Re: Efficient multiplication by a diagonal matrix

[Mario Storti]

>>>>> On Thu, 14 Nov 1996 17:43:56 -0400 (EDT), 
                       address@hidden said:

> Mario Storti writes:
> >I found  myself repeatedly with the following  problem. Given a matrix
> >A(n,m)  and a vector  v(n), I  have to  multiply   each row  A(j,:) by
> >v(j). This is equivalent to compute:
> >
> >B = diag(v) * A                     (1)
> >
> >Now, for large    n, (1) is  very  inefficient ...
> 
> Right, try using "Tony's Trick", it's been around for years. 
> 
> Assuming v is a column vector (if not do v=v(:);) try
> 
> B=v(:,ones(length(v),1)) .* A;
> 
> This is a kind-of MATLAB specific thing but I think 
> it works in octave o.k.
> 
> Scott Sands

(...)

> Sorry about the previous post, the right answer is
> 
> B=v(:,ones(1,m)) .*A;
> 
> ss


I tried, and it works also in Octave. Curiously enough, both work:

>>    octave:3> v=rand(5,1)
>>    v =
>>    
>>      0.397911
>>      0.517248
>>      0.876939
>>      0.025083
>>      0.895795
>>    
>>    octave:4> v(:,ones(5,1))
>>    ans =
>>    
>>      0.397911  0.397911  0.397911  0.397911  0.397911
>>      0.517248  0.517248  0.517248  0.517248  0.517248
>>      0.876939  0.876939  0.876939  0.876939  0.876939
>>      0.025083  0.025083  0.025083  0.025083  0.025083
>>      0.895795  0.895795  0.895795  0.895795  0.895795
>>    
>>    octave:5> v(:,ones(1,5))
>>    ans =
>>    
>>      0.397911  0.397911  0.397911  0.397911  0.397911
>>      0.517248  0.517248  0.517248  0.517248  0.517248
>>      0.876939  0.876939  0.876939  0.876939  0.876939
>>      0.025083  0.025083  0.025083  0.025083  0.025083
>>      0.895795  0.895795  0.895795  0.895795  0.895795
>>    

But it is equivalent to kron(v,ones(1,m)) and it has the same problems
of inefficiency as mentioned in the original post:

> Now, for large    n, (1) is  very  inefficient,   because it  requires
> constructing the square matrix diag(v) which requires storage and many
> redundant operations since most elements  of diag(v) are null. If n>>m
                                                                 ^^^^^^^
> then:
> 
> B= kron(v,ones(1,m)).*A             (2)
> 
> does the job  and is better.  But the more  efficient way is computing
  ^^^^^^^^^^^^^^^^^^^^^^^^^^^
> row by row if m>>n and column by column  if n>>m. However, I repeat, I
> find this problem so many times and in so many  areas that it seems to
(...)

Mario

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