如何在Matlab中沿轴分割矩阵？

Question

如何在Matlab中沿着带有矢量的轴划分矩阵 - 或进行其他算术运算？

示例：

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

使用@rdivide选项完美设置 bsxfun ，让v内部扩展为M，然后执行元素划分 - < / p>

d = bsxfun(@rdivide,M,v)

---

解决方案基准

基准代码

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;

基准测试结果

Answer 2

几种方式：

%# 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 );

Answer 3

您可以使用repmat使v与M具有相同的维度：

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