Dear all, We like to announce the release of a Haskell binding to Manolis Lourakis's C levmar library at: http://www.ics.forth.gr/~lourakis/levmar/ This library implements the Levenberg-Marquardt algorithm which is an iterative technique that finds a local minimum of a function that is expressed as the sum of squares of nonlinear functions. It has become a standard technique for nonlinear least-squares problems and can be thought of as a combination of steepest descent and the Gauss-Newton method. When the current solution is far from the correct one, the algorithm behaves like a steepest descent method: slow, but guaranteed to converge. When the current solution is close to the correct solution, it becomes a Gauss-Newton method. Our binding consists of three packages: * http://hackage.haskell.org/package/bindings-levmar-0.1 A low-level wrapper around the C library. Note that the C library is lightly patched so that the functions can be safely called inside unsafePerformIO. The patched C library is bundled with this package. * http://hackage.haskell.org/package/levmar-0.1 A high-level wrapper around bindings-levmar. It provides a more familiar Haskell interface. For example, instead of passing a 'Ptr r' to the levmar function you can pass a [r]. levmar also provides some higher-level modules that use some type-level programming to add more type safety. * http://hackage.haskell.org/package/levmar-chart-0.1 Finally levmar-chart is a small package for quickly viewing the output of levmar in a chart. Unfortunately the documentation of these libraries is not available from hackage because bindings-levmar won't configure because of a missing dependency (lapack) on the hackage server. Instead I put the documentation at the following places: http://code.haskell.org/bindings-levmar/bindings-levmar-0.1/doc/html/binding... http://code.haskell.org/levmar/levmar-0.1/doc/html/levmar/index.html Here follows a quick example: Suppose we have the following model functions: constant :: Num r => Model N1 r r linear :: Num r => Model N2 r r quadratic :: Num r => Model N3 r r cubic :: Num r => Model N4 r r constant a _ = a linear b a x = b * x + constant a x quadratic c b a x = c * x*x + linear b a x cubic d c b a x = d * x*x*x + quadratic c b a x And the jacobians: constantJacob :: Num r => Jacobian N1 r r linearJacob :: Num r => Jacobian N2 r r quadraticJacob :: Num r => Jacobian N3 r r cubicJacob :: Num r => Jacobian N4 r r constantJacob _ _ = 1 ::: Nil linearJacob _ a x = x ::: constantJacob a x quadraticJacob _ b a x = x*x ::: linearJacob b a x cubicJacob _ c b a x = x*x*x ::: quadraticJacob c b a x Now assume we have some sample data. If you call levmar like this: levmar cubic (Just cubicJacob) (-0.05 ::: 0.5 ::: -12 ::: 10 ::: Nil) samples 1000 defaultOpts Nothing Nothing noLinearConstraints Nothing You get the following fit (using levmar-chart): http://code.haskell.org/~roelvandijk/code/levmar-chart/cubicFit.png Note that levmar contains a demo with a lot more examples: http://code.haskell.org/levmar/Demo.hs Happy fitting, Roel and Bas van Dijk