root.py

#!/usr/bin/python
# -*- coding: utf-8 -*-

# author  : eclipse
# email   : adooadoo@163.com


def root(x, debug=False, iterMax=100):
    """
    root for none-negative number
    """

    if x == 0:
        return 0
    elif x < 0:
        print '***Erro,x must be nonnegative'
        return None
    assert x > 0. and type(x) is float or int, 'Unrecognized input'
    s = 1.0
    tol = 1.e-14
    for k in range(iterMax):
        s1 = s
        s = 0.5 * (s + x / s)
        if debug:
            print 'Before iteration %s,s=%20.15f' % (k, s)
        if abs((s - s1) / x) < tol:
            return s
    return s


def test():
    from numpy import sqrt
    xvalues = [0., 2., 100., 10000., 1.e-4]
    for x in xvalues:
        print 'Testing with x = %20.15e' % x
        s = root(x)
        s_numpy = sqrt(x)
        print ' s = %20.15e, numpy.sqrt = %20.15e' % (s, s_numpy)
        assert abs(s - s_numpy) < 1.e-14, 'Disagree for x = %20.15e' % x


if __name__ == '__main__':
    print 'Running test.'
    test()