How to fill a matrix column by column better than by a for loop?

Want to parametrize areas for plotting/numerical integration/whatnot.

E.g. x-values: 0..1

y-values: x-1 ... x^3+1

This does the job, but it is awful:

xx=0:0.1:1;
nxx=length(xx);
nyy=10;
xm=repmat(xx',1,nyy);
ym=zeros(nxx,nyy);
for ii=1:nxx
    xii=xx(ii);
    ym(ii,:)=linspace(xii-1,xii^3+1,nyy);
end

Thanks in advance!

Answer 1

[Tommy]

How about something like this?

xx = 0:0.1:1;
nxx = numel(xx);
nyy = 10;
xm = repmat(xx',1,nyy);

base = linspace(0,1,nyy);
starts = xx-1;
stops = xx.^3+1;
ym = starts(:) + base.*(stops(:)-starts(:));

Credit to the following answer:

https://www.mathworks.com/matlabcentral/answers/363214-how-to-create-array-of-linearly-spaced-values-from-starting-and-ending-points#answer_287709

[Ulrich Becker]

The answer is a massive improvement in performance and logic! Thanks indeed for this quickest reply!

I wonder if one could condense it even further, so I'd like to leave this question open a little longer. In particular, as the issue has wider applicability, as your reference is indicating.

Again, thanks ideed!

[Tommy]

Happy to help!

Answer 2

[Ulrich Becker]

Taking the ideas of the accepted answer, I learned more about rows and columns and since this forum is about learning, here is a more homogeneous/symmetric version:

nxx = 15;                  % number of points in x direction
nyy = 11;                  % number of points in y direction
x1=0; x2=1;                % start and end value for x-values
xx = linspace(x1,x2,nxx)'; % Want a column vector! Length is first matrix dimension: number of rows.
yy = linspace(0,1,nyy);    % Want a row vector! Length is second matrix dimension: number of columns.
y1 = xx-1;                 % Column vector. Start values of y depending on x.
y2 = xx.^3+1;              % Column vector. End values of y depending on x.
xm = repmat(xx,1,nyy);     % xx needs to be a column vector for this to work.
ym = y1 + yy.*(y2-y1);     % Need columns and rows for this to give a matrix!

Also note:

a=[1 2 3] % is a row vector
a'        % is a column vector ... no surprise
a(:)      % is a column vector, too!   Well, it's in the documentation. So no surprise ... anymore.

Again, thanks for the accepted answer!

[Tommy]

Nice and neat, thanks for this! In case anyone reading isn't already aware:

a=[1;2;3] % is a column vector
a(:)      % is still a column vector