{-# LANGUAGE ForeignFunctionInterface #-} ----------------------------------------------------------------------------- {- | Module : Numeric.GSL.Polynomials Copyright : (c) Alberto Ruiz 2006 License : GPL-style Maintainer : Alberto Ruiz (aruiz at um dot es) Stability : provisional Portability : uses ffi Polynomials. -} ----------------------------------------------------------------------------- module Numeric.GSL.Polynomials ( polySolve ) where import Data.Packed.Internal import Data.Complex import System.IO.Unsafe (unsafePerformIO) {- | Solution of general polynomial equations, using /gsl_poly_complex_solve/. For example, the three solutions of x^3 + 8 = 0 @\> polySolve [8,0,0,1] [(-1.9999999999999998) :+ 0.0, 1.0 :+ 1.732050807568877, 1.0 :+ (-1.732050807568877)]@ The example in the GSL manual: To find the roots of x^5 -1 = 0: @\> polySolve [-1, 0, 0, 0, 0, 1] [(-0.8090169943749475) :+ 0.5877852522924731, (-0.8090169943749475) :+ (-0.5877852522924731), 0.30901699437494734 :+ 0.9510565162951536, 0.30901699437494734 :+ (-0.9510565162951536), 1.0 :+ 0.0]@ -} polySolve :: [Double] -> [Complex Double] polySolve = toList . polySolve' . fromList polySolve' :: Vector Double -> Vector (Complex Double) polySolve' v | dim v > 1 = unsafePerformIO \$ do r <- createVector (dim v-1) app2 c_polySolve vec v vec r "polySolve" return r | otherwise = error "polySolve on a polynomial of degree zero" foreign import ccall "gsl-aux.h polySolve" c_polySolve:: TVCV