【发布时间】：2014-10-02 09:59:56
【问题描述】：
我对 scipy 的牛顿法有疑问。当我使用带有给定导数的牛顿时出现错误（请参阅下面的错误输出）。
我正在尝试以 x0 = 2.0 的起始值计算 x**2 的根：
def test_newtonRaphson():
def f(x):
resf = x**2
return resf
assert(derivative(f, 1.0)) == 2.0
assert(round(newton(f, 0.0), 10)) == 0.0
dfx0 = derivative(f, 2.0)
assert(round(newton(f, 2.0, dfx0), 10)) == 0.0
整个错误输出如下：
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
func = <function f at 0x04049EF0>, x0 = 2.0, fprime = 4.0, args = ()
tol = 1.48e-08, maxiter = 50, fprime2 = None
def newton(func, x0, fprime=None, args=(), tol=1.48e-8, maxiter=50,
fprime2=None):
"""
Find a zero using the Newton-Raphson or secant method.
Find a zero of the function `func` given a nearby starting point `x0`.
The Newton-Raphson method is used if the derivative `fprime` of `func`
is provided, otherwise the secant method is used. If the second order
derivate `fprime2` of `func` is provided, parabolic Halley's method
is used.
Parameters
----------
func : function
The function whose zero is wanted. It must be a function of a
single variable of the form f(x,a,b,c...), where a,b,c... are extra
arguments that can be passed in the `args` parameter.
x0 : float
An initial estimate of the zero that should be somewhere near the
actual zero.
fprime : function, optional
The derivative of the function when available and convenient. If it
is None (default), then the secant method is used.
args : tuple, optional
Extra arguments to be used in the function call.
tol : float, optional
The allowable error of the zero value.
maxiter : int, optional
Maximum number of iterations.
fprime2 : function, optional
The second order derivative of the function when available and
convenient. If it is None (default), then the normal Newton-Raphson
or the secant method is used. If it is given, parabolic Halley's
method is used.
Returns
-------
zero : float
Estimated location where function is zero.
See Also
--------
brentq, brenth, ridder, bisect
fsolve : find zeroes in n dimensions.
Notes
-----
The convergence rate of the Newton-Raphson method is quadratic,
the Halley method is cubic, and the secant method is
sub-quadratic. This means that if the function is well behaved
the actual error in the estimated zero is approximately the square
(cube for Halley) of the requested tolerance up to roundoff
error. However, the stopping criterion used here is the step size
and there is no guarantee that a zero has been found. Consequently
the result should be verified. Safer algorithms are brentq,
brenth, ridder, and bisect, but they all require that the root
first be bracketed in an interval where the function changes
sign. The brentq algorithm is recommended for general use in one
dimensional problems when such an interval has been found.
"""
if tol <= 0:
raise ValueError("tol too small (%g <= 0)" % tol)
if fprime is not None:
# Newton-Rapheson method
# Multiply by 1.0 to convert to floating point. We don't use float(x0)
# so it still works if x0 is complex.
p0 = 1.0 * x0
fder2 = 0
for iter in range(maxiter):
myargs = (p0,) + args
fder = fprime(*myargs)E TypeError: 'numpy.float64' 对象不可调用
File "C:\Anaconda\lib\site-packages\scipy\optimize\zeros.py", line 116
TypeError
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标签： python numpy scipy pydev anaconda