我在一个函数中使用quad_vec，该函数包含一个用解析方法无法求解的积分.我需要将这个方程式与数据点相匹配.
然而，即使使用固定值进行判断也需要数秒，总拟合时间也会增加到7分钟.
有没有办法加速计算？我知道quad_vec有workers关键字，但当我try 使用该关键字时，计算根本没有完成.
如果这有什么意义的话，我现在正在用一台Jupyter笔记本工作.
这是函数定义，我已经try 在这里使用Numba，但收效甚微.
from scipy.special import j0, j1
from scipy.integrate import quad_vec
import numpy as np
import numba as nb
h = 0.00005
G = 1000
E = 3*G
R= 0.0002
upsilon = 0.06
gamma = 0.072
@nb.jit(nb.float64(nb.float64, nb.float64, nb.float64, nb.float64, nb.float64),cache=True)
def QSzz_1(s,h,z, upsilon, E):
# exponential form of the QSzz^-1 function to prevent float overflow,
# also assumes nu==0.5
numerator = (1+2*s**2*h**2)*np.exp(-2*s*z) + 0.5*(1+np.exp(-4*s*z))
denominator = 0.5*(1-np.exp(-4*s*z)) - 2*s*h*np.exp(-2*s*z)
return (3/(2*s*E)) / (numerator/denominator + (3*upsilon/(2*E))*s)
def integrand(s, r, R, upsilon, E, h):
return s*(R*j0(s*R) - 2*j1(s*R)/s) * QSzz_1(s,h,h, upsilon, E) * j0(s*r)
def style_exact(r, gamma, R, upsilon, E, h):
int_out = quad_vec(integrand, 0, np.inf, args=(r,R,upsilon,E,h))
return gamma * int_out[0]
# calculate fixed ~10s
x_ax = np.linspace(0, 0.0004,101, endpoint=True, dtype=np.float64)
zeta = style_exact(x_ax, gamma, 0.0002, upsilon, E, h)
# fit to dataset (wetting ridge) ~7 min
popt_hemi, pcov_hemi = curve_fit(lambda x, upsilon, E, h: style_exact(x, gamma, R, upsilon, E, h) ,points_x, points_y, p0=(upsilon, E, h), bounds=([0,0,0],[np.inf,np.inf,np.inf]))
编辑: 以下是一些样本值:
points_x =[0.00040030286, 0.00040155788, 0.00040281289, 0.00040406791000000003, 0.00040532292, 0.00040657794, 0.00040783296, 0.00040908797, 0.00041034299, 0.00041159801, 0.00041285302, 0.00041410804, 0.00041536305, 0.00041661807, 0.00041787309, 0.0004191281, 0.00042038312, 0.00042163814, 0.00042289315000000003, 0.00042414817000000003, 0.00042540318, 0.0004266582, 0.00042791322, 0.00042916823, 0.00043042325, 0.00043167827, 0.00043293328, 0.0004341883, 0.00043544332, 0.00043669833, 0.00043795335, 0.00043920836, 0.00044046338, 0.0004417184, 0.00044297341000000003, 0.00044422843000000003, 0.00044548345, 0.00044673846, 0.00044799348, 0.00044924849, 0.00045050351, 0.00045175852999999996, 0.00045301354000000006, 0.00045426856, 0.00045552357999999995, 0.00045677859000000005, 0.00045803361, 0.00045928863000000006, 0.00046054364000000004, 0.00046179866, 0.00046305367, 0.00046430869000000004, 0.00046556371, 0.00046681871999999997, 0.00046807374000000003, 0.00046932876, 0.00047058376999999996, 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points_y = [-2.4929826e-07, -2.3248189e-07, -4.4305314e-07, -1.0689171e-06, -7.0144722e-07, -1.3773717e-06, -9.3672285e-07, -1.6876499e-06, -9.8346007e-07, -1.7992562e-06, -1.0198111e-06, -1.721233e-06, -8.9082583e-07, -1.1925362e-06, -8.3776501e-07, -6.9998957e-07, -7.1134901e-07, -4.5476849e-07, -6.4449894e-07, -3.8765887e-07, -6.3044764e-07, -7.4224008e-07, -7.6114851e-07, -1.0377502e-06, -1.3589471e-06, -1.3342596e-06, -1.3712255e-06, -1.3510569e-06, -1.2278933e-06, -8.2319036e-07, -1.4040568e-06, -6.4183121e-07, -1.1649824e-06, -7.3197454e-07, -1.0537769e-06, -8.3223932e-07, -1.1644648e-06, -1.2177416e-06, -1.4045247e-06, -1.6934001e-06, -1.6157397e-06, -1.8595331e-06, -1.7097882e-06, -1.8031869e-06, -1.5406345e-06, -1.5851084e-06, -1.5695719e-06, -1.4990693e-06, -1.8087735e-06, -1.7151045e-06, -1.8353234e-06, -1.71844e-06, -1.7904118e-06, -1.5297879e-06, -1.6064767e-06, -1.4520618e-06, -1.1090131e-06, -1.2475477e-06, -7.4591269e-07, -1.0619496e-06, -7.5699762e-07, -1.3883064e-06, 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