Julia 中的循环。 语法混乱

Question

I am a complete noob in Julia and its syntax. I am trying to follow this article on semi-definite-programming on Julia.

I would apprecieate if someone can help me figure out what the for loop in In[4] actually does:

for i in 1:m
A[:, (i-1)*n+1:i*n] .= random_mat_create(n)
b[i] = tr(A[:, (i-1)*n+1:i*n]*X_test)
end

To my understanding it should create a vector of matrices A (m of those) as well as an m-dimensional vector b . I am totally confused though on the indexing of A and the indexing of b .

I would like an explanation of the :, (i-1)*n+1:i*n part of this code . The reason I ask here is because I also dont know what to Google or what to search for in Julia documentation.

Answer 1

(i-1)*n+1:i*n creates a range from (i-1)*n + 1 to i*n . For example, if i =2 and n =10, this range becomes 11:20 , so A[:, (i-1)*n+1:i*n] will grab all the rows of A (that's what : does), and columns 11-20.

Answer 2

There are two operations there that are not clear to you:

• : operator. Consider a Matrix a = zeros(3,3) . You could use array slicing operator (similarly to numpy or Matlab) to select the entire second columns as: a[1:end,2] . However, when selecting everything from start to the end those two values can be omitted and hence you can write a[:,2] (this always looked the easiest way for me to remember that)
• . (dot) operator. Julia is very careful about what gets vectorized and what not. In numpy or R, vectorizing operations happens kind of always automatically. In Julia you have the control - but with the control comes the responsibility. Hence trying to assign values to the second column by writing a[:, 2] = 5.0 will throw an error because there is vector on the right and a scalar on the left. If you want to vectorize you need to tell that to Julia. Hence the dot operator .= means "perform element-wise assignment". Note that any Julia function or operator, even your own functions can be decorated by such dot . . Since this is a very important language feature have a look at https://docs.julialang.org/en/v1/manual/arrays/#Broadcasting