为什么 sympy lambdify 函数无法识别 numpy sum 函数和

Question

我想用 sympy 和 numpy 来学习机器学习。因为 symoy 提供了非常方便的偏导数计算。但是在使用过程中发现sympy lambdify函数并不能识别numpy sum函数和multiply函数。

举个例子

y_ = np.sum(np.dot(w,x)+b)

print(y_)

y_f = lambdify((w,x,b),y_,"numpy")

w_l = np.mat([1,1,1,1,1])

x_l= np.mat([1,1,1,1,1]).T

b_l = np.mat([0,0,0,0,0]).T

y_l = np.mat([6,6,6,6,6]).T

print(y_f(w_l,x_l,b_l))

b + w*x

[[5]

 [5]

 [5]

 [5]

 [5]]

Process finished with exit code 0

y_ = np.multiply(w,x)+b

print(y_)

y_f = lambdify((w,x,b),y_,"numpy")

w_l = np.mat([1,1,1,1,1]).T

x_l= np.mat([1,1,1,1,1]).T

b_l = np.mat([0,0,0,0,0]).T

y_l = np.mat([6,6,6,6,6]).T

print(y_f(w_l,x_l,b_l))

b + w*x

Traceback (most recent call last):

  File "G:/lijie/PycharmProjects/hw3/test.py", line 24, in <module>

    print(y_f(w_l,x_l,b_l))

  File "<lambdifygenerated-1>", line 2, in _lambdifygenerated

  File "C:\Users\lijie\AppData\Local\Programs\Python\Python36\lib\site-packages\numpy\matrixlib\defmatrix.py", line 220, in __mul__

    return N.dot(self, asmatrix(other))

ValueError: shapes (5,1) and (5,1) not aligned: 1 (dim 1) != 5 (dim 0)

b + w*x

Traceback (most recent call last):

  File "G:/lijie/PycharmProjects/hw3/test.py", line 24, in <module>

    print(y_f(w_l,x_l,b_l))

  File "<lambdifygenerated-1>", line 2, in _lambdifygenerated

  File "C:\Users\lijie\AppData\Local\Programs\Python\Python36\lib\site-packages\numpy\matrixlib\defmatrix.py", line 220, in __mul__

    return N.dot(self, asmatrix(other))

ValueError: shapes (5,1) and (5,1) not aligned: 1 (dim 1) != 5 (dim 0)

如您所见，lambdify 只接受 lamda 表达式而不检查操作符号。如何解决这个问题呢。谢谢您的帮助

Answer 1

混合可能很棘手numpy；再加上由 .而不是基本数组类型sympy引起的潜在混淆。np.matndarray总共y_ = np.sum(np.dot(w,x)+b)评估 sympy 对象上的 python/numpy 表达式。结果是一个同情的表达w*x+b。sympy 对象是标量，因此它不编码任何类型的矩阵乘法或数组求和。multiply表达式的计算方式相同。然后，lambdify表达式将相同的内容转换为y_相同的 Python 函数。这种评估取决于np.mat论点的维度和类别。细节暂时忽略sympy部分：In [310]: w = np.mat([1,1,1,1,1])&nbsp;&nbsp; &nbsp; &nbsp;...: x= np.mat([1,1,1,1,1]).T&nbsp;&nbsp; &nbsp; &nbsp;...: b = np.mat([0,0,0,0,0]).T&nbsp;&nbsp; &nbsp; &nbsp;...: y = np.mat([6,6,6,6,6]).T&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;In [311]: np.sum(np.dot(w,x)+b)&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;Out[311]: 25In [312]: np.multiply(w,x)+b&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp;Out[312]:&nbsp;matrix([[1, 1, 1, 1, 1],&nbsp; &nbsp; &nbsp; &nbsp; [1, 1, 1, 1, 1],&nbsp; &nbsp; &nbsp; &nbsp; [1, 1, 1, 1, 1],&nbsp; &nbsp; &nbsp; &nbsp; [1, 1, 1, 1, 1],&nbsp; &nbsp; &nbsp; &nbsp; [1, 1, 1, 1, 1]])因为它们是，np.mat两者都是 2d：wxIn [316]: w.shape&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;Out[316]: (1, 5)In [317]: x.shape&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;Out[317]: (5, 1)np.dot(1,5) 和 (5,1) 是 (1,1) 结果：In [313]: np.dot(w,x)&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;Out[313]: matrix([[5]])而对于np.matrix,*被定义为dot:In [314]: w*x&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;Out[314]: matrix([[5]])元素方面：In [315]: np.multiply(w,x)&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;# elementwise produces (5,5)&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;Out[315]:&nbsp;matrix([[1, 1, 1, 1, 1],&nbsp; &nbsp; &nbsp; &nbsp; [1, 1, 1, 1, 1],&nbsp; &nbsp; &nbsp; &nbsp; [1, 1, 1, 1, 1],&nbsp; &nbsp; &nbsp; &nbsp; [1, 1, 1, 1, 1],&nbsp; &nbsp; &nbsp; &nbsp; [1, 1, 1, 1, 1]])np.sum(np.dot(w,x)+b)做dot, 然后添加b, 并以 asum结束所有元素。np.multiply(w,x)+b这是否相乘，增加b。没有sum。更正使用w.T我第一次错过的：In [322]: np.multiply(w.T,x)&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp;Out[322]:&nbsp;matrix([[1],&nbsp; &nbsp; &nbsp; &nbsp; [1],&nbsp; &nbsp; &nbsp; &nbsp; [1],&nbsp; &nbsp; &nbsp; &nbsp; [1],&nbsp; &nbsp; &nbsp; &nbsp; [1]])In [323]: w.T*x&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;---------------------------------------------------------------------------ValueError&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; Traceback (most recent call last)<ipython-input-323-11ad839cfa88> in <module>----> 1 w.T*x/usr/local/lib/python3.6/dist-packages/numpy/matrixlib/defmatrix.py in __mul__(self, other)&nbsp; &nbsp; 218&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;if isinstance(other, (N.ndarray, list, tuple)) :&nbsp; &nbsp; 219&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;# This promotes 1-D vectors to row vectors--> 220&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;return N.dot(self, asmatrix(other))&nbsp; &nbsp; 221&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;if isscalar(other) or not hasattr(other, '__rmul__') :&nbsp; &nbsp; 222&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;return N.dot(self, other)<__array_function__ internals> in dot(*args, **kwargs)ValueError: shapes (5,1) and (5,1) not aligned: 1 (dim 1) != 5 (dim 0)np.multiply(5,1) 和 (5,1) 产生 (5,1)，元素乘法w.T*x是 的矩阵乘法np.mat，因此有np.dot误差。不鼓励使用np.mat（如果没有正式贬低）。此外消除了它的符号优势numpy。如果你坚持使用基数组类，matmul/@生活会更简单， . 我意识到仍然使用二维矩阵概念，作为矩阵乘法。 numpyndarraysympy*同情在一个isympy会话中，我发现我需要定义w,x,b为符号：y_ = np.sum(np.dot(w,x)+b)如果w,x,b只是符号，它们是标量，而不是矩阵或数组。你的np.sum(np.dot(1,2)+4),np.multiply(1,2)+4并且1*2+4都产生同样的东西。只有当变量是数组，或者np.mat，或者sympy.Matrix表达式不同时。问题不在于lambdify. 在这两种情况下，它都是相同的y_（由 验证print(y_)。您会收到错误，因为参数是np.mat，并且*是矩阵乘法。带x,y,z符号：In [55]: f = lambdify((x,y,z),x*y+z, 'numpy')&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;使用isympy内省：In [56]: f??&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp;Signature: f(x, y, z)Docstring:Created with lambdify. Signature:func(x, y, z)Expression:x*y + zSource code:def _lambdifygenerated(x, y, z):&nbsp; &nbsp; return (x*y + z)Imported modules:Source:&nbsp; &nbsp;def _lambdifygenerated(x, y, z):&nbsp; &nbsp; return (x*y + z)File:&nbsp; &nbsp; &nbsp; ~/mypy/<lambdifygenerated-4>Type:&nbsp; &nbsp; &nbsp; function阅读lambdify. 请注意，它基本上是一个词法替换https://docs.sympy.org/latest/modules/utilities/lambdify.html本文档警告：作为一般规则，NumPy 函数不知道如何对 SymPy 表达式进行操作，而 SymPy 函数也不知道如何对 NumPy 数组进行操作。这就是 lambdify 存在的原因：在 SymPy 和 NumPy 之间架起一座桥梁。同化https://docs.sympy.org/latest/modules/core.html#module-sympy.core.sympify说它使用eval. 定义x,y,z为符号：In [66]: eval('np.dot(x,y)+z')&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp;Out[66]: x⋅y + zIn [67]: eval('np.sum(np.dot(x,y)+z)')&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp;Out[67]: x⋅y + zIn [68]: eval('np.multiply(x,y)+z')&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;Out[68]: x⋅y + z换句话说，它只是将符号传递给 numpy 函数（和/或运算符），In [69]: np.dot(x,y)&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp;Out[69]: x⋅ydot将其输入转换为数组：In [70]: np.array(x)&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp;Out[70]: array(x, dtype=object)In [71]: np.dot(np.array(x), np.array(y))&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;Out[71]: x⋅y这是有效的，因为符号定义了“*”和“+”。sympy文档警告说，评估numpy对 sympy 对象一无所知。它将它们视为对象 dtype 数组，这可能会或可能不会起作用：In [72]: sin(x)&nbsp; &nbsp; &nbsp; &nbsp;# sympy sin&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp;Out[72]: sin(x)In [73]: np.sin(x)&nbsp; &nbsp; &nbsp; &nbsp; # numpy sin&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp;---------------------------------------------------------------------------AttributeError&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; Traceback (most recent call last)AttributeError: 'Symbol' object has no attribute 'sin'The above exception was the direct cause of the following exception:TypeError&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;Traceback (most recent call last)<ipython-input-73-92f2c2d0df9d> in <module>----> 1 np.sin(x)TypeError: loop of ufunc does not support argument 0 of type Symbol which has no callable sin methodnp.sin执行然后np.sin(np.array(x))将操作委托给不存在的sin方法。x