但是......如果我只想在一个维度上积分我的被积函数 - 但在其他维度上输入一组输入,事情就会失败 - 似乎“scipy”quadpack 包无法执行任何操作numpy 用来处理数组输入。有没有其他人看到过这个 - 或者找到了解决它的方法 - 或者我误解了它。我从四边形得到的错误是:
Traceback (most recent call last):
File "C:\Users\JP\Documents\Python\TestingQuad\TestingQuad_v2.py", line 159, in <module>
fnIntegrate_x(0, 1, NCALLS_SET, True)
File "C:\Users\JP\Documents\Python\TestingQuad\TestingQuad_v2.py", line 35, in fnIntegrate_x
I = Integrate_x(yarray)
File "C:\Users\JP\Documents\Python\TestingQuad\TestingQuad_v2.py", line 23, in Integrate_x
return quad(Integrand, 0, np.pi/2, args=(y))[0]
File "C:\Python27\lib\site-packages\scipy\integrate\quadpack.py", line 247, in quad
retval = _quad(func,a,b,args,full_output,epsabs,epsrel,limit,points)
File "C:\Python27\lib\site-packages\scipy\integrate\quadpack.py", line 312, in _quad
return _quadpack._qagse(func,a,b,args,full_output,epsabs,epsrel,limit)
quadpack.error: Supplied function does not return a valid float.
我在下面放了一个我想要做的事情的卡通版本 - 我实际上正在做的事情有一个更复杂的被积函数,但这就是 gyst。
重点在顶部 - 底部正在做基准测试来表明我的观点。
import numpy as np
import time
from scipy.integrate import quad
def Integrand(x, y):
'''
Integrand
'''
return np.sin(x)*np.sin( y )
def Integrate_x(y):
'''
Integrate over x given (y)
'''
return quad(Integrand, 0, np.pi/2, args=(y))[0]
def fnIntegrate_x(ystart, yend, nsteps, ArrayInput = False):
'''
'''
yarray = np.arange(ystart,yend, (yend - ystart)/float(nsteps))
I = np.zeros(nsteps)
if ArrayInput :
I = Integrate_x(yarray)
else :
for i,y in enumerate(yarray) :
I[i] = Integrate_x(y)
return y, I
NCALLS_SET = 1000
NSETS = 10
SETS_t = np.zeros(NSETS)
for i in np.arange(NSETS) :
XInputs = np.random.rand(NCALLS_SET, 2)
t0 = time.time()
for x in XInputs :
Integrand(x[0], x[1])
t1 = time.time()
SETS_t[i] = (t1 - t0)/NCALLS_SET
print "Benchmarking Integrand - Single Values:"
print "NCALLS_SET: ", NCALLS_SET
print "NSETS: ", NSETS
print "TimePerCall(s): ", np.mean(SETS_t) , np.std(SETS_t)/ np.sqrt(SETS_t.size)
print "TotalTime: ",np.sum(SETS_t) * NCALLS_SET
'''
Benchmarking Integrand - Single Values:
NCALLS_SET: 1000
NSETS: 10
TimePerCall(s): 1.23999834061e-05 4.06987868647e-06
'''
NCALLS_SET = 1000
NSETS = 10
SETS_t = np.zeros(NSETS)
for i in np.arange(NSETS) :
XInputs = np.random.rand(NCALLS_SET, 2)
t0 = time.time()
Integrand(XInputs[:,0], XInputs[:,1])
t1 = time.time()
SETS_t[i] = (t1 - t0)/NCALLS_SET
print "Benchmarking Integrand - Array Values:"
print "NCALLS_SET: ", NCALLS_SET
print "NSETS: ", NSETS
print "TimePerCall(s): ", np.mean(SETS_t) , np.std(SETS_t)/ np.sqrt(SETS_t.size)
print "TotalTime: ",np.sum(SETS_t) * NCALLS_SET
'''
Benchmarking Integrand - Array Values:
NCALLS_SET: 1000
NSETS: 10
TimePerCall(s): 2.00009346008e-07 1.26497018465e-07
'''
NCALLS_SET = 1000
NSETS = 100
SETS_t = np.zeros(NSETS)
for i in np.arange(NSETS) :
t0 = time.time()
fnIntegrate_x(0, 1, NCALLS_SET, False)
t1 = time.time()
SETS_t[i] = (t1 - t0)/NCALLS_SET
print "Benchmarking fnIntegrate_x - Single Values:"
print "NCALLS_SET: ", NCALLS_SET
print "NSETS: ", NSETS
print "TimePerCall(s): ", np.mean(SETS_t) , np.std(SETS_t)/ np.sqrt(SETS_t.size)
print "TotalTime: ",np.sum(SETS_t) * NCALLS_SET
'''
NCALLS_SET: 1000
NSETS: 100
TimePerCall(s): 0.000165750000477 8.61204306241e-07
TotalTime: 16.5750000477
'''
NCALLS_SET = 1000
NSETS = 100
SETS_t = np.zeros(NSETS)
for i in np.arange(NSETS) :
t0 = time.time()
fnIntegrate_x(0, 1, NCALLS_SET, True)
t1 = time.time()
SETS_t[i] = (t1 - t0)/NCALLS_SET
print "Benchmarking fnIntegrate_x - Array Values:"
print "NCALLS_SET: ", NCALLS_SET
print "NSETS: ", NSETS
print "TimePerCall(s): ", np.mean(SETS_t) , np.std(SETS_t)/ np.sqrt(SETS_t.size)
'''
**** Doesn't work!!!! *****
Traceback (most recent call last):
File "C:\Users\JP\Documents\Python\TestingQuad\TestingQuad_v2.py", line 159, in <module>
fnIntegrate_x(0, 1, NCALLS_SET, True)
File "C:\Users\JP\Documents\Python\TestingQuad\TestingQuad_v2.py", line 35, in fnIntegrate_x
I = Integrate_x(yarray)
File "C:\Users\JP\Documents\Python\TestingQuad\TestingQuad_v2.py", line 23, in Integrate_x
return quad(Integrand, 0, np.pi/2, args=(y))[0]
File "C:\Python27\lib\site-packages\scipy\integrate\quadpack.py", line 247, in quad
retval = _quad(func,a,b,args,full_output,epsabs,epsrel,limit,points)
File "C:\Python27\lib\site-packages\scipy\integrate\quadpack.py", line 312, in _quad
return _quadpack._qagse(func,a,b,args,full_output,epsabs,epsrel,limit)
quadpack.error: Supplied function does not return a valid float.
'''
你可以这样使用它:
vectorized_function = numpy.vectorize(your_function)
output = vectorized_function(your_array_input)
我通过创建一个接受 *args 的包装函数、将 args 转换为 numpy 数组并集成包装函数来修复它。
我认为使用 numpy 的向量化仅整合所有值都相等的子空间。
这是一个例子:
from scipy.integrate import nquad
from scipy.stats import multivariate_normal
mean = [0., 0.]
cov = np.array([[1., 0.],
[0., 1.]])
bivariate_normal = multivariate_normal(mean=mean, cov=cov)
def pdf(*args):
x = np.array(args)
return bivariate_normal.pdf(x)
integration_range = [[-18, 18], [-18, 18]]
nquad(pdf, integration_range)
Output: (1.000000000000001, 1.3429066352690133e-08)