Python Scipy&x27；s quad在“上失败”；“相当顺利”；功能

数据生成函数非常混乱，因此我将尽可能清楚。如果做得不够好，请发表评论

我有一个包含多个变量的函数，并尝试将其积分，保持另一个常数。然而，对于第二个变量的不同值，积分过程产生完全不同的结果——尽管函数变化不大

这是我的示例代码（不可复制）：

quad

的输出为

tPrime 0.16 value 6.63310536371 erorr 0.000345564616621
tPrime 0.18 value 5.93645658492 erorr 0.00045956820487
tPrime 0.22 value 0.359208009237 erorr 3.98801002485e-15

所有的错误都在我的容忍范围之内，但是价值跳跃了很多。下面是图表：

所以这些函数的形状非常相似。用肉眼看，积分的差别是没有意义的。然后我“手动”计算它们：

这意味着小值实际上是正确的。因此，我还将在这里为其中一个错误添加

quad（）

的完整输出：

integrate.quad(myFunc, lowerBar, upperBar, args=(0.6, 0.16, Param), full_output=True)
Out[19]: 
(6.634157704675579,
 0.004721148834250418,
 {'alist': array([ 1.99994895,  1.78826738,  1.86060326,  1.79090489,  1.93030163,
          1.72120652,  1.96515082,  1.75605571,  1.98257541,  1.7734803 ,
          1.9912877 ,  1.7821926 ,  1.99564385,  1.78872682,  1.99782193,
          1.78654874,  1.99940018,  1.78763778,  1.99945548,  1.99891096,
          1.78845456,  1.99972774,  1.99918322,  1.78831843,  1.99988939,
          1.99931935,  1.7881823 ,  1.99999149,  1.99942145,  1.7882844 ,
          1.9998979 ,  1.9999447 ,  1.99940443,  1.78825036,  1.99996597,
          1.99986387,  1.99991492,  1.99995746,  1.99938742,  1.78827589,
          1.99993194,  1.99990641,  1.99998298,  1.99988089,  1.99995321,
          1.99939592,  1.78827164,  1.99994044,  1.99995108,  1.99940231]),
  'blist': array([ 1.99995108,  1.78827164,  1.93030163,  1.86060326,  1.96515082,
          1.75605571,  1.98257541,  1.7734803 ,  1.9912877 ,  1.7821926 ,
          1.99564385,  1.78654874,  1.99782193,  1.79090489,  1.99891096,
          1.78763778,  1.99940231,  1.7881823 ,  1.99972774,  1.99918322,
          1.78872682,  1.99986387,  1.99931935,  1.78845456,  1.9998979 ,
          1.99938742,  1.78825036,  2.        ,  1.99945548,  1.78831843,
          1.99990641,  1.99994895,  1.99942145,  1.78826738,  1.99998298,
          1.99988089,  1.99993194,  1.99996597,  1.99939592,  1.7882844 ,
          1.99994044,  1.99991492,  1.99999149,  1.99988939,  1.99995746,
          1.99940018,  1.78827589,  1.9999447 ,  1.99995321,  1.99940443]),
  'elist': array([  4.61134496e-03,   4.14135579e-06,   1.27804393e-15,
           1.55808958e-15,   5.54429458e-16,   0.00000000e+00,
           2.90617202e-16,   0.00000000e+00,   2.27720143e-15,
           0.00000000e+00,   3.91514838e-15,   0.00000000e+00,
           2.15987477e-14,   5.40749179e-17,   1.19682144e-12,
           0.00000000e+00,   1.03521880e-04,   0.00000000e+00,
           2.48275100e-08,   6.85735811e-13,   6.78454062e-18,
           8.65204618e-09,   1.64268148e-13,   3.39437556e-18,
           4.65487056e-08,   1.12644353e-13,   0.00000000e+00,
           6.19443638e-08,   4.08066769e-09,   8.48813317e-19,
           5.99147851e-07,   1.21478039e-06,   9.39741081e-10,
           0.00000000e+00,   6.32087778e-14,   2.19912539e-10,
           6.97448944e-09,   1.85114515e-13,   1.28558440e-13,
           2.12217047e-19,   8.89451362e-08,   8.45167083e-09,
           1.25621961e-14,   2.59393721e-08,   2.45738052e-15,
           1.19106919e-12,   1.06110581e-19,   4.91812027e-08,
           2.72831861e-15,   3.06819516e-12]),
  'iord': array([ 1, 17, 50, 49, 48, 47, 46, 45, 44, 43, 42, 29, 40, 39, 38, 23, 35,
         11, 34,  3,  7, 21, 30, 18, 12,  8,  6,  0,  0,  0,  0,  0,  0,  0,
          0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0], dtype=int32),
  'last': 50,
  'neval': 2079,
  'rlist': array([  1.04205921e-01,   6.52426361e-06,   1.15115963e-01,
           1.40340233e-01,   4.99385660e-02,   0.00000000e+00,
           2.33230318e-02,   0.00000000e+00,   1.12779305e-02,
           0.00000000e+00,   5.54633015e-03,   0.00000000e+00,
           2.75040018e-03,   4.87063561e-03,   1.36955727e-03,
           0.00000000e+00,   8.85474806e-03,   0.00000000e+00,
           1.73731989e+00,   3.41803845e-04,   6.11097092e-04,
           1.73678061e+00,   1.70814248e-04,   3.05738170e-04,
           2.00530044e-01,   8.53852175e-05,   0.00000000e+00,
           5.29681716e-06,   1.51991445e-01,   7.64543067e-05,
           2.17985628e-01,   2.00512965e-01,   7.26773425e-02,
           0.00000000e+00,   1.06564581e-05,   3.34545761e-01,
           5.59012296e-01,   5.32838374e-06,   1.06721256e-05,
           1.91148122e-05,   3.34512038e-01,   2.38773007e-01,
           5.32807434e-06,   1.85664300e-01,   2.66423055e-06,
           5.33597722e-06,   9.55759147e-06,   1.85647516e-01,
           1.33212494e-06,   8.93844378e-03])},
 'The maximum number of subdivisions (50) has been achieved.\n  If increasing the limit yields no improvement it is advised to analyze \n  the integrand in order to determine the difficulties.  If the position of a \n  local difficulty can be determined (singularity, discontinuity) one will \n  probably gain from splitting up the interval and calling the integrator \n  on the subranges.  Perhaps a special-purpose integrator should be used.')

以下是我的相关问题：

为什么在形状如此相似的情况下，有些参数起作用而有些参数不起作用？我如何“预测”未来的这些失败

完整输出（如下）告诉我已达到最大细分数。它并没有告诉我错误可能未被估计。那一定是暗示了吗<代码>5.9-0.0004与

0.3

不接近

由于增加限额没有帮助（见下文），有哪些潜在的替代方案？如何集成此功能

我尝试增加

限制

，但这只给了我以下（不是更好的）输出：

---

quad

在

full\u输出

为真时，其返回值有点古怪。如果

quad

没有检测到任何问题，它将返回

y、abserr、infodict

。如果

quad

检测到某种形式的故障，它将返回

y、abserr、infodict、message

infodict

不包含指示故障的简单

status

字段，因此必须检查是否存在第四个返回值。如果存在，则是描述问题的字符串。（在您的代码中，如果len（h）>3:…处理故障…，您可能会添加类似于

的内容。在坏案例的完整输出中，您可以看到
消息
是包含以下内容的字符串：

The maximum number of subdivisions (50) has been achieved.
If increasing the limit yields no improvement it is advised to analyze
the integrand in order to determine the difficulties.  If the position of a
local difficulty can be determined (singularity, discontinuity) one will
probably gain from splitting up the interval and calling the integrator
on the subranges.  Perhaps a special-purpose integrator should be used.

这意味着数值积分失败了。如果对被积函数
myFunc
没有更多了解，很难说它失败的原因

integrate.quad(myFunc, lowerBar, upperBar, args=(0.6, 0.16, Param), full_output=True)
Out[19]: 
(6.634157704675579,
 0.004721148834250418,
 {'alist': array([ 1.99994895,  1.78826738,  1.86060326,  1.79090489,  1.93030163,
          1.72120652,  1.96515082,  1.75605571,  1.98257541,  1.7734803 ,
          1.9912877 ,  1.7821926 ,  1.99564385,  1.78872682,  1.99782193,
          1.78654874,  1.99940018,  1.78763778,  1.99945548,  1.99891096,
          1.78845456,  1.99972774,  1.99918322,  1.78831843,  1.99988939,
          1.99931935,  1.7881823 ,  1.99999149,  1.99942145,  1.7882844 ,
          1.9998979 ,  1.9999447 ,  1.99940443,  1.78825036,  1.99996597,
          1.99986387,  1.99991492,  1.99995746,  1.99938742,  1.78827589,
          1.99993194,  1.99990641,  1.99998298,  1.99988089,  1.99995321,
          1.99939592,  1.78827164,  1.99994044,  1.99995108,  1.99940231]),
  'blist': array([ 1.99995108,  1.78827164,  1.93030163,  1.86060326,  1.96515082,
          1.75605571,  1.98257541,  1.7734803 ,  1.9912877 ,  1.7821926 ,
          1.99564385,  1.78654874,  1.99782193,  1.79090489,  1.99891096,
          1.78763778,  1.99940231,  1.7881823 ,  1.99972774,  1.99918322,
          1.78872682,  1.99986387,  1.99931935,  1.78845456,  1.9998979 ,
          1.99938742,  1.78825036,  2.        ,  1.99945548,  1.78831843,
          1.99990641,  1.99994895,  1.99942145,  1.78826738,  1.99998298,
          1.99988089,  1.99993194,  1.99996597,  1.99939592,  1.7882844 ,
          1.99994044,  1.99991492,  1.99999149,  1.99988939,  1.99995746,
          1.99940018,  1.78827589,  1.9999447 ,  1.99995321,  1.99940443]),
  'elist': array([  4.61134496e-03,   4.14135579e-06,   1.27804393e-15,
           1.55808958e-15,   5.54429458e-16,   0.00000000e+00,
           2.90617202e-16,   0.00000000e+00,   2.27720143e-15,
           0.00000000e+00,   3.91514838e-15,   0.00000000e+00,
           2.15987477e-14,   5.40749179e-17,   1.19682144e-12,
           0.00000000e+00,   1.03521880e-04,   0.00000000e+00,
           2.48275100e-08,   6.85735811e-13,   6.78454062e-18,
           8.65204618e-09,   1.64268148e-13,   3.39437556e-18,
           4.65487056e-08,   1.12644353e-13,   0.00000000e+00,
           6.19443638e-08,   4.08066769e-09,   8.48813317e-19,
           5.99147851e-07,   1.21478039e-06,   9.39741081e-10,
           0.00000000e+00,   6.32087778e-14,   2.19912539e-10,
           6.97448944e-09,   1.85114515e-13,   1.28558440e-13,
           2.12217047e-19,   8.89451362e-08,   8.45167083e-09,
           1.25621961e-14,   2.59393721e-08,   2.45738052e-15,
           1.19106919e-12,   1.06110581e-19,   4.91812027e-08,
           2.72831861e-15,   3.06819516e-12]),
  'iord': array([ 1, 17, 50, 49, 48, 47, 46, 45, 44, 43, 42, 29, 40, 39, 38, 23, 35,
         11, 34,  3,  7, 21, 30, 18, 12,  8,  6,  0,  0,  0,  0,  0,  0,  0,
          0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0], dtype=int32),
  'last': 50,
  'neval': 2079,
  'rlist': array([  1.04205921e-01,   6.52426361e-06,   1.15115963e-01,
           1.40340233e-01,   4.99385660e-02,   0.00000000e+00,
           2.33230318e-02,   0.00000000e+00,   1.12779305e-02,
           0.00000000e+00,   5.54633015e-03,   0.00000000e+00,
           2.75040018e-03,   4.87063561e-03,   1.36955727e-03,
           0.00000000e+00,   8.85474806e-03,   0.00000000e+00,
           1.73731989e+00,   3.41803845e-04,   6.11097092e-04,
           1.73678061e+00,   1.70814248e-04,   3.05738170e-04,
           2.00530044e-01,   8.53852175e-05,   0.00000000e+00,
           5.29681716e-06,   1.51991445e-01,   7.64543067e-05,
           2.17985628e-01,   2.00512965e-01,   7.26773425e-02,
           0.00000000e+00,   1.06564581e-05,   3.34545761e-01,
           5.59012296e-01,   5.32838374e-06,   1.06721256e-05,
           1.91148122e-05,   3.34512038e-01,   2.38773007e-01,
           5.32807434e-06,   1.85664300e-01,   2.66423055e-06,
           5.33597722e-06,   9.55759147e-06,   1.85647516e-01,
           1.33212494e-06,   8.93844378e-03])},
 'The maximum number of subdivisions (50) has been achieved.\n  If increasing the limit yields no improvement it is advised to analyze \n  the integrand in order to determine the difficulties.  If the position of a \n  local difficulty can be determined (singularity, discontinuity) one will \n  probably gain from splitting up the interval and calling the integrator \n  on the subranges.  Perhaps a special-purpose integrator should be used.')

integrate.quad(expectedUtility, lowerBar, upperBar, args=(0.6, 0.16, Param), full_output=True, limit=500)
Out[24]: 
(6.633112814769514,
 4.74743687572826e-06,
[...]
 'The occurrence of roundoff error is detected, which prevents \n  the requested tolerance from being achieved.  The error may be \n  underestimated.')

The maximum number of subdivisions (50) has been achieved.
If increasing the limit yields no improvement it is advised to analyze
the integrand in order to determine the difficulties.  If the position of a
local difficulty can be determined (singularity, discontinuity) one will
probably gain from splitting up the interval and calling the integrator
on the subranges.  Perhaps a special-purpose integrator should be used.