我需要对类型g（u）jn（u）进行积分，其中g（u）是不带零的平滑函数，而在Bessel函数中具有无穷零的jn（u），但出现以下错误：
TypeError: Cannot cast array data from dtype('O') to dtype('float64') according to the rule 'safe'
首先，我需要将变量x更改为变量u，并在新变量u中进行积分，但是函数u（x）在解析上是不可逆的，因此我需要使用插值对这一数值进行反演。
import numpy as np
from scipy.interpolate import InterpolatedUnivariateSpline
x = np.linspace(0.1, 100, 1000)
u = lambda x: x*np.exp(x)
dxdu_x = lambda x: 1/((1+x) * np.exp(x)) ## dxdu as function of x: not invertible
dxdu_u = InterpolatedUnivariateSpline(u(x), dxdu_x(x)) ## dxdu as function of u: change of variable
此后，积分为：
from mpmath import mp
def f(n):
integrand = lambda U: dxdu_u(U) * mp.besselj(n,U)
bjz = lambda nth: mp.besseljzero(n, nth)
return mp.quadosc(integrand, [0,mp.inf], zeros=bjz)
我使用quadosc中的mpmath，而不使用quad中的scipy，因为quadosc更适合于集成快速振荡函数（如Bessel函数）。但是，另一方面，这迫使我使用两个不同的包，scipy通过插值来计算dxdu_u，而mpmath来计算Bessel函数mp.besselj(n,U)及其积分产品dxdu_u(U) * mp.bessel(n,U)，因此我怀疑两个不同软件包的混合使用会产生一些问题/冲突。所以当我做的时候：
print(f(0))
我得到了错误：
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
<ipython-input-38-ac2976a6b736> in <module>
12 return mp.quadosc(integrand, [0,mp.inf], zeros=bjz)
13
---> 14 f(0)
<ipython-input-38-ac2976a6b736> in f(n)
10 integrand = lambda U: dxdu_u(U) * mp.besselj(n,U)
11 bjz = lambda nth: mp.besseljzero(n, nth)
---> 12 return mp.quadosc(integrand, [0,mp.inf], zeros=bjz)
13
14 f(0)
TypeError: Cannot cast array data from dtype('O') to dtype('float64') according to the rule 'safe'
有人知道我可以解决这个问题吗？ 谢谢
答案 0 :(得分：2)
完整的追溯（截取的部分）表明该错误出在univariatespline对象的__call__方法中。因此，实际上的问题是，mpmath集成例程以其mpf小数形式输入，而scipy无法处理它们。
然后最简单的解决方法是将integrand参数的有问题的部分手动转换为浮点数：
integrand = lambda U: dxdu_u(float(U)) * mp.besselj(n,U)
通常，这容易产生数字错误（mpmath故意使用其高精度变量！），因此请谨慎操作。在这种特定情况下，这可能没问题，因为插值实际上是以双精度完成的。不过，最好检查一下结果。
一种可能的选择是避免使用mpmath并在weights中使用scipy.integrate.quad参数，请参见docs（向下滚动到weights="sin"部分）
另一种选择是始终坚持使用mpmath并在纯python中实现插值（这样，mpf对象可能很好，因为它们应该支持常用的算术）。一个简单的线性插值可能就足够了。如果不是，那么编写自己的三次样条插值器就没什么大不了了。
答案 1 :(得分：0)
完整的追溯：
In [443]: f(0)
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
<ipython-input-443-6bfbdbfff9c4> in <module>
----> 1 f(0)
<ipython-input-440-7ebeff3611f6> in f(n)
2 integrand = lambda U: dxdu_u(U) * mp.besselj(n,U)
3 bjz = lambda nth: mp.besseljzero(n, nth)
----> 4 return mp.quadosc(integrand, [0,mp.inf], zeros=bjz)
5
/usr/local/lib/python3.6/dist-packages/mpmath/calculus/quadrature.py in quadosc(ctx, f, interval, omega, period, zeros)
998 # raise ValueError("zeros do not appear to be correctly indexed")
999 n = 1
-> 1000 s = ctx.quadgl(f, [a, zeros(n)])
1001 def term(k):
1002 return ctx.quadgl(f, [zeros(k), zeros(k+1)])
/usr/local/lib/python3.6/dist-packages/mpmath/calculus/quadrature.py in quadgl(ctx, *args, **kwargs)
807 """
808 kwargs['method'] = 'gauss-legendre'
--> 809 return ctx.quad(*args, **kwargs)
810
811 def quadosc(ctx, f, interval, omega=None, period=None, zeros=None):
/usr/local/lib/python3.6/dist-packages/mpmath/calculus/quadrature.py in quad(ctx, f, *points, **kwargs)
740 ctx.prec += 20
741 if dim == 1:
--> 742 v, err = rule.summation(f, points[0], prec, epsilon, m, verbose)
743 elif dim == 2:
744 v, err = rule.summation(lambda x: \
/usr/local/lib/python3.6/dist-packages/mpmath/calculus/quadrature.py in summation(self, f, points, prec, epsilon, max_degree, verbose)
230 print("Integrating from %s to %s (degree %s of %s)" % \
231 (ctx.nstr(a), ctx.nstr(b), degree, max_degree))
--> 232 results.append(self.sum_next(f, nodes, degree, prec, results, verbose))
233 if degree > 1:
234 err = self.estimate_error(results, prec, epsilon)
/usr/local/lib/python3.6/dist-packages/mpmath/calculus/quadrature.py in sum_next(self, f, nodes, degree, prec, previous, verbose)
252 case the quadrature rule is able to reuse them.
253 """
--> 254 return self.ctx.fdot((w, f(x)) for (x,w) in nodes)
255
256
/usr/local/lib/python3.6/dist-packages/mpmath/ctx_mp_python.py in fdot(ctx, A, B, conjugate)
942 hasattr_ = hasattr
943 types = (ctx.mpf, ctx.mpc)
--> 944 for a, b in A:
945 if type(a) not in types: a = ctx.convert(a)
946 if type(b) not in types: b = ctx.convert(b)
/usr/local/lib/python3.6/dist-packages/mpmath/calculus/quadrature.py in <genexpr>(.0)
252 case the quadrature rule is able to reuse them.
253 """
--> 254 return self.ctx.fdot((w, f(x)) for (x,w) in nodes)
255
256
<ipython-input-440-7ebeff3611f6> in <lambda>(U)
1 def f(n):
----> 2 integrand = lambda U: dxdu_u(U) * mp.besselj(n,U)
3 bjz = lambda nth: mp.besseljzero(n, nth)
4 return mp.quadosc(integrand, [0,mp.inf], zeros=bjz)
5
这时它开始使用scipy插值代码
/usr/local/lib/python3.6/dist-packages/scipy/interpolate/fitpack2.py in __call__(self, x, nu, ext)
310 except KeyError:
311 raise ValueError("Unknown extrapolation mode %s." % ext)
--> 312 return fitpack.splev(x, self._eval_args, der=nu, ext=ext)
313
314 def get_knots(self):
/usr/local/lib/python3.6/dist-packages/scipy/interpolate/fitpack.py in splev(x, tck, der, ext)
366 return tck(x, der, extrapolate=extrapolate)
367 else:
--> 368 return _impl.splev(x, tck, der, ext)
369
370
/usr/local/lib/python3.6/dist-packages/scipy/interpolate/_fitpack_impl.py in splev(x, tck, der, ext)
596 shape = x.shape
597 x = atleast_1d(x).ravel()
--> 598 y, ier = _fitpack._spl_(x, der, t, c, k, ext)
599
600 if ier == 10:
TypeError: Cannot cast array data from dtype('O') to dtype('float64') according to the rule 'safe'
_fitpack._spl_可能是编译后的代码（为了提高速度）。它不能直接使用mpmath对象；它必须通过与C兼容的double传递其值。
为说明问题，请制作一个mpmath对象的numpy数组：
In [444]: one,two = mp.mpmathify(1), mp.mpmathify(2)
In [445]: arr = np.array([one,two])
In [446]: arr
Out[446]: array([mpf('1.0'), mpf('2.0')], dtype=object)
In [447]: arr.astype(float) # default 'unsafe' casting
Out[447]: array([1., 2.])
In [448]: arr.astype(float, casting='safe')
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
<ipython-input-448-4860036bcca8> in <module>
----> 1 arr.astype(float, casting='safe')
TypeError: Cannot cast array from dtype('O') to dtype('float64') according to the rule 'safe'
使用integrand = lambda U: dxdu_u(float(U)) * mp.besselj(n,U)，
In [453]: f(0) # a minute or so later
Out[453]: mpf('0.61060303588231069')