lambdified sympy表达式返回不正确的结果

Question

我遇到以下问题，首先我会简单解释一下这是怎么回事：

f(x) 
g(x, y) = f(x) - y 

从那里，我们预计

g(x, f(x)) = f(x) - f(x) = 0 

lambdified g(x,y)回报的东西非常接近零，而不是为零。这是一个重现问题的代码。它只有当我把log评估足量到达f(x)

要点：https://gist.github.com/marekyggdrasil/39a24213ebaba6293464d116821cc334

来源：

from sympy import Symbol, pprint, log, lambdify 

# setting symbols 
g1 = Symbol("gamma1") 
g2 = Symbol("gamma2") 
g3 = Symbol("gamma3") 
g4 = Symbol("gamma4") 
rt = Symbol("rt") 

# setting expressions 
criteria = (g1 * log(g1, 2.0))/2.0 
criteria += (g2 * log(g2, 2.0))/2.0 
criteria += (g3 * log(g3, 2.0))/2.0 
criteria += (g4 * log(g4, 2.0))/2.0 
rooteq = criteria - rt 

print "\ncriteria function: " 
pprint(criteria) 

print "\ncriteria function - rt: " 
pprint(rooteq) 

# lambdifying expressions to callable functions 
tsymbols = [g1, g2, g3, g4, rt] 
lambfun_criteria = lambdify(tsymbols, criteria) 
lambfun_rooteq = lambdify(tsymbols, rooteq) 

# example point x 
x = [0.25006462253641376, 2.2501938662000542, 2.2501938662000542, 2.2501938662000542, 0.0] 

# evaluating of criteria on x 
rootval = lambfun_criteria(*x) 

# setting rt to this evaluation 
x[4] = rootval 

print "\nactual evaluation of rooteq: " + str(lambfun_rooteq(*x)) 
print "\nexpected evaluation of rooteq: " + str(- x[4] + lambfun_criteria(*x)) 

输出

$ python lambdifytest.py 

criteria function: 
0.721347520444482⋅γ₁⋅log(γ₁) + 0.721347520444482⋅γ₂⋅log(γ₂) + 0.721347520444482⋅γ₃⋅log(γ₃) + 0.721347520444482⋅γ₄⋅log(γ₄) 

criteria function - rt: 
0.721347520444482⋅γ₁⋅log(γ₁) + 0.721347520444482⋅γ₂⋅log(γ₂) + 0.721347520444482⋅γ₃⋅log(γ₃) + 0.721347520444482⋅γ₄⋅log(γ₄) - rt 

actual evaluation of rooteq: 4.4408920985e-16 

expected evaluation of rooteq: 0.0 

Answer 1

我发现一个自定义的数学模块可当SymPy表达式被指定时指定。在我的情况下，mpmath帮助。

导入mpmath并设置精密的东西，你找到足够

from mpmath import mp 
mp.dps = 15 

告诉SymPy你希望你的lambda函数使用mpmath处理浮点运算

lambfun_criteria = lambdify(tsymbols, criteria, "mpmath") 
lambfun_rooteq = lambdify(tsymbols, rooteq, "mpmath") 

于是最后我得到的输出

actual evaluation of rooteq: 0.0 
expected evaluation of rooteq: 0.0 

T导致问题的原因如下，创建的lambda函数中使用的默认浮点运算与脚本中用于比较结果的算法不同。

我更新了完整的解决方案文件的要点，如果有人需要复制粘贴

https://gist.github.com/marekyggdrasil/39a24213ebaba6293464d116821cc334#file-lambdify_test_solution-py

编辑：忘了给文档引用

http://docs.sympy.org/dev/modules/utilities/lambdify.html