Copyright	(c) Alberto Ruiz 2009
License	GPL
Maintainer	Alberto Ruiz
Stability	provisional
Safe Haskell	None
Language	Haskell98

Numeric.GSL.Root

Description

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

Synopsis

Documentation

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

data UniRootMethod Source #

Constructors

Bisection
FalsePos
Brent

Instances

Bounded UniRootMethod Source #
Methods minBound :: UniRootMethod # maxBound :: UniRootMethod #
Enum UniRootMethod Source #
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 Source #
Methods (==) :: UniRootMethod -> UniRootMethod -> Bool # (/=) :: UniRootMethod -> UniRootMethod -> Bool #
Show UniRootMethod Source #
Methods showsPrec :: Int -> UniRootMethod -> ShowS # show :: UniRootMethod -> String # showList :: [UniRootMethod] -> ShowS #

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

data UniRootMethodJ Source #

Constructors

UNewton
Secant
Steffenson

Instances

Bounded UniRootMethodJ Source #
Methods minBound :: UniRootMethodJ # maxBound :: UniRootMethodJ #
Enum UniRootMethodJ Source #
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 Source #
Methods (==) :: UniRootMethodJ -> UniRootMethodJ -> Bool # (/=) :: UniRootMethodJ -> UniRootMethodJ -> Bool #
Show UniRootMethodJ Source #
Methods showsPrec :: Int -> UniRootMethodJ -> ShowS # show :: UniRootMethodJ -> String # showList :: [UniRootMethodJ] -> ShowS #

root Source #

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 Source #

Constructors

Hybrids
Hybrid
DNewton
Broyden

Instances

Bounded RootMethod Source #
Methods minBound :: RootMethod # maxBound :: RootMethod #
Enum RootMethod Source #
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 Source #
Methods (==) :: RootMethod -> RootMethod -> Bool # (/=) :: RootMethod -> RootMethod -> Bool #
Show RootMethod Source #
Methods showsPrec :: Int -> RootMethod -> ShowS # show :: RootMethod -> String # showList :: [RootMethod] -> ShowS #

rootJ Source #

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 Source #

Constructors

HybridsJ
HybridJ
Newton
GNewton

Instances

Bounded RootMethodJ Source #
Methods minBound :: RootMethodJ # maxBound :: RootMethodJ #
Enum RootMethodJ Source #
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 Source #
Methods (==) :: RootMethodJ -> RootMethodJ -> Bool # (/=) :: RootMethodJ -> RootMethodJ -> Bool #
Show RootMethodJ Source #
Methods showsPrec :: Int -> RootMethodJ -> ShowS # show :: RootMethodJ -> String # showList :: [RootMethodJ] -> ShowS #