help-octave
[Top][All Lists]
Advanced

[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]

## Re: Efficient multiplication by a diagonal matrix

 From: Mario Storti Subject: Re: Efficient multiplication by a diagonal matrix Date: Thu, 14 Nov 1996 20:18:26 -0300

```>>>>> 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

%%%%%%<>%%%%%%<>%%%%%%<>%%%%%%<>%%%%%%<>%%%%%%<>%%%%%%<>%%%%%%<>%%%%%%<>%%%
Mario Alberto Storti               | Fax: (54)(42) 55.09.44               |
Grupo de Tecnologia Mecanica       | Tel: (54)(42) 55.91.75               |
INTEC, Guemes 3450 - 3000 Santa Fe | http://venus.unl.edu.ar/gtm-eng.html |
Argentina                          | Home: Gob. Vera 3161                 |
Reply: address@hidden  |       (54)(42) 55.00.23              |

```

reply via email to

 [Prev in Thread] Current Thread [Next in Thread]