analysis: analysis::C2Functions::InterpolatingFunction::value_with

def value_with_derivatives	(	self,
		x
	)

get the value of the function, and its first & second derivative

Parameters:

the point at which to evaluate the function

Returns:: (f(x), f'(x), f''(x))

Reimplemented from C2Function.

Definition at line 1177 of file C2Functions.py.

01177                                        : 
01178         if self.xNonLin or self.yNonLin: #skip this if this is a completely untransformed spline
01179             y0, yp0, ypp0=_splint(self.X, self.F, self.y2, self.fXin(x), derivs=True)
01180             y=self.fYout(y0)
01181             fpi=1.0/self.fYinP(y)
01182             gp=self.fXinP(x)
01183 
01184             # from Mathematica Dt[InverseFunction[f][g[y[x]]], x]
01185             yprime=gp*yp0*fpi # the real derivative of the inverse transformed output 
01186             fpp=self.fYinPP(y)
01187             gpp=self.fXinPP(x)
01188             #also from Mathematica Dt[InverseFunction[f][g[y[x]]], {x,2}]
01189             yprimeprime=(gp*gp*ypp0 + yp0*gpp - gp*gp*yp0*yp0*fpp*fpi*fpi)*fpi
01190             return native(y, yprime, yprimeprime)
01191         else:
01192             return _splint(self.X, self.F, self.y2, x, derivs=True)