问题
I want solve differential equation using sympy on Python3. My equation is relatively simple with two variables. However, the equation has log, power, and exp operators. Whether I use np.exp or sym.exp, it gives me one of the two errors below:
TypeError: 'module' object is not callable
AttributeError: 'Mul' object has no attribute 'log'
AttributeError: 'Mul' object has no attribute 'exp'
I am importing numpy and sympy separately. I am not sure if these two libraries are conflicting.
import math
import sympy as sym
from sympy import symbols, diff, exp, log, power
from sympy import *
data = [3, 33, 146, 227, 342, 351, 353, 444, 556, 571, 709, 759, 836, 860, 968, 1056, 1726, 1846, 1872, 1986, 2311, 2366, 2608, 2676, 3098, 3278, 3288, 4434, 5034, 5049, 5085, 5089, 5089, 5097, 5324, 5389,5565, 5623, 6080, 6380, 6477, 6740, 7192, 7447, 7644, 7837, 7843, 7922, 8738, 10089, 10237, 10258, 10491, 10625, 10982, 11175, 11411, 11442, 11811, 12559, 12559, 12791, 13121, 13486, 14708, 15251, 15261, 15277, 15806, 16185, 16229, 16358, 17168, 17458, 17758, 18287, 18568, 18728, 19556, 20567, 21012, 21308, 23063, 24127, 25910, 26770, 27753, 28460, 28493, 29361, 30085, 32408, 35338, 36799, 37642, 37654, 37915, 39715, 40580, 42015, 42045, 42188, 42296, 42296, 45406, 46653, 47596, 48296, 49171, 49416, 50145, 52042, 52489, 52875, 53321, 53443, 54433, 55381, 56463, 56485, 56560, 57042, 62551, 62651, 62661, 63732, 64103, 64893, 71043, 74364, 75409, 76057, 81542, 82702, 84566, 88682]
n = len(data)
tn = data[n-1]
b, c = sym.symbols('b c', real=True)
f = -(-n +sum(np.log(b*c*np.power(data,(c-1))*exp(-b*np.power(data,c)))))
diff(f,b)
diff(f,c)
Expecting to derive partial derivative of equation 'f' with respect to parameters 'b' and 'c'
This is not similar to What causes this error (AttributeError: 'Mul' object has no attribute 'cos') in Python? since the cause is not the namespace issue
回答1:
In an isympy session (similar to your imports), plus a np import:
In [12]: data = [1,2,3,4,5]
In [13]: np.power(data,c)
Out[13]: array([1, 2**c, 3**c, 4**c, 5**c], dtype=object)
In [14]: b*c*np.power(data,c)
Out[14]: array([b*c, 2**c*b*c, 3**c*b*c, 4**c*b*c, 5**c*b*c], dtype=object)
So far these work. When numpy functions and operators encounter an object dtype array (non-numeric ones), they try to apply corresponding operators or methods of the objects. b and c as symbols do respond to ** and *.
But np.log applied to the object array fails with your error message. The elements of the array a sympy Mul objects:
In [17]: type(Out[14][0])
Out[17]: sympy.core.mul.Mul
In [18]: Out[14][0].log()
---------------------------------------------------------------------------
AttributeError: 'Mul' object has no attribute 'log'
Same for np.exp.
math.log expects a number, so it won't work with array or the sympy objects either.
sympy.log(Out[14][0]) works - the argument is a sympy Mul. But it doesn't work with Out[14] which a numpy array.
===
I know numpy a lot better than sympy. But I was able to get this sequence of calculations to work:
In [24]: [d**c for d in data] # list comprehension
Out[24]:
⎡ c c c c⎤
⎣1, 2 , 3 , 4 , 5 ⎦
In [25]: [b*c*num**c for num in data]
Out[25]:
⎡ c c c c ⎤
⎣b⋅c, 2 ⋅b⋅c, 3 ⋅b⋅c, 4 ⋅b⋅c, 5 ⋅b⋅c⎦
In [26]: [log(b*c*num**c) for num in data]
Out[26]:
⎡ ⎛ c ⎞ ⎛ c ⎞ ⎛ c ⎞ ⎛ c ⎞⎤
⎣log(b⋅c), log⎝2 ⋅b⋅c⎠, log⎝3 ⋅b⋅c⎠, log⎝4 ⋅b⋅c⎠, log⎝5 ⋅b⋅c⎠⎦
In [27]: sum([log(b*c*num**c) for num in data])
Out[27]:
⎛ c ⎞ ⎛ c ⎞ ⎛ c ⎞ ⎛ c ⎞
log(b⋅c) + log⎝2 ⋅b⋅c⎠ + log⎝3 ⋅b⋅c⎠ + log⎝4 ⋅b⋅c⎠ + log⎝5 ⋅b⋅c⎠
sympy.sum expects an iterable, which this list qualifies.
Now I can do the sympy.diff
In [29]: diff(sum([log(b*c*num**c) for num in data]),b)
Out[29]:
5
─
b
In [30]: diff(sum([log(b*c*num**c) for num in data]),c)
Out[30]:
-c ⎛ c c ⎞ -c ⎛ c c ⎞ -c ⎛ c
1 5 ⋅⎝5 ⋅b⋅c⋅log(5) + 5 ⋅b⎠ 4 ⋅⎝4 ⋅b⋅c⋅log(4) + 4 ⋅b⎠ 3 ⋅⎝3 ⋅b⋅c⋅l
─ + ────────────────────────── + ────────────────────────── + ─────────────
c b⋅c b⋅c b⋅
c ⎞ -c ⎛ c c ⎞
og(3) + 3 ⋅b⎠ 2 ⋅⎝2 ⋅b⋅c⋅log(2) + 2 ⋅b⎠
───────────── + ──────────────────────────
c b⋅c
[log(item) for item in Out[14]] produces the same output as Out[26]. Out[14] is simply the object array equivalent of the Out[25] list.
回答2:
As per @hpaulj suggestion, I was able to solve this by using list comprehension. The working code is below:
f = -(-n +sum([sym.log(b*c*(num**(c-1))*sym.exp(-b*(num**c))) for num in data]))
来源：https://stackoverflow.com/questions/56210112/error-using-exp-in-sympy-typeerror-and-attribute-error-is-displayed