Creating a matrix of sinusoids with time increasing over rows, and frequency + phase increasing stepwise over columns

I need to create a matrix/array of sinusoids with time vector increasing along rows and frequency vector increasing along columns together with a phase vector. The frequency vector and phase component of the sinusoids each increase stepwise on a logarithmic scale.

Something like this:

t = t1:int:n;

f = logspace(-1,4,100);

p = logspace(-1,pi,100);

y(t, f, p) = sin(2*pi*f*t + p)

The desired result is as follows (column and row headings are added for clarity of the question here):

Y{} =

           f1/p1                 f2/p2        ...          f100/p100
   --                                                                    --
t1 |sin(2*pi*f1*t1 + p1) sin(2*pi*f2*t1 + p2) ...  sin(2*pi*f100*t1 + p100)|
t2 |sin(2*pi*f1*t2 + p1) sin(2*pi*f2*t2 + p2) ...  sin(2*pi*f100*t2 + p100)|
...|       ...                 ...            ...           ...            |
tn |sin(2*pi*f1*tn + p1) sin(2*pi*f2*tn + p2) ...  sin(2*pi*f100*tn + p100)|
   --                                                                     --

Help is hugely appreciated, thanks

[Star Strider]

What about the answers provided to you in Creating a matrix of sinusoids with frequency increasing over columns and time increasing over rows didn’t work for you after you accepted it and got more than one good answer?

[Nate]

In that previous question there was no phase vector. The answers to my prior question do not work in this setting since they involved simple matrix multiplication. Here I need matrix multiplication + an addition of the phase component.

Answer 1

[Guillaume]

You would use ndgrid or meshgrid:

t = t1:int:n;
f = logspace(-1,4,100);
p = logspace(-1,pi,100);

[tt, ff] = ndgrid(t, f);
[~, pp] = ndgrid(t, p); %already got tt with first ndgrid
y = sin(2*pi*ff.*tt + pp); % be mindful of the by element multiply .*