Divide each column by the sum of the column in a matrix

I am sure this is an elementary question, but I could not find the answer when searching the Matlab website. I was wondering how to divide each column in a matrix by the sum of that column and do the same process for all the columns in a matrix. The result should then be returned as a new matrix.

As an example take the following matrix

D = [-0.442898926677253	-0.165258150390309	0.850111606631490	-0.801783725737275;
    -0.505610279127129	0.455832504673115	-0.205467096352270	4.76435784320108e-15;
    -0.540885414880185	-0.746406858955920	-0.439177413926944	0.534522483824847;
    -0.505610279127129	0.455832504673115	-0.205467096352275	0.267261241912423];

Now, for the first column;

U(:,1)/sum(U(:,1))

gets the first column of D divided by the sum of the column, but how do I do this for all of the columns and return the output as a new matrix?

[Matt J]

U(:,1)/sum(U(:,1)) gets the first column of D divided by the sum of the column

No, it does that for U, not D.

[Fredrik Scheie]

Yes, well observed I should have written D in the expression.

Answer 1

[Matt J]

D./sum(D)

[Jan]

Exactly. To be safe specify the dimension to sum over:

D ./ sum(D, 1)

Then providing a row vector does not sum over the wrong direction.

[Fredrik Scheie]

Thanks, this solves my problems for numeric computattions. I tried using this with the symbolic toolbox and I end up with some infinity entries and . Is it because when I use an unkown parameter (for example 'd') then the magnitude is uknown since the parameter is unknown and I cannot use the sum() function behaves weirdly?

[Torsten]

Or you have columns that sum to 0.

[Fredrik Scheie]

@Torsten yes, If the columns sum to 0 then the parameter must cancel each other out and infinity is returned. I also get NaN returned for some entries. Wonder what could cause it to return as 'not a number'?

[Torsten]

Just display D and look at the respective columns. You should be able to find the reason by inspection.

[Matt J]

Wonder what could cause it to return as 'not a number'?

That would happen if the column sum is zero, and the column also contains some zeros, e.g.,

D=[-1;0;1];
D/sum(D)

ans = 3×1

-Inf NaN Inf