问题描述
我正在用 python 实时拟合指数数据。数百万次调用我的指数衰减函数“fexp”，因此加速它可以大大提高性能。我最近偶然发现了 numexpr 模块，但它似乎是为更大的数组量身定制的。在我的健身程序中使用它会产生更差的性能。两个拟合函数的timeit结果：
import numexpr as ne
t=np.arange(0,1400)
a0,a1,a2=[-0.034913174979286636,0.634038654906443,0.010961607601301245]
%timeit (a0 + a1*np.exp(-t*a2))
25.5 µs ± 225 ns per loop (mean ± std. dev. of 7 runs,10000 loops each)
%timeit ne.evaluate('(a0 + a1*exp(-t*a2))')
33.1 µs ± 570 ns per loop (mean ± std. dev. of 7 runs,10000 loops each)
import numba as nb
@nb.njit(error_model="numpy",parallel=True)
def fexp_nb(t,a0,a2):
return a0 + a1*np.exp(-t*a2)
%timeit fexp_nb(t,a2)
26.4 µs ± 974 ns per loop (mean ± std. dev. of 7 runs,10000 loops each)
大概这是由于 numpy 评估编译开销。有没有办法预编译？或者我可以做的其他优化（将块大小更改为适合数组的长度？我在文档中没有看到任何此类选项。
我也遇到过 cpython 和 numba，这些是否适合加速 scipy fit？ （编辑：Numba 似乎也没有帮助，请参阅上面的结果）这是相关的拟合代码，其中 y 是原始数据：
from scipy.optimize import curve_fit
...
x=np.arange(0,leny-syfd)
(M,pcov)=curve_fit(fexp,x,y[syfd:],p0=(M,),sigma=None,method='lm',ftol=0.001,xtol=0.001)
还有 fexp 函数的格式：
def fexp(t,a2):
return a0 + a1*np.exp(-t*a2)
def fexp_ne(t,a2):
return ne.evaluate('a0 + a1*exp(-t*a2)')
这已经在使用多处理例程运行。当前限制是 fexp 计算的速度。任何在 Python 中优化指数调用的帮助或见解将不胜感激。
编辑：为了完整性，这里是一个示例 y：
array([ 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解决方法
有几个选项：
您可以使用一小部分数据进行第一次优化，然后将结果用作对完整数据进行最终优化的种子。
您还可以提供雅可比行列式以避免其数值计算，这涉及对 fexp 的多次调用。在这种情况下，雅可比行列式将是：
def jacobian(t,_,a1,a2):
j = np.empty((len(t),3))
j[:,0] = 1.
j[:,1] = np.exp(-t * a2)
j[:,2] = -a1 * t * j[:,1]
return j
如果你想用 Numba 并行化 fexp，你可以使用 prange：
@nb.njit(parallel=True)
def fexp_nb(t,a0,a2):
result = np.empty_like(t)
for i in nb.prange(len(t)):
result[i] = a0 + a1 * np.exp(-t[i] * a2)
return result
你也可以用同样的方式并行化雅可比行列式。