;ò …Rã?c@s“dklZd„ZedjoldklZlZlZd„ZeedddƒZ dZ d GHd GHd GHd GHd Ge GHd e GHd GHndS((sDerivVarcCs\d} |t|ƒƒ}|d}|t|ƒƒ}|d}|djo |djp|djo |djo dGHtSn|djo|Sn|djo|Sn|djo|}|} n |} |}d||} t ||ƒ}|}|t| ƒƒ}|d}|dd} x,t| ƒD]}| | | || || |djpt d|ƒt || ƒjo7|}d| |}||} || jo| Sqén6|}|| }| } | |} | | jo| Snt |ƒ|jo| Sn|t| ƒƒ}|d}|dd} |djo | }q-| } q-WdGHdSd S( sFinds the root of |function| which is bracketed by values |lox| and |hix| to an accuracy of +/- |xacc|. The algorithm used is a safe version of Newton-Raphson (see page 366 of NR in C, 2ed). |function| must be a function of one variable, and may only use operations defined for the DerivVar objects in the module FirstDerivatives. Example: >>>from Scientific.Functions.FindRoot import newtonRaphson >>>from Numeric import pi, sin, cos >>>def func(x): >>> return (2*x*cos(x) - sin(x))*cos(x) - x + pi/4.0 >>>newtonRaphson(func, 0.0, 1.0, 1.0e-12) yields '0.952847864655'. iôif0.0s)Root must be bracketed in newtonRaphson()f0.5if2.0s8Maximum number of iterations exceeded in newtonRaphson()N(smaxitsfunctionsDerivVarsloxstmpsflshixsfhsNonesxlsxhsrtssabssdxoldsdxsfsdfsrangesjstempsxacc(sfunctionsloxshixsxaccstmpsdxsxlsfsjsxhsdfsmaxitstempsrtssfhsflsdxold((sH/mit/python/lib/python2.3/site-packages/Scientific/Functions/FindRoot.pys newtonRaphson s`  4      J         s__main__(spissinscoscCs6d|t|ƒt|ƒt|ƒ|tdSdS(Nif4.0(sxscosssinspi(sx((sH/mit/python/lib/python2.3/site-packages/Scientific/Functions/FindRoot.pysfuncTsf0.0f1.0f9.9999999999999998e-13f0.95284786465494198ss*Finding the root (between 0.0 and 1.0) of:s/ (2*x*cos(x) - sin(x))*cos(x) - x + pi/4 = 0s2Safe-style Newton-Raphson gives (xacc = 1.0e-12) =s:Theoretical result (correct to all shown digits) = %15.14fN( sFirstDerivativessDerivVars newtonRaphsons__name__sNumericspissinscossfuncsrstheo(stheoscossrsDerivVarsfuncs newtonRaphsonspissin((sH/mit/python/lib/python2.3/site-packages/Scientific/Functions/FindRoot.pys? s  D