如何获得列表的加权平均值，其权重受 Python 3.6 中的变量限制

Question

我希望标题有意义。我想要实现的是获得鞋子的加权平均价格，这些鞋子的价格不同，数量也不同。所以我有例如：

list_prices = [12,12.7,13.5,14.3]
list_amounts = [85,100,30,54]
BuyAmount = x

我想知道我的加权平均价，以及每只鞋我支付的最高价如果我买了 x 数量的鞋（假设我想先买最便宜的）

这是我现在拥有的（我使用 numpy）：

    if list_amounts[0] >= BuyAmount:
        avgprice = list_prices[0]
        highprice = list_prices[0]

    elif (sum(list_amounts[0: 2])) >= BuyAmount:
        avgprice = np.average(list_prices[0: 2], weights=[list_amounts[0],BuyAmount - list_amounts[0]])
        highprice = list_prices[1]

    elif (sum(list_amounts[0: 3])) >= BuyAmount:
        avgprice = np.average(list_prices[0: 3], weights=[list_amounts[0],list_amounts[1],BuyAmount - (sum(list_amounts[0: 2]))])
        highprice = list_prices[2]

    elif (sum(list_amounts[0: 4])) >= BuyAmount:
        avgprice = np.average(list_prices[0: 4], weights=[list_amounts[0],list_amounts[1],list_amounts[2],BuyAmount - (sum(list_amounts[0: 3]))])
        highprice = list_prices[3]

    print(avgprice)
    print(highprice)

此代码有效，但可能过于复杂和庞大。特别是因为我希望能够处理包含 20 多个项目的数量和价目表。

执行此操作的更好方法是什么？

Answer 1

这是一个通用的矢量化解决方案，使用 cumsum 替换那些切片求和，并使用 argmax 获取适当的索引以用于设置那些 IF-case 操作的切片限制 -

# Use cumsum to replace sliced summations - Basically all those 
# `list_amounts[0]`, `sum(list_amounts[0: 2]))`, `sum(list_amounts[0: 3])`, etc.
c = np.cumsum(list_amounts)

# Use argmax to decide the slicing limits for the intended slicing operations.
# So, this would replace the last number in the slices - 
# list_prices[0: 2], list_prices[0: 3], etc.
idx = (c >= BuyAmount).argmax()

# Use the slicing limit to get the slice off list_prices needed as the first
# input to numpy.average
l = list_prices[:idx+1]

# This step gets us the weights. Now, in the weights we have two parts. E.g.
# for the third-IF we have : 
# [list_amounts[0],list_amounts[1],BuyAmount - (sum(list_amounts[0: 2]))]
# Here, we would slice off list_amounts limited by `idx`.
# The second part is sliced summation limited by `idx` again.
w = np.r_[list_amounts[:idx], BuyAmount - c[idx-1]]

# Finally, plug-in the two inputs to np.average and get avgprice output.
avgprice = np.average(l,weights=w)

# Get idx element off list_prices as the highprice output.
highprice = list_prices[idx]

我们可以进一步优化以删除连接步骤（使用 np.r_）并达到 avgprice，就像这样 -

slice1_sum = np.multiply(list_prices[:idx], list_amounts[:idx]).sum()
        # or np.dot(list_prices[:idx], list_amounts[:idx])
slice2_sum = list_prices[idx]*(BuyAmount - c[idx-1])
weight_sum = np.sum(list_amounts[:idx]) + BuyAmount - c[idx-1]
avgprice = (slice1_sum+slice2_sum)/weight_sum

Answer 2

你说的没错，你的代码缺乏灵活性。但是在我看来，你是从正确的角度来看问题的，但还不够笼统。

换句话说，您的解决方案实现了这个想法："let me check first - given the quantities available for each price (which I sorted beautifully in an array) - what are the different sellers I have to buy from, then do all the computation."

更灵活的想法可以是："Let me start buying the from cheaper available, as much as I can. I will stop when my order is fulfilled, and compute the math step by step"。这意味着您构建一个迭代代码，逐步累积总花费金额，并在完成后计算每件的平均价格和最高价格（即您订购列表中最后访问的价格）。

将此想法转化为代码：

list_prices = [12,12.7,13.5,14.3]
list_amounts = [85,100,30,54]
BuyAmount = x

remaining = BuyAmount
spent_total = 0
current_seller = -1 # since we increment it right away 

while(remaining): # inherently means remaining > 0
    current_seller += 1
    # in case we cannot fulfill the order
    if current_seller >= len(list_prices):
        # since we need it later we have to restore the value
        current_seller -= 1
        break
    # we want either as many as available or just enough to complete 
    # BuyAmount
    buying = min([list_amounts[current_seller], remaining])
    # update remaining
    remaining -= buying
    # update total
    spent_total += buying * list_prices[current_seller]

# if we got here we have no more remaining or no more stock to buy

# average price
avgprice = spent_total / (BuyAmount - remaining) 

# max price - since the list is ordered -
highprice = list_prices[current_seller]

print(avgprice)
print(highprice)

如何获得列表的加权平均值，其权重受 Python 3.6 中的变量限制

How to get a weighted average of a list of which it's weights is limited by a variable in Python 3.6

python

list

numpy

average

weighted