Consider the function Newton(),
def Newton(f, dfdx, x, eps=1E-7, maxit=100):
if not callable(f): raise TypeError( 'f is %s, should be function or class with __call__' % type(f) )
if not callable(dfdx): raise TypeError( 'dfdx is %s, should be function or class with __call__' % type(dfdx) )
if not isinstance(maxit, int): raise TypeError( 'maxit is %s, must be int' % type(maxit) )
if maxit <= 0: raise ValueError( 'maxit=%d <= 0, must be > 0' % maxit )
n = 0 # iteration counter
while abs(f(x)) > eps and n < maxit:
try:
x = x - f(x)/float(dfdx(x))
except ZeroDivisionError:
raise ZeroDivisionError( 'dfdx(%g)=%g - cannot divide by zero' % (x, dfdx(x)) )
n += 1
return x, f(x), n
This function is supposed to be able to handle exceptions such as divergent iterations (which we discussed in the lecture), and division-by-zero. The latter error happens when dfdx(x)=0 in the above code, which represents a zero-valued derivative of the function $f(x)$. Write a test code that ensures the above code can correctly identify a division-by-zero exception and raise the correct assertionError.
Tip: To do so, you need to consider a test mathematical function as input to Newton. One example could be $f(x)=\cos(x)$ with a starting search value $x=0$. This would result in derivative value $f’(x=0)=-\sin(x=0)=0$, which should lead to a ZeroDivisionError exception. Now, write a test function test_Newton_div_by_zero that can explicitly handle this exception by introducing a boolean variable success that is True if the exception is raised and otherwise False*.
