我正在用python实时拟合指数数据。数以百万计的对我的指数衰减函数的调用，因此加速它可以极大地提高性能。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。在我的健身计划中使用它的效果更差。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,a1,a2):
return a0 + a1*np.exp(-t*a2)
%timeit fexp_nb(t,a0,a1,a2)
26.4 µs ± 974 ns per loop (mean ± std. dev. of 7 runs, 10000 loops each)
这可能是由于numpy计算编译开销。有办法预编译吗?或者我可以做的另一个优化(将我的chunksize更改为我的fit数组的长度)?我在文档中没有看到任何这样的选项。
我也运行过cpython和numba，它们是否适合加速scipy适配?(编辑:Numba似乎也没有帮助，见上面的结果)这里是相关的适合代码，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)
也是fexp函数的格式:
def fexp(t,a0,a1,a2):
return a0 + a1*np.exp(-t*a2)
def fexp_ne(t,a0,a1,a2):
return ne.evaluate('a0 + a1*exp(-t*a2)')
这已经在一个多进程例程中运行了。目前的限制是fexp计算的速度。任何帮助或洞察力优化指数调用在python将不胜感激。
编辑:这里是一个完整的例子:
array([ 6.77582760e-01, 6.71805572e-01, 6.62855412e-01, 6.54604329e-01,
6.47518077e-01, 6.40244555e-01, 6.33497217e-01, 6.25381033e-01,
6.17461716e-01, 6.11452674e-01, 6.03328389e-01, 5.97276341e-01,
5.90335893e-01, 5.83810521e-01, 5.77519704e-01, 5.70318901e-01,
5.64502798e-01, 5.58176217e-01, 5.51840170e-01, 5.45846183e-01,
5.40182764e-01, 5.31834927e-01, 5.26967196e-01, 5.21053537e-01,
5.13871378e-01, 5.08438374e-01, 5.03092689e-01, 4.97433669e-01,
4.91322442e-01, 4.85540282e-01, 4.78926889e-01, 4.73335312e-01,
4.69494226e-01, 4.63500965e-01, 4.57355641e-01, 4.51666783e-01,
4.47087242e-01, 4.41797146e-01, 4.36845384e-01, 4.31697062e-01,
4.26889273e-01, 4.22507944e-01, 4.16283962e-01, 4.12060334e-01,
4.06914605e-01, 4.02757403e-01, 3.97040053e-01, 3.92698393e-01,
3.87453958e-01, 3.82990676e-01, 3.79885919e-01, 3.74404426e-01,
3.70689325e-01, 3.66252384e-01, 3.61609911e-01, 3.57343305e-01,
3.53040276e-01, 3.48222287e-01, 3.43435412e-01, 3.40570855e-01,
3.36410098e-01, 3.32147335e-01, 3.28278134e-01, 3.23822881e-01,
3.20550978e-01, 3.15701573e-01, 3.12430630e-01, 3.08407969e-01,
3.05027449e-01, 3.02299415e-01, 2.97209405e-01, 2.94273878e-01,
2.90333001e-01, 2.86942177e-01, 2.83282482e-01, 2.79976710e-01,
2.76577305e-01, 2.73129084e-01, 2.71373570e-01, 2.66898124e-01,
2.63082368e-01, 2.59528578e-01, 2.56441631e-01, 2.53613598e-01,
2.51009741e-01, 2.46518043e-01, 2.44198633e-01, 2.40293215e-01,
2.38216907e-01, 2.34451158e-01, 2.32501154e-01, 2.29227875e-01,
2.26828373e-01, 2.23271660e-01, 2.20187713e-01, 2.17651154e-01,
2.14815004e-01, 2.12273672e-01, 2.09486921e-01, 2.07808467e-01,
2.04258261e-01, 2.01695808e-01, 1.98213932e-01, 1.96140969e-01,
1.94807019e-01, 1.89744628e-01, 1.89274492e-01, 1.87326534e-01,
1.83796672e-01, 1.82229243e-01, 1.79545829e-01, 1.78007550e-01,
1.75067117e-01, 1.71509604e-01, 1.71647877e-01, 1.68529915e-01,
1.64850192e-01, 1.62491681e-01, 1.62054741e-01, 1.59605217e-01,
1.56905657e-01, 1.56494100e-01, 1.53703593e-01, 1.50716588e-01,
1.48780532e-01, 1.47442009e-01, 1.45447195e-01, 1.42603381e-01,
1.41557222e-01, 1.39193149e-01, 1.37259584e-01, 1.35013117e-01,
1.34160615e-01, 1.31822213e-01, 1.29757188e-01, 1.27075812e-01,
1.25988605e-01, 1.25003127e-01, 1.23063061e-01, 1.21201713e-01,
1.19385533e-01, 1.17488818e-01, 1.14957141e-01, 1.13375794e-01,
1.13162993e-01, 1.10977052e-01, 1.09198020e-01, 1.08012072e-01,
1.06087446e-01, 1.05099185e-01, 1.03226144e-01, 1.01090762e-01,
9.89268290e-02, 9.84298054e-02, 9.74088178e-02, 9.57077008e-02,
9.34094478e-02, 9.34770285e-02, 9.16919224e-02, 9.02382531e-02,
8.96615820e-02, 8.71530839e-02, 8.61682304e-02, 8.42724668e-02,
8.46299322e-02, 8.21125377e-02, 7.98889165e-02, 8.04244477e-02,
7.84594084e-02, 7.76000882e-02, 7.54094009e-02, 7.45808875e-02,
7.40301258e-02, 7.27424577e-02, 7.12559804e-02, 7.04680289e-02,
6.85277010e-02, 6.87051292e-02, 6.76578279e-02, 6.42697271e-02,
6.40199091e-02, 6.36143478e-02, 6.15051025e-02, 6.13128604e-02,
6.05643017e-02, 5.82606683e-02, 5.74001989e-02, 5.71317747e-02,
5.60278909e-02, 5.51050378e-02, 5.39380398e-02, 5.37979092e-02,
5.20580658e-02, 5.04491614e-02, 5.05715122e-02, 4.92034685e-02,
4.75611572e-02, 4.69520119e-02, 4.64852536e-02, 4.59729697e-02,
4.55283250e-02, 4.42763236e-02, 4.28236355e-02, 4.27546272e-02,
4.19050488e-02, 4.04688277e-02, 3.94272902e-02, 3.95748321e-02,
3.89298743e-02, 3.73866731e-02, 3.72141633e-02, 3.65430784e-02,
3.44737817e-02, 3.42898759e-02, 3.31612552e-02, 3.26311197e-02,
3.18868672e-02, 3.04010275e-02, 3.06206431e-02, 2.94735156e-02,
2.96741315e-02, 2.88437650e-02, 2.76153159e-02, 2.77555857e-02,
2.58538605e-02, 2.54368711e-02, 2.44673277e-02, 2.56250910e-02,
2.33827364e-02, 2.26483672e-02, 2.27238410e-02, 2.03568150e-02,
2.14757502e-02, 2.01854003e-02, 1.97837673e-02, 1.97186331e-02,
1.77891223e-02, 1.91265448e-02, 1.73643535e-02, 1.63559444e-02,
1.64184309e-02, 1.60763341e-02, 1.56667306e-02, 1.53286118e-02,
1.40528680e-02, 1.40642010e-02, 1.50253718e-02, 1.23722700e-02,
1.18349807e-02, 1.16952932e-02, 1.10814560e-02, 1.12464417e-02,
9.02985284e-03, 9.90810088e-03, 9.90613947e-03, 8.33110496e-03,
8.03159218e-03, 7.55101564e-03, 7.87897600e-03, 6.63023548e-03,
6.02989494e-03, 6.19476245e-03, 5.14076580e-03, 5.09559047e-03,
3.78939236e-03, 3.91231009e-03, 3.87641581e-03, 2.88336640e-03,
2.62317124e-03, 2.07934571e-03, 2.31619406e-03, 1.60184113e-03,
8.19957252e-04, 1.55867472e-03, 9.11270374e-04, 7.60252051e-04,
-2.49981482e-04, 1.61518200e-04, -1.50757208e-03, -1.40549609e-03,
-2.15401175e-03, -2.55539057e-03, -2.26817884e-03, -3.42271219e-03,
-3.61592119e-03, -3.78268491e-03, -3.83210682e-03, -5.32324729e-03,
-5.99929258e-03, -4.99760968e-03, -5.18682072e-03, -7.09107309e-03,
-6.17065428e-03, -6.49019882e-03, -7.28126650e-03, -8.18286576e-03,
-8.10584493e-03, -8.38154570e-03, -7.94357643e-03, -8.73734918e-03,
-8.66833752e-03, -8.81083174e-03, -9.63921586e-03, -9.36494609e-03,
-1.05607430e-02, -9.98560128e-03, -9.90366976e-03, -1.11094682e-02,
-1.06379207e-02, -1.06525755e-02, -1.21732000e-02, -1.13729375e-02,
-1.16419153e-02, -1.27108551e-02, -1.25469346e-02, -1.27152863e-02,
-1.17560316e-02, -1.33894917e-02, -1.36998304e-02, -1.35083165e-02,
-1.38339452e-02, -1.46794008e-02, -1.46427131e-02, -1.48451722e-02,
-1.41840269e-02, -1.45224640e-02, -1.54875774e-02, -1.60601588e-02,
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-2.79248766e-02, -2.79176487e-02, -2.75685659e-02, -2.75524150e-02,
-2.86517306e-02, -2.82334042e-02, -2.82021609e-02, -2.87045516e-02,
-2.79073930e-02, -2.80293837e-02, -2.90965831e-02, -2.91120301e-02,
-2.86658119e-02, -2.96395014e-02, -2.81576011e-02, -2.85221055e-02,
-2.93785647e-02, -2.90209844e-02, -2.93115642e-02, -2.95479562e-02,
-2.91992171e-02, -3.00063362e-02, -2.93740143e-02, -2.94714359e-02,
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有几个选项:
你可以用一小部分数据进行第一次优化，然后使用结果作为使用全部数据进行最后优化的种子。
您还可以提供雅可比矩阵以避免其数值计算，这涉及到多次调用fexp。在这种情况下，雅可比矩阵将是:
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
如果你想并行化fexp和Numba，你可以使用prange:
@nb.njit(parallel=True)
def fexp_nb(t, a0, a1, 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法并行化雅可比矩阵。