Skip to main content

Most Efficient Way to Calculate the Product of All Items in a List?


Say that I have a list of returns on a financial asset over time and want to know the total compounded return. To get the answer, I need to add 1 to each return and then calculate the product of all of them. So, I'm looking for a function like Total, except that it computes the product. The Product function works, but seems clumsy and slower than my alternatives (at first, I was having trouble getting Product to work, so I wrote a few of my own functions). Here are the alternatives:


listProduct[x_List] := Exp[Total[Log[x]]];
listProduct2[x_List] := Last[FoldList[Times, 1, x]];
listProduct3[x_List] := Fold[Times, 1, x];
listProduct4[x_List] := Product[x[[i]], {i, 1, Length[x]}];


Those are in the order that I thought of them. A couple of surprising things: The first seems to be the fastest by quite a lot (though none are super slow). The slowest is the last one using Product, which I thought would be highly optimized and fast.


Here are my tests:


s = RandomVariate[NormalDistribution[0.05, 0.1], 10^6];
listProduct[1 + s] - 1; // AbsoluteTiming
listProduct2[1 + s] - 1; // AbsoluteTiming
listProduct3[1 + s] - 1; // AbsoluteTiming
listProduct4[1 + s] - 1; // AbsoluteTiming

which produces these results:


{0.0312000, Null} {1.4820026, Null} {1.4040025, Null} {1.8252032, Null}


So, the question is: Is there a faster way, and am I missing some built-in function that would do this better? I won't be using lists this long, but I may be doing a lot of lists if I can get the rest of my idea implemented.



Answer



The function you're looking for is Times. Use it as Times@@list, or keeping in line with your functions,


listProduct[x_List] := Times @@ x

Comments

Popular posts from this blog

plotting - How to draw lines between specified dots on ListPlot?

I would like to create a plot where I have unconnected dots and some connected. So far, I have figured out how to draw the dots. My code is the following: ListPlot[{{1, 1}, {2, 2}, {3, 3}, {4, 4}, {1, 4}, {2, 5}, {3, 6}, {4, 7}, {1, 7}, {2, 8}, {3, 9}, {4, 10}, {1, 10}, {2, 11}, {3, 12}, {4,13}, {2.5, 7}}, Ticks -> {{1, 2, 3, 4}, None}, AxesStyle -> Thin, TicksStyle -> Directive[Black, Bold, 12], Mesh -> Full] I have thought using ListLinePlot command, but I don't know how to specify to the command to draw only selected lines between the dots. Do have any suggestions/hints on how to do that? Thank you. Answer One possibility would be to use Epilog with Line : ListPlot[ {{1, 1}, {2, 2}, {3, 3}, {4, 4}, {1, 4}, {2, 5}, {3, 6}, {4, 7}, {1, 7}, {2, 8}, {3, 9}, {4, 10}, {1, 10}, {2, 11}, {3, 12}, {4, 13}, {2.5, 7}}, Ticks -> {{1, 2, 3, 4}, None}, AxesStyle -> Thin, TicksStyle -> Directive[Black, Bold, 12], Mesh -> Full, Epilog -> { Line[ ...

dynamic - How can I make a clickable ArrayPlot that returns input?

I would like to create a dynamic ArrayPlot so that the rectangles, when clicked, provide the input. Can I use ArrayPlot for this? Or is there something else I should have to use? Answer ArrayPlot is much more than just a simple array like Grid : it represents a ranged 2D dataset, and its visualization can be finetuned by options like DataReversed and DataRange . These features make it quite complicated to reproduce the same layout and order with Grid . Here I offer AnnotatedArrayPlot which comes in handy when your dataset is more than just a flat 2D array. The dynamic interface allows highlighting individual cells and possibly interacting with them. AnnotatedArrayPlot works the same way as ArrayPlot and accepts the same options plus Enabled , HighlightCoordinates , HighlightStyle and HighlightElementFunction . data = {{Missing["HasSomeMoreData"], GrayLevel[ 1], {RGBColor[0, 1, 1], RGBColor[0, 0, 1], GrayLevel[1]}, RGBColor[0, 1, 0]}, {GrayLevel[0], GrayLevel...

list manipulation - Selecting multiple columns from a matrix?

Sample data: data = { {{2013, 1, 1}, 24.13, 167.67, 231.82}, {{2013, 1, 2}, 32.15, 170.92, 225.99}, {{2013, 1, 3}, 35.43, 172.68, 221.67}, {{2013, 1, 4}, 36.73, 173.05, 218.32}, {{2013, 1, 5}, 58.19, 165.96, 197.05}, {{2013, 1, 6}, 69.99, 163.50, 187.52}, {{2013, 1, 7}, 71.37, 154.21, 175.58}, {{2013, 1, 8}, 72.51, 149.66, 163.25}}; I want a DateListPlot with three graphs, so for a matrix formed by columns 1 and 2, one for columns 1 and 3, and 1 for columns 1 and 4. At the moment I'm using this code: data2 = Transpose[{data[[All, 1]], data[[All, 2]]}]; data3 = Transpose[{data[[All, 1]], data[[All, 3]]}]; data4 = Transpose[{data[[All, 1]], data[[All, 4]]}]; DateListPlot[{data2, data3, data4}, Joined -> True, Filling -> {3 -> {1}}] but I have a hunch that this can be done more efficiently. I don't like the Transpose s in particular. Any ideas? edit (for extra credit) What if I need to multiply the second column by 2, which in my solution is simp...