hmatrix-gsl-0.18.0.1: Numerical computation

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

Constructors

 Bisection FalsePos Brent

Instances

 Source # Methods Source # Methods Source # Methods Source # MethodsshowList :: [UniRootMethod] -> ShowS #

Constructors

 UNewton Secant Steffenson

Instances

 Source # Methods Source # Methods Source # Methods Source # MethodsshowList :: [UniRootMethodJ] -> ShowS #

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.

Constructors

 Hybrids Hybrid DNewton Broyden

Instances

 Source # Methods Source # Methods Source # Methods Source # MethodsshowList :: [RootMethod] -> ShowS #

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.

Constructors

 HybridsJ HybridJ Newton GNewton

Instances

 Source # Methods Source # Methods Source # Methods Source # MethodsshowList :: [RootMethodJ] -> ShowS #