我想将操作 curve_fit（找到系数 c1-c7）应用于积分函数
问题是次积分函数取决于几个变量（列出 defor、stress、init_def）并且积分限制也是可变的（列出 init_def、defor）。
所以，积分函数是
time=f(defor,stress)积分应该超过参数（defor）
我尝试了以下代码，但出现了错误。如果你能帮助我，我将不胜感激。非常感谢您。
import numpy as np
from scipy import integrate
from scipy.optimize import curve_fit
from scipy.integrate import quad
time =np.array([0, 18, 24, 42, 48, 66, 72, 0, 4, 22, 28, 46, 52, 70])
defor =np.array([0.11, 0.62, 0.73, 0.91, 1.0, 1.17, 1.22, 0.15, 0.26, 0.4, 0.43, 0.51, 0.51, 0.58])
init_def =np.array([0.11, 0.11, 0.11, 0.11, 0.11, 0.11, 0.11, 0.15, 0.15, 0.15, 0.15, 0.15, 0.15, 0.15])
stress =np.array([10.0, 10.0, 10.0, 10.0, 10.0, 10.0, 10.0,7.5, 7.5, 7.5, 7.5, 7.5, 7.5, 7.5])
temp=943
e=2.71828
arg=zip(defor,stress,init_def)
# subint_funct- enter subintegral function with с1-с7 uncertain coefficients
def subint_funct(arg, c1,c2, c3,c4,c5,c6,c7):
return ((c1**(-1))*(temp**c2)*(stress**(-c3))*e**((c5-c6*stress)/temp)*
((defor+1)**(-c3))*(defor**c4)*e**(-((c6*stress+c7)*defor/temp)) )
# integration- integration of subint_funct with lower and upper integration bounds init_def and defor
def integration(arg,c1,c2,c3,c4,c5,c6,c7):
return [quad(subint_funct,init_def,defor,args= (c1,c2,c3,c4,c5,c6,c7) )[0] for defor,stress,init_def in arg ]
# curve fitting, dependent data-time
parameter = sp.curve_fit(integration,
arg,
time)
parameter=parameter[0]
print (parameter)
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [11], in <cell line: 25>()
22 def integration(arg,c1,c2,c3,c4,c5,c6,c7):
23 return [quad(subint_funct,init_def,defor,args= (c1,c2,c3,c4,c5,c6,c7) )[0] for defor,stress,init_def in arg ]
---> 25 parameter = sp.curve_fit(integration,
26 arg,
27 time)
28 parameter=parameter[0]
29 print (parameter)
File ~\anaconda3\lib\site-packages\scipy\optimize\minpack.py:789, in curve_fit(f, xdata, ydata, p0, sigma, absolute_sigma, check_finite, bounds, method, jac, **kwargs)
787 # Remove full_output from kwargs, otherwise we're passing it in twice.
788 return_full = kwargs.pop('full_output', False)
--> 789 res = leastsq(func, p0, Dfun=jac, full_output=1, **kwargs)
790 popt, pcov, infodict, errmsg, ier = res
791 ysize = len(infodict['fvec'])
File ~\anaconda3\lib\site-packages\scipy\optimize\minpack.py:410, in leastsq(func, x0, args, Dfun, full_output, col_deriv, ftol, xtol, gtol, maxfev, epsfcn, factor, diag)
408 if not isinstance(args, tuple):
409 args = (args,)
--> 410 shape, dtype = _check_func('leastsq', 'func', func, x0, args, n)
411 m = shape[0]
413 if n > m:
File ~\anaconda3\lib\site-packages\scipy\optimize\minpack.py:24, in _check_func(checker, argname, thefunc, x0, args, numinputs, output_shape)
22 def _check_func(checker, argname, thefunc, x0, args, numinputs,
23 output_shape=None):
---> 24 res = atleast_1d(thefunc(*((x0[:numinputs],) + args)))
25 if (output_shape is not None) and (shape(res) != output_shape):
26 if (output_shape[0] != 1):
File ~\anaconda3\lib\site-packages\scipy\optimize\minpack.py:485, in _wrap_func.<locals>.func_wrapped(params)
484 def func_wrapped(params):
--> 485 return func(xdata, *params) - ydata
Input In [11], in integration(arg, c1, c2, c3, c4, c5, c6, c7)
22 def integration(arg,c1,c2,c3,c4,c5,c6,c7):
---> 23 return [quad(subint_funct,init_def,defor,args= (c1,c2,c3,c4,c5,c6,c7) )[0] for defor,stress,init_def in arg ]
Input In [11], in <listcomp>(.0)
22 def integration(arg,c1,c2,c3,c4,c5,c6,c7):
---> 23 return [quad(subint_funct,init_def,defor,args= (c1,c2,c3,c4,c5,c6,c7) )[0] for defor,stress,init_def in arg ]
File ~\anaconda3\lib\site-packages\scipy\integrate\quadpack.py:351, in quad(func, a, b, args, full_output, epsabs, epsrel, limit, points, weight, wvar, wopts, maxp1, limlst)
348 flip, a, b = b < a, min(a, b), max(a, b)
350 if weight is None:
--> 351 retval = _quad(func, a, b, args, full_output, epsabs, epsrel, limit,
352 points)
353 else:
354 if points is not None:
File ~\anaconda3\lib\site-packages\scipy\integrate\quadpack.py:463, in _quad(func, a, b, args, full_output, epsabs, epsrel, limit, points)
461 if points is None:
462 if infbounds == 0:
--> 463 return _quadpack._qagse(func,a,b,args,full_output,epsabs,epsrel,limit)
464 else:
465 return _quadpack._qagie(func,bound,infbounds,args,full_output,epsabs,epsrel,limit)
TypeError: only size-1 arrays can be converted to Python scalars
由于我不是 100% 确定 OP 的细节，这里有一个做类似事情的例子。简单的修改应该可以解决问题。
import numpy as np
from scipy.integrate import quad
from scipy.optimize import curve_fit
### not clever, but whatever...
def integ( arg, c1, c2, c3 ):
x, k1 = arg
return k1**c1 * x**c2 + c3
def integ_first_wrapper( x, k, c):
return(integ( ( x, k ), *c ) )
def fitwrapper( xlist, c1, c2, c3 ):
if len( xlist.shape ) == 2: ##array
out = np.fromiter(
( fitwrapper( x, c1, c2, c3 ) for x in xlist ),
np.float
)
else:
l, u, s = xlist
out = quad(
integ_first_wrapper, l, u, args=( s, ( c1, c2, c3 ) )
)[0]
return out
c10 = 2.33
c20 = 3.11
c30 = 4.11
lolimits = 5 * np.random.random( size=10 )
uplimits = 10 + 5 * np.random.random( size=10 )
stress = 28 * np.random.random( size=10 )
xin = np.transpose( ( lolimits, uplimits, stress ) )
### create test data
data = list()
for l,u, s in zip( lolimits, uplimits, stress ):
# ~data.append( quad( integ_first_wrapper, l, u, args=( s, (c10, c20, c30 ) ) )[0] ) ### without error
data.append(
( 1 + 0.01 * ( 1 - 2 * np.random.random() ) )
* quad(
integ_first_wrapper, l, u, args=( s, (c10, c20, c30 ) )
)[0]
) ### wit relative error
# ~print(xin)
res, err = curve_fit( fitwrapper, xin, data, p0=( 1, 1, 1 ) )
print( res )
print( err )