def value_with_derivatives (   self,
  x 
)

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

Parameters:
x the point at which to evaluate the function
Returns:
(f(x), f'(x), f''(x))

Reimplemented from C2Function.

Definition at line 1516 of file C2Functions.py.

01516                                        :
01517         fhinv=self.fhinv
01518         dx=(x-self.fx1)*fhinv
01519         q1=(x-self.fx0)*(x-self.fx2)*fhinv*fhinv # exactly vanish all bits at both ends
01520         q2=dx*q1
01521         
01522         r1=self.fa+self.fb*dx
01523         r2=self.fc+self.fd*dx
01524         r3=self.fe+self.ff*dx
01525         
01526         y=self.fy1+dx*r1+q2*r2+q1*q2*r3
01527         
01528         q3=3*q1+2
01529         q4=5*q1+4
01530         yprime=(self.fa+2*self.fb*dx+self.fd*q2+r2*q3+self.ff*q1*q2+q1*q4*r3)*fhinv
01531         yprime2=2*(self.fb+self.fd*q3+3*dx*r2+self.ff*q1*q4+r3*(2*dx*(5*q1+2)))*fhinv*fhinv
01532         return y, yprime, yprime2
01533     
class C2LHopitalRatio(C2Ratio):


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