将多个常数转换为矩阵并将其转换为Matlab中的块对角矩阵 [英] Multiple constant to a matrix and convert them into block diagonal matrix in matlab

问题描述

我有a1 a2 a3.它们是常数.我有一个矩阵A.我要做的是得到三个矩阵a1 * A，a2 * A，a3 * A.然后，我想将它们转移到对角线块矩阵中.对于三个常数的情况，这很容易.我可以让b1 = a1 * A，b2 = a2 * A，b3 = a3 * A，然后在matlab中使用blkdiag(b1，b2，b3).

I have a1 a2 a3. They are constants. I have a matrix A. What I want to do is to get a1*A, a2*A, a3*A three matrices. Then I want transfer them into a diagonal block matrix. For three constants case, this is easy. I can let b1 = a1*A, b2=a2*A, b3=a3*A, then use blkdiag(b1, b2, b3) in matlab.

如果我有n个常数，a1 ... an.我怎么能不做任何循环呢?我知道这可以通过kronecker产品来完成，但这非常耗时，您需要做很多不必要的0 *常量.

What if I have n constants, a1 ... an. How could I do this without any looping?I know this can be done by kronecker product but this is very time-consuming and you need do a lot of unnecessary 0 * constant.

谢谢.

推荐答案

讨论和代码

这可能是使用 bsxfun(@plus ，它有助于 linear indexing (以函数格式编码-

Discussion and code

This could be one approach with bsxfun(@plus that facilitates in linear indexing as coded in a function format -

function out = bsxfun_linidx(A,a)
%// Get sizes
[A_nrows,A_ncols] = size(A);
N_a = numel(a);

%// Linear indexing offsets between 2 columns in a block & between 2 blocks
off1 = A_nrows*N_a;
off2 = off1*A_ncols+A_nrows;

%// Get the matrix multiplication results
vals = bsxfun(@times,A,permute(a,[1 3 2])); %// OR vals = A(:)*a_arr;

%// Get linear indices for the first block
block1_idx = bsxfun(@plus,[1:A_nrows]',[0:A_ncols-1]*off1);  %//'

%// Initialize output array base on fast pre-allocation inspired by -
%// http://undocumentedmatlab.com/blog/preallocation-performance
out(A_nrows*N_a,A_ncols*N_a) = 0; 

%// Get linear indices for all blocks and place vals in out indexed by them
out(bsxfun(@plus,block1_idx(:),(0:N_a-1)*off2)) = vals;

return;

使用方法:要使用上面列出的功能代码，假设您将a1，a2，a3，....，an存储在向量a，然后执行类似out = bsxfun_linidx(A,a)的操作，以在out中获得所需的输出.

How to use: To use the above listed function code, let's suppose you have the a1, a2, a3, ...., an stored in a vector a, then do something like this out = bsxfun_linidx(A,a) to have the desired output in out.

本节针对运行时性能将本答案中列出的方法与其他答案中列出的其他两种方法进行比较或基准测试.

This section compares or benchmarks the approach listed in this answer against the other two approaches listed in the other answers for runtime performances.

其他答案已转换为函数形式，例如-

Other answers were converted to function forms, like so -

function B = bsxfun_blkdiag(A,a)
B = bsxfun(@times, A, reshape(a,1,1,[])); %// step 1: compute products as a 3D array
B = mat2cell(B,size(A,1),size(A,2),ones(1,numel(a))); %// step 2: convert to cell array
B = blkdiag(B{:}); %// step 3: call blkdiag with comma-separated list from cell array

和

function out = kron_diag(A,a_arr)
out = kron(diag(a_arr),A);

为进行比较，测试了A和a大小的四个组合，即-

For the comparison, four combinations of sizes of A and a were tested, which are -

• A作为500 x 500，a作为1 x 10
• A作为200 x 200，a作为1 x 50
• A作为100 x 100，a作为1 x 100
• A作为50 x 50，a作为1 x 200

• A as 500 x 500 and a as 1 x 10
• A as 200 x 200 and a as 1 x 50
• A as 100 x 100 and a as 1 x 100
• A as 50 x 50 and a as 1 x 200

使用的基准测试代码列在下面-

The benchmarking code used is listed next -

%// Datasizes
N_a = [10  50  100 200];
N_A = [500 200 100 50];

timeall = zeros(3,numel(N_a)); %// Array to store runtimes
for iter = 1:numel(N_a)

    %// Create random inputs
    a = randi(9,1,N_a(iter));
    A = rand(N_A(iter),N_A(iter));

    %// Time the approaches
    func1 = @() kron_diag(A,a);
    timeall(1,iter) = timeit(func1); clear func1

    func2 = @() bsxfun_blkdiag(A,a);
    timeall(2,iter) = timeit(func2); clear func2

    func3 = @() bsxfun_linidx(A,a);
    timeall(3,iter) = timeit(func3); clear func3
end

%// Plot runtimes against size of A
figure,hold on,grid on
plot(N_A,timeall(1,:),'-ro'),
plot(N_A,timeall(2,:),'-kx'),
plot(N_A,timeall(3,:),'-b+'),
legend('KRON + DIAG','BSXFUN + BLKDIAG','BSXFUN + LINEAR INDEXING'),
xlabel('Datasize (Size of A) ->'),ylabel('Runtimes (sec)'),title('Runtime Plot')

%// Plot runtimes against size of a
figure,hold on,grid on
plot(N_a,timeall(1,:),'-ro'),
plot(N_a,timeall(2,:),'-kx'),
plot(N_a,timeall(3,:),'-b+'),
legend('KRON + DIAG','BSXFUN + BLKDIAG','BSXFUN + LINEAR INDEXING'),
xlabel('Datasize (Size of a) ->'),ylabel('Runtimes (sec)'),title('Runtime Plot')

在我最后获得的

运行时图为-

结论:如您所见，可以使用基于bsxfun的方法之一，具体取决于您要处理的数据大小是哪种！

Conclusions: As you can see, either one of the bsxfun based methods could be looked into, depending on what kind of datasizes you are dealing with!

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