优化MATLAB代码 [英] Optimizing MATLAB code

问题描述

此代码需要非常长的时间才能运行(超过10分钟).有什么方法可以优化它，使其在不到一分钟的时间内完成?

This code takes an extremely long time to run (more than 10 minutes). Is there any way in which I can optimize it so that it finishes in less than one minute?

clear all;
for i = 1:1000000
    harmonicsum = 0;
    lhs = 0;
    for j = 1:i
        % compute harmonic sum
        harmonicsum = harmonicsum + 1/j;
        % find sum of factors
        if (mod(i,j)==0)
            lhs = lhs + j;
        end
    end
    %define right hand side (rhs) of Riemann Hypothesis
    rhs = harmonicsum + log(harmonicsum) * exp(harmonicsum);

    if lhs > rhs
        disp('Hypothesis violated')
    end
end

推荐答案

@ b3很棒rhs的向量化.

@b3 has a great vectorization of rhs.

不过有一个错字，需要使用times而不是mtimes:

One typo though, needs to use times and not mtimes:

harmonicsum = cumsum(1 ./ (1:1e6));
rhs = harmonicsum + log(harmonicsum) .* exp(harmonicsum);

对于lhs，我大致根据Eratosthenes的筛子提出以下建议:

For lhs, I propose the following, loosely based on Eratosthenes' Sieve:

lhs = 1 + [1:1e6];
lhs(1) = 1;
for iii = 2:numel(lhs)/2
    lhs(2*iii:iii:end) = lhs(2*iii:iii:end) + iii;
end;

执行时间仅为2.45秒(针对问题的这一半).包括计算rhs和find在内的总计不到3秒.

Execution time is just 2.45 seconds (for this half of the problem). Total including calculation of rhs and find is under 3 seconds.

我目前正在运行其他版本，以确保结果相同.

I'm currently running the other version to make sure that the results are equal.

发现一个带有lhs(1)的错误并将其特殊化(这是特殊情况，这是唯一的自然数，其中1和N不是不同的因素)

found a bug with lhs(1) and special-cased it (it is a special case, the only natural number where 1 and N aren't distinct factors)

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