

maxBound :: UniRootMethodJ

Enum UniRootMethodJ

Methods

succ :: UniRootMethodJ -> UniRootMethodJ

pred :: UniRootMethodJ -> UniRootMethodJ

toEnum :: Int -> UniRootMethodJ

fromEnum :: UniRootMethodJ -> Int

enumFrom :: UniRootMethodJ -> [UniRootMethodJ]

enumFromThen :: UniRootMethodJ -> UniRootMethodJ -> [UniRootMethodJ]

enumFromTo :: UniRootMethodJ -> UniRootMethodJ -> [UniRootMethodJ]

enumFromThenTo :: UniRootMethodJ -> UniRootMethodJ -> UniRootMethodJ -> [UniRootMethodJ]

Eq UniRootMethodJ

Methods

(==) :: UniRootMethodJ -> UniRootMethodJ -> Bool

(/=) :: UniRootMethodJ -> UniRootMethodJ -> Bool

Show UniRootMethodJ

Methods

showsPrec :: Int -> UniRootMethodJ -> ShowS

show :: UniRootMethodJ -> String

showList :: [UniRootMethodJ] -> ShowS

root

Arguments

:: RootMethod

-> Double

maximum residual

-> Int

maximum number of iterations allowed

-> ([Double] -> [Double])

function to minimize

-> [Double]

starting point

-> ([Double], Matrix Double)

solution vector and optimization path

Nonlinear multidimensional root finding using algorithms that do not require any derivative information to be supplied by the user. Any derivatives needed are approximated by finite differences.

data RootMethod

Constructors

Hybrids

Hybrid

DNewton

Broyden

Instances

Bounded RootMethod

Methods

minBound :: RootMethod

maxBound :: RootMethod

Enum RootMethod

Methods

succ :: RootMethod -> RootMethod

pred :: RootMethod -> RootMethod

toEnum :: Int -> RootMethod

fromEnum :: RootMethod -> Int

enumFrom :: RootMethod -> [RootMethod]

enumFromThen :: RootMethod -> RootMethod -> [RootMethod]

enumFromTo :: RootMethod -> RootMethod -> [RootMethod]

enumFromThenTo :: RootMethod -> RootMethod -> RootMethod -> [RootMethod]

Eq RootMethod

Methods

(==) :: RootMethod -> RootMethod -> Bool

(/=) :: RootMethod -> RootMethod -> Bool

Show RootMethod

Methods

showsPrec :: Int -> RootMethod -> ShowS

show :: RootMethod -> String

showList :: [RootMethod] -> ShowS

rootJ

Arguments

:: RootMethodJ

-> Double

maximum residual

-> Int

maximum number of iterations allowed

-> ([Double] -> [Double])

function to minimize

-> ([Double] -> [[Double]])

Jacobian

-> [Double]

starting point

-> ([Double], Matrix Double)

solution vector and optimization path

Nonlinear multidimensional root finding using both the function and its derivatives.

data RootMethodJ

Constructors

HybridsJ

HybridJ

Newton

GNewton

Instances

Bounded RootMethodJ

Methods

minBound :: RootMethodJ

maxBound :: RootMethodJ

Enum RootMethodJ

Methods

succ :: RootMethodJ -> RootMethodJ

pred :: RootMethodJ -> RootMethodJ

toEnum :: Int -> RootMethodJ

fromEnum :: RootMethodJ -> Int

enumFrom :: RootMethodJ -> [RootMethodJ]

enumFromThen :: RootMethodJ -> RootMethodJ -> [RootMethodJ]

enumFromTo :: RootMethodJ -> RootMethodJ -> [RootMethodJ]

enumFromThenTo :: RootMethodJ -> RootMethodJ -> RootMethodJ -> [RootMethodJ]

Eq RootMethodJ

Methods

(==) :: RootMethodJ -> RootMethodJ -> Bool

(/=) :: RootMethodJ -> RootMethodJ -> Bool

Show RootMethodJ

Methods

showsPrec :: Int -> RootMethodJ -> ShowS

show :: RootMethodJ -> String

showList :: [RootMethodJ] -> ShowS