analysis: analysis::C2Functions::C2Power::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 858 of file C2Functions.py.

00858                                        :
00859         y0, yp0, ypp0=self.left.value_with_derivatives(x)
00860         y1, yp1, ypp1=self.right.value_with_derivatives(x)
00861         if isinstance(self.right, C2Constant): #all derivatives of right side are zero, save some time
00862             ab2=_myfuncs.power(y0, (y1-2.0)) #this if a^(b-2), which appears often
00863             ab1=ab2*y0 #this is a^(b-1)
00864             ab=ab1*y0 #this is a^b
00865             ab1 *= yp0
00866             ab1 *= y1 #ab1 is now the derivative
00867             ab2 *= y1*(y1-1)*yp0*yp0+y0*y1*ypp0 #ab2 is now the second derivative
00868             return  native(ab,  ab1, ab2)
00869         else:
00870             loga=_myfuncs.log(y0)
00871             ab2=_myfuncs.exp(loga*(y1-2.0)) #this if a^(b-2), which appears often
00872             ab1=ab2*y0 #this is a^(b-1)
00873             ab=ab1*y0 #this is a^b
00874             yp=ab1*(yp0*y1+y0*yp1*loga)
00875             ypp=ab2*(y1*(y1-1)*yp0*yp0+2*y0*yp0*yp1*(1.0+y1*loga)+y0*(y1*ypp0+y0*(ypp1+yp1*yp1*loga)*loga))
00876             return  native(ab, yp, ypp)
00877 
##