矢量元素的乘积之和

我有一个矢量，比如Y2。我想找出产品的总和达到某种顺序，比如说10。一种天真的方式如下。有没有一种很好的方法在matlab中做到这一点？矢量元素的乘积之和

for tt=1:length(Y2)-10 
    LHS(tt) = Y2(tt) + Y2(tt)*Y2(tt+1) + Y2(tt)*Y2(tt+1)*Y2(tt+2) + Y2(tt)*Y2(tt+1)*Y2(tt+2)*Y2(tt+3) ... 
     + Y2(tt)*Y2(tt+1)*Y2(tt+2)*Y2(tt+3)*Y2(tt+4) + Y2(tt)*Y2(tt+1)*Y2(tt+2)*Y2(tt+3)*Y2(tt+4)*Y2(tt+5) ... 
     + Y2(tt)*Y2(tt+1)*Y2(tt+2)*Y2(tt+3)*Y2(tt+4)*Y2(tt+5)*Y2(tt+6) ... 
     + Y2(tt)*Y2(tt+1)*Y2(tt+2)*Y2(tt+3)*Y2(tt+4)*Y2(tt+5)*Y2(tt+6)*Y2(tt+7) ... 
     + Y2(tt)*Y2(tt+1)*Y2(tt+2)*Y2(tt+3)*Y2(tt+4)*Y2(tt+5)*Y2(tt+6)*Y2(tt+7)*Y2(tt+8) ... 
     + Y2(tt)*Y2(tt+1)*Y2(tt+2)*Y2(tt+3)*Y2(tt+4)*Y2(tt+5)*Y2(tt+6)*Y2(tt+7)*Y2(tt+8)*Y2(tt+9); 
end

来源

2016-08-28 user27808

这将做的工作：

k=10; 
LHS = zeros(T-k-1,1); 
for tt=1:length(Y2)-k 
    for j=0:k-1 
     for i=0:j 
      YY = prod(Y2(tt:tt+i)); 
     end 
     LHS(tt) = LHS(tt)+ YY; 
    end 
end

来源

2016-08-28 11:51:54 user27808

这里是一个解决方案，O(n)：

order_prod_sum.m

function [ result ] = order_prod_sum(v, k) 
    result = zeros(length(v)-k,1); 
    last = 1; 
    for i = 1:k 
     last = last * v(i); 
     result = result + last; 
    end 

    n = length(v) - k; 
    for i = 2:n 
     cur_sum = result(i-1)/v(i-1) -1; 
     last = v(i+k-1) * last/v(i-1); 
     result(i) = last + cur_sum; 
    end 
end

比较

three_loops.m（解决方案）

function [ result ] = three_loops(v, k) 

result = zeros(length(v)-k,1); 
for tt=1:length(v)-k 
    for j=0:k-1 
     for i=0:j 
      YY = prod(v(tt:tt+i)); 
     end 
     result(tt) = result(tt)+ YY; 
    end 
end 

end

k=10; 
Num = 100000; 
v = randi(10,1,Num); 
tic; 
result1 = three_loops(v, k); 
toc; 

tic 
result2 = order_prod_sum(v, k); 
toc; 

assert(sum(result1-result2) == 0)

输出

Elapsed time is 4.739388 seconds. 
Elapsed time is 0.005321 seconds.

来源

2016-08-28 13:41:19

矢量元素的乘积之和

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