我正在努力提高以下功能的性能
import numpy as np
import time
r_0 = 0.1
drt_measurement = 9.999999999999991269e+04 3.305791191233514031e-02
9.083278409243831993e+04 6.686534998595229651e-02
8.250594665983537561e+04 9.752796826379055151e-02
7.494244839295065321e+04 1.222236211928119098e-01
6.807231234235593001e+04 1.391699770128363156e-01
6.183197649666256621e+04 1.475585893958198669e-01
5.616370571130075405e+04 1.474552502508378327e-01
5.101505754705831350e+04 1.396688202647400068e-01
4.633839707635276136e+04 1.255930866175393457e-01
4.209045616826028709e+04 1.070282638824464200e-01
3.823193317483828287e+04 8.599030685293859722e-02
3.472712931506624591e+04 6.451708658095048343e-02
3.154361839225600124e+04 4.448062538821159762e-02
2.865194678918063437e+04 2.741401408285973687e-02
2.602536096529677889e+04 1.436044167210013059e-02
2.363955993488576496e+04 5.750104576781006442e-03
2.147247043605739236e+04 1.308807047969248521e-03
1.950404271049667659e+04 0.000000000000000000e+00
1.771606500452241744e+04 0.000000000000000000e+00
1.609199507523391185e+04 0.000000000000000000e+00
1.461680714285303839e+04 0.000000000000000000e+00
1.327685287327581318e+04 0.000000000000000000e+00
1.205973510465334584e+04 0.000000000000000000e+00
1.095419314972977190e+04 5.884342919743409559e-05
9.949998612762719858e+03 7.998619890618585823e-04
9.037860757131376886e+03 2.500965172969732246e-03
8.209340548100375599e+03 5.183567450782240564e-03
7.456772575469013645e+03 8.693985479427597876e-03
6.773194133739925746e+03 1.277455657793208701e-02
6.152280803661701611e+03 1.712274094295426416e-02
5.588287939150567581e+03 2.143744150510841495e-02
5.075997518232417860e+03 2.545264530106331607e-02
4.610669866273584375e+03 2.895921274282790836e-02
4.187999804847402629e+03 3.181618818319655040e-02
3.804076820528789085e+03 3.395336714100914005e-02
3.455348885101409905e+03 3.536703974806452988e-02
3.138589592444641312e+03 3.611085706109572885e-02
2.850868308052988141e+03 3.628366608266923865e-02
2.589523055013517478e+03 3.601596333981682552e-02
2.352135885584347307e+03 3.545635735989378923e-02
2.136510510513593999e+03 3.475913507228068494e-02
1.940651979127065943e+03 3.407371862599613277e-02
1.762748222186123712e+03 3.353649513263438908e-02
1.601153286751617770e+03 3.326521661020837711e-02
1.454372107944078152e+03 3.335591277678888467e-02
1.321046676709491976e+03 3.388204564707710670e-02
1.199943475615865282e+03 3.489547101805602625e-02
1.089942066437459971e+03 3.642866487850397045e-02
9.900247239398013335e+02 3.849762676627922764e-02
8.992670199579990822e+02 4.110488763025969133e-02
8.168292706529540510e+02 4.424212280193264707e-02
7.419487678160369342e+02 4.789199229029628135e-02
6.739327223468492321e+02 5.202898717068607515e-02
6.121518546176058635e+02 5.661923512902567596e-02
5.560345724226672246e+02 6.161939118388957970e-02
5.050616826479952124e+02 6.697489246448506961e-02
4.587615877332899572e+02 7.261797229246705343e-02
4.167059224848219401e+02 7.846589642339019122e-02
3.785055908710423296e+02 8.441989610198158411e-02
3.438071661337024238e+02 9.036522727306788016e-02
3.122896209085568557e+02 9.617268729145930783e-02
2.836613571029640752e+02 1.017017794343546278e-01
2.576575080510160092e+02 1.068055453270566474e-01
2.340374879859364512e+02 1.113369027524976212e-01
2.125827661576324488e+02 1.151561489961011597e-01
1.930948450016954894e+02 1.181391348882323278e-01
1.753934236540186191e+02 1.201854967485512515e-01
1.593147298199906459e+02 1.212262639441004930e-01
1.447100045648438140e+02 1.212301466547610895e-01
1.314441260065423194e+02 1.202078563468665651e-01
1.193943591777153443e+02 1.182139221125656503e-01
1.084492204904446879e+02 1.153456380429484229e-01
9.850744629801818064e+01 1.117390045066268961e-01
8.947705601085354488e+01 1.075617976309274221e-01
8.127450109860885163e+01 1.030041958936550872e-01
7.382389210510589805e+01 9.826768020589901620e-02
6.705629652446552313e+01 9.355316527274525062e-02
6.090910104245309498e+01 8.904947235118862436e-02
5.532543224253661407e+01 8.492327754931115746e-02
5.025363041707156952e+01 8.131154005122069595e-02
4.564677161535060890e+01 7.831712920216649110e-02
4.146223350653990991e+01 7.600795657985991161e-02
3.766130104089801023e+01 7.441943814465099005e-02
3.420880826088217219e+01 7.355964469118533855e-02
3.107281294820336370e+01 7.341613608640509825e-02
2.822430109668880149e+01 7.396329262714643193e-02
2.563691847675508129e+01 7.516899705860667635e-02
2.328672680794541350e+01 7.699977592398718484e-02
2.115198228365702704e+01 7.942392015010443784e-02
1.921293439898502697e+01 8.241257439738865209e-02
1.745164322045190985e+01 8.593920060703628960e-02
1.585181340701575792e+01 8.997808644364771458e-02
1.439864344673082641e+01 9.450262800985891054e-02
1.307868871420905421e+01 9.948396777326518059e-02
1.187973708189962707e+01 1.048902674310989852e-01
1.079069593435122876e+01 1.106865359470413646e-01
9.801489540120787325e+00 1.168346253750716379e-01
8.902965831820848663e+00 1.232928486931701845e-01
8.086811731841407891e+00 1.300147229633645263e-01
7.345476240345480079e+00 1.369465983564550071e-01
6.672100573954371505e+00 1.440243362646556891e-01
6.060454708770327770e+00 1.511696326583486516e-01
5.504879740637368180e+00 1.582869059047162796e-01
5.000235529361520825e+00 1.652617562821384889e-01
4.541853142498352369e+00 1.719617888968693886e-01
4.125491658721156973e+00 1.782400906636870952e-01
3.747298931117743592e+00 1.839409756266481011e-01
3.403775947400438096e+00 1.889069396630453090e-01
3.091744457292589399e+00 1.929852944771389966e-01
2.808317567582508723e+00 1.960328443678645005e-01
2.550873032792241979e+00 1.979173071537675133e-01
2.317028994348411697e+00 1.985149376242555386e-01
2.104621943795689454e+00 1.977048651618161235e-01
1.911686706170022010e+00 1.953618156009037932e-01
1.736438258339263463e+00 1.913499288641969109e-01
1.577255214095804270e+00 1.855210883531741572e-01
1.432664823206368121e+00 1.777213502891315244e-01
1.301329345631354384e+00 1.678085462088224900e-01
1.182033674848871785e+00 1.556828286648617721e-01
1.073674095775390969e+00 1.413298085763469714e-01
9.752480732721008350e-01 1.248730508724671950e-01
8.858449767609145598e-01 1.066292127040442267e-01
8.046376551349524453e-01 8.715528763529736822e-02
7.308747840151903485e-01 6.727361123710773327e-02
6.638739145505944128e-01 4.805690587820010684e-02
6.030151594497604739e-01 3.075315477876142470e-02
5.477354578276738550e-01 1.662898258880479707e-02
4.975233658063408781e-01 6.710983667767722420e-03
4.519143246723060781e-01 1.407583407585111072e-03
4.104863628123966990e-01 0.000000000000000000e+00
3.728561916622883388e-01 0.000000000000000000e+00
3.386756595478945808e-01 0.000000000000000000e+00
3.076285306107807704e-01 0.000000000000000000e+00
2.794275590164317924e-01 0.000000000000000000e+00
2.538118313761663081e-01 0.000000000000000000e+00
2.305443527949769256e-01 0.000000000000000000e+00
2.094098542115712391e-01 0.000000000000000000e+00
1.902128007442865087e-01 4.295370599089006446e-03
1.727755826162377384e-01 2.640854551111869453e-02
1.569368719222600794e-01 7.259131510582693403e-02
1.425501300345730638e-01 1.423914344911824392e-01
1.294822518377939102e-01 2.296111516784170581e-01
1.176123342498509028e-01 3.236305655613548882e-01
1.068305576352440167e-01 4.110383626909880905e-01
9.703716976156935570e-02 4.774860553090806148e-01
8.814156289893920748e-02 5.096622216542943118e-01
8.006143552369422711e-02 4.972726694760475352e-01
7.272203087054407433e-02 4.349122174992410828e-01
6.605544528827768380e-02 3.237240623831713071e-01
5.999999999999999778e-02 1.727623254500962879e-01
def backcalculate_impedance_from_drt_freq(drt_measurement, r_0):
# Extract frequency and DRT from drt_measurement matrix
drt_frequency = drt_measurement[:,0]
drt = drt_measurement[:,1]
# Frequency to angular frequency, ω, and scaling factor
ω_drt = -np.log(2*np.pi*drt_frequency)
ds = ω_drt[2] - ω_drt[1] # ds is a constant
# Unscaling the DRT
unscaled_drt = drt*ds
# Initializing Zreal and ZImag vectors
ZReal = np.empty((len(drt_frequency),1))
ZImag = np.empty((len(drt_frequency),1))
print("\nBackImpedance For loop")
tic = time.time()
# Solve for ZReal and ZImag
for i in range(len(drt_frequency)):
K1 = 1 / (1 + np.exp(2 * (-ω_drt[i] + ω_drt))) * unscaled_drt
K2 = -np.exp(-ω_drt[i] + ω_drt) * K1
ZReal[i,0] = sum(K1) + r_0
ZImag[i,0] = sum(K2)
toc = time.time()
diff = toc - tic
print(f'Executed in {diff} seconds or {diff*1000} milliseconds')
# Save Backcalculated Impedance into a (x,3) matrix
drt_frequency = drt_frequency[:,None]
backcalculated_impedance = np.hstack((drt_frequency,ZReal,ZImag))
return backcalculated_impedance
目前，每次调用此函数时，我都会花费大约 10 毫秒，其中 for 循环占据了大部分时间，这确实减慢了整体执行速度。有没有比 for 循环更好的替代方案或者向量化其操作的方法？
你可以测试一下吗
def backcalculate_impedance_from_vectorized(drt_measurement, r_0):
drt_frequency, drt = drt_measurement[:, 0], drt_measurement[:, 1]
ω_drt = -np.log(2 * np.pi * drt_frequency)
ds = ω_drt[2] - ω_drt[1]
unscaled_drt = drt * ds
ω_drt_expanded = ω_drt[:, np.newaxis]
K1 = 1 / (1 + np.exp(2 * (ω_drt_expanded - ω_drt))) * unscaled_drt
ZReal = K1.sum(axis=1) + r_0
ZImag = (-np.exp(ω_drt_expanded - ω_drt) * K1).sum(axis=1)
return np.hstack((drt_frequency[:, np.newaxis], ZReal[:, np.newaxis], ZImag[:, np.newaxis]))