How can I create new rows in my table?

Hello I am creating a Euler's Method Calculator that plots and creates a table for the outgoing data. I am new to the tables and when creating my table the table just creates one long row with my data rather than creating new rows. I would like the table to be 2 columns holding all of the data.

f = @(t,y) y - t;
h = 0.01;
y0 = 1;
t0 = 0;
tmax = 1;
n = (tmax-t0)/h;
t(1) = t0;
y(1) = y0;

for i = 1 : n
    y(i+1) = y(i) + h * f(t(i), y(i));
    t(i+1) = t0 + i * h;
    fprintf('y(%.2f) = %.4f\n', t(i+1), y(i+1))
end

plot(t, y)
title('Eulers Method h = 0.1');
xlabel('t')
ylabel('y')

g = table();
g.t = t;
g.y = y;

fig = uifigure;
uit = uitable(fig,"Data",g);

Answer 1

[Walter Roberson]

t(1) = t0;
y(1) = y0;
for i = 1 : n
    y(i+1) = y(i) + h * f(t(i), y(i));
    t(i+1) = t0 + i * h;
    fprintf('y(%.2f) = %.4f\n', t(i+1), y(i+1))
end

You start with a scalar t and y, and you extend them by writing new elements to the vector.

When you start with scalar values and extend the vectors by writing new elements using single indices, then the vectors are created as row vectors

So when you

g = table();
g.t = t;
g.y = y;

You are making g.t and g.y as row vectors . But in order to form proper table entries, they need to be column vectors

The easiest fix is

g.t = t(:);
g.y = y(:);

but you could instead do

t = zeros(n+1,1);
y = zeros(n+1,1);

before initializing t(1) and y(1) -- and doing so would be more efficient.

[Graham]

Thanks so much!

Answer 2

[dpb]

@Walter explained the row orientation, just a very slight recasting to the same end. Almost as easy (ten characthers added instead of six) would be to write

...
for i = 1 : n
    y(i+1,1) = y(i,1) + h * f(t(i,1), y(i,1));
    t(i+1,1) = t0 + i * h;
    ...

which will force the column vectors by explicitly writing to first column only.

Alternatively (just a very slight efficiency improvement besides if n is not humongous, in which case it can become noticeable)..."preallocation" is an important concept when it's feasible although for small problems it may be immaterial, getting into the habit is agoodthing™.

t=nan(n+1,1); y=t;      % initialize column vectors to nan 
t(1) = t0;
y(1) = y0;
for i = 1 : n
    y(i+1) = y(i) + h * f(t(i), y(i));
    t(i+1) = t0 + i * h;
    fprintf('y(%.2f) = %.4f\n', t(i+1), y(i+1))
end

Now, t and y will already be column vectors so then

...
g=table(t,y);
fig = uifigure;
uit = uitable(fig,"Data",g);

There's no need for the struct; uitable supports the MATLAB table class as well.

[Graham]

Thank you!