如何在Matlab中沿轴分割矩阵？

Question

如何使用Matlab中的矢量沿矩阵划分矩阵或进行其他算术运算？

例子：

M = [2 4 6 ; ... 
    8 4 2 ]; 

v = [2 4 2]; 

d = M/v;   % divide along first axis 

d = 
    1 1 3 
    4 1 1 

Answer 1

完美设置为bsxfun与@rdivide选项，让v内部扩展到尺寸的M，然后执行元素划分 -

d = bsxfun(@rdivide,M,v) 

---

的解决方案

标杆

基准测试代码

N_arr = [100 200 500 1000 2000 4000]; 
timeall = zeros(4,numel(N_arr)); 
for k1 = 1:numel(N_arr) 

    N = N_arr(k1); 
    M = rand(N,N); 
    v = rand(1,N); 

    f = @() bsxfun(@rdivide,M,v); 
    timeall(1,k1) = timeit(f); 
    clear f 

    f = @() M ./ repmat(v, size(M, 1), 1); 
    timeall(2,k1) = timeit(f); 
    clear f 

    f = @() M ./ (ones(size(M,1),1)*v); 
    timeall(3,k1) = timeit(f); 
    clear f 

    f = @() ele_div(M,v); 
    timeall(4,k1) = timeit(f); 
    clear f 
end 
figure,hold on,grid on 
plot(N_arr,timeall(1,:),'-ro'),plot(N_arr,timeall(2,:),'-kx') 
plot(N_arr,timeall(3,:),'-g+'),plot(N_arr,timeall(4,:),'-b.') 
legend('BSXFUN','REPMAT','ONES','FOR-LOOP'), 
xlabel('Datasize ->'),ylabel('Time(sec) ->') 

相关的功能

function MM = ele_div(M,v) 
MM = zeros(size(M)); 
for i=1:size(M,1) 
    MM(i,:) = M(i,:) ./ v; 
end 
return; 

标结果

Answer 2

你可以使用repmat使v尺寸相同M：

d = M ./ repmat(v, size(M, 1), 1) 

Answer 3

几种方法：

%# FOR-loop 
MM = zeros(size(M)); 
for i=1:size(M,1) 
    MM(i,:) = M(i,:) ./ v; 
end 

%# BSXFUN 
MM = bsxfun(@rdivide, M, v); 

%# REPMAT 
MM = M ./ repmat(v,size(M,1),1); 

%# repetition by multiplication 
MM = M ./ (ones(size(M,1),1)*v);