Matlab的：如何向量化的矢量功能

Question

我在MATLAB有一個for循環和其計算的正弦函數之和，如下所示：

% preliminary constants, etc. 
tTot = 2; 
fS = 10000;dt = 1/fS; % total time, sampling rate 
Npts = tTot * fS; %number of points 
t = dt:dt:tTot; 
c1 = 2*pi/tTot; 
c2 = pi/fS;  
s = zeros(1,Npts) 

% loop to optimize: 
for(k=1:Npts/2) 
    s = s + sin(c1*k*t - c2*k*(k-1)) 
end 

基本上，一個班輪for循環變得NPTS變得很慢大。困難來自於我對k個參數k定義的向量求和。

有沒有辦法通過矢量化來提高效率？一種方法到目前爲止，我已經採取是定義一個矩陣，總結出來的結果，但是這給了我較大的向量的內存不足的錯誤：

[K,T] = meshgrid(1:1:Npts,t); 
s = sum(sin(c1*K.*T - c2*K.*(K-1)),2); 

任何幫助，將不勝感激。

Answer 1

方法＃1

利用差分式的正弦：sin(A-B) = sin A cos B - cos A sin B，使我們能夠充分利用fast matrix multiplication -

K = 1:Npts/2; 
p1 = bsxfun(@times,c1*K(:),t(:).'); 
p2 = c2*K(:).*(K(:)-1); 
s = cos(p2).'*sin(p1) - sin(p2).'*cos(p1); 

方法2

隨着bsxfun -

K = 1:Npts/2; 
p1 = bsxfun(@times,c1*K(:),t(:).'); 
p2 = c2*K(:).*(K(:)-1); 
s = sum(sin(bsxfun(@minus, p1,p2)),1); 

---

方法＃1可被修改以更小尺寸的環帶，以適應具有較大的數據數組如下所示的問題 -

num_blks = 100;%// Edit this based on how much RAM can handle workspace data 
intv_len = Npts/(2*num_blks); %// Interval length based on number of blocks 

KP = 1:Npts/2; 
P2 = c2*KP(:).*(KP(:)-1); 
sin_P2 = sin(P2); 
cos_P2 = cos(P2); 

s = zeros(1,Npts); 
for iter = 1:intv_len:Npts/2 
    K = iter:iter+intv_len-1; 
    p1 = bsxfun(@times,c1*K(:),t(:).'); 
    s = s + (cos_P2(K).'*sin(p1) - sin_P2(K).'*cos(p1)); 
end