计数算术运算 [英] Counting arithmetic operations

问题描述

有没有办法计算函数/表达式中数字运算(+、-、/、*)的次数?

Is there a way to evalute the number of numeric operations (+, -, /, *) in a function/expression?

以一个简单的线性代数问题为例(Ax = b):

In example, lets take a simple linear algebra problem (Ax = b):

A_data = np.array([[1, -4, 1],
                  [1, 6, -1],
                  [2, -1, 2]], dtype=float)

b_data = np.array([[7],
                  [13],
                  [5]], dtype=float)

接下来，让我们应用高斯消元过程:

Next, lets apply Gauss elimination procedure:

def gauss_elim(A, b):
    Ab = np.column_stack((A, b))
    for k, pivot_row in enumerate(Ab[:-1]):
        for row in Ab[k+1:]:
            if pivot_row[k] != 0:
                row[k:] = row[k:] - pivot_row[k:] * row[k]/pivot_row[k]
    return Ab

结果是:

array([[  1. ,  -4. ,   1. ,   7. ],
       [  0. ,  10. ,  -2. ,   6. ],
       [  0. ,   0. ,   1.4, -13.2]])

我如何计算操作次数?

注意:我知道可以事先用数学方法评估运算次数(即对于 高斯消元法a> 是 O(n^3)).

Note: I know the number of operations can be evaluated mathematically beforehand (i.e. for Gaussian elimination it is O(n^3)).

推荐答案

如果你能花点时间，应该有一个方法:创建一个数字类并覆盖基本的算术方法:__add__, __mul__, __sub__, __div__ 通过在其中嵌入计数器系统(例如与某些全局变量相关).然后，您应该能够通过使用 dtype=object 参数(在创建数组时)来强制 Numpy 使用您的类型，以确保 Numpy 不会将您的数字转换为任何其他类型.我有时会为了更简单的任务而这样做；我从来没有用 Numpy 做过，但它应该可以工作.希望能帮到你.

If you can take a little time for it, there should be a way: create a class of numbers and override the basic arithmetic methods: __add__, __mul__, __sub__, __div__ by embedding a counter system in it (related to some global variable for instance). You should then be able to force Numpy to use your type by using the dtype=object parameter (at array creation) to make sure that Numpy doesn't convert your numbers to any other type. I sometimes did it for simpler task; I never did it with Numpy, but it should probably work. Hope it can help.

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